Inverse Reliability Problem

Consider a reliability problem with a limit‐state function involving one unknown parameter. We seek to determine the unknown parameter such that a prescribed first‐order reliability index is attained. In this paper, an efficient algorithm is developed for the solution of this inverse reliability problem. The algorithm is an extension of the well known Hasofer‐Lind‐Rackwitz‐Fiessler algorithm used in reliability analysis, where the search space of the random variables is extended here to include the unknown parameter. A search direction and a merit function are introduced to guide the sequence of iteration points to the design point and the parameter solution in a balanced manner. The proposed method can be used in reliability‐based design optimization, or in determining the admissible response threshold for a specified first‐order probability, without performing repeated reliability analyses. Two examples are presented: one demonstrating the characteristics of the convergence sequence, and another describing application of the algorithm to finite‐element reliability analysis of an elastoplastic plate.