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Prediction of exhaust emission in transient conditions of a diesel engine fueled with animal fat using Artificial Neural Network and Symbolic Regression
Energy 149 (2018) 675e683
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Energy journal homepage: www.elsevier.com/locate/energy
Prediction of exhaust emission in transient conditions of a diesel engine fueled with animal fat using Artificial Neural Network and Symbolic Regression ez a, *, Giuseppe A. Ratta b, Carmen C. Barrios a Aida Domínguez-Sa a b
Environmental Department, Research Centre for Energy, Environment and Technology (CIEMAT), Avda. Complutense, 40, 28040, Madrid, Spain n, Research Centre for Energy, Environment and Technology (CIEMAT), Avda. Complutense, 40, 28040, Madrid, Spain Laboratorio Nacional de Fusio
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 July 2017 Received in revised form 16 February 2018 Accepted 17 February 2018 Available online 19 February 2018
The objective of this study is the development and evaluation of two models to predict instantaneous exhaust emissions of CO2, NOx, particle number concentration and geometric mean diameter in accumulation mode (30e560 nm) and in nucleation mode (5.6e30 nm) of a 2.0 euro 4 diesel engine fueled with pure diesel and animal fat in different proportions. To acquire data for training, validation and testing, 4 repetitions of the urban part of the New European Driving Cycle and 5 steady-state conditions (15, 30, 50, 70 and 100 km/h) were reproduced in a dynamic engine test bench. The used prediction models were Artificial Neural Networks and Symbolic Regression. Vehicle speed and acceleration, engine speed and torque, air intake temperature, boost pressure, mass air flow and fuel consumption were used as inputs variables. Artificial Neural Networks provided a R2 for testing dataset equal to 0.91, 0.78, 0.87 and 0.81 for CO2, NOx, number of particles in accumulation mode and geometric mean diameter, respectively. Symbolic regression showed a R2 of 0.91, 0.82, 0.87 and 0.82 for the mentioned pollutants. Particle number concentration in nucleation mode presents low correlation with the considered inputs due to the variability of the formation process of this particle mode. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Diesel engine Particle number Exhaust emission Artificial Neural Network Symbolic regression Biodiesel
1. Introduction There is a growing interest in biofuel study to enhance fuel diversification and to limit excessive use and dependence on fossil fuels. Within the wide range of biofuels for diesel engines, fuels from waste are presented as a very valuable alternative due to the reduction of land use impacts and revaluation of waste products. Fuel from animal fat has received increasing attention in recent years [1]. Animal fats are composed of a mixture of fatty acids whose proportions depend on the source material (beef tallow,
Abbreviations: ANN, Artificial Neural Network; CO, Carbon oxide; CO2, carbon dioxide; DPF, Diesel Particulate Filter; ECU, electronic control unit; EGR, Exhaust Gas Recirculation; FF, Fitness Function; GAs, Genetic Algorithms; GMD, geometric mean diameter; HU, Hidden Units; MSE, Mean-square error; MOLF, Multiple Optimal Learning Factors; NEDC, New European driving cycle; NOx, Nitrogen oxides; PD, pure diesel; PM, Particulate Matter; PN, Particle Number; RMSE, rootmean-square error; SFC, specific fuel consumption; SR, Symbolic Regression; TDI, Turbocharged direct injection; THC, Total hydrocarbons; UDC, Urban driving cycle. * Corresponding author. ez). E-mail address: [email protected] (A. Domínguez-Sa https://doi.org/10.1016/j.energy.2018.02.080 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
pork lard, and chicken fat). This fatty acid composition has influence over some fuel properties such as the length of the carbon chain or the degree of saturation. All these fuel properties will finally affect the fuel quality [2] and, consequently, the exhaust emissions. In recent years, pollutant emissions and performance of animal fat are being investigated in detail in diesel engines [3e6]. In these studies, NOx emissions increase [3e5] but THC emissions decrease [3,4,6] in comparison with conventional diesel fuel. To date, there are few studies that examine the nanoparticle emissions when animal fat is used as fuel in diesel engines. According to Awad et al. [4], Particulate Matter (PM) emissions were reduced at low and medium engine loads with the use of animal fat, but no differences were observed at high engine loads. Barrios et al., in 2014 [5], showed that with a blend ratio of 50% of Animal Fat and pure diesel, the total particle number concentration (in the size-range of 5.6e560 nm) decreased drastically for all the experimental conditions in comparison to pure diesel. In this study [5], the data in transient conditions were discarded, considering only the average emissions of steady-state. In the present study, second-to-second data of all engine conditions (steady-state and transient operating), have been
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considered. The exhaust emission of a 2.0 TDI Euro 4 diesel engine running on the urban part of the New European Driving Cycle (NEDC cycle) and five steady-state conditions have been measured with pure diesel and 6 different proportions of animal fat/pure diesel. Subsequently, it has been modeled using the actual measured emissions database as training, validation and testing data. Since linear models (or deterministic models) do not adjust to the complexity of emission-forming mechanisms [7] and combustion models to predict pollutant emissions are generally very sophisticated and complex, and need strictly defined boundary conditions [8,9] with data that is not always easy provide, refined alternatives to estimate the emissions must be addressed. In the case of this work, two different machine learning techniques have been applied in order to forecast the emissions in transient conditions. The first one, Artificial Neural Networks (ANN), have been used for years to solve many problems of science, especially in areas where normal methods of modeling do not work properly, e.g. financial and economic modeling, medical applications, optimization of industrial processes and quality control, and a long list of scientific areas. ANN models have proven their accuracy and their ability to re-learn from new data [10], they have shown flexibility in the selection/elimination of input variables, they are computationally faster than iterative mathematical models [11]. The second one, also biologically inspired and able to automatically develop non-linear equations to fit a function, has been Symbolic Regression (SR) [12]. One of the main advantages of this method is that, instead ANN and other machine learning techniques, the regression formula (the final equation) is provided at the end of its optimization. The analysis of the regression equation goes beyond the scope of this article, devoted to pragmatic estimations, but its assessment may help to shed some light upon emissions formation depending on engine operation parameters. Therefore the full utility of the results obtained with this technique can be exploited in the future. The data, accessible from the engine Electronic Control Unit (ECU), have been used as input values of the model, and CO2, NOx, particle number concentration (accumulation and nucleation mode particle) and geometric mean diameter (GMD) have been the variables to be estimated. Obtaining a good model reduces the number of new experiments and the need to repeat experimental conditions (different concentrations of Animal Fat/diesel blends, different engine operating conditions, etc.), which results in economic and time saving. On the other hand, both Genetic Algorithms (GAs) and ANNs are powerful tools for identifying complex relationships between input and output data or potential real-time control applications focused on emission reduction (modifications of diesel catalyst or exhaust gas recirculation increase). To the best of our knowledge, the present work is the first one that: 1) performs a comparison of two machine learning models for the prediction of engine emissions, 2) predicts the particle number in steady-states and transient conditions for diesel engines, and 3) uses symbolic regression to predict emissions under transient conditions. There are no ANN or regression models available for particle number prediction for diesel engine, although there are studies applied to PM or smoke levels [13e17], PM size [18] and particle number for gasoline engines [19]. Pu et al., in 2017 [19] predicted the particle number emitted by gasoline direct injection in steady state conditions in 5 sizes-ranges. However, other types of particle number concentration and size distribution modeling in real traffic conditions have been developed depending on the type of driving [20]. In the past few years, some applications of predictive models using ANN to pollutant emissions of CO2, NOx or HC
[10,11,21e23] or other engine parameters related to engine performance [24e26] or combustion processes [27] have been published. On the other hand, only one study from 2017 [28] has used genetic algorithms to predict emissions and performance of a diesel engine in steady-state conditions. Most of these studies have been performed under steady-state engine operating conditions. For the case of transient conditions there are fewer applications of predictive models of pollutant emissions and these models have lower correlation values. Under transient conditions, the number of variables influencing pollutant emissions is larger and lower repeatability values are obtained. Mudgal et al., in 2011 [14], used ANN to predict emission from biodiesel in buses in on-board conditions obtaining an R2 (coefficient of determination to quantify the goodness of the fit) of 0.96, 0.94, 0.82, 0.98 and 0.78 for NOx, HC, CO, CO2 and PM, respectively. In a study of Hashemi and Clark in 2007 [29], ANN was trained on chassis dynamometer data from heavy-duty diesel vehicles reaching an average accuracy of 0.97, 0.89, 0.70 and 0.48 for CO2, NOx, CO and HC, respectively. The improvement of the prediction models in transient conditions and the inclusion of the particle number (emission included in the most current regulations) can be of great interest and help a more efficient control of emissions. The main objective of this work is the development, evaluation and comparison of two predictive models, artificial neural network model and symbolic regression model, of the instantaneous exhaust emissions of a diesel 2.0 TDI engine operating with different proportions of animal fat/pure diesel and using as input the variables that can be read by the electronic control unit (ECU). In this article, Section 2 has been devoted to introduce the engine testing procedure. In Section 3 the fuels used in the study have been detailed whereas in Section 4 the ANN and symbolic regression principles and their application are explained. In Section 5 the results are shown and discussed and the conclusions of the work are finally summarized in Section 6. 2. Engine testing procedure The engine test bench used was composed of a diesel engine and dynamometer (SCHENK W150) controlled by a HORIBA's SPARC system. The diesel engine was a 2.0 Volkswagen TDI (2005) 140 hp @ 4000 rev-1, Euro 4, in-line 4-cylinder, turbocharged, direct injection, Compression ratio of 18, with exhaust gas recirculation (EGR) and without diesel particulate filter (DPF). This engine has been previously used in a large number of experiments with different types of fuels and engine conditions [5,30,31]. Particle number and size distribution data were measured using an Engine Exhaust Particle Sizer 3090 (EEPS) by TSI Inc. and a Rotating Disc Raw Gas Diluter MD19-2E (Matter Engineering). The dilution system and particle sampling has been thoroughly explained in previous publications [32,33]. In order to measure pollutant concentrations of exhaust gases, an OBS 2200 (HORIBA Inc.) was used. Additionally, different engine operating parameters were recorded such as engine speed, engine torque, throttle position, intake air temperature, temperature of the exhaust gas, flow of exhaust gas, the percentage of exhaust gas recirculation, fuel temperature, boost pressure, mass air flow and fuel consumption. Regulated emissions and particle number concentration and size distribution emissions were measured in a driving cycle composed of 4 repetitions of the UDC (Urban Driving Cycle or NEDC-urban part of the New European Driving Cycle) and five steady-state conditions (15, 30, 50, 70 and 100 km/h). In a previous study, pollutant emissions were analyzed using only emission mean values of each experimental steady-state condition [5], discarding the data of the transient states. The operational phase at cold start was not considered for this study. There was a preheat
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stage with exhaust gas temperature higher than 100 C. Each fuel change was preceded by the execution of an intermediate cleaning test consisting in 4 UDC þ steady-state conditions with pure diesel. The driving cycle was programmed into the electronic control of the engine test bench and second-to-second emission data (NOx, CO2, particle number concentration and GMD in accumulation mode and particle number concentration in nucleation mode) of all engine conditions, steady-state, transient operating conditions and transient conditions between steady-states have been included in the present study. Engine torque and engine speed from the dynamic engine test bench can be controlled. Then, to simulate a driving cycle, we have considered vehicle speed, acceleration, gear engaged and vehicle characteristics (mass, frontal area, drag coefficient and coefficient of rolling resistance) of a vehicle with the same engine (Seat Alhambra 2.0 TDI, 2005). The equivalent engine speed and engine torque to simulate the UDC and the 5 steady-state conditions are represented in Fig. 1. Three tests were performed of each driving cycle with each fuel blend in order to ensure repeatability of measurements. 3. Fuels The fuels used in this study were pure diesel (PD) without fatty acid methyl ester (biodiesel) and 6 blends of animal fat based biodiesel/pure diesel. The percentages of biodiesel/pure diesel were 10, 20, 25, 30, 40 and 50%. The maximum was set at 50% to prevent alterations on the operation of engine fuel feed system. The animal fat based biodiesel is a blend of pork, poultry and beef fat. The main physical and chemical properties of pure diesel and biodiesel are contained in Table 1. 4. Model design 4.1. ANN development In addition to the development and evaluation of two models to predict exhaust emissions in transient conditions, this study aims to demonstrate that predicting particle number concentration emitted by a diesel engine is feasible. For that, a neural network with a reduced number of hidden layers (to avoid overfitting) [21] was trained. A fully-connected multilayer perceptron with just a single hidden layer has been used (Fig. 2). Multiple optimal learning factors (MOLF) were used in training
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data. They have been introduced [34] as a family of learning algorithms targeting the optimization in the training of a fixed architecture, fully connected multi-layer perceptron with a single hidden layer (Fig. 2), capable of learning from regression/approximation type application and data. The MOLF methods require fewer multiplies per iteration than traditional second order methods based on Newton’s method as it has been detailed in Ref. [32]. The developed ANN models have been trained with experimental data. The 9 input nodes consisted of percentage of animal fat in the biodiesel/diesel blend, speed set by the selected driving cycle (km/h), acceleration (m/s2), engine speed (min1), engine torque (Nm), air intake temperature ( C), boost pressure (mbar), mass air flow (mg/st), fuel consumption (l/h). The proportion of biodiesel in the biodiesel/diesel blend is an independent variable selected by researchers. In the case of the experiments carried out, the levels are 0, 10, 20, 25, 30, 40 and 50% of Animal Fat in the diesel/biodiesel blend. The fuel characteristics, that may affect emissions from diesel engines, are: the oxygen content, the ratio of carbon atoms to hydrogen, the viscosity, the density or cetane number [35]. These features change according to the different proportions of diesel/biodiesel blend. Instantaneous speed and instantaneous acceleration are two independent variables selected by researchers. In the 1990s, the new emission models emphasized the high effect of instantaneous vehicle speed (km/h) and, specially, instantaneous acceleration over exhaust pollutant emissions [36,37]. Later, with the appearance of more modern equipment of particle measurement in number and size distribution, the influence of the acceleration [32] has gained notoriety. Nowadays, the consideration of these variables for the prediction of emissions under transient conditions is advisable because of their direct influence on pollutant emissions. Engine speed and torque are read by the engine's ECU and represent the actual torque and speed during the experiments (not the required by the driver). The torque required by the driver is fixed by the selected speed profile to reproduce the driving cycle as shown in Fig. 1. The effect of engine speed and torque on any type of pollutant is widely demonstrated [38]. Also relevant factors to take into account are air intake temperature, boost pressure, mass air flow and fuel consumption. These variables, which depend on the operating condition and other parameters such as ambient temperature, can be read by the electronic control unit of the vehicle. To a greater or lesser extent, all these parameters are related to pollutant emissions. Air
Fig. 1. Required engine torque and engine speed to simulate the vehicle speed profile of the selected driving cycle.
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Table 1 Fatty acid compositions and main fuel properties of pure diesel and animal fat biodiesel. Fuel Fatty acid composition %
Cetane Number Viscosity (cSt) 40 C Density 15 C (Kg/m3) Iodine Number (g I2/100 g) Flash Point ( C) Lower Heating Value (KJ/Kg) Boiling Temperature ( C) %C %H %N %S %O
Lauric acid Miristic acid Palmitic acid Palmitoleic acid Estaric acid Oleic acid Linoleic acid a-linolenic acid
Pure diesel
Animal Fat
Methods
e e e e e e e e 51.3 2.9 840 0 66 40584.8 e e e e e 0
e 1.86 18.31 3.21 10.85 40.51 22.18 3.07 57.49 4.42 871 81.60 161.50 37442.6 337.2 81.11 11.67 0.064 0.266 6.89
UNE-EN 14103/03 and UNE-EN ISO 550/038
e UNE-EN 3104 UNE-EN ISO 12185 UNE-EN 14111/03 UNE EN 2719/03 ASTM D-240/09 e Elemental analysis Elemental analysis Elemental analysis Elemental analysis Elemental analysis
remaining 15% were used for testing. A total of 26.658 s-to-second emission data have been used. All data were previously randomized. Before the training, the input and output were normalized between 0 and 1 using minemax normalization. Different ANN architectures (inputs/HU/outputs) were trained. Validation and final selection of ANN architecture was done by selecting the minimum values of mean square error, HU number and epochs.
4.2. Genetic algorithms and symbolic regression Genetic Algorithms are biologically inspired computational methods. In nature, the “better adapted” individuals have higher chances to survive, attract possible partners and breed descendants. These individuals will transmit their main characteristics (i.e. their genes) and, subsequently, their progeny will inherit a combination of these “well-adapted” features. These simple premises are emulated by GAs to tackle a wide range of optimization problems. To achieve that, GAs follow these steps:
Fig. 2. Fully connected feed-forward multi-layer perceptron with one hidden layer.
temperature has an influence on combustion, and therefore on pollutant emissions [39,40]. Similarly, the boost pressure [40,41]. Even if the mass air flow is not a variable of maximum influence its combination with other ones, as the fuel consumption, has a considerable effect on combustion and pollutant emissions. Finally, fuel consumption has a high dependence on all variables that affect emissions so its relation with the polluting emissions is direct; therefore it is essential to include as input to predict accurately emissions. In this study, one ANN model with five outputs corresponding to pollutant emissions was used. The outputs were: CO2 (%), NOx (ppm), Particle number concentration in accumulation mode (#/cm3), Particle number concentration in nucleation mode (#/cm3), Geometric Mean Diameter of the particle in accumulation mode (nm). The predictions models were trained with 70% of the data and were validated with 15% of the dataset while the
1 Creation of a population: a population of possible solutions (its analog in nature would be a living being or individual) for a problem is created. Each solution/individual has its own intrinsic characteristics that define how the problem should be solved. A population size (total amount of individuals/solutions of the population) must be defined. 2 Fitness evaluation of each individual with the Fitness Function (FF): in order to quantify which solutions are "better adapted", a metric that measures how accurately each individual solves the problem (the FF), is applied. 3 Selection of parents: in this step, a higher probability to be selected as parent is assigned to those individuals with higher FF values. Their selection is performed as a ‘lottery’, where individuals with higher FF scores have more ‘tickets’ (i.e. chances) to win. 4 Creation of children: descendants are created as a combination of parent's genes. It is expected that newer generations outperform the former ones. Two main genetic operators were used to create new individuals (children) in this step. The first one (crossover) mixes the genes of the selected parents to create children. The second (mutations) are unlikely events that occur in nature and they help to skip local minimums. Mutations
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consist of randomly (with a 0.05% probability of occurrence) modifying a gene value in children. 5 Unless ending condition, iterate from step 2, where the new population (created in step 4) replaces the previous one. Notice that, in this step, an ending condition (normally a number of iterations, or minimum error) must be assigned. These steps, commonly used for GAs optimization, have been adapted to solve non-linear regression problems in the technique called Symbolic Regression. In SR, individuals adopt a tree structure where each one of their leaves is called node (Fig. 3). Two classes of nodes exist. The ‘operator nodes’ imply an arithmetic operation or mathematical function. The ‘variable nodes’ include the parameters to be considered. Each tree/individual/solution can be reconstructed as a regression function. They are read from left to right and bottom-up. In the example of Fig. 3, at the left of the tree one variable (Engine Torque) is linked with the operator "-" to the rest of the tree. At right, two other variables are linked by a division (i.e. Mass air flow/Engine Speed). The final equation represented by this example tree would be:
Engine Torque ðMass air flow = Engine SpeedÞ Each individual of the population (each tree) is created randomly in the first iteration (step 1 of the before mentioned GA guidelines) whereas the newer populations are replaced by the children (created in step 4). In agreement with the premises of the step 2 of the GA, each tree/individual is evaluated with the FF. A value according its performance is assigned to each tree. In this work the FF has been set as the mean quadratic regression error (between the tree estimation and the validation values). Then, higher probabilities to be selected as parents are assigned to individuals with better FF scores (step 3). The genetic operators crossover and mutation are applied to create improved children (step 4) from the selected parents. For it (see Fig. 4), randomly chosen parts of the parents strings are cropped and interchanged. The mutation operator assigns a low chance (in this case 0.05%) of randomly changing a part of the tree. This operator is useful to avoid local minima. In each iteration a new population is created and it replaces the previous one (step 5).
Fig. 3. An individual can be read as the combination of ‘operator nodes’ (black/purple shaded) and ‘variable nodes’ (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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To attain reliable tree representations, some closure properties are need to be established to avoid unproductive argument values (as negative square roots or divisions by zero). These restrictions are applied in the open source SR MATLAB toolbox GPTIPS [12] used in this work. The randomized training/validation/testing data set used for the symbolic regression-based estimation is exactly the same one applied for the ANN model in order to make a reliable comparison of the accuracy of both regression models. 5. Results and discussion 5.1. Summary Table 2 contains a summary of the output data description and the best-performance of regression models for ANN and SR. To compare both prediction models, the normalized data used in ANN were converted into the original value applying a reverse normalization procedure. Table 2 shows root-mean-square error (RMSE) for normalized testing data and testing data with reverse normalization. For the prediction of emissions through ANN, a network with one layer (MOLF method application) and 40 neurons was selected. The selection of the network structure was made by means of the trial and error method, selecting the appropriate number of hidden units to guarantee maximum accurate (minimum mean squared error) and performance for validation dataset. Fig. 5 shows the mean-square error (MSE) for different hidden units (HU) and until 4000 epochs that are sufficient for the minimum MSE to decrease asymptotically. The total error of the training and validation dataset suggests that for 40 HU the network converges to a final state and cannot be improved with more training. 45 HU presents worse MSE values than 40 HU for training dataset. Regarding SR, a limit of 1000 iterations/generations was set since the mean squared error per iteration decreased asymptotically and remained without significant changes after iteration 600. A population of 1000 individuals was created per iteration, ensuring a diverse enough seed of possible solutions in affordable computational times (~2 h per variable to be regressed in an Intel (R) Core (TM) i7-3770 [email protected] GHz). For both models, the CO2 emission presents the higher accuracies (R2 ¼ 0.91, in the testing data comparison) whereas the particle number concentration in nucleation mode shows the worst correlation (R2 ¼ 0.40 and 0.41, for ANN and SR, respectively, in the testing data comparison). This fact strongly suggests that with these fuels and operating conditions, the particle number in nucleation mode is hardly predictable. However, other studies with different biofuels [30], with the same measuring equipment and the same engine, show a higher percentage of particles in nucleation mode (that depend on type of fuel and operating condition). In Table 2 strikes the attention the high correlations obtained for the particle number concentration in accumulation mode. In spite of the uncertainties associated with the measurement of particles (dilution, removal or not of volatile material, etc.) and taking into account transient conditions, the results indicate it is possible to estimate the accumulation particle number concentration with both models. The comparison of the results of the regression analysis between the estimated and experimental data shows that both models have similar coefficients of determination. However, for the prediction of the NOx, SR presents higher correlation values. Table 3 shows the coefficient of determination as function of the percentage of animal fat in the biodiesel/diesel blend for the five outputs. Fig. 6 shows the Artificial Neural Network and Symbolic Regression prediction for CO2, NOx, particle number concentration in accumulation mode, particle number concentration in
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Fig. 4. Selected parents structures are cropped and interchanged by the crossover method. By this way, two children are created as a combination of two "well-adapted" parents.
Table 2 Summary of the best-performance of ANN prediction model and Symbolic regression.
Output Data Description
ANN model
Train Validation Testing Testing: reverse normalization
Symbolic Regression
Train Validation Testing
Max Min Average Standard deviation R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE
nucleation mode and GMD for testing data with the regression equation for each variable. 5.2. CO2 prediction results The highest correlation between the estimated data and the measured data is observed for the CO2 emissions, with an R2 of 0.91 for the ANN model and for the SR calculated over the testing
CO2
NOx
PN in accumulation mode
PN in nucleation mode
GMD
9.57 0.40 4.59 1.88 0.93 0.0533 0.92 0.055 0.92 0.0548 0.91 0.5694 0.93 0.50149 0.92 0.5406 0.91 0.55234
283.32 15.02 111.61 34.10 0.86 0.0453 0.87 0.0445 0.85 0.0470 0.78 16.142 0.84 13.5415 0.84 13.944 0.81 14.32
1.26E8 3.42E6 4.41E7 1.98E7 0.89 0.0509 0.89 0.0521 0.89 0.0531 0.87 7.23E6 0.89 6.43E6 0.89 6.72E6 0.89 6.8E6
2.08E7 0 3.42E6 1.92E6 0.39 0.0732 0.33 0.0731 0.40 0.0718 0.40 1.49E6 0.44 1.43E6 0.33 1.50E6 0.41 1.48E6
92.06 54.70 63.94 4.76 0.82 0.0539 0.82 0.0538 0.81 0.0574 0.81 2.14 0.83 1.9848 0.82 2.0308 0.82 2.099
dataset. The close dependency between fuel consumption and CO2 emissions makes it easier to predict CO2 than the rest of outputs. These outcomes are in line with recently published results by other authors who also observed the best correlations of CO2 emissions for diesel and for biofuels. The results obtained for the estimation of CO2 emissions in diesel engines are generally very accurate, with R2 higher than 0.99 [42]. This premise stands for emission predictions using a considerable lower amount of data than the used in this
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Fig. 5. Evolution of training and validation errors as a function of the number of training epochs and hidden units.
Table 3 Coefficient of determination for testing dataset, depending on the blend of ANN prediction model and Symbolic regression. R2 Prediction Method
% of Animal Fat
CO2
NOx
PN in accumulation mode
PN in nucleation mode
GMD
ANN model
0 10 20 25 30 40 50 0 10 20 25 30 40 50
0,92 0,92 0,90 0,88 0,91 0,90 0,93 0,90 0,93 0,92 0,90 0,91 0,93 0,92
0,71 0,81 0,79 0,76 0,69 0,77 0,82 0,82 0,86 0,83 0,78 0,84 0,82 0,87
0,89 0,81 0,84 0,81 0,81 0,84 0,80 0,90 0,81 0,87 0,83 0,84 0,85 0,86
0,23 0,14 0,18 0,00 0,55 0,03 0,38 0,20 0,15 0,24 0,11 0,64 0,12 0,38
0,79 0,81 0,81 0,76 0,78 0,76 0,74 0,74 0,80 0,83 0,73 0,78 0,78 0,69
SR model
Fig. 6. Regression analysis of ANN model results (data in black) and SR model results (data in grey) of testing dataset. From left to right: CO2, NOx, PN in accumulation mode, PN in nucleation mode and GMD.
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paper and under steady-state conditions (instead of aiming to predict transient conditions). Kiani et al. [21], for instance, obtained a R2 equal to 0.96 (training data) under steady-state conditions in a spark ignition engine and with ethanol-gasoline blend, while Silitonga et al., in 2015 [43] reached a value of 0.97 using Jatropha Curcas in a turbocharged diesel engine. In the case of SR, Ghambari et al., in 2017 [28], through the application of genetic programming, obtained a R2 equal to 0.94 (testing data) of a diesel engine in steady-state conditions and using biodiesel/diesel blends. The accuracy of one model (regardless of the methodology used) will depend on the number and the correct selection of the input parameters, and the variability of the output data. The results obtained for CO2 in this model, based on the available literature, can be considered at least as acceptable.
5.3. NOx prediction results The NOx emission estimation had an R2 equal to 0.78 for testing data, for the ANN model and a R2 equal to ¼ 0.82 for the testing dataset for the SR model. In this case SR presents a better fit than ANN. On the other hand, the prediction of NOx does not depend on the percentage of animal fat in the biodiesel/diesel blend. In the reviewed literature, the accuracy of the NOx prediction is lower than that obtained for CO2. Kiani et al., in 2010 [21], obtained a R2 of 0.71 (compared to 0.96 obtained for CO2). In the comparative of Hashemi and Clark [29], the values of R2 for NOx oscillate between 0.68 and 0.93. Yusaf et al., in 2011 [44] showed a R2 equal to 0.93 for NOx emission with crude palm oil and ordinary diesel in 11 steady-state conditions. Ghanbari et al. [28], through GA, obtained a coefficient of determination equal to 0.98 in steady state conditions. These results show that GA models are a powerful tool for NOx prediction. Since the formation processes of nitrogen oxides are more complex than for other pollutants, model accuracies are expected to be always lower. Nevertheless, the control of the emission of nitrogen oxides in diesel vehicles is of vital importance, so a correct modeling of this pollutant is a priority task.
5.4. Particle number concentration in accumulation mode prediction results The particle number concentration in accumulation mode (in the size-range of 30e560 nm) presented very high correlations. The main problem to contrast these results with other studies is that, to the best of author's knowledge, there are only PM prediction studies (mass of particles) and not of particle number for diesel engines. Particle number measurements have greater uncertainties (submicrometric particles, volatile material, high dilutions, strict temperature control) than PM's. However, in some researches, lower determination coefficients of PM have been attained than the ones obtained for particle number concentration (in accumulation mode). A relevant example is the study of Mudgal et al., in 2011 [14] that applied an ANN model to predict PM emissions from biodiesel in buses, in on-board conditions, getting an R2 of 0.78. In a gasoline engines under steady-state conditions (engine speed from 1500 to 3500 rpm and engine load from 20 to 110 Nm), Pu et al. [19] show a mean R2 of 0.92 for particle number concentration in a size-range of 23e1000 nm. Both prediction models applied provide a R2 equal to 0.87 for the testing dataset which is a good coefficient compared to the information available. Both methods worked with a similar high accuracy, independently to the blend fuel used (Table 3).
5.5. Geometric mean diameter Geometric mean diameter can be predicted with the same coefficient of determination (for SR) or even higher (for ANN) than NOx with the two models applied (R2 equal to 0.81 for ANN and R2 equal to 0.82 for SR calculated over the testing dataset). Both models seem to obtain slightly higher coefficients of determination for low concentrations of animal fat in the fuel blend (Table 3). Having acceptable regression coefficients confirms that it is possible to predict particle sizes in accumulation mode and not just the number. 6. Conclusions In this paper the task of developing accurate predictive models under transient operating conditions of a diesel engine has been carried out. These estimations are interesting to reduce the experiment number in an engine test-bench with their consequent savings of money and time, but also are relevant having in mind the potential real-time control applications focused on the reduction of pollutants, with particular attention on nitrogen oxides, since the large number of variables involved in the emission of this pollutant demands refined non-linear regressions methods, as the two ones used in this article. A 2.0 TDI Euro 4 diesel engine has been tested under the transient operating conditions, with pure diesel and six different proportions of animal fat. The measured pollutant emission data have been used to develop two prediction models (based on artificial neural network and genetic algorithm) using as input variables the data obtained from the engine control unit. The obtained R2 (test dataset) in ANN model for CO2, NOx, particle number concentration in accumulation mode, particle number concentration in nucleation mode and GMD were 0.91, 0.78, 0.87, 0.4 and 0.81, respectively. The prediction by SR has provided an R2 of 0.91, 0.82, 0.87, 0.41 and 0.82 for the same pollutants. Both models predict emissions similarly except for NOx, in which the prediction obtained by the symbolic regression presents greater accuracy than that obtained with artificial neural network model. Moreover, both models predict emissions with similar coefficients of determination regardless of the percentage of animal fat in the biodiesel/diesel blend. The results show that the highest R2 is observed for the prediction of CO2 with an R2 equal to 0.93 using ANN and 50% AF or using SR and 10 or 40% AF. The lowest values are observed for the particle number in nucleation mode when is predicted with ANN (R2 ¼ 0 if AF ¼ 25%). When comparing both models, it is necessary to take into account that the SR was also more costly in terms of computation time. However, one advantages of this method is that the regression formula (the final equation) is provided at the end of its optimization, allowing the possibility of studying the relative contribution factors. The main advantage of the two models is to allow the prediction of the engine exhaust emission in any other operative conditions and running with commercial diesel or any animal fat/diesel animal blend. One of the main conclusions of this work is the demonstration of the viability of the application of both prediction models to particle number concentration in accumulation mode and its possible application under other conditions (steady-state conditions, other fuels, on-board conditions). The results suggest that it is difficult to obtain predictive models for particles in nucleation mode due to the high variability and randomness of the formation processes of particles smaller than 30 nm. Another possible utility is the application of predictive models to particle number distribution, a fact that has been demonstrated with the prediction of the geometric mean diameter. To apply this
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methodology to particle size distribution curves, it would be desirable to conduct the experiments, in a first exploratory stage, in steady-state and non-transitory conditions, in order to minimize errors.
[23]
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Prediction of exhaust emission in transient conditions of a diesel engine fueled with animal fat using Artificial Neural Network and Symbolic Regression ez a, *, Giuseppe A. Ratta b, Carmen C. Barrios a Aida Domínguez-Sa a b
Environmental Department, Research Centre for Energy, Environment and Technology (CIEMAT), Avda. Complutense, 40, 28040, Madrid, Spain n, Research Centre for Energy, Environment and Technology (CIEMAT), Avda. Complutense, 40, 28040, Madrid, Spain Laboratorio Nacional de Fusio
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 July 2017 Received in revised form 16 February 2018 Accepted 17 February 2018 Available online 19 February 2018
The objective of this study is the development and evaluation of two models to predict instantaneous exhaust emissions of CO2, NOx, particle number concentration and geometric mean diameter in accumulation mode (30e560 nm) and in nucleation mode (5.6e30 nm) of a 2.0 euro 4 diesel engine fueled with pure diesel and animal fat in different proportions. To acquire data for training, validation and testing, 4 repetitions of the urban part of the New European Driving Cycle and 5 steady-state conditions (15, 30, 50, 70 and 100 km/h) were reproduced in a dynamic engine test bench. The used prediction models were Artificial Neural Networks and Symbolic Regression. Vehicle speed and acceleration, engine speed and torque, air intake temperature, boost pressure, mass air flow and fuel consumption were used as inputs variables. Artificial Neural Networks provided a R2 for testing dataset equal to 0.91, 0.78, 0.87 and 0.81 for CO2, NOx, number of particles in accumulation mode and geometric mean diameter, respectively. Symbolic regression showed a R2 of 0.91, 0.82, 0.87 and 0.82 for the mentioned pollutants. Particle number concentration in nucleation mode presents low correlation with the considered inputs due to the variability of the formation process of this particle mode. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Diesel engine Particle number Exhaust emission Artificial Neural Network Symbolic regression Biodiesel
1. Introduction There is a growing interest in biofuel study to enhance fuel diversification and to limit excessive use and dependence on fossil fuels. Within the wide range of biofuels for diesel engines, fuels from waste are presented as a very valuable alternative due to the reduction of land use impacts and revaluation of waste products. Fuel from animal fat has received increasing attention in recent years [1]. Animal fats are composed of a mixture of fatty acids whose proportions depend on the source material (beef tallow,
Abbreviations: ANN, Artificial Neural Network; CO, Carbon oxide; CO2, carbon dioxide; DPF, Diesel Particulate Filter; ECU, electronic control unit; EGR, Exhaust Gas Recirculation; FF, Fitness Function; GAs, Genetic Algorithms; GMD, geometric mean diameter; HU, Hidden Units; MSE, Mean-square error; MOLF, Multiple Optimal Learning Factors; NEDC, New European driving cycle; NOx, Nitrogen oxides; PD, pure diesel; PM, Particulate Matter; PN, Particle Number; RMSE, rootmean-square error; SFC, specific fuel consumption; SR, Symbolic Regression; TDI, Turbocharged direct injection; THC, Total hydrocarbons; UDC, Urban driving cycle. * Corresponding author. ez). E-mail address: [email protected] (A. Domínguez-Sa https://doi.org/10.1016/j.energy.2018.02.080 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
pork lard, and chicken fat). This fatty acid composition has influence over some fuel properties such as the length of the carbon chain or the degree of saturation. All these fuel properties will finally affect the fuel quality [2] and, consequently, the exhaust emissions. In recent years, pollutant emissions and performance of animal fat are being investigated in detail in diesel engines [3e6]. In these studies, NOx emissions increase [3e5] but THC emissions decrease [3,4,6] in comparison with conventional diesel fuel. To date, there are few studies that examine the nanoparticle emissions when animal fat is used as fuel in diesel engines. According to Awad et al. [4], Particulate Matter (PM) emissions were reduced at low and medium engine loads with the use of animal fat, but no differences were observed at high engine loads. Barrios et al., in 2014 [5], showed that with a blend ratio of 50% of Animal Fat and pure diesel, the total particle number concentration (in the size-range of 5.6e560 nm) decreased drastically for all the experimental conditions in comparison to pure diesel. In this study [5], the data in transient conditions were discarded, considering only the average emissions of steady-state. In the present study, second-to-second data of all engine conditions (steady-state and transient operating), have been
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considered. The exhaust emission of a 2.0 TDI Euro 4 diesel engine running on the urban part of the New European Driving Cycle (NEDC cycle) and five steady-state conditions have been measured with pure diesel and 6 different proportions of animal fat/pure diesel. Subsequently, it has been modeled using the actual measured emissions database as training, validation and testing data. Since linear models (or deterministic models) do not adjust to the complexity of emission-forming mechanisms [7] and combustion models to predict pollutant emissions are generally very sophisticated and complex, and need strictly defined boundary conditions [8,9] with data that is not always easy provide, refined alternatives to estimate the emissions must be addressed. In the case of this work, two different machine learning techniques have been applied in order to forecast the emissions in transient conditions. The first one, Artificial Neural Networks (ANN), have been used for years to solve many problems of science, especially in areas where normal methods of modeling do not work properly, e.g. financial and economic modeling, medical applications, optimization of industrial processes and quality control, and a long list of scientific areas. ANN models have proven their accuracy and their ability to re-learn from new data [10], they have shown flexibility in the selection/elimination of input variables, they are computationally faster than iterative mathematical models [11]. The second one, also biologically inspired and able to automatically develop non-linear equations to fit a function, has been Symbolic Regression (SR) [12]. One of the main advantages of this method is that, instead ANN and other machine learning techniques, the regression formula (the final equation) is provided at the end of its optimization. The analysis of the regression equation goes beyond the scope of this article, devoted to pragmatic estimations, but its assessment may help to shed some light upon emissions formation depending on engine operation parameters. Therefore the full utility of the results obtained with this technique can be exploited in the future. The data, accessible from the engine Electronic Control Unit (ECU), have been used as input values of the model, and CO2, NOx, particle number concentration (accumulation and nucleation mode particle) and geometric mean diameter (GMD) have been the variables to be estimated. Obtaining a good model reduces the number of new experiments and the need to repeat experimental conditions (different concentrations of Animal Fat/diesel blends, different engine operating conditions, etc.), which results in economic and time saving. On the other hand, both Genetic Algorithms (GAs) and ANNs are powerful tools for identifying complex relationships between input and output data or potential real-time control applications focused on emission reduction (modifications of diesel catalyst or exhaust gas recirculation increase). To the best of our knowledge, the present work is the first one that: 1) performs a comparison of two machine learning models for the prediction of engine emissions, 2) predicts the particle number in steady-states and transient conditions for diesel engines, and 3) uses symbolic regression to predict emissions under transient conditions. There are no ANN or regression models available for particle number prediction for diesel engine, although there are studies applied to PM or smoke levels [13e17], PM size [18] and particle number for gasoline engines [19]. Pu et al., in 2017 [19] predicted the particle number emitted by gasoline direct injection in steady state conditions in 5 sizes-ranges. However, other types of particle number concentration and size distribution modeling in real traffic conditions have been developed depending on the type of driving [20]. In the past few years, some applications of predictive models using ANN to pollutant emissions of CO2, NOx or HC
[10,11,21e23] or other engine parameters related to engine performance [24e26] or combustion processes [27] have been published. On the other hand, only one study from 2017 [28] has used genetic algorithms to predict emissions and performance of a diesel engine in steady-state conditions. Most of these studies have been performed under steady-state engine operating conditions. For the case of transient conditions there are fewer applications of predictive models of pollutant emissions and these models have lower correlation values. Under transient conditions, the number of variables influencing pollutant emissions is larger and lower repeatability values are obtained. Mudgal et al., in 2011 [14], used ANN to predict emission from biodiesel in buses in on-board conditions obtaining an R2 (coefficient of determination to quantify the goodness of the fit) of 0.96, 0.94, 0.82, 0.98 and 0.78 for NOx, HC, CO, CO2 and PM, respectively. In a study of Hashemi and Clark in 2007 [29], ANN was trained on chassis dynamometer data from heavy-duty diesel vehicles reaching an average accuracy of 0.97, 0.89, 0.70 and 0.48 for CO2, NOx, CO and HC, respectively. The improvement of the prediction models in transient conditions and the inclusion of the particle number (emission included in the most current regulations) can be of great interest and help a more efficient control of emissions. The main objective of this work is the development, evaluation and comparison of two predictive models, artificial neural network model and symbolic regression model, of the instantaneous exhaust emissions of a diesel 2.0 TDI engine operating with different proportions of animal fat/pure diesel and using as input the variables that can be read by the electronic control unit (ECU). In this article, Section 2 has been devoted to introduce the engine testing procedure. In Section 3 the fuels used in the study have been detailed whereas in Section 4 the ANN and symbolic regression principles and their application are explained. In Section 5 the results are shown and discussed and the conclusions of the work are finally summarized in Section 6. 2. Engine testing procedure The engine test bench used was composed of a diesel engine and dynamometer (SCHENK W150) controlled by a HORIBA's SPARC system. The diesel engine was a 2.0 Volkswagen TDI (2005) 140 hp @ 4000 rev-1, Euro 4, in-line 4-cylinder, turbocharged, direct injection, Compression ratio of 18, with exhaust gas recirculation (EGR) and without diesel particulate filter (DPF). This engine has been previously used in a large number of experiments with different types of fuels and engine conditions [5,30,31]. Particle number and size distribution data were measured using an Engine Exhaust Particle Sizer 3090 (EEPS) by TSI Inc. and a Rotating Disc Raw Gas Diluter MD19-2E (Matter Engineering). The dilution system and particle sampling has been thoroughly explained in previous publications [32,33]. In order to measure pollutant concentrations of exhaust gases, an OBS 2200 (HORIBA Inc.) was used. Additionally, different engine operating parameters were recorded such as engine speed, engine torque, throttle position, intake air temperature, temperature of the exhaust gas, flow of exhaust gas, the percentage of exhaust gas recirculation, fuel temperature, boost pressure, mass air flow and fuel consumption. Regulated emissions and particle number concentration and size distribution emissions were measured in a driving cycle composed of 4 repetitions of the UDC (Urban Driving Cycle or NEDC-urban part of the New European Driving Cycle) and five steady-state conditions (15, 30, 50, 70 and 100 km/h). In a previous study, pollutant emissions were analyzed using only emission mean values of each experimental steady-state condition [5], discarding the data of the transient states. The operational phase at cold start was not considered for this study. There was a preheat
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stage with exhaust gas temperature higher than 100 C. Each fuel change was preceded by the execution of an intermediate cleaning test consisting in 4 UDC þ steady-state conditions with pure diesel. The driving cycle was programmed into the electronic control of the engine test bench and second-to-second emission data (NOx, CO2, particle number concentration and GMD in accumulation mode and particle number concentration in nucleation mode) of all engine conditions, steady-state, transient operating conditions and transient conditions between steady-states have been included in the present study. Engine torque and engine speed from the dynamic engine test bench can be controlled. Then, to simulate a driving cycle, we have considered vehicle speed, acceleration, gear engaged and vehicle characteristics (mass, frontal area, drag coefficient and coefficient of rolling resistance) of a vehicle with the same engine (Seat Alhambra 2.0 TDI, 2005). The equivalent engine speed and engine torque to simulate the UDC and the 5 steady-state conditions are represented in Fig. 1. Three tests were performed of each driving cycle with each fuel blend in order to ensure repeatability of measurements. 3. Fuels The fuels used in this study were pure diesel (PD) without fatty acid methyl ester (biodiesel) and 6 blends of animal fat based biodiesel/pure diesel. The percentages of biodiesel/pure diesel were 10, 20, 25, 30, 40 and 50%. The maximum was set at 50% to prevent alterations on the operation of engine fuel feed system. The animal fat based biodiesel is a blend of pork, poultry and beef fat. The main physical and chemical properties of pure diesel and biodiesel are contained in Table 1. 4. Model design 4.1. ANN development In addition to the development and evaluation of two models to predict exhaust emissions in transient conditions, this study aims to demonstrate that predicting particle number concentration emitted by a diesel engine is feasible. For that, a neural network with a reduced number of hidden layers (to avoid overfitting) [21] was trained. A fully-connected multilayer perceptron with just a single hidden layer has been used (Fig. 2). Multiple optimal learning factors (MOLF) were used in training
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data. They have been introduced [34] as a family of learning algorithms targeting the optimization in the training of a fixed architecture, fully connected multi-layer perceptron with a single hidden layer (Fig. 2), capable of learning from regression/approximation type application and data. The MOLF methods require fewer multiplies per iteration than traditional second order methods based on Newton’s method as it has been detailed in Ref. [32]. The developed ANN models have been trained with experimental data. The 9 input nodes consisted of percentage of animal fat in the biodiesel/diesel blend, speed set by the selected driving cycle (km/h), acceleration (m/s2), engine speed (min1), engine torque (Nm), air intake temperature ( C), boost pressure (mbar), mass air flow (mg/st), fuel consumption (l/h). The proportion of biodiesel in the biodiesel/diesel blend is an independent variable selected by researchers. In the case of the experiments carried out, the levels are 0, 10, 20, 25, 30, 40 and 50% of Animal Fat in the diesel/biodiesel blend. The fuel characteristics, that may affect emissions from diesel engines, are: the oxygen content, the ratio of carbon atoms to hydrogen, the viscosity, the density or cetane number [35]. These features change according to the different proportions of diesel/biodiesel blend. Instantaneous speed and instantaneous acceleration are two independent variables selected by researchers. In the 1990s, the new emission models emphasized the high effect of instantaneous vehicle speed (km/h) and, specially, instantaneous acceleration over exhaust pollutant emissions [36,37]. Later, with the appearance of more modern equipment of particle measurement in number and size distribution, the influence of the acceleration [32] has gained notoriety. Nowadays, the consideration of these variables for the prediction of emissions under transient conditions is advisable because of their direct influence on pollutant emissions. Engine speed and torque are read by the engine's ECU and represent the actual torque and speed during the experiments (not the required by the driver). The torque required by the driver is fixed by the selected speed profile to reproduce the driving cycle as shown in Fig. 1. The effect of engine speed and torque on any type of pollutant is widely demonstrated [38]. Also relevant factors to take into account are air intake temperature, boost pressure, mass air flow and fuel consumption. These variables, which depend on the operating condition and other parameters such as ambient temperature, can be read by the electronic control unit of the vehicle. To a greater or lesser extent, all these parameters are related to pollutant emissions. Air
Fig. 1. Required engine torque and engine speed to simulate the vehicle speed profile of the selected driving cycle.
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Table 1 Fatty acid compositions and main fuel properties of pure diesel and animal fat biodiesel. Fuel Fatty acid composition %
Cetane Number Viscosity (cSt) 40 C Density 15 C (Kg/m3) Iodine Number (g I2/100 g) Flash Point ( C) Lower Heating Value (KJ/Kg) Boiling Temperature ( C) %C %H %N %S %O
Lauric acid Miristic acid Palmitic acid Palmitoleic acid Estaric acid Oleic acid Linoleic acid a-linolenic acid
Pure diesel
Animal Fat
Methods
e e e e e e e e 51.3 2.9 840 0 66 40584.8 e e e e e 0
e 1.86 18.31 3.21 10.85 40.51 22.18 3.07 57.49 4.42 871 81.60 161.50 37442.6 337.2 81.11 11.67 0.064 0.266 6.89
UNE-EN 14103/03 and UNE-EN ISO 550/038
e UNE-EN 3104 UNE-EN ISO 12185 UNE-EN 14111/03 UNE EN 2719/03 ASTM D-240/09 e Elemental analysis Elemental analysis Elemental analysis Elemental analysis Elemental analysis
remaining 15% were used for testing. A total of 26.658 s-to-second emission data have been used. All data were previously randomized. Before the training, the input and output were normalized between 0 and 1 using minemax normalization. Different ANN architectures (inputs/HU/outputs) were trained. Validation and final selection of ANN architecture was done by selecting the minimum values of mean square error, HU number and epochs.
4.2. Genetic algorithms and symbolic regression Genetic Algorithms are biologically inspired computational methods. In nature, the “better adapted” individuals have higher chances to survive, attract possible partners and breed descendants. These individuals will transmit their main characteristics (i.e. their genes) and, subsequently, their progeny will inherit a combination of these “well-adapted” features. These simple premises are emulated by GAs to tackle a wide range of optimization problems. To achieve that, GAs follow these steps:
Fig. 2. Fully connected feed-forward multi-layer perceptron with one hidden layer.
temperature has an influence on combustion, and therefore on pollutant emissions [39,40]. Similarly, the boost pressure [40,41]. Even if the mass air flow is not a variable of maximum influence its combination with other ones, as the fuel consumption, has a considerable effect on combustion and pollutant emissions. Finally, fuel consumption has a high dependence on all variables that affect emissions so its relation with the polluting emissions is direct; therefore it is essential to include as input to predict accurately emissions. In this study, one ANN model with five outputs corresponding to pollutant emissions was used. The outputs were: CO2 (%), NOx (ppm), Particle number concentration in accumulation mode (#/cm3), Particle number concentration in nucleation mode (#/cm3), Geometric Mean Diameter of the particle in accumulation mode (nm). The predictions models were trained with 70% of the data and were validated with 15% of the dataset while the
1 Creation of a population: a population of possible solutions (its analog in nature would be a living being or individual) for a problem is created. Each solution/individual has its own intrinsic characteristics that define how the problem should be solved. A population size (total amount of individuals/solutions of the population) must be defined. 2 Fitness evaluation of each individual with the Fitness Function (FF): in order to quantify which solutions are "better adapted", a metric that measures how accurately each individual solves the problem (the FF), is applied. 3 Selection of parents: in this step, a higher probability to be selected as parent is assigned to those individuals with higher FF values. Their selection is performed as a ‘lottery’, where individuals with higher FF scores have more ‘tickets’ (i.e. chances) to win. 4 Creation of children: descendants are created as a combination of parent's genes. It is expected that newer generations outperform the former ones. Two main genetic operators were used to create new individuals (children) in this step. The first one (crossover) mixes the genes of the selected parents to create children. The second (mutations) are unlikely events that occur in nature and they help to skip local minimums. Mutations
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consist of randomly (with a 0.05% probability of occurrence) modifying a gene value in children. 5 Unless ending condition, iterate from step 2, where the new population (created in step 4) replaces the previous one. Notice that, in this step, an ending condition (normally a number of iterations, or minimum error) must be assigned. These steps, commonly used for GAs optimization, have been adapted to solve non-linear regression problems in the technique called Symbolic Regression. In SR, individuals adopt a tree structure where each one of their leaves is called node (Fig. 3). Two classes of nodes exist. The ‘operator nodes’ imply an arithmetic operation or mathematical function. The ‘variable nodes’ include the parameters to be considered. Each tree/individual/solution can be reconstructed as a regression function. They are read from left to right and bottom-up. In the example of Fig. 3, at the left of the tree one variable (Engine Torque) is linked with the operator "-" to the rest of the tree. At right, two other variables are linked by a division (i.e. Mass air flow/Engine Speed). The final equation represented by this example tree would be:
Engine Torque ðMass air flow = Engine SpeedÞ Each individual of the population (each tree) is created randomly in the first iteration (step 1 of the before mentioned GA guidelines) whereas the newer populations are replaced by the children (created in step 4). In agreement with the premises of the step 2 of the GA, each tree/individual is evaluated with the FF. A value according its performance is assigned to each tree. In this work the FF has been set as the mean quadratic regression error (between the tree estimation and the validation values). Then, higher probabilities to be selected as parents are assigned to individuals with better FF scores (step 3). The genetic operators crossover and mutation are applied to create improved children (step 4) from the selected parents. For it (see Fig. 4), randomly chosen parts of the parents strings are cropped and interchanged. The mutation operator assigns a low chance (in this case 0.05%) of randomly changing a part of the tree. This operator is useful to avoid local minima. In each iteration a new population is created and it replaces the previous one (step 5).
Fig. 3. An individual can be read as the combination of ‘operator nodes’ (black/purple shaded) and ‘variable nodes’ (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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To attain reliable tree representations, some closure properties are need to be established to avoid unproductive argument values (as negative square roots or divisions by zero). These restrictions are applied in the open source SR MATLAB toolbox GPTIPS [12] used in this work. The randomized training/validation/testing data set used for the symbolic regression-based estimation is exactly the same one applied for the ANN model in order to make a reliable comparison of the accuracy of both regression models. 5. Results and discussion 5.1. Summary Table 2 contains a summary of the output data description and the best-performance of regression models for ANN and SR. To compare both prediction models, the normalized data used in ANN were converted into the original value applying a reverse normalization procedure. Table 2 shows root-mean-square error (RMSE) for normalized testing data and testing data with reverse normalization. For the prediction of emissions through ANN, a network with one layer (MOLF method application) and 40 neurons was selected. The selection of the network structure was made by means of the trial and error method, selecting the appropriate number of hidden units to guarantee maximum accurate (minimum mean squared error) and performance for validation dataset. Fig. 5 shows the mean-square error (MSE) for different hidden units (HU) and until 4000 epochs that are sufficient for the minimum MSE to decrease asymptotically. The total error of the training and validation dataset suggests that for 40 HU the network converges to a final state and cannot be improved with more training. 45 HU presents worse MSE values than 40 HU for training dataset. Regarding SR, a limit of 1000 iterations/generations was set since the mean squared error per iteration decreased asymptotically and remained without significant changes after iteration 600. A population of 1000 individuals was created per iteration, ensuring a diverse enough seed of possible solutions in affordable computational times (~2 h per variable to be regressed in an Intel (R) Core (TM) i7-3770 [email protected] GHz). For both models, the CO2 emission presents the higher accuracies (R2 ¼ 0.91, in the testing data comparison) whereas the particle number concentration in nucleation mode shows the worst correlation (R2 ¼ 0.40 and 0.41, for ANN and SR, respectively, in the testing data comparison). This fact strongly suggests that with these fuels and operating conditions, the particle number in nucleation mode is hardly predictable. However, other studies with different biofuels [30], with the same measuring equipment and the same engine, show a higher percentage of particles in nucleation mode (that depend on type of fuel and operating condition). In Table 2 strikes the attention the high correlations obtained for the particle number concentration in accumulation mode. In spite of the uncertainties associated with the measurement of particles (dilution, removal or not of volatile material, etc.) and taking into account transient conditions, the results indicate it is possible to estimate the accumulation particle number concentration with both models. The comparison of the results of the regression analysis between the estimated and experimental data shows that both models have similar coefficients of determination. However, for the prediction of the NOx, SR presents higher correlation values. Table 3 shows the coefficient of determination as function of the percentage of animal fat in the biodiesel/diesel blend for the five outputs. Fig. 6 shows the Artificial Neural Network and Symbolic Regression prediction for CO2, NOx, particle number concentration in accumulation mode, particle number concentration in
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Fig. 4. Selected parents structures are cropped and interchanged by the crossover method. By this way, two children are created as a combination of two "well-adapted" parents.
Table 2 Summary of the best-performance of ANN prediction model and Symbolic regression.
Output Data Description
ANN model
Train Validation Testing Testing: reverse normalization
Symbolic Regression
Train Validation Testing
Max Min Average Standard deviation R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE R2 RMSE
nucleation mode and GMD for testing data with the regression equation for each variable. 5.2. CO2 prediction results The highest correlation between the estimated data and the measured data is observed for the CO2 emissions, with an R2 of 0.91 for the ANN model and for the SR calculated over the testing
CO2
NOx
PN in accumulation mode
PN in nucleation mode
GMD
9.57 0.40 4.59 1.88 0.93 0.0533 0.92 0.055 0.92 0.0548 0.91 0.5694 0.93 0.50149 0.92 0.5406 0.91 0.55234
283.32 15.02 111.61 34.10 0.86 0.0453 0.87 0.0445 0.85 0.0470 0.78 16.142 0.84 13.5415 0.84 13.944 0.81 14.32
1.26E8 3.42E6 4.41E7 1.98E7 0.89 0.0509 0.89 0.0521 0.89 0.0531 0.87 7.23E6 0.89 6.43E6 0.89 6.72E6 0.89 6.8E6
2.08E7 0 3.42E6 1.92E6 0.39 0.0732 0.33 0.0731 0.40 0.0718 0.40 1.49E6 0.44 1.43E6 0.33 1.50E6 0.41 1.48E6
92.06 54.70 63.94 4.76 0.82 0.0539 0.82 0.0538 0.81 0.0574 0.81 2.14 0.83 1.9848 0.82 2.0308 0.82 2.099
dataset. The close dependency between fuel consumption and CO2 emissions makes it easier to predict CO2 than the rest of outputs. These outcomes are in line with recently published results by other authors who also observed the best correlations of CO2 emissions for diesel and for biofuels. The results obtained for the estimation of CO2 emissions in diesel engines are generally very accurate, with R2 higher than 0.99 [42]. This premise stands for emission predictions using a considerable lower amount of data than the used in this
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Fig. 5. Evolution of training and validation errors as a function of the number of training epochs and hidden units.
Table 3 Coefficient of determination for testing dataset, depending on the blend of ANN prediction model and Symbolic regression. R2 Prediction Method
% of Animal Fat
CO2
NOx
PN in accumulation mode
PN in nucleation mode
GMD
ANN model
0 10 20 25 30 40 50 0 10 20 25 30 40 50
0,92 0,92 0,90 0,88 0,91 0,90 0,93 0,90 0,93 0,92 0,90 0,91 0,93 0,92
0,71 0,81 0,79 0,76 0,69 0,77 0,82 0,82 0,86 0,83 0,78 0,84 0,82 0,87
0,89 0,81 0,84 0,81 0,81 0,84 0,80 0,90 0,81 0,87 0,83 0,84 0,85 0,86
0,23 0,14 0,18 0,00 0,55 0,03 0,38 0,20 0,15 0,24 0,11 0,64 0,12 0,38
0,79 0,81 0,81 0,76 0,78 0,76 0,74 0,74 0,80 0,83 0,73 0,78 0,78 0,69
SR model
Fig. 6. Regression analysis of ANN model results (data in black) and SR model results (data in grey) of testing dataset. From left to right: CO2, NOx, PN in accumulation mode, PN in nucleation mode and GMD.
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paper and under steady-state conditions (instead of aiming to predict transient conditions). Kiani et al. [21], for instance, obtained a R2 equal to 0.96 (training data) under steady-state conditions in a spark ignition engine and with ethanol-gasoline blend, while Silitonga et al., in 2015 [43] reached a value of 0.97 using Jatropha Curcas in a turbocharged diesel engine. In the case of SR, Ghambari et al., in 2017 [28], through the application of genetic programming, obtained a R2 equal to 0.94 (testing data) of a diesel engine in steady-state conditions and using biodiesel/diesel blends. The accuracy of one model (regardless of the methodology used) will depend on the number and the correct selection of the input parameters, and the variability of the output data. The results obtained for CO2 in this model, based on the available literature, can be considered at least as acceptable.
5.3. NOx prediction results The NOx emission estimation had an R2 equal to 0.78 for testing data, for the ANN model and a R2 equal to ¼ 0.82 for the testing dataset for the SR model. In this case SR presents a better fit than ANN. On the other hand, the prediction of NOx does not depend on the percentage of animal fat in the biodiesel/diesel blend. In the reviewed literature, the accuracy of the NOx prediction is lower than that obtained for CO2. Kiani et al., in 2010 [21], obtained a R2 of 0.71 (compared to 0.96 obtained for CO2). In the comparative of Hashemi and Clark [29], the values of R2 for NOx oscillate between 0.68 and 0.93. Yusaf et al., in 2011 [44] showed a R2 equal to 0.93 for NOx emission with crude palm oil and ordinary diesel in 11 steady-state conditions. Ghanbari et al. [28], through GA, obtained a coefficient of determination equal to 0.98 in steady state conditions. These results show that GA models are a powerful tool for NOx prediction. Since the formation processes of nitrogen oxides are more complex than for other pollutants, model accuracies are expected to be always lower. Nevertheless, the control of the emission of nitrogen oxides in diesel vehicles is of vital importance, so a correct modeling of this pollutant is a priority task.
5.4. Particle number concentration in accumulation mode prediction results The particle number concentration in accumulation mode (in the size-range of 30e560 nm) presented very high correlations. The main problem to contrast these results with other studies is that, to the best of author's knowledge, there are only PM prediction studies (mass of particles) and not of particle number for diesel engines. Particle number measurements have greater uncertainties (submicrometric particles, volatile material, high dilutions, strict temperature control) than PM's. However, in some researches, lower determination coefficients of PM have been attained than the ones obtained for particle number concentration (in accumulation mode). A relevant example is the study of Mudgal et al., in 2011 [14] that applied an ANN model to predict PM emissions from biodiesel in buses, in on-board conditions, getting an R2 of 0.78. In a gasoline engines under steady-state conditions (engine speed from 1500 to 3500 rpm and engine load from 20 to 110 Nm), Pu et al. [19] show a mean R2 of 0.92 for particle number concentration in a size-range of 23e1000 nm. Both prediction models applied provide a R2 equal to 0.87 for the testing dataset which is a good coefficient compared to the information available. Both methods worked with a similar high accuracy, independently to the blend fuel used (Table 3).
5.5. Geometric mean diameter Geometric mean diameter can be predicted with the same coefficient of determination (for SR) or even higher (for ANN) than NOx with the two models applied (R2 equal to 0.81 for ANN and R2 equal to 0.82 for SR calculated over the testing dataset). Both models seem to obtain slightly higher coefficients of determination for low concentrations of animal fat in the fuel blend (Table 3). Having acceptable regression coefficients confirms that it is possible to predict particle sizes in accumulation mode and not just the number. 6. Conclusions In this paper the task of developing accurate predictive models under transient operating conditions of a diesel engine has been carried out. These estimations are interesting to reduce the experiment number in an engine test-bench with their consequent savings of money and time, but also are relevant having in mind the potential real-time control applications focused on the reduction of pollutants, with particular attention on nitrogen oxides, since the large number of variables involved in the emission of this pollutant demands refined non-linear regressions methods, as the two ones used in this article. A 2.0 TDI Euro 4 diesel engine has been tested under the transient operating conditions, with pure diesel and six different proportions of animal fat. The measured pollutant emission data have been used to develop two prediction models (based on artificial neural network and genetic algorithm) using as input variables the data obtained from the engine control unit. The obtained R2 (test dataset) in ANN model for CO2, NOx, particle number concentration in accumulation mode, particle number concentration in nucleation mode and GMD were 0.91, 0.78, 0.87, 0.4 and 0.81, respectively. The prediction by SR has provided an R2 of 0.91, 0.82, 0.87, 0.41 and 0.82 for the same pollutants. Both models predict emissions similarly except for NOx, in which the prediction obtained by the symbolic regression presents greater accuracy than that obtained with artificial neural network model. Moreover, both models predict emissions with similar coefficients of determination regardless of the percentage of animal fat in the biodiesel/diesel blend. The results show that the highest R2 is observed for the prediction of CO2 with an R2 equal to 0.93 using ANN and 50% AF or using SR and 10 or 40% AF. The lowest values are observed for the particle number in nucleation mode when is predicted with ANN (R2 ¼ 0 if AF ¼ 25%). When comparing both models, it is necessary to take into account that the SR was also more costly in terms of computation time. However, one advantages of this method is that the regression formula (the final equation) is provided at the end of its optimization, allowing the possibility of studying the relative contribution factors. The main advantage of the two models is to allow the prediction of the engine exhaust emission in any other operative conditions and running with commercial diesel or any animal fat/diesel animal blend. One of the main conclusions of this work is the demonstration of the viability of the application of both prediction models to particle number concentration in accumulation mode and its possible application under other conditions (steady-state conditions, other fuels, on-board conditions). The results suggest that it is difficult to obtain predictive models for particles in nucleation mode due to the high variability and randomness of the formation processes of particles smaller than 30 nm. Another possible utility is the application of predictive models to particle number distribution, a fact that has been demonstrated with the prediction of the geometric mean diameter. To apply this
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methodology to particle size distribution curves, it would be desirable to conduct the experiments, in a first exploratory stage, in steady-state and non-transitory conditions, in order to minimize errors.
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