Solving the inverse reliability problem using decomposition techniques

The paper introduces a new general method for solving the inverse reliability problem with multiple design variables and constraints that is specially suitable for practitioner engineers. We seek to determine the unknown parameters such that prescribed first-order reliability indices are obtained. The method uses standard optimization frameworks to obtain the reliability indices and a decomposition iterative scheme to solve the global problem. The sensitivities with respect to the parameters are also obtained by means of the dual variables, so that the method not only attains the solution parameters of the problem, but also shows how sensitive they are with respect to the reliability indices. In addition, the proposed algorithm detects the no-solution case and the existence of infinite solutions. In this case, it also gives the local increments of each design variable to obtain new solutions. Next, the inverse reliability problem is extended to include reliability bounds and other constraints. The proposed methods are illustrated by applications to several cases described in the literature and to the problem of bridge crane design.