Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates

Parallel software for nonlinear systems of equations. Final report, February 28, 1995--June 30, 1997

The nonlinear systems of equations arising in circuit simulation, structural optimization, closed loop optimal control, chemical engineering of distillation systems, combustion chemistry, CAD/CAM modeling, robotics, computer vision, and orbital mechanics have several properties that make them especially amenable to homotopy methods. Even so, the homotopy zero curves are not trivial to track, and sophisticated curve tracking techniques are sometimes required. The size of typical engineering problems also presents some interesting numerical linear algebra challenges, and the supported work has been geared toward developing parallel sparse matrix techniques specifically tailored to the sparsity structures corresponding to the mentioned problem areas, in the context of homotopy algorithms. There are many different algorithms for tracking the zero curve {gamma}; the previous proposal discussed three such algorithms: ordinary differential equation based, normal flow, and augmented Jacobian matrix. The descriptions of these algorithms are now in the literature for the software package HOMPACK, so will not be repeated here. The development of sparse homotopy algorithms within HOMPACK specifically tailored for various parallel machines (e.g., distributed memory, shared memory, and vector) and problem areas (e.g., circuit simulation, structural optimization, optimal control, and combustion chemistry) was the central theme of this research

Compute as Fast as the Engineers Can Think! Utrafast Computing Team Final Report

This report documents findings and recommendations by the Ultrafast Computing Team (UCT). In the period 10-12/98, UCT reviewed design case scenarios for a supersonic transport and a reusable launch vehicle to derive computing requirements necessary for support of a design process with efficiency so radically improved that human thought rather than the computer paces the process. Assessment of the present computing capability against the above requirements indicated a need for further improvement in computing speed by several orders of magnitude to reduce time to solution from tens of hours to seconds in major applications. Evaluation of the trends in computer technology revealed a potential to attain the postulated improvement by further increases of single processor performance combined with massively parallel processing in a heterogeneous environment. However, utilization of massively parallel processing to its full capability will require redevelopment of the engineering analysis and optimization methods, including invention of new paradigms. To that end UCT recommends initiation of a new activity at LaRC called Computational Engineering for development of new methods and tools geared to the new computer architectures in disciplines, their coordination, and validation and benefit demonstration through applications

HPCCP/CAS Workshop Proceedings 1998

This publication is a collection of extended abstracts of presentations given at the HPCCP/CAS (High Performance Computing and Communications Program/Computational Aerosciences Project) Workshop held on August 24-26, 1998, at NASA Ames Research Center, Moffett Field, California. The objective of the Workshop was to bring together the aerospace high performance computing community, consisting of airframe and propulsion companies, independent software vendors, university researchers, and government scientists and engineers. The Workshop was sponsored by the HPCCP Office at NASA Ames Research Center. The Workshop consisted of over 40 presentations, including an overview of NASA's High Performance Computing and Communications Program and the Computational Aerosciences Project; ten sessions of papers representative of the high performance computing research conducted within the Program by the aerospace industry, academia, NASA, and other government laboratories; two panel sessions; and a special presentation by Mr. James Bailey

Three-Dimensional Aerodynamic Design Optimization Using Discrete Sensitivity Analysis and Parallel Computing

A hybrid automatic differentiation/incremental iterative method was implemented in the general purpose advanced computational fluid dynamics code (CFL3D Version 4.1) to yield a new code (CFL3D.ADII) that is capable of computing consistently discrete first order sensitivity derivatives for complex geometries. With the exception of unsteady problems, the new code retains all the useful features and capabilities of the original CFL3D flow analysis code. The superiority of the new code over a carefully applied method of finite-differences is demonstrated. A coarse grain, scalable, distributed-memory, parallel version of CFL3D.ADII was developed based on derivative stripmining . In this data-parallel approach, an identical copy of CFL3D.ADII is executed on each processor with different derivative input files. The effect of communication overhead on the overall parallel computational efficiency is negligible. However, the fraction of CFL3D.ADII duplicated on all processors has significant impact on the computational efficiency. To reduce the large execution time associated with the sequential 1-D line search in gradient-based aerodynamic optimization, an alternative parallel approach was developed. The execution time of the new approach was reduced effectively to that of one flow analysis, regardless of the number of function evaluations in the 1-D search. The new approach was found to yield design results that are essentially identical to those obtained from the traditional sequential approach but at much smaller execution time. The parallel CFL3D.ADII and the parallel 1-D line search are demonstrated in shape improvement studies of a realistic High Speed Civil Transport (HSCT) wing/body configuration represented by over 100 design variables and 200,000 grid points in inviscid supersonic flow on the 16 node IBM SP2 parallel computer at the Numerical Aerospace Simulation (NAS) facility, NASA Ames Research Center. In addition to making the handling of such a large problem possible, the use of parallel computation provided significantly reduced overall execution time and turnaround time

The Second ICASE/LaRC Industry Roundtable: Session Proceedings

The second ICASE/LaRC Industry Roundtable was held October 7-9, 1996 at the Williamsburg Hospitality House, Williamsburg, Virginia. Like the first roundtable in 1994, this meeting had two objectives: (1) to expose ICASE and LaRC scientists to industrial research agendas; and (2) to acquaint industry with the capabilities and technology available at ICASE, LaRC and academic partners of ICASE. Nineteen sessions were held in three parallel tracks. Of the 170 participants, over one third were affiliated with various industries. Proceedings from the different sessions are summarized in this report

The Cost of Numerical Integration in Statistical Decision-theoretic Methods for Robust Design Optimization

The Bayes principle from statistical decision theory provides a conceptual framework for quantifying uncertainties that arise in robust design optimization. The difficulty with exploiting this framework is computational, as it leads to objective and constraint functions that must be evaluated by numerical integration. Using a prototypical robust design optimization problem, this study explores the computational cost of multidimensional integration (computing expectation) and its interplay with optimization algorithms. It concludes that straightforward application of standard off-the-shelf optimization software to robust design is prohibitively expensive, necessitating adaptive strategies and the use of surrogates

확률 통계적 기법을 이용한 다분야 통합 최적설계 공간의 탐색 및 재설정에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2012. 8. 이동호.In this study, a stochastic and statistic approach for the systematic design space exploration and rearrangement is proposed. To efficiently investigate the feasibility of the design space, surrogate model and Monte Carlo simulation have been used. With these methods, probability density function, cumulative distribution function and reliability of the design space are calculated to identify the probability of design success. Then, the design space is moved and rearranged into the higher feasible region using Chebyshev inequality and reliability index. First of all, a number of test cases composed of algebraic functions were carried out to investigate the validity of the suggested method. For two exact functions, multidisciplinary feasible and collaborative optimization formulations were performed to verify the utility of proposed methods. As a result, converged design space included the feasible region located outside of the initial design space. Based on these results, the proposed method was applied to the multidisciplinary design optimization of the aircraft wing which also considered collaborative optimization with three subsystems (aerodynamics, structure, and performance). And then, design optimizations were performed for the initial and converged design space separately. Consequently, the feasibility and optimization result of the converged design space were improved in comparison with those of the initial design space. In conclusion, it is verified that the design space exploration and rearrangement method proposed in this study has the capability of searching for the feasible region which is excluded in the initial design space, and can rearrange the design space into the higher feasible design space automatically.본 연구에서는 확률 통계적 기법을 이용한 설계 공간의 탐색과 재설정에 관한 연구를 수행하였다. 설계 공간의 가용성을 효율적으로 계산하기 위해 근사 모델과 몬테카를로 시뮬레이션 기법을 적용하였다. 제시된 기법을 이용하여 설계 공간의 확률 밀도 함수와 누적 분포 함수, 신뢰성 지수 등의 확률 통계적 수치 값들을 효율적으로 계산하고 설계 성공 확률을 확인하였다. 계산된 설계 공간의 확률 통계적 특성 값들을 기반으로, Chebyshev 부등식과 신뢰성 지수를 이용하여 좀 더 넓은 가용 영역을 포함하는 설계 공간으로의 자동 재설정을 수행하였다. 먼저, 제안된 기법의 검증을 위하여 대수식으로 구성된 엄밀 함수에 대한 설계 공간의 탐색과 재설정을 수행하여 유용성을 검증하였다. 두 가지의 엄밀 함수에 대해 단일 단계 최적화 기법인 다분야 만족 기법 (multi-disciplinary feasible, MDF) 과 다단계 최적화 기법인 협동 최적화(collaborative optimization, CO) 로 정식화를 수행하여 다양한 다분야 통합 최적화 기법에 대한 유용성을 검증하였다. 그 결과로 수렴된 설계 공간은 초기 설계 공간의 외부에 놓여져 포함되지 않았던 가용 영역을 포함한 공간으로 자동 재설정 되었다. 이러한 결과를 바탕으로 제안된 기법을 대표적인 다분야 통합 최적설계 문제인 공력과 구조, 성능 분야를 함께 고려하는 항공기 날개의 다분야 통합 최적화 문제에 적용하였으며, 단일 단계 최적화와 더불어 대표적인 다단계 최적화 기법인 협동 최적화 기법도 적용하였다. 또한, 초기 설계 공간과 수렴된 설계 공간 각각에서의 최적화를 개별적으로 수행하여 그 값 들을 비교하여 수렴된 설계 공간의 가용성과 최적해가 초기 설계 공간의 값보다 향상된 값을 지니고 있음을 확인하였다. 이러한 결과를 통해서, 본 논문에서 제시된 확률 통계적 기법을 이용한 설계 공간의 탐색 및 재설정 기법은 다양한 다분야 통합 최적설계 문제에 적용함에 있어 초기 설계 공간에서 제외된 가용 영역까지도 포함한 가용성이 높은 영역으로 설계 공간을 효율적으로 탐색하고 자동적으로 재설정 할 수 있으며, 보다 향상된 최적해를 수렴된 설계 공간에서 도출할 수 있음을 확인하였다.ABSTRACT I TABLE OF CONTENTS III NOMENCLATURES VI LIST OF FIGURES IX LIST OF TABLES XII CHAPTER 1. INTRODUCTION - 1 - 1.1 Motivations - 1 - 1.2 Literature Survey - 6 - 1.3 Dissertation Objectives and Outline - 10 - CHAPTER 2. NUMERICAL ANALYSIS - 11 - 2.1 High-Fidelity Aeroelastic Analysis - 11 - 2.1.1 Aerodynamic Analysis - 11 - 2.1.1.1 Governing Equation: Three Dimensional Euler Equation - 11 - 2.1.1.2 Spatial Discretization - 13 - 2.1.1.3 Time Integration - 18 - 2.1.1.4 Grid System and Validation - 20 - 2.1.2 Structural Analysis - 22 - 2.1.2.1 Nine-node Shell Mixed Finite Element and Drilling DOF - 22 - 2.1.2.2 Validation of Nine-node Shell Mixed Finite Element - 24 - 2.1.2.3 Modeling of Wing Structure - 25 - 2.1.2.4 CFD and CSM Connection Scheme - 25 - 2.1.2.5 Sizing of Structural Component by Ultimate Loading Condition - 26 - 2.1.3 Aeroelastic Analysis - 27 - 2.2 Low-Fidelity Aeroelastic Analysis - 35 - CHAPTER 3. STOCHASTIC APPROACHES FOR THE DSE AND REARRANGEMENT - 38 - 3.1 Surrogate Model - 38 - 3.1.1 Response Surface methodology - 39 - 3.1.2 Artificial Neural Network - 41 - 3.2 Design of Experiment (DOE) - 44 - 3.3 Analysis of Variance (ANOVA) - 47 - 3.4 Monte-Carlo Simulation (MCS) - 49 - 3.5 Calculate the probability of success - 50 - 3.6 Chebyshev Inequality Condition - 54 - 3.7 Reliability Index - 57 - CHAPTER 4. DESIGN SPACE EXPLORATION AND REARRANGEMENT RESULTS AND DISCUSSION - 60 - 4.1 DSE and Rearrangement of the Design space to Improve the Feasibility with Chebyshev Inequality - 61 - 4.1.1 Test Functions - 62 - 4.1.1.1 Goldstein Function - 62 - 4.1.1.2 Branin Function - 63 - 4.1.1.3 Collaborative Optimization (CO) of Goldstein Function with Chebyshev Inequality Condition - 64 - 4.1.2 MDO of the Aircraft Wing - 66 - 4.1.2.1 Aero-structural Optimization of the Supersonic Fighter Wing with High Fidelity Analysis - 66 - 4.1.2.2 Aero-structural Optimization of the Transonic Wing with Low Fidelity Analysis - 68 - 4.1.2.3 CO of the Transonic Wing with Low Fidelity Analysis - 71 - 4.2 DSE and Rearrangement of the Design space to Improve the Feasibility with Reliability Index - 100 - 4.2.1 Test Functions - 101 - 4.2.1.1 Goldstein function - 101 - 4.2.1.2 Branin Function - 103 - 4.2.1.3 Collaborative Optimization (CO) of Goldstein Function with Reliability Index - 104 - 4.2.2 CO of the Transonic Wing with Low Fidelity Analysis Using RI Based Method - 107 - 4.3 Discussion - 123 - CHAPTER 5. CONCLUSIONS AND FUTURE WORKS - 125 - REFERENCE - 127 - 초 록 - 136 -Docto

Reducing the Computational Effort Associated with Evolutionary Optimisation in Single Component Design

The dissertation presents innovative Evolutionary Search (ES) methods for the reduction in computational expense associated with the optimisation of highly dimensional design spaces. The objective is to develop a semi-automated system which successfully negotiates complex search spaces. Such a system would be highly desirable to a human designer by providing optimised design solutions in realistic time. The design domain represents a real-world industrial problem concerning the optimal material distribution on the underside of a flat roof tile with varying load and support conditions. The designs utilise a large number of design variables (circa 400). Due to the high computational expense associated with analysis such as finite element for detailed evaluation, in order to produce "good" design solutions within an acceptable period of time, the number of calls to the evaluation model must be kept to a minimum. The objective therefore is to minimise the number of calls required to the analysis tool whilst also achieving an optimal design solution. To minimise the number of model evaluations for detailed shape optimisation several evolutionary algorithms are investigated. The better performing algorithms are combined with multi-level search techniques which have been developed to further reduce the number of evaluations and improve quality of design solutions. Multi-level techniques utilise a number of levels of design representation. The solutions of the coarse representations are injected into the more detailed designs for fine grained refinement. The techniques developed include Dynamic Shape Refinement (DSR), Modified Injection Island Genetic Algorithm (MiiGA) and Dynamic Injection Island Genetic Algorithm (DiiGA). The multi-level techniques are able to handle large numbers of design variables (i.e. > 100). Based on the performance characteristics of the individual algorithms and multi-level search techniques, distributed search techniques are proposed. These techniques utilise different evolutionary strategies in a multi-level environment and were developed as a way of further reducing computational expense and improve design solutions. The results indicate a considerable potential for a significant reduction in the number of evaluation calls during evolutionary search. In general this allows a more efficient integration with computationally intensive analytical techniques during detailed design and contribute significantly to those preliminary stages of the design process where a greater degree of analysis is required to validate results from more simplistic preliminary design models