Secant Hyperplane Method for Structural Reliability Analysis

The first-order reliability method (FORM) is a powerful tool for structural reliability analysis, providing a good trade-off between computational accuracy and efficiency. Nevertheless, it has two main drawbacks: (1)its approximation is not necessarily adequate for limit state surfaces which depart significantly from linearity, and (2)it does not give information about the degree of accuracy achieved. In this paper, the secant hyperplane method (SHM) is proposed, which is a new linear approximation of the limit state surface based on the support vector method (SVM). The key idea is to treat structural reliability as a classification problem and to seek a suitable secant hyperplane to the limit state that gives improved approximation over the use of a tangent hyperplane. The two drawbacks of FORM are thereby resolved, while keeping the geometrical simplicity and ease of implementation of FORM. The implication of very high-dimensional geometry is examined, demonstrating that FORM can give good approximations if reinterpreted as a linear classifier, and SHM has the potential of scalability to spaces of high dimensionality. Two numerical examples, including stochastic dynamic analysis, show the accuracy and effectiveness of SHM.