Optimization Intevac Aug23 7f
- 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 Equipment Products Division
- 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) Equipment Products Division 2
- 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? Equipment Products Division 3
- 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 Equipment Products Division 4
- 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. Equipment Products Division 5
- 6. Facebook Analogy: Cost of “Human Delay” to Engineering Computing How to bring exponential growth to engineering computing? Eliminate weak link, eliminate “Human Delay”. Equipment Products Division 6
- 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. Equipment Products Division 7
- 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). Equipment Products Division 8
- 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 Equipment Products Division 9
- 10. INTEVAC’S CASE STUDY Equipment Products Division 10
- 11. Intevac c-Si Technology Si Substrates move on conveyer and heated http://www.intevac.com Equipment Products Division 11
- 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 Equipment Products Division 12
- 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. Equipment Products Division 13
- 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. Equipment Products Division 14
- 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 Equipment Products Division 15
- 16. eArtius – new word in multi-objective optimization capabilities Used in this study www.eartius.com Equipment Products Division 16
- 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. Equipment Products Division 17
- 18. Optimization Flow Chart in ModeFrontier Optimization (HMGE) Inputs: Setup ANSYS WB Interface Design of Optimizer Experiment Setup Estimations Constraints Constraints Objectives- to minimize Equipment Products Division 18
- 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; Equipment Products Division 19
- 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 Equipment Products Division 20
- 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. Equipment Products Division 21
- 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). Equipment Products Division 22
- 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. Equipment Products Division 23
- 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 Equipment Products Division
- 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 Equipment Products Division 25
- 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 Equipment Products Division 26
- 27. OPTIMIZATION RESULTS Equipment Products Division 27
- 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 Equipment Products Division 28
- 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 Equipment Products Division 29
- 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 Equipment Products Division 30
- 31. Optimization Solution: Pareto Front Zoom-In Detail deg.C Two conflicting Temperature Objectives Uniformity Best Designs Maximum Temperature, (T-Tmax) Equipment Products Division 31
- 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 Equipment Products Division 32
- 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. Equipment Products Division 33
- 34. Scatter Optimization Summary Matrix Equipment Products Division 34
- 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. Equipment Products Division 35
- 36. Student t-Test for our System - 2 Increase in the gap between Row1 and Row2 provides inverse effect on temperature difference. Equipment Products Division 36
- 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. Equipment Products Division 37
- 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” Equipment Products Division 38
- 39. Conclusion: Optimization = Innovation modeFrontier ANSYS eArtius WorkBench Equipment Products Division
- 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 . Equipment Products Division 40
- 41. SUPPLEMENTS Equipment Products Division 41
- 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. Equipment Products Division 42
- 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 Equipment Products Division
- 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 Equipment Products Division 44
- 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 Equipment Products Division