Post on 27-Mar-2018
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.
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 ...
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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 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 – 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.