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Mathematical Problems in Engineering
Volume 2015, Article ID 964238, 11 pages
Research Article

Multidisciplinary Inverse Reliability Analysis Based on Collaborative Optimization with Combination of Linear Approximations

1School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
2School of Mechatronics, Northwestern Polytechnical University, Xi’an 710072, China
3Mechanical and Electrical Engineering Institute, Hebei University of Engineering, Handan 056038, China
4School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

Received 22 October 2014; Revised 24 April 2015; Accepted 2 May 2015

Academic Editor: P. Beckers

Copyright © 2015 Xin-Jia Meng 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.


Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO). However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO) is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP) search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.