A Comparison of Some Algorithms for Reliability Based Structural Optimization and Sensitivity Analysis

Abstract

Reliability based structural optimization requires a combined usage of numerical methods for structural reliability analysis and structural optimization. In analyses presented in the literature the approach has been to use nested analyses, where the structural reliability analysis is done within the structural optimization analysis. This means that the reliability and possibly also partial derivatives of the reliability are calculated each time the value of the objective function or constraints in the optimization are required. The reliability is typically calculated using a first- or second-order reliability method, while standard routines for non-linear optimization are used for the optimization part. Sensitivity factors, i.e. the sensitivity of the optimal solution for e.g. the structural dimensions to changes in cost or statistical input parameters, are computed by numerical differentiation.

Another approach to reliability based optimization is to combine the numerical analysis for the reliability analysis with the numerical analysis in the optimization. In this paper a reliability analysis applying a first-order reliability method is combined with an optimization for minimization of total expected cost including the expected failure cost. The combined analysis is formulated as a non-linear optimization problem, where the reliability analysis in effect enters the cost optimization as an additional constraint. The combined optimization can then be solved by a standard solver, and sensitivity factors are a simple by-product of the analysis.

The two approaches are described and are compared for two simple examples. The comparison is with respect to the number of times the limit state function is computed, as this is the part of the optimization which typically governs the total analysis time.