Non-probabilistic design optimization with insufficient data using possibility and evidence theories

Abstract

Early in the engineering design cycle, it is difficult to quantify product reliability due to insufficient data or information for modeling the uncertainties. Design decisions are therefore, based on fuzzy information that is vague, imprecise, qualitative, linguistic or incomplete. The uncertain information is usually available as intervals with lower and upper limits. In this chapter, the possibility and evidence theories are used to account for uncertainty in design with incomplete information. Possibility-based and evidence-based design optimizationmethods are presented which handle a combination of probabilistic and non-probabilistic design variables. Also, a computationally efficient sequential possibility-based design optimization (SPDO) method is implemented, which decouples the design loop and the reliability assessment of each constraint. Two numerical examples demonstrate the application of possibility and evidence theories in design and highlight the trade-offs among reliability-based, possibility-based and evidence-based designs.