Advanced virtual model assisted most probable point capturing method for engineering structures
提出一种基于扩展支持向量回归的虚拟模型辅助方法，用于高效捕捉工程结构的最可能点，解决传统一阶可靠性方法在高维隐式极限状态函数下的精度低和计算成本高问题。
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.