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iHorizon driver energy management for PHEV real-time control 6.1

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Online PHEV energy management

This chapter focuses on the iHorizon main framework, which is based on driver driving style recognition and speed prediction algorithms to provide an estimation of the future route. Realistically, iHorizon’s simplistic approach and limited amount of information processed cannot return speed and energy prediction results with the accuracy of more sophisticated platforms, such as eHorizon. Nevertheless, the strong disturbances that affect entire driving cycles can never be fully anticipated, due to the erratic behaviour of other drivers, pedestrians, weather conditions, accidents and a host of other uncontrollable factors. In the context of these uncertain cycle conditions, iHorizon is found to be a suitable solution for speed and energy consumption anticipation, along with energy management, of electrified vehicles. Conventional powertrains are well understood and historically have been successfully used on various scales from industrial applications to public and private transportation. Despite the high complexity of internal combustion engines, these vehicles have dominated the transport sector over the past decades. They are provided with a single power source and therefore have zero degrees of freedom in vehicle energy management. In contrast, fully electrified vehicles incorporate simple solutions in terms of control and energy management, with the exception of remaining range prediction. Battery electric vehicles (BEVs) also have a single power source, which implies zero degrees of freedom for energy management, and simpler controllers when compared to conventional powertrains. However, these vehicles have additional disadvantages due to their high recharging time and the lack of availability of sufficient infrastructure charging points, so they cannot currently compete with internal combustion engines in refueling time and number of petrol stations. The previous examples, conventional and fully electrified vehicles, present the two extremes of 0% and 100% electrification level. Hybrid powertrains are confined within those boundaries and are classified according to their electrical component capabilities in comparison to combustion engines. Although hybrid powertrains combine the complexities of conventional and electric vehicles, they also compensate for their deficiencies in terms of emissions, fuel consumption and range anxiety. On the one hand, conventional vehicles cannot meet the new emissions limits and are forced into engine downsizing. The power loss caused by downsizing must be supplied by alternative sources, such as electric components, which results in hybridisation. On the other hand, fully electrified powertrains are hampered by an underdeveloped infrastructure that does not provide sufficient charging points. Furthermore, society, which iHorizon-Enabled Energy Management for Electrified Vehicles. https://doi.org/10.1016/B978-0-12-815010-8.00006-5 © 2019 Elsevier Inc. All rights reserved.

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is used to fast refuelling, does not readily accept the battery-charging interval duration, which can last several minutes in the best-case scenarios. The immediate solution to improve emissions generation and relieve range anxiety is found in hybridised powertrains, which combine a conventional propulsion system, through an internal combustion engine, with one or more electric motors. An adequate coordination of these power sources can gain higher efficiency values and substitute for fuel energy with electricity, thanks to regenerative braking and charging grid support in the case of pluggable vehicles. Both hybrid electric vehicles (HEVs) and plugin hybrid electric vehicles (PHEVs) of any architecture incorporate at least one degree of freedom in the vehicle propulsion system. That is the shared power supply that can be distributed between the alternative energy sources, which consists of deciding when to use the electric motor, the combustion engine or their combination. This degree or degrees of freedom needs to be filled with a controller, called the energy management strategy. Although energy management is generally a complex task, this degree of freedom also provides a margin for energy optimisation, fuel consumption and emissions reduction, among others. The level of complexity and margin of improvement are directly related to the characteristics of the hybrid platform and electric components, including motor, battery and power electronics. Considering a simple case of a parallel HEV with one motor and therefore one degree of freedom, the energy management strategy complexity and fuel displacement potential mainly depend on the motor nominal power, battery storage and power capacity and availability of external grid support to recharge in stationary conditions. Low power electric motors cannot contribute to the power demand with comparable torque to internal combustion engines. As the motor power increases and approaches the engine capabilities, its functionality also increases. In particular, low-power motors are integrated in mildly HEVs, which only have the function of assisting the combustion engine but are never used alone to propel the vehicle. Motors of higher power are used in full hybrids, where the electric machine is able to provide full electric drive. An ultimate complexity level is achieved with PHEVs, due to the grid support asset. HEVs can only recharge their batteries through either regenerative braking or using an engine recharging mode and therefore consuming extra fuel. Consequently, HEVs are very limited in terms of depth of discharge allowed, which is usually situated around 20% of useful charge, generally within a 40% and 60% state of charge. Nonetheless, plug-in hybrid grid support permits the use of batteries as in full electric powertrains, which encourages a storage capacity increment and a useable charge to 50%, 70% or even higher percentages [1–3]. The battery size in PHEVs also allows the use of more powerful electric motors that become coleaders with the internal combustion engine in vehicle propulsion. These powertrains have larger margins for emissions reduction, but also become more complex in terms of energy management. Full exploitation of these hybrid platforms can be achieved, provided that full depletion is achieved before reaching the next charging point and this depletion is optimised to favour the overall powertrain efficiency. It is therefore of utmost importance to anticipate information about the future cycle length and power requirements so that the optimisation can be performed. Within this context, iHorizon cycle-length

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speed and acceleration prediction have direct applications for HEV and PHEV energy management and favour a considerable improvement over current strategies used in industry by reducing the cycle uncertainty.

6.1.1 Online energy management strategies Prior to presenting the proposed energy management strategy in the context of iHorizon, it is necessary to review the current approaches available in the literature and implemented in industry, so as to identify advantages and disadvantages of the existing technology. The immediate solution for plug-in vehicle control can be found in the extension of HEVs energy management via charge depleting/charge sustaining [4, 5]. Hybrid vehicles operate within a constrained state of charge values that allows a depth of discharge around 20%. These vehicles implement a charge-sustaining mode to prevent deep battery depletion and therefore avoid future charging cost using the internal combustion engine. The uncertainty regarding future braking events and speed and torque demand scenarios, where the combustion engine is particularly efficient, prevents anticipation of future recharging scenarios. Charge sustaining, a wellproven strategy, can be extrapolated to plug-in vehicles using a charge-depleting/ charge-sustaining mode. This strategy consists of fast depletion of the battery at the beginning of the drive cycle until a safety boundary is reached, to maximise the electric energy used in case the cycle comes to an end. The condition for switching from charge-depleting mode into charge-sustaining mode is expressed in terms of state of charge. When the battery charge drops below a specific limit, the aggressive battery depletion is stopped and the controller changes into the regular HEV strategy that prevents rapid battery depletion and maintains the state of charge around constant values within a window of 20%. Charge depletion emulates the strategy followed by a full electric vehicle within the motor power limits, electric components that are generally more powerful in battery electric powertrains. In contrast, charge sustaining coincides with hybrid vehicles with no grid support [6]. This strategy does not guarantee optimality, inasmuch as plug-in hybrids with batteries depleted lose their margin for improvement against regular hybrids. On the one hand, intense initial depletion can cause electrical components to operate at lower efficiency values. The electric component power electronics, electric motors and batteries are less efficient when operated at high charge and discharge currents. On the other hand, when the battery has been drained, the electric sources can only cooperate in the vehicle propulsion within a reduced margin similar to regular hybrids, losing the margin for improvement available with vehicles having grid support [5, 7, 8]. The lack of optimality of charge depleting/charge sustaining has been proven on numerous occasions in simulation environments by authors expert in the field. These publications point out the disadvantages of this strategy and claim the need for more detailed approaches able to outperform the existing solutions. These publications compare the previous strategy with other optimal and close-to-optimal approaches and provide exact margins for improvement. However, fuel and emission reduction benefits are drive cycle dependent due to the adaptability of optimal strategies and inadaptability of charge depleting/charge sustaining [3, 9–11].

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The alternative strategy is the so-called blended mode, which consists of gradual battery depletion along the entire drive cycle, ideally attending to the best combination of electricity and fuel that minimises or maximises a target. Each cycle is subjected to variable power requirements, depending on the route characteristics, traffic congestion and driving style. Ideally, the energy strategy needs to adapt to the previous characteristics and to the powertrain’s most efficient working conditions [12–15]. Nevertheless, an appropriate programming of the battery depletion requires information about the length and energy requirements of the future cycle prior to the beginning. Besides, the optimal strategy can only be possible if the level of power requirements per cycle segments is also available and therefore the best coordination of fuel and electricity sources can be anticipated. Consequently, the blended mode can only be guaranteed to outperform charge-depleting/charge-sustaining mode when detailed information prior to the beginning of the drive cycle is available. However, this assumption is not necessarily feasible a priori in the context of the current technology implemented in private transportation, although it might be possible in public transportation systems that generally follow preestablished routes repeated daily on well-established schedules [6, 8]. Furthermore, blended mode requires advanced controllers, more complex than rules implemented for charge depleting/charge sustaining, which require higher computational effort and memory resources. Fuel consumption improvement is therefore associated with higher development, increased implementation cost and more powerful electronic control units [11]. The blended mode’s high complexity is one of the main issues that hinder its implementation in industry. The increased difficulty of these algorithms can prevent robust solutions from being obtained, ones that are implementable in vehicle real-time control, a field in which they cannot compete against rule-based and fuzzy logic controllers. Strategies based on rules are simple to implement, perform in real time, are easily understandable and are inexpensive to compute when compared to optimisation-based controllers. Both rule-based and fuzzy logic are based on thresholds that are preestablished in a calibration process usually inspired in an optimised solution calculated on a selected set of drive cycles. These parameters are fixed offline and are implemented into a rigid framework, usually without adaptive capabilities. Consequently, unless the drive cycle is ‘similar to’ those used in the parameters selection, the resulting control strategy returns suboptimal control and charge-depleting/chargesustaining modes when operated in real life. Their easy understanding, interpretation and implementation situates them as preferred controllers in current electrified powertrains, despite the listed limits in real fuel consumption reduction [4, 5, 12, 16]. Whilst the previous controllers have sufficient emissions reduction requirements, the increasing environmental consciousness and emissions legislation have motivated intense research in the past decade in alternative control strategies that, while approaching to an optimal solution, are simultaneously implementable in real-time with robust performance [17]. A priori, any optimisation tool can be applied to solve the energy management problem, the reason why literature approaches are varied and concern authors who are experts in very specific areas and algorithms. Within the literature offered, the dominant strategy designs for PHEV control involve [11]: dynamic programming [18, 19], equivalent consumption minimisation strategy

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[8, 20], simulated annealing, genetic algorithm, particle swarm optimisation, DIRECT method [21], neural networks, game theory [22, 23], sliding mode control and convex programming [24]. Although all of them have proper representation in the literature, dynamic programming is the only one able to return, by definition, global optimal solutions. This algorithm computes global optimal solutions for a given drive cycle and presents convenient efficiency qualities when compared to alternative algorithms for global optimisation. However, it fails to meet most of the real-time implementation requirements due to its high computational cost and backwards computation direction, from ending conditions until initial conditions, characteristics a priori incompatible with online control [1, 18]. Dynamic programming is particularly suitable to analysis of the combined optimal strategy for cycles and vehicle modes and to generate expert data to develop alternative controllers, but its baseline algorithm is not directly implementable for vehicle control. In parallel, several modifications of the baseline algorithm can be found in the literature with online control applications. These ease the computational effort but in return no longer guarantee the solution optimality [6, 7, 25]. One of the most popular approaches to reduce the computational effort consists of relaxing the conditions for optimality into local optimisation. An example is found in the so-called equivalent consumption minimisation strategy, known to reduce the computational burden when compared to dynamic programming. However, this simplified strategy still requires information about the drive cycle in order to provide a suitable value for the equivalence factor and generate satisfactory solutions and still requires derivative computations that are sometimes calculated offline and implemented in map or vector format to guarantee controller robustness [26, 27]. The instability of derivatives and issues for robust control can be compensated for with derivative-free algorithms that search for the optimal solution through alternative methodologies. Derivative-free methods are numerically well-behaved and include the DIRECT method and metaheuristic algorithms inspired by natural processes such as simulated annealing, genetic algorithms and particle filters. Nevertheless, the solution yielded from the previous is highly dependent on the parameters selection phase, solution initialisation and requires iterative computations. Although it is numerically stable, it is usually not possible to guarantee that their solution converges into the optimal results for a limited number of iterations. Either the results accuracy or computational time can be guaranteed, but not both simultaneously. Consequently, real-time applications through a prefixed number of iterations do not ensure close-to-optimal results [21]. Advantages and disadvantages can also be found in the application of game theory, sliding mode controller and convex programming applications to hybrid vehicles energy management, which is the main reason why the literature fails to agree on a recommended solution.

6.1.2 Intelligent control Although all previous algorithms present valid solutions, there is no agreement on the best approach for the particular case of PHEV energy management. Nevertheless, the introduction of advanced driver assistance systems and autonomous driving has

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increased the importance of data and with it, the data mining and machine learning algorithm applications for vehicle control. Artificial intelligence can be also used to approximate optimal strategies with reduced computational effort. Machine learning has been extensively implemented for control algorithms in various application, but its extension to the automotive sector for energy management in PHEVs has not been yet properly documented. The key characteristics that recommend the use of this approach against the previous ones are the absence of iterations and fast computation, which allow for real-time control applications [28]. Vehicle energy management could be theoretically approached with both reinforcement learning and supervised learning. On the one hand, reinforcement learning can be applied, establishing a cost function based on fuel consumption and energy efficiency to promote learning towards optimal operating conditions. This is possible when the solution selection criteria are clear and do not require labelled data. Reinforcement learning is particularly useful to learn from processes not fully understood but possible to evaluate through cost functions. In addition, it facilitates the implementation in the presence of scarce labelled data or when data cannot be easily obtained. On the other hand, in the presence of labelled data, which can be generated through offline optimisation algorithms, supervised learning is also applicable. This time the desired output is explicitly detailed labelled data provided for training, validation and testing. Data is obtained through direct measurements or through offline computation in case the process is fully known [13, 29, 30]. Hybrid vehicle control involves a wellknown powertrain simulated successfully on numerous occasions for research and development both in industry and academia. Besides, powerful optimisation engines are available to generate expert labelled data and provide insights into the solution characteristics. In the following, the approach applied is the supervised option, given the amount of data available for training and testing, which can be offline optimised, although reinforcement learning solutions are also interesting from research and applications points of view. Supervised learning gathers numerous algorithms recommended for several applications. In particular, neural networks are known to be able to capture the underlying relationship between a series of input variables and desired outputs, as detailed in the training data. Furthermore, under the assumption of a network of sufficient complexity, these are claimed to be able to approximate a given process. These statements guarantee the existence of a solution, although they are not able to provide guidelines to suggest which should be the networks structure that provides satisfactory results for specific applications [31, 32]. Neural networks present high learning capabilities and can emulate highly nonlinear processes that cannot be mathematically derived. These problems can be tackled with neural networks by developing simpler mathematically well-behaved solutions that can be implemented in the vehicle [33]. This beneficial characteristic has been widely proven and exploited in the literature, which supports neural networks application for vehicle control. The specific use for energy management was introduced by Murphey et al., to develop a control strategy for a power-split HEV with no plug-in capacity. The authors considered the availability of limited route information that involved the driving trend, road type and traffic [29, 30]. Variables that contain important information about the power demand were used for speed and

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acceleration prediction in driving style and speed prediction algorithms throughout the iHorizon framework definition. Similarly, Prokhorov presented an energy management strategy based on neural networks applied again to a power-split HEV. A Toyota Prius was controlled through instantaneous power demand as a unique input without considering external route-related information [34, 35]. Despite being simplistic, the strategy described for hybrid vehicles with no grid support is directed to the charge-sustaining mode and therefore is not highly sensitive to the route characteristics, as happens in plug-in hybrids. Suzuki et al., authors who tackled the energy management of a hybrid electric truck to improve fuel consumption using neural networks [36], took an equivalent approach. Albeit the previous approaches presented satisfactory solutions for hybrid energy management, their application to plug-in strategies is not directly extendable. Hybrid vehicles have limited usable charge margin, which forces a charge-sustaining operation, which implies that future long-term drive cycle information is not as relevant as in electric and plug-in powertrains. Consequently, it is reasonable to expect the necessity of additional inputs to achieve optimal battery depletion and a minimum state of charge by the end of the cycle. Only one example of neurocontrollers in plug-in energy management is found in the literature [13], where the authors implement a dual controller based on two independent neural networks. The distinction between two controllers responds to the future drive cycle information availability. One network was active in the absence of route information, whilst the second was triggered when both the duration and trip length were known. The first made use of seven inputs listed as: vehicle speed, driveline power, battery current state of charge, average speed, maximum acceleration, minimum deceleration and idle rate. The second network was developed using four additional drive cycle–related signals that gathered trip length, trip duration, current drive length and current drive time [13]. The vehicle control was performed making a distinction between three case scenarios. The first was triggered when the battery charge was above 30% and the cycle length was below the available electric range, a situation in which the all-electric drive was activated and there was no need for an energy split between motor and engine. In the event that the electric range was below the cycle length, one of the previous neural networks was activated. The drive cycle sensitive network actuated when the cycle information was available and the battery charge above 30%, whilst the other network is activated otherwise [13]. That implies that the trip sensitive controller can only be activated in the presence of the required trip information and provided that enough charge is available in the battery, whilst in the second neural networks support the absence of trip information and critical state of charge situations. Although Chen et al. accounted for trip information of unquestionable importance in plug-in vehicles, the number of inputs and information density could be optimised [13]. On the one hand, the authors combined vehicle speed and acceleration statistics, when the major influencing factors for vehicle energy management are torque demand and transmission speed. It can be argued that both longitudinal speed and acceleration influences the power demand at the engine level, but this happens through the gearbox and its gearshift policy. Consequently, the use of vehicle longitudinal measures forces the neurocontroller to learn not only the optimal motor and combustion engine

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combination, but also the gear change control strategy. Applications in which the variables to control involve the combined gear policy and torque share between power sources would require the previous inputs. However, in the event that only energy management is implemented as the control variable, the previous approach would require unnecessarily complex controllers. The neural network would have to learn simultaneously the gearshift strategy and the optimal torque split between the engine and the motor. These controllers would require more complex structures and a greater amount of training data. In addition, more complex neural networks would be more difficult to test for robustness, whilst not providing additional performance benefits. Also, the authors implemented imprecise route data. Both time duration and length can hide important information about the actual power and energy demand. The route speed limit, traffic level and external disruptions can classify two routes of similar length and duration differently in terms of power control. Consequently, the previous signals might not contain enough information to anticipate the vehicle’s future power demand. Furthermore, energy management–relevant data consists of the remaining cycle and not the characteristics of the route already past, which cannot be optimised. The previous discussion suggests the presence of redundant signals and nonrelevant information within the 11 input variables. Such an input layer size would require large amounts of training and testing data quantity, a longer time in training processes and a larger space in memory and greater computational effort to store the respective weights and compute the control strategies. Also, a neurocontroller for in-vehicle implementation should be designed as a trade-off between computational effort, storage capacity and results accuracy. Consequently, the input signals need to be carefully evaluated so that only the key signals are used and no redundant or misleading information is fed to the neural networks. In the following subsections, several neural network candidates are proposed to minimise the structure complexity and improve controller efficiency.

6.1.3 Energy management in iHorizon Before tackling an energy management strategy design using neural networks, it is worth examining the context of the controller in iHorizon, as iHorizon is provided with a cycle-length speed and acceleration prediction that can be used to anticipate the power and energy demand along the entire cycle. Although this long-term prediction cannot accurately anticipate the instantaneous power demand, the overall energy requirements per cycle segment can be confidently estimated. This information is of utmost importance in computing the overall cycle energy management and can be used to reduce fuel consumption and optimise the battery depletion schedule. The prediction is computed making use of information about the driving style, road type, speed limit and traffic level. Furthermore, this information is processed by the predictor and generates a direct signal for the controller, in contrast to the previous approaches reviewed in the literature, where such signals are used directly as inputs into the networks without previous processing. In the context of iHorizon, the neurocontroller does not need to capture the information and influences of driving style and traffic on the power demand and respective energy management, as illustrated in Fig. 6.1.

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Fig. 6.1 The iHorizon framework formed by three main modules: (1) driving style recognition algorithm; (2) short-term speed prediction module; and (3) long-term cycle-length speed prediction module.

However, even after simplifying the network inputs, the controllers obtained through machine learning are complex to analyse in terms of the strategy robustness. The solutions developed using neural networks are considered to be black boxes, whose performance is opaque to the designer and difficult to understand. The simpler the network, the easier the solution is to be tested, understood and validated for realtime control. With these precedents, iHorizon appears to be a suitable framework to detach power demand from energy management and simplify the controllers’ development and implementation. Both driving style and limited route information are used to obtain a realistic estimation of speed and acceleration profiles over the complete cycle length. This is possible through Markov chains obtained for particular conditions of driving style, route type, speed limit and traffic congestion. The predictors are able to capture the driver level of aggressiveness through the driving style algorithm and return profiles of higher average speed and acceleration with aggressive drivers, whilst segments under heavy traffic conditions generate considerably lower average speed and numerous deceleration and stopping events. This valuable information is used to further enhance the energy management and maintain simultaneously a limited number of input signals. In addition, speed and acceleration prediction are also provided by short-term horizons no longer than 10 s that can locally improve the output quality to adapt to instantaneous measures along the cycle. This information along with long-term

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predictions is useful for energy management in vehicles with plug-in capability to achieve complete battery depletion by the end of the drive cycle. As illustrated in Fig. 6.1, the cycle-length speed prediction can be used, along with the vehicle model, to predict the cycle energy demand and estimate the driver power demand, essential to compute close-to-optimal energy management strategies. In the following section, a neural networks–based controller is described and assessed with respect to strict optimal solutions obtained using dynamic programming.

6.2

Expert data

Data-driven and machine learning algorithms are highly dependent on the suitability of the data used for training, testing and validation. Each application requires an area of validity, accuracy and complexity, which are directly dependent on the data quality, quantity and variability, which implies that all feasible case scenarios need to be represented in the training data with a sufficient number of samples and accuracy to meet the application requirements. The quality of the algorithm results will never be better than the data used for training.

6.2.1 Data collection The data used to generate training samples consists of historic and real-time data sets, as already used in earlier chapters for speed prediction in long and short horizons. More information about the set characteristics can be found in Sections 4.2.1 and 5.2.1 respective to short- and long-term speed prediction algorithms. This data proceeds directly from the controller area network (CAN) and is acquired in the vehicle during real-life routes completed by nonprofessional drivers. The routes proceed from roads in the United Kingdom and represent commuting routes, daily routines and sporadic trips at different times of day and days of the week. The data collected is accurate and presents a high sampling rate, but it cannot be directly used for training as it requires data processing, as occurred with the previously elaborated speed prediction algorithms. In this case, the objective is to provide labelled data, that is, optimal strategies that minimise the fuel consumption in each drive cycle and that can be implemented in-vehicle for real-time control. In the following discussion, the cycles collected are used to obtain the driver power demand, making use of a vehicle model, and are optimised using dynamic programming. In order to provide enough and varied data to train the controller, the cycles belonging to historic and real-time tests are optimised using different initial states of charge values: 90%, 80%, 70%, 60%, 50% and 40%. The allowed state of charge margins that limit maximum and minimum charge values can oscillate within the limits of 90% and 33%. Consequently, cycles initiated at a high battery charge, such as 90% and 80%, would presumably return discharging battery schedules as optimal solutions, whilst cycles initiated with 40% state of charge would probably result in strategies similar to charge-sustaining mode. Each initial state of charge forces the optimal strategy

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to a different discharge schedule, to make the best use of the electric energy stored in the battery. The optimal control strategy obtained in each case scenario is analysed to yield the underlying criteria that guarantee optimisation and provide important information for the design of the neurocontroller.

6.2.2 Optimal solution: Dynamic programming Dynamic programming is herewith implemented offline with low requirements in terms of computational time and effort. The algorithm is implemented with a simplified vehicle model with sufficient accuracy to capture the optimal working conditions of the hybrid components, but limited computational requirements as provided by a processor, the Intel CORE i7. This offline implementation allows the use of a dynamic programming algorithm implemented in MATLAB and used to optimise a vehicle model included in a MATLAB function file. Although there are numerous approaches in the literature to obtain optimal results that can reduce the computational effort required, the beneficial characteristics and numerous satisfactory implementations in the research on dynamic programming suggest the implementation of this methodology for this application. The dynamic programming algorithm can obtain global optimal results of multivariable nonlinear problems. In common with other optimisation algorithms, the solution is found by minimising an unwanted outcome or maximising a sought benefit. In minimisation problems, this unwanted outcome is called a cost function, although other commonly used terms include target and objective function. The optimal solution is strongly conditioned by the target or targets of interest, which determine the control strategy to follow [18]. Dynamic programming is particularly recommended for offline energy management optimisation due to the possibility of achieving global optimal solutions and reducing the baseline problem into subproblems. N-Dimensional problems are divided into N problems of one dimension, easier and faster to solve, whose optimality is guaranteed through the principle of optimality [37–39]. This optimisation algorithm is particularly useful when dealing with solutions distributed in common branches that converge into a single state. In the event that more than one solution candidate converges into the same instantaneous conditions, the strategies associated with higher cost can be automatically discarded, as it can be ensured that they would not outperform the candidate converging into the same state with lower cost; “optimal policies have optimal subpolicies” [37]. This implies that, given a common state, alternative branches that lead to it can be simplified, maintaining only the ones that provide minimum cost [40]. This process reduces the solution candidates that need to be further elaborated and carried forward and consequently decrements considerably the computational effort required. Hybrid vehicle control is known to have a solution of the characteristics described, which is why they benefit from dynamic programming as observed in numerous publications. More information about the characteristics of this algorithm are detailed in Section 2.4.2. Dynamic programming is implemented with its deterministic version, since the characteristics of the cycles are perfectly known and collected with complete information from real-life conditions. In offline optimisation and with the aim of

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generating expert data for training, it is assumed that all disturbances are perfectly controlled. After implementation, the optimal controller would operate based on the predicted future power demand, as generated by the long-term speed prediction algorithm. Although the methodology implementation is clear, the solution is particularly dependent on the selection criteria, that is, the cost function. The most popular objective is fuel consumption reduction; the objective function can be expressed in terms of other variables such as tailpipe emissions reduction, performance enhancement or a combination of these with multiobjective approaches. When dealing with conflicting objectives, the combined optimal values require parallel computation and pareto solutions analysis. This computationally expensive resolution can be simplified using a single objective function in which the objectives are mixed through weight summation or constrained within desired intervals. Whilst constrained objectives cannot be efficiently optimised, the combination of weighted objectives can achieve an optimal trade-off, provided the weights are properly selected, that is, they properly represent the relative importance of each objective and their selection is mathematically justified. The approach taken here consists of a combination of electric and chemical power weighted using the relative cost between the sources of energy. Fuel and electricity prices are used to combine the two power signals and generate a cost function that targets the minimisation of the overall energy cost. This approach allows an analysis of the trade-off between electricity and fuel and the effect of the energy cost in the control strategy. However, in practise and due to the higher cost of fuel and the lower efficiency of the internal combustion engine compared to the electric components, the previous cost function is equivalent to fuel consumption minimisation. Nevertheless, it also allows for modification of the relative price of the electricity and fuel cost and study of their effect on the energy management strategy.

6.2.3 Vehicle model In order to compute a global optimal solution, it is necessary to implement a vehicle model able to capture the powertrain characteristics and key interaction between the engine and electrical motor. An appropriate simulation is required of the external resistances to obtain the power demand and a representation of the electrical components, internal combustion engine efficiency and power response to achieve solutions applicable for vehicle control. The vehicle model is able to simulate both plug-in and full hybrid electric powertrains. This is possible by limiting the useable state of charge and the initial and final charge conditions and modifying the battery capacity. The integrated motor and engine have characteristics suitable for both powertrains and they allow for all vehicle modes that will be included in Section 6.2.4 and enumerated herewith as: electric vehicle mode, conventional vehicle mode, hybrid vehicle mode, engine recharging mode, regenerative braking mode, friction brake mode and assisted braking mode. The model is implemented in a MATLAB function script using map-based formulation dependent transmission torque demand and rotational speed, and contains one state, the state of charge. The vehicle model function is used by the dynamic

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programming solver to optimise the coordination between engine and electric motor, within the constraints included through feasibility matrices. The possible component values are limited by the maps implemented and infeasible flags that detect nonallowed working points. Dynamic programming calculates the optimal solution within the feasible strategies and returns the control variable, which is defined as the torque split coefficient between the electric motor and the combustion engine. The value of this coefficient determines when to use each of the power sources and how much torque is provided by each of the sources. The implementation consists of a quasistatic model of a parallel hybrid configuration that receives four inputs, vehicle longitudinal speed, vehicle longitudinal acceleration, gear number and road slope. Only longitudinal dynamics are considered for the purposes of this study. In this first approach, the gear change policy is not optimised along with the energy management to simplify the results analysis. Nevertheless, ideally these two signals could be combined and optimised simultaneously to further improve the powertrain efficiency. The parallel configuration contains one degree of freedom and consequently only one control signal is calculated, which is the power-split coefficient between the motor and the engine. A summary of the variables use is included in Table 6.1. Dynamic programming needs to anticipate the instantaneous torque demand to compute the power needs and therefore the individual contributions of the electric motor and the internal combustion engine. This is calculated starting at the vehicle level and advancing through the transmission up to the torque split device, whose operation is described by the torque split coefficient. This variable is defined as a control variable and determined in the control equations that allow computing combustion engine and electric motor torque demand, as well as friction brake torque. The model is able to include external road resistances, vehicle inertia, differential and transmission losses, gearbox efficiency and characteristics of engine, motor and battery components. At the vehicle level, the torque at the wheel, Tqwheel, is calculated, taking into account the road rolling resistance, gradient resistance and aerodynamic coefficient: Table 6.1

Model variables summary

Function

Variables

Inputs

Vehicle longitudinal speed Vehicle longitudinal acceleration Gear number Road gradient Battery state of charge Torque split coefficient Energy combined price Fuel consumption and electricity consumption Fuel consumption, state of charge schedule and othersa

State Control variable Cost function Targets Output a

All intermediate variables can be defined as outputs to analyse the torque evolution, energy losses, battery use…

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 Tqwheel ¼ R  gCr m cos ðθÞ + gm sin ðθÞ + Cd Aρair v2 =2 + ma where R, g, Cr, m, Cd, A and ρair are respectively wheel radius, gravity, rolling coefficient, vehicle mass, aerodynamic coefficient, frontal vehicle area and air density. The variables used consist of three of the four inputs, v, a and θ, which are respectively vehicle longitudinal speed, vehicle longitudinal acceleration and road gradient angle. Wheel torque represents the resistances external to the vehicle caused by the contact with the road, aerodynamics and the vehicle inertia. This torque demand calculated at the wheels is the torque required to maintain a certain speed and acceleration and overtake the mentioned resistances. This demand is translated to the transmission torque demand, TqtransmOut, taking into account the braking efficiency through the brake torque, Tqbrake, for negative torque demand during braking events.  TqtransmOut ¼

for Tqwheel > 0 Tqwheel Tqwheel + Tqbrake for Tqwheel  0

The torque out of the transmission connects to the final drive, which is characterised by its respective efficiency, ηFinalDrive, to calculate the torque demand at the final drive, TqfinalDrive:  TqfinalDrive ¼

TqtransmOut =ηFinalDrive for TqtransmOut > 0 TqtransmOut  ηFinalDrive for TqtransmOut  0

The ideal torque demand at the gearbox, TqGearIdeal, is obtained taking into account the gear reduction and the transmission inertia, which represents the inertial of all elements present until the gearbox: TqGearIdeal ¼ TqfinalDrive =gear reduction ðgear Þ + Jtransm  ω where gearreduction and Jtransm are respectively the reduction coefficient as a result of a specific gear selection and the transmission inertia and ω and gear are the transmission rotational speed and gear selection. Then, the real torque demand at the gear box includes the losses, TqGearLoss, calculated according to the transmission speed, gear selection and gearbox torque demand: TqGearBox ¼ TqGearIdeal + TqGearLoss ðω, TqGearIdeal , gear Þ The final torque demand before the engine and motor, TqDemand, is obtained, also taking into account the inertia of the power source machines: TqDemand ¼ ðJICE + JMotor Þα + TqGearBox where JICE and JMotor are respectively internal combustion engine and motor inertia and α represents the transmission rotational acceleration. TqDemand represents the torque demand at the power-split device, where the torque split between engine and

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motor needs to be computed for minimum energy cost, according to the cost function and the components characteristics. The internal combustion engine torque demand is calculated according to its sign, positive or negative, to account for engine or brake torque:  TqICEIdeal ¼

ð1  SplitÞ  TqDemand for TqDemand > 0 0 for TqDemand  0 

TqfrictionBrake ¼

for TqDemand > 0 0 ð1  SplitÞ  TqDemand for TqDemand  0

where the control signal is Split and represents the proportion of torque used from electric sources as shown in the equation: TqMotorIdeal ¼ Split  TqDemand The previous equations compute the torque share between engine and motor and are considered the control equations. Nevertheless, the real motor and engine torque demand also require taking into account the components efficiency. It is therefore necessary to account for the efficiency map of both power sources, parameters that are key to representing the relative efficiency and the optimal energy management strategy. On the one hand, the engine consumption is calculated using a fuel map that considers the engine speed and torque demand and provides the real fuel necessary to supply the driver demand: FuelFlow ¼ FuelFlow ðω, TqICEIdeal Þ On the other hand, the motor losses are added to the motor torque demand and transform into power demand to determine the battery use: PwMotor ¼ Pwðω, TqMotorIdeal Þ + ω  TqMotorIdeal The battery power demand is obtained, taking into account the motor torque demand and the power consumed by the auxiliary systems, modelled herewith as a constant power consumption, PwAux: PwBattery ¼ PwMotor + PwAux The battery variables voltage, VBattery, and current, IBattery, are then computed according to the power demand and the state of charge. First, the battery voltage is obtained using its characteristic map, state of charge dependent and secondly the actual battery current is obtained. VBattery ¼ VBattery ðSoCÞ

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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  IBattery ¼ e  VBattery + VBattery 2  4rPwBattery =2r where e and r are respectively the Coulomb efficiency and battery internal resistance and SoC alludes to the battery instantaneous state of charge. This last variable, a single-state variable of the model presented, is obtained through the state functions: SoCðt + 1Þ ¼ IBattery Ts=CapBattery  3600 + SoCðtÞ where Ts and CapBattery are respectively the model sampling time and the battery capacity in Ah. Finally, the cost function to minimise includes both fuel and electric power, multiplied by their respective prices to obtain the overall energy cost: C ¼ PwICE  pricefuel =LHV  ρfuel + PwBattery  priceelectricity where LHV, ρfuel, pricefuel and priceelectricity represent respectively the fuel low heat value, fuel density, fuel price and electricity price. All the parameters include in the previous are summarised in Table 6.2. The cost function used allows adaptation to changing energy prices and to the energetic policies of each country and time period. The energy prices can oscillate considerably, depending on the fuel taxes, renewables availability and transport policies. Nevertheless, as shown in the following paragraphs with the simulation results, the superior efficiency of the electric components compensates for fuel price fluctuations. Furthermore, the analysis of the effect of the energy price on the control strategy also provides important insights into the effect of the internal combustion engine and electric motor efficiency characteristics. For instance, a sensitivity analysis could provide the relative price difference required between fuel and electricity to compensate for the beneficial electric component efficiency and result in charge sustaining as an optimal strategy. That is, how much more expensive does the electricity need to be, to avoid the net use of battery energy by the end of the drive cycle and consume fuel instead?

Table 6.2

Vehicle mode parameters

R g Cr m Cd A ρair ηFinalDrive gearreduction Jtransm

Wheel radius Gravity Rolling coefficient Vehicle mass Aerodynamic coefficient Vehicle frontal area Air density Final drive efficiency Gear reduction coefficient Transmission inertia

JICE JMotor e r Ts CapBattery LHV ρfuel pricefuel priceelectricity

Engine inertia Motor inertia Coulomb efficiency Battery internal resistance Simulation sampling time Battery energy capacity Fuel low heating value Fuel density Fuel price Electricity price

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6.2.4 Hybrid operating modes The model previously implemented allows us to simulate a parallel hybrid configuration. This implies a single electric motor and an engine connected mechanically at the power split device. When coordinating the combined operation of motor and engine, seven options of vehicle modes can be differentiated. The modes selection depends on the energy management strategy and they are obtained using the dynamic programming optimisation. The vehicle modes are differentiated between positive and negative torque demand and the engine and motor states. On state is considered when they provide torque and off state when they remain latent or switched off. The possible vehicle modes that can be selected under positive driver torque demand are listed in the following: (1) Electric vehicle mode (EV): the electric motor is used alone to propel the vehicle with positive torque, whilst the engine remains off. This is possible when the state of charge is high and the motor alone can suffice for the driver torque demand. This mode is used when the engine operating conditions are very deficient in terms of efficiency, which generally happens at low torque and speed demand. (2) Hybrid vehicle mode (HY): consists of the coordination of both electric motor and internal combustion engine in the vehicle propulsion system with positive torque. The motor is used to displace the engine operating points to more efficient conditions and absorb the power demand transients, which penalise fuel consumption. Hybrid vehicle mode causes both battery depletion and fuel consumption. (3) Conventional vehicle mode (CV): the engine is used alone to propel the vehicle. This mode is generally used when the engine operating conditions are optimal and the state of charge is low. This mode is more dominant in HEVs and plug-in vehicles with low state of charge. (4) Engine recharging mode (ER): the engine is operated at higher torque to the driver demand and it is distributed to propel de vehicle and recharge the battery simultaneously. The engine is operated at higher power to displace it to more efficient conditions, which generally happens at high torque and speed values. This mode is used when the power demand is high and the battery state of charge is low.

Table 6.3 includes the characteristics of the previous modes in terms of torque demand, internal combustion engine and motor provided torque. The possible vehicle modes available in the event of negative torque demand include three different options:

Table 6.3 Hybrid vehicle modes for positive driver torque demand and demand distribution between engine and motor Mode

TqICE

TqMotor

HY ER CV EV

TqMotor +TqICE ¼TqDemand TqICE ¼TqDemand +TqMotor TqICE ¼TqDemand 0

0 TqDemand

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Table 6.4 Hybrid vehicle modes for negative driver torque demand and demand distribution between friction brakes and motor Mode

TqMotor

TqBrk

RB FB AB

TqMotor ¼TqDemand 0 TqMotor +TqBrk ¼TqDemand

TqBrk ¼TqDemand

(1) Regenerative braking mode (RB): consists of the use of the electric motor to brake the vehicle and recover the energy using it as a generator. This is the most efficient braking mode, since the energy is fully recovered, and it is only limited by the motor efficiency as a generator and can be reused in the future to propel the vehicle. (2) Friction brake mode (FB): the friction brakes are used alone to brake the vehicle. This is used when the state of charge is very high and the battery cannot store the energy recovered during braking. (3) Assisted braking mode (AB): both friction and regenerative brakes are used to brake the vehicle. This is used when the negative torque demand cannot be sufficed by the electric motor used as generator due to aggressive braking events.

Table 6.4 includes the torque characteristics of the previous hybrid modes at negative driver torque demand in terms of motor and braking mode relationship with respect to the torque demand. The vehicle modes depend on the battery state of charge and component efficiency maps, but eventually they are highly dependent on the driver power demand. For instance, aggressive deceleration requires torque values that cannot be provided by the regenerative braking mode and need the assistance of friction brakes, which reduce the recovered energy. Besides, under high decelerations the energy is not as efficiently recovered when compared to gradual decelerations. The same effects can be observed with positive torque demand. The increase of the power demand might force the transitions from electric mode to hybrid mode or from hybrid mode to engine regenerative mode, due to the motor torque limit and premature battery depletion.

6.2.5 Feasible energy management strategy The global optimal solution obtained using dynamic programming returns the best power share to minimise the overall energy consumption cost within the torque and power constraints of all components, as included in the vehicle model. Nevertheless, the vehicle model does not impose any constraint on the vehicle mode transitions. Consequently, dynamic programming might return working points that are possible individually but cannot be implemented in practise, due to excessive mode transitions in a short time. That is, dynamic programming might transit from electric vehicle mode to conventional vehicle mode on numerous occasions in short time windows that cannot be met, due to the engine starting time or the component reaction capacities, and that would doubtless affect the component durability and driveability comfort.

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Engine-on and engine-off state durations are not limited in the optimisation, and the mode transitions are not constrained. These infeasible working conditions could be prevented by including additional states in the optimisation problem and controlling the state transition and duration, but this would increase considerably the computational effort required to achieve the optimal solution, as well as the modelling complexity. Consequently, it was decided to optimise the powertrain by focusing on the vital importance of component efficiency and process the results a posteriori to yield realistic outcomes that could be implemented in-vehicle. The resulting strategy would not be strictly optimal as a consequence of the postprocessing but would be oriented to preserving the optimal working conditions, to achieve close-to-optimal results by focusing on the engine efficiency, known to be the weak component in terms of vehicle efficiency. The feasibility target is located on the engine mode transition, which requires a longer time to start, is more sensitive to fast transitions into on and off states and has a very low efficiency when compared to the electric motor. An algorithm was developed in a MATLAB script to detect infeasible mode transitions and return a viable alternative that gathers the required conditions for real-time control. This code mainly identifies the engine state and the mode duration, with particular interest on transitions that require engine on–off or off–on states. The mode minimum duration is limited, to allow for a realistic engine starting time, assumed to be just below 1 s, and prevent high transition frequency, to protect the components. The algorithm guarantees feasibility, component health and minimal driveability issues associated with the dynamic programming solution. The fewer engine starting events also reduced noise and vibrations considerably, and therefore improved the driver and passenger comfort. The alternative modes are selected through attending to the engine operating points, given a power demand and state of charge. The algorithm searches for the best engine efficiency achievable with a security charge margin, which returns close-tooptimal alternative strategies. The fuel map that was implemented characterises the highest engine efficacy just above 33%, in contrast to the motor efficiency, usually well above 75%. The engine operating points situated round 33% efficiency are located within the limits TqICEOptTop and TqICEOptLow, an interval that contains the maximum efficiency curve, referred to as TqICEOpt. Figs 6.2 and 6.3 show the flow diagrams that summarise the mode selection implemented to replace the original engine modes. The first focuses on the engine state transition from on to off, whilst the second covers the second transition. Fig. 6.2 identifies transitions to the engine-on state that are infeasible and finds an alternative solution to maintain the engine off when possible. This case scenario can only be experienced under positive torque demand, which can only be replaced by using electric vehicle mode. Consequently, the engine can remain off only when the state of charge is favourable and can supply enough energy for the electric drive. These episodes are generally very short in time, which allows for forcing the electric drive without risking important changes in the battery state of charge and therefore in the remainder of the optimal strategy. When the state of charge is equal to 38% or greater, the engine is maintained off and the power demand is fully supplied by the electric motor. When the torque demand is higher than the maximum motor torque

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Fig. 6.2 Flow chart for feasible strategy calculation from optimal DP infeasible engine-on results.

capacity, the real motor demand is located at its maximum feasible value and the driver torque demand is not fully sufficient. Once more, the brief duration of these events and the high torque capability of the electric motor do not allow major disruptions in the vehicle response and driver desired speed and acceleration. In the event of low charge, the engine starting is inevitably triggered, but it is maintained on for a longer time window than that stipulated through dynamic programming results. Fig. 6.3 covers the second case scenario, where the engine is switched off as part of an infeasible transition, and therefore an alternative strategy must be found to maintain it on, when possible. This case scenario is more complex than the previous one, since it can include both positive and negative torque demand. Under negative torque demand, for example a brief braking event, the regenerative and friction brakes are triggered, not requiring the engine support for a few instants. According to the vehicle model and control equations, in cases of negative torque the engine torque is forced to zero, whilst the motor torque used as a generator is coordinated with the friction brakes. The only possible solution to maintain the internal combustion engine on is therefore to keep it idling. In contrast, it could be the case that the torque demand is still positive but the operating conditions of the engine during a short time step are inefficient, and the needs can be met using the support of the electric motor alone. Under positive torque demand, most hybrid modes involve engine use, including hybrid vehicle mode, conventional vehicle mode and engine recharging mode. Consequently, in finding an alternative mode transition there are more options available using suitable engine operating points with minimum fuel consumption penalty. The flow diagram illustrated in Fig. 6.3 makes a distinction between positive and negative torque and sends

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Correction: ICE OFF to ICE ON

Yes

TqDemand >

Yes

TqICEOptTop ?

Yes

SoC ³ 38%?

HY mode: TqICE = TqICEOptTop

No

No

Maintain ICE ON TqICE = 0 (idling)

No

TqDemand ³ 0?

TqMotor=TqDemand –TqICEOptTop TqDemand > TqICEOptLow ?

No CV mode: TqICE = TqDemand

Yes SoC ³ 38%?

Yes

No TqDemand > TqICEOpt ?

HY mode: TqICE = TqICEOpt TqMotor=TqDemand –TqICEOpt

Yes

CV mode: TqICE = TqDemand

No ER mode: TqICE = TqICEOpt TqMotor = TqDemand –TqICEOpt

Fig. 6.3 Flow chart for feasible strategy calculation from optimal DP infeasible engine-off results.

the engine state to idle in the case of negative torque demand. Under positive torque, the torque demand is classified within three intervals: above the TqICEOptTop, between TqICEOptTop and TqICEOptLow, and below TqICEOptLow. Due to the strong interdependency of torque demand and engine efficiency, this distinction is necessary to find the best mode selection, given a vehicle speed. The decision is also associated with the state of charge to prevent extreme depletion with a low charged battery. If the torque demand is above TqICEOptTop and the state of charge is above the 38% limit, the mode transition is to hybrid mode, where the engine is operated at its most efficient torque and the motor supplies the rest of the torque demand. When the torque demand is below TqICEOptLow or above TqICEOptTop with a low battery charge, the engine is transited into conventional vehicle mode and it is used alone to propel the vehicle. If the engine torque is situated within TqICEOptTop and TqICEOptLow, the engine is operated at its most efficient torque and the motor is used to supply the difference in the torque demand. In this case, the motor torque might be positive or negative, depending

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on the difference between the torque demand and the engine optimal torque at a specific vehicle speed. Nonetheless, considering the previous case and a low state of charge, the motor is always operated at a negative or zero torque. If the torque demand is below the engine optimal torque, it is operated in engine recharging mode using TqICEOpt and the remaining torque to recharge the battery. Nonetheless, if the torque demand is above the engine’s most convenient working point, it is used in conventional vehicle mode. The previous strategies are not strictly optimal but are feasible and close-to-optimal engine operating conditions. This step is crucial in providing valid training data to develop the neurocontroller to be implemented that will be responsible for the vehicle operation. The neural networks cannot provide results of higher quality than the data used for training and it is therefore of utmost importance to provide the best quality training data possible. Furthermore, online control applications require robustness and must guarantee safe vehicle operation, to meet the industry and customer requirements and expectations. The substitution of the strictly optimal strategies obtained with dynamic programming by the feasible modifications discussed causes a deviation in the final state of charge and a minor increment in the final fuel consumption. This implies that some strategies do not return minimum battery depletion and others incur into a minimum charge limit violation. In order to facilitate network learning and prevent reaching nonallowed states of charge values, the cycles are truncated at 33%, which is the minimum allowed value. Consequently, the amount of data is slightly reduced and not all training and testing data cycles finalise in steady-state speed conditions.

6.3

Neural network design

The real-life data collected in historic and real-time tests is processed to find the optimal solution for various initial states of charge values. The optimal strategies are further processed to obtain alternative ones that are feasible and in-vehicle implementable, whilst close-to-optimal. This final data set needs to be divided for training testing and validation. The cycles are initially divided randomly, to provide 70% of them for training and 30% for testing and validation. Complete cycles are used both for training and testing as indivisible units; consequently, the distribution of 70% of cycles for training does not imply 70% of the total training samples. In order to distribute the data quantity accordingly, some cycles are permuted from the first random distribution to guarantee that at least 70% of the number of samples is used for training. Nevertheless, the design of neural networks not only depends on the data used for training, but also implies the selection of a specific structure and size able to capture the underlying process. Prior to network training, the network structure needs to be selected, which is the connection between inputs, hidden layers and outputs. Furthermore, the number of hidden layers and neurons per layer must be anticipated and, although the output layer is already given by the requirements of the controller, the number of inputs used might still need to be decided upon.

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6.3.1 Input signal selection The input signal selection is crucial to provide enough information to the neural network to reproduce the process of interest. If the input signals do not contain all the relevant factors that influence the optimal control strategy, the neural network will not be able to capture it, no matter which size or degree of complexity is used. Besides, the number of inputs simultaneously influences the size of the input layer and therefore the complexity of the network. An excessive number of inputs would cause an unnecessary complex input layer, that requires more input data to be trained and would be more complex to validate for robustness in online applications. Simpler neurons require less space in memory, as every new input implies as many weights as neurons in the following hidden layer, as well as lower training time and computational effort. Although the main relevant signals in energy management might be reasonably deduced, the required inputs for plug-in hybrids have not yet been agreed upon in the literature reviewed. Within the scarce examples that can be found in the literature for energy management of hybrid vehicles, the majority concentrate on vehicles with no plug-in capability. HEVs operate in charge-sustaining mode, which is not as sensitive to detailed drive cycle information as a blended mode. It is assumed that this simpler energy management requires fewer inputs to develop a neurocontroller. The list of inputs found in the literature to derive an energy management strategy for an HEV based on neural networks is included in Table 6.5. In Table 6.5 the authors agree on the necessity of power demand, either directly or through the combination of torque and speed. The benefit of the second option is to capture the engine and motor efficiency curves that generally depend on both of the previous variables. In addition, some authors include traffic information, driving trend, road type or vehicle speed as additional information. Finally, the authors

Table 6.5 Inputs and outputs used to develop energy management strategies for HEVs based on neural networks Ref.

Inputs

[30]

(1) (2) (3) (1) (2) (3)

[34] [35]

[36]

Outputs

Road type Driving trend v SoC(t) SoC(t  1) TqDemand(t)

NN1:

(1) ωICE (2) TqICE

(4) (5) (6) (4) (5)

PwDemand SoC traffic ω(t) Fuel rate(t)

NN2:

(1) ωICE (2) TqMotor (3) SoC

(1) PwICE (2) ωICE (1) TqICE (2) ωICE

NN1: Fuel rate NN2: IBattery

Where v, SoC, PwDemand, PwICE, ωICE and Ibattery are respectively vehicle longitudinal speed, battery state of charge, power demand, internal combustion engine power demand, internal combustion engine speed and battery current.

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include the state of charge information, crucial to guarantee charge-sustaining mode and protect the battery from deep discharge and charging events. Nevertheless, few examples are available in the literature of neurocontrollers for plug-in vehicle control, as previously anticipated. Chen et al. provide the following inputs list for plug-in hybrid control introduced in Table 6.6 for different levels of route information [13]. NN1 is used when no information about the drive cycle is available and agrees with the previous approaches of regular hybrid control in the necessity of power and speed information combined with the state of charge. In addition, the authors also include information about the speed and acceleration statistics and idle rate. Although this information can be beneficial to anticipate future speed and acceleration tendencies, the number of inputs used is rather large and might not concentrate optimal information density relevant for energy management. This is also observed in NN2, which incorporates duplications in the trip duration in distance and time through the signals trip length, current trip length, trip duration and current time. Furthermore, it is not clear that these four signals can provide accurate information on the drive cycle power requirements, which is key for energy management. It is possible to find cycles that combine similar length and duration but different power requirements, due to the combination of driving styles and road types along with traffic disruptions. Furthermore, the previous number of inputs requires an input layer with 11 neurons and the respective number of additional weights to connect with the hidden layer. Herewith, the number of necessary inputs and the selection of variables is minimised to limit the network size. The target of this study is to investigate and identify the most influential signals and the set of inputs that returns an input layer of small size and yet Table 6.6 Inputs and outputs used to develop energy management strategies for PHEVs based on neural networks Ref.

NN

Inputs

Output

[13]

NN1 (no trip info)

(1) v (2) PwDriveLine (3) SoC (4) vaverge (5) aMax (6) aMin (7) Idle rate NN1 inputs

IBattery

NN2 (trip info)

(8) (9) (10) (11)

Trip length Trip duration Current length (distance) Current time

Where PwDriveLine, vaverage, aMax and aMin represent the power demand at the driveline, average speed, maximum acceleration and minimum deceleration.

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Table 6.7 List of inputs and outputs used in neural network candidates 1 and 2 to develop energy management strategies for HEVs and PHEVs Candidate

Framework

Inputs

1

PHEV (with HEV inputs)

2

PHEV

(1) (2) (3) (1) (2) (3) (4)

TqDemand(t) ω(t) SoC(t) TqDemand(t) ω(t) SoC(t) ERemaining

Output SoC(t + 1)

Where TqDemand and ω(t) combine power demand and transmission speed, which are key signals to represent the motor and engine efficiencies and therefore would presumably provide vital information for energy management.

still complies with satisfactory accuracy requirements. Only signals that contain highdensity information are proposed as input candidates. As a first approach, two sets of input signals are proposed for two network candidates. The first emulates the approaches taken in the literature for HEV control and the second includes route information, expecting an improvement for PHEV control, as shown in Table 6.7. Candidate 1 also includes the battery state of charge to guarantee that the NN can maintain the state of charge within the allowed limits and does not produce deep discharge and charging profiles. Furthermore, candidate 2 includes the state of charge to guarantee that the network learns to deplete the battery completely by the end of the drive cycle, along with the remaining energy ERemaining. The state of charge is combined with the total amount of energy required to finish the drive cycle. Candidate 2 incorporates four signals that are related to power demand and cycle length and that condense in one variable the route information, which unifies time and distance into the energy requirements. Furthermore, in the table ‘remaining’ alludes to the total amount of energy required to finalise the drive cycle, which is defined as the energy required by the combined operation of the internal combustion engine and motor. This variable, along with the state of charge tendency, is expected to provide information to guide the battery discharge to minimum energy at the end of the cycle. The selection of the remaining energy unifies in one input signal maximum information about the future energy demand. The output selected for both network candidates is the future state of charge, which is equivalent to IBattery, since the state of charge is calculated through coulomb counting in a simulation environment. This is used as a baseline to develop novel neurocontrollers and test their robustness and real-time applications. After analysing the results, a step forward could be taken by including additional signals able to further represent the power requirements in detail by road sectors, so that the network can anticipate temporary situations such as heavy congestion or prolonged highway driving at high speed. But this analysis is covered in the last chapter and is proposed as a further development.

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6.3.2 Network size and structure As the input set and the targeted output are defined, the input layer and output layer sizes are automatically fixed. The parameters that need to be determined to finalise the neuron structure require specifying the number of hidden layers, selecting the number of neurons per hidden layer and identifying the connection between those neurons and other layers. The layers can be connected in forward and backward directions and the neurons can be fully connected or can avoid connections between consecutive neurons and layers. In terms of PHEV control, a relationship could be expected between current input and previous input values through the driver power demand and state of charge. The state of charge schedule, mode transitions, feasible mode selection, etc. depend on the previous engine state and state of charge values, and therefore the neural network structure needs to be able to capture these dependencies. Between the possible neural network candidates, the most used ones include forward-connected and feedback-connected layers. The first connect consecutive layers in the direction towards the output, feed-forward neural networks, whilst the second also connects layers in the backward direction to themselves or other layers located toward the inputs. Recurrent neural networks are provided by the memory capability that would be ignored by a feedforward structure. The so-called layer recurrent structure is dynamic, due to the feedback connections that act as states, a delayed processed version of the layer output. Furthermore, these feedback connections can also be interpreted as a delayed processed input that consequently provides memory to the network [33]. Although the previous reasoning applies to both hybrid and plug-in hybrid vehicle control, the literature approaches do not always implement networks connected in backward directions. This memory deficit is alleviated by Prokhrov, using the state of charge and the state of charge delayed one sample time as inputs to the network [34, 35]. The recurrent configuration is observed in the literature using Elman-type neural networks. These approaches base this structure selection on the necessity to incorporate past information to describe the future system behaviour. Directly extracted from Haykin’s publication, “… any nonlinear dynamic system may be approximated by a recurrent neural network to any desired degree of accuracy…” [41]. Vehicle powertrains and in particular hybrid powertrains are highly nonlinear and dynamic and therefore comply with recurrent network requirements. Besides, only one hidden layer is selected, which simplifies the network training and testing, the network performance interpretation and its validation for online applications. It is assumed that sufficient accuracy can be achieved using a single layer, as long as it contains enough neurons to capture the process nonlinearities. This decision is supported by the quote made by experts that claims that single-layer networks with a sufficiently large number of neurons can achieve the same accuracy as a multilayer network equivalent configuration [41]. Nonetheless, the neural network design does not have any stringent guidelines, as such designs strongly depend on the application and the complexity of the process to model or control. The hidden layer size is consequently selected by trial and error to find a suitable trade-off between network complexity, prediction accuracy and

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generalisation capability. The target is to find the simplest network that achieves the expected accuracy and generalisation requirements. Simpler networks would be easier to test and validate for robust applications in online control. Vehicle applications require robust results able to operate in real time and comply with the law. On the one hand, a very low number of hidden nodes would not be able to represent the process complexity, whilst on the other hand a very large number is susceptible to overfitting, which can cause poor generalisation and is susceptive to capturing sample noise [41, 42]. Overfitting is an effect to avoid and simplicity is preferred and supported by the Ockham’s razor criteria, which claims that complex models have greater possibility of error [41, 43]. This must all be considered to prevent overfitting and find an efficient network size using the so-called ‘growing strategy’ [42]. This method consists of the layer size initialisation with a low size that is expected to be insufficient. Next, the layer size is gradually increased during training and simulation results monitoring. Each network candidate is trained and tested to detect the accuracy improvement in the results [42]. When the increment of the network size does not imply an accuracy improvement, or the required accuracy is achieved, the ‘growing strategy’ is assumed to have converged into the simplest fit that complies with the designer requirements. In the following section, the network is initialised with five neurons and its size is increased up to 15–20 neurons with both candidate 1 and candidate 2 input sets.

6.4

Training and testing

The training and testing data sets contain approximately 70% and 30% of the available data, respectively. The training data is used as input for the initialised network and guided output to correct the network results and backpropagate the error to correct the weights selection. The training methods to follow need to comply with the network selection, layer recurrent, and are referred to as “temporally supervised learning algorithms” as introduced by [44].

6.4.1 Training algorithm Probably the most commonly used algorithms to train neural networks, and in particular recurrent structures, are the gradient-based methods, which consist of computing the gradient of a performance measure to update the weights. These gradients can be computed using various methods that target faster convergence and suggest more-orless complex procedures. The so-called error backpropagation baseline algorithm is used in feedforward neural networks, but layer recurrent approaches require a modified training algorithm [44]. The most commonly used algorithms are backpropagation through time (BPTT) and real-time recurrent learning (RTRL), which are continuous in time implementations of the baseline backpropagation algorithm [41, 44]. Both algorithms implement the propagation of derivatives calculated on the output prediction against the weights to update their values. The weights are updated forward in RTRL and backwards

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in BPTT. Consequently, BPTT can be implemented on an epoch basis, whilst RTRL needs to be implemented as continuous training. The characteristics of RTRL return algorithms more computationally intensive when compared to BPTT, but with fewer memory requirements, dependent of the truncation length selection. The previous comparison recommends BPTT as offline training, when no real-time implementation is required, due to its associated computational effort. Nevertheless, online and adaptive training require the use of RTRL [41, 44]. Herewith, the offline training of the network candidates is performed through BPTT with truncation depth of 1 s–10 s. Furthermore, this approach is compared to RTRL and returns higher accuracy for the same training time. Besides, offline training does not require online weight updates capacity and, although online training could presumably further improve the network accuracy with additional training data, it could also potentially modify the baseline weight selections and endanger the network generalisation capability and robustness. This situation is unstable and could not be confidently implemented in online control. The BPTT algorithm can be interpreted as an unfolded version of the baseline backpropagation in time, that is, backpropagation unfolded in a ‘time-layered’ network. The unfolded time layers are treated as ‘hidden layers’ in a “feedforward network in time”. This is illustrated in Fig. 6.4 representing several ‘time layers’ as the algorithm unfolds the original network in time [44]. Similarly to baseline backpropagation, RPTT is based on the calculation of the square error based on the desired output and the network result. This error is propagated from the output layer in the backwards direction to the hidden layer up to the inputs. The weights are corrected along with this propagation using the error derivatives with respect to the weight from each neuron [45]. Nonetheless, gradient-descent methods are well-known for causing convergence issues and are susceptible to converging into local minima, which can condition the final network accuracy. In order to encourage fast and accurate convergence into appropriate weight selections, the baseline BPTT algorithm is modified using an extended Kalman filter for the weights update stage. Although this modification introduces high computational cost, it can improve the convergence speed and the results accuracy, reducing the overall necessary iterations. The extended Kalman filter-BPTT proved to be beneficial in this application, achieving higher accuracy with a lower number of iterations when compared to the baseline BPTT [44, 46]. This approach replaces the BPTT weights update with the extended Kalman filter, as illustrated in Fig. 6.5 modified from Ref. [46]. The baseline algorithm operates the neural network forward with a new set of inputs, uk, and produces an output. The error is calculated by comparing to the desired training data

Fig. 6.4 Recurrent neural network with one input, one hidden and one output layer unfolded in time for the BPTT algorithm application.

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Fig. 6.5 Flow chart of extended Kalman filter backpropagation through time. Modified from G.V. Puskorius, L.A. Feldkamp, Parameter-based Kalman filter training: theory and implementation, in: Kalman Filtering and Neural Networks, S. 23, 2001.

output labels, yk. This error is backpropagated using the derivatives calculation with respect to each weight, where the Kalman filter plays an important role in calculating the final update value (as represented in the right-bottom corner in Fig. 6.5). The updated weights are used to perform a new forward simulation and calculate the new error to continue with the weights update until the final conditions are achieved, which can be expressed in terms of weight changes, number of iterations, output accuracy, etc. [46]. The use of the extended Kalman filter during weight updating can be interpreted as finding the minimum square error of the network weights estimation through the Kalman process. Detailed information about these training algorithms and the use of an extended Kalman filter is provided in Appendix.

6.4.2 Training and testing procedure The data used for training and testing incorporate approximately 70% for training and 30% for testing, using a complete cycles as the unit. It is preferred to use complete cycles, due to the relationship between the inputs and outputs in time. That is, the optimal strategy at the beginning of the drive cycle is dependent on the future cycle. Therefore, in order to encourage the neural network to capture this dependency, the use of complete depletion cycles from any initial state of charge to full battery use is required. Furthermore, recurrent neurons internally redirect the outputs processed to the inputs. The recurrent network connections redirect the delayed inputs processed and combine them with the current inputs and delayed processed output one step in time. In order to provide consistent training, the network needs to receive chronologically observed signals and consequently the network has to be trained and tested using cycle units. As anticipated in Section 6.5.1 and after testing various training algorithms and modifications of the previous (BPTT, RTRL and their respective combinations with extended Kalman filter weights updates), the selected method consists of the combination of extended Kalman filter weight updated implementing BPTT. The network

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weights are updated on an epoch basis during training, which consists of performing the weights update when a batch of data of a defined size has been processed. However, due to this dependency within consecutive network states in a cycle, the training is also performed on a cycle basis within every epoch. During training, there are transitions of data from the end of a cycle to the beginning of the next one, as structured in the training set. The final state of charge of a cycle generally does not coincide with the initial state of charge of the next one. Consequently, the internal network state would not comply with a sudden artificial change on the input that would never be seen in real -life operating conditions. In real scenarios, the charge does not change abruptly but evolves gradually along the drive cycle, with dependence on the power demand and previous vehicle modes. This misleading training scenario is avoided by conveniently initialising the internal network states every time a new cycle is initiated within the training set. The network activities, which refer to the internal state, are initiated using the initial state of charge of the next cycle, so that when proceeding with the training, the internal activity complies with the inputs in all cases. An example of this is illustrated in Fig. 6.6, which shows the discontinuity of two consecutive cycles. Although this is particularly critical for the state of charge that is the targeted output and the recurrent state, this discontinuity also happens in the presence of the other input variables. The particular case illustrated shows two consecutive cycle candidates where the initial state of charge is situated at 80% in both cases. The point’s final state of charge of the first cycle registers 33%, full battery depletion at the end of the cycle. This is followed by an abrupt change of the charge, again to 80%, that cannot be directly used as input unless the network is conveniently initialised to such a state of charge difference. Figs 6.7 and 6.8 illustrate the same discontinuity respective to the input transmission speed and torque demand. As a result of the feasible strategy development from dynamic programming optimal results, the first cycle is truncated just before the end to avoid further battery depletion of 33% in Fig. 6.7. This causes a final point which does not comply with steady-state conditions and registers a transmission speed different SoC training input in consequetive drive cycles (%)

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from zero. The same effect is observed in Fig. 6.8, which does not finalise the first cycle at zero torque demand. It is therefore of vital importance to conveniently initialise the network activities to be consistent along the batch training. Furthermore, the inputs are not presented with their physical value, but are instead normalised within the limits 0 and 1 for the state of charge and transmission speed,

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which only register positive values in real life and within 1 and 1 for the torque demand, in order to constrain the weights and facilitate their interpretation. Within the neural network body, the signals are multiplied by weights at the hidden level and summed with the other transformed inputs. Large differences in the order of magnitude between inputs and within the input values themselves prevents the network from learning the proper weight values and, in some cases, requires more complex structures. When normalising the inputs, the weight values also become constrained, which eases the training process. Besides, the weights are easier to interpret in terms of their relative values among each other and therefore insights over the network controller can be yielded. When using very disparate input values, the weights need to filter these and therefore the signal influences in the output are complex to understand. Nevertheless, when using inputs of the same order of magnitude, the weight values are also limited and directly interpretable after training. Consequently, a cycle initiated at maximum state of charge and finalised at minimum value is fed into the network as illustrated in Fig. 6.9, where the value is normalised for the maximum and minimum allowed values, 90% and 33% charge. Similarly, the transmission speed is normalised with respect to its minimum value, 0 at stand-still, and the maximum value that can be registered according to the gear change strategy and the component limits. Generally, regular cycles do not achieve such speed values and the normalised value will be below 1, as illustrated in Fig. 6.10, representing the same cycle included in Fig. 6.9. Fig. 6.11 includes the normalised torque for completeness of this training set for network candidate 1. Input sets for candidate 2 also contain the remaining energy, which is normalised attending to the maximum energy registered in the longest and most demanding cycle collected in the data set of almost 3 h duration and mainly based on highway driving and high average speed. This value represents in the context of the collected cycles a reasonable normalisation strategy, although it might be strongly dependent on the driver driving habits and regular cycle lengths. The error is calculated point-by-point comparing the network computed future state of charge with the labelled value. This implies that, every sample, the error can be calculated and used to correct the weight values and every new sample used

Fig. 6.9 Normalised state of charge used as input for the neural network.

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provides a fresh input with a renewed state of charge. However, when the network is used in real applications and during testing, the actual state of charge in time is unknown and only the initial value is available. The network needs to receive as input its delay output, a result of the control strategy selected. Consequently, it operates with a state of charge value that is not exact, assuming no perfectly optimal strategy is achieved, which conditions the accuracy of consecutive computations. The network implementation for testing and real simulation is illustrated in Fig. 6.12, where only the initial state of charge is available and the following values are produced directly by

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the network. In order to provide the real algorithm error, the network is tested as shown in the figure with a connection to its own prediction, whilst the rest of the inputs are obtained directly from the test data as generated due to the driver demand and cycle characteristics. The predicted state of charge schedule is compared point-bypoint with the test data label to determine the deviation accumulated from the optimal control strategy.

6.5

Training and testing results—Input set 1

The previously described training algorithm and training procedure are used to develop the neural networks with candidates 1 and 2 using the same amount of data. Both candidates are trained with the same number of samples, although candidate 2 receives an additional signal that includes the amount of energy required to finalise the cycle. Consequently, despite the amount of data being apparently the same, candidate 1 is completely unaware of the characteristics of the drive cycle. Both neural network structures are initiated with five neurons in the hidden layer, a number that is increased gradually to 7, 10 and 15 neurons for model candidate 1 and up to 20 neurons for candidate 2. A higher number of neurons is expected to be required for candidate 2, since it has a higher complexity caused by the additional input. The additional input implies a larger number of weights to be trained, but also the capacity to capture a more complex process, in particular for PHEV energy management.

6.5.1 Candidate 1 training error Candidate 1 is designed to capture the optimal strategy for an HEV or PHEV with information about the instantaneous power demand, through the combination of torque and transmission speed inputs, and instantaneous state of charge, but in the absence of future route information. This instantaneous battery charge proceeds at the first time step from the initial battery state of charge and at successive time steps from the network output, one time step delayed. The inputs provided do not incorporate information about the cycle length or future power requirements. Consequently, although it might be sufficient for HEV charge-sustaining control, it is not clear that candidate 1 will be able to schedule close-to-optimal battery depletion for a plug-in hybrid in cycles of any characteristics. The training is initialised with five neurons. The network weights are randomly initialised before the training starts, with initial values that will be corrected every iteration to approach the process of interest. A priori the process is unknown and no information about the shape of the solution is available. Therefore, there is a risk that the neural network will converge into a local optimal weight selection and prevent improvement of the controller accuracy. In order to keep this from happening if at all possible, various networks with the same number of neurons are trained independently and initialised with different weight values. It is expected that either all networks converge into the same or similar weight values, or that they adopt radically different results, which would suggest the presence of more than one local minima.

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An example of error convergence during training of a network with five neurons in the hidden layer is illustrated in Fig. 6.13. This training uses error BPTT modified with the extended Kalman filter and training batches of 10 samples. Refer to Appendix to obtain more information about the training algorithm. The graph at the top shows the error convergence at iterations one, two and three. The first iteration consists of the neuron results after initialising the weight randomly and proceeding to update the weights based on the error backpropagated, as calculated when the network has seen all the training data once. The second iteration again calculates the network outputs using the weights updated from the first iteration and again updates the weights to prepare the new set for iteration three. Due to the random weight initialisation, the initial error is considerably high and the convergence during the first iterations is very fast. The graph at the bottom in Fig. 6.13 depicts the convergence from the second iteration until the 100th training step. The convergence velocity decelerates as the network improves the weights values. This is a result of the backpropagation algorithm itself, that encourages higher weights gradients when the error is large, to accelerate the convergence under inaccurate results. As the weight values improve, the convergence decelerates so that the solution can be conveniently approached and so that high convergence speed updates do not cause divergence from the solution sought. Networks initialised with different weights might converge into different solutions and with different convergence speeds. The network output mean square errors can be used to compare the network convergence into a specific solution. Different weight selections are assumed to provide different behaviour and error measurements, which is the reason that this should be patent in the error measurement after each iteration. Fig. 6.14 illustrates the mean square error of two neural networks with seven neurons in their hidden layers. Both networks have identical structure and are trained with the Mean square error converge in first iterations MSE = 0.046

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same data set using the same training algorithm but are initialised with different weight values. Network 2 exhibits higher error measure and slower convergence in the first 10 epochs. Nevertheless, as the training continues, network 1 error stabilises and even worsens, whilst network 2 continues improving the average error measure. Although network 2 presents a better convergence tendency, if the training continues, and after 60 iterations, the error convergence also decelerates and reverts. The minimum average square error is obtained at training iteration 55 with a value of 1.8625e  6. If the network is trained further, the error increases, reaching a value of 2.2103e  6 at iteration 85, a 3.478e  7 worse value. This result seems to be unreasonable, since it could be a priori expected that the network training error always improves. Nevertheless, this behaviour can be explained by attending to the training data and algorithm. The mean square error measure is calculated per epoch, that is, after the network has seen all training data and an overall error is calculated and backpropagated. Nevertheless, the weight values are updated many times within one epoch, each time 10 training samples are seen. This implies that every weight update depends on the mean error measured after 10 samples are registered, an input batch. This batch-based implementation does not update the weights every training sample is fed that reduces the computational time and the convergence stability, where generalisation prevails over point-by-point accuracy. Consequently, it is mathematically possible to observe this behaviour of mean square error worsening with increasing number of epochs. Briefly introduced without mathematical strictness and qualitative interpretation, the causes of this behaviour can be due to the characteristics of the training set and network structure. On the one hand, it is possible that the training data could be inaccurate and contain noise that the network is trying to fit. With the presence of noisy data, the network might fit the high-frequency characteristics of the training data to reduce the overall error. On the other hand, the network might have deficient complexity and it might not be able to improve the process fitting above a specific accuracy. The first issue can be solved by improving the data quality and reducing the measurement noise, so that the network weights update to capture slow

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dynamics in the data and do not fit the noise. The second can be tackled by improving the network structure into higher complexity, to promote more complex fitting processes. In any case, both issues can be solved using the ‘early stopping’ strategy, which consists of monitoring the error measure to detect when the error cannot be improved. The training task is finalised when the error stabilises or evolves into worse values compared to previous iterations. A detailed square error evolution point-by-point after iterations 1 and 30 is illustrated at the top of Fig. 6.15, which corresponds to the previous networks with seven neurons, illustrated as network 1 in Fig. 6.14. The graph shows a clear improvement of the error measured from the first iteration after 30 epochs; however, this tendency is not maintained when comparing 30 and 60 iterations in the bottom illustrations. Iteration 60 registers a higher mean square error but reduces the error standard deviation point-by-point, which suggests better consistency of results. Examples of neural network candidates initialised independently are contained in Table 6.8, including two candidates per network size. The first two rows illustrate two networks with five neurons, which are initialised interdependently but seem to converge into the same solution with equal error tendency. The second network is stopped after 68 iterations, as it is already clear that it cannot outperform candidate 1 and returns the same solution accuracy. The network comparison is included in row 3 where the error difference is calculated, although the weight values difference is not implicit. The rows 4–6 include two networks with seven neurons in the hidden layer that experience different error convergence, as illustrated in Fig. 6.14, previously

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commented. Rows 7–9 include a similar example using 10 neurons in the hidden layer. This case compares two candidates that continue improving the error measure iteration after iteration, probably due to their higher complexity in comparison to the previous seven-neuron and five-neuron candidates. Again, independent network weights initialisation causes a disparate initial error measure and convergence, where the second candidate presented is able to outperform the first. However, the increased network complexity does not always guarantee an error convergence into an eversmaller value. More complex networks would fail to improve the results if the weights initialisation is far from the optimal solution and causes local optimal convergence. Other causes are deficient training data information, which does not provide all influencing signals, or a deficient network structure itself, which cannot capture the process dynamics. In any case, the error measure achieved by all candidates is very low, which suggests that they can fit the training data every time the network sees a new input that is compared to the desired output. Nonetheless the networks are eventually implemented receiving their own state of charge schedule calculations, which means that one of the inputs is output of the network. Consequently, the following outputs are susceptible to incurring a higher error due to inaccuracies in the inputs.

6.5.2 Candidate 1 test inputs The best training candidates according to the error measures with 5, 7, 10 and 15 neurons are tested using approximately 30% of the available data. During the test, the networks receive cycles that they might have seen before during training but with a different initial state of charge and new cycles not ever seen before. The first case is valid due to considerable differences between energy management strategies belonging to an identical drive cycle initiated at different states of charge. An example is depicted in Fig. 6.16, where the same cycle optimal state of charge schedule is illustrated for different initial battery charges. Despite presenting similar tendencies, the depth of discharge allowed from 90% initial state of charge is considerably deeper when compared to a 50% initial charge, an effect that needs to be properly addressed by the network to prevent excessive battery depletion and maximal battery use simultaneously. A 90% initial state of charge always depletes the battery, whilst 50% initial values register increments in the state of charge through engine recharging mode. Fig. 6.17 shows another drive cycle with smaller power requirements. A 90% initial battery charge allows completing the entire cycle without reaching the minimum battery state of charge. The strategy therefore targets electric vehicle mode as long as the motor alone can entirely cover the driver power demand. Similarly, 80% initial charge seems to be enough initial charge to allow for electric vehicle use, as observed in the parallelisms between the 90% and 80% charge schedule. However, a lower initial state of charge reproduces different battery schedules that become more conservative with the battery depletion, as the initial electric energy decreases. Consequently, the use of identical drive cycles optimised at different initial states of charge is accepted not only for training, but also for testing and validating.

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6.5.3 Candidate 1 results The candidates selected for testing include two networks with five neurons, two with seven neurons, two with 10 neurons and two with 15 neurons at the hidden layer. A total of 68 cycles are available to test the networks with various lengths, power requirements and initial states of charge. In the following paragraphs, the results are described to facilitate reader interpretation and analyse the consequences of using only three inputs with the aim of computing charge-depleting optimal strategies. The results are illustrated using the state of charge schedule comparison between the optimal strategy and those obtained using the neural networks in the testing cycles with

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common initial conditions. The optimal strategy consists of the modified original dynamic programming results, for implementing purposes. These results depict the accuracy of the network control but do not represent the actual benefit of the strategy in terms of energy consumption and fuel displacement. This is included through the fuel overconsumption, which is calculated as the difference between the minimum fuel consumption obtained using the optimal feasible results and the consumption produced with the state of charge schedules as obtained using the neural networks. This value cannot be directly obtained from the neuron output, but rather needs to be calculated using the vehicle model previously introduced, implemented backwards. The state of charge schedule is used to obtain the power provided by the battery, the actual motor power after losses and consequently the respective internal combustion engine torque required to meet the driver power demand. This torque value is used to obtain the respective fuel consumptions caused when implementing the neural networks strategies. a. Five-neuron candidate results

The networks selected coincide with those measured in Table 6.8, which present practically identical average mean errors, despite the weights being initialised differently. Although the overall error measured during training is similar, the convergence into different weight values would presumably return different behaviour during testing and therefore strategies for vehicle control that are more or less similar to the optimal solution. Although five-neuron networks are very simple, these can approximate some test cycles very well, as illustrated in Fig. 6.18. Both candidates reproduce the

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discharge schedule strategy in a similar fashion to the optimal reference, although candidate 2 slowly deviates with an increasing bias from the optimal final state of charge. The results in Fig. 6.18 are repeated in cycles of similar length and power demand characteristics but are not as accurate as the ones registered in cycles that cover longer distances, as illustrated in Fig. 6.19. Cycles of longer distance cannot be captured, presumably due to the lack of information about the cycle demand. The inputs used include the data on the cycle length and the cycles included in the test set present a higher number of short and medium length cycles. Furthermore, the battery capacity seems to be designed for cycles of medium size. The networks trained with this data can capture depletions in cycles of medium and short distance but are not able to control those of other characteristics. As a result, both network candidates provoke a rapid discharge that does not comply with the optimal strategy and causes a sharp low state of charge maintained for more than half of the cycles. A low state of charge eliminates all possible benefits for improvement when using a plug-in hybrid instead of a regular hybrid electric vehicle. Furthermore, candidate 2 does not seem to be able to always reach a maximal depth of discharge and leaves a state of charge window for an additional 27% depth of discharge in cycle 3 energy management. In general, a better prediction is detected for network candidate 1, as presented in Fig. 6.19 (top). However, both candidates return very deficient strategies in long cycles, where the charge depleting cannot be captured. The optimal results maintain the charge with slow battery depletion at the beginning of the cycle, which allows for a state of charge margin by the end of the route. The charge and discharge margin in plug-in hybrids permits the engineassisting mode along the entire drive cycle, as illustrated in the cycle 4 portion in Fig. 6.19 (bottom). It is nevertheless worthwhile to highlight the superiority of candidate 2 in the test results with respect to candidate 1, despite both presenting similar error measures. The results depicted in Fig. 6.20 can be observed throughout many test cycles. Although both networks seem to present a similar state of charge reduction tendency with

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Fig. 6.19 Energy management obtained with five-neuron networks in test cycles 3 and 4.

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similar intensity, candidate 2 cannot emulate the accurate depth of discharge and returns final charge values with a large bias with respect to the optimal results. It is worth highlighting that the optimal strategy does not always achieve a strictly minimum state of charge, due to the data postprocessing to achieve feasible schedules. Despite the fact that both neurons show far from optimal results in many test cycles, candidate 1 always tends to maximise the use of the energy in the battery, which is considerably more beneficial in terms of fuel consumption and emission reduction. This can be analysed mathematically by computing the optimal fuel consumption and the resulting fuel that would be consumed if the illustrated strategies are implemented in-vehicle. Despite the fact that candidate 2 does not deplete the battery completely in cycle 3, it follows a better strategy and achieves better results regarding fuel than candidate 1. A clearer difference can be observed in cycle 6, where candidate 1 follows the optimal strategy better and achieves maximum battery depletion and a considerably better fuel consumption, saving 24.4% more fuel than candidate 2, as shown in Table 6.9. The table shows the network candidate fuel overconsumption with respect to the minimum registered with optimal energy management in total, in kilograms and in relative percentages with respect to the minimum reference consumption. When analysing cycle 7, the consumption obtained with the neural networks is very close to optimal with both candidates, but in particular candidate 1, which approaches optimal with high accuracy. Overall, maximum overconsumption is included to compare networks, whilst the real maximum overconsumption would be the maximum relative one. Although both candidates present high maximum error, they both also register very low minimum error. Unfortunately, neither the network size nor the inputs selected seem to be large enough to provide enough accuracy for energy management and vehicle implementation. The results are very sensitive to the cycle characteristics and the schedule predicted cannot approach the optimal strategy local tendency with enough accuracy, which suggests the necessity of more complex structures. b. Seven-neuron candidate results

Following the growing strategy, seven-neuron networks are tested in a similar fashion to the five-neuron networks. The results obtained do not seem to improve the fiveneuron deficiencies and are not sufficiently accurate for in-vehicle implementation. Both candidates presented failed to follow the local charge tendency in the test cycle illustrated in Figs 6.21 and 6.22. Short cycles again seem to be better captured, but the power demand intensity plays an important role in the results and seems to prevent achieving satisfactory results in all short cycles tested. Long cycles are again susceptible to speed initial depletion, eliminating all plug-in margin for fuel displacement in the latter cycle portions. Some test cycles are nevertheless satisfactorily predicted, as illustrated in Fig. 6.23, but the overall results regarding fuel consumption are similar to the five-neuron candidates and are insufficient for in-vehicle applications. Furthermore, despite the fact that the network is more complex and theoretically a better predictor than the previous candidate with five neurons, it cannot achieve such an accuracy in fuel consumption reduction in test cycle 7. Candidate 1 with five

kg (%) kg (%)

1 2

0.625 (13.4) 0.537 (11.5)

C3 0.297 (7.1) 0.287 (6.8)

C4 0.097 (12.7) 0.283 (37.1)

C6

0.004 (1.4) 0.019 (5.1)

C7

0.648 0.678

Max

0 0.019

Min

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

Fuel overconsumption

Fuel overconsumption in networks with five neurons in the hidden layer

Cand.

Table 6.9

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Testing cycle 1

90 80 SoC (s)

70 60 50

Optimal Cand. 1 (7n) Cand. 2 (7n)

40 30

0

200

400

600

800

1000

1200

1400

1600

1800

Time (s)

Fig. 6.21 Energy management obtained with seven-neuron networks in test cycle number 1.

Fig. 6.22 Energy management obtained with seven-neurons network in test cycle number 11. Testing cycle 7

SoC (s)

90

85

80

Optimal Cand. 1 (7n) Cand. 2 (7n)

75 0

50

100

150 200 Time (s)

250

300

350

Fig. 6.23 Energy management obtained with seven-neuron networks in test cycle number 7.

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247

neurons (Fig. 6.18) provides a closer battery schedule, behaviour that is also mathematically proven in the fuel consumption result. Furthermore, the high sensitivity of hybrid mode transitions as a result of the allowed battery energy use is also evident. For instance, although candidate 2 results, with five neurons, seems to be similar to the seven-neuron candidate results, its implementation outperforms that of the complex networks by more than 3%. These results could be due to two main causes: (1) The seven-neuron networks have fitted a different process from the training cycles, which does not comply with cycle 7 in particular and with the test cycles randomly selected in general; (2) The inputs are deficient and therefore a more complex structure would not be able to capture the process of interest.

The first could imply that the training data has been fitted better, but generalisation capability has been affected. The generalisation capability could also explain the worse results experienced in fuel consumption. Although this first hypothesis might be true, it seems clear that the second has a deeper effect and that the inputs do not contain enough information to provide more accurate energy management strategies. When focusing on the maximum and minimum overconsumption values, none of the candidates can outperform candidate 1 with five neurons, although candidate 2 with seven neurons is slightly better than candidate 2 with five neurons, as included in Table 6.10. When focusing on the maximum and minimum overconsumption values, none of the candidates can outperform candidate 1 with five neurons, although candidate 2 with seven neurons is slightly better than candidate 2 with five neurons. It could be the case that candidate 1 with five neurons was very successfully initialised and no other candidates could achieve such satisfactory initial weights values to converge into a local optimal solution with better performance. c. 10-neurons candidate results

Network structures of 10 and 15 neurons in the hidden layer allow for higher model complexity and theoretically closer-to-optimal results. Some of the results obtained with 10-neuron networks are illustrated in test cycles 41 and 44 in Fig. 6.24 and test

Fuel overconsumption in networks with seven neurons in the hidden layer

Table 6.10

Cand.

Fuel overconsumption

1

kg (%)

2

kg (%)

C1

C7

C11

Max

Min

0.324 (42.6) 0.291 (38.3)

0.038 (8.5) 0.031 (8.3)

0.362 (6.7) 0.318 (5.9)

0.719

0.037

0.675

0.014

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

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Testing cycle 41

SoC (s)

50 48 Optimal Cand. 1 (10n) Cand. 2 (10n)

46 44 0

50

100

250

300

350

Testing cycle 44

70

SoC (s)

150 200 Time (s)

65 Optimal Cand. 1 (10n) Cand. 2 (10n)

60 55 0

50

100

150 200 Time (s)

250

300

350

Fig. 6.24 Energy management obtained with 10-neuron networks in test cycles 41 and 44.

cycle 12 in Fig. 6.25. Candidate 1 seems to return better results than Candidate 2 and captures better local discharge schedule tendencies, which is especially evident in cycle 41. Again, the lack of information about the cycle length and power requirements does not allow the final charge value state to be approached. Once more, the reference optimal strategy does not always achieve a minimum state of charge when compared to the candidates due to the optimal strategies processing to obtain feasible results. Despite implementing three additional neurons and consequently nine

Fig. 6.25 Energy management obtained with 10-neuron networks in test cycle 12.

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249

Fuel overconsumption in networks with 10 neurons in the hidden layer

Table 6.11

Cand.

Fuel overconsumption

1

kg (%)

2

kg (%)

C12

C41

C44

Max

Min

0.185 (11.0) 0.232 (13.8)

0.053 (13.7) 0.122 (31.6)

0.083 (21.8) 0.106 (28.1)

0.656

0.027

0.598

0.018

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

additional weight parameters, only at the hidden layer, these networks still present inaccurate strategies, as illustrated in Fig. 6.25. On the one hand, candidate 1 opts for deep battery depletion and drains the battery prematurely. On the other hand, candidate 2 is very conservative and does not achieve full battery depletion by the end of the cycle, leaving 10% unused. Table 6.11 includes the fuel consumption results from the previous cycles illustrated with 10-neuron networks. The overconsumption aligns with the results illustrated in state of charge deviation from the optimal strategy. As expected, higher overconsumption is registered in cycle 12 due to its duration and the cumulative characteristics of the fuel consumption. In all cases, candidate 1 is superior, as is also observed in the state of charge results, and the state of charge deviation causes different mode transitions that produce an overconsumption, which is serious and is not suitable for in-vehicle control. When focusing on the maximum and minimum values, the results seem to outperform in all cases the seven-neuron networks, but still do not achieve the convenient results obtained with five neurons. These values do not suggest much improvement when increasing the network size, the main reason why the growing method is stopped at 15 neurons. d. 15-neuron candidate results

The 15-neuron networks are high-complexity models. Two final testing candidates with 15 neurons are analysed similarly to the previous candidates and the results obtained with these network candidates are illustrated in Figs 6.26 and 6.27. The first illustrates testing cycles that were satisfactorily approximated in state of charge terms, whilst the second depicts cycles where the networks failed to capture either tendency or final state of charge. Fig. 6.26 (top) illustrates test cycle 6, which is well captured in terms of overall state of charge by candidate 1, but not in terms of local tendencies. Candidate 1 accurately approaches the final state of charge but skips two intermediate deep depletion events, which suggests that in reality the candidate cannot capture the optimal control. More evident is the deficient performance of candidate 2, which not only does not locally capture the optimal strategy, but also deviates from the final state of charge by more than 7%. The cycle in Fig. 6.26 (bottom) is however better captured

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Testing cycle 6

SoC (s)

50 45 40

Optimal Cand. 1 (15n) Cand. 2 (15n)

35 0

200

600 Time (s)

400

800

1000

1200

Testing cycle 67

SoC (s)

40 38 36

Optimal Cand. 1 (15n) Cand. 2 (15n)

34 32

0

200

400

600 Time (s)

800

1000

Fig. 6.26 Energy management obtained with 15-neuron networks in test cycles 6 and 67.

Testing cycle 5

55

Optimal Cand. 1 (15n) Cand. 2 (15n)

SoC (s)

50 45 40 35 0

500

1000

1500

2000 2500 3000 Time (s)

3500

4000

4500

Testing cycle 15

SoC (s)

50 45 40

Optimal Cand. 1 (15n) Cand. 2 (15n)

35 0

50

100

150

200

250 300 Time (s)

350

400

450

500

Fig. 6.27 Energy management obtained with 15-neuron networks in test cycles 5 and 15.

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251

by both candidates, although candidate 1, and in the last seconds also candidate 2, incurs into speed depletion that drains the battery prematurely. Fig. 6.27 presents two testing cycles, in which premature battery depletion is achieved at early stages (top) and insufficient depth of discharge can be implemented (bottom). Whilst the first causes premature annulling of the hybrid’s benefits, the second leaves useful charge stored in the battery unused and consequently replaced with fuel overconsumption. The low cycle duration and large state of charge deviation in cycle 15 is considerably penalised with relative overconsumption, as can be seen in Table 6.12. This is not as obvious in cycle 5, where the fuel deviation is concealed by the cycle length. Cycles 6 and 67, although appearing to present better state of charge predictions, do not provide overconsumption below 10%. This final analysis shows the relationship between the state of charge schedules, but also highlights the nonproportional relationship between the state of charge schedule deviation and the fuel overconsumption, due to the vehicle’s high nonlinearities and the complexity of the hybrid powertrain. When focusing on the minimum and maximum overconsumption values, the figures seem to improve considerably, even when compared to the five-neuron candidates. Both 15-neuron networks present minimum errors that suggest quasioptimal control and reduce the maximum error registered. Nevertheless, there is a high inconsistency in the consumption results that is not suitable for in-vehicle implementation. A robust controller should not present such an unstable deviation from the optimal fuel consumption and should always outperform the existing strategies based on rulebased implementation. e. Candidate comparisons

It can be concluded from the previous results analysis that none of the previous candidates are suitable for in-vehicle implementation for energy management. In the following paragraphs, the best candidates of each neural network size are compared in terms of state of charge schedule to better summarise and highlight the disadvantages of three input signals used for hybrid vehicle control when applied to plug-in hybrids. Probably the most evident deficiencies are found in cycles with characteristics similar to the test cycle 54 portion illustrated in Fig. 6.28, when dealing with long distances. Long cycles cannot be captured by any candidate, due to the lack of information about the cycle characteristics in the input signals. Furthermore, it is also obvious that no candidate can reproduce charge-sustaining mode and limit the state of charge schedule in the presence of a drained battery to very brief electric assistance use. All networks cause premature deep depletion and maintain the state of charge quasiconstant, not allowing for engine recharging mode. It is also necessary to highlight herewith that, despite the obvious deficiencies of the presented network candidates, none of the networks trained violated the safety minimum and maximum state of charge margins. The training data did not register a value above 90% or below 33%, which has guaranteed that it is not possible to register a network output out of those values. The training data combines various states of charge and power demand combinations, covers the extremes and successfully returns controllers deficient on the optimal side, but implementable on the safety side.

kg (%) kg (%)

1 2

0.139 (7.8) 0.091 (5.2)

C5 0.163 (21.3) 0.209 (27.3)

C6 0.115 (78.2) 0.132 (89.8)

C15

0.030 (11.0) 0.027 (10.0)

C67

0.580 0.621

Max

0.010 0.007

Min

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

Fuel overconsumption

Fuel overconsumption in networks with 15 neurons in the hidden layer

Cand.

Table 6.12

252 iHorizon-Enabled Energy Management for Electrified Vehicles

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253

Testing cycle 54

55 Optimal

5n 7n 10n 15n

SoC (s)

50 45 40 35 0

1000

2000

3000 Time (s)

4000

5000

Fig. 6.28 Energy management obtained with 5-, 7-, 10- and 15-neuron networks in test cycle 54.

Fig. 6.29 Energy management obtained with 5-, 7-, 10- and 15-neuron networks in test cycle 65.

Cycles having different power characteristics or reduced length are better captured by the previous candidates. Fig. 6.29 illustrates cycle 65, which implies a large length, but it is better approximated. In this particular case, the 15-neuron candidate seems to obtain better results, followed by the seven-neuron candidate. Nevertheless, this classification does not apply throughout all test cycles. Again, speed changes in the optimal battery depletion cannot be anticipated by any of the controllers. It could be assumed that these modifications of the optimal strategy might be due to anticipation of specific cycle characteristics, such as heavy congestion or highway driving at high power demand, a reason why they might be ignored by the networks. Table 6.13 also includes a mathematical comparison of the error in the state of charge schedule of the previous network candidates. The increase on the network size does not seem to improve the accuracy in mean absolute error (MAE) and final state of

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Error in state of charge values in network candidates from 5 to 15 neurons

Table 6.13

Three-input network candidates

SoC MAE (%)

SoC end (%)

Neurons

Mean

Std

Max

Mean

Std

Max

5 7 10 15

10.4 9.8 10.6 10.1

8.5 7.0 6.2 6.4

40 37 27 30

7.2 10.3 6.6 6.6

6.5 8.1 6.8 6.8

27.8 34.4 29.3 29.3

charge error by the end of the drive cycle. Both measures are absolute calculations with respect to the optimal strategy and include the mean value throughout all cycles, standard deviation and maximum and most pessimistic accuracy.

6.6

Training and testing results—Input set 2

Input set 2 adds a new variable that unifies information about the length and energy requirements of the drive cycle and provides the network with information about the total instantaneous energy required to finalise the route. This signal does not detail how this energy would be demanded, that is, what would be the power demand characteristics along the drive cycle or its length. Consequently, instant detailed information about the future is not provided. Instead the networks can operate with an overall idea of the future required power to be provided from both electric motor and fuel. It is expected therefore that the network will be able to at least avoid fast battery depletion at the beginning of the cycle and guarantee that the available battery energy is minimised by the end of the trip. The strategy followed for combined training and network design consists again of the growing method, starting with 5 neurons per hidden layer and gradually increasing to 7, 10, 15 and 20 neurons. The linear increase of neurons does not produce a linear increase of the number of parameters to fit and therefore of the model complexity. This is due to the recurrent neuron connections and evolves as shown in Table 6.14. In the table, the increment from 5 to 10 neurons causes an increment of 105 neurons, whilst the increment from 10 to 15 neurons implies an increment of 155.

Neural network complexity comparison from 5 to 20 neurons at the hidden layer in terms of number of parameters to fit

Table 6.14

Number of neurons (hidden layer) Number of weights

5 56

7 92

10 161

15 316

20 521

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255

6.6.1 Input candidate 2 training error The networks are trained following the same procedure used with those trained with input candidate 1. The network candidates are initialised randomly and trained monitoring the overall mean square error measured every iteration, that is, each time all training data has been seen by the network. Once more, the error registered at the first iteration is very varied depending on the initialisation values and the convergence at the first steps is very rapid in all network candidates, as observed in Fig. 6.30. This figure includes the convergence behaviour at the first four iterations of a network of 10 neurons (top) and 15 neurons (bottom). This convergence is usually faster when the error measure is higher and decelerates as the error diminishes, behaviour especially true at the first iterations, as compared between the error at iteration 1 and iteration 2. Fig. 6.31 also illustrates convergence at the first iterations of networks of increasing complexity. Convergence at the first iterations is disparate and depends on the initialisation, but after the third iteration different convergence speeds are observed among the different candidate sizes. In Fig. 6.31, the error convergence speed is considerably different depending on the structure size. Networks with fewer neurons converge faster than larger ones. This is expected due to the capacity of larger networks to fit more complex behaviour and train a larger number of parameters. This causes a substantially more complex training process that requires longer computing time per epoch and a larger number of epochs to converge. The error convergence curve presents a speed descent at the first iteration and decelerates abruptly between iterations 5 and 10. In contrast, the convergence Mean training square error (10 neurons)

0.04

MSE = 0.0379

MSE

0.03 0.02 0.01 MSE = 2e−05 0 1

1.5

2

2.5

3

3.5

4

Iterations number

Mean training square error (15 neurons)

0.1

MSE

MSE = 0.0974

0.05

0

MSE = 1e−05 1

1.5

2

2.5

3

3.5

4

Iterations number

Fig. 6.30 Error convergence at the first iterations during training of a network of 10 neurons (top) and 15 neurons (bottom).

256

iHorizon-Enabled Energy Management for Electrified Vehicles

3

×10−5

Mean training square error (from 3 Iter.) 5n 10n 15n 20n

MSE

2

1

0

5

10

15

20 25 30 35 Iterations number

40

45

50

Fig. 6.31 Error convergence in networks with 5, 10, 15 and 20 neurons in the hidden layer.

with 20 neurons is considerably slower and requires up to 35 iterations to decelerate convergence. This behaviour implies an exponential computational effort and training time required to train networks of increasing size. This particular example evolves from a few minutes to more than several hours. Concretely, as illustrated in Fig. 6.32, the number of weights to train increases from 5-neuron networks to 20-neuron networks in 465 weights, which also increases the memory requirements necessary to implement the resulting controllers.

MSE

3

×10−5

5 Neurons candidates

2 1 0 5

10

15

20

25

30

35

30

35

Iterations number

20 Neurons candidates

MSE

−5 3 ×10

2 1 0 5

10

15

20

25

Iterations number

Fig. 6.32 Error convergence at the first iterations during training a network of 5 neurons (top) and 20 neurons (bottom).

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6.6.2 Input candidate 2 results Herewith the results obtained with neural networks with various neurons in the hidden layer are illustrated, commented on and compared in terms of state of charge and fuel overconsumption results. In a similar fashion to input candidate 1 with torque demand, transmission speed and state of charge, candidate 2, using the additional energyremaining signal, is implemented to analyse the effect of additional information on the prediction results. The comparison is vital to determine how the limited route information can improve the control strategies achieved in the presence of the same amount of data and using the same neural network structure. a. Results with five-neuron networks

Networks of five neurons are trained using 70% of the data and four inputs. The resulting network candidates change considerably depending on the weights initialisation, as illustrated in Figs 6.33–6.35. Despite using the same training data and number of epochs, some candidates cannot capture all test drive cycles. Fig. 6.33 illustrates two cases of cycles of very different power characteristics. Almost all candidates, with the exception of candidate 1, approximately reproduce the battery discharge tendency and meet a final state of charge values by the end of the cycle. This behaviour contrasts with the previous input candidate 1, which was not able to achieve maximum electricity use in most of the test cases. Nevertheless, the optimal battery discharge schedule cannot be perfectly approached. The controllers cause excessive charging or deep discharging events approaching the optimal strategy both from above and below, but are not able to capture the local state of charge tendencies. Despite the additional information about the cycle characteristics, the networks receive as input their own state of charge calculation, which is not accurate enough and causes further deviation. Although the strategies obtained approach the optimal ones much more accurately, there are still cycles that cannot be accurately obtained, as illustrated in Fig. 6.34. These generally imply partial battery discharge and do not imply meeting a minimum final state of charge. In those case scenarios it seems that the networks lose the reference and incur into inaccurate strategies. The increase of the network size is expected to improve the network capabilities and improve strategies in those case scenarios. Another important improvement with respect to the previous candidates is the possibility of approaching charge-sustaining strategies as illustrated in Fig. 6.35. Previous candidates analysed reproduced similar behaviour to candidate 2. In this case, candidates 1 and 3 can return charge sustaining even when the initial state of charge is low. Previous results with cycles with low initial state of charge with input candidate 1 proved to be unable to approach charge-sustaining strategies. Nonetheless, these network candidates seem to be able to perform battery charge and discharge and reproduce a complex state of charge profile events with a low number of neurons. In Fig. 6.35, the final optimal state of charge does not meet the minimum battery charge due to the postprocessing applied to global optimal dynamic programming results to return feasible control strategies, the reason why the final values cannot be directly interpreted.

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Battery discharge with 5 neurons networks (cycle 1) 90 Optimal Cand. 1 Cand. 2 Cand. 3

SoC (%)

85

80

75

70 0

100

200

300

400 Time (s)

500

600

700

Battery discharge with 5 neurons networks (cycle 4)

90

Optimal Cand. 1 Cand. 2 Cand. 3

80

SoC (%)

70 60 50 40

30

0

1000

2000

3000

4000

5000

6000

7000

Time (s)

Fig. 6.33 State of charge schedule obtained with network candidates with five neurons in the hidden layer in test cycles 1 and 4.

The error values of the previous cycles are shown in Table 6.15. The deviation of candidates 2 and 3 in cycle 1 is evidenced with an error that is an order of magnitude higher, despite the fact that both candidates 1 and 2 approach very accurately to the final state of charge value. All candidates exhibit difficulties with cycle 4, which implies full battery discharge in long drive cycles with high power requirements. The candidates cannot capture local discharge tendencies that deviate considerably from the optimal strategy. Besides, the neurons cannot reproduce close-to-optimal control strategies in short cycles with low power requirements and that are initiated

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259

Battery discharge with 5 neurons networks (cycle 7) Optimal Cand. 1 Cand. 2

80

Cand. 3

SoC (%)

75

70

65

0

100

200

300

400

500

Time (s)

Fig. 6.34 State of charge schedule obtained with network candidates with five neurons in the hidden layer in test cycle 7.

Fig. 6.35 State of charge schedule obtained with network candidates with 5 neurons in the hidden layer in a portion of test cycle 10.

at large state of charge values. Proof of that is found in cycle 7, as illustrated in Fig. 6.34, where the optimal controller does not achieve minimum battery charge by the end of the cycle. The loss of the 33% minimum reference might cause a larger state of charge deviation of the neuron controller results.

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Mean square error and final state of charge deviation with 5-neuron networks in test cycles 1, 4, 7 and 10

Table 6.15

C1

Network

C4

C7

C10

Error measure

MSE

End (%)

MSE

End (%)

MSE

End (%)

MSE

Cand. 1 Cand. 2 Cand. 3

3.6e 4 0.0013 0.0055

0.5 0.6 12.4

0.0033 0.0046 0.0062

0.3 0.3 1.8

8.2e 4 4.3e 4 0.0050

2.6 1.0 6.5

7.8e 4 0.0021 6.8e 4

Nevertheless, the discharge tendency is better captured with this input set, as shown in Table 6.15. It is also worthwhile to highlight the comparison between the candidates in cycle 10. Candidate 2 is clearly unable to reproduce the charge-sustaining mode, as illustrated in Fig. 6.35 and included in Table 6.15, whilst candidates 1 and 2 maintain the state of charge longer and considerably reduce the mean square error. However, none of the candidates exhibit enough accuracy for implementation purposes. The five-neuron networks are not complex enough to provide robust controllers able to outperform rule-based equivalent controllers in all case scenarios. In terms of fuel consumption, it is expected that higher overconsumption will be found in networks that present a larger state of charge deviation from optimal results, but due to the model nonlinearities involved, this does not necessarily need to hold in all cases. For example, cycle 1 is better approximated by candidate 1, with an error one order of magnitude smaller than candidates 2 and 3, but only improves by 3.9% the overconsumption caused with candidate 2. Candidate 3 deviation and final state of charge error cause a considerably high penalisation in fuel consumption, as expected, although the MSE errors measured in cycles 1 and 4, as shown in Table 6.15, do not linearly correlate with the overconsumption registered in Table 6.16. Once more the model nonlinearities, mode transitions and particular characteristics of the drive cycles cause this disparity. That is, the state of charge deviation penalises the fuel consumption differently, depending on the torque demand, absolute state of charge and powertrain working conditions. Consequently, improving the discharging schedule does not always imply a proportional improvement in fuel consumption. The previous results show a considerable improvement with respect to input set 1 formed by only three signals. The additional information substantially improves the overall results, but either the network complexity or the information in the inputs is still not enough to provide robust energy management strategies. b. Results with seven neurons networks

Network candidates using seven neurons in the hidden layer are trained and tested and analysed visually and statistically. Some representative examples are illustrated in Figs 6.36–6.39. The first shows an example in which the candidates cannot locally approach the optimal discharge tendency but are able to capture the overall state of charge trajectory. Point by point, the candidates exhibit the same tendency direction

0.055 (33.3%) 0.061 (37.2%) 0.118 (71.5)

Cand. 1 Cand. 2 Cand. 3

0.201 (3.9%) 0.209 (4.1%) 0.155 (3.0%)

C4 0.081 (95.4%) 0.051 (60.3%) 0.083 (97.9%)

C7 0.196 (17.0%) 0.171 (14.8%) 0.103 (8.9%)

C10 30.4 25.6 30.8

Mean

133.5 111.9 118.2

Max

0.7 1.7 0.3

Min

Statistics (%)

30.6 26.2 32.2

Std

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

C1

Fuel consumption (kg)

Fuel overconsumption with 5-neuron networks in test cycles 1, 4, 7 and 10

Network

Table 6.16

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Battery discharge with 7 neurons networks (cycle 7)

85

Optimal Cand. 1 Cand. 2

SoC (%)

80

75 70

65 60 0

100

200

300 Time (s)

400

500

Fig. 6.36 State of charge schedule obtained with network candidates with seven neurons in the hidden layer in a portion of test cycle 7.

Fig. 6.37 State of charge schedule obtained with network candidates with seven neurons in the hidden layer in a portion of test cycle 13.

but not the step value. Nevertheless, this positive and negative error seems to compensate and approach the overall strategy. The discharge strategies are penalised with very low average square error and minimum final state of charge deviation, always below 1.3%, detailed in Table 6.17. This is not the case for cycle 13, as illustrated in Fig. 6.37. Initially the candidates, and particularly candidate 2, approach the optimal strategy with high accuracy. The error increases after approximately 2000 s of simulation, causing a large deviation that prevents the rest of the candidates from converging back to the optimal strategy. Besides, this deviation prevents the achieving of a minimum final state of charge with both network candidates, which is almost 14% in candidate 2, as shown in Table 6.17.

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263

Battery discharge with 7 neurons networks (cycle 17)

90

Optimal Cand. 1 Cand. 2

SoC (%)

85 80

75

70 65

0

100

200

300

400

500

600

700

800

Time (s)

Fig. 6.38 State of charge schedule obtained with network candidates with seven neurons in the hidden layer in a portion of test cycle 17.

Battery discharge with 7 neurons networks (cycle 34)

60

Optimal Cand. 1 Cand. 2

55

SoC (%)

50 45 40 35 30

0

1000

2000

3000

4000 Time (s)

5000

6000

7000

Fig. 6.39 State of charge schedule obtained with network candidates with seven neurons in the hidden layer in a portion of test cycle 34.

Despite the performance exhibited in cycle 7, candidate 2 cannot approach cycle 17 with high fidelity, although both cycles have similar length. Although candidate 2 presents better behaviour than candidate 1 at the first time steps, it begins to deviate after 170 s and finally diverges. Nonetheless, strategies that diverge considerably from the optimal results at a specific point in the cycle do not necessarily incur a high overconsumption. These strategies locally, point-by-point, deviate from optimal conditions, which prevent from reaching global optimal solutions. Nonetheless, the strategy achieved could still result in a close-to-optimal battery schedule considering

End (%)

1.29 1.17

MSE

3.0e 4 2.2e 4

Cand. 1 Cand. 2

C7

Error measure

Network

0.0053 0.0118

MSE

C13

3.77 13.94

End (%) 0.0028 3.7e 4

MSE

C17

4.67 1.42

End (%)

0.0025 0.0030

MSE

C34

2.09 4.43

End (%)

Table 6.17 Mean square error and final state of charge deviation with seven-neuron networks in test cycles 7, 13, 17 and 34

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265

the new state of charge deviated from the global optimal discharge. For instance, candidate 1 in Fig. 6.38 deviated for the optimal state of charge around 200 s and 500 s, but later produced an alternative discharge strategy, based on a higher state of charge, that might itself be close-to-optimal and emulate a hypothetical controller starting with the same charge percentage. In addition, strategies that initiate close to the optimal results but diverge in one direction are sometimes not able to come back to the optimal results. This behaviour is, however, reasonable, since charge schedules that deviate considerably adopt new state of charge conditions that might be solved using a radically different approach to that illustrated as the optimal reference. Consequently, despite the deviation, it is still possible that candidate 2 better approaches the optimal behaviour, the main reason why fuel consumption analysis is vital for analysing the network performance. Table 6.17 demonstrates the superiority of candidate 2, which registers an average square error that is almost half that of candidate 1. Finally, Fig. 6.39 illustrates an optimal strategy that implies charge sustaining, known to be a critical scenario as it does not initially follow the discharging tendency characteristic of plug-in hybrids. Charge-sustaining strategy characteristics contrast with the charge-depleting approach and generally all candidates struggle to capture it. The additional inputs used in these tests show an improvement in the behaviour of these controllers and allow the networks to maintain the state of charge longer and even recharge the batteries in anticipation of the future cycle demands. Although the figure depicts clear deficiencies of both candidates, these seem to average the optimal schedule and finally meet minimal state of charge values to maximise the electric energy use. The fuel overconsumption registered in cycle 7 complies with the state of charge error, although not linearly. More evident is the disparate relationship of both errors in cycle 13, where the strong deviation of candidate 2 is not as penalised in fuel consumption. These results support the hypothesis that strategies that deviate widely from the initial optimal might still be able to evolve within optimality values, due to the change in charge state when compared to the optimal reference. In this case, candidate 2 seems to have approached a local minimum that does not penalise fuel consumption, as might have been anticipated. Overconsumption and discharge strategies comply, however, in both cycles 17 and 34 as included in Table 6.18. The fuel consumption results in overall statistics that can be used to compare the network performance of five and seven neurons. Taking five-neuron candidate 1 and seven-neuron candidate 2, the increased number of neurons does not improve the mean error deviation in fuel consumption, increases marginally the maximum value and reduces the variation slightly. These results can either indicate that the network sizes are still far from the appropriate one, or that the inputs do not contain information sufficient to improve the results. By gradually increasing the network size, the first approach can be tested to guide future network design for plug-in energy management. c. Results with 10-neuron networks

Neural networks with 10 neurons are expected to improve the performance with respect to the previous networks examined. A selection of representative cycles is shown in Figs 6.40–6.43. Cycle 8 shows candidate 1, the very accurate performance

0.066 (77.8%) 0.054 (64.0%)

Cand. 1 Cand. 2

0.357 (6.9%) 0.422 (8.1%)

C13 0.088 (65.0%) 0.035 (26.1%)

C17 0.329 (5.8%) 0.385 (6.8%)

C34 26.8 25.5

Mean

120.4 108.8

Max

0.8 1.1

Min

Statistics (%)

27.7 23.4

Std

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

C7

Fuel consumption (kg)

Fuel overconsumption with seven-neuron networks in test cycles 7, 13, 17 and 34

Network

Table 6.18

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267

Battery discharge with 10 neurons networks (cycle 8) 70 Optimal Cand. 1 Cand. 2

SoC (%)

65 60 55 50 45 0

200

400

600

800

1000

Time (s)

Fig. 6.40 State of charge schedule obtained with network candidates with 10 neurons in the hidden layer in a portion of test cycle 8.

Fig. 6.41 State of charge schedule obtained with network candidates with 10 neurons in the hidden layer in a portion of test cycle 9.

of which seems to approximate the optimal discharge with high fidelity. Nevertheless, candidate 1 loses its optimal tendency during a deceleration of the optimal discharge, which is not followed by candidate 1 during the last 200 s. In contrast, candidate 2 diverges at the first part of the cycle and continues parallel to the optimal strategy from 500 s. The results in terms of state of charge deviation characterise candidate 1 with an error one order of magnitude below candidate 2. However, the overconsumption registered with candidate 1 is higher, due to the deeper battery depletion registered with candidate 2. Although the strategy clearly diverges from the optimal, a deeper battery depletion allows saving additional fuel that can be replaced by the battery’s electricity. If the cycle had continued until complete battery depletion, candidate 2 might not have found such a convenient overconsumption. Consequently, the fuel consumption can be used as indicative for the network performance only when the final optimal state of

268

iHorizon-Enabled Energy Management for Electrified Vehicles

Battery discharge with 10 neurons networks (cycle 14)

50

Optimal Cand. 1 Cand. 2

SoC (%)

45

40

35 0

50

100

150

200

250

300

350

400

450

500

Time (s)

Fig. 6.42 State of charge schedule obtained with network candidates with 10 neurons in the hidden layer in a portion of test cycle 14.

Battery discharge with 10 neurons networks (cycle 10) 42

Optimal Cand. 1 Cand. 2

SoC (%)

40 38 36 34 0

200

400

600

800

1000

1200

1400

1600

1800

2000

Time (s)

Fig. 6.43 State of charge schedule obtained with network candidates with 10 neurons in the hidden layer in a portion of test cycle 10.

charge achieves battery depletion and therefore all other candidates can be evaluated in comparable condition. The candidates that compute strategies that do not reach minimum state of charge, would generally incur in overconsumption when compared to the alternative ones that make use of all charge available. In contrast to cycle 8, cycle 9 is long enough to achieve complete battery depletion in both optimal conditions and approximated strategies. Both network candidates follow a similar discharge schedule, with the exception of approximately the second half of the cycle, where candidate 1 comes close to meeting the optimal strategy in the last stages. The error deviation in state of charge is therefore considerably lower in candidate 2, although the final battery discharge is very similar between them and the minimum achievable. The results illustrated in Figs 6.40 and 6.41 contrast with

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269

Fig. 6.42. The cycle 14 duration is well below that of cycle 9 and half of cycle 8. Despite the fact that the final optimal state of charge approached the minimum allowed at 33% and information about the cycle energy demand is available, none of the candidates seem to be able to raise the discharge tendency. Both length and cycle power characteristics seem to deceive the controllers and cause a major final state of charge divergence. Furthermore, these network candidates also demonstrate the capability of maintaining the charge values in charge-sustaining mode, even in long drive cycles. The final state of charge cannot be conveniently assessed, since the optimal results do not achieve the minimum energy values as a result of the recalculation of feasible and implementable optimal strategies. Nonetheless, the overall trajectory can be compared through MSE in Table 6.19, which exhibits very satisfactory results taking into account the difficulties of maintaining charge-sustaining results with controllers trained mainly for charge depletion. The cycle 9 overconsumption shows consistent results with the error in the state of charge deviation, probably due to the analogy between the network outputs. This is not the case with cycles 10 and 14, where the error inverts or is very minimal, respectively. In cycle 10 the error in state of charge is almost twice that in candidate 1, but the overconsumption is only 1.2% lower, which once more highlights that the steep deviations of the optimal results at a point along the cycle do not imply high overconsumption, as long as the controllers continue following close-to-optimal strategies. Different initial states of charge return alternative strategies to solve the same cycles. With respect to networks of seven and 10 neurons, the fuel overconsumption increases the average value slightly, but reduces considerably the maximum consumption, measures that can be compared in Table 6.20. d. Results with 15-neuron networks

When the neuron number is increased to 15, the complexity of the network escalates considerably in terms of number of parameters. Nonetheless, these networks seem to show very minor improvements in the state of charge approximation accuracy, despite the complexity of the model, as observed in Fig. 6.44. Although cycle 9 is well captured by candidate 2, cycle 14 is still far from being optimally approached. In addition, the candidates alternate their error measures, do not always outperform the other and

Mean square error and final state of charge deviation with 10-neuron networks in test cycles 8, 9, 10 and 14

Table 6.19

Network

C8 (Portion)

C10 (Portion)

Error measure

MSE

MSE

End (%)

MSE

MSE

End (%)

Cand. 1 Cand. 2

2.5e 4 0.0027

0.0019 0.0030

0.95 0.16

7.8e 4 4.6e 4

8.3e 4 6.5e 4

5.66 4.79

C9

C14

0.025 (17.5%) 0.019 (13.3%)

Cand. 1 Cand. 2

0.096 (7.6%) 0.144 (11.4%)

C9 0.123 (10.7%) 0.137 (11.9%)

C10 0.064 (93.3%) 0.061 (89.2%)

C14 24.9 25.7

Mean

106.9 92.8

Max

1.5 2.6

Min

Statistics (%)

24.6 23.6

Std

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

C8

Fuel consumption (kg)

Fuel overconsumption with 10-neuron networks in test cycles 8, 9, 10 and 14

Network

Table 6.20

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271

Fig. 6.44 State of charge schedule obtained with network candidates with 15 neurons in the hidden layer in a portion of test cycles 9 and 14.

register errors deviations very differently, depending on the cycle characteristics. However, an apparent improvement in charge-sustaining mode is seen, as illustrated in Fig. 6.45 in cycle 10 with respect to candidates with 10 neurons, but to the detriment of cycle 34, whose error measures are worse than those obtained with seven-neuron networks. The overall state of charge approximation improves with 15 neurons measured in all test cycles, but this minor improvement does not compensate for the increase in complexity and the fuel overconsumption. When analysing the results in Tables 6.21 and 6.22, it is observed that 15 neurons reduced the mean overconsumption throughout all cycles, along with the standard deviation, which implies better results consistency, but it increased the maximum deviation with respect to the 10-neuron candidates. Candidate 2 superiority in cycle 9 is evidenced with an error an order of magnitude lower. This is inverted in cycle 14, where candidate 1 considerably deviated from the optimal strategy. Both candidates exhibit similar error measures in cycle 10, which approach an optimal strategy, but diverge in cycle 34, despite this also being a case of charge sustaining. Cycle 34 initiates at a low state of charge of 40%, but the optimal charge schedule reaches values close to 60%, a state of charge window that cannot be reproduced by networks trained for plug-in hybrid vehicle control, which are generally dominated by charge depleting. The state of charge error penalisation in cycle 9 is not translated into a high fuel consumption deviation, as it only incurs an additional 2.3% with respect to candidate 1. The situation is repeated in cycle 14 with inverse proportion. Similarly, the results in cycle 10 show a battery schedule of similar accuracy in both candidates and identical

272

iHorizon-Enabled Energy Management for Electrified Vehicles

Fig. 6.45 State of charge schedule obtained with network candidates with 15 neurons in the hidden layer in a portion of test cycles 10 and 34.

fuel consumption. In contrast, the higher error registered in cycle 34 by candidate 1 is also penalised with fuel overconsumption. e. Results with 20-neuron networks

Network candidates with 20 neurons are compared with 15-neuron candidates using the same test cycles in Figs 6.46 and 6.47. No 20-neuron networks can outperform cycle 9 prediction of candidate 2 in Fig. 6.44 and, apparently, 20-neuron networks present worse control strategies than the previous 15-neuron networks. In contrast, cycle 14 is considerably better approached with 20-neuron candidates, which show an overall better behaviour than networks with a lower number of neurons. When comparing cycles 10 and 34, both network sizes exhibit similar deficiencies, as visually observed in Figs 6.45 and 6.47. It is therefore necessary to analyse the error measured to perform a strict comparison. Cycle 9 is better approached by the 15-neuron networks, as anticipated from Fig. 6.46 (top), whilst cycle 14 is considerably better controlled with the 20-neuron candidates. Besides, the results of charge sustaining in cycles 10 and 34 are similar throughout the network sizes. As with 15-neuron networks, 20 neurons do not imply a large improvement in the state of charge depletion strategy accuracy, when compared to the increment in the model complexity. a. Overall results discussion. After analysing the results of each neural network structure, it is evident the improvement achieved with higher weight number selection. Nonetheless, the performance of each candidate is strongly influenced by the training process and weights

MSE

0.0039 3.82e 4

Error measure

Cand. 1 Cand. 2

Network

C9

0.15 1.96

End (%) 8.09e 4 0.0026

MSE

C14

5.22 9.21

End (%)

MSE 0.0096 0.0064

MSE 5.17e 4 4.37e 4

C10 (Portion)

C34

0.37 2.58

End (%)

Table 6.21 Mean square error and final state of charge deviation with 10-neuron networks in test cycles 9, 10, 14 and 34

iHorizon driver energy management for PHEV real-time control 273

0.155 (12.3%) 0.127 (10.0%)

Cand. 1 Cand. 2

0.065 (94.8%) 0.084 (123.1%)

C14 0.130 (11.3%) 0.130 (11.3%)

C10 0.449 (7.9%) 0.424 (7.4%)

C34 22.2 29.6

Mean

101.9 123.1

Max

1.6 0

Min

Statistics (%)

23.0 29.3

Std

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

C9

Network

Fuel consumption (kg)

Fuel overconsumption simulated when using and energy management strategy based on a 15-neuron networks in test cycles 9, 10, 14 and 34

Table 6.22

274 iHorizon-Enabled Energy Management for Electrified Vehicles

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275

Fig. 6.46 State of charge schedule obtained with network candidates with 20 neurons in the hidden layer in a portion of test cycles 9 and 14.

Fig. 6.47 State of charge schedule obtained with network candidates with 20 neurons in the hidden layer in a portion of test cycles 10 and 34.

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iHorizon-Enabled Energy Management for Electrified Vehicles

initialisation, which suggests the existence of many local minima solutions to the same training data. These results are included in Tables 6.23 and 6.24. The first compares the neural network candidates trained with 10 neurons in four cycles of very different characteristics in terms of duration and power demand. The mean square error and final error in terms of state of charge prediction is compared within cycles and candidates. Although candidate 1 seems to outperform candidate 2 in terms of final state of charge, this difference is not as evident when analysing also MSE in all cases. Table 6.24 includes the results obtained with 15 neurons networks in the same cycles, this time in terms of fuel consumption. Candidate 2 is generally worse, but outperforms candidate 1 in cycle 9, which suggest the necessity of more complex network structures to be able to capture the entire complexity of the problem in hand.

The overall results in terms of prediction of fuel consumption are shown in Table 6.25, where the fuel overconsumption statistics are compared with networks with 5, 7, 10, 15 and 20 neurons. A colour scale identifies the maximum in red, the minimum in green and a gradual degradation to yellow and orange for intermediate values. The green tones identify the 20-20-neuron network as the candidate that presents minimum mean, maximum, minimum and standard deviation of fuel cover consumption. The next candidate is 15 neurons in terms of mean and maximum overconsumption. Furthermore, the mean values escalate gradually in conjunction with the network size, but that is not the case for the maximum, minimum and standard deviation. The worst candidate appears to be the 5-neuron network, with an overconsumption 5.1% higher than the respective measures for the 20-neuron candidate, which shows a clear benefit regarding the network size increment. This evident superiority in fuel overconsumption results is not observed in the state of charge error measure. The increment in size of the neural network structures does not seem a priori to improve the control strategies when looking into the controller target, but are able to better capture the optimal strategy, which at a final stage targets fuel consumption reduction. The targets to optimise during optimal dynamic programming are fuel power and electric power cost minimisation which, due to the higher fuel price along with the higher efficiency of electric components, returns fuel consumption minimisation. When the neural network complexity is increased, the networks seem to be able to better capture the process analysed, although the control labels are not better captured point-by-point.

Mean square error and final state of charge deviation with 10-neuron networks in test cycles 9, 10, 14 and 34

Table 6.23

Network

C9

C10 (Portion)

C14

C34

Error measure

MSE

End (%)

MSE

End (%)

MSE

MSE

End (%)

Cand. 1 Cand. 2

0.0042 0.0066

0.19 0.17

2.0e 4 5.1e 4

2.85 4.6

5.3e 4 4.8e 4

0.0129 0.0040

0.41 0.40

0.225 (17.8%) 0.162 (14.0%)

Cand. 1 Cand. 2

0.057 (83.0%) 0.061 (88.7%)

C14 0.127 (11.0%) 0.162 (14.0%)

C10 0.331 (5.8%) 0.500 (8.8%)

C34

21.6 20.5

Mean

99.3 88.7

Max

1.26 0.1

Min

Statistics (%)

21.5 17.9

Std

Where Cand. stands for candidate and CX indicates the test cycle used to extract the data. Max and Min are maximum and minimum fuel consumption measured throughout all 68 test cycles.

C9

Fuel consumption

Fuel overconsumption with 15-neuron networks in test cycles 9, 10, 14 and 34

Network

Table 6.24

iHorizon driver energy management for PHEV real-time control 277

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iHorizon-Enabled Energy Management for Electrified Vehicles

Fuel overconsumption statistics in networks of increasing size

Table 6.25

Where Max, Min and Std stand for maximum, minimum and standard deviation of fuel consumption in each test cycle.

This is possible due to the high nonlinearities that affect the vehicle model and vehicle mode selection. As a consequence, a very minor state of charge deviations from the optimal schedule might incur into modes transition under specific power demand conditions and battery charge scenarios, whilst large charge deviations under different surrounding conditions might develop similar consumption. This relationship between discharge profiles and fuel overconsumption is complex and requires networks of a large number of neurons. However, the reduction in fuel consumption is very slow with the increase in network size, the reason why it is necessary to find a trade-off between model complexity and results accuracy.

6.6.3 Critical evaluation and applications The results obtained with network candidates of 15 and 20 neurons show satisfactory accuracy in many testing cycles, although not all case scenarios can be accurately approached. Nonetheless, the modes transition and use of the engine approach optimal results locally. This is of vital importance, due to the random characteristics of the real-life drive cycles. The network results need to be analysed in the context of iHorizon and future speed and acceleration prediction. The remaining energy provided input to these network candidates is assumed to be inaccurate point-by-point, due to the local cycle disturbances and the random characteristics associated with real-life cycles. Within these circumstances, it would be unreasonable to demand higher fuel consumption displacement in a simulation environment. This implies that, although a high accuracy in the overall network prediction is preferred, high performance is not required, presuming that locally the results will need to be corrected to comply with the instantaneous power demand. This long-term controller, when implemented in real life, needs to always be compensated by a local controller having independence of its accuracy and exhibiting optimality characteristics as a result of the so-called disturbances that surround the driver task. In addition, the increase to 25-neuron networks implies a high number of additional weights and considerably

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279

larger training time and memory resources required, which would presumably demand additional expert data. Alternatively, it might be more efficient to increase the number of input signals and provide more information about the future drive cycle to the network candidates.

6.7

Conclusion

HEVs and especially PHEVs have a high potential to displace fuel use and reduce harmful emissions, for better population health and mitigation of climate change. However, this theoretical benefit cannot be exploited unless an intelligent energy management strategy is applicable real-time. This implies a controller able to adapt to the drive cycle characteristics and approach by any means possible to an optimal battery depletion and vehicle mode selection. Within this context, neural networks provide adaptive controllers, able to learn from optimal strategies and simple to implement and simulate with high speed. Controllers developed using neural networks and expert data optimised with dynamic programming are able to approach optimal strategies and return close to optimal fuel consumption with a limited amount of inputs and cycle information. These qualities allow their implementation within the iHorizon framework and compliance with its requirements. Memory requirements, computational effort and prediction accuracy make them suitable for in-vehicle implementation and PHEV control in substitution for rule-based strategies. This novel application of neural networks requires, however, further testing to investigate the appropriate combination of input and network structure that can outperform the candidates presented in the previous and further approach optimal working conditions. Furthermore, the networks show performance consistent with the components’ feasible working conditions and protect the battery from reaching dangerous state of charge scenarios.

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