Segmental multi-point linearization for parameter sensitivity approximation in reliability analysis

This paper proposes an efficient method named segmental multi-point linearization for accurate approximation of the sensitivity of failure probability with respect to design parameters. The method is established based on a piecewise linear fitting of the limit state surface and the analytical integral of the gradient of the failure probability with respect to parameters in the limit state function. The proposed method presents an attractive ratio of accuracy to computational cost. The general framework is scalable such that, by adjusting its complexity, different levels of accuracy can be achieved. The method is especially suitable to be implemented in gradient-based routines for solving reliability-based design optimization problems where accuracy of the parameter sensitivity is essential for convergence to an optimal solution.