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

1

Symposium on Automotive/

Symposium on Automotive/AvionicsAvionics Systems Engineering Systems Engineering (SAASE) 2009, UC San Diego

(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

Contents 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

3

Motivation 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

Engine Engine

Engine Control Unit

Engine Control Unit

Parameterization (Design Variables)

Constraints

Working Point Working Point

Constraints Optimization Goals

(Objective Values)

Engine

Engine Control Unit Control Unit

• Central part of modern automotive engines

• High computational complexity

5

Optimization

Optimization Approach 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

( ( Constraint Constraint ) ) Multi Multi - - objective objective Optimization Optimization

minimize Z = (z₁(x), z₂(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 ⊂ Rⁿ (search space)

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Pareto

Pareto - - Optimality 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: x₁ ≺ x₂

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

Non Non Dominance Dominance and and Pareto Pareto - - Front Front

• Pareto-optimal set: non-dominated set of the entire feasible region of the search space

• Pareto-Front: corresponding set in the objective space

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Genetic

Genetic Algorithms Algorithms (GA) (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

Principles

Principles of GA 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

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GA GA Flow Flow

Individual

Individual Encoding Encoding

• Representation of decision variables

• Components encoded as genes

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Population

Population Encoding Encoding

• Population of generations: set of individuals

Genetic

Genetic Operators (1/4) 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

…

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Genetic

Genetic Operators (2/4) Operators (2/4)

• Crossover (recombination): mates two individuals to produce two offsprings

Genetic

Genetic Operators (3/4) Operators (3/4)

• Crossover with multiple crossover points

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Genetic

Genetic Operators (4/4) Operators (4/4)

• Mutation: spontaneous changes on individuals

Evolutionary

Evolutionary Process Process

• Further GA Settings:

Population Size N

Crossover probability P_c

Mutation probability P_m

…

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Case Case Study Study : 4 : 4 - - stroke stroke Internal Internal Combustion Combustion Engine Engine

• Cycle process:

4 movements (strokes)

Crankshaft rotates 720°

• Angle of crankshaft:

Point in time for operations of the strokes

Controlled by ECU

4 4 Movements 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

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Engine

Engine Model Model

• WAVE® model (http://www.ricardo.com)

• Parameterized simulation ⇒ performance values

parameterization

simulation

Design Variables

Design Variables – – Engine Engine Parameters Parameters

[326, 386]

degree [deg]

Intake valve open x₇

[-30, 30]

degree [deg]

Combustion start x₆

[0, 240]

degree [deg]

Injection duration x₅

[-360, 60]

degree [deg]

Injection start x₄

[20, 110]

bar [bar]

Fuel pressure x₃

[40, 51.7]

millimeter [mm]

Diameter of throttle x₂

[0.5, 0.1111]

- Fuel/Air ratio

x₁

Scope Unit

Description Variable

• Optimization: adjusting parameters by the ECU

• Constraint: x₄ + x₅ < x₆

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Objective

Objective Values Values – – Requirements Requirements

≤ 180000 rpm

Speed of turbine y₇

in [0,400]

mm² Area of waste-gate attached to turbine

y₈

y₁₀ – y₉ ≤ 180 K

Temperature of thermocouple in duct of inlet y₉

K Temperature of thermocouple in exhaust of duct

y₁₀

≤ 1323.15 K K

Temperature of thermoelement of turbine inlet y₁₁

≤ 1223.15 K K

Temperature of thermoelement of turbine outlet y₁₂

= 0

≤ 8

≤ 130 (mechanical pressure)

≈ 14.5 ([10.5,18.5] acceptable) Maximum in (0, ∞∞∞∞)

Maximum in (0,∞∞∞)∞ Minimum in [0,1]

Objective / Constraint

- Normalized stall magnitude of compressor

y₁₃

bar/° KW Maximum rate of pressure rise in cylinder

y₆

bar Maximum cylinder pressure of cylinder 1

y₅

- Air/Fuel ratio trapped, multi-cylinder average

y₄

bar Brake mean effective pressure

y₃

bar Net indicated mean effective pressure

y₂

kg/KW /h Brake specific fuel consumption

y₁

Unit Description

f_i

Optimization

Optimization Approach Approach

minimize y = f(x) = (f₁(x), -f₂(x), -f₃(x))

subject to x₁ + x₅ < x₆ 0 ≤ f₁(x) ≤ 1 f₂(x) > 0 f₃(x) > 0

| f₄(x) – 14.5 | ≤ 4 f₅(x) ≤ 130

f₆(x) ≤ 8 f₇(x) ≤ 180000

0 ≤ f₈(x) ≤ 400 f₁₀(x) – f₉(x) ≤ 180 f₁₁(x) ≤ 1323.15 f₁₂(x) ≤ 1223.15 f₁₃(x) = 0

where x ∈ S ⊂ R⁷

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Tool Tool - - based based Framework Framework for for GA GA Application Application

GA Optimization Tool

Interface

GA

Model File Simulation Output File

GA Settings

ParetoOptimal Solutions

Individual Encoding

Individual Fitness Performance Values,

Constraints Design Variables,

Simulation Settings

WAVE ®

Engine Model Simulation

Archived Individuals

Experiments Experiments

100 200

200 population size

80 40

40 generations

0.9 0.8

0.8 crossover probability

0.1 0.2

0.2 mutation probability

Gaussian Gaussian

Gaussian mutation

Blend Uniform

Uniform crossover

Rank Roulette Wheel

Roulette Wheel selection scheme

Elitist Elitist

Elitist replacement

no yes

no preselection

no yes

yes discretized decision variables

Case 3 Case 2

Case 1

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Observations

Observations (1/2) (1/2)

• Collecting individual data during GA application

• Deriving further relations between design variables and objectives values

⇒ Simplified engine model

Observations

Observations (2/2) (2/2)

• y₂ and y₃: linear increasing dependency ⇒ neglecting y₃

• y₁ and y₂: competitive ⇒ 2-dimensional objective space

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Initialization

Initialization

1st Generation

1st Generation

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2nd Generation

2nd Generation

3rd Generation

3rd Generation

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4th Generation

4th Generation

5th Generation

5th Generation

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Final Generation

Final Generation

Dominated

Dominated Space Space

• Measering size of dominated space ⇒ final Pareto-Front

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Pareto

Pareto - - Front Front for for Case Case 1 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

Observations 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

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Convergence Convergence

• Case 2: preselection

• Case 1 and 2: discretized decision variables

ca. 8 d, 19 h ca. 12 d, 17 h

Overall duration

ca. 120 sec ca. 180 sec

Simulation duration

5760 5555

Total

simulations

Case 2 Case 1

Some Some Statistics Statistics

78 71

53 Individuals in Pareto-front of

final generation

60 43

36 Average individuals in

Pareto-front of generations

2 4

4 Individuals in Pareto-front of

initial generation

7653 5760

5555 Total simulated individuals

2304 5312

5496 Total infeasible individuals

68 72

68 Average feasible individuals

of generation

5412 2885

2703 Total feasible individuals

7716 8197

8199 Total created individuals

Case 3 Case 2

Case 1

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Scalability

Scalability of GA 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

Future

Future Work 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

…