Scientific Research and Essays Vol. 5 (23), pp. 3781-3793, 4 December, 2010 Available online at http://www.academicjournals.org/SRE ISSN 1992-2248 ©2010 Academic Journals Full Length Research Paper

The effects of intercooling on performance of a turbocharged diesel engine’s specific fuel consumption

with neural network

Abdullah Uzun

Computer Programming, Sakarya Vocational school, Sakarya University, 4187 Sakarya, Turkey. E -mail: auzun@sakarya.edu.tr.

Accepted 28 July, 2010

Currently, fuel economy and thermal efficiency are more important to all engines. Efficiency is increased with cooled air by intercooler. Most of researches regarding engineering problems generally deal with experimental studies. But, the experimental researches are quite expensive and time consuming. In the last decades, Neural Networks (NN) had been used increasingly in a variety of engineering applications. The objective of the study is to investigate the adequacy of neural networks (NN) as a quicker, more secure and more robust method to determine the effects of intercooling on performance of a turbocharged diesel engine’s specific fuel consumption. The data are obtained from experimental research that is performed by the author. NN based model is developed, trained and tested through a based MATLAB program by using of these data. In the study, break specific fuel consumption (BSFC, g/kWh) was analysed with intercooling and without intercooling. The statistical analysis is performed to explain the performance of the NN based model. NN based model outputs are also compared with the experimental results. The statistical results and the comparison demonstrated that the NN based model is highly successful to determine the effects of intercooling on performance of a turbocharged diesel engine’s specific fuel consumption. Key words: Neural networks, intercooling, specific fuel consumption, scaled conjugate gradient algorithm, diesel engine.

INTRODUCTION The increased use motor vehicles, the exacerbation of traffic intensity in the cities and the decrease of oil reserves on the earth result in the daily increase of oil prices. 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. 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 (Celik and Arcaklioglu, 2005). The emphasis on fuel conservation in the 1970’s stimulated the use of turbocharging to improve the fuel economy of those diesel engines that run at or near full load for long periods of time. This category includes marine, stationary

and heavy-road vehicle engines. By improving structural design; many engines in these services are super-charged to high mean effective pressure, often accompanied by reduced piston speed, with resulting improved mechanical efficiency (Stone, 1992).

In the turbocharged engines, especially at high speeds and loads, compressor output temperatures rises, the density and consequently the amount of air induced into engine decreased. To avoid this decrease in engine induction air and engine power, compressor output air must be cooled.

In vehicles, a charge air cooler system is mounted in front of the radiator. In air-to-water charge cooling, the compressed air is cooled in a heat exchanger either in

3782 Sci. Res. Essays Table 1. Specification of the test engine (Otosan, 1992). Engine type FORD 6.0 LT T/C Intercooling, DI Stroke 4 Cylinder 6 Cylinder diameter (mm) 104.77 Piston stroke (mm) 114.9 compression ratio 16.5/1 Max. engine power (kW) 136 (2400 rpm ) Max speed (rpm) 2750-2780 Idle speed (rpm) 665-685 Engine volume ( lt ) 5.947 Injection timing (°CA ) 20 Ignition order 1-5-3-6-2-4 Engine weight (kg) 500

separate or built into the intake manifold. In air-to air charge coolers, the lower-temperature ambient air is utilized directly for cooling rather than using engine coolant as the intermediate system. During movement of vehicles, the coolant must be directed to the atmosphere and space (Brady, 1996).

Diesel engine performance is basically related with the engine design, running parameters and fuel properties. These are important for the optimization of the engine’s performance (Icingur and Altiparmak, 2003). Break specific fuel consumption (BSFC) is a measure of engine and fuel efficiency within a shaft reciprocating engine. BSFC is the rate of fuel consumption divided by the power produced. BSFC allows the fuel efficiency of different reciprocating engines to be directly compared. The lower the BSFC, the better the engine.

In the study, a four-stroke, direct-injection, six cylinders, turbocharged, intercooling diesel engine were selected as test engine. First, the engine was tested as equipped with a water-cooler intercooler, at different speeds and loads conditions. Then, this engine was again tested without intercooler at the same conditions. In that experiment, the fuel consumption had been measured by operating the test diesel engine at different loads and speeds with and without intercooler. What works best in this range was more economical than trying to find the engine that had been targeted (Uzun, 1998). Experimental research is not always easy to obtain for all parameters in any engineering problem. Neural networks (NNs) have been used increasingly in a variety of engineering applications.

There are many studies about diesel engine performance related NN in literature (Arcaklıo�lu and Çelikten, 2005; Arcaklıo�lu et al., 2004; Taylor, 1985). All diesel engine performances’ data cannot be measured in an experimental method. Measuring ranges are 1200-1400-1600-1800-2000-2200-2400 rpm and 18-20-22-24 CA, 300-350-400-450-500-550 N, all number of cycles

for each test load and crankshaft angle values. Similarly, performance data have been developed by the usage NNs. Studies using experiment based data to train the NNs may be found. After the training period, the network is used to estimate the values of the parameter, which has not been presented to the system.

The main purpose of the paper is to study the effects of intercooling on performance parameters of a turbocharged diesel engine by using a neural-network (NN). The break specific fuel consumption (BSFC, g/kWh) is studied for both; with intercooling and without intercooling. The statistical analysis is carried out to evaluate the performance of the NN based model. NN based model outputs are also compared with experimental results. The statistical results and the comparison revealed that the NN based model is highly successful to determine the effects of intercooling on performance of a turbocharged diesel engine’s specific fuel consumption. Details of the experiment The experimental set up used are, a six-cylinder, four-stroke, diesel engine with a intercooler and turbocharger, which is assembled on an hydraulically dynamometer. The specifications of the diesel engine are given in Table 1.

All the experiments (Uzun, 1998) were performed for various speeds and loads with intercooler and without intercooler. Heat exchanger is used to cool engine water. 300lt tank volume is made of a damping. The entering and leaving air temperature of intercooler are measured. Intercooler cooling water flow rate is measured as 8.5 lt/min. During the test, engine speed, load, intake manifold temperature, exhaust gas temperature, cooling water inlet and outlet temperatures, intercooler input and output temperatures, oil temperature, the test cabin temperature, oil pressure, media pressure, ambient temperature, intake manifold pressure, air intake pressure difference (in oblique manometer), cooling water pressure difference (U-manometer) and fuel consumption values were measured and recorded. At the end of each experiment, the period had changed. Of the engine with and without intercooler, different loads (that is, angle and speed injected into tables and graphs in the characteristic values) are presented as a comparative. Measuring ranges are 1200-1400-1600-1800-2000-2200-2400 rpm and 18-20-22-24 CA, 300-350-400-450-500-550 N, all number of cycles for each test load and crankshaft angle values. Some values were calculated with the measured values as specific fuel consumption, effective efficiency, and excess air coefficient. Engine installation and testing scheme can be seen in Figure 1 and test engine picture can be seen in Figure 2. All experimental measurements were made with a precision of 3%. Neural networks (NN) Recently, NNs have been employed successfully to solve the complex problems in various engineering fields as a computational tool. NN is an alternative computational model inspired from neurological model of human brain. NN can simulate operational features of the human brain. The NN architecture is composed of one input layer, one output layer and one or more hidden layers. In the NN architecture, the layers are composed of neurons and the

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Figure 1. Testing scheme.

Figure 2. Test engine set.

neurons are the fundamental processing element of NN (Caglar, 2009, Pala 2006).

Neurons in each layer are fully connected to other neurons in

following layers. These NN architectures are commonly referred to as a fully interconnected feedforward multilayer perceptron. There are two biases. One of them is connected to neurons in the hidden

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Table 2. Range of parameters in the database and normalization values. Input parameter Min Max Normalization values CA 18 24 24 Load(F) 300 550 550 rpm 1000 2400 2400 Output parameter

Min

Max

Normalization values

BSFC with intercooler 120.58 188.37 250 BSFC without intercooler 129.49 207.56 250

layer and the other one is connected to neurons in output layer of the NN. The number of neurons in input and output layer may vary depending on the problem (Caglar 2009).

The back-propagation (BP) algorithm is quite a widely used training algorithm for multi-layered feedforward networks. The BP algorithm basically consists of two phases. The first one is the forward phase where the activations are propagated from the input to the output layer. In the first phase (forward phase), the activations are propagated from the input to the output layer. In the next phase, backward phase, the error between the observed actual value and the desired nominal value in the output layer is propagated backwards in order to modify the weights and bias values.

All of data used in the NN must be initialized before the training of feed work network. In the forward phase, the weighted sum of input components is calculated as:

�=

+=n

1ijiijj biasxwnet (1)

where jnet is the weighted sum of the j th neuron for the input

received from the preceding layer with n neurons, ijw is the

weight between the thj neuron and the thi neuron in the preceding

layer, ix is the output of the thi neuron in the preceding layer. The

output of the thj neuron jout is calculated with a sigmoid function

as follows:

( ))net(jj

je1

1netfout

−+== (2)

During the process of training, the weights are modified to capture the relationship between the input and output patterns. The training of the network is carried out by adjusting the weights. The objective of the training procedure is to find the optimal set of weights.

The most known training algorithm for the multi-layer feed-forward neural network is back-propagation algorithm. Two back-propagation training algorithms, which are gradient descent and gradient descent with momentum, are drastically slow. Therefore, several adaptive training algorithms for NN, have in recent times, been developed such as Conjugate Gradient Algorithm (CG) and Scaled Conjugate Gradient Algorithm (SCG). In the study, SCG is used as optimization algorithm. The detail of SCG algorithm can be found in literature (Moller, 1993).

The output of the NN model is compared with the experimental results to produce an error. The sum of the squares error (SSE ) is used as the performance function for feed forward networks. The

process of the training continues until the required sum of the squares error is determined. The SSE is defined as:

( )�=

−=m

1i

2ii outTSSE (3)

where iT and iout are the target outputs and output of neural

network values, respectively, for thi output neuron, and m is the number of neurons in the output layer. Numerical study In the study, the NN based model was applied to estimate the specific fuel consumption with and without intercooling of turbocharged diesel engine. Firstly, the experimental studies were conducted. Then, the data of NN based model are obtained from the experimental results.

The data are divided into two parts: The training and testing sets for both models. 60 data of database are selected as training set and employed to train NN based model. 34 data, which are not used in the training process, are selected as the testing set and used to validate the generalization capability of NN based model. The training and testing sets are tabulated in Tables 3 to 4, respectively.

Inputs and outputs are normalized in the 0 to 1 range by using simple normalization methods and values are given in Table 2. The maximum and minimum values of inputs and outputs are also given in Table 2.

In the NN model, the numbers of neurons in input and output layers are based on the geometry of the problem. But, there is no general rule for determining the number of neurons in a hidden layer and the number of the hidden layers (Caglar, 2009). For this reason, the number of neurons in a hidden layer and the number of the hidden layers are selected by trial and error method in the study. In order to determine the most appropriate NN model, a lot of different NN models with neurons in hidden layers are trained and tested for 2500 epochs. The criterion to establish the most appropriate NN model is selected as the sum of the squares errors (SSE). The required sum of the squares error (SSE) is selected as 10e–5. The most appropriate NN models are chosen corresponding to the performance of both training and testing sets in terms of SSE. The SSEs of the NN models were determined for one hidden layers with various numbers of neurons. Figure 3 illustrates the obtained results of SSE values for one hidden layers to get the NN model with the best performance.

Figure 3 also demonstrate the effect of the number of neurons in the hidden layers on the NN based model accuracy. In the figure, the performance of NN based models in terms of SSE with number of neurons in one hidden layer is drawn for 6 different NN based

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Table 3a. Comparison of NN based model with experimental results for training set.

With intercooling Without intercooling

Samples ca Loads (N) rpm BSFC (g/kWh)

NN .Exp

NN BSFC

(g/kWh) NN

.ExpNN

1 18 400 1200 165.000 162.362 0.9840 169.000 167.222 0.9895 2 18 400 1400 158.750 158.968 1.0014 165.000 165.530 1.0032 3 18 400 2200 150.950 150.667 0.9981 161.730 167.094 1.0332 4 18 400 2400 153.740 149.705 0.9738 166.040 168.951 1.0175 5 18 450 1600 175.715 174.243 0.9916 178.516 177.078 0.9919 6 18 450 1800 166.801 172.363 1.0333 169.647 177.332 1.0453 7 18 450 2000 180.743 170.719 0.9445 188.425 178.083 0.9451 8 18 500 2200 134.175 152.950 1.1399 164.685 164.906 1.0013 9 18 500 2400 150.961 151.348 1.0026 174.768 166.317 0.9516

10 18 550 1600 148.969 147.516 0.9902 150.969 152.019 1.0070 11 18 550 1800 147.083 144.412 0.9818 149.083 151.567 1.0167 12 18 550 2000 145.936 141.780 0.9715 150.936 151.854 1.0061 13 20 400 1000 160.000 157.683 0.9855 159.000 158.042 0.9940 14 20 400 1200 161.000 159.016 0.9877 163.000 162.859 0.9991 15 20 400 1400 160.000 160.274 1.0017 170.000 167.290 0.9841 16 20 400 1600 159.650 161.428 1.0111 177.900 171.300 0.9629 17 20 400 1800 153.740 162.455 1.0567 172.960 174.860 1.0110 18 20 400 2000 153.270 163.342 1.0657 177.900 177.972 1.0004 19 20 400 2200 153.500 164.079 1.0689 181.140 180.646 0.9973 20 20 400 2400 172.960 164.660 0.9520 188.680 182.893 0.9693 21 20 450 1600 128.826 135.077 1.0485 149.574 148.524 0.9930 22 20 450 1800 135.823 136.584 1.0056 153.761 152.867 0.9942 23 20 450 2000 143.199 138.137 0.9647 152.682 156.890 1.0276 24 20 450 2200 144.717 139.844 0.9663 154.806 160.672 1.0379 25 20 450 2400 151.094 141.865 0.9389 160.444 164.331 1.0242 26 20 500 1600 146.500 150.066 1.0243 155.683 158.251 1.0165 27 20 500 1800 152.682 151.268 0.9907 163.992 162.250 0.9894

models. The numbers of neurons in one hidden layer are formed from 5 to 10. The performance of NN based model with 5, 6, 7, 8, 9 and 10 neurons in one hidden layer are shown in Figures 3a, 3b, 3c, 3d, 3e and 3f, respectively. As can be seen in Figure 3, the comparison of the performance of the NN based models revealed that the best model is Figure 3a model. Consequently, the NN model is selected as having 3 neurons in input layer, 5 neurons in hidden layer and 2 neurons in output layer to define specific fuel consumption of intercooling diesel engine. Architecture of the NN model is shown in Figure 4.

A MATLAB based program with a graphical user interface (GUI) was developed to train and test the NN model (Caglar, 2009). In the NN model, the type of back-propagation is scaled conjugate gradient algorithm (SCGA), activation function is the sigmoidal function, and number of epochs (learning cycle) are 40 000.

The values of parameters used in this research are summarized as follow for the NN based model:

1. Number of input layer unit = 3. 2. Number of hidden layers = 1. 3. Number of first hidden layer units = 5. 4. Number of output layer units = 2.

5. Learning algorithm = scaled conjugate gradients algorithm (SCGA). 6. Learning cycle = 40 000. RESULTS AND DISCUSSION The performance of the neural network model is shown in Tables 3 and 4 for training and testing sets, respectively. In Tables 3 and 4, the NN based model results are compared with experimental results for both cases; with and without intercooling diesel engines. The NN based model results are also normalized with the experimental results in Tables 3 and 4. As can be seen from the results of the training set (Table 3) and the testing set (Table 4), NN based model results agree well with the experimental results.

The statistical analyses are performed to reveal the success of the NN based model for generalization. The

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Table 3b. Comparison of NN based model with experimental results for training set.

With intercooling Without intercooling

Samples ca Loads (N) rpm BSFC (g/kWh)

NN .Exp

NN BSFC

(g/kWh) NN

.ExpNN

28 20 500 2000 153.258 152.313 0.9938 166.030 165.773 0.9985 29 20 500 2200 157.527 153.203 0.9726 172.498 168.832 0.9787 30 22 400 2000 177.889 181.280 1.0191 177.889 191.036 1.0739 31 22 400 2200 181.141 180.914 0.9987 184.851 190.981 1.0332 32 22 400 2400 184.501 180.468 0.9781 207.557 190.741 0.9190 33 22 450 1200 177.300 166.820 0.9409 175.700 176.415 1.0041 34 22 450 1400 172.400 167.176 0.9697 174.230 177.710 1.0200 35 22 450 1600 170.300 167.390 0.9829 175.700 178.677 1.0169 36 22 450 1800 169.850 167.476 0.9860 175.700 179.349 1.0208 37 22 500 1800 145.160 152.189 1.0484 170.287 166.404 0.9772 38 22 500 2000 142.311 155.054 1.0895 189.748 169.093 0.8911 39 22 500 2200 147.881 158.846 1.0741 176.732 172.295 0.9749 40 22 500 2400 166.046 163.489 0.9846 174.768 175.971 1.0069 41 22 550 1600 161.717 164.234 1.0156 167.719 173.390 1.0338 42 22 550 1800 167.707 164.807 0.9827 171.296 174.519 1.0188 43 22 550 2000 172.498 165.265 0.9581 172.498 175.371 1.0167 44 22 550 2200 164.673 165.624 1.0058 173.324 175.978 1.0153 45 22 550 2400 167.719 165.896 0.9891 172.520 176.369 1.0223 46 24 400 2400 184.501 178.336 0.9666 188.702 180.124 0.9545 47 24 450 1600 170.314 175.812 1.0323 172.981 179.047 1.0351 48 24 450 1800 172.610 175.265 1.0154 172.610 178.340 1.0332 49 24 450 2000 173.648 174.697 1.0060 173.648 177.566 1.0226 50 24 450 2200 171.296 174.114 1.0165 171.296 176.735 1.0318 51 24 450 2400 171.603 173.520 1.0112 175.693 175.859 1.0009 52 24 500 1400 174.980 168.245 0.9615 175.440 172.629 0.9840 53 24 500 1600 172.780 167.890 0.9717 174.780 172.141 0.9849 54 24 500 1800 167.300 167.505 1.0012 170.300 171.567 1.0074 55 24 500 2000 166.040 167.096 1.0064 169.570 170.923 1.0080 56 24 500 2200 168.500 166.669 0.9891 172.510 170.218 0.9867 57 24 550 2000 181.141 179.217 0.9894 185.767 179.979 0.9688 58 24 550 2200 178.006 183.122 1.0287 182.966 182.861 0.9994 59 18 400 1600 155.000 156.140 1.0074 163.370 164.790 1.0087

Min. 0.9389 Min. 0.8911 Max. 1.1399 Max. 1.0739 std dev. 0.0023 std dev. 0.0015

statistical analyses of NN based model are carried out in terms of 2R , cov , SSE and standard deviation ( .dev .std ). The results of statistical analyses are given in Table 5 for both cases.

The statistical results of the sum of squares error (SSE), R-square ( 2R ) and standard deviation ( .dev .std ) are charted for NN based model in Table 5. During the process of training and testing of NN model, the normalization value of the BSFC is selected as 250. The normalized SSE statistical values are also obtained through the same normalization value. As can be seen

from Tables 3 and 4, the values of standard deviation are obtained through the normalized outcomes of NN based model with experimental results. The proximity of the standard deviation and SSE to zero and R-square to 1, reveals the accuracy of the model. It should be pointed out, however, that the statistical values being good for training set does not support the accuracy of the NN model. The statistical values from the results of testing set are the main performance indicator of NN based model. Table 5 clearly demonstrates that NN based model is very good in terms of the statistical values, 2R ,

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5 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

a)

6 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

b) 7 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

c)

8 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

d) 9 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

e)

10 nodes in hidden layer

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4

Number of training

Sum

of s

quar

e er

rors

(SS

E)

Training Testing

f)

Figure 3. The SSE of NN based models with number of neurons in one hidden layer.

cov , SSE and .dev .std .

The sum of the squares error (SSE ), the absolute fraction of variance ( 2R ), the root-mean-square (RMS) and the coefficient of variation in percent (cov) are defined as follow respectively:

���

�

�

���

�

� −−=

�

�

j

2j

j

2jj

2

)o(

)ot(1R

(4)

100*oRMS

covmean

= (5)

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Table 4. Comparison of NN based model with experimental results for testing set.

With intercooling Without intercooling

Samples ca Loads

(N) rpm BSFC

(g/kWh) NN

.ExpNN

BSFC

(g/kWh) NN

.ExpNN

1 18 400 1800 153.740 153.845 1.0007 162.780 164.889 1.0130 2 18 400 2000 150.950 152.036 1.0072 160.680 165.699 1.0312 3 18 450 2200 178.910 169.324 0.9464 191.665 179.259 0.9353 4 18 450 2400 175.693 168.166 0.9572 184.495 180.760 0.9798 5 18 500 1600 150.942 159.962 1.0598 171.767 163.779 0.9535 6 18 500 1800 142.813 157.199 1.1007 163.992 163.498 0.9970 7 18 500 2000 137.414 154.882 1.1271 166.030 163.919 0.9873 8 18 550 2200 147.714 139.553 0.9448 149.714 152.740 1.0202 9 18 550 2400 141.749 137.671 0.9712 143.749 154.078 1.0719

10 20 300 1600 175.520 198.725 1.1322 179.520 202.987 1.1307 11 20 300 2400 188.370 199.521 1.0592 189.330 209.762 1.1079 12 20 350 1600 172.280 183.213 1.0635 178.190 189.790 1.0651 13 20 350 2400 184.630 185.171 1.0029 188.970 198.799 1.0520 14 20 500 2400 166.046 153.938 0.9271 174.768 171.439 0.9809 15 20 550 1200 120.580 123.218 1.0219 129.490 127.087 0.9814 16 20 550 1400 127.630 124.403 0.9747 138.190 131.951 0.9548 17 20 550 1600 137.220 125.507 0.9146 146.080 136.464 0.9342 18 20 550 1800 146.370 126.505 0.8643 161.010 140.566 0.8730 19 20 550 2000 157.510 127.378 0.8087 164.670 144.230 0.8759 20 20 550 2200 156.830 128.115 0.8169 164.670 147.447 0.8954 21 20 550 2400 167.720 128.707 0.7674 177.580 150.206 0.8459 22 22 400 1600 183.125 181.727 0.9924 183.125 190.498 1.0403 23 22 400 1800 172.981 181.554 1.0496 181.450 190.883 1.0520 24 22 450 2000 170.300 167.447 0.9832 184.490 179.756 0.9743 25 22 450 2200 175.010 167.315 0.9560 178.900 179.927 1.0057 26 22 450 2400 175.700 167.095 0.9510 184.490 179.889 0.9751 27 22 500 1600 146.500 150.071 1.0244 171.767 164.075 0.9552 28 24 400 1600 175.398 181.047 1.0322 177.874 183.656 1.0325 29 24 400 1800 181.450 180.392 0.9942 184.517 182.858 0.9910 30 24 400 2000 174.768 179.719 1.0283 177.889 181.997 1.0231 31 24 400 2200 177.594 179.031 1.0081 181.141 181.081 0.9997 32 24 500 2400 174.780 166.231 0.9511 179.500 169.466 0.9441 33 24 550 1800 178.910 174.631 0.9761 182.984 176.539 0.9648

Min. 0.7674 Min. 0.8459 Max. 1.1322 Max. 1.1307 Std dev. 0.0083 Std dev. 0.0067

Table 5. Statistical parameters of the NN based model.

With intercooler Without intercooler

Training Testing Training Testing 2R 0.9988 0.9931 0.9990 0.9958

cov 0.0351 0.0840 0.0321 0.0653

SSE 0.0304 0.0950 0.0285 0.0649

.dev .std 0.0023 0.0083 0.0015 0.0067

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be1

biasbias

CA

F

rpmbe2

hidden layer

Figure 4. Architecture of the NN model.

2j

jj )to(SSE −=� (6)

where t is the target value, o is the output value, p is the pattern, and meano is the mean value of all output data. The R2 values have about 99.88% training and 99.31% test for that with intercooling diesel engine, while 99.90% training and 99.58% testing for that without intercooling diesel engine, respectively.

The NN based model results are compared with the experimental results following figures.

The comparisons of NN based model results with experimental results, with intercooling diesel engine, are shown in Figures 5 and 6 for training and testing sets, respectively. As shown in Figures 5 to 6, the BSFC determined by NN based model shows reasonably close values to the experimental results.

The comparisons of NN based model results with experimental results, without intercooling diesel engine, are also shown in Figures 7 and 8 for training and testing sets, respectively. A careful study of the results in Figs. 5-8 leads to observations of excellent agreement between NN based model results and experimental results.

The performance of the NN based model, with intercooling diesel engine, showed that the correlations between experimental results and NN based model results are consistent as shown in Figure 9 for training

and testing sets. The performance of the NN based model, without

intercooling diesel engine, are shown in Figure 10. The Figure 10 showed that the correlations between targets and outputs are reliable for training and testing sets.

Figures 9 and 10 indicate that the NN based models are successful in learning the relationship between the input parameters and outputs. The results of testing phase in Figures 9 and 10 show that the NN based models are capable of generalizing between input and output variables. Conclusion The aim of the paper is to use NN for the estimation of diesel engine performance for break specific fuel consumption (BSFC) with and without intercooling. The overall results show that the NN based model can be used as an alternative method for estimating the effects of intercooling on performance of a turbocharged diesel engine’s BSFC. The statistical analyses are performed to explain the performance of the NN based model. NN based model outputs are also compared with experi-mental results. It is shown that the NN based model produces results that are close to the experimental data. Hence they can be used as an alternative method in same systems. The all statistical results and the comparison

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100

150

200

250

0 10 20 30 40 50 60

Patterns

BS

FC (g

/kW

h)

Experimental NN

Figure 5. The comparisons of NN based model with experimental results for training set (diesel engine with intercooling).

100

150

200

250

0 5 10 15 20 25 30 35

Patterns

BS

FC (g

/kW

h)

Experimental NN

Figure 6. The comparisons of NN based model with experimental results for testing set (diesel engine with intercooling).

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100

150

200

250

0 10 20 30 40 50 60

Patterns

BS

FC (g

/kW

h)

Experimental NN

Figure 7. The comparisons of NN based model with experimental results for training set (diesel engine without intercooling).

100

150

200

250

0 5 10 15 20 25 30 35

Patterns

BS

FC (g

/kW

h)

Experimental NN

Figure 8. The comparisons of NN based model with experimental results for testing set (diesel engine without intercooling).

revealed that the NN based model is highly successful to determine the effects of intercooling on performance of a turbocharged diesel engine’s BSFC.

The use of experimental methods in determining the effects of intercooling on performance of a turbocharged diesel engine’s specific fuel consumption are relatively

cumbersome. Consequently, soft computing techniques such as NN based model can be useful in overcoming engineering problems.

However, the process of training of the NN based model can take some time; the trained NN based model can easily be adapted and used as a reliable alternative

3792 Sci. Res. Essays

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Figure 9a-b. The performance of NN based model for diesel engine with intercooling.

method. The NN based model applied in this study is highly successful for determining the effects of inter-cooling on performance of a turbocharged diesel engine’s BSFC. The examination of the results in Figures 5 to 10 indicates very good agreement between the NN esti-mations and experimental results.

The outcomes of the study are considered as important contributions for researchers as the use of the NN model is more convenient in saving time and money than the fully experimental studies.

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b Figure 10a-b. The performance of NN based model for diesel engine without intercooling.

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