iSIGHT/GT-Power Coupling

Brake Torque Design Exploration with Constrained Knock Index and NOx

Brad Tillock, GTICharles Yuan, Engineous Software, Inc

Problem Definition

! Using 4 cylinder GT-Power model and iSIGHT, perform multi-variable, constrained, design exploration of brake torque

! Use EngCylCombSITurb model in GT-Power with knock and NOx prediction

! Determine which of the independent parameters are the most important

! Evaluate design/quality interdigitation

Variables

! Independent Variables (input ranges on this page)" Spark timing -25 – 0 CA" Intake cam timing 229 – 249 Cam Angle" Exhaust cam timing 116 – 136 Cam Angle" Intake runner length 100 – 400 mm" Cylinder 1 and 4 exhaust runner length 300 – 500 mm" Cylinder 2 and 3 exhaust runner length 100 – 300 mm" Intake helmholtz diameter 50 – 200 mm

! Dependent Variables" Brake Torque (larger is better)" NOx – Must be less than 7.0 g/kWhr" Knock Index – Must be less than 5.0

Process (basic overview)

! In GT-Power" Validate model " Make parameters of the independent variables" Run the model

! In iSIGHT" Use iSIGHT to parse the independent parameters in the GT-Power

.dat file" Use iSIGHT to parse the output variables in the GT-Power .rlt file" Set up the command line execution of GT-Power

" After choosing a strategy in iSIGHT, the user can run the model.iSIGHT will read the output variables from the .rlt file at the end of each case and then replace the independent variables in the .dat file before the next case begins.

GT-Power Model

iSIGHT is a Complete Design Exploration Environment! Integration

" Linking of Commercial and Proprietary Tools " Leverages Existing Tools" Flexible Coupling Methods

! Automation" Automates current Manual Design-Evaluate-Redesign Process

! Design Exploration Tools" Design of Experiments " Optimization" Approximations " Quality Engineering Methods

! Solution Monitoring

What is iSIGHT

There is no limit on number of design variables and constraints

iSIGHT Automates Repetitive Tasks and ...

??

SimulationSimulation--basedbased

ProcessesProcessesInputInput OutputOutput

SimulationSimulation--basedbased

ProcessesProcessesInputInput OutputOutput

Explore Engine

Explore Explore EngineEngine

Exploration Engines

Optimization

# Rule-based# Exploratory (GA etc)# Gradient-based# Mixed Variable

Approx.Models

# Taylor series# Response Surface# Variable complexity

Design ofExperiment

# Central Composite# Full Factorial# Orthogonal Array# Latin Hypercube# Parameter# Database

Deterministic Methods

Deterministic Methods

QualityEngineering

# Monte Carlo# Taguchi Robust

Design# Reliability Analysis# Reliability-based

Optimization# 6-Sigma Robust

DesignStochastic Methods

Stochastic Methods

Design of Experiments

It is a good idea to do a DOE study before optimization to understand the

feature of the problem

DOE Studies

! A linear DOE study with 8 points was performed.! A quadratic DOE study with 36 points was

performed.! It was found out that both linear and quadratic DOE

study can’t capture the feature of this problem. As a result, a DOE study with 100 points was performed and its results are reported here.

! For complex problems, it is a good idea to do a DOE study before optimization to understand the feature of the problems.

DOE Studies – Linear Model

! 8 points are calculated to build a linear model! Plot is btorque as a function of icta and ilength! It clearly shows that a linear polynomial can’t represent its

feature

DOE Studies – Quadratic Model

! 36 points are calculated to build a quadratic model! Plot is btorque as a function of icta and ilength! It clearly shows that a quadratic polynomial can’t represent

its feature

DOE Studies – 100 Points

! 100 points are calculated to build a more realistic model! Plot is btorque as a function of icta and ilength! It clearly shows that a 100 point polynomial reveals a

different feature from linear or quadratic! A more than one step

optimization is needed

btorque: 155.4 to 169.3 btorque: 169.4 to 181.8

btorque: 181.8 to 192.3 btorque: 192.3 to 203.0

DOE – 100 Points – beyond quadratic

DOE – 100 Points – beyond quadratic

DOE – 100 Points – beyond quadratic

DOE Study Results

! From the DOE study, it is concluded that the following 4 design variables have much more impact on the design responses:" ecta" elength12" icta" Timing

! A normal one step optimization can’t find the global optimization.

Optimization

Interdigitation is needed for optimization of this kind of complex

problems

Optimization – TechniquesSequential quadratic programming technique and simulated annealing were selected to find the global optimal solution.

! Sequential Quadratic Programming" Exploits local area around initial design point. Rapidly obtains local

optimum design. It builds a quadratic approximation to the Lagrange function at each iteration. On each iteration, a quadratic programming problem is solved to find an improved design until the final convergence to the optimum design.

! Simulated Annealing" Obtain a solution with a minimal cost, from a problem which potentially has

a great number of solutions. Distinguishes between different local optima.

Optimization – Convergence History

donlp

sa

nlpql

Sequential quadratic programming – donlpSimulated annealing – saSequential quadratic programming - nlpql

Optimization – Convergence History

donlp

sa

nlpql

Sequential quadratic programming – donlpSimulated annealing – saSequential quadratic programming - nlpql

Optimization – Convergence History

donlp

sa

nlpql

183 234Sequential quadratic programming – donlpSimulated annealing – saSequential quadratic programming - nlpql

Optimization - Results

ecta 126.0 128.0659elength12 400.0 378.2638elength23 200.0 145.4489hdia 125.0 89.2501icta 239.0 229.0000ilength 250.0 255.0940timing -12.5 -10.1487btorque 188.545 203.422bsnox 6.78538 6.58559knockindex 3.02326 3.07923

baseline optimal

Optimization Results

305 330 355 380 405 430 455elength12

140

160

180

200

btor

que

115 120 125 130 135ecta

140

160

180

200

btor

que

105 130 155 180 205 230 255elength23

140

160

180

200

btor

que

60 80 100 120 140 160 180 200hdia

140

160

180

200

btor

que

230 235 240 245 250icta

140

160

180

200

btor

que

100 150 200 250 300 350 400ilength

140

160

180

200

btor

que

-25 -20 -15 -10 -5timing

140

160

180

200

btor

que

! The optimization history plots reveal that this is a difficult optimization problem to solve.

! iSIGHT’s interdigitation strategy works for this kind of optimization problem.

Approximation

Approximation can be used to speed up the computation and smooth out

the effect of noise factors

ecta = 116 – 136

elength = 300 - 500

elength23=200

hdia=130

icta=239

ilength=250

timing=-12

Approximation Models

Kriging Model Quadratic Model

Model Accuracy

100120140160180200220240260280300

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97

Point Number

btor

que

Exact Quadratc Polynomial Kriging

Max Error Average Error Max Error Average Error Max Error Average ErrorKriging 3.11% 0.86% 5.83% 1.72% 41.86% 11.34%Quadratic Plynimial 36.39% 7.58% 19.06% 4.82% 257.48% 43.60%

btorque bsnox knockindex

Approximation Models

Quality Engineering

Quality engineering methods can be used to understand the random nature

of the problem

! Risks of “Optimized” Design:

"Sensitive “peak” solutions – small changes in inputs results in significant loss of performance

Effects of Uncertainty: Performance Variation

OptimizationConstraintBoundary

X1

X2

Feasible Infeasible (safe) (failed)Initial Design

Failed Designs

"Active Constraints – uncertainty, variation leads to failed designs

Optimized Design

PotentialPerformance

Loss

Reliability Analysis – MCS (376 Runs)

**************Reliability Analysis Results*************Constraint { bsnox lower 0 }, reliability = 1Constraint { bsnox upper 7 }, reliability = 0.962667Constraint { knockindex lower 0 }, reliability = 0.76Constraint { knockindex upper 5 }, reliability = 1*******************************************************

The optimal solution is not stable. The lower bound of knockindex Is lest reliable.

Design for Six Sigma - DFSS

ecta 128.0659 127.0627elength12 378.2638 498.3097elength23 145.4489 145.4489hdia 89.2501 89.2501icta 229.0000 229.0ilength 255.0940 255.0940timing -10.1487 -13.5591btorque 203.422 200.922bsnox 6.58559 6.68375 10.0 100.0knosindex 3.07923 5.502 10.0 100.0

optimal DFSS sigma P. Of Success

The DFSS is performed by using the 4 important design variables from DOE study.