Update of explicit limit state functions constructed using Support Vector Machines

This article presents a method for the explicit construction of limit state functions using Support Vector Machines (SVM). An algorithm is proposed for updating the SVM decision function by carefully selecting the training samples. This results in the construction of an accurate limit state function with a reduced number of function evaluations. Speciflcally, the SVM-based approach aims at handling the di‐culties associated with the reliability assessment of problems exhibiting discontinuous responses and disjoint failure domains. The explicit construction of limit state functions allows for an easy calculation of a probability of failure and enables the association of a speciflc system behavior with a region of the design space. Three problems are presented to demonstrate the explicit construction of a limit state function. The proposed update scheme is validated by comparing the obtained explicit function to actual analytical limit state functions. Non-linear problems are often characterized by various and sudden behavioral changes which, in structural mechanics, are associated with the presence of critical points. A typical example is a geometrically nonlinear structure which globally buckles for a load larger than the limit load. Because these abrupt changes can be triggered by inflnitesimally small modiflcations of design parameters or loading conditions, the responses of the system are discontinuous in a mathematical sense. In the context of reliability, these slight variations often fall in the range of uncertainties. In simulation-based design, discontinuities present a serious problem for optimization or probabilistic techniques because it is usually assumed that the system’s responses are continuous. In optimization, this limits any traditional gradient-based methods or response surface techniques. When considering reliability, discontinuities might hamper the use of approximation methods such as First Order and Second Order Reliability Methods (FORM and SORM), 1 Advanced Mean Value (AMV), 2 or Monte-Carlo simulations 3 with response surfaces. 4