Evidence theory-based reliability optimization design using polynomial chaos expansion

Abstract

With the development of reliability technique, the safety assessment for the problem with epistemic uncertainty has attracted widespread attention. Evidence theory is a useful tool to deal with such uncertainty, and this paper aims to develop an efficient approach for the evidence theory-based reliability analysis and optimization design. By using mutually exclusive intervals to quantify the focal elements of evidence variable, a confidence range bounded by belief measure and plausibility measure is derived for system reliability assessment, by which the relatively conservative and radical optimization models can be respectively established. To decrease the huge computational burden in repetitive limit state function evaluations under the time-consuming implicit computational model, an explicit surrogate model is constructed by the Legendre polynomial chaos expansion in the support box. A Clenshaw–Curtis point-based collocation method with Smolyak algorithm is then developed to predict the unknown coefficients in surrogate model, where the collocation level can be flexibly selected according to the accuracy requirement. Compared with the traditional deterministic optimization model under nominal value assumption, the results in two numerical examples verify the effectiveness of proposed method in mathematical theory and engineering application.