Uncertainty Quantification of Structural Response Using Evidence Theory

Abstract

Over the past decade, classical probabilistic analysis has been a popular approach among the uncertainty quantification methods. As the complexity and performance requirements of a structural system are increased, the quantification of uncertainty becomes more complicated, and various forms of uncertainties should be taken into consideration. Because of the need to characterize the distribution of probability, classical probability theory may not be suitable for a large complex system such as an aircraft, in that our information is never complete because of lack of knowledge and statistical data. Evidence theory, also known as Dempster-Shafer theory, is proposed to handle the epistemic uncertainty that stems from lack of knowledge about a structural system. Evidence theory provides us with a useful tool for aleatory (random) and epistemic (subjective) uncertainties. An intermediate complexity wing example is used to evaluate the relevance of evidence theory to an uncertainty quantification problem for the preliminary design of airframe structures. Also, methods for efficient calculations in large-scale problems are discussed.