Title: Design Optimization with Insufficient Data using Possibility and Evidence Theories

Speaker: Zissimos P. Mourelatos, Oakland University

Date/Time: Monday, December 4, 2006, 10:00am – 11:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Deterministic optimal designs are usually unreliable because they do not consider the uncertainty/variation effect. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. We will show how the possibility and evidence theories may be used to account for uncertainty in design with incomplete information. A possibility-based design methodology will be presented, including a computationally efficient sequential optimization algorithm which consists of a sequence of cycles of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. It will be shown that the method gives a conservative solution compared with all conventional reliability-based designs obtained with different probability distributions. Also, a design optimization method using evidence theory will be presented. The method can be used when limited and often conflicting, information is available from “expert” opinions. A computationally efficient design optimization formulation is used, which can handle a mixture of epistemic and random uncertainties. It quickly identifies the vicinity of the optimal point and the active constraints by moving a hyper-ellipse in the original design space, using a reliability-based design optimization (RBDO) algorithm. Subsequently, a derivative-free optimizer calculates the evidence-based optimum, starting from the close-by RBDO optimum, considering only the identified active constraints. The computational cost is kept low by first moving to the vicinity of the optimum quickly and subsequently using local surrogate models of the active constraints only. Numerical examples will demonstrate the application of possibility and evidence theories in design and will highlight the trade-offs among reliability-based, possibility-based and evidence-based designs.