Uncertainty and sensitivity analysis methods for improving design robustness and reliability

Abstract

Engineering systems of the modern day are increasingly complex, often involving numerous components, countless mathematical models, and large, globally-distributed design teams. These features all contribute uncertainty to the system design process that, if not properly managed, can escalate into risks that seriously jeopardize the design program. In fact, recent history is replete with examples of major design setbacks due to failure to recognize and reduce risks associated with performance, cost, and schedule as they emerge during the design process. The objective of this thesis is to develop methods that help quantify, understand, and mitigate the effects of uncertainty in the design of engineering systems. The design process is viewed as a stochastic estimation problem in which the level of uncertainty in the design parameters and quantities of interest is characterized probabilistically, and updated through successive iterations as new information becomes available. Proposed quantitative measures of complexity and risk can be used in the design context to rigorously estimate uncertainty, and have direct implications for system robustness and reliability. New local sensitivity analysis techniques facilitate the approximation of complexity and risk in the quantities of interest resulting from modifications in the mean or variance of the design parameters. A novel complexity-based sensitivity analysis method enables the apportionment of output uncertainty into contributions not only due to the variance of input factors and their interactions, but also due to properties of the underlying probability distributions such as intrinsic extent and non-Gaussianity. Furthermore, uncertainty and sensitivity information are combined to identify specfic strategies for uncertainty mitigation and visualize tradeoffs between available options. These approaches are integrated with design budgets to guide decisions regarding the allocation of resources toward improving system robustness and reliability. The methods developed in this work are applicable to a wide variety of engineering systems. In this thesis, they are demonstrated on a real-world aviation case study to assess the net cost-benet of a set of aircraft noise stringency options. This study reveals that uncertainties in the scientific inputs of the noise monetization model are overshadowed by those in the scenario inputs, and identifies policy implementation cost as the largest driver of uncertainty in the system.