Design Under Uncertainty: Balancing Expected Performance and Risk

The problem of quantifying uncertainty in the design process is approached indirectly. Nonquantifiable variability resulting from lack of knowledge is treated as epistemic uncertainty and quantifiable variability caused by random influences is treated as aleatory uncertainty. The emphasis in this approach is on the effects of epistemic uncertainty, left unquantified, on design performance. Performance is treated as a random function of the epistemic uncertainties that are considered as independent variables, and a design decision is based on the mean and variance of design performance. Since the mean and variance are functions of the uncertainties, multicriteria decision methods are employed to determine the preferred design. The methodology is illustrated on a three-spring model with stochastic forcing and two uncertain damping coefficients. Based on the example, the concept of balancing expected performance and risk is explored in an engineering context. Risk is quantified using aleatory uncertainty for fixed values of epistemic uncertainty. The study shows the unique features of this approach in which risk-based design decisions are made under both aleatory and epistemic uncertainties without assuming a distribution for epistemic uncertainty.