Reliability-based design optimization with the generalized inverse distribution function

Abstract

This paper presents an approach to optimization under uncertainty that is very well and naturally suited to reliability-based design optimization problems and it is a possible alternative to traditional approaches to robust design based on the optimization of statistical moments. The approach shown here is based on the direct use of the generalized inverse distribution function estimated using the empirical cumulative distribution function (ECDF). The optimization approach presented is illustrated with the application to some test functions for both robust optimization and reliability-based design optimization. In the robust optimization test case, the bootstrap statistical technique is used to estimate the error introduced by the usage of the ECDF for quantile estimation.