Linear Engine / L2V4bGlicmlzL2R0bC9kM18xL2FwYWNoZV9tZWRpYS83MTc1

Csaba Tóth-Nagy Linear Engine Development for Series Hybrid Electric Vehicles

Shoukry [85] recommended the values Mp=0.5, Md=3, and a=1.2 so they were used in the present study. The other constants were chosen tp=150µs (premix burning time), td=5 ms (diffusion burning time) to result in a burning time usual in a diesel engine.

5.1.3 Friction force

Friction force was accounted for with a damping term in the simulation. The damping coefficient for the simulation model was determined by trial and error by visually matching simulated engine operation with engine behavior. The model behavior matched the engine behavior well. Correlation coefficient for the simulated and measured position was 0.995. Figure 38 and Figure 39 show the ringing down portion of a test run with no load on it for both simulated and experimental data.

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Figure 38. Simulated and experimental translator position after engine was turned off by cutting the fuel. (This phenomena is referred to ringing down).

Figure 39. Simulated vs. experimental translator position after engine was turned off (ringing down). Correlation coefficient: 0.995.

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5.2 The predictor/simulator model

A combination of an artificial neural network model and a genetic algorithm along with the simulation model was used to find the engine parameter set that provided the highest efficiency. Figure 40 shows the flow chart of the predictive simulation technique that was used to find the set of engine parameters that had the highest efficiency.

Figure 40. The flow diagram of the predictor/simulator algorithm used to find the engine with the highest efficiency.

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5.2.1 Artificial neural network (ANN) model

Artificial neural networks were invented while searching how the human brain works. The learning mechanism of an ANN imitates the learning mechanism of the brain. Artificial neural networks have been used to control and/or to predict in many different applications including engine and emissions research [86-89]. Because neural networks were showed to be a powerful tool to predict nonlinear relationships, an ANN architecture was chosen to predict engine efficiency in this study. The neural network was trained on simulation data. The ANN was used to replace the simulation model to decrease computation time. In this study, MATLAB’s neural network toolbox [90] was used. Figure 41 shows the actual neural network architecture. It was a feed-forward back-propagation network. The seven input parameters were bore, stroke, free travel, mass of translator, amount of fuel injected, injection timing, ignition timing and the output parameter was engine efficiency. The inputs were normalized between –1 and +1 before being presented to the neural network. The hidden layer consisted of 25 neurons and the activation functions were tangent sigmoid.

Figure 41. The neural network architecture used for predicting engine efficiency based on bore, stroke, free travel, mass of translator, amount of fuel injected, injection timing, ignition timing. IW and LW indicate the weights in the input and the hidden layer respectively. b(1) and b(2) indicate the thresholds in the input and the hidden layer respectively.

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The neural network was used in a two separate modes. In mode one, the training mode, the neural network was initialized with random weights and thresholds then presented with the training data set and the desired output data set. In several iterations of batch training, the neural network learned (by adjusting the weights and thresholds) the relationship between the inputs and the desired output. In mode two, the predicting mode, once the neural network was trained, it was presented with the input data from the genetic algorithm and predicted the engine efficiency. The neural network prediction was used to replace the simulation model to decrease the computational time.

5.2.2 The genetic algorithm (GA)

Genetic algorithms imitate the evolution of genes [108]. They are a powerful tool for optimization problems. A genetic algorithm was used in this study, to find the combination of engine parameters that yielded the highest mechanical efficiency.

5.2.2.1 The initial gene pool

As the first step, the engine parameters were coded into 10 digit binary codes and stringed together to form a chromosome. Engine parameters included bore, effective stroke, free travel, translator mass, amount of fuel injected, injection timing, and ignition timing. Each chromosome was a 70 digits long binary code and represented the seven engine parameters. An original gene pool of 50 chromosomes was created by randomly choosing engine parameters. The parameters were stored in binary form to prevent the accumulation of round off error that occurred when data were converted from binary form to decimal form and vice versa or normalized and scaled back to unnormalized form for the neural network use. The parameters were translated back to decimal code and the

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simulation model was run on each set of parameters to obtain the simulated efficiencies. The neural network was trained on the initial gene pool using the engine parameters as the input data and the simulated efficiencies as the desired output.

5.2.2.2 Survival of the fittest / multiplication

The survival of the fittest function worked in two steps. In the first step, the GA chose the chromosome that resulted in the highest efficiency and replaced the five lowest efficiency chromosomes with it. Then it made the new chromosomes propagate to the top of the gene pool. In the second step, the GA found the second, third, fourth … sixth best efficiency chromosomes and the worse six chromosomes and replaced the six worst with the six best. Then it propagated the new chromosomes to the top of the gene pool right behind the best chromosomes in decreasing order. This yielded the survival and the multiplication of the fittest.

5.2.2.3 Crossover

The genetic algorithm kept the first two chromosomes unchanged and crossed the other ones. In every even numbered chromosome the GA crossed a randomly chosen binary string with a string in the same position from the chromosome above it. This generated a new pool of genes.

5.2.2.4 Mutation

The GA kept the first chromosome unchanged and mutated the rest of the gene pool. The best chromosome on the top stayed unchanged. The mutation process randomly flipped the binary bits in the chromosomes. The mutation rate was 3%.

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5.2.2.5 Neural network prediction/Genetic algorithm

The new gene pool was presented to the trained ANN and the neural network predicted the efficiency for each chromosome.

The genetic algorithm was run again on the new gene pool based on the predicted efficiency values. The GA with the ANN was iteratively applied until the best chromosome surfaced. This chromosome yielded the best mechanical efficiency only for the given neural network model.

5.2.2.6 Testing the genetic algorithm

The engine parameters formed a seven dimensional variable space that made the testing of the genetic algorithm difficult. Therefore the GA was tested on twodimensional functions. Equation 19 and Equation 20 show the two functions that were used to test the genetic algorithm. The GA was used to find the global maximum of the functions.

Equation 19

z = 3(1- x) 2e(-x2 -(y+1) 2) -10( x5 - x3 - y5 )e(-x2 -y2 ) - 13 e(-(x+1)2 -y2 )

Equation 20

z =sin2x - sin3y +(x + y)0.03

The genetic algorithm always converged for the function shown in Equation 19 since the local and global maximums were substantially different. This was not the case for Equation 20. Equation 20 resulted in 5 local maximums that hardly differed from the global maximum. However, the genetic algorithm found the global maximum in about 60% of the attempts. In the case of the other 40% it settled on one of the local

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maximums. This was not a problem in this application because the neural network had to be retrained and the GA had to be reapplied to the data set several times. The iterations of the GA testing can be found in Appendix A.

5.2.3 Recursion of the neural network training

The ANN was trained on a limited number of data sets therefore its prediction capabilities were also limited. This was the reason for the iterative retraining of the ANN. The chromosome that was found to be the best by the GA was decoded and the decoded engine data was presented to the simulation model that simulated the engine efficiency. This new set of engine parameters, along with the simulated efficiency, was added to the original neural network training set and the ANN was retrained. Then the neural network was applied to the engine data stored in the new set of chromosomes and engine efficiencies were predicted again. The genetic algorithm was run again on the original gene pool extended with the new gene. This process was applied iteratively until the neural network predicted efficiency and the simulated efficiency were equal. Results are presented in Section 8.6.

5.3 Conclusions

A simple simulation model was developed to verify that the trends of the experimental data and to gain extra insight into the behavior of the linear engine. The simulation model used dynamic and thermodynamic equations to simulate engine behavior, and Wiebe functions to simulate heat release rate. The model did not account for fuel vaporizing effects, fluid flow, swirl in the cylinder, or cylinder geometry. The model was created with the assumption that the cylinder intake was a homogeneous

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charge of ideal gas at the point of port closure. The model was verified with the ringing down portion of a test run and showed a correlation coefficient of 0.995.

A combined neural network / genetic algorithm routine, which also incorporated the simulation model, was created to find the set of engine parameters that yielded the highest efficiency. The recursive routine was tested on two different two-dimensional functions and was found appropriate for the purpose of finding the linear engine with the highest efficiency.

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6 Prototype design

WVU’s second-generation linear engine design incorporated a linear engine and a linear alternator to form an electrical generator set that could be used as an auxiliary power unit of a hybrid vehicle or as a mobile generator set. Figure 42 shows the major components of the linear engine.

Figure 42. The second-generation linear engine at WVU.

Figure 42 shows the linear engine in a semi-disassembled state. The cylinder head on the left was removed for modifications.

6.1 Linear alternator

At the time of the experiments the alternator was still under development. The alternator was required to operate in two modes, namely alternator mode and actuator mode. When in actuator mode the linear alternator would provide the cranking force to start the engine. Once the engine is started the alternator would operate in alternator mode to generate electricity. There were two possibilities considered: permanent magnet

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