An improvement of the response surface method

The coupling of the Monte Carlo method and the finite element method for the reliability analysis of structures leads often to a prohibitive computational cost. The response surface method is a powerful reliability method that approximates the limit state function with a polynomial expression using the values of the function at specific points. This type of analytical function replaces the exact limit state function in the Monte Carlo simulation. Therefore, the computational effort required for the assessment of the reliability of structural systems can be reduced significantly. The position of the sample points and the type of polynomial response surface have been investigated by several authors and the performance of the response surface method is still under discussion. In this paper an improvement of the response surface method is proposed. An iterative strategy is used to determine a response surface that is able to fit the limit state function in the neighbourhood of the design point. The locations of the sample points used to evaluate the free parameters of the response surface are chosen according to the importance sensitivity of each random variable. Several analytical and structural examples are considered to demonstrate the advantages of the proposed improvement.

Research highlights
► An improvement of the RSM based on the rotation of the grid of sample points is proposed.
► A better approximation of the LSF with a reasonable CPU effort is achieved.
► The proposed improvement enables more accurate reliability estimates.