Uncertainty analysis and sensitivity analysis for multidisciplinary systems design

The objective of this research is to quantify the impact of both aleatory and epistemic uncertainties on performances of multidisciplinary systems. Aleatory uncertainty comes from the inherent uncertain nature and epistemic uncertainty comes from the lack of knowledge. Although intensive research has been conducted on aleatory uncertainty, few studies on epistemic uncertainty have been reported. In this work, the two types of uncertainty are analyzed. Aleatory uncertainty is modeled by probability distributions while epistemic uncertainty is modeled by intervals. Probabilistic analysis (PA) and interval analysis (IA) are integrated to capture the effect of the two types of uncertainty. The First Order Reliability Method is employed for PA while nonlinear optimization is used for IA. The unified uncertainty analysis, which consists of PA and IA, is employed to develop new sensitivity analysis methods for the mixture of the two types of uncertainty. The methods are able to quantify the contribution of each input variable with either epistemic uncertainty or aleatory uncertainty. The analysis results can then help better decision making on how to effectively mitigate the effect of uncertainty. The other major contribution of this research is the extension of the unified uncertainty analysis to the reliability analysis for multidisciplinary systems. The major findings of this research are as follows. (1) Sensitivity analysis method is an effective tool for reducing the impact of epistemic uncertainty. (2) The proposed new reliability sensitivity indexes can easily measure the changes in output uncertainty with respect to those in input uncertainty. (3) The effect of aleatory uncertainty can be primarily measured by the distribution of a performance; and the effect of epistemic uncertainty can be measured by the bounds of the distribution. (4) The unified uncertainty analysis methods for single-disciplinary systems can be extended to the reliability analysis for multidisciplinary systems. (5) All the proposed methods can be ultimately integrated with multidisciplinary design optimization.