Discuss on Approximate Optimization Strategies Using Design of Computer Experiments and Metamodels for Flight Vehicle Design

Although the wide use of high fidelity analysis models in modern flight vehicle design is beneficial to improving the design credibility and overall performance of flight vehicle systems, it also causes high computational cost and complexity. In order to alleviate the computational difficulty, approximate optimization strategies using design of computer experiments(DoCE) and metamodels for flight vehicles have become more and more popular, which construct reasonable approximation models to enable efficient convergence to the optimal solution with much less computational burden and shorter design cycles. An extensive literature survey of the state-of-the-art of approximate optimization strategies in the context of flight vehicle design is provided. The definition, solution process, features and key technologies of approximate optimization strategies are presented, and then the development of DoCE, metamodeling, accuracy assessment and metamodel selection, as well as corresponding typical methodologies, are reviewed. Moreover, metamodel management and updating schemes and termination criteria used in both static and adaptive approximate optimization strategies are specifically discussed. The efficiency and convergence behaviors of approximate optimization strategies for solving multidisciplinary design optimization (MDO) problems are analyzed via comparison with decomposition-based strategies. A number of well-known numerical benchmark problems are employed to discuss the characteristics of the aforementioned key technologies. Furthermore, the overall performance and applicability of different approximate optimization strategies are discussed through flight vehicle design applications. Comparative studies demonstrate that approximate optimization strategies show obvious advantages in optimization efficiency, convergence and robustness, which are important for engineering applications. Future research directions of approximate optimization strategies are given.

[1]  Shenmin Zhang,et al.  Surrogate-based parameter optimization and optimal control for optimal trajectory of Halo orbit rendezvous , 2013 .

[2]  Hui Wang,et al.  Aero-Structure-Stealth Coupled Optimization for High Aspect Ratio Wing Using Adaptive Metamodeling Method , 2014 .

[3]  Johann Sienz,et al.  Formulation of the Optimal Latin Hypercube Design of Experiments Using a Permutation Genetic Algorithm , 2004 .

[4]  Teng Long,et al.  Global Optimization Method with Enhanced Adaptive Response Surface Method for Computation-Intensive Design Problems , 2012 .

[5]  R. Haftka,et al.  Multiple surrogates: how cross-validation errors can help us to obtain the best predictor , 2009 .

[6]  Singiresu S. Rao Engineering Optimization : Theory and Practice , 2010 .

[7]  Masoud Rais-Rohani,et al.  Ensemble of Metamodels with Optimized Weight Factors , 2008 .

[8]  Troy David Altus,et al.  A Response Surface Methodology for Bi-Level Integrated System Synthesis (BLISS) , 2002 .

[9]  Greg F. Naterer,et al.  Extended Collaboration Pursuing Method for Solving Larger Multidisciplinary Design Optimization Problems , 2007 .

[10]  Raphael T. Haftka,et al.  Control-Oriented Design Using H-infinity Synthesis and Multiple Surrogates , 2010 .

[11]  Bin Zhang,et al.  Experimental design and data processing of twin GEO SAR interferometry based on Beidou IGSO satellites , 2017, 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).

[12]  Teng Long,et al.  Study of Sequential Radial Basis Function for Computational Intensive Design Problem , 2012 .

[13]  G. G. Wang,et al.  Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions , 2008 .

[14]  Greg F. Naterer,et al.  Collaboration pursuing method for multidisciplinary design optimization problems , 2007 .

[15]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[16]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[17]  Andy J. Keane,et al.  Surrogate-based aerodynamic shape optimization of a civil aircraft engine nacelle , 2007 .

[18]  Teng Long,et al.  Truss structure satellite bus geometry-structure optimization involving mixed variables and expensive models using metamodel-based optimization strategy , 2014 .

[19]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[20]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments: Design and Analysis , 2001 .

[21]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[22]  Teng Long,et al.  Wing Structural Optimization Using Adaptive Metamodels Based on Fuzzy Clustering , 2011 .

[23]  Liu Qiuhong,et al.  Surrogate Model Based Optimization for Airfoil Design , 2011 .

[24]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[25]  Xiao Jian Zhou,et al.  Ensemble of surrogates with recursive arithmetic average , 2011 .

[26]  Ning Qin,et al.  Surrogate-Based Multi-Objective Aerothermodynamic Design Optimization of Hypersonic Spiked Bodies , 2011 .

[27]  Lei Peng Optimization Strategy Using Dynamic Radial Basis Function Metamodel , 2011 .

[28]  G. Matheron Principles of geostatistics , 1963 .

[29]  Russell R. Boyce,et al.  Nozzle design optimization for axisymmetric scramjets by using surrogate-assisted evolutionary algorithms , 2012 .

[30]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[31]  Marios K. Karakasis,et al.  Low-cost genetic optimization based on inexact pre-evaluations and the sensitivity analysis of design parameters , 2001 .

[32]  Z. Gürdal,et al.  Improved Shepard's Method for the Optimization of Composite Structures , 2011 .

[33]  Leifur Þ. Leifsson,et al.  Surrogate-Based Aerodynamic Shape Optimization by Variable-Resolution Models , 2013 .

[34]  Ilan Kroo,et al.  Implementation and Performance Issues in Collaborative Optimization , 1996 .

[35]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[36]  Li Liu,et al.  Metamodel-based global optimization using fuzzy clustering for design space reduction , 2013 .

[37]  Dimitri N. Mavris,et al.  Conceptual Design of an N+2 Supersonic Airliner , 2009 .

[38]  G. Gary Wang,et al.  An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions , 2005 .

[39]  R. Haftka,et al.  Efficient Global Optimization with Adaptive Target Setting , 2014 .

[40]  G. G. Wang,et al.  Efficient adaptive response surface method using intelligent space exploration strategy , 2015 .

[41]  G. Gary Wang,et al.  Performance study of mode-pursuing sampling method , 2009 .

[42]  Li Liu,et al.  Aero-structure Coupled Optimization of High Aspect Ratio Wing Using Enhanced Adaptive Response Surface Method , 2012 .

[43]  Layne T. Watson,et al.  Efficient global optimization algorithm assisted by multiple surrogate techniques , 2012, Journal of Global Optimization.

[44]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[45]  G. Gary Wang,et al.  Trust Region based MPS Method for Global Optimization of High Dimensional Design Problems , 2012 .

[46]  Joseph Giesing,et al.  A summary of industry MDO applications and needs , 1998 .

[47]  Jianqiao Chen,et al.  A surrogate-based particle swarm optimization algorithm for solving optimization problems with expensive black box functions , 2013 .

[48]  Dimitri N. Mavris,et al.  Variable Fidelity Conceptual Design Environment for Revolutionary Unmanned Aerial Vehicles , 2008 .

[49]  Zafer Gürdal,et al.  Minimum Weight Design of Composite Structures with Local Postbuckling and Blending Constraints , 2006 .

[50]  Saqlain Akhtar,et al.  Support Vector Machine Based Trajectory Metamodel for Conceptual Design of Multi-stage Space Launch Vehicle , 2005, CIS.

[51]  Jeong‐Soo Park Optimal Latin-hypercube designs for computer experiments , 1994 .

[52]  M. Sasena,et al.  Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization , 2002 .

[53]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[54]  Teng Long,et al.  Optimization Strategy Using Dynamic Radial Basis Function Metamodel Based on Trust Region , 2014 .

[55]  Teng Long,et al.  An efficient truss structure optimization framework based on CAD/CAE integration and sequential radial basis function metamodel , 2014 .

[56]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[57]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[58]  P. Villon,et al.  Moving least squares response surface approximation: Formulation and metal forming applications , 2005 .

[59]  Timothy W. Simpson,et al.  Analysis of support vector regression for approximation of complex engineering analyses , 2003, DAC 2003.

[60]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[61]  Timothy W. Simpson,et al.  Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come? , 2014 .

[62]  Wei Chen,et al.  Optimizing Latin hypercube design for sequential sampling of computer experiments , 2009 .

[63]  Yong Zhang,et al.  Uniform Design: Theory and Application , 2000, Technometrics.

[64]  Patrick Guillaume,et al.  Development of an adaptive response surface method for optimization of computation-intensive models , 2009, Comput. Ind. Eng..

[65]  T. Simpson,et al.  Computationally Inexpensive Metamodel Assessment Strategies , 2002 .

[66]  Ke-Shi Zhang,et al.  Coupled Aerodynamic/Structural Optimization of a Subsonic Transport Wing Using a Surrogate Model , 2008 .

[67]  E. Acar Various approaches for constructing an ensemble of metamodels using local measures , 2010 .

[68]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[69]  Fred J. Hickernell,et al.  A generalized discrepancy and quadrature error bound , 1998, Math. Comput..

[70]  G. Venter,et al.  An algorithm for fast optimal Latin hypercube design of experiments , 2010 .

[71]  Li Liu,et al.  Integrated Aerodynamic Thermal Structure Design Optimization Method of Lifting Surfaces , 2012 .

[72]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[73]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[74]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[75]  Dimitri N. Mavris,et al.  Improved Submerged Inlet Conceptual Design Process using Data Mining and Surrogate Modeling , 2010 .

[76]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[77]  Sobieszczanski Jaroslaw,et al.  Bi-Level Integrated System Synthesis (BLISS) , 1998 .

[78]  Panos Y. Papalambros,et al.  Convergence properties of analytical target cascading , 2002 .

[79]  Wang Hu,et al.  Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method , 2008 .

[80]  Jack P. C. Kleijnen,et al.  A Comment on Blanning's “Metamodel for Sensitivity Analysis: The Regression Metamodel in Simulation” , 1975 .

[81]  G. G. Wang,et al.  Mode-pursuing sampling method for global optimization on expensive black-box functions , 2004 .

[82]  Gyung-Jin Park,et al.  Comparison of MDO methods with mathematical examples , 2008 .

[83]  John E. Renaud,et al.  Adaptive experimental design for construction of response surface approximations , 2001 .

[84]  Joseph Ray Carroll Time-averaged surrogate modeling for small scale propellers based on high-fidelity CFD simulations , 2013 .

[85]  Matthew B. Parkinson,et al.  Improving an Ergonomics Testing Procedure via Approximation- based Adaptive Experimental Design , 2005 .

[86]  N. Cressie The origins of kriging , 1990 .

[87]  T. Simpson,et al.  Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization , 2004 .

[88]  Teng Long,et al.  Sequential RBF surrogate-based efficient optimization method for engineering design problems with expensive black-box functions , 2014 .

[89]  A. Sudjianto,et al.  An Efficient Algorithm for Constructing Optimal Design of Computer Experiments , 2005, DAC 2003.

[90]  Ernesto Benini,et al.  Multi-Objective Optimization of Helicopter Airfoils Using Surrogate-Assisted Memetic Algorithms , 2012 .

[91]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[92]  Teng Long,et al.  Optimized Radial Basis Function Metamodel for Expensive Engineering Design Optimization , 2012 .

[93]  Juan J. Alonso,et al.  Multi-Fidelity Trajectory Optimization with Response Surface Based Aerodynamic Performance Prediction , 2008 .

[94]  Kenny Q. Ye,et al.  Algorithmic construction of optimal symmetric Latin hypercube designs , 2000 .

[95]  Yu Xiong,et al.  MULTIDISCIPLINARY DESIGN OPTIMIZATION A SURVEY OF ITS ALGORITHMS AND APPLICATIONS TO AIRCRAFT DESIGN , 2000 .

[96]  Teng Long,et al.  A Simultaneous Computing Framework for Metamodel-Based Design Optimization , 2014, DAC 2014.

[97]  Xiongqing Yu,et al.  Aerodynamic/Stealthy/Structural Multidisciplinary Design Optimization of Unmanned Combat Air Vehicle , 2009 .

[98]  David Levin,et al.  The approximation power of moving least-squares , 1998, Math. Comput..

[99]  A. P. Panayi,et al.  On the optimization of piston skirt profiles using a pseudo-adaptive response surface method , 2009 .

[100]  Shawn E. Gano,et al.  Update strategies for kriging models used in variable fidelity optimization , 2006 .

[101]  G. A. Gabriele,et al.  Improved coordination in nonhierarchic system optimization , 1993 .

[102]  Li Liu,et al.  A novel algorithm of maximin Latin hypercube design using successive local enumeration , 2012 .

[103]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[104]  G. Gary Wang,et al.  ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS , 2001 .

[105]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[106]  Dick den Hertog,et al.  Maximin Latin Hypercube Designs in Two Dimensions , 2007, Oper. Res..