Uncertainty Theory-Based Structural Reliability Analysis and Design Optimization under Epistemic Uncertainty

Abstract

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.

Keywords

• structural reliability
• uncertainty quantification
• epistemic uncertainty
• uncertainty theory
• reliability-based design optimization