A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity

This paper presents a multifidelity approach for the construction of explicit decision boundaries (constraints or limit-state functions) using support vector machines. A lower fidelity model is used to select specific samples to construct the decision boundary corresponding to a higher fidelity model. This selection is based on two schemes. The first scheme selects samples within an envelope constructed from the lower fidelity model. The second technique is based on the detection of regions of inconsistencies between the lower and the higher fidelity decision boundaries. The approach is applied to analytical examples as well as an aeroelasticity problem for the construction of a nonlinear flutter boundary.

[1]  Robert Haimes,et al.  Multifidelity Optimization for Variable-Complexity Design , 2006 .

[2]  Shawn E. Gano,et al.  Hybrid Variable Fidelity Optimization by Using a Kriging-Based Scaling Function , 2005 .

[3]  Samy Missoum,et al.  Failure Prediction and Robust Design of Grafts for Aortic Aneurysms , 2007 .

[4]  Samy Missoum,et al.  A Sampling-Based Approach for Probabilistic Design with Random Fields , 2008 .

[5]  Antonio Harrison Sánchez,et al.  Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains , 2008 .

[6]  Michael R Wisnom,et al.  48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference , 2007 .

[7]  Daniel M. Dunlavy,et al.  Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models , 2006 .

[8]  W. K. Anderson,et al.  First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization , 2000 .

[9]  Samy Missoum,et al.  Design Space Decomposition using Support Vector Machines for Reliability-based Design Optimization , 2006 .

[10]  Andy J. Keane,et al.  Wing Optimization Using Design of Experiment, Response Surface, and Data Fusion Methods , 2003 .

[11]  Ethem Alpaydin,et al.  Introduction to machine learning , 2004, Adaptive computation and machine learning.

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

[13]  Vassili Toropov,et al.  The use of simplified numerical models as mid-range approximations , 1996 .

[14]  Michael S. Eldred,et al.  Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies , 2004 .

[15]  Mikael A. Langthjem,et al.  Multifidelity Response Surface Approximations for the Optimum Design of Diffuser Flows , 2001 .

[16]  Bernard Grossman,et al.  MULTIFIDELITY RESPONSE SURFACE MODEL FOR HSCT WING BENDING MATERIAL WEIGHT , 1998 .

[17]  Raphael T. Haftka,et al.  Design of Shell Structures for Buckling Using Correction Response Surface Approximations , 1998 .

[18]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[19]  A. Basudhar,et al.  Adaptive explicit decision functions for probabilistic design and optimization using support vector machines , 2008 .

[20]  Raphael T. Haftka,et al.  Variable complexity design of composite fuselage frames by response surface techniques 1 This articl , 1998 .

[21]  Bruno Sudret,et al.  Handling Bifurcations in the Optimal Design of Transient Dynamic Problems , 2004 .

[22]  Timothy W. Simpson,et al.  Design and Analysis of Computer Experiments in Multidisciplinary Design Optimization: A Review of How Far We Have Come - Or Not , 2008 .

[23]  Vicente J. Romero,et al.  Comparison of pure and "Latinized" centroidal Voronoi tessellation against various other statistical sampling methods , 2006, Reliab. Eng. Syst. Saf..

[24]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[25]  Raphael T. Haftka,et al.  A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems , 2007 .

[26]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[27]  Raphael T. Haftka,et al.  CORRECTION RESPONSE SURFACE APPROXIMATIONS FOR STRESS INTENSITY FACTORS OF A COMPOSITE STIFFENED PLATE , 1998 .

[28]  Mohammad H. Kurdi,et al.  Reliability-Based Design Optimization of Nonlinear Aeroelastic Problems , 2008 .

[29]  Nello Cristianini,et al.  Support Vector Machines and Kernel Methods: The New Generation of Learning Machines , 2002, AI Mag..

[30]  Lei-Yong Jiang,et al.  FLUTTER OF AN AIRFOIL WITH A CUBIC RESTORING FORCE , 1999 .