Coupled Aerostructural Design Optimization Using the Kriging Model and Integrated Multiobjective Optimization Algorithm

The paper develops and implements a highly applicable framework for the computation of coupled aerostructural design optimization. The multidisciplinary aerostructural design optimization is carried out and validated for a tested wing and can be easily extended to complex and practical design problems. To make the framework practical, the study utilizes a high-fidelity fluid/structure interface and robust optimization algorithms for an accurate determination of the design with the best performance. The aerodynamic and structural performance measures, including the lift coefficient, the drag coefficient, Von-Mises stress and the weight of wing, are precisely computed through the static aeroelastic analyses of various candidate wings. Based on these calculated performance, the design system can be approximated by using a Kriging interpolative model. To improve the design evenly for aerodynamic and structure performance, an automatic design method that determines appropriate weighting factors is developed. Multidisciplinary aerostructural design is, therefore, desirable and practical.

[1]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[2]  Raphael T. Haftka,et al.  Structural optimization complexity: what has Moore’s law done for us? , 2004 .

[3]  Kwok Leung Lai,et al.  Application of Three-Dimensional Interfaces for Data Transfer in Aeroelastic Computations , 2004 .

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

[5]  D. V. Griffiths,et al.  Programming the finite element method , 1982 .

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  O. A. Elwakeil,et al.  Global optimization methods for engineering applications: A review , 1995 .

[8]  G. G. Maisuradze,et al.  Interpolating moving least-squares methods for fitting potential energy surfaces: Illustrative approaches and applications , 2003 .

[9]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[11]  Achille Messac,et al.  Extended Radial Basis Functions: More Flexible and Effective Metamodeling , 2004 .

[12]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[13]  Anthony A. Giunta,et al.  Aircraft Multidisciplinary Design Optimization using Design of Experiments Theory and Response Surface Modeling Methods , 1997 .

[14]  Kalyanmoy Deb,et al.  Current trends in evolutionary multi-objective optimization , 2007 .

[15]  T Watson Layne,et al.  Wing Design for a High-Speed Civil Transport Using a Design of Experiments Methodology , 1996 .

[16]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

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

[18]  Ruby Krishnamurti,et al.  Finite amplitude convection with changing mean temperature. Part 1. Theory , 1968, Journal of Fluid Mechanics.

[19]  J. Z. Zhu,et al.  The finite element method , 1977 .

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  Richard H. Crawford,et al.  Multidimensional sequential sampling for NURBs-based metamodel development , 2007, Engineering with Computers.

[22]  Jiri Blazek,et al.  Computational Fluid Dynamics: Principles and Applications , 2001 .

[23]  F. Blom.  Considerations on the spring analogy , 2000 .

[24]  Ranjan Ganguli,et al.  Aeroelastic optimization of a helicopter rotor using orthogonal array-based metamodels , 2006 .

[25]  Bharat K. Soni,et al.  Handbook of Grid Generation , 1998 .

[26]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[27]  Shigeru Obayashi,et al.  Multidisciplinary design optimization of wing shape for a small jet aircraft using kriging model , 2006 .

[28]  Dong-Ho Lee,et al.  Multidisciplinary Aerodynamic- Structural Design Optimization of Supersonic Fighter Wing Using Response Surface Methodology , 2002 .

[29]  Martin T. Hagan,et al.  Neural network design , 1995 .

[30]  Martin Spieck,et al.  State-of-the-Art and Future Trends in Multidisciplinary Design Optimization , 2007 .

[31]  Ian R. Chittick,et al.  Aero-structural optimization using adjoint coupled post-optimality sensitivities , 2008 .

[32]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[33]  T. Chung.  Computational Fluid Dynamics: FOUR. AUTOMATIC GRID GENERATION, ADAPTIVE METHODS, AND COMPUTING TECHNIQUES , 2002 .

[34]  J. Anderson,et al.  Computational fluid dynamics : the basics with applications , 1995 .

[35]  Ken Badcock,et al.  A grid deformation technique for unsteady flow computations , 2000 .

[36]  Gene Hou,et al.  High-Fidelity Computational Optimization for 3-D Flexible Wings: Part I—Simultaneous Aero-Structural Design Optimization (SASDO) , 2005 .

[37]  D. Carroll.  Chemical laser modeling with genetic algorithms , 1996 .

[38]  Xin Yao,et al.  Simulated annealing with extended neighbourhood , 1991, Int. J. Comput. Math..

[39]  J. Reddy.  An introduction to the finite element method , 1989 .

[40]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[41]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[42]  J. Alonso,et al.  Aero-Structural Wing Design Optimization Using High-Fidelity Sensitivity Analysis , 2001 .

[43]  Kazuomi Yamamoto,et al.  Efficient Optimization Design Method Using Kriging Model , 2005 .

[44]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[45]  Yasushi Ito,et al.  MULTIDISCIPLINARY DESIGN OPTIMIZATION OF WING SHAPE WITH NACELLE AND PYLON , 2006 .

[46]  Ramji Kamakoti,et al.  Fluid–structure interaction for aeroelastic applications , 2004 .

[47]  Achille Messac,et al.  Metamodeling using extended radial basis functions: a comparative approach , 2006, Engineering with Computers.

[48]  Guru P. Guruswamy,et al.  A review of numerical fluids/structures interface methods for computations using high-fidelity equations , 2002 .

[49]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[50]  Ian P Bond,et al.  48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, Hawaii, USA , 2007 .

[51]  David P. Schmidt,et al.  An Experimental Investigation of the Influence of Gas and Solid Particle Interaction on the Heat Transfer Effectiveness of a Falling-Bed Heat Exchanger , 2005 .

[52]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[53]  Joaquim R. R. A. Martins,et al.  An Object-Oriented Framework for Multidisciplinary Design Optimization , 2007 .

[54]  T. Simpson,et al.  Analysis of support vector regression for approximation of complex engineering analyses , 2005, DAC 2003.

[55]  J. Martins.  A coupled-adjoint method for high-fidelity aero-structural optimization , 2002 .

[56]  V. Mukhopadhyay,et al.  MULTIDISCIPLINARY HIGH-FIDELITY ANALYSIS AND OPTIMIZATION OF AEROSPACE VEHICLES, PART 1: FORMULATION , 2013 .

[57]  K. Bathe.  Finite Element Procedures , 1995 .

[58]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary aerospace design optimization - Survey of recent developments , 1996 .

[59]  L E Reinstein,et al.  A new genetic algorithm technique in optimization of permanent 125I prostate implants. , 1998, Medical physics.

[60]  Sean Wakayama,et al.  Lifting surface design using multidisciplinary optimization , 1995 .

[61]  H. Tsai,et al.  Unsteady Flow Calculations with a Parallel Multiblock Moving Mesh Algorithm , 2001 .

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

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

[64]  J. Kok,et al.  A Simple, Robust and Fast Algorithm to Compute Deformations of Multi-Block Structured Grids , 2002 .

[65]  Eric R. Ziegel,et al.  Handbook of Statistics 13: Design and Analysis of Experiments , 2000 .