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Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures
Alexandria Engineering Journal (2016) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures Erdi Tosun a,*, Kadir Aydin b, Mehmet Bilgili b a b
Department of Mechanical Engineering, C¸ukurova University, Adana, Turkey Department of Automotive Engineering, C¸ukurova University, Adana, Turkey
Received 15 June 2016; revised 12 August 2016; accepted 18 August 2016
KEYWORDS Diesel engine; Biodiesel; Alcohol; Linear regression; Artificial neural network
Abstract This study deals with usage of linear regression (LR) and artificial neural network (ANN) modeling to predict engine performance; torque and exhaust emissions; and carbon monoxide, oxides of nitrogen (CO, NOx) of a naturally aspirated diesel engine fueled with standard diesel, peanut biodiesel (PME) and biodiesel-alcohol (EME, MME, PME) mixtures. Experimental work was conducted to obtain data to train and test the models. Backpropagation algorithm was used as a learning algorithm of ANN in the multilayered feedforward networks. Engine speed (rpm) and fuel properties, cetane number (CN), lower heating value (LHV) and density (q) were used as input parameters in order to predict performance and emission parameters. It was shown that while linear regression modeling approach was deficient to predict desired parameters, more accurate results were obtained with the usage of ANN. Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction In today’s world, high thermal efficiency of diesel engine makes them attractive and popular to use. Conventionally, compression ignition engines operate with diesel fuel derived from crude oil [1]. In the late 1970s and early 1980s, an energy crisis occurred over world due to the depletion of fossil based fuels [2]. Therefore, scientists have been working on this issue for many years. Recently, usage of alternative fuels in internal combustion engines has been an important research area. In * Corresponding author. E-mail address: [email protected] (E. Tosun). Peer review under responsibility of Faculty of Engineering, Alexandria University.
this respect, vegetable oils, and alcohols such as ethanol and methanol have been investigated to be able to use in internal combustion engines [3]. Requirement of little or no engine modification makes those alternatives remarkable. There are lots of study about fuel properties, performance and emission characteristics of an internal combustion engine operated with various alternative fuels [4–10]. Determination of performance and emission characteristics of an internal combustion engine is complex, time consuming and costly [11]. Therefore, in order to eliminate these disadvantages and complexities, performance and emission of an engine can be modeled with using artificial neural network (ANN). An ANN system works as a biological neuron. Neurons receive input from the source, perform a non-linear operation, and predict final output [12]. In recent years, parallel to devel-
http://dx.doi.org/10.1016/j.aej.2016.08.011 1110-0168 Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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opments in computer technology, ANN has been applied to many problems in automotive engineering [13–25]. In this paper, firstly, fuel properties and experimental results of diesel engine fueled with diesel, biodiesel and biodiesel-alcohol mixtures were obtained from another work of author [6]. Standard diesel, peanut methyl ester as biodiesel and methanol-ethanol-butanol as alcohols were utilized in the experiments. Then LR method was applied to experimental data to predict performance and emission data (torque, CO, NOx). It was seen that regression model approach was deficient to predict desired parameters. Therefore, ANN approach was used and seen that more accurate results were obtained than LR. There are lots of studies about internal combustion engines for prediction of performance and emission results. The distinctive property of this paper is using alcohol mixtures with biodiesel as fuel and using only fuel properties (density, cetane number, lower heating value) of these mixtures and engine speed (rpm) as input parameters in ANN structure for estimation. 2. Material and methods
Fuel properties and measurement devices.
Property
Device
Cetane Number Lower Heating Value (LHV) Density
Zeltex ZX440 IKA-Werke C2000 bomb calorimeter Kyoto electronics DA-130
operated for 15 min with diesel fuel to reach the operation temperature. Accuracy of the measurements is given in Table 4. 2.3. Linear regression Regression analysis is a method to find a functional relationship between dependent variables (response) and independent variables (predictor) [27]. In LR, the function is linear equation and dependent variable can be expressed as a function of independent variable(s) in the form of [28]: Y ¼ b0 þ b1 X1 þ b2 X2 þ þ bn Xn
2.1. Fuel properties determination
where Y is dependent variable, b0 to bn are equation parameters for linear relation and X1 to X2 are independent variables.
The fuels and fuel-alcohol mixtures used in experiments and the devices used to determine the fuel properties are demonstrated in Table 1 and 2, respectively. Cetane number is a measure of ignition characteristics of a diesel engine. It is an important parameter to determine quality of diesel fuel. Heating value is energy released when the fuel is burned. It is very important parameter to carry out efficiency and work calculations [26]. Density can be defined as mass per unit volume. The measurement devices are shown in Fig. 1. 2.2. Experimental set-up Engine performance experiments were conducted on a four cylinder, four stroke, naturally aspirated, direct injection diesel engine. Technical specifications of the engine are given in Table 3. Photographic view and schematic representation of the diesel engine are shown in Fig. 2. Engine gives 89 kW maximum power at 3200 rpm engine speed and has 295 Nm maximum torque at 1800 rpm engine speed. The engine was
Table 1 [6].
Table 2
Fuels and their mixtures with alcohols by percentage
Fuel
Diesel
Peanut Methyl Ester (PME) (%)
Ethanol +Peanut Methyl Ester (EME) (%)
Methanol +Peanut Methyl Ester (MME) (%)
Butanol +Peanut Methyl Ester (BME) (%)
Diesel Peanut biodiesel Ethanol Methanol Butanol
100 –
– 100
– 80
– 80
– 80
– – –
– – –
20 – –
– 20 –
– – 20
2.4. Artificial neural networks Human brain is highly complex, nonlinear and parallel computer [29]. Source of inspiration of ANN is the basic structure of human brain [30]. An ANN is composed of a number of simple and highly interconnected processing elements as neurons in brain. Model can be defined as a black box consisting of a series of equations for the calculation of output with use of given input values [31]. The block diagram of a model of neuron is shown in Fig. 3 on the basis of designing an ANN [29]. Haykin [29] stated that mathematically, we can describe a neuron k by the following equations: uk ¼
m X wkj xj j¼1
yk ¼ uðuk þ bk Þ Bias, denoted by bk, has the effect of increasing or lowering the net input of the activation function. x1, x2, . . ., xm are the inputs; wk1, wk2, . . ., wkm are the weights of the neuron k; uk is the linear combiner output due to input signals; uð:Þ is the activation function; yk is the output signal of the neuron. Backpropagation algorithm is commonly used as a learning algorithm of ANN in the multilayered feedforward networks. In backpropagation networks, data are processed from the input layer to the hidden layer then to the output layer. Finding optimal weights is the purpose in order to obtain close values to targets as an output [28]. In this study, Levenberg-Marquardt (LM) learning algorithm was used to adjust the weights in the multilayered feedforward networks. In hidden layer, logistic sigmoid nonlinear function (logsig) and in output layer, linear transfer function (purelin) were used as an activation function.
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine
Figure 1
Table 3
(a) Zeltex ZX440, (b) IKA-Werke C2000 bomb calorimeter and (c) Kyoto electronics DA-130.
Technical specifications of the test engine.
Brand Model Configuration Type Displacement Bore Stroke Power Torque Oil cooler Air cleaner Weight
3
Mitsubishi Canter 4D34-2A In line 4 Direct injection diesel with glow plug 3907 cc 104 mm 115 mm 89 kW @ 3200 rpm 295 Nm @ 1800 rpm Water cooled Paper element type 325 kg
2.5. Data specification In this study, performance and emission tests were conducted in a direct injected diesel engine fueled by diesel, PME, EME, MME and BME [6]. Fig. 4 and Table 5 show performance and emission curves and fuel properties of each fuel, respectively. As seen from the following figures that, alcohol additions into
Figure 2
biodiesel generally improve engine performance and reduce emissions. Extra oxygen content of alcohols increases number of rich mixture regions in cylinder and causes to enhance combustion [6]. 3. Results and discussions 3.1. LR results SPSS is software used for statistical analysis. It can be used to relate independent variables with dependent variables in LR model. The results of LR analysis are given in Table 6. Figs. 5–7 present the comparison between experimental and predicted data. Firstly, 80% of experimental data was used to constitute regression equation. Then, remaining randomly selected 20% of data was tested with the use of equation. In the following figures, a vertical line separates data used to constitute regression equation and data used to test the equation performance. Selecting predictor variables is the most important issue in order to define best prediction equation in regression method [28]. On the other hand, supplied number of data to obtain
(a) Photographic view and (b) schematic representation of the engine test rig.
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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E. Tosun et al. Table 4
Accuracy of the measurements.
Property
Accuracy
Engine speed Torque Carbon monoxide Nitrogen oxides Cetane number Density
±2 rpm ±2% ±10 ppm ±1 ppm 3% ±0.001 g/cm3
regression equation is another issue. Using much more data to constitute equation will increase prediction performance. It was clearly seen from the figures that, LR modeling approach was not enough to predict data accurately. Best agreement was obtained for CO prediction between experimental and predicted results with usage of LR. 3.2. ANN results Neural Network toolbox of MATLAB software was used for ANN model. The main structure of ANN is shown in Fig. 8.
Figure 3
Figure 4
Block diagram of model of a neuron.
(a, b) Performance and (c, d) emission curves [6].
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine Table 5
Fuel Properties.
Property
Diesel
PME
MME
EME
BME
Cetane Number Heating Value (kJ/kg) Density (kg/m3)
59.5 45,856 837
53.21 38,708 880
60.38 38,727 855
57.24 38,732 873
69.51 38,979 874
Table 6
5
There were an input layer, hidden layer and output layer. Input layer consists of 4 neurons and output layer consists of 1 neuron (all output parameters analysed separately). Neuron number of hidden layer was determined by trial and error method. It means that there was not a certain number of hidden layer neuron.
Results of linear regression.
Output Parameter
Equation
R2
Torque CO NOx
Torque = 543,357 0,102 * (rpm) 0,239 * (CN) + 0,05 * (LHV) 0,448 * (Density) CO = 827,513 + 0,257 * (rpm) 4,194 * (CN) + 0,010 * (LHV) + 0,685 * (Density) NOx = 4621,616 0,611 * (rpm) + 8,886 * (CN) 0,024 * (LHV) 2,702 * (Density)
0.726 0.898 0.919
Figure 5
Comparison between experimental and predicted data for torque.
Figure 6
Comparison between experimental and predicted data for CO.
Figure 7
Comparison between experimental and predicted data for NOx.
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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Figure 8
Figure 9
The main structure of ANN.
Comparison between actual and predicted data for torque.
Learning algorithm and ANN structure are given in Table 7 for each parameter. Rpm, CN, LHV and q were used as input neuron to predict torque in the network. Prediction equation of torque is given below: Torque ¼ 7; 9755 F1 þ 27; 0340 F2 93; 3236 F3 þ 96; 4421 F4 þ 5; 7018 F5 24; 3317 F6 þ 30; 9032 F7 þ 117; 7479 Sigmoid function was used to calculate each F value. Fi ¼
1 1 þ eEi
Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i
Rpm, CN, LHV and q were used as input neuron to predict CO in the network. Prediction equation of CO is given below: CO ¼ 47; 4444 F1 191; 1111 F2 142; 2222 F3 þ 32; 5236 F4 þ 388; 4580 F5 þ 83; 6667 F6 þ 99; 1133 F7 188; 3333 F8 148; 1111 F9 þ 391; 2086 Sigmoid function was used to calculate each F value. 1 Fi ¼ 1 þ eEi Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i Rpm, CN, LHV and q were used as input neuron to predict NOx in the network. Prediction equation of NOx is given below:
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine
Table 7
Figure 10
Comparison between actual and predicted data for CO.
Figure 11
Comparison between actual and predicted data for NOx.
Table 9 Weight and bias values between input and hidden layer for CO prediction.
Learning algorithms and ANN structures.
Output Parameter
Learning Algorithm
ANN Structure
Hidden Layer Transfer Function
Output Layer Transfer Function
Torque
Levenberg– Marquardt Levenberg– Marquardt Levenberg– Marquardt
4-7-1
logsig
purelin
4-9-1
logsig
purelin
4-13-1
logsig
purelin
CO NOx
7
i
W1i
W2i
W3i
W4i
i
bi
1 2 3 4 5 6 7 8 9
6.3035 2.3156 16.4184 2.9497 0.5917 14.5499 7.1104 24.4875 39.7832
1.4295 0.7944 0.5451 0.7705 6.2499 0.0468 0.1483 2.1424 1.4110
0.3935 0.4867 1.0430 0.0647 0.0716 0.6872 115.7263 1.1956 1.3627
3.1566 30.3244 2.0841 14.6638 2.9751 2.3568 26.0755 15.1036 3.2666
1 2 3 4 5 6 7 8 9
80.4540 95.9337 148.1982 15.6436 154.8052 112.0702 143.7120 45.1141 97.9484
NOx ¼ 0; 5306 F1 þ 21; 6029 F2 0; 1043 F3 þ 50; 1298 F4 þ 453; 4412 F5 28 F6 þ 274; 7941 F7
Table 8 Weight and bias values between input and hidden layer for torque prediction.
þ 1; 9096 F8 þ 0; 3404 F9 þ 40; 7623 F10
i
W1i
W2i
W3i
W4i
i
bi
þ 49; 5639 F11 þ 48; 6242 F12 þ 48; 8891 F13
1 2 3 4 5 6 7
3.3305 4.3771 5.3781 4.3680 0.0228 2.4200 0.6102
97.6738 41.3274 97.5159 1.7581 5.1877 0.4794 0.3744
0.6992 39.9587 0.2034 0.1965 0.6637 0.3408 0.0480
29,3846 8,4538 11,4652 4,7418 30,2536 21,5033 6,2920
1 2 3 4 5 6 7
104.3517 114.1732 50.2300 33.8932 151.2201 5.4968 61.9001
þ 49; 0307 Sigmoid function was used to calculate each F value. Fi ¼
1 1 þ eEi
Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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E. Tosun et al. Table 10 Weight and bias values between input and hidden layer for NOx prediction. i
W1i
W2i
W3i
W4i
i
bi
1 2 3 4 5 6 7 8 9 10 11 12 13
12.5133 42.8641 19.3421 18.4471 3.8993 12.1997 6.5627 62.6611 1.4964 6.3243 15.1193 10.9933 1.7183
0.5029 0.1102 0.5260 0.0224 1.5954 0.1933 0.5023 0.5614 1.2212 0.0669 0.4025 0.3894 0.5865
0.3404 2.3541 1.8624 0.2913 0.2406 0.7819 0.1990 3.8057 0.1476 0.7237 1.6381 0.1040 0.4811
0.0696 0.4106 0.4460 3.1840 3.2165 4.3650 23.8889 5.5248 2.2288 10.0390 0.2028 1.1023 0.4410
1 2 3 4 5 6 7 8 9 10 11 12 13
159.0413 72.4009 90.5721 40.9710 185.5012 52.6386 95.3561 73.5869 138.0217 132.3532 67.4554 41.4348 46.9212
Table 11
Performance values of models. MAPE (%) LR
ANN
Torque Train Test
39.03 24.96
15.53 16.22
CO Train Test
11.25 11.9
9.11 3.56
NOx Train Test
21.61 22.1
18.96 9.63
Figs. 9–11 present the comparison between actual and predicted data. 80% of experimental data was used for training of neural network. Remaining random 20% of data was used for testing. As shown from above figure ANN modeling approach gives more accurate results than LR. Best agreement between experimental and predicted values was obtained for CO as in LR. 3.3. Performance comparison of LR and ANN Convergency of target and model output values can be observed with the use of Mean Error (BIAS), mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE). In this study, MAPE was used as performance parameter to compare models [28]. Weight and bias values between input and hidden layer for predictions are given in Tables 8–10. MAPE ¼
n 1X joi ti j 100 n i¼1 oi
where t is target value, o is output value and n is total number of data. Table 11 gives comparison of MAPE values of both training and test stage for LR and ANN.
4. Conclusions The purpose of this study was to predict some performance and emission data (torque, CO, NOx) obtained from diesel engine by using two different modeling methods. The developed model has three layer structures: one input layer with four neurons, one hidden layer (7 neuron for torque prediction, 9 neuron for CO prediction, 13 neuron for NOx prediction), and one output layer. Logistic sigmoid (logsig) and linear transfer function (purelin) were used in the hidden layer and output layer as an activation function, respectively. The learning algorithm used was Levenberg-Marquardt algorithm. To predict each parameter, rpm, CN, LHV and q of fuels were used as an input parameter. In LR model, R2 values were 0.726, 0.898 and 0.919 for torque, CO and NOx, respectively. When results of LR and ANN were compared, it was seen that ANN modeling approach gives more accurate results for all predicted parameters. It means MAPE values of ANN model were less than LR. Best correlation was obtained between input parameters and CO for both LR and ANN (MAPE values were 11.9 and 3.56, respectively). The models suggested in this paper were given to predict performance and emission of internal combustion engine. Since performing these tests is both costly and time consuming, by using fuel properties and engine speed as predictor parameters, experimental results can be estimated. But the performance of models can be enhanced by supplying more data in training section. With much more data the generalization capacity of models will increase. Eventually, using ANN modeling can be suggested to predict performance and emission of diesel engine operated with various fuels. Using ANN can avoid time consuming and costly experimental studies. References [1] W. Tutak, K. Lukacs, S. Szwaja, A. Bereczky, Alcohol–diesel fuel combustion in the compression ignition engine, Fuel 154 (2015) 196–206. [2] G. Tu¨ccar, E. Tosun, T. O¨zgu¨r, K. Aydin, Diesel engine emissions and performance from blends of citrus sinensis biodiesel and diesel fuel, Fuel 132 (2014) 7–11. [3] N. Yilmaz, M.V. Vigil, Potential use of a blend of diesel, biodiesel, alcohols and vegetable oil in compression ignition engines, Fuel 124 (2014) 168–172. [4] M.K. Balki, C. Sayin, M. Canakci, The effect of different alcohol fuels on the performance, emission and combustion characteristics of a gasoline engine, Fuel 115 (2014) 901–906. [5] E. Alptekin, M. Canakci, Determination of the density and the viscosities of biodiesel– diesel fuel blends, Renew. Energy 33 (2008) 2623–2630. [6] E. Tosun, A.C. Yilmaz, M. Ozcanli, K. Aydin, Determination of effects of various alcohol additions into peanut methyl ester on performance and emission characteristics of a compression ignition engine, Fuel 126 (2014) 38–43. _ ¸ , E. C¸ilg˘in, H. Aydin, Terebinth oil for biodiesel [7] C. Ilkilic production and its diesel engine application, J. Energy Inst. 88 (2015) 292–303. [8] H. Serin, M. Ozcanli, M.K. Gokce, G. Tuccar, Biodiesel production from tea seed (Camellia Sinensis) oil and its blends with diesel fuel, Int. J. Green Energy 10 (2013) 370–377. [9] N.M.S. Hassan, M.G. Rasul, C.A. Harch, Modelling and experimental investigation of engine performance and
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Alexandria University
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ORIGINAL ARTICLE
Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures Erdi Tosun a,*, Kadir Aydin b, Mehmet Bilgili b a b
Department of Mechanical Engineering, C¸ukurova University, Adana, Turkey Department of Automotive Engineering, C¸ukurova University, Adana, Turkey
Received 15 June 2016; revised 12 August 2016; accepted 18 August 2016
KEYWORDS Diesel engine; Biodiesel; Alcohol; Linear regression; Artificial neural network
Abstract This study deals with usage of linear regression (LR) and artificial neural network (ANN) modeling to predict engine performance; torque and exhaust emissions; and carbon monoxide, oxides of nitrogen (CO, NOx) of a naturally aspirated diesel engine fueled with standard diesel, peanut biodiesel (PME) and biodiesel-alcohol (EME, MME, PME) mixtures. Experimental work was conducted to obtain data to train and test the models. Backpropagation algorithm was used as a learning algorithm of ANN in the multilayered feedforward networks. Engine speed (rpm) and fuel properties, cetane number (CN), lower heating value (LHV) and density (q) were used as input parameters in order to predict performance and emission parameters. It was shown that while linear regression modeling approach was deficient to predict desired parameters, more accurate results were obtained with the usage of ANN. Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction In today’s world, high thermal efficiency of diesel engine makes them attractive and popular to use. Conventionally, compression ignition engines operate with diesel fuel derived from crude oil [1]. In the late 1970s and early 1980s, an energy crisis occurred over world due to the depletion of fossil based fuels [2]. Therefore, scientists have been working on this issue for many years. Recently, usage of alternative fuels in internal combustion engines has been an important research area. In * Corresponding author. E-mail address: [email protected] (E. Tosun). Peer review under responsibility of Faculty of Engineering, Alexandria University.
this respect, vegetable oils, and alcohols such as ethanol and methanol have been investigated to be able to use in internal combustion engines [3]. Requirement of little or no engine modification makes those alternatives remarkable. There are lots of study about fuel properties, performance and emission characteristics of an internal combustion engine operated with various alternative fuels [4–10]. Determination of performance and emission characteristics of an internal combustion engine is complex, time consuming and costly [11]. Therefore, in order to eliminate these disadvantages and complexities, performance and emission of an engine can be modeled with using artificial neural network (ANN). An ANN system works as a biological neuron. Neurons receive input from the source, perform a non-linear operation, and predict final output [12]. In recent years, parallel to devel-
http://dx.doi.org/10.1016/j.aej.2016.08.011 1110-0168 Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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opments in computer technology, ANN has been applied to many problems in automotive engineering [13–25]. In this paper, firstly, fuel properties and experimental results of diesel engine fueled with diesel, biodiesel and biodiesel-alcohol mixtures were obtained from another work of author [6]. Standard diesel, peanut methyl ester as biodiesel and methanol-ethanol-butanol as alcohols were utilized in the experiments. Then LR method was applied to experimental data to predict performance and emission data (torque, CO, NOx). It was seen that regression model approach was deficient to predict desired parameters. Therefore, ANN approach was used and seen that more accurate results were obtained than LR. There are lots of studies about internal combustion engines for prediction of performance and emission results. The distinctive property of this paper is using alcohol mixtures with biodiesel as fuel and using only fuel properties (density, cetane number, lower heating value) of these mixtures and engine speed (rpm) as input parameters in ANN structure for estimation. 2. Material and methods
Fuel properties and measurement devices.
Property
Device
Cetane Number Lower Heating Value (LHV) Density
Zeltex ZX440 IKA-Werke C2000 bomb calorimeter Kyoto electronics DA-130
operated for 15 min with diesel fuel to reach the operation temperature. Accuracy of the measurements is given in Table 4. 2.3. Linear regression Regression analysis is a method to find a functional relationship between dependent variables (response) and independent variables (predictor) [27]. In LR, the function is linear equation and dependent variable can be expressed as a function of independent variable(s) in the form of [28]: Y ¼ b0 þ b1 X1 þ b2 X2 þ þ bn Xn
2.1. Fuel properties determination
where Y is dependent variable, b0 to bn are equation parameters for linear relation and X1 to X2 are independent variables.
The fuels and fuel-alcohol mixtures used in experiments and the devices used to determine the fuel properties are demonstrated in Table 1 and 2, respectively. Cetane number is a measure of ignition characteristics of a diesel engine. It is an important parameter to determine quality of diesel fuel. Heating value is energy released when the fuel is burned. It is very important parameter to carry out efficiency and work calculations [26]. Density can be defined as mass per unit volume. The measurement devices are shown in Fig. 1. 2.2. Experimental set-up Engine performance experiments were conducted on a four cylinder, four stroke, naturally aspirated, direct injection diesel engine. Technical specifications of the engine are given in Table 3. Photographic view and schematic representation of the diesel engine are shown in Fig. 2. Engine gives 89 kW maximum power at 3200 rpm engine speed and has 295 Nm maximum torque at 1800 rpm engine speed. The engine was
Table 1 [6].
Table 2
Fuels and their mixtures with alcohols by percentage
Fuel
Diesel
Peanut Methyl Ester (PME) (%)
Ethanol +Peanut Methyl Ester (EME) (%)
Methanol +Peanut Methyl Ester (MME) (%)
Butanol +Peanut Methyl Ester (BME) (%)
Diesel Peanut biodiesel Ethanol Methanol Butanol
100 –
– 100
– 80
– 80
– 80
– – –
– – –
20 – –
– 20 –
– – 20
2.4. Artificial neural networks Human brain is highly complex, nonlinear and parallel computer [29]. Source of inspiration of ANN is the basic structure of human brain [30]. An ANN is composed of a number of simple and highly interconnected processing elements as neurons in brain. Model can be defined as a black box consisting of a series of equations for the calculation of output with use of given input values [31]. The block diagram of a model of neuron is shown in Fig. 3 on the basis of designing an ANN [29]. Haykin [29] stated that mathematically, we can describe a neuron k by the following equations: uk ¼
m X wkj xj j¼1
yk ¼ uðuk þ bk Þ Bias, denoted by bk, has the effect of increasing or lowering the net input of the activation function. x1, x2, . . ., xm are the inputs; wk1, wk2, . . ., wkm are the weights of the neuron k; uk is the linear combiner output due to input signals; uð:Þ is the activation function; yk is the output signal of the neuron. Backpropagation algorithm is commonly used as a learning algorithm of ANN in the multilayered feedforward networks. In backpropagation networks, data are processed from the input layer to the hidden layer then to the output layer. Finding optimal weights is the purpose in order to obtain close values to targets as an output [28]. In this study, Levenberg-Marquardt (LM) learning algorithm was used to adjust the weights in the multilayered feedforward networks. In hidden layer, logistic sigmoid nonlinear function (logsig) and in output layer, linear transfer function (purelin) were used as an activation function.
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine
Figure 1
Table 3
(a) Zeltex ZX440, (b) IKA-Werke C2000 bomb calorimeter and (c) Kyoto electronics DA-130.
Technical specifications of the test engine.
Brand Model Configuration Type Displacement Bore Stroke Power Torque Oil cooler Air cleaner Weight
3
Mitsubishi Canter 4D34-2A In line 4 Direct injection diesel with glow plug 3907 cc 104 mm 115 mm 89 kW @ 3200 rpm 295 Nm @ 1800 rpm Water cooled Paper element type 325 kg
2.5. Data specification In this study, performance and emission tests were conducted in a direct injected diesel engine fueled by diesel, PME, EME, MME and BME [6]. Fig. 4 and Table 5 show performance and emission curves and fuel properties of each fuel, respectively. As seen from the following figures that, alcohol additions into
Figure 2
biodiesel generally improve engine performance and reduce emissions. Extra oxygen content of alcohols increases number of rich mixture regions in cylinder and causes to enhance combustion [6]. 3. Results and discussions 3.1. LR results SPSS is software used for statistical analysis. It can be used to relate independent variables with dependent variables in LR model. The results of LR analysis are given in Table 6. Figs. 5–7 present the comparison between experimental and predicted data. Firstly, 80% of experimental data was used to constitute regression equation. Then, remaining randomly selected 20% of data was tested with the use of equation. In the following figures, a vertical line separates data used to constitute regression equation and data used to test the equation performance. Selecting predictor variables is the most important issue in order to define best prediction equation in regression method [28]. On the other hand, supplied number of data to obtain
(a) Photographic view and (b) schematic representation of the engine test rig.
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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E. Tosun et al. Table 4
Accuracy of the measurements.
Property
Accuracy
Engine speed Torque Carbon monoxide Nitrogen oxides Cetane number Density
±2 rpm ±2% ±10 ppm ±1 ppm 3% ±0.001 g/cm3
regression equation is another issue. Using much more data to constitute equation will increase prediction performance. It was clearly seen from the figures that, LR modeling approach was not enough to predict data accurately. Best agreement was obtained for CO prediction between experimental and predicted results with usage of LR. 3.2. ANN results Neural Network toolbox of MATLAB software was used for ANN model. The main structure of ANN is shown in Fig. 8.
Figure 3
Figure 4
Block diagram of model of a neuron.
(a, b) Performance and (c, d) emission curves [6].
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine Table 5
Fuel Properties.
Property
Diesel
PME
MME
EME
BME
Cetane Number Heating Value (kJ/kg) Density (kg/m3)
59.5 45,856 837
53.21 38,708 880
60.38 38,727 855
57.24 38,732 873
69.51 38,979 874
Table 6
5
There were an input layer, hidden layer and output layer. Input layer consists of 4 neurons and output layer consists of 1 neuron (all output parameters analysed separately). Neuron number of hidden layer was determined by trial and error method. It means that there was not a certain number of hidden layer neuron.
Results of linear regression.
Output Parameter
Equation
R2
Torque CO NOx
Torque = 543,357 0,102 * (rpm) 0,239 * (CN) + 0,05 * (LHV) 0,448 * (Density) CO = 827,513 + 0,257 * (rpm) 4,194 * (CN) + 0,010 * (LHV) + 0,685 * (Density) NOx = 4621,616 0,611 * (rpm) + 8,886 * (CN) 0,024 * (LHV) 2,702 * (Density)
0.726 0.898 0.919
Figure 5
Comparison between experimental and predicted data for torque.
Figure 6
Comparison between experimental and predicted data for CO.
Figure 7
Comparison between experimental and predicted data for NOx.
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Figure 8
Figure 9
The main structure of ANN.
Comparison between actual and predicted data for torque.
Learning algorithm and ANN structure are given in Table 7 for each parameter. Rpm, CN, LHV and q were used as input neuron to predict torque in the network. Prediction equation of torque is given below: Torque ¼ 7; 9755 F1 þ 27; 0340 F2 93; 3236 F3 þ 96; 4421 F4 þ 5; 7018 F5 24; 3317 F6 þ 30; 9032 F7 þ 117; 7479 Sigmoid function was used to calculate each F value. Fi ¼
1 1 þ eEi
Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i
Rpm, CN, LHV and q were used as input neuron to predict CO in the network. Prediction equation of CO is given below: CO ¼ 47; 4444 F1 191; 1111 F2 142; 2222 F3 þ 32; 5236 F4 þ 388; 4580 F5 þ 83; 6667 F6 þ 99; 1133 F7 188; 3333 F8 148; 1111 F9 þ 391; 2086 Sigmoid function was used to calculate each F value. 1 Fi ¼ 1 þ eEi Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i Rpm, CN, LHV and q were used as input neuron to predict NOx in the network. Prediction equation of NOx is given below:
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
Comparison of linear regression and artificial neural network model of a diesel engine
Table 7
Figure 10
Comparison between actual and predicted data for CO.
Figure 11
Comparison between actual and predicted data for NOx.
Table 9 Weight and bias values between input and hidden layer for CO prediction.
Learning algorithms and ANN structures.
Output Parameter
Learning Algorithm
ANN Structure
Hidden Layer Transfer Function
Output Layer Transfer Function
Torque
Levenberg– Marquardt Levenberg– Marquardt Levenberg– Marquardt
4-7-1
logsig
purelin
4-9-1
logsig
purelin
4-13-1
logsig
purelin
CO NOx
7
i
W1i
W2i
W3i
W4i
i
bi
1 2 3 4 5 6 7 8 9
6.3035 2.3156 16.4184 2.9497 0.5917 14.5499 7.1104 24.4875 39.7832
1.4295 0.7944 0.5451 0.7705 6.2499 0.0468 0.1483 2.1424 1.4110
0.3935 0.4867 1.0430 0.0647 0.0716 0.6872 115.7263 1.1956 1.3627
3.1566 30.3244 2.0841 14.6638 2.9751 2.3568 26.0755 15.1036 3.2666
1 2 3 4 5 6 7 8 9
80.4540 95.9337 148.1982 15.6436 154.8052 112.0702 143.7120 45.1141 97.9484
NOx ¼ 0; 5306 F1 þ 21; 6029 F2 0; 1043 F3 þ 50; 1298 F4 þ 453; 4412 F5 28 F6 þ 274; 7941 F7
Table 8 Weight and bias values between input and hidden layer for torque prediction.
þ 1; 9096 F8 þ 0; 3404 F9 þ 40; 7623 F10
i
W1i
W2i
W3i
W4i
i
bi
þ 49; 5639 F11 þ 48; 6242 F12 þ 48; 8891 F13
1 2 3 4 5 6 7
3.3305 4.3771 5.3781 4.3680 0.0228 2.4200 0.6102
97.6738 41.3274 97.5159 1.7581 5.1877 0.4794 0.3744
0.6992 39.9587 0.2034 0.1965 0.6637 0.3408 0.0480
29,3846 8,4538 11,4652 4,7418 30,2536 21,5033 6,2920
1 2 3 4 5 6 7
104.3517 114.1732 50.2300 33.8932 151.2201 5.4968 61.9001
þ 49; 0307 Sigmoid function was used to calculate each F value. Fi ¼
1 1 þ eEi
Ei ¼ W1i rpm þ W2i CN þ W3i LHV þ W4i q þ b1i
Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011
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E. Tosun et al. Table 10 Weight and bias values between input and hidden layer for NOx prediction. i
W1i
W2i
W3i
W4i
i
bi
1 2 3 4 5 6 7 8 9 10 11 12 13
12.5133 42.8641 19.3421 18.4471 3.8993 12.1997 6.5627 62.6611 1.4964 6.3243 15.1193 10.9933 1.7183
0.5029 0.1102 0.5260 0.0224 1.5954 0.1933 0.5023 0.5614 1.2212 0.0669 0.4025 0.3894 0.5865
0.3404 2.3541 1.8624 0.2913 0.2406 0.7819 0.1990 3.8057 0.1476 0.7237 1.6381 0.1040 0.4811
0.0696 0.4106 0.4460 3.1840 3.2165 4.3650 23.8889 5.5248 2.2288 10.0390 0.2028 1.1023 0.4410
1 2 3 4 5 6 7 8 9 10 11 12 13
159.0413 72.4009 90.5721 40.9710 185.5012 52.6386 95.3561 73.5869 138.0217 132.3532 67.4554 41.4348 46.9212
Table 11
Performance values of models. MAPE (%) LR
ANN
Torque Train Test
39.03 24.96
15.53 16.22
CO Train Test
11.25 11.9
9.11 3.56
NOx Train Test
21.61 22.1
18.96 9.63
Figs. 9–11 present the comparison between actual and predicted data. 80% of experimental data was used for training of neural network. Remaining random 20% of data was used for testing. As shown from above figure ANN modeling approach gives more accurate results than LR. Best agreement between experimental and predicted values was obtained for CO as in LR. 3.3. Performance comparison of LR and ANN Convergency of target and model output values can be observed with the use of Mean Error (BIAS), mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE). In this study, MAPE was used as performance parameter to compare models [28]. Weight and bias values between input and hidden layer for predictions are given in Tables 8–10. MAPE ¼
n 1X joi ti j 100 n i¼1 oi
where t is target value, o is output value and n is total number of data. Table 11 gives comparison of MAPE values of both training and test stage for LR and ANN.
4. Conclusions The purpose of this study was to predict some performance and emission data (torque, CO, NOx) obtained from diesel engine by using two different modeling methods. The developed model has three layer structures: one input layer with four neurons, one hidden layer (7 neuron for torque prediction, 9 neuron for CO prediction, 13 neuron for NOx prediction), and one output layer. Logistic sigmoid (logsig) and linear transfer function (purelin) were used in the hidden layer and output layer as an activation function, respectively. The learning algorithm used was Levenberg-Marquardt algorithm. To predict each parameter, rpm, CN, LHV and q of fuels were used as an input parameter. In LR model, R2 values were 0.726, 0.898 and 0.919 for torque, CO and NOx, respectively. When results of LR and ANN were compared, it was seen that ANN modeling approach gives more accurate results for all predicted parameters. It means MAPE values of ANN model were less than LR. Best correlation was obtained between input parameters and CO for both LR and ANN (MAPE values were 11.9 and 3.56, respectively). The models suggested in this paper were given to predict performance and emission of internal combustion engine. Since performing these tests is both costly and time consuming, by using fuel properties and engine speed as predictor parameters, experimental results can be estimated. But the performance of models can be enhanced by supplying more data in training section. With much more data the generalization capacity of models will increase. Eventually, using ANN modeling can be suggested to predict performance and emission of diesel engine operated with various fuels. Using ANN can avoid time consuming and costly experimental studies. References [1] W. Tutak, K. Lukacs, S. Szwaja, A. Bereczky, Alcohol–diesel fuel combustion in the compression ignition engine, Fuel 154 (2015) 196–206. [2] G. Tu¨ccar, E. Tosun, T. O¨zgu¨r, K. Aydin, Diesel engine emissions and performance from blends of citrus sinensis biodiesel and diesel fuel, Fuel 132 (2014) 7–11. [3] N. Yilmaz, M.V. Vigil, Potential use of a blend of diesel, biodiesel, alcohols and vegetable oil in compression ignition engines, Fuel 124 (2014) 168–172. [4] M.K. Balki, C. Sayin, M. Canakci, The effect of different alcohol fuels on the performance, emission and combustion characteristics of a gasoline engine, Fuel 115 (2014) 901–906. [5] E. Alptekin, M. Canakci, Determination of the density and the viscosities of biodiesel– diesel fuel blends, Renew. Energy 33 (2008) 2623–2630. [6] E. Tosun, A.C. Yilmaz, M. Ozcanli, K. Aydin, Determination of effects of various alcohol additions into peanut methyl ester on performance and emission characteristics of a compression ignition engine, Fuel 126 (2014) 38–43. _ ¸ , E. C¸ilg˘in, H. Aydin, Terebinth oil for biodiesel [7] C. Ilkilic production and its diesel engine application, J. Energy Inst. 88 (2015) 292–303. [8] H. Serin, M. Ozcanli, M.K. Gokce, G. Tuccar, Biodiesel production from tea seed (Camellia Sinensis) oil and its blends with diesel fuel, Int. J. Green Energy 10 (2013) 370–377. [9] N.M.S. Hassan, M.G. Rasul, C.A. Harch, Modelling and experimental investigation of engine performance and
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Please cite this article in press as: E. Tosun et al., Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.011