Advanced virtual model assisted most probable point capturing method for engineering structures

In real-world engineering, the most probable point (MPP) capturing is a fundamental goal of the widely used MPP-based structural analysis and design methods. Traditionally, the MPP is searched by using the First Order Reliability Method (FORM). However, inaccurate results and redundant computational costs are the main challenges for engineering applications, especially when involving high-dimensional implicit limit state functions. In this study, an advanced virtual model assisted MPP capturing method is introduced. A supervised machine learning technique, namely the Extended Support Vector Regression (X-SVR), is adopted for virtual model construction. The virtual model alternatively describes the underpinned relationship between the system inputs and the quantity of interest mathematically. Furthermore, to improve the robustness of the X-SVR technique, a novel generalized kernel is proposed to serve as an additional option for kernel mapping. Then, on the established virtual model, both gradient-based and metaheuristic optimization programs can be easily implemented to capture the MPP effectively. Moreover, within the established virtual model assisted MPP capturing framework, the information update can be fulfilled in a computationally efficient manner. To demonstrate the applicability and computational efficiency of the proposed approach, verification cases and practical engineering applications (involving static, fractural and high dimensional problems) are thoroughly investigated.