Super parametric convex model and its application for non-probabilistic reliability-based design optimization

Abstract

• A general hyper parametric convex model is created. • The minimum volume method is developed to select the type of hyper parametric convex model properly. • Nominal value and advanced nominal value methods are proposed simultaneously to perform the non-probabilistic analysis effectively. • Effective non-probabilistic reliability-based design optimization approach is developed based on advanced nominal value method. In this study, we attempt to propose a new super parametric convex model by giving the mathematical definition, in which an effective minimum volume method is constructed to give a reasonable enveloping of limited experimental samples by selecting a proper super parameter. Two novel reliability calculation algorithms, including nominal value method and advanced nominal value method, are proposed to evaluate the non-probabilistic reliability index. To investigate the influence of non-probabilistic convex model type on non-probabilistic reliability-based design optimization, an effective approach based on advanced nominal value method is further developed. Four examples, including two numerical examples and two engineering applications, are tested to demonstrate the superiority of the proposed non-probabilistic reliability analysis and optimization technique.