Reliability and Robustness in Engineering Design

1. Feasible Region Response X1 g1(X1,X2)=0 g2(X1,X2)=0 Increased Performance Reliable Optimum Design Variable X Deterministic Optimum X2 x x x x 2 2 1 1 Preference Aggregation Function 1 1 s.t. 0 h2 Indifference Points 1 0 Percentile Difference Approach PDFf f ΔRf Y Z t w L=100 in s.t. where Reliability and Robustness in Engineering Design Zissimos P. Mourelatos; Associate Prof. Jinghong Liang; Graduate Student • Objectives RBDO: Reliability-Based Design Optimization Deterministic to Probabilistic Optimization • Extend deterministic design optimization by including uncertainties. • Develop efficient and accurate RBDO algorithms for practical design problems. • Simultaneously design for reliability (performance satisfaction under uncertainty) and robustness (performance insensitivity to variation). • Consider inherent variability of materials and manufacturing processes at the design stage. General RBDO Problem Formulation • A unified Approach to Reliability & Robustness Performance Insensitivity to Variation • Advantages: • Simultaneously considers reliability and robustness. • Resolves competing objectives (performance vs. robustness) under uncertainty and identifies the “best” design. • It is based on an efficient and accurate single-loop RBDO method. • Key Algorithm Features: • Variation of performance measure: • Percentile difference approach • Aggregation of Objectives: • Preference aggregation function • Trade-offs in multi-objective design: • Indifference point approach • Optimization under uncertainty: • Single-loop method; Pareto frontier Preference Function • Beam Example The objective is to minimize the beam weight and the variability of tip displacement. One non-linear failure mode is used representing yielding at the fixed end of the cantilever. Pareto Set with s=-5 and different weights