Abstract
Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.
Highlights
Structural systems operate in variable and uncertain environments that impact building performance and integrity
The uniform applicability of the proposed approach to reliability-based design optimization (RBDO) of structures is confirmed through four numerical examples
This paper focuses on the component RBDO (CRBDO) with probabilistic constraints of multiple failure modes of a design
Summary
Structural systems operate in variable and uncertain environments that impact building performance and integrity. RBDO is performed using a nested approach, such that each iteration in the design optimization process involves a sub-loop of iterations for reliability assessment at the current stage of design. To improve the computational efficiency of reliability analysis and optimization procedure, many RBDO approaches, such as decoupling [14,15] and single-loop (SL) methods [16,17,18,19,20], have been proposed. The sensitivity analysis of failure probability, a probabilistic constraint of RBDO, is proposed using complex-step (CS) approximation integrated with. This paper presents the RBDO method utilizing the FORM and presents a sensitivity analysis of probabilistic constraints with respect to design and random variable parameters to use a gradient-based optimization algorithm
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