A unified framework for reliability assessment and reliability-based design optimization of structures with probabilistic and nonprobabilistic hybrid uncertainties

In the reliability assessment of structures, a situation we frequently encounter is that by means of available information some parameters involved can be depicted accurately by their probability distributions and others can only be described by the bounds or ranges of variations. So, it is meaningful to construct a reliability model by which the probabilistic and nonprobabilistic uncertainties can be treated reasonably in an integrated framework. The main purpose of this paper is to establish a strictly mathematical foundation and a unified framework for reliability assessment and reliability-based design optimization (RBDO) of structures in the presence of both probabilistic and nonprobabilistic (bounded) hybrid uncertainties. The input uncertain parameters are divided into two different groups and treated respectively as random variables and interval variables, and the traditional probability and convex set models are adopted to describe the probabilistic and bounded uncertainties, respectively. In the reliability measuring system developed in the paper, dimensionless hybrid reliability indices are defined in different situations by adopting a similar method as for the traditional probabilistic reliability method for structures. A computational procedure for performing the RBDO of structures with hybrid uncertainties is presented. Two numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.