Uncertainty Analysis of Flood Control Measures Including Epistemic and Aleatory Uncertainties: Probability Theory and Evidence Theory

Abstract

Encountering uncertainty in engineering design problems is inevitable. Probability theory is a traditional method for uncertainty analysis despite the nature of uncertainties (i.e., aleatory or epistemic). Because of some limitations of probability theory in analyzing epistemic uncertainty, new methods such as evidence theory have been developed. This paper describes the analysis of uncertainty by means of both probability and evidence theories. Monte Carlo simulation is used along with the two theories to propagate the uncertainty. A computational strategy based on random sampling is used to analyze and represent the epistemic and aleatory uncertainty. Despite its advantage, the application of evidence theory in civil engineering is limited because of its mathematical complexities. This paper attempts to make this theory more applicable by using practical design problems, as well as by highlighting its advantages compared with probability theory. Three hypothetical flood-control-related problems are considered. The uncertainty of a design storm intensity resulting from an experimental equation and a design discharge resulting from the rational method are analyzed assuming storm intensity as a stochastic variable with Level 2 (i.e., both aleatory and epistemic) uncertainties. The design diameter of the pipes in a stormwater collection system is estimated. It is assumed that the input parameters have only epistemic uncertainty. The results show that if the desired risk changes, some diameters may stay fixed and some may change. The design of a flood control levee is considered. The levee height is an output variable, and it is assumed that the design discharge has Level 2 uncertainty, whereas all other inputs have epistemic uncertainty. The results of uncertainty analysis with the two theories are represented appropriately, discussed, and compared. Compared with probability theory, evidence theory offers more insight for decision makers when they encounter epistemic and/ or aleatory uncertainties in design problems.