UNCERTAINTY ANALYSIS USING POLYNOMIAL CHAOS THEORY

Abstract

This paper presents the soft computing technique on computational mathematics for current research. Current research on computational mathematics basically needs to address the issues of uncertainty for reliability analysis and optimization process. Research on reliability modeling can not be addressed completely by probability distribution of the governing parameters because some of the parameters may be of imprecise due to lack of knowledge or information about them. It is also true that the imprecise information can not be translated or transformed into probability distribution. Hence, it is mandatory to treat the imprecise nature of parameters of a reliability model in a different manner. The methodology of handling the uncertainty of such parameters is basically carried out by using evidence theory which provides the belief and plausibility – lower and upper bounds of the epistemic uncertainty of the model. Traditional probability exists between belief and plausibility. The body of evidence for the model to be tested for its reliability is gathered by expert’s opinion by assigning a basic probability mass to each of the focal sets comprising the evidence. Soft computing technique also includes the chaos theory so called as polynomial chaos which also can be applied to quantify the uncertainty. Polynomial chaos theory is an efficient version of traditional Monte Carlo method of handling aleatory uncertainty. Potential capability of polynomial chaos theory in handling aleatory or stochastic uncertainty is illustrated with a case study of contaminant transport through groundwater.