A Design Optimization Method using Evidence Theory

1. Power Set (All sets) Element (X) Model (Transfer Function) Evidence Theory (Possibility Theory) Output Input • What is possible may not be probable • What is impossible is also improbable B A Evidence Theory Evidence Theory Probability Theory Possibility Theory Uncertainty (Quantified) Uncertainty (Calculated) No Conflicting Evidence , we have Considering that Uncertainty (Quantified) If feasibility is expressed with positive null form then, constraint g is ALWAYS satisfied if where : (Possibility Theory) or for Universe A B C E E1 E11 E1 E2 E12 Partition E into E1 and E2 Partition E1 into E11 and E12 E12 E122 E121 Partition E12 into E121 and E122 Partition example Possibility Based Design Formulation s.t. Reliable Evidence Theory Det. Opt. mum Based Opti Optimum Design Variables =0.2 =0.0013 =0.1 s.t. w 2.0470 2.4781 2.3148 2.4692 2.5298 t 3.7459 3.8421 3.7346 4.1376 4.1726 Objective (X) f 7.6679 9.5212 8.645 10.217 10.556 A Design Optimization Method using Evidence Theory Zissimos P. Mourelatos; Associate Prof. Jun Zhou; Graduate Student Objectives • Design under uncertainty with incomplete information. • Develop accurate and efficient algorithms to calculate “fuzzy” response. • Extend design optimization from Reliability-Based Design Optimization (RBDO) to Possibility-BDO (PBDO) and Evidence-BDO (EBDO). Design Under Uncertainty Theoretical Aspects • Design under uncertainty • Uncertainty theories; Fuzzy measures • Possibility and Evidence Theory • Belief and Plausibility Measures Uncertainty Theories Possibility Based Design Possibility Theory Possibility-Based Design Optimization; Evidence-Based Design Optimization • Move hyper-ellipse to approximate design point • Partition domain of interest to evaluate plausibility of failure Cantilever Beam Example EBDO--Beam Example Geometrical interpretation of EBDO algorithm Comparison of PBDO and RBDO Results Comparison of EBDO and RBDO Results 2. Possibility-based optimization design