Efficient reliability-based optimization of linear dynamic systems with random structural parameters

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 4; pp. 2593 - 2608
• Main Authors: Yuan, Xiukai, Gu, Jian, Wu, Mingying, Zhang, Feng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Design optimization; Engineering; Engineering Design; Mathematical analysis; Parameters; Reliability analysis; Research Paper; Theoretical and Applied Mechanics; Reliability-based optimization; Uncertain systems; Linear dynamic system; High dimensions; Decoupling approach; Importance sampling
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-03011-0

This paper proposes a novel method to address the challenges associated with reliability-based design optimization (RBDO) of a class of problems, namely design of a linear system with random structural parameters subject to stochastic excitation. This method effectively estimates the failure probability as an explicit function of the design variables by representing the failure probability function (FPF) as a weighted average of sample values, which are generated by means of a single reliability analysis. The resulting estimation of the FPF is then used to decouple the target RBDO problem into a deterministic optimization problem, which can be solved by any appropriate deterministic optimization algorithm. In addition, a sequential approximate optimization framework is adopted to iteratively seek the solution of the RBDO problem. Several examples are provided to demonstrate the high accuracy and efficiency of the proposed method.