Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis

In structural reliability, simulation methods are oriented to the estimation of the probability integral over the failure domain, while solver-surrogate methods are intended to approximate such a domain before carrying out the simulation. A method combining these two purposes at a time and intended to obtain a drastic reduction of the computational labor implied by simulation techniques is proposed. The method is based on the concept that linear or nonlinear transformations of the performance function that do not affect the boundary between safe and failure classes lead to the same failure probability than the original function. Useful transformations that imply reducing the number of performance function calls can be built with several kinds of squashing functions. A most practical of them is provided by the pattern recognition technique known as support vector machines. An algorithm for estimating the failure probability combining this method with importance sampling is developed. The method takes advantage of the guidance offered by the main principles of each of these techniques to assist the other. The illustrative examples show that the method is very powerful. For instance, a classical series problem solved with O(1000) importance sampling solver calls by several authors is solved in this paper with less than 40 calls with similar accuracy.