Model-based Parameter Optimization of an Engine Control Unit using Genetic Algorithms

Transcription

1 Symposium on Automotive/Avionics Avionics Systems Engineering (SAASE) 2009, UC San Diego Model-based Parameter Optimization of an Engine Control Unit using Genetic Algorithms Dipl.-Inform. Malte Lochau M.Sc. Bo Sun Prof. Dr. Ursula Goltz Dr. Petra Huhn Institute for Programming and Reactive Systems 1

2 Contents 1. Constraint Multi-objective Optimization, Pareto-Optimality, and Genetic Algorithms (GA) 2. Case Study: 4-stroke Internal Combustion Engine 3. Design of Experiments and GA Application 4. Results and Observations 2

3 Motivation Combustion engine callibration/regulation Multitude of electronically influenced controlling parameters Growing number of requirements Conflicting optimization goals for objective values Maximization: engine performance Minimization: fuel consumption Constraints Depends on working point Parameterization (Design Variables) Working Point Working Point Optimization Goals (Objective Values) Engine Engine Control Control Unit Unit Engine Constraints Constraints 3

4 Engine Control Unit Central part of modern automotive engines High computational complexity 4

5 Optimization Approach (Constrained) Multi-Objective Optimization Problem (MOP) Large, nonconvex search space High inner complexity with interdisciplinary influences Conventional analytical optimization approaches inapplicable Blind optimization Random search techniques Continuous validation of possible solutions on the engine test bed costly and impracticable Engine model simulation as objective function 5

6 (Constraint) Multi-objective Optimization minimize Z = (z 1 (x), z 2 (x),, z m (x)) (objective functions) subject to h j (x) = 0, j = 1, 2,, p (constraint functions) g k (x) 0, k = 1, 2,, q where x S (decision variables) and S R n (search space) 6

7 Pareto-Optimality Contradicting objectives: Min. fuel consumption Max. power values Selection of a solution from a set of best rated value combinations: Domination relation on decision vectors: x 1 x 2 Pareto-optimal set: non-dominated set of objectives in S Pareto-Front: corresponding set in the objective space Set of optimal solutions constitute different possible tradeoffs between objectives 7

8 Non Dominance and Pareto-Front Pareto-optimal set: non-dominated set of the entire feasible region of the search space Pareto-Front: corresponding set in the objective space 8

9 Genetic Algorithms (GA) Random, stochastic search technique for a defined MOP search space Evolutionary optimization approach inspired by natural selection ( survival of the fittest ) A population of abstract representations of candidate solutions (individuals) to an optimization problem evolves towards better solutions Independent of the complexity and internal structure of the optimization problem 9

10 Principles of GA Initialization: Population composed of random/preselected individuals in the search space Iteration: chain of generations Fitness of each individual in the population is evaluated according to optimization goals Multiple individuals are stochastically selected from the current population based on their fitness Selected individuals are modified, recombined, and possibly randomly mutated to form a new population (genetic operators) Infeasible individuals are refused Termination: A specified number of generations has been met, or A satisfactory fitness level has been reached for the population 10

11 GA Flow 11

12 Individual Encoding Representation of decision variables Components encoded as genes 12

13 Population Encoding Population of generations: set of individuals 13

14 Genetic Operators (1/4) Selection: choose individuals in a population to produce the next generation Individuals are selected mainly based on their fitness value expressing their survivability in the population Examples: Elitist selection Roulette-Wheel selection Tournament selection Rank selection 14

15 Genetic Operators (2/4) Crossover (recombination): mates two individuals to produce two offsprings 15

16 Genetic Operators (3/4) Crossover with multiple crossover points 16

17 Genetic Operators (4/4) Mutation: spontaneous changes on individuals 17

18 Evolutionary Process Further GA Settings: Population Size N Crossover probability P c Mutation probability P m 18

19 Case Study: : 4-stroke 4 Internal Combustion Engine Cycle process: 4 movements (strokes) Crankshaft rotates 720 Angle of crankshaft: Point in time for operations of the strokes Controlled by ECU 19

20 4 Movements 1. Intake / induction stroke fuel / air injection 2. Compression stroke ignition 3. Power / combustion stroke engine gives power 4. Exhaust stroke gas leaves combustion chamber 20

21 Engine Model WAVE model ( Parameterized simulation performance values parameterization simulation 21

22 Design Variables Engine Parameters Optimization: adjusting parameters by the ECU Variable Description Unit Scope x 1 Fuel/Air ratio - [0.5, ] x 2 Diameter of throttle millimeter [mm] [40, 51.7] x 3 Fuel pressure bar [bar] [20, 110] x 4 Injection start degree [deg] [-360, 60] x 5 Injection duration degree [deg] [0, 240] x 6 Combustion start degree [deg] [-30, 30] x 7 Intake valve open degree [deg] [326, 386] Constraint: x 4 + x 5 < x 6 22

23 Objective Values Requirements f i Description Unit Objective / Constraint y 1 Brake specific fuel consumption kg/kw /h y 2 Net indicated mean effective pressure bar Minimum in [0,1] Maximum in (0, ) y 3 Brake mean effective pressure bar Maximum in (0, ) y 4 Air/Fuel ratio trapped, multi-cylinder average - y 5 Maximum cylinder pressure of cylinder 1 bar 14.5 ([10.5,18.5] acceptable) 130 (mechanical pressure) y 6 Maximum rate of pressure rise in cylinder bar/ KW 8 Speed of turbine rpm y 7 Area of waste-gate attached to turbine in [0,400] mm 2 y 8 y10 y 9 Temperature of thermocouple in duct of inlet K y9 180 y 10 Temperature of thermocouple in exhaust of duct K y 11 Temperature of thermoelement of turbine inlet K K y 12 Temperature of thermoelement of turbine outlet = 0 K K y 13 Normalized stall magnitude of compressor - 23

24 Optimization Approach minimize y = f(x) = (f 1 (x), -f 2 (x), -f 3 (x)) subject to x 1 + x 5 < x 6 0 f 1 (x) 1 f 2 (x) > 0 f 3 (x) > 0 f 4 (x) f 5 (x) 130 f 6 (x) 8 f 7 (x) f 8 (x) 400 f 10 (x) f 9 (x) 180 f 11 (x) f 12 (x) f 13 (x) = 0 where x S R 7 24

25 Tool-based Framework for GA Application Design Variables, Simulation Settings WAVE Engine Model Simulation Performance Values, Constraints Model File Individual Encoding GA Optimization Tool Interface Simulation Output File Individual Fitness Archived Individuals GA GA Settings Pareto Optimal Solutions 25

26 Experiments Case 1 Case 2 Case 3 discretized decision variables yes yes no preselection no yes no replacement Elitist Elitist Elitist selection scheme Roulette Wheel Roulette Wheel Rank crossover Uniform Uniform Blend mutation Gaussian Gaussian Gaussian population size generations crossover probability mutation probability

27 Observations (1/2) Collecting individual data during GA application Deriving further relations between design variables and objectives values Simplified engine model 27

28 Observations (2/2) y 2 and y 3 : linear increasing dependency neglecting y 3 y 1 and y 2 : competitive 2-dimensional objective space 28

29 Initialization 29

30 1st Generation 30

31 2nd Generation 31

32 3rd Generation 32

33 4th Generation 33

34 5th Generation 34

35 Final Generation 35

36 Dominated Space Measering size of dominated space final Pareto-Front 36

37 Pareto-Front for Case 1 Comprehensive coverage of the search space Selection of a solution: Further analyses Ranking Validation on the real engine test best: Plausibility of optimization results Ensuring correctness of the model 37

38 Observations Final Pareto sets stable Clear and consistent solution identification in all 3 Cases Validation on the engine test bed But: convergence speed depends on GA settings Speed vs. Accuracy 38

39 Convergence Case 2: preselection Case 1 and 2: discretized decision variables Total simulations Simulation duration Overall duration Case ca. 180 sec ca. 12 d, 17 h Case ca. 120 sec ca. 8 d, 19 h 39

40 Some Statistics Case 1 Case 2 Case 3 Total created individuals Total feasible individuals Average feasible individuals of generation Total infeasible individuals Total simulated individuals Individuals in Pareto-front of initial generation Individuals in Pareto-front of final generation Average individuals in Pareto-front of generations

41 Scalability of GA Independent of inner complexity Supplying no further information on system under optimization Adaptable optimization framework: Engine Model Optimization goals und constraints GA Settings Adaptive GA: Adjustable object function (working point) Integration of learning approaches 41

42 Future Work Improving efficiency of GA: Enhanced genetic operators Punishment for constraint violations Parallel computation of individuals Improving accuracy of GA: Hybrid approaches Domain knowledge for different engine classes Improving usability of GA: Engineering workflow integration Result selection, statistics capabilities 42