[PPT] - Multi-Objective Optimization of a Kinetics-Based HCCI Model Ali M. PowerPoint Presentation

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Multi-Objective Optimization of a Kinetics-Based HCCI Model

Ali M. Aldawood, Sebastian Mosbach, Markus Kraft

University of Cambridge

Amer A. Amer

Saudi Aramco

JSAE Paper No. 20119051 SAE Paper No. 2011-01-1783

SLIDE 2

Outline

 Introduction & Motivation  Optimization setup

─ Engine & model ─ Optimization variables ─ Objective functions ─ Search method

 Results  Conclusions 2

SLIDE 3

Introduction

 Detailed-kinetics

modeling is computationally intensive, and thus reduced kinetics are favored when time and resources are limited

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SLIDE 4

Reduced-Mechanism Performance

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P= 40 bar, =1.0 Shock tube data from Fieweger et al.

SLIDE 5

Reduced-Mechanism Performance

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50

50 20 40 60 80

Cylinder Pressure (bar)

1200 rpm, PRF40, =0.19

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50 20 40 60 80

1200 rpm, PRF40, =0.26

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50 20 40 60 80

1200 rpm, PRF60, =0.26

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50 20 40 60 80

CAD (deg)

Cylinder Pressure (bar)

1200 rpm, PRF60, =0.32

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50 20 40 60 80

CAD (deg) 1200 rpm, PRF60, =0.29

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50 20 40 60 80

CAD (deg) 1200 rpm, PRF60, =0.21

Experiment 767-Species 157-Species 33-Species

Pin=1.5 bar Tin=75 oC HCCI, PFI

SLIDE 6

Motivation

 Kinetic mechanism reduction speeds up computations

but could compromise model predictivity of certain responses of interest

 Reduced mechanisms are normally optimized to

preserve good fit with ignition delay data. How does this affect other responses?

 Use multi-objective optimization to examine the

interplay among different responses

 Understand best ways for optimizing kinetic engine

models for better prediction of engine responses

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SLIDE 7

Optimization Setup

SLIDE 8

Optimization Scheme

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SLIDE 9

Experimental Setup

Number of cylinders 1 Operation cycle 4-stroke Combustion mode HCCI Number of valves 4 Displacement (litres) 0.5 Bore (mm) 84 Stroke (mm) 90 Connecting rod (mm) 159 Crank radius (mm) 45 Compression ratio 12:1 Fuel delivery PFI Intake pressure (bar) 1.5 Intake temperature (oC) 75

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SLIDE 10

Experimental Setup

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Stochastic HCCI Model

Non-spatial notional particles

represent cylinder charge space

Volume, density, and pressure

are treated as global variables

Temperature and composition

evolve locally in each particle according to a probability density function

Inter-particle mixing is based
n temperature proximity
Convective heat transfer with

the cylinder wall is calculated by Woschni's coefficient

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SAE Papers: 2004-01-0561, 2005-01-0161, 2006-01-1362, 2009-01-1134

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Optimization Variables

 Four SRM parameters (wall

temperature, residual gas fraction, turbulent mixing time and stochastic heat transfer coefficient)

 Arrhenius equation's pre-

exponential factor (A) , temperature exponent () and activation Energy (E)

 Optimization was

constrained and carried out against 12 experiments at each iteration

        RT E AT k exp



Arrhenius Equation 12

SLIDE 13

Sensitivity Analysis

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SLIDE 14

Objective Function Formulation

 Sum of squared differences

between experiment and model values

 Nine points for ignition delay

curve, five on cylinder pressure curve, and single points for CO and HC emissions

 SRM parameters optimized

for best pressure fit are used as basis for estimating improvement in predictivity

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SLIDE 15

Search Method

 Search for global minimum

within nonlinear constrained search space

 Stochastic search using multi-

bjective genetic algorithm

 GA is based on evolution theory,

where variable values (chromosomes ) of best solutions from initial population (parents) are used to produce next generation (children)

 Randomization (mutation)

allows experimenting new regions within the search space, therefore escaping local minima

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SLIDE 16

Optimization Results

SLIDE 17

Cylinder Pressure vs. Ignition Delay

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SLIDE 18

Ignition Delay

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SLIDE 19

Engine Model Responses

0.5 1 1.5 2 2.5 x 10

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50 100 150 2 4 6 8 10 12 x 10

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Pressure Objective Function CO Objective Function HC Objective Function Solution points Pareto front

Pressure & HC Best Fit CO Best Fit Original Model

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SLIDE 20

Cylinder Pressure (1200 rpm)

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50 20 40 60 80 1200 rpm, PRF40, =0.21

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50

50 20 40 60 80 1200 rpm, PRF80, =0.35

CAD (deg) CAD (deg)

r Pressure (bar)

SLIDE 21

Cylinder Pressure (1200 rpm)

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50 20 40 60 80 Cylinder Pressure (bar) 1200 rpm, PRF40, =0.19

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50 20 40 60 80 1200 rpm, PRF40, =0.21

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50 20 40 60 80 1200 rpm, PRF40, =0.26

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50 20 40 60 80 1200 rpm, PRF40, =0.29

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50 20 40 60 80 Cylinder Pressure (bar) 1200 rpm, PRF40, =0.32

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50 20 40 60 80 1200 rpm, PRF60, =0.21

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50 20 40 60 80 1200 rpm, PRF60, =0.26

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50 20 40 60 80 1200 rpm, PRF60, =0.29

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50 20 40 60 80 CAD (deg) Cylinder Pressure (bar) 1200 rpm, PRF60, =0.32

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50 20 40 60 80 CAD (deg) 1200 rpm, PRF80, =0.29

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50 20 40 60 80 CAD (deg) 1200 rpm, PRF80, =0.32

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50 20 40 60 80 CAD (deg) 1200 rpm, PRF80, =0.35

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SLIDE 22

Cylinder Pressure (1500 rpm)

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50 20 40 60 80 1500 rpm, PRF40, =0.23

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50

50 20 40 60 80 1500 rpm, PRF80, =0.36 CAD (deg) CAD (deg)

r Pressure (bar)

SLIDE 23

Cylinder Pressure (1500 rpm)

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50 20 40 60 80 Cylinder Pressure (bar) 1500 rpm, PRF40, =0.20

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50 20 40 60 80 1500 rpm, PRF40, =0.23

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50 20 40 60 80 1500 rpm, PRF40, =0.26

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50 20 40 60 80 1500 rpm, PRF40, =0.29

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50 20 40 60 80 Cylinder Pressure (bar) 1500 rpm, PRF40, =0.33

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50 20 40 60 80 1500 rpm, PRF60, =0.23

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50 20 40 60 80 1500 rpm, PRF60, =0.27

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50 20 40 60 80 1500 rpm, PRF60, =0.30

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50 20 40 60 80 CAD (deg) Cylinder Pressure (bar) 1500 rpm, PRF60, =0.32

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50 20 40 60 80 CAD (deg) 1500 rpm, PRF80, =0.34

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50 20 40 60 80 CAD (deg) 1500 rpm, PRF80, =0.35

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50 20 40 60 80 CAD (deg) 1500 rpm, PRF80, =0.36

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SLIDE 24

Cylinder Peak Pressure

0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar) 1200 rpm - IAT 75oC PRF40 Original Model Best Pressure Fit 0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar) 1200 rpm - IAT 75oC PRF60 Original Model Best Pressure Fit 0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar) 1200 rpm - IAT 75oC PRF80 Original Model Best Pressure Fit 0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar)



1500 rpm - IAT 75oC PRF40 Original Model Best Pressure Fit 0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar)



1500 rpm - IAT 75oC PRF60 Original Model Best Pressure Fit 0.1 0.2 0.3 0.4 40 50 60 70 80 90 Peak Pressure (bar)



1500 rpm - IAT 75oC PRF80 Original Model Best Pressure Fit

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SLIDE 25

CO & HC Emissions

0.2 0.25 0.3 1 2 3 4 5



CO (%) 1200 rpm - PRF40 0.2 0.25 0.3 1 2 3 4 5 CO (%)



1200 rpm - PRF60 0.25 0.3 0.35 0.4 1 2 3 4 5 CO (%)



1200 rpm - PRF80 0.2 0.25 0.3 1000 2000 3000 4000 5000 HC (ppm)



1200 rpm - PRF40 0.2 0.25 0.3 1000 2000 3000 4000 5000 6000 7000 HC (ppm)



1200 rpm - PRF60 0.25 0.3 0.35 0.4 2000 4000 6000 8000 10000 12000 14000 HC (ppm)



1200 rpm - PRF80 Experimental data Orignal Model Best HC Fit Experimental data Original Model Best CO Fit

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SLIDE 26

Conclusions

 Conflicting trends observed among objectives normally used in

mechanism optimization

 Reduced mechanisms, normally optimized for ignition delay

prediction, may not be as predictive of engine responses

 Careful selection of optimization objectives increases the

likelihood of better predictivity of reduced mechanisms

 Multi-objective optimization could offer great help for guiding

mechanism reduction process

 Multi-objective optimization offers more freedom for customizing

kinetic models based on intended purpose

 Useful in practical applications where high degree of predictivity

for limited number of responses is needed, but only a reasonable computational expense is afforded

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