A Concurrent Approach for a Reliability-Based Optimization Design Problem

A concurrent approach, which considers variability in design parameters, is proposed for a reliability-based design optimization (RBDO) problem. The RBDO is reformulated as a system with a bi-level structure, consisting of upper and lower levels. The upper level has one sub-system, while the lower level includes two sub-systems. Two major calculations in the RBDO, the reliability analysis (RA) and the deterministic optimization (DO), are decoupled via two sets of pseudo-linking variables, which are copies of the responses in both levels. The objective of the upper level is to minimize the difference in the pseudo-linking variables between the two levels. The main tasks in the lower level are to execute the DO and RA concurrently. The proposed procedure prevents the RBDO from performing the inherited double-loop calculation and improves the computational efficiency. Another benefit is that the RBDO can be solved by any individual RA and DO software. Convergence of the proposed bi-level approach is discussed through the concept of overlapping coordination methodology. Details of a RBDO problem that was solved by the bi-level algorithm are revealed through three numerical examples.