An Efficient Approach for Uncertainty Analysis in Multidisciplinary Design Optimization

Abstract

Abstract. In this paper, an efficient multidisciplinary design optimization method based on evidence theory is proposed. Evidence theory is used to quantify uncertainty in terms of uncertainty measures of belief and plausibility. Since uncertainty measures provided by evidence theory are discontinuous functions, the response surface is utilized to obtain smooth functions so that the traditional gradient-based algorithms can be used in optimization. IntroductionIn general, probability theory is very effective when sufficient data about uncertainty are available to precisely construct probability distributions. However, when sufficient data are not available or there is lack of information due to ignorance, the classical probability theory may not be suitable. For example, the reliability of a complex system is assessed in the presence of incomplete information on the variability of certain design variables, parameters, operating conditions, boundary conditions, etc. A similar problem is: when quantification of a product's reliability or compliance to performance targets, it is practically very difficult due to insufficient data for modeling uncertainties during the early stages of product development.Many of these new representations of uncertainty are able to more accurately represent epistemic uncertainty than traditional probability theory. Engineering applications of some of these theories can be found in recent publications [1,2]. One of the modern theories of uncertainty representation is evidence theory (Dempster-Shafer theory). The advantage of using evidence theory lies in the fact that it can be successfully used to quantify the degree of uncertainty when the amount of information available is small. Like most modern uncertainty theories, evidence theory also provides two uncertain measures known as belief and plausibility. In this paper, a formulation of evidence-based multidisciplinary optimization and design (EBMDO) is proposed for engineering design optimization.