Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion

• Published in: Structural and multidisciplinary optimization Vol. 65; no. 1
• Main Authors: Lee, Dongjin, Rahman, Sharif
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2022; Springer Nature B.V
• Subjects: Algorithms; Compressor blades; Computational Mathematics and Numerical Analysis; Dependent variables; Design optimization; Design standards; Engineering; Engineering Design; Jet engines; Mathematical functions; Mechanical systems; Polynomials; Random variables; Reliability analysis; Research Paper; Theoretical and Applied Mechanics; Design sensitivity analysis; Reliability analysis; GPCE; Stochastic optimization; RBDO; Score functions
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-03123-7

This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems.