Multi Objective Computational Optimization with HMGE, eArtius and modeFrontier

1. Multi-Objective Optimization of Solar Cells
Thermal Uniformity Using Combined Power
of ANSYS Multi-Physics, modeFrontier and
eArtius
Vladimir Kudriavtsev, Terry Bluck (Intevac)
Vladimir Sevastyanov
(eArtius, Irvine, CA)
ANSYS Regional Users Conference, “Engineering the
System”, Santa Clara, CA Aug.23, 2011
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2. Current Computational Design Process
8 threads i7
CPU
Computer DELAY Ingenious
Solutions
240 cores TESLA Graphic
Processing Unit GPU (x2)
Human Thinking
and Analysis
slowest component
fastest component (meetings, reviews,
and grows exponentially faster
alignments, cancelations)
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3. Underused Resources – What to do?
8 cores i7 CPU
PC Computer
1 case study
All these fast growing
256-512 processor resources to do just one
TESLA Graphic case study or parametric
Processing Unit investigation?
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4. Morning after Effect
10 times CPU speed
improvement
10 hours overnight job Makes no difference
or at 8 AM in the morning
1 hour overnight job
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5. What to Do - Dilemma
Improvement in software strength and parallelization
Improvement in software multi-Physics coupling
Multi-processor PC boxes (i7, Phenom)
Tesla GPU computing with up to 100x speedups
with hundreds of processing cores
-“Nothing to run” as single user mental bottleneck is reached,
computer resource is underutilized, software is idle.
-Single license can be shared across many users, results in
less demand for software and related services.
-Results in poor return on software investment, slowing in
growth.
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6. Facebook Analogy: Cost of “Human
Delay” to Engineering Computing
How to bring exponential growth to engineering computing?
Eliminate weak link, eliminate “Human Delay”.
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7. Why Optimization by Computer?
Human can not match computer in repetitive tasks and consistency.
Assuming computational problem takes 30 minutes of CPU time,
then in one day (between 8AM to 8 AM) computer is capable of
producing 48 design evaluations, with 144 designs completed in
just 3 work days.
Coupled with multi-processing capability of i7 workstation this number can
easily be multiplied by factors ranging from two to six.
Computer will work during the weekend; it will work when user is on vacation,
on sick leave or on business trip.
Personal “super computer” cost is now
inconsequential for the bottom line.
Software cost sky-rocketed, and its ROI and
utilization efficiency is now most important.
Computer needs algorithmic analogy of “human brain”
to self-guide solution steps.
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8. New Paradigm
New paradigm of multi-objective computational design is now
being born.
No longer designer needs to approach it through “trial-and-error”
simulations, but can rather use “artificial intelligence” of optimization
method to automatically seek and to find best combination of input
parameters (design). Depending on problem size (CPU time) this process
can take from minutes to weeks.
However, now engineer can view tens and hundreds of possible solutions,
automatically singling first truly best designs and then evaluate design
trade-offs between conflicting objectives (Pareto Frontier).
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9. Benefits
Computational software companies:
- new demand for products for optimization software modules and
schedulers
-number of required computations per user increase 100 to 5000 times
- new demand for computer speed-up via parallelization, number of CPUs
(simultaneous processing), number of PCs(clusters)
Engineering users:
-detailed computational characterization of designs and new level of
understanding
-finding truly optimal and innovative engineering solutions
-computer does “dirty work”, user spends more time analyzing data
and tuning optimization engine
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10. INTEVAC’S CASE
STUDY
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11. Intevac c-Si Technology
Si Substrates move on conveyer and heated
http://www.intevac.com
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12. Heating Challenge to Address
Great number of companies and technologists in Silicon Valley are now
focused on developing lower-cost processing methods and capital
equipment to manufacture solar cells. It is typically done through a variety
of high temperature thermal processes, where temperature uniformity is
the most critical factor.
Using ANSYS Workbench we developed lamp heating surface-to-surface
thermal conduction-radiation model for simultaneous transient multi-step
heat-up of silicon substrates. Lamp locations, lamp to substrate
distances, lamp dimensions, lamp power and its distribution are being
optimized to achieve industry standard ±5 degrees thermal uniformity
requirement.
http://www.intevac.com/solar-process-sources
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13. Problem Formulation
Minimize thermal variation across single substrate and across a group
of substrates during radiant heating stage (TempDiff)
Operate in required process temperature window, T-dev1<Top<T+dev2
Optimization Formulation ANSYS WB Formulation:
Top=400 deg.C
min (TempDiff)
min abs(Tmax-Top) & min abs(Tmin-Top)
Constraints to determine design feasibility:
T<Tmax.constr & T>Tmin.constr, where
Tmin.constr= Top-dev1, Tmax.constr=Top+dev2
If dev1 and dev2 are small, then optimization problem is very restrictive.
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14. Problem Analogy – Hidden Valley in the Mountains
Narrow optimum
Sub-Optimal
range
Optimal
range
xT^4 nonlinear
steep change
Narrow process window
Gradient method requires path, to enter narrow optimal range (due to nonlinearity)
it requires guidance or coincidence. Guidance comes from the previous history
(steps taken before, gradients) and coincidence from DOE or random mutations.
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15. Detail of modeFrontier GUI & Functions
Design of
Experiments DOE
Methods:
Work flow Optimization
Problem Definition
Rich selection of
optimization
methods SolidWorks Interface
Design Table
ANSYS Interface
Can automatically email results
Excel,Matlab,Labview,etc Interfaces
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16. eArtius – new word in multi-objective
optimization capabilities
Used
in this
study
www.eartius.com
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17. Mode Frontier and eArtius Roles
In our study we used modeFrontier as optimization enabling (Scheduler)
and statistical data post-processing tool and eArtius multi-objective
optimization methods plug-in tool to guide continuous process of
selecting better input variables to satisfy multiple design objectives.
This process follows “fire and forget” principle and relies on combination
of self-guiding gradient methods with genetic selection (crossover and
mutation). Algorithm automatically use current results to best select
inputs for the next design decision step. Gradient based computer
thinking combines advantages of precise analytics with human like
decision making (selecting roads that lead to improvement, avoiding weak
links, pursuing best options, connecting dots). Genetic component guides
selection and allows to jump out if local improvements can not be found.
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18. Optimization Flow Chart in ModeFrontier
Optimization (HMGE)
Inputs: Setup
ANSYS WB
Interface
Design of Optimizer
Experiment
Setup Estimations
Constraints Constraints
Objectives- to minimize
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19. Problem Parameters – Geometry and
Temperature
<Tempdiff> =Tmax-Tmin
between 3 substrates
Si subst
minus rate T1
gap
T2
plus
Lamp Bank 1
Lamp Bank 2
lamps
height T1-radiation temperature of first
substrates lamp array;
T2-radiation temperature of
T1,T2 control heat flux from lamps. second lamp array;
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20. Thermal Problem – Setup
<Tdiff>= Tmax-Tmin Parameters set inside
between 3 substrates ANSYS Workbench:
Geometry in Design Modeler and
temperature in Workbench Model
Optimization Parameters:
Mesh Elements
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21. Thermal Heating (Radiation) Solution
Interplay between
two lamp arrays
Substrate Motion
Lamp Bank 1 Lamp Bank 2 Direction
Multi-Step Transient History
Transient Heating Scenario: Row1 of substrates is first heated by Lamp Bank1,
then these Substrates moved to Lamp Bank2 and get heated again till desired Top=400 deg.C is
reached. Simultaneously, new substrates with T=Tambient populate Row1 and get heated.
Thus, Row1 heats from 22 to 250 deg.c and Row 2 from 250 to 400 deg.C.
at time t=3.5 sec Row1 T is reset at 22 deg.C; Row2 T is reset at 250 deg.C.
at time t=0 sec Row1 T is set at 22 deg.C; Row2 T is set at 250 deg.C.
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22. Hybrid Multi-Gradient Explorer (HMGE)-1
New Hybrid Multi-Gradient Explorer (HMGE) algorithm for global multi-
criteria optimization of objective functions considered in a multi-
dimensional domain is utilized in this study. This hybrid algorithm relies
on genetic variation operators for creating new solutions, but in addition
to a standard random mutation operator, HMGE uses a gradient mutation
operator, which improves convergence.
Thus, random mutation helps find global Pareto frontier, and gradient
mutation improves convergence to the Pareto frontier. In such a way
HMGE algorithm combines advantages of both gradient-based and
Genetics-based optimization techniques: it is as fast as a pure gradient-
based algorithm, and is able to find the global Pareto frontier with
robustness similar to genetic algorithms (GA).
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23. Hybrid Multi-Gradient Explorer-2
Method also dynamically recognizes the most significant design
variables, and builds local approximations based only on these variables.
This allows high efficiency in gradients estimation and can be achieved
within 4-5 model evaluations without significant loss of accuracy.
On test problems HMGE efficiency is 2-10 times higher when compared to
the most advanced commercial genetic algorithms.
As a result, HMGE is a natural choice to be coupled with ANSYS
Workbench for fully automatic computational engineering optimization.
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24. HMGE Algorithm
Generate Initial Designs
The crowding distance value of a solution provides an
Add New Designs to Archive
estimate of the density of designs surrounding that design
The crowding distance mechanism together with a Sort Designs by Crowding
mutation operator maintains the diversity of non- Distance (descent)
dominated designs in the archive
Crossover is a genetic operator used to vary the Apply Crossover Operator
programming of chromosomes from one generation to the
next—to find new designs inheriting best features of
previously found designs Apply Gradient Mutation
Operator
Random Mutation: take any random individual and take
a random design. Change the gene on that design with Apply Random Mutation
another random value—to find global optimum Operator
Gradient Mutation: take any non-dominated individual No Check Exit
and perform a gradient-based step towards simultaneous Condition
improvement of all objective functions—to increase
convergence towards local Pareto frontier
Exit
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25. Dynamically Dimensioned Response Surface
DDRS Method is a fast and scalable algorithm for estimating gradients
DDRSM can be used as an element for designing any gradient-based optimization
algorithms, including hybrid algorithms.
How DDRSM operates:
Automatically determines the most significant design variables for each response variable
separately
Builds local approximations for each response based only on the most significant design
variables
Estimates gradients analytically based on local approximations
Repeats the above sequence on each optimization step
DDRSM Benefits:
Equally efficient and accurate for any task dimension
Requires just 0-7 model evaluations regardless of task dimension
Fast— it builds a local approximation in 10-30 milliseconds
Automatic and hidden from users
Eliminates necessity in global response surface methods
Eliminates necessity in a sensitivity analysis
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26. Multi-Gradient Analysis for Multi-Objective
Optimization
The MGA pseudo-code:
1 Begin
2 Input initial point X0.
3 Evaluate criteria gradients on X0.
4 Determine ASI for all criteria.
5 Determine the direction of simultaneous improvement for all objectives for the next step.
6 Determine the length of the step.
5 Perform the step, and evaluate new point X’ belonging to ASI.
7 If X’ dominates X0 then report improved point X’ and go to 10.
8 If X’ does not dominate X0 then report X0 as Pareto optimal point.
10 End
©Copyright eArtius Inc 2010 All Rights Reserved
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27. OPTIMIZATION RESULTS
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28. Thermal System Optimization Task
Formulation
Need to
carefully
consider
Minimize+ – preferable
objectives
278 feasible designs of 317 evaluations
Minimize – regular objective
18 Pareto+ designs of 35 Pareto optimal designs
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29. “Fire And Forget” Solution Process - HMGE
deg.C
Temperature
Uniformity
21
First Wave Second Wave
17
13
9
Touchdown
DOE
5 Design ID (#)
46 92 138 184 230 276 300
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30. HMGE Optimization of Temperature
Difference
25.2 deg.C
Temperature
Uniformity
DOE Builds
approximations
15.2 around best
data
designs
accumulation
9.2
DOE
Design ID (#)
34 104 184
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31. Optimization Solution: Pareto Front
Zoom-In Detail
deg.C
Two conflicting
Temperature Objectives
Uniformity
Best Designs
Maximum Temperature, (T-Tmax)
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32. Multi-Design Decision Making in mFrontier
MDDM—
initially very
cluttered and
confusing
Tempdiff is
narrowed to
Less than 6 deg.C
and suddenly way
more clarity
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33. Best Designs Selected -MDDM
Tempdiff is narrowed to less than 6 deg.C and allowable
deviation from maximum temperatuire reduced to 10 deg.C.
Only several acceptable designs are left to consider.
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34. Scatter Optimization Summary Matrix
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35. Student t-Test for our System -1
Increase in Height+ has direct effect on
uniformity and proximity to desired operating T;
Increase in T1 (lamp bank1 flux) has direct
positive effect on TempDiff and proximity to
desired T; an increase in T2 achieves opposite
effect.
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36. Student t-Test for our System - 2
Increase in the gap between Row1 and Row2 provides inverse effect on
temperature difference.
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37. Pareto Optimal Solution
dev1
dev2
Pareto+ and Pareto optimal designs
belong to different brunches of Pareto
Pareto optimal points in design space have two
frontier in criteria space
disjoint areas. It is noticeable that majority of
Pareto+ and Pareto optimal designs belong to
different disjoint areas
We hypothesized that there are two zones of optimality in this problem.
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38. Going Head-to-Head with Human
In head-to-head competitions best “human guided” (case-by-case) studies
resulted in system design with ±10-20 deg.C thermal uniformity and took
several weeks to accomplish, while computer optimization based
approach allowed to quickly yield multiple solutions capable of reaching
± 3 deg. C. It took only two 24 hour cycles for CPU to “independently”
accomplish this task.
But most importantly, multi-objective optimization analysis provided
unique insights into system behavior and lead to innovative enabling
design solutions. Statistical analysis of designs provided confidence that
we found solutions that are truly best.
Thus, we can conclude that “Optimization Equals Innovation”
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39. Conclusion: Optimization = Innovation
modeFrontier ANSYS eArtius
WorkBench
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40. Acknowledgement
Authors are thankful to ESTECO engineers for developing
eArtius HMGE modeFrontier plug-in; to Alberto Bassanese
(ESTECO) for introducing and helping with modeFrontier; to
ANSYS Distributor in Bay Area Ozen Engineering
www.ozeninc.com (Kaan Diviringi, Chris Cowan and Metin
Ozen) for help and dedicated support with ANSYS Workbench
model development and integration with modeFrontier .
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41. SUPPLEMENTS
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42. Design Explorer with ANSYS Workbench
T1 T2 Height TempDiff
Seeking desired (Target) Top Minimize temperature
(operational temperature variation, TempDiff
T=400 deg.C)
Excellent tool for Design of Experiment Studies with extension to Response Surface based
optimization. DOE data analyzed after the fact, Response surfaces created and
theoretically optimal values are predicted. Accuracy of this prediction is limited by
number of design points available for approximation and nonlinearity inherent to physics.
Theoretical estimates need to be re-run again to verify their accuracy.
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43. Optimization Using NSGAII modeFrontier
20.3 deg. C
Temperature
Uniformity
14.3. TempDiff dev2
6.6/ 2.76
6.33
32 64 Design ID (#)
96 128 160
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44. Fast MOGAII Optimization with mode
Frontier
deg.C
Temperature
Uniformity
TempDiff dev2
5.89/ 1.2
15.77
9.77
5.77
Design ID (#)
32 128 Touchdown
176
80
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45. Example of Extremely Long Run
9.83 deg. C
Temperature
Uniformity
Design table
reloaded
7.5
DOE,
preselected
Best points,
4.9
1056 2336
Design ID (#) TempDiff dev2
5.56/ 8.93
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