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Mathematical Problems in Engineering
Volume 2015, Article ID 569016, 14 pages
Research Article

Improved Reliability-Based Optimization with Support Vector Machines and Its Application in Aircraft Wing Design

1College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA

Received 25 September 2014; Revised 20 January 2015; Accepted 13 April 2015

Academic Editor: Marc Dahan

Copyright © 2015 Yu Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new reliability-based design optimization (RBDO) method based on support vector machines (SVM) and the Most Probable Point (MPP) is proposed in this work. SVM is used to create a surrogate model of the limit-state function at the MPP with the gradient information in the reliability analysis. This guarantees that the surrogate model not only passes through the MPP but also is tangent to the limit-state function at the MPP. Then, importance sampling (IS) is used to calculate the probability of failure based on the surrogate model. This treatment significantly improves the accuracy of reliability analysis. For RBDO, the Sequential Optimization and Reliability Assessment (SORA) is employed as well, which decouples deterministic optimization from the reliability analysis. The improved SVM-based reliability analysis is used to amend the error from linear approximation for limit-state function in SORA. A mathematical example and a simplified aircraft wing design demonstrate that the improved SVM-based reliability analysis is more accurate than FORM and needs less training points than the Monte Carlo simulation and that the proposed optimization strategy is efficient.