Slide 1IntroductionOutlineGenetic AlgorithmGen4μGA codeCodingCoding ExampleCost FunctionReproductionCrossoverConvergence and restartingResults and Discussion (1)Results and Discussion (2)Results and Discussion (3)Multi Layer Perceptron (1)Multi Layer Perceptron (2)ConclusionReferencesUWECE 539 Class ProjectEngine Operating Parameter Optimization using Genetic Algorithm ECE 539 –Introduction to Artificial Neural Networks and Fuzzy Systems Final Project, Fall 2005Yong SunUWECE 539 Class ProjectIntroduction• Future diesel engine technologies will need to incorporate advanced combustion strategies with optimized engine operating parameters for achieving low emissions while maintaining fuel economy and power density •Genetic algorithms (GA) are being used by engine researchers to optimize engine design and operating parameters to achieve these goalsUWECE 539 Class ProjectOutline•A micro-Genetic Algorithm (μGA) code was coupled with a 3D engine Computational Fluid Dynamic (CFD) code KIVA to optimize six engine operating parameters •The results were used as inputs for the development of a multi-layer perceptron (MLP) configuration •The MLP network can be used to predict the engine performance based on the engine operating parametersUWECE 539 Class ProjectGenetic Algorithm•Classification•Simple Genetic Algorithm (SGA) – large population•Micro-Genetic Algorithm (μGA) -- small population •Micro-Genetic Algorithm •μpopulation of five individuals •fewer number of total function evaluations compared to SGAs • Gen4μGA codeUWECE 539 Class ProjectGen4μGA code•By Carroll (1996)UWECE 539 Class ProjectCodingParameter Baseline range Resolution # of possible values λiA -143 -143~-83 4 16 4B 0.44 0~1 0.067 (1/15) 16 4C 0 0~75 5 16 4D 60 48~141 3 32 5E 125 48~141 3 32 5F 0.5 0.0~1.0 0.143 (1/7) 8 3UWECE 539 Class ProjectCoding Examplereal number binary representation0 0001/7 0012/7 0103/7 0114/7 1005/7 1016/7 1101 111•Coding example – parameter FUWECE 539 Class ProjectCost Function•Cost (merit) function12 21000fX Y Z=+ +X- NOx emissions, Y- Unburned Hydrocarbon (HC)Z- Break Specific Fuel Consumption (BSFC) Several penalty functions have also been applied to the merit function based on the peak in-cylinder pressure, exhaust temperature and pressure, maximum rate of pressure rise, soot emissions misfire and the wall-film amount at Exhaust Valve Opening (EVO)UWECE 539 Class ProjectReproduction•The present generation is first “mixed up” such that the order of individuals is completely random. •The fitness of individual 1 is compared with the fitness of individual 2. The individual with the higher fitness is chosen as “parent 1.” •The fitness of individual 3 is compared with the fitness of individual 4. The individual with the higher fitness is chosen as “parent 2.” •Parents 1 and 2 are used in the crossover operation. •“elitist approach” (Goldberg 1989)UWECE 539 Class ProjectCrossover•Single-point crossover•Multi-point crossover•Uniform corssoverUWECE 539 Class ProjectConvergence and restarting •Convergence is defined as the progression towards chromosome uniformity •A gene may be considered to be converged, if 95% of that particular gene in the entire population shares the same value •A population is then converged when all of the genes are converged •Process can be restarted without any loss of informationUWECE 539 Class ProjectResults and Discussion (1) •351 generation was run to get the ‘optimum’ case •16×16×16×32×32×8=33,554,432 possible combinations of the six parameters •GA was able to find a satisfying case with great improvement compared with the baseline case and the maximum merit was observed to not change for more than 200 generations. It is considered that an ‘optimum’ case was foundUWECE 539 Class ProjectResults and Discussion (2) Maximum merit as a function of generation numberUWECE 539 Class ProjectResults and Discussion (3) Comparison between the baseline and optimum case Input Output MeritA B C D E F X Y Z MeritBaseline -143 0.440 0 60 125 0.5 11.7 139.7 1.386 -5.7Optimum -139 0.267 15 90 141 0.857 2.3 1.2 1.333 125.4Significant improvements have been achievedUWECE 539 Class ProjectMulti Layer Perceptron (1) •Multi-Layer Perceptron (MLP) network is setup to correlate the six inputs and three outputs •30% of the data was selected randomly and reserved for testing. Only 70% of the data was used for training •6-8-3 MLP network structure•The final training error is 0.0090 and the testing error is 0.0127UWECE 539 Class ProjectMulti Layer Perceptron (2) •The weight matrix of the hidden layer: -0.0928 0.9782 -0.7673 0.3791 5.9811 1.4702 -1.3212 1.5729 0.3189 -0.3103 -1.8411 -4.5168 1.1668 0.0312 1.8331 -0.5381 2.1315 1.1248 -0.1184 0.4692 -0.2042 2.9580 -0.0267 -0.5908 -0.2677 3.3509 0.0241 1.0066 4.4803 1.4442 -3.8054 -0.5408 0.7064 0.6601 0.1934 -2.0629 0.7693 -2.3483 0.0138 -0.5446 -0.0094 1.7161 1.4502 -0.2288 -1.4001 -0.7772 4.8072 0.0577 -2.5117 -2.1469 2.2675 2.4541 3.2225 0.1221 -2.6403 -0.6212The weight matrix of the output layer: 0.2365 0.3723 0.1336 0.3715 -0.4441 -0.1610 -0.1951 0.0984 -0.0809 1.3772 0.4357 -0.5307 0.0127 -0.8271 -0.3923 0.5913 0.1959 0.4667 0.5020 0.0197 -0.1090 0.0477 -0.4352 -0.1570 0.1923 0.0680 0.7139UWECE 539 Class Project• Genetic algorithm is a global optimization tool and can be used for engine design and operating parameter optimization effectively and efficiently. • Optimization results can be used to train the MLP network, and the developed network can be used to predict engine performance based on the inputs of the six engine operating parameters. ConclusionUWECE 539 Class ProjectReferences•Carroll, D. L., “Chemical Laser Modeling with Genetic Algorithms,” AIAA Journal, 34, 338, 1996.•Krishnakumar, K., “Micro-Genetic Algorithms for Stationary and Non-Stationary Function Optimization,” SPIE 1196, Intelligent Control and Adaptive Systems, 1989.•Senecal, P.K., and Reitz, R.D., “Simultaneous Reduction of Engine Emissions and Fuel Consumption Using Genetic Algorithms and Multi-Dimensional Spray and Combustion Modeling,” SAE 2000-01-1890, 2000.•Senecal, P.K., “Numerical Optimization Using the Gen4 Micro-Genetic Algorithm Code”, ERC Document,
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