- Email: [email protected]
Performance maps of a diesel engine
APPLIED ENERGY
Applied Energy 81 (2005) 247–259
www.elsevier.com/locate/apenergy
Performance maps of a diesel engine Veli C ¸ elik, Erol Arcakliog˘lu
*
Engineering Faculty, Department of Mechanical Engineering, Kirikkale University, Yahsihan, 71450 Kirikkale, Turkey Accepted 10 August 2004 Available online 28 October 2004
Abstract This paper suggests a mechanism for determining the constant specific-fuel consumption curves of a diesel engine using artificial neural-networks (ANNs). In addition, fuel–air equivalence ratio and exhaust temperature values have been predicted with the ANN. To train the ANN, experimental results have been used, performed for three cooling-water temperatures 70, 80, 90, and 100 °C for the engine powers ranging from 1000 to 2300 – for six different powers of 75–450 kW with incremental steps of 75 kW. In the network, the back-propagation learning algorithm with two different variants, single hidden-layer, and logistic sigmoid transfer function have been used. Cooling water-temperature, engine speed and engine power have been used as the input layer, while the exhaust temperature, break specific-fuel consumption (BSFC, g/kWh) and fuel–air equivalence ratio (FAR) have also been used separately as the output layer. It is shown that R2 values are about 0.99 for the training and test data; RMS values are smaller than 0.03; and mean errors are smaller than 5.5% for the test data. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Artificial neural-network; Performance maps; Fuel–air equivalence ratio; Diesel engine
1. Introduction Diesel engines are able to operate at higher compression-ratios than gasoline engines because the fuel is mixed with the air at the outset of the combustion process. *
Corresponding author. Tel.: +90 318 3573571; fax: +90 318 3572459. E-mail addresses: [email protected], [email protected] (E. Arcakliog˘lu).
0306-2619/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2004.08.003
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
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Nomenclature ANN BMEP BSFC FAR IC LM N Pe R2 RMS SCG Tcw Tex
artificial neural-network break mean effective pressure break specific-fuel consumption fuel–air equivalance ratio injection compression Levenberg–Marquardt engine speed power fraction of variance root-mean squared scaled conjugate gradient cooling-water temperature exhaust temperature
Since the diesel engines are more efficient and sturdier than gasoline engines, they are widely used. However, due to economic considerations, fuel economy is still pursued. Fuel economy in internal-combustion engines means that it is the aim that the chemical energy is converted to the maximum amount of useful work. Some factors affecting fuel economy in the engines are the engine power, efficiency and mixing properties. On the other hand, the efficiency of a diesel engine depends on the conversion rate of the chemical energy of the fuel into heat release. Engines are expected to operate under wide ranges of speeds and loads. The fuel consumed by a moving vehicle during a trip is calculated by the break specific fuelconsumption (BSFC), the break mean effective pressure (BMEP) and mean piston speed. A common way of presenting these three data is a contour plot showing lines of constant fuel-consumption on a load and speed plane. This graph is referred to as the engine or performance map. It contains the necessary information to estimate the fuel consumption by an engine given the load and speed. Diesel-engine performance is basically related to the engine design, running parameters and fuel properties. These are important for the optimisation of the engineÕs performance [1]. The BSFC is a measure of engine efficiency. In fact, BSFC and engine efficiency are inversely related, so that the lower the BSFC the better the engine. By definition, the BSFC is the fuel-flow rate divided by the brake power. A parameter that scales out the effect of engine size is the BMEP. The BMEP is the work done per unit displacement volume. Engineers use BSFC rather than thermal efficiency, primarily because a more or less universally-accepted definition of thermal efficiency does not exist [2]. The fuel–air equivalence ratio (FAR) is the actual fuel–air ratio divided by the stoichiometric fuel–air ratio. If the ratio is less than unity, the mixture is called lean, if the ratio is greater than unity, the mixture is said to be rich.
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In this study, the effects of the cooling-water temperature on the fuel consumption have been investigated for a water-cooled, eight-cylinder, four-stroke turbocharge diesel-engine by using an artificial neural-network (ANN). The data have been obtained from a previous study [3]. In that study, the fuel consumption had been measured by operating the test engine at different speeds and loads. The economic working region of the engine had been targeted. In other words, to be able to find the economic operating region (i.e. to find the low fuel-consumption) for the test motor it has been operated under different temperatures for different speeds and loads. The engine performances of the diesel engines have been studied [4,5]. In these studies, the performance maps as functions of the diesel-engineÕs speed and load have been produced using data obtained from the experiments. Several pertinent studies have made use of ANNs [6–8]. Similarly performance maps have been developed by the usage of ANNs. We may select some experiment results to train the network while using the remaining results for testing it. Studies using experiment-based results to train the ANNs may be found in [9,10]. After the training session, the network is used to predict the values of the parameter which has not been presented to the system. This avoids us doing the experiments for the whole range of possible parameters and thus saves us time and effort by producing results almost instantly after a query has been made. Combustion in a diesel engine is a complicated physical and chemical process: it depends on many different parameters, such as the injection pressure and time [1]. Thus showing that the ANNs produce good predictions for the combustion process is especially important.
2. Details of the experiment The experimental set up is an eight-cylinder, four-stroke, diesel engine with a precombustion chamber which has been produced for military purposes. The specifications of the diesel engine are given in Table 1. All the experiments [3] were performed for various speeds and loads for a selected entrance-temperatures of the cooling water. Then the values of the BSFC, exhaust temperature and air-flow rate were recorded. In addition, the effective power and energy-distribution values were calculated to explore the best operation conditions such as speed, load and cooler
Table 1 Specifications of test engine Make and model Motor type Number of cylinders Compression ratio Bore and stroke Maximum engine-power Total volume
Mercedes Benz, type 837, special diesel-engine Water-cooled, four-stroke Eight cylinders 19.5:1 165 mm and 175 mm 500 kW at 2300 rpm 29.92 l
250
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
temperature. For each measurement, four experiments had been performed and, to obtain more accurate values, their averages were considered. Therefore, the most suitable speed, load and the cooling-water temperature were investigated. The selected cooling-water temperatures are 70, 80, 90 and 100 °C, engine speeds ranged from 1000 to 2300 rpm, and engine powers from 75 to 450 kW with step values of 75 kW. The temperature of the cooling water was kept constant by controlling it via a valve at outlet of the exchanger.
3. Artificial neural-networks and modelling the system with the network ANNs are computational models, which replicate the functions of a biological network, composed of neurons and are used to solve complex functions in various scientific applications, such as process control, forecasting, optimization, classification and speech recognition. In the ANN system, there are three fundamental layers, namely the input, the hidden and the output layers. The input layer consists of all the input factors: information from the input layer is then processed in the hidden-layer section, and the output vector is computed in the output layer. Each node has an activation function and can receive signals from nodes in the previous layer. In all the models developed, the following procedure is executed: (i) database collection; (ii) analysis and pre-processing of the data; (iii) training of the neural network; (iv) testing the trained network; and (v) using the trained ANN for simulation and prediction. An important stage of a neural network is the training step, in which an input is introduced to the network together with the desired output: the weights and bias values are initially chosen randomly and the weights adjusted so that the network produces the desired output. After training, the weights contain meaningful information, contrary to the initial stage where they are random and meaningless. When a satisfactory level of performance is reached, the training stops, and the network uses the weights to make decisions. Many alternative training processes are available, such as back-propagation. The goal of any training algorithm is to minimize the global error percentage such as the mean percentage error, root-mean-squared error or R2 [11]. In order to train an artificial neural-network, experimental results have been used. Basic parameters for the experiments are the cooling-water temperature (Tcw, °C), engine speed (N, rpm) and power (Pe, kW). The experiments were completed by changing the values of the parameters. We used these parameters as the input layer, in each network which has been set up, while the exhaust temperature, BSFC and FAR were used separately as the output-layer components of the ANNs. As mentioned above, the ratios of energy distribution had been calculated in the experiments. We also tried to train the network with energy-distribution ratios: however, the results obtained contained unacceptable errors. Therefore, we excluded this from our study. In the application, the back-propagation learning algorithm has been used, with a single hidden-layer. Variants used in the study are the scaled conjugate gradient
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(SCG), and Levenberg–Marquardt (LM) algorithm. A logistic sigmoid (logsig) transfer-function has been used and inputs and outputs are normalized within the range of (0, 1). The MATLAB software has been used to train and test the ANN on a personal computer. In the training stage, to define the output accurately, we tried to increase the number of neurons step-by-step (i.e 3–5) in the hidden layer. After the successful training of the network, the network was tested with the test data. Using the results produced by the network, statistical methods have been used to make comparisons. At the learning and testing stages, the RMS and R2 errors and mean error percentage values were estimated: these are defined as follows: !1=2 X 2 RMS ¼ ð1=pÞ j t j oj j ; ð1Þ j
P 2
R ¼1
j ðt j
P
oj Þ
j ðoj Þ
Mean% Error ¼
2
2
! ð2Þ
;
1 X t j oj 100 ; p j tj
ð3Þ
where t is the target value, o is the output value, and p is the pattern [12]. There are 160 patterns obtained from the experiments for each output. Among them, six patterns have been randomly selected and used as the test data. Table 2 contains selected sample values. Fig. 1 shows the single hidden-layer ANN architecture used in our application. After the successful training of the network, new inputs were prepared: these ranged from 70 to 100 °C with a step increase value of 5 °C, 1000–2300 rpm with a step increase a value of 100 rpm, and 75–450 kW with a step increase value of 25 kW. By using these new inputs, predictions have been obtained from the ANN. Investigations based on experiments are usually complex, time consuming and costly. The statistical results prove that the predictions provided by the network are close to the experiment-based results; therefore they can be used to obtain performance maps.
Table 2 Input and output samples Tcw (°C)
N (rpm)
Pe (kW)
BSFC (g/kWh)
Tex (°C)
FAR
70 70 90 90 100 100
1000 1800 1200 1600 1400 2000
75 300 150 225 375 450
278.8 228.7 218 224.5 226.7 227.3
173 356 271 274 492 445
2.765 1.93 2.507 2.165 1.255 1.68
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Fig. 1. ANN architecture with 4 hidden neurons in a single hidden-layer.
4. Results and discussion In Table 3, the statistical values for predictions and the best algorithmic results have been shown. Algorithms with a varying number of hidden neurons produce varying outputs. As shown in the table, the best algorithms are the SCG with 5 neurons, the SCG with 5 neurons and the SCG with 3 neurons for the BSFC, FAR and exhaust temperature, respectively. The formulations of the outputs have been prepared according to the hidden number of neurons mentioned above. The maximum mean error for the test data is obtained for the exhaust temperature. The mean error for the BSFC is 1.03% for the test data. R2 values are very close to unity, and the RMS values are very small for all the performance values. The formulations of the outputs obtained from the weights are given using Eqs. (4)–(6).
Table 3 Statistical values of predictions and best algorithm with hidden number of neurons
Algorithm Hidden number RMS R2 MAPE (%) RMS-test R2-test MAPE-test (%)
BSFC
FAR
Tex
SCG 5 0.010802 0.999385 1.859 0.010592 0.999511 2.0134
SCG 5 0.025309 0.997196 3.850351 0.026127 0.996925 3.375806
SCG 3 0.023621 0.998395 3.525851 0.030223 0.996968 5.242741
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
BSFC ¼ FAR ¼ T ex ¼
1
253
;
ð4Þ
1 ; 1 þ eð2:7323F 1 4:3227F 2 þ0:7841F 3 þ5:9182F 4 þ5:4184F 5 6:1048Þ
ð5Þ
1þ
eð1:8272F 1 þ0:4259F 2 1:3807F 3 1:9367F 4 þ8:6784F 5 þ0:4682Þ
1 ; 1 þ eð3:3122F 1 2:1812F 2 þ6:1111F 3 0:8627Þ
ð6Þ
where Fi (i = 1,2,3,. . .,6) can be calculated according to Eq. (7). Fi ¼
1 ; 1 þ eEi
ð7Þ
where Ei is the weighted sum of the input, and is given by equations as seen in Tables 4–6.
Table 4 The weights between input layer and hidden layer for BSFC i
1 2 3 4 5
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
1.6641 0.7396 0.6688 4.2688 0.9103
7.7004 4.7656 7.6387 5.3032 3.7069
4.3870 6.7772 2.2392 6.0685 11.0931
6.6762 8.7926 6.4226 1.8895 2.6408
Table 5 The weights between input layer and hidden layer for FAR i
1 2 3 4 5
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
0.3754 0.8971 2.8202 16.8549 1.2993
0.1086 5.6596 9.0112 13.6447 7.4605
3.0811 11.0812 0.7663 6.6059 6.3824
1.2396 5.7384 6.9645 3.6795 5.1538
Table 6 The weights between input layer and hidden layer for exhaust temperature i
1 2 3
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
8.0782 3.0397 0.0762
5.4300 11.3460 0.5803
0.6969 4.8408 1.2035
5.6625 0.8487 1.1457
254
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
The equations in Tables 4–6 are dependent on the cooling-water temperature, the engine speed and the power, which are the inputs of the network, while the coefficients in Eqs. (4)–(6) are the weights, which lie between the hidden and output layers. When using the equations in Tables 4–6, Tcw, N, and Pe values are normalized by dividing them with 120, 2500 and 500, respectively, to obtain the output of the networks in Eqs. (4)–(6). BSFC, FAR and exhaust-temperature values need to be multiplied by 600, 5 and 600, respectively.
Fig. 2. Engine-performance map with contours of BSFC as a function of BMEP and N for Tcw = 75 °C.
Fig. 3. Engine-performance map with contours of BSFC as a function of BMEP and N for Tcw = 100 °C.
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Since the necessary formulae have been given above, anyone could use these variables to get predictions from the ANN as if the experiments had been done. Fig. 2 shows the performance maps (i.e. constant BSFC curves) which depend upon the diesel-engineÕs speed (N, d/d) and BMEP (kPa) in the case of the 75 °C
Fig. 4. Engine-performance map of constant 240 g/kWh with BSFC contours as a function of BMEP and N based on the cooling-water temperature.
Fig. 5. Change of BSFC with Tcw for constant N and BMEP.
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Fig. 6. Comparison of actual and ANN approach values for BSFC training data.
Fig. 7. Comparison of actual and ANN approach values for BSFC test data.
cooling-water temperature. In the figure, there are three BSFC values, namely 240, 260 and 280 g/kWh. For each BSFC, the tolerance of ±5 is considered. In other words, 240 may also include 235 and 245. In Fig. 3 for the 100 °C cooling water, the corresponding BFSC curve has been presented. As both of the curves indicate the model works in line with the expectations. As Fig. 4 illustrates, in the performance maps, for the cooling water of varying temperatures, the region of 240 g/kWh appears as the constant BSFC curves. The figure also illustrates that, at higher levels of cooling-water temperatures, the region of constant BSFC widens and, in the randomly-selected points within the middle sections, a lower BSFC will occur. Fig. 5 shows the variance BSFC with the cooling-water temperature under constant BMEP and N. As the figure shows the BSFC decreases with increases of N
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257
and BMEP. This decrease is faster in the case of lower temperatures of the cooling water. In the figure, for example, for N = 1000 d/d and BMEP = 301 kPa, the variance of BSFC and Tcw are given. Figs. 6 and 7 compare the actual and predicted BSFC values of the training and test data, respectively. As shown in the figures, the actual and predicted values are very close to each other. Figs. 8 and 9 compare the actual and predicted exhaust-temperature values of the training and test data, respectively. Similarly, Figs. 10 and 11 also compare the actual and predicted FAR values of the training and test data. Here, results are not as near as for the BSFC. In other words, the error levels for the exhaust temperature and FAR are higher and appear on the graphs.
Fig. 8. Comparison of actual and ANN approach values for exhaust-temperature training data.
Fig. 9. Comparison of actual and ANN approach values for exhaust-temperature test data.
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Fig. 10. Comparison of actual and ANN approach values for FAR training data.
Fig. 11. Comparison of actual and ANN approach values for FAR test data.
5. Conclusions The aim of this paper has been to show the possibility of using neural networks for obtaining performance maps for a diesel engine. Results show that, in most cases, the network produces results parallel to the experimental data. Therefore they can be used as an alternative in these systems. The RMS error values are smaller than 0.03 and the R2 values are about 0.99, which may easily be considered to be within the acceptable range. One deduction made from the experimental results and the predictions produced by ANNs is that, if the experiments are producing steady and reliable results (i.e. repeating an experiment under the same conditions produces almost the same result), the usage of ANNs will be highly recommended. However, in some cases (i.e. such as in the case of energy distribution) due to the complexity of the operation, we may not get similar results even under the same experimental conditions. In such cases, the
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usage of neural networks may not be appropriate. To be able to train a neural network, there must be either a logical linear relation or a logical non-linear relation between the input and the output. In this study, we aimed at modelling an experimental data using the ANNs. Therefore, the factors that limit the temperatures of the cooling water are not emphasised. However, the findings of this study also give useful hints to researchers who wish to explore these aspects.
References _ ¸ ingu¨r Y, Altiparmak D. Effect of fuel cetane number and injection pressure on a diesel-engineÕs [1] Ic performance and emissions. Energy Convers Manage 2003;44:389–97. [2] Ferguson CR. Internal-combustion engines. New York: Wiley; 1986. [3] S ß ahin F. Unpublished MSc thesis [in Turkish]. [4] Parlak A, Yasßar H, S ß ahin B. Performance and exhaust-emission characteristics of a lower compression ratio LHR Diesel engine. Energy Convers Manage 2003;44:163–75. [5] Labeckas G, Slavinskas S. Performance and exhaust emission characteristics of direct-injection diesel engine when operating on shale oil. Energy Convers Manage [in press]. _ Performance and exhaust emissions in a diesel engine. Appl Energy [in [6] Arcakhog˘lu E, C ¸ elikten I. press]. [7] Yuanwang D, Meilin Z, Dong X, Xiaobei C. An analysis for effect of cetane number on exhaust emissions from engine with the neural network. Fuel 2002;81:1963–70. [8] Arcakhog˘lu E, C ¸ avusßog˘lu A, Erisßen A. Thermodynamic analysis of refrigerant mixtures using artificial neural-networks. Appl Energy 2004;78:219–30. [9] Arcakhog˘lu E, Erisßen A, Yilmaz R. Artificial neural-network analysis of heat pumps using refrigerant mixtures. Energy Convers Manage 2004;45:1917–29. ¨ zalp M. A new approach to the thermodynamic analysis of the ejector[10] So¨zen A, Arcakhog˘lu E, O absorption cycle using artificial neural-networks. Appl Therm Eng 2003;23:937–52. [11] More A, Deo MC. Forecasting wind with neural networks. Marine Struct 2003;16:35–49. [12] So¨zen A, Arcakhog˘lu E. Prediction of solar potential in Turkey. Appl Energy 2005;80:35–45.
Applied Energy 81 (2005) 247–259
www.elsevier.com/locate/apenergy
Performance maps of a diesel engine Veli C ¸ elik, Erol Arcakliog˘lu
*
Engineering Faculty, Department of Mechanical Engineering, Kirikkale University, Yahsihan, 71450 Kirikkale, Turkey Accepted 10 August 2004 Available online 28 October 2004
Abstract This paper suggests a mechanism for determining the constant specific-fuel consumption curves of a diesel engine using artificial neural-networks (ANNs). In addition, fuel–air equivalence ratio and exhaust temperature values have been predicted with the ANN. To train the ANN, experimental results have been used, performed for three cooling-water temperatures 70, 80, 90, and 100 °C for the engine powers ranging from 1000 to 2300 – for six different powers of 75–450 kW with incremental steps of 75 kW. In the network, the back-propagation learning algorithm with two different variants, single hidden-layer, and logistic sigmoid transfer function have been used. Cooling water-temperature, engine speed and engine power have been used as the input layer, while the exhaust temperature, break specific-fuel consumption (BSFC, g/kWh) and fuel–air equivalence ratio (FAR) have also been used separately as the output layer. It is shown that R2 values are about 0.99 for the training and test data; RMS values are smaller than 0.03; and mean errors are smaller than 5.5% for the test data. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Artificial neural-network; Performance maps; Fuel–air equivalence ratio; Diesel engine
1. Introduction Diesel engines are able to operate at higher compression-ratios than gasoline engines because the fuel is mixed with the air at the outset of the combustion process. *
Corresponding author. Tel.: +90 318 3573571; fax: +90 318 3572459. E-mail addresses: [email protected], [email protected] (E. Arcakliog˘lu).
0306-2619/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2004.08.003
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
248
Nomenclature ANN BMEP BSFC FAR IC LM N Pe R2 RMS SCG Tcw Tex
artificial neural-network break mean effective pressure break specific-fuel consumption fuel–air equivalance ratio injection compression Levenberg–Marquardt engine speed power fraction of variance root-mean squared scaled conjugate gradient cooling-water temperature exhaust temperature
Since the diesel engines are more efficient and sturdier than gasoline engines, they are widely used. However, due to economic considerations, fuel economy is still pursued. Fuel economy in internal-combustion engines means that it is the aim that the chemical energy is converted to the maximum amount of useful work. Some factors affecting fuel economy in the engines are the engine power, efficiency and mixing properties. On the other hand, the efficiency of a diesel engine depends on the conversion rate of the chemical energy of the fuel into heat release. Engines are expected to operate under wide ranges of speeds and loads. The fuel consumed by a moving vehicle during a trip is calculated by the break specific fuelconsumption (BSFC), the break mean effective pressure (BMEP) and mean piston speed. A common way of presenting these three data is a contour plot showing lines of constant fuel-consumption on a load and speed plane. This graph is referred to as the engine or performance map. It contains the necessary information to estimate the fuel consumption by an engine given the load and speed. Diesel-engine performance is basically related to the engine design, running parameters and fuel properties. These are important for the optimisation of the engineÕs performance [1]. The BSFC is a measure of engine efficiency. In fact, BSFC and engine efficiency are inversely related, so that the lower the BSFC the better the engine. By definition, the BSFC is the fuel-flow rate divided by the brake power. A parameter that scales out the effect of engine size is the BMEP. The BMEP is the work done per unit displacement volume. Engineers use BSFC rather than thermal efficiency, primarily because a more or less universally-accepted definition of thermal efficiency does not exist [2]. The fuel–air equivalence ratio (FAR) is the actual fuel–air ratio divided by the stoichiometric fuel–air ratio. If the ratio is less than unity, the mixture is called lean, if the ratio is greater than unity, the mixture is said to be rich.
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
249
In this study, the effects of the cooling-water temperature on the fuel consumption have been investigated for a water-cooled, eight-cylinder, four-stroke turbocharge diesel-engine by using an artificial neural-network (ANN). The data have been obtained from a previous study [3]. In that study, the fuel consumption had been measured by operating the test engine at different speeds and loads. The economic working region of the engine had been targeted. In other words, to be able to find the economic operating region (i.e. to find the low fuel-consumption) for the test motor it has been operated under different temperatures for different speeds and loads. The engine performances of the diesel engines have been studied [4,5]. In these studies, the performance maps as functions of the diesel-engineÕs speed and load have been produced using data obtained from the experiments. Several pertinent studies have made use of ANNs [6–8]. Similarly performance maps have been developed by the usage of ANNs. We may select some experiment results to train the network while using the remaining results for testing it. Studies using experiment-based results to train the ANNs may be found in [9,10]. After the training session, the network is used to predict the values of the parameter which has not been presented to the system. This avoids us doing the experiments for the whole range of possible parameters and thus saves us time and effort by producing results almost instantly after a query has been made. Combustion in a diesel engine is a complicated physical and chemical process: it depends on many different parameters, such as the injection pressure and time [1]. Thus showing that the ANNs produce good predictions for the combustion process is especially important.
2. Details of the experiment The experimental set up is an eight-cylinder, four-stroke, diesel engine with a precombustion chamber which has been produced for military purposes. The specifications of the diesel engine are given in Table 1. All the experiments [3] were performed for various speeds and loads for a selected entrance-temperatures of the cooling water. Then the values of the BSFC, exhaust temperature and air-flow rate were recorded. In addition, the effective power and energy-distribution values were calculated to explore the best operation conditions such as speed, load and cooler
Table 1 Specifications of test engine Make and model Motor type Number of cylinders Compression ratio Bore and stroke Maximum engine-power Total volume
Mercedes Benz, type 837, special diesel-engine Water-cooled, four-stroke Eight cylinders 19.5:1 165 mm and 175 mm 500 kW at 2300 rpm 29.92 l
250
V. C¸elik, E. Arcakliog˘lu / Applied Energy 81 (2005) 247–259
temperature. For each measurement, four experiments had been performed and, to obtain more accurate values, their averages were considered. Therefore, the most suitable speed, load and the cooling-water temperature were investigated. The selected cooling-water temperatures are 70, 80, 90 and 100 °C, engine speeds ranged from 1000 to 2300 rpm, and engine powers from 75 to 450 kW with step values of 75 kW. The temperature of the cooling water was kept constant by controlling it via a valve at outlet of the exchanger.
3. Artificial neural-networks and modelling the system with the network ANNs are computational models, which replicate the functions of a biological network, composed of neurons and are used to solve complex functions in various scientific applications, such as process control, forecasting, optimization, classification and speech recognition. In the ANN system, there are three fundamental layers, namely the input, the hidden and the output layers. The input layer consists of all the input factors: information from the input layer is then processed in the hidden-layer section, and the output vector is computed in the output layer. Each node has an activation function and can receive signals from nodes in the previous layer. In all the models developed, the following procedure is executed: (i) database collection; (ii) analysis and pre-processing of the data; (iii) training of the neural network; (iv) testing the trained network; and (v) using the trained ANN for simulation and prediction. An important stage of a neural network is the training step, in which an input is introduced to the network together with the desired output: the weights and bias values are initially chosen randomly and the weights adjusted so that the network produces the desired output. After training, the weights contain meaningful information, contrary to the initial stage where they are random and meaningless. When a satisfactory level of performance is reached, the training stops, and the network uses the weights to make decisions. Many alternative training processes are available, such as back-propagation. The goal of any training algorithm is to minimize the global error percentage such as the mean percentage error, root-mean-squared error or R2 [11]. In order to train an artificial neural-network, experimental results have been used. Basic parameters for the experiments are the cooling-water temperature (Tcw, °C), engine speed (N, rpm) and power (Pe, kW). The experiments were completed by changing the values of the parameters. We used these parameters as the input layer, in each network which has been set up, while the exhaust temperature, BSFC and FAR were used separately as the output-layer components of the ANNs. As mentioned above, the ratios of energy distribution had been calculated in the experiments. We also tried to train the network with energy-distribution ratios: however, the results obtained contained unacceptable errors. Therefore, we excluded this from our study. In the application, the back-propagation learning algorithm has been used, with a single hidden-layer. Variants used in the study are the scaled conjugate gradient
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(SCG), and Levenberg–Marquardt (LM) algorithm. A logistic sigmoid (logsig) transfer-function has been used and inputs and outputs are normalized within the range of (0, 1). The MATLAB software has been used to train and test the ANN on a personal computer. In the training stage, to define the output accurately, we tried to increase the number of neurons step-by-step (i.e 3–5) in the hidden layer. After the successful training of the network, the network was tested with the test data. Using the results produced by the network, statistical methods have been used to make comparisons. At the learning and testing stages, the RMS and R2 errors and mean error percentage values were estimated: these are defined as follows: !1=2 X 2 RMS ¼ ð1=pÞ j t j oj j ; ð1Þ j
P 2
R ¼1
j ðt j
P
oj Þ
j ðoj Þ
Mean% Error ¼
2
2
! ð2Þ
;
1 X t j oj 100 ; p j tj
ð3Þ
where t is the target value, o is the output value, and p is the pattern [12]. There are 160 patterns obtained from the experiments for each output. Among them, six patterns have been randomly selected and used as the test data. Table 2 contains selected sample values. Fig. 1 shows the single hidden-layer ANN architecture used in our application. After the successful training of the network, new inputs were prepared: these ranged from 70 to 100 °C with a step increase value of 5 °C, 1000–2300 rpm with a step increase a value of 100 rpm, and 75–450 kW with a step increase value of 25 kW. By using these new inputs, predictions have been obtained from the ANN. Investigations based on experiments are usually complex, time consuming and costly. The statistical results prove that the predictions provided by the network are close to the experiment-based results; therefore they can be used to obtain performance maps.
Table 2 Input and output samples Tcw (°C)
N (rpm)
Pe (kW)
BSFC (g/kWh)
Tex (°C)
FAR
70 70 90 90 100 100
1000 1800 1200 1600 1400 2000
75 300 150 225 375 450
278.8 228.7 218 224.5 226.7 227.3
173 356 271 274 492 445
2.765 1.93 2.507 2.165 1.255 1.68
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Fig. 1. ANN architecture with 4 hidden neurons in a single hidden-layer.
4. Results and discussion In Table 3, the statistical values for predictions and the best algorithmic results have been shown. Algorithms with a varying number of hidden neurons produce varying outputs. As shown in the table, the best algorithms are the SCG with 5 neurons, the SCG with 5 neurons and the SCG with 3 neurons for the BSFC, FAR and exhaust temperature, respectively. The formulations of the outputs have been prepared according to the hidden number of neurons mentioned above. The maximum mean error for the test data is obtained for the exhaust temperature. The mean error for the BSFC is 1.03% for the test data. R2 values are very close to unity, and the RMS values are very small for all the performance values. The formulations of the outputs obtained from the weights are given using Eqs. (4)–(6).
Table 3 Statistical values of predictions and best algorithm with hidden number of neurons
Algorithm Hidden number RMS R2 MAPE (%) RMS-test R2-test MAPE-test (%)
BSFC
FAR
Tex
SCG 5 0.010802 0.999385 1.859 0.010592 0.999511 2.0134
SCG 5 0.025309 0.997196 3.850351 0.026127 0.996925 3.375806
SCG 3 0.023621 0.998395 3.525851 0.030223 0.996968 5.242741
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BSFC ¼ FAR ¼ T ex ¼
1
253
;
ð4Þ
1 ; 1 þ eð2:7323F 1 4:3227F 2 þ0:7841F 3 þ5:9182F 4 þ5:4184F 5 6:1048Þ
ð5Þ
1þ
eð1:8272F 1 þ0:4259F 2 1:3807F 3 1:9367F 4 þ8:6784F 5 þ0:4682Þ
1 ; 1 þ eð3:3122F 1 2:1812F 2 þ6:1111F 3 0:8627Þ
ð6Þ
where Fi (i = 1,2,3,. . .,6) can be calculated according to Eq. (7). Fi ¼
1 ; 1 þ eEi
ð7Þ
where Ei is the weighted sum of the input, and is given by equations as seen in Tables 4–6.
Table 4 The weights between input layer and hidden layer for BSFC i
1 2 3 4 5
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
1.6641 0.7396 0.6688 4.2688 0.9103
7.7004 4.7656 7.6387 5.3032 3.7069
4.3870 6.7772 2.2392 6.0685 11.0931
6.6762 8.7926 6.4226 1.8895 2.6408
Table 5 The weights between input layer and hidden layer for FAR i
1 2 3 4 5
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
0.3754 0.8971 2.8202 16.8549 1.2993
0.1086 5.6596 9.0112 13.6447 7.4605
3.0811 11.0812 0.7663 6.6059 6.3824
1.2396 5.7384 6.9645 3.6795 5.1538
Table 6 The weights between input layer and hidden layer for exhaust temperature i
1 2 3
Ei = C1Tcw + C2N + C3Pe + C4 C1
C2
C3
C4
8.0782 3.0397 0.0762
5.4300 11.3460 0.5803
0.6969 4.8408 1.2035
5.6625 0.8487 1.1457
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The equations in Tables 4–6 are dependent on the cooling-water temperature, the engine speed and the power, which are the inputs of the network, while the coefficients in Eqs. (4)–(6) are the weights, which lie between the hidden and output layers. When using the equations in Tables 4–6, Tcw, N, and Pe values are normalized by dividing them with 120, 2500 and 500, respectively, to obtain the output of the networks in Eqs. (4)–(6). BSFC, FAR and exhaust-temperature values need to be multiplied by 600, 5 and 600, respectively.
Fig. 2. Engine-performance map with contours of BSFC as a function of BMEP and N for Tcw = 75 °C.
Fig. 3. Engine-performance map with contours of BSFC as a function of BMEP and N for Tcw = 100 °C.
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Since the necessary formulae have been given above, anyone could use these variables to get predictions from the ANN as if the experiments had been done. Fig. 2 shows the performance maps (i.e. constant BSFC curves) which depend upon the diesel-engineÕs speed (N, d/d) and BMEP (kPa) in the case of the 75 °C
Fig. 4. Engine-performance map of constant 240 g/kWh with BSFC contours as a function of BMEP and N based on the cooling-water temperature.
Fig. 5. Change of BSFC with Tcw for constant N and BMEP.
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Fig. 6. Comparison of actual and ANN approach values for BSFC training data.
Fig. 7. Comparison of actual and ANN approach values for BSFC test data.
cooling-water temperature. In the figure, there are three BSFC values, namely 240, 260 and 280 g/kWh. For each BSFC, the tolerance of ±5 is considered. In other words, 240 may also include 235 and 245. In Fig. 3 for the 100 °C cooling water, the corresponding BFSC curve has been presented. As both of the curves indicate the model works in line with the expectations. As Fig. 4 illustrates, in the performance maps, for the cooling water of varying temperatures, the region of 240 g/kWh appears as the constant BSFC curves. The figure also illustrates that, at higher levels of cooling-water temperatures, the region of constant BSFC widens and, in the randomly-selected points within the middle sections, a lower BSFC will occur. Fig. 5 shows the variance BSFC with the cooling-water temperature under constant BMEP and N. As the figure shows the BSFC decreases with increases of N
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and BMEP. This decrease is faster in the case of lower temperatures of the cooling water. In the figure, for example, for N = 1000 d/d and BMEP = 301 kPa, the variance of BSFC and Tcw are given. Figs. 6 and 7 compare the actual and predicted BSFC values of the training and test data, respectively. As shown in the figures, the actual and predicted values are very close to each other. Figs. 8 and 9 compare the actual and predicted exhaust-temperature values of the training and test data, respectively. Similarly, Figs. 10 and 11 also compare the actual and predicted FAR values of the training and test data. Here, results are not as near as for the BSFC. In other words, the error levels for the exhaust temperature and FAR are higher and appear on the graphs.
Fig. 8. Comparison of actual and ANN approach values for exhaust-temperature training data.
Fig. 9. Comparison of actual and ANN approach values for exhaust-temperature test data.
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Fig. 10. Comparison of actual and ANN approach values for FAR training data.
Fig. 11. Comparison of actual and ANN approach values for FAR test data.
5. Conclusions The aim of this paper has been to show the possibility of using neural networks for obtaining performance maps for a diesel engine. Results show that, in most cases, the network produces results parallel to the experimental data. Therefore they can be used as an alternative in these systems. The RMS error values are smaller than 0.03 and the R2 values are about 0.99, which may easily be considered to be within the acceptable range. One deduction made from the experimental results and the predictions produced by ANNs is that, if the experiments are producing steady and reliable results (i.e. repeating an experiment under the same conditions produces almost the same result), the usage of ANNs will be highly recommended. However, in some cases (i.e. such as in the case of energy distribution) due to the complexity of the operation, we may not get similar results even under the same experimental conditions. In such cases, the
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usage of neural networks may not be appropriate. To be able to train a neural network, there must be either a logical linear relation or a logical non-linear relation between the input and the output. In this study, we aimed at modelling an experimental data using the ANNs. Therefore, the factors that limit the temperatures of the cooling water are not emphasised. However, the findings of this study also give useful hints to researchers who wish to explore these aspects.
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