Response surface method and reliability calculation based on the generating function method

The generating function method is an important tool for the structural reliability analysis and performance assessment of multi-state systems. However, no corresponding solving method is available for implicit limited state functions. Therefore, a response surface method based on the generating function method is proposed, and its reliability is calculated. This method is improved based on the classical response surface method by using the present most dangerous point (minimum) of fitting the limited state function obtained as the design point and the expansion point of the next iteration, making the expansion point closer to the failure surface, enhancing the approximate precision of the limited state function near the failure surface, and providing a feasible way for calculating the system reliability in a highly precise manner with the generating function method of non-uniform discretization. Examples are provided to demonstrate that the new method improves the convergence rate and calculation accuracy and reduces the iterative and cumulative error.