Reliability analysis and trade-offs between safety and cost with insufficient data represent an inevitable problem during the early stage of structural design. In this paper, efficient uncertainty theory-based reliability analysis and a design method are proposed under epistemic uncertainty. The factors influencing the structure are regarded as uncertain variables. Based on this, a new metric termed uncertain measure is employed to define an uncertainty reliability indicator (URI) for estimating the reliable degree of structure. Two solving methods, namely, the crisp equivalent analytical method and uncertain simulation (US) method, are introduced to calculate the URI and acquire reliability. Thereafter, a URI-based design optimization (URBDO) model is constructed with target reliability constraints. To solve the URBDO model and obtain optimal solutions, crisp equivalent programming and a genetic-algorithm combined US approach are developed. Four physical examples are solved to verify the adaptability and advantage of the established model and corresponding solving techniques.

To address the fuzzy random uncertainty in structural reliability analysis, a novel method for obtaining the membership function of fuzzy reliability is proposed on the two orders four central moments (TOFM) method based on envelope distribution. At each cut level, the envelope distribution is first constructed, which is a new expression to describe the bound of the fuzzy random variable distribution. The central moments of the bound distribution are determined by generating samples from the envelope distribution, and they are used to calculate the central moments of the limit state function based on the first two orders of the Taylor expansion. Thereafter, the modern approximation method is used to approximate the polynomial expression for the limit state function probability density function (PDF) by considering the central moments as constraint conditions. Thus, the reliability boundaries can be calculated under the considered cut level, and the membership function of the fuzzy reliability is subsequently obtained. Three examples are evaluated to demonstrate the efficiency and accuracy of the proposed method. Moreover, a comparison is made between the proposed method, Monte Carlo simulation (MCS) method, and fuzzy first-order reliability method (FFORM). The results show the superiority of the proposed method, which is feasible for the analysis of structural reliability with fuzzy randomness.