Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine

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Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine Yue Huang, Fanhua Ma* State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China

article info

abstract

Article history:

Support vector machine (SVM) method has got rapid development and application because

Received 9 February 2016

of its advantages in solving problems of small sample regression. In this paper, support

Received in revised form

vector machine (SVM) method was applied to the engine test data regression analysis.

30 March 2016

Quadratic polynomial method, neural network and SVM method are respectively used to

Accepted 30 March 2016

establish a mathematical model between operating & control parameters and performance

Available online xxx

parameters based on calibration experiment data for a Hydrogen enriched compressed natural gas (HCNG) engine. Through the comparison of the three methods, SVM method

Keywords:

has a higher fitting accuracy than other ways, showing certain superiority in nonlinear

HCNG

system regression. As SVM method is a generic methodology, it may be a new direction for

SVM

engine calibration algorithm study.

Engine calibration

© 2016 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.

Introduction Automotive industry has achieved big progress with the rapid development of world economy in recent decades, which also results in increasingly serious energy and environmental problems. Natural gas, a kind of clean energy, has been developed because of less content of carbon compared to gasoline. Hydrogen has a much larger laminar burning velocity, about 8 times as fast as CNG (compressed natural gas), and it needs a lower ignition energy. As a result, to add some hydrogen into CNG, the ignition energy is sharply down, and the dilute limit can be broadened, the combustion condition can be improved, which has very good effect on improving the thermal efficiency and decreasing the engine emissions.

Engines fueled with small quantities of H2 have been studied by a lot of researchers. In 1992, Mathur and his group added some hydrogen into a diesel engine, and the results showed that up to 38% of full-load energy could be substituted by hydrogen while the efficiency and power output maintain no loss [1]. Mikalsen and his group conducted series of experiment to study a direct injection compression ignition hydrogen engine. Results showed hydrogen direct injection into a diesel engine gave a higher power to weight ratio. As a result, under the test condition of 2100r/min in speed, the peak power increased by 14%, the brake thermal efficiency increased from 27.9% to 42.8%, compared with diesel-fueled mode [2]. Professor Tomita and his group have done a lot of research on hydrogen and dual-fuel engine. They investigated the effect of hydrogen content in producer gas on the performance and exhaust emissions. Two types of producer gases

* Corresponding author. Tel./fax: þ86 10 62785946. E-mail address: [email protected] (F. Ma). http://dx.doi.org/10.1016/j.ijhydene.2016.03.204 0360-3199/© 2016 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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Nomenclature Symbols f CO BTDC HCNG LS-SVM EMS SRM MAP GA PSO CNG SVM HC BSFC BSNOx NN

equivalence fuel-air ratio carbon monoxide before top dead center hydrogen enriched compressed natural gas least square support vector machine engine management system structural risk minimization manifold absolute pressure genetic algorithm particle swarm optimization compressed natural gas support vector machine hydrocarbon brake specific fuel consumption brake specific NOx emission neural network

were involved in his study, one with low hydrogen content (13.7%) and one with high content (20%). Results showed that better combustion, engine performance, and exhaust emissions (except NOx) were obtained with the high H2-content producer gas than with the low H2-content producer gas, especially under leaner conditions [3]. Moreover, they also performed charge dilution by N2 into H2-diesel dual-fuel engine to obtain lower NOx emissions, with 100% reduction of NOx emissions and 13% higher IMEP [4]. In recent years, kinds of detailed studies on HCNG engine have been carried out at home and abroad. Collier and his group have done some research on the emissions characteristics of HCNG engine. The test results show that the mixing of hydrogen can effectively reduce the unburned hydrocarbon (HC), and the cyclic variations of the engine can also be obviously decreased. In 2005, they conducted series tests on a Daewoo heavy engine [5]. When using 30% (in volume) hydrogen in HCNG as fuel and keeping the carbon monoxide (CO) and smoldering HC emissions staying the same with the original CNG engine, they found that the NOx emissions were sharply reduced. The researchers [6] from Cummins-West Port company studied different hydrogen ratio (volume ratio 15%, 20%, 25%) effect on emissions of HCNG engine. The results showed that HCNG with 20% hydrogen in volume had the best reduction for NOx emissions, with a reduction of as high as 43% compared to the original CNG engine. The results also showed that with hydrogen content continuing increasing, the NOx emissions also increased [6]. Huang and his group from Xi An Jiao Tong University investigated the influence of different hydrogen fractions and EGR rates on the performance and emissions of a spark-ignition engine fueled with natural gas-hydrogen. Test results showed that natural gas-hydrogen blend combining with ERG can realize highefficiency and low-emission spark-ignition engine [7e9]. Ma and his group from Tsinghua University also studied the effect of compression ratio, fuel-air ratio, ignition timing and hydrogen blend ratio on the power performance, combustion characteristics and emissions of HCNG engine. They

concluded that NOx emission decreases when either spark timing delays or smaller fuel-air ratio is used, and that the best hydrogen blend ratio for engine is around 20% in volume [10e12]. In order to satisfy the increasingly strict emission regulation and further raise the performance of the engine, efforts on improvement of the engine management system (EMS) are also very important besides using alternative fuels. It's of great use for improving the power and economic performance of the engine and reducing the engine emissions that the EMS of the engine is developed. To ensure proper operation of the EMS and to really make a sense, however, the key point lies in the calibration of those different control parameters of the EMS. In total, the calibration of the control parameters is of great significance to engine's performance. The core content of engine calibration is to simulate a model to speculate the best value of various parameters under all conditions based on experimental data, which belongs to the category of machine learning and regression analysis in essence. Intelligent algorithms have been developed and applied rapidly in regression analysis of complex nonlinear systems in recent years. Based on the principle of Structural Risk Minimization (SRM) put forward by V. Vapnik in 1982 [13], support vector machine (SVM) method was proposed and got fully development. According to SVM method, the actual risk of machine learning can be divided into two parts: one is the experience risk which means the training error of the model, the other is the incredible range. This principle successfully explained the phenomenon of “over-learning” which usually occurs in the regression analysis with neural network and other intelligent algorithms in theory. Moreover, SVM method maps the model from low dimension to high dimension space with a kernel function, converting the original complex nonlinear system into a linear system in high dimensional space, effectively solving the problem of the nonlinear system [14]. In a word, SVM method shows great advantages in regression analysis in complex nonlinear systems with relatively small data, thus obtained widespread application. In 2003, Feng used fuzzy SVM to build the model on the process of titration [15]. In the same year, Lee studied the identification of continuous mixing reaction kettle in industrial process with SVM method [16]. In 2004, Yan did some research on modeling for the forecast of the solidifying point of light diesel oil with least square SVM (LS-SVM) method [17]. In terms of automobile engine, Chen applied a nested loop search method into SVM to set up the engine torque and fuel consumption model in 2010 [18]. At the same time, Zhao set up an engine idle-speed model with LS-SVM method based on sample data got from the experiment [19]. Then genetic algorithm (GA) and particle swarm optimization (PSO) are applied to obtain an optimal electronic control unit setting automatically, under various user-defined constraints. Another group, Wong P. K and Vong C. M from University of Macau also did some studies. They applied SVM method into the prediction of the power performance of a petrol vehicle engine by training the sample engine performance data acquired from the dynamometer. LS-SVM and incremental algorithms were involved in their researches [20e22]. In 2015, Xu used LS-SVM method based on chaotic sequence and established a model to predict transient air-fuel ratio of a gasoline engine [23]. Also in 2015,

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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Lee used LS-SVM method for prediction of oil film parameters in transient operating mode of a gasoline engine [24]. All these researches have got satisfying results and thus proving that SVM method has excellent generalization ability and accurate prediction of nonlinear systems. Though the SVM method has already been applied in automotive engines, the application was limited to failure analysis, process simulation and concise model establishment. No application has been found to apply SVM method in engine calibration algorithm in and out abroad yet according to our literature retrieval. As the EMS becomes more and more complicated, the calibration of related control parameters will also become more and more complex and show strong nonlinearity. SVM method in no doubt shows great potential in solving this problem. In this paper we have selected the WP6NG240E5 natural gas engine made by Weifang diesel engine factory. 20% HCNG (20% hydrogen and 80% CNG in volume) has been used as the fuel to conduct a series of detailed calibration tests, getting the new fuel-air ratio and the ignition timing figure which fits the new fuel, 20% HCNG. After getting mass of experiment data, three different methods including quadratic polynomial, neural network and support vector machine (SVM) are used to establish a multiple regression model which builds the mathematical relationship between the performance parameters (torque, equivalent natural gas flow under unit power (BSFC), and NOx emissions under unit power (BSNOx)) and the operation and control parameters (speed, manifold absolute pressure (MAP), fuel-air ratio and ignition timing). Intelligent algorithms are used to optimize the SVM model. Through the comparison of the actual prediction accuracy by three methods, it is concluded that SVM method shows a superiority. As SVM method is a generic methodology, it can be used to guide the calibration of different kinds of vehicle engines [20].

Experiment system The WP6NG240E5 natural gas engine made by Weifang diesel engine factory has been used in the experiment. The main parameters are shown in Table 1. The engine is coupled to an eddy-current dynamometer for the measurement and control of speed and load. The exhaust concentration of HC, NOx, CO and CH4 are monitored by HORIBA-MEXA-7100DEGR emission monitoring system and the air/fuel ratio was measured by a HORIBA wide-range

Table 1 e Test engine specifications. Item Engine type Aspiration method Displacement volume (L) Compression ratio Bore (mm) Stroke (mm) Rated power (kW) Rated speed (r/min) Emission standard

Value In-line 6 cylinders, spark ignition Turbocharged intercooled 6,75 11.5:1 105 130 177 2300 Euro V

lambda analyzer. An online mixing system is developed in order to blend desired amount of hydrogen with natural gas in a pressure stabilizing tank just before entering the engine. The tank was divided into two chambers with a damping line used to improve the mixture uniformity. The mass flow rate of CNG and hydrogen are measured by DFM-1-1-5 Coriolis mass flowmeter with the range of 0e40 kg/h and the accuracy of ±0.2%. The mass flow rate of the air is measured by the thermal type gas mass flowmeter Toceil20N100114LI with a range of 0e1000 m3/h and the accuracy of ±1%.

Results analysis Detailed calibration experiment has been carried on under full conditions to the WP6NG240E engine from Weifang diesel engine factory with 20% HCNG as fuel, aiming at calibrating the fuel-air ratio and ignition timing of the engine. The range of the experiment conditions is shown in Table 2. According to the experiment results, taking the condition of 800 r/min in speed and 90 kPa in MAP as an example, influences on engine performance and emissions brought by fuel-air ratio and ignition timing are analyzed. Moreover, various performance data of the 20% HCNG and the original CNG engine are compared in the condition of 120 kPa and wide open throttle in load, showing the benefits of the hydrogen enriched. NOx emission is focused in this article when discussing the exhaust emissions. As we know, HCs and CO are also very important harmful emissions of engine. However, a lot of research has been done on the exhaust emissions including HC and CO at home and abroad, the author included. According to previous study, with hydrogen blended in, the combustion speed of the mixture increases, fuel-air ratio can be even lower, carbon content of the mixture reduces greatly, leading to a great reduction of HC and CO emissions and effectively improve the trade-off relation between NOx and HC emissions [11]. Therefore, NOx emission is selected to represent the emission performance of the engine because NOx emission is the most important and hardest part to meet more strict emission regulations including Euro VI. Fig. 1 shows performances of Torque, BSFC (Brake specific fuel consumption) and BSNOx (Brake specific NOx emission) verses Equivalent fuel-air ratio (4) and ignition timing under the condition of 800 r/min in speed and 90 kPa in MAP. The equivalent fuel-air ratio 4 varies from 0.720 to 0.840, while the ignition advance changes from 5 to 25 . From the figure we can easily find that all performance parameters of the engine change obviously along with the change of 4 and ignition timing. As for the torque, the equivalent fuel-air ration 4 reflects how rich the concentration of the mixture is. When keeping the MAP staying the same, as 4 increases, more fuel

Table 2 e Range of experiment conditions. Item Engine speed/(r/min) MAP/(kPa) Fuel-air ratio Ignition timing/CA BTDC

Range 800e2300 35e220 0.6e0.85 5e35

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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the maximum torque. As to the emissions, the increase of the fuel-air ratio and the ignition advance both will lead to the increasing of the burning temperature, which plays a key role in the formation of NOx, bringing the result that the NOx emission increases sharply. And when it comes to the economics, we use the equivalent natural gas flow under unit power to describe, which means the equivalent natural gas flow compared to current fuel in low calorific value (BSFC). With equivalent fuel-air ratio 4 increasing, the mixture becomes relative richer, the thermal efficiency of the engine decreases, and incomplete burning increases, hence the natural gas mass flow increases. And the effects brought by ignition timing seem the same as that to the torque. Moreover, the best ignition timing for torque is just also the best timing for the lowest natural gas mass flow. Fig. 2 shows the comparison of the torque, equivalent natural gas mass flow and NOx emission verses engine speed between natural gas and 20% HCNG under the conditions of respective 120 kPa and wide open throttle in MAP. Under each condition, we choose the best equivalent fuel-air ratio 4 and ignition timing referred to the calibration results for the fuel of HCNG, while for natural gas, we apply the original data for CNG engine from the factory. From the figure we can see that compared to natural gas, when we add some hydrogen, in most conditions, the performance of the engine becomes much better. The specific 4 and ignition timings for HCNG and CNG under the condition of 120 MPa are shown in Table 3. From Table 3 we can see, compared to CNG, when ensuring

CNG HCNG

400 200 800

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2200

1000

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2200

5000

BSFC/

g/(kW.h)

NOx/(ppm)

Torque/(N.m)

CNG and 20%HCNG, MAP=120kPa 600

0 800 20 10 0 800

1400 1600 engine speed/(r/min)

600

BSNOx/(ppm)

800

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1200

1400

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2400

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1400

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2400

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1400 1600 1800 Engine speed/(r/min)

2000

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2400

5000

g/(kW.h)

will come into the cylinder per cycle, thus increasing the calorific value of the mixture. As a result, the output torque increases. However, when 4 increases into a certain value, the output torque increases slowly and even decreases instead. That is because the mixture becomes relatively richer (in fact the mixture is still lean) that the combustion becomes incompletely. Ignition timing also plays an important role in combustion. From the figure we can see that with the ignition advance increasing, the output torque first increases and then decreases. That is, there is a best ignition timing that makes

CNG HCNG

800

BSFC/

Fig. 1 e Torque, BSFC and BSNOx of the engine verses ignition timings under different Equivalent fuel-air ratios, engine speed of 800 rpm, engine MAP of 90 kPa.

Torque/(N.m)

CNG and 20%HCNG, wide open throttle 1000

0 800 40 20 0 800

Fig. 2 e Torque, NOx emission and BSFC of the engine verses engine speed for CNG and 20% HCNG, engine MAP of 120 kPa and wide throttle. MBT ignition timing.

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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Table 3 e Fuel-air ratio and ignition timings for CNG and HCNG under condition of 120 MPa. Engine speed/(r/min)

800 1000 1200 1400 1600 1800 2000 2200

CNG

HCNG

Fuel-air ratio

Ignition timing

Fuel-air ratio

Ignition timing

0.823 0.822 0.764 0.704 0.693 0.683 0.684 0.686

13 15 17 20 21.8 22 23.9 25

e 0.73 0.72 0.695 0.679 0.659 0.64 e

e 15 17 21 22 24 28 e

output torque remaining the same with the original machine, the fuel-air ratio 4 decreases significantly, while the ignition timing increases slightly. As former analysis, lower fuel-air ratio will sharply lower down the combustion temperature of the engine, so that the NOx emission is greatly reduced, which is the theory basis for HCNG engine to reduce NOx emissions. As to the external characteristics, with 20% HCNG as the fuel, the torque can remain almost the same as the original CNG engine, while natural gas mass flow and NOx emission decrease significantly, especially in low speed condition. The exact performance data for wide open throttle condition are shown in Table 4. In Table 4 we find that under condition of wide open throttle, after hydrogen enriched, the equivalence fuel-air ratio decreases about 0.03e0.06 in all speed, BSFC lowers for about 1e6%, and the NOx emission decreases for an amazing 50% or so.

Regression analysis As we know, engine's operation condition can be basically determined by a pair of state parameters (speed and MAP) and a pair of control parameters (equivalent fuel-air ratio and ignition timing). Based on experimental data for calibration, we try to find the mathematical relationship between the performance of the engine and the above-mentioned parameters with different regression methods to build a useful mathematical model of certain accuracy. Taking advantage of the above calibration data, we select the above-mentioned 4 parameters as independent variables, and three performance parameters as dependent variables.

The output torque (N m) is to describe the dynamic performance, the equivalent mass flow of natural gas under unit power (g/(kW h)) (marked as BSFC) is to describe the economic performance and the NOx emission (g/(kW h)) (marked as BSNOx) is to describe the emission performance. Among a total of 445 groups of effective data, we pick out a random sample of 59 sets of data as regression testing data, and the remaining 386 groups of data are used to build the mathematical model with three methods respectively, the quadratic polynomial, neural network and support vector machine (SVM). To ensure the operation conditions for prediction can cover the full conditions of the engine, the testing data are selected based on the engine speed and MAP. The parameters of these testing data are shown in Table 5. Before the regression fitting, as the 4 independent variables are of different ranges, to get rid of the impact of the different ranges of the independent variables, all the independent variables should firstly be normalized into the same range of [0,1]. We use formula 1 to do the normalization. x¼

x  xmin xmax  xmin

(1)

Quadratic polynomial method Quadratic polynomial method is a widely used method of nonlinear fitting. The MATLAB function, “rstool”, which is especially used for multiple quadratic polynomial fitting, is used in this article to fit the calibration data above. The function “rstool” provides four types of quadratic function: “Linear”, in which the regression function includes only the constant and linear terms; “purequadratic”, in which the regression function includes constant, linear and pure quadratic terms; “interaction”, in which the regression function includes constant, linear and cross terms; “quadratic”, in which the regression function includes only the cross and pure quadratic terms. All the four types of function are respectively used to do the fitting and it is concluded that the type of “interaction” and “purequadratic” can get better results. The training and testing results with the two types are shown in Figs. 3e5. We can see from above figures that when using multiple quadratic polynomial method to predict the torque, the accuracy can be within 10%, which can be considered very accurate. While for equivalent CNG mass flow, the accuracy drops to 20%, which can still be considered relatively accurate. As to the NOx emissions, however, the prediction error can be

Table 4 e Comparison between 20% HCNG and CNG for equivalence ratio (F), BSFC and BSNOx in wide throttle condition. Speed/r/min

4 CNG

4 HCNG

D4

BSFC CNG/g/(kW h)

BSFC HCNG/g/(kW h)

Reduce/%

NOx CNG/ppm/kW

NOx HCNG/ppm/kW

Reduce/%

800 1000 1200 1400 1600 1800 2000 2200 2300

0.843 0.819 0.722 0.698 0.683 0.683 0.683 0.684 0.683

0.781 0.774 0.700 0.670 0.636 0.650 0.660 0.640 0.640

0.062 0.045 0.022 0.028 0.047 0.033 0.023 0.044 0.043

207.20 203.21 198.37 193.82 207.24 199.07 214.47 210.79 223.61

196.83 197.06 193.63 191.26 193.18 199.35 203.83 209.15 209.66

5.01 3.02 2.39 1.32 6.78 0.14 4.96 0.78 6.24

97.46 57.80 14.65 11.01 6.87 6.98 6.81 6.28 7.01

45.76 28.68 12.34 8.61 4.05 3.87 5.11 3.22 3.70

53.05 50.38 15.73 21.79 41.03 44.53 25.02 48.75 47.25

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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Table 5 e Experiment conditions for 59 pairs of prediction data. No. Speed/(r/min) MAP/kPa Fuel-air ratio Ignition timing No. Speed/(r/min) MAP/kPa Fuel-air ratio Ignition timing 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

800 800 800 800 800 800 800 800 800 800 800 800 800 800 800 800 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 1200 1200 1200 1400

60 60 60 60 60 60 60 60 90 90 90 90 90 90 90 90 90 70 70 70 100 100 100 140 140 140 70 70 70 90

0.694 0.694 0.694 0.694 0.775 0.775 0.775 0.775 0.775 0.775 0.775 0.8 0.8 0.8 0.84 0.84 0.84 0.77 0.77 0.77 0.749 0.775 0.775 0.729 0.729 0.729 0.78 0.78 0.78 0.719

14 16 18 20 12 15 17 20 11 14 16 16 18 20 5 8 12 14 16 18 20 13 15 13 15 17 14 16 18 23

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

1400 1400 1400 1400 1400 1600 1600 1600 1600 1600 1600 1800 1800 1800 1800 1800 1800 1800 2000 2000 2000 2000 2000 2200 2200 2200 2200 2200 2200

90 90.6 140 140 140 80 80 80 180 180 180 80 80 80 80 80 150 150 80 80 180 180 180 70 70 70 140 140 140

0.689 0.689 0.698 0.698 0.698 0.68 0.68 0.68 0.67 0.67 0.67 0.65 0.65 0.65 0.65 0.65 0.64 0.64 0.649 0.649 0.64 0.64 0.64 0.618 0.618 0.618 0.605 0.605 0.605

25 23 21 23 24 20 22 24 22 24 26 21 23 25 27 29 26 28 25 27 23 25 27 28 30 34 24 27 30

Torque(N.m) 12

BSFC

INTER PURE

g/kw.h

25

10

INTER PURE

20

relative error/%

relative error/%

8

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5

2

0

15

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Fig. 3 e The training and testing results of torque with “interaction” and “purequadratic”.

Fig. 4 e The training and testing results of BSFC with “interaction” and “purequadratic”.

as large as more than 100%, which means accurate mathematical relationship fails to be established effectively.

number of neurons in each layer, the best structure of the neural network for the data is finally found out. Any nonlinear model can be approximated by a three-layer neural network model in theory [25]. The fitting performance of the model is closely associated with the structure of the model. The more complex the model is, the better the performance will be. After times of training, simulation and adjustment, the 4-layer neural network model is finally decided.

Neural network method Neural network method has its unique advantages in solving nonlinear regression problems. Taking advantage of the MATLAB neural network toolbox, we select the three-layer BP neural network to fit the calibration data. After adjusting the

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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BSNOx

g/kw.h

180

INTER PURE

160

relative error/%

140 120 100 80 60 40 20 0

0

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30

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60

Fig. 5 e The training and testing results of BSNOx with “interaction” and “purequadratic”. Three neural 4-layer network models of 4-inputs-1output are respectively built to fit the mathematical relationship between the three performance parameters and

the independent variables. In accordance with the Kolmogorur theorem [26], the number of the input layer is 4, that of the output layer is 1, and the number of the hidden layers can be calculated to be around 4e10. To get the best neural network model, the exhaustive method is used. All possible neural network models are built and test to compare. The best model is finally picked out according to their testing results. In the process of building the neural network model, as results of the models are closely related to the initial value, which is randomly generated by the computer in the toolboxes of MATLAB, results differs with each test even for the same model structure. The results always change because the neural network model may be caught in the local minimum value all the time. Moreover, sometimes the results would be completely useless due to the phenomenon of over-learning [27]. In order to get a stable and reliable model, oft-repeated training and testing are conducted for each possible neural network model. From these results we can pick these adequate ones. Tables 6 and 7 give some of the training and testing results among the proper ones.

Table 6 e Testing results for BSFC with NN model verses different structures. Hidden layer 1

4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10

Hidden layer 2

4 4 4 6 6 6 8 8 8 4 4 6 6 6 8 8 8 8 4 4 4 6 6 6 8 8 8 8 4 4 4 6 6 6 8 8 8

Average error/%

3.70 4.52 3.60 3.33 3.73 3.41 13.98 4.84 3.67 4.71 2.66 2.89 4.25 4.68 7.16 3.60 6.15 2.92 3.56 3.60 5.80 6.60 3.60 3.65 2.98 5.88 4.76 3.87 2.66 5.54 3.54 2.68 2.66 4.31 6.80 6.94 4.19

Maximum error/%

53.55 74.42 9.01 9.00 10.95 12.03 38.86 11.14 8.38 14.00 7.55 10.78 53.08 14.57 33.96 9.00 86.33 12.18 8.48 9.00 21.16 14.90 9.00 16.36 12.86 16.72 17.30 46.27 7.55 37.71 11.86 29.89 7.55 11.36 194.84 56.60 23.55

Error distribution 0e5%

5e10%

10e20%

20e30%

30%above

52 43 43 48 41 46 20 32 39 35 55 50 46 35 39 43 45 47 40 43 34 24 43 46 54 28 39 47 55 40 44 52 55 38 47 31 39

5 12 16 11 16 10 4 24 20 22 4 7 11 20 6 16 9 10 19 16 13 22 16 11 1 19 9 10 4 13 14 6 4 19 8 19 15

0 3 0 0 2 3 9 3 0 2 0 2 0 4 5 0 2 2 0 0 10 13 0 1 4 10 7 1 0 3 1 0 0 2 1 5 4

1 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

1 1 0 0 0 0 19 0 0 0 0 0 2 0 9 0 3 0 0 0 1 0 0 1 0 2 4 1 0 3 0 1 0 0 3 3 0

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Table 6 shows the forecasting error of the equivalent CNG mass flow by different models. We can see that the average relative error can be controlled within 10%, and the relative error of the prediction mainly concentrates in the range of 0e7%. Table 7 shows the same results for NOx emissions. The relative error of the prediction for NOx is larger than the equivalent CNG mass flow, which is much alike the quadratic polynomial method. However, the average relative error is still within 20%, while that by quadratic polynomial method can be as much as 100%. Among these trained models, the best structure of the model is determined, from which more detailed testing results are shown. Figs. 6 and 7 tell us the relative error of the training and the prediction results on output torque by the neural network model. This neural network model is made of three layers. The number of neuron in each layer is 4, 8, 1. And the final correlation coefficient of the model is 0.99707. From the figures we can see the model can accurately predict the output torque, with a prediction accuracy of 9%. Different model structures are chosen for other performances. For the equivalent natural gas flow, the neuron numbers of the three neuron layers are 6, 8, 1, with the final correlation coefficient being 0.92411. And the same result for NOx emissions is 0.99371, with the same model structure as

for the equivalent natural gas flow. And the training and prediction results are shown in Figs. 8 to 11. From Figs. 8 to 11 we can see the prediction accuracy of the neural network model for the equivalent natural gas flow can also be very high, with the relative error within 10%. The relative error for NOx emissions is still the worst one, mainly within 40%, not unacceptable, however.

The support vector machine (SVM) Significant attention has been paid to support vector machine (SVM) on machine learning in recent years, which is widely used in classification, regression analysis and other aspects. In this article we apply the libSVM program written by Professor Lin Chih-Jen from Taiwan University [28], and the expansion program written by Faruto and his group [29]. Three methods, Grid parameters optimization, particle swarm optimization (PSO) and genetic algorithm (GA), are respectively adopted in Faruto's program to optimize the best parameters for the SVM model. Finally PSO method has been chosen to obtain the SVM model. The biggest characteristic of SVM method in solving nonlinear problems is to use a nonlinear mapping function (which is called kernel function) to map related data to higher dimensional linear space. Then the linear regression can be done in the high-dimensional space. Therefore, the type of the

Table 7 e Testing results for BSNOx with NN model verses different structures. Hidden layer 1

4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10

Hidden layer 2

4 6 6 8 8 10 10 4 6 6 8 8 8 10 10 4 6 6 8 8 10 10 4 4 6 6 8 8 10 10

Average error/%

11.89 13.43 14.83 14.33 13.13 15.56 16.99 20.35 10.11 13.65 15.79 21.02 13.03 15.16 16.51 12.40 8.70 13.90 14.24 15.66 19.89 10.98 13.85 11.40 9.30 9.58 11.55 14.11 12.42 14.48

Maximum error/%

47.60 67.67 51.06 52.31 80.14 105.71 100.77 194.25 34.54 56.44 79.69 288.15 176.03 105.36 106.99 64.94 36.98 77.51 55.85 58.04 234.19 27.60 104.12 57.44 36.70 41.40 43.19 66.07 60.50 49.13

Error distribution 0e5%

5e10%

10e20%

20e30%

30% above

19 20 17 18 20 12 12 15 20 13 15 16 25 11 18 19 22 24 20 11 19 13 16 18 22 27 11 19 17 19

14 11 11 12 15 12 20 17 11 18 18 12 8 14 10 16 22 9 15 11 5 16 20 14 18 8 17 10 20 9

10 11 7 7 11 11 10 8 13 11 8 6 11 13 8 8 5 8 4 12 11 16 6 13 9 12 18 5 9 10

2 3 4 1 3 6 3 3 4 2 3 5 7 7 4 5 2 2 3 3 5 4 2 3 3 2 4 6 3 3

14 14 20 21 10 18 14 16 11 15 15 20 8 14 19 11 8 16 17 22 19 10 15 11 7 10 9 19 10 18

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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BSFC /(g/(kW.h))-training

Touque(N.m)-training 50

14

45

12

40

10

30

relative error/%

relative error/%

35

25 20 15

8

6

10

4

5 0

0

50

100

150

200

250

300

350

2

400

Fig. 6 e The relative error of the training results on output torque by the neural network model.

0 0

10

20

30

40

50

60

Fig. 9 e The relative error of the prediction results on BSFC by the neural network model. Touque/(N.m)-prediction 10 BSNOx /(g/(kW.h))-training

8

450

7

400

6

350

5 relative error/%

relative error/%

9

4 3 2 1 0

300 250 200 150 100

0

10

20

30

40

50

60

50

Fig. 7 e The relative error of the prediction results on output torque by the neural network model.

0

0

50

100

150

200

250

300

350

400

Fig. 10 e The relative error of the training results on BSNOx by the neural network model. BSFC /(g/(kW.h))-training 70 BSNOx /(g/(kW.h))-prediction 80

60 70 60

40

relative error/%

relative error/%

50

30

50 40 30

20 20

10

0

10

0

50

100

150

200

250

300

350

400

Fig. 8 e The relative error of the training results on BSFC by the neural network model.

0

0

10

20

30

40

50

60

Fig. 11 e The relative error of the prediction results on BSNOx by the neural network model.

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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kernel function and its parameters plays a decisive role in the performance of the SVM model. By means of the libSVM program written by Lin Zhilin from Taiwan University, we decide the RBF function as the kernel function, which is the most widely used in regression analysis, with the expression as follows:

Two parameters C and g should be determined in this function. C represents the error penalty of the model, while g describes the width of the kernel function. These two parameters are the most important when building the SVM model [30]. After comparing the three methods to get the two parameters for the SVM model, we finally decide to choose the PSO method. PSO method is a kind of stochastic optimization method based on species. Cluster behavior of insects, herd, birds and fish is mimicked in this method. In these clusters every member learns from their own and the others' experience to adjust their own behavior so that they can cooperate with each other more efficiently [31]. According to the PSO optimization program written by Faruto, we can get the best value of the parameters, C and g. Then the proper libSVM model can be built to do the prediction. Figs. 12 to 14 argues the training and prediction results for output torque by the libSVM model. Figs. 15 to 17 tells us the training and prediction result for equivalent natural gas flow. And Figs. 18 to 20 indicates the same results for NOx emissions. From the figures we can conclude that the SVM method has quite high accuracy. Compared to the neural network method, the prediction accuracy for equivalent natural gas flow can also be controlled within 10%. However, the NOx emission prediction is still relatively poor, only within 40% or so. Table 8 gives the comparison of the performance prediction with the three different regression methods. It is concluded that SVM method shows the best performance in various aspects including the maximum relative prediction error (Err_max), the average prediction error (Err_ave), and the range of the relative prediction error.

Training result for torque 900

600

500

Torque /(N.m)

(2)

700

400

300

200

100

0

10

20

30

40

50

60

Fig. 13 e The prediction results for output torque by the libSVM model.

Relative error for torque prediction

10 9 8 7

relative error /(%)

K(u,v) ¼ exp(rjuvj^2)

experimental data regression data

prediction result for torque

6 5 4 3 2 1 0

0

10

20

30

40

50

60

Fig. 14 e Relative error for torque prediction by the libSVM model.

experimental data regression data

Training result for BSFC

800

800

experimental data regression data

700

700

600

BSFC /(g/(kW.h))

Torque /(N.m)

600 500 400 300

400 300

200 100 0

500

200 0

50

100

150

200

250

300

350

Fig. 12 e The training results for output torque by the libSVM model.

400

100

0

50

100

150

200

250

300

350

400

Fig. 15 e The training results for BSFC by the libSVM model.

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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18

experimental data regression data

320

14

BSNOx /(g/(kW.h))

BSFC /(g/(kW.h))

experimental data regression data

16

300 280 260 240 220

12 10 8 6 4

200 180

Prediction result for BSNOx

Prediction result for BSFC

340

2 0

10

20

30

40

50

0

60

Fig. 16 e The prediction results for BSFC by the libSVM model.

0

10

20

30

40

50

60

Fig. 19 e The prediction results for BSNOx by the libSVM model.

Relative error for BSNOx prediction

60

Relative error for BSFC prediction

9

50

8 Relative error/(%)

Relative error/(%)

7 6 5 4 3

40

30

20

10

2 0

1 0

0

10

20

30

40

50

60

Fig. 17 e Relative error for BSFC prediction by the libSVM model.

Training result for BSNOx

25

experimental data regression data

BSNOx /(g/(kW.h))

20

15

10

5

0

0

50

100

150

200

250

300

350

Fig. 18 e The training results for BSNOx by the libSVM model.

400

0

10

20

30

40

50

60

Fig. 20 e Relative error for BSNOx prediction by the libSVM model.

From all the above results, it can be sum up that the four independent variables and the three dependent variables do have complex nonlinear relationship. By applying simple quadratic function the relationship can not be effectively forecast. The neural network method and SVM method show huge superiority compared to the quadratic function method. Especially on the relationship for output torque and equivalent natural gas flow, the two methods can both ensure a high prediction accuracy. In a word, a rough prediction for the engine calibration experiment is feasible by means of neural network and SVM methods. When comparing neural network and SVM method, the latter can successfully avoid getting caught in the local minimum value and over-learning because of its theory, showing a greater advantage over the former.

Conclusion 1) The calibration experiment results indicate that after adding 20% hydrogen in volume into natural gas, the

Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204

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Table 8 e Comparison of three regression methods in performance prediction. Title method

Err_max/% Err_ave/% No._0e5% No._5e10% No._10e20% No._20e30% No._30% above No._total

Torque

BSFC

BSNOx

QP

NN

SVM

QP

NN

SVM

QP

NN

SVM

10.7143 2.4172 51 7 1 0 0 59

9.05 2.48 49 10 0 0 0 59

9.16 1.98 52 7 0 0 0 59

20.98 6.04 26 26 5 1 1 59

12.18 2.92 47 10 2 0 0 59

8.24 2.53 51 8 0 0 0 59

88.48 54.83 2 5 2 0 50 59

79.69 15.79 15 18 8 3 15 59

59.84 15.25 19 11 9 3 17 59

Err_max: maximum relative error of the prediction; Err_ave: average relative error of the prediction; No._***: the number of sample located in ***.

equivalent fuel-air ratio of the mixture can be decreased. When the ignition timing is adjusted, on the premise of keeping the output torque not decreasing, the equivalent natural gas flow can be significantly reduced, as well as NOx emissions. Taking the condition of wide open throttle as an example, after hydrogen enriched, the equivalence fuel-air ratio decreases about 0.03e0.06 in all speed. As a result, BSFC lowers for about 1e6%, and the NOx emission decreases for an amazing 50% or so. 2) Based on the regression analysis of the calibration data of the HCNG engine, there is complex nonlinear relationship between the independent variables, including engine speed, MAP, equivalent fuel-air ratio and ignition timing, and the dependent variables, including the output torque, the equivalent natural gas flow and the NOx emissions. Compared to conventional quadratic function method, a more accurate mathematical model can be got by using the neural network and SVM methods. The prediction accuracy for output torque and equivalent natural gas can be within 10%, while the NOx emission prediction accuracy can be around 30%, which is enough to guide the forecast for the calibration of the engine. As a widely applied method, SVM shows greater potential over neural network because it can avoid the phenomenon of over-learning and the problem of local minimum value. 3) From the prediction results we can conclude the relationship between the NOx emissions and the parameters of the engine should be more than complex. Besides normal SVM method, some improved SVM methods are fully studied and developed, such as LSSVM (least squares SVM), BTSVM (binary tree SVM), LSVM (Lagrangian SVM), NLSVM (Finite Newton Lagrangian SVM), etc. These improved methods may achieve more accurate results. More efforts should be done to find out a more effective model to describe their relationship.

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Please cite this article in press as: Huang Y, Ma F, Intelligent regression algorithm study based on performance and NOx emission experimental data of a hydrogen enriched natural gas engine, International Journal of Hydrogen Energy (2016), http://dx.doi.org/ 10.1016/j.ijhydene.2016.03.204