Time-dependent reliability-based design optimization considering aleatory and epistemic uncertainties

Directly solving time-dependent reliability-based design optimization (TRBDO) with aleatory and epistemic uncertainties is time-demanding, which limits its engineering application. By treating aleatory and epistemic uncertainties with probability and evidence variables respectively, an advanced decoupling method named sequential optimization and unified time-dependent reliability analysis (SOUTRA) is proposed in this work. By the SOUTRA, the original nested optimization process is solved by a sequence of unified time-dependent reliability analysis, updated reliability index target estimation and deterministic optimization. Only few numbers of the unified time-dependent reliability analysis are required to derive the optimum by the SOUTRA; thus, it is highly efficient. Furthermore, in order to construct the deterministic optimization, a new probability transformation method named focal element midpoint (FEM) is established to convert the evidence variable into a random one. FEM can avoid the issues of uniformity approach and equal areas method, and both are used in the existing probability transformation. Several numerical and engineering applications are introduced to illustrate the effectiveness of the proposed SOUTRA.