Homotopy methods for constraint relaxation in unilevel reliability based design optimization

Reliability based design optimization is a methodology for finding optimized designs that are characterized with a low probability of failure. The main objective in reliability based design optimization is to minimize a merit function while satisfying the reliability constraints. The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the system or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. During the last few years, a variety of different techniques have been developed for reliability based design optimization. Traditionally, these have been formulated as a double-loop (nested) optimization problem. The upper level optimization loop generally involves optimizing a merit function subject to reliability constraints and the lower level optimization loop(s) compute the probabilities of failure corresponding to the failure mode(s) that govern the system failure. This formulation is, by nature, computationally intensive. A new efficient unilevel formulation for reliability based design optimization was developed by the authors in earlier studies. In this formulation, the lower level optimization (evaluation of reliability constraints in the double loop formulation) was replaced by Graduate Research Assistant, Aerospace and Mechanical Engineering, email: [email protected]. Graduate Research Assistant, Aerospace and Mechanical Engineering, email: [email protected]. Professor, Aerospace and Mechanical Engineering, email:[email protected]. GE-CIAT, Queretaro, Mexico. email: [email protected]. Professor, Departments of Computer Science and Mathematics. email: [email protected]