Robust design with Variability Response Functions; an alternative approach

Abstract

In this work a different Robust Design Optimization (RDO) approach is proposed implementing the concept of Variability Response Function (VRF), which is a function that when combined with the power spectral density of the stochastic field that models the system’s uncertainty, formulates an integral expression for the variance of the system’s response. The basic idea is to exploit a very well-known property of the VRF, which is its independence of the stochastic system parameters, in order to obtain global optima that depend only on the deterministic parameters of the problem. This way, optimal structural designs are achieved which are globally insensitive to uncertainties, that is to say they are free of the spectral-distribution characteristics of the stochastic fields modeling the uncertainties. This is achieved by setting in addition to the total material cost, the maximum VRF value as an objective function. The advantages of using the proposed methodology over traditional Robust Design Optimization are illustrated through an application to a frame-type structure where it is demonstrated that the designs achieved through classical RDO for a given stochastic field description are not optimal for a variation on the spectral properties of the random field modeling the system uncertainty, while optimal designs obtained with the VRF-based RDO remain optimum for the worst case scenario stochastic fields.