A single-loop method for reliability-based design optimisation

Reliability-based design optimisation (RBDO) can provide optimum designs in the presence of uncertainty. It can, therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimisation loops, where the design optimisation (outer) loop repeatedly calls a series of reliability (inner) loops. Due to the nested optimisation loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper. Its accuracy is comparable with the double-loop approach and its efficiency is almost equivalent to deterministic optimisation. It collapses the nested optimisation loops into an equivalent single-loop optimisation process by using the Karush–Kuhn–Tucker optimality conditions of the inner reliability loops in the outer design optimisation loop, converting therefore the probabilistic optimisation problem into a deterministic optimisation problem. Two numerical applications, including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.