Belief reliability-based design optimization of structures

Traditional reliability-based design optimization (RBDO) methods of structures are based on probability theory, which cannot handle with epistemic uncertainties existing in actual systems very well. This paper adopts belief reliability theory and puts forward a new structural design optimization method named belief reliability-based design optimization (BRBDO), in which epistemic uncertainties are treated with uncertainty theory. First, some basic concepts and formulations of belief reliability theory is briefly introduced. Then, the BRBDO model is proposed by assuming all the parameters affected by epistemic uncertainty are uncertain variables. Subsequently, the belief reliability calculation methods, which are critical in the BRBDO loops, are given in two aspects. For monotone limit state functions with respect to parameters, the operational laws in terms of uncertainty theory are utilized. For other more general functions, this paper resorts to uncertain simulation approaches. As for the solution of BRBDO models, typical heuristic algorithms work out well. To illustrate the effectiveness of the BRBDO model, examples of some typical structures are also presented. The outcomes show that the optimization results of structures using BRBDO models are usually more conservative than the traditional models based on probability theory.