Multidisciplinary Statistical Sensitivity Analysis Considering Both Aleatory and Epistemic Uncertainties

Abstract

The performance of a multidisciplinary system is ineluctably affected by various sources of uncertainties, which are often categorized as aleatory (e.g., input variability) or epistemic (e.g., model uncertainty). Statistical sensitivity analysis methods allow for studying the impact of different sources of uncertainty on system performance. However, epistemic model uncertainty is seldom taken into consideration in statistical sensitivity analysis. Applying statistical sensitivity analysis for a multidisciplinary system is even more challenging due to the complexity in system analysis as well as the coupling relationships between subsystems. In this paper, a multidisciplinary statistical sensitivity analysis approach is presented to analyze the contributions from various sources of uncertainties. Both global and local sensitivity analyses are conducted; the former examines the impact of variations over the entire range of design inputs, and the latter compares the impacts of aleatory and epistemic uncertainties to facilitate resource allocation decisions for reducing system uncertainty. Two types of sensitivity metrics are proposed for multidisciplinary statistical sensitivity analysis: the extension of traditional variance-based sensitivity indices and relative-entropy-based sensitivity indices for situations with irregular system performance distributions. To overcome the computational challenges in multidisciplinary statistical sensitivity analysis, a multidisciplinary uncertainty analysis technique is employed for handling the complexity associated with coupling among multiple disciplines and propagating uncertainty across multiple levels (component/subsystem/system). An aircraft design problem consisting of three coupled disciplines is used to demonstrate the effectiveness of the proposed multidisciplinary uncertainty analysis method and multidisciplinary statistical sensitivity analysis approaches.