Investigation of Evidence Theory for Engineering Applications

tional simulation, computer simulations can appear most In the recent mathematical and risk assessment convincing. Terminology such as “virtual prototyping”, literature on uncertainty estimation, it has been argued “virtual testing”, “full physics simulation”, and that the traditional application of probability theory “modeling and simulation based acquisition” are provides an inadequate model to capture the full scope of extremely appealing when budgets are highly constrainepistemic uncertainty. Epistemic uncertainty is also ed, competitors are taking market share, or when referred to as subjective uncertainty, reducible political constraints do not allow testing of certain uncertainty, or uncertainty due to lack of knowledge. systems. To assess the accuracy and usefulness of This paper applies an alternative representation of computational simulations, three key aspects are needed uncertainty, evidence theory (also referred to as in the analysis and experimental process: code and Dempster-Shafer theory), to a simple example. The solution verification, experimental validation of the example system involves an algebraic equation with two mathematical models of the process being simulated, and uncertain input parameters and one system response estimation of the uncertainty of both the inputs and variable. The information for each of the uncertain outputs of the simulation. The topics of verification and parameters is given by multiple sources of intervalvalidation are not addressed here, but these are covered at valued data, so that large epistemic uncertainty exists in length in the literature. A number of fields have the parameters. The example is solved with traditional contributed to the development of uncertainty estimation probability theory and evidence theory. The discussion techniques and procedures, such as, nuclear reactor safety, stresses the mathematical and procedural steps needed to underground storage of radioactive and toxic wastes, and compute uncertainty bounds in the system response structural dynamics (see, for example, Refs. 1-15). using evidence theory, as well as the similarities and Uncertainty estimation for engineered systems is differences between evidence theory and the traditional sometimes referred to as the simulation of approach. Given the nature of the specified uncertainty nondeterministic systems. The mathematical model of information, it is found that a traditional application of the system, which includes the influence of the probability theory significantly underestimates the environment on the system, is considered nonlikelihood of a hypothetical unsafe region as compared to deterministic in the sense that: a) the model can produce evidence theory. Strengths and weaknesses of evidence nonunique system responses because of the existence of theory are discussed, and several important open issues uncertainty in the input data for the model, or b) there are are identified that must be addressed before evidence multiple alternative mathematical models for the system. theory can be used confidently and productively in The mathematical models, however, are assumed to be engineering applications. deterministic in the sense that when all necessary input data for the model are specified, the model produces only