Reliability‐based design optimisation of technical systems: analytical response surface moments method

Abstract

Reliability-based design optimisation is a process of finding an optimum economical design while conforming to a set of reliability constraints. In this context, the reliability analysis that is simultaneously accurate and computationally efficient is imperative. Since the analytical evaluation of evaluating reliability constraints is mathematically complex, the most probable point search approach using the first and second orders of reliability approximation has become the mainstream technique. However, it is characterised as having a high computational cost and poor convergence in some design problems involving a large number of design variables with highly nonlinear constraints. To overcome the problem, this paper introduces a novel response surface with analytical moment-based reliability analysis technique. It performs distribution fitting using the exact analytical expression of high-order moments of response surface that are precisely calculated using Mellin transform. To boost the computational efficiency, a selective sampling technique is used in constructing the response surface model. Consequently, the proposed method not only provides final solutions of high quality, but it is also significantly faster than representatives of the mainstream reliability approximation methods. For example, when applied to complex design problems, the proposed method is able to converge to dependable solutions while offering the high speed of single-loop optimisation approaches.