3_chen_wcsmo_anel3_chen_wcsmo_panel3_chen_wcsmo_panel3_chen_wcsmo_panel.ppt

Design Optimization under Uncertainty: Status Promises Design Scenario Uncertainty Representation Quantification Probabilistic (distribution function, random field) Non-probabilistic Possibility-based (fuzzy set) Interval analysis Evidence theory Aleatory (stochastic, irreducible) vs. Epistemic (reducible) reliability interval, Bayesian reliability Uncertainty Propagation Estimation Local expansion based methods Taylor series method Simulation based method Monte Carlo Simulation Importance sampling, stratified sampling, adaptive sampling,… MPP (Most probable point based methods) FORM (first order reliability method) SORM (second order reliability method) Numerical integration based method Full factorial numerical integration (tensor product quadrature) Dimension reduction method Functional expansion based method Polynomial chaos expansion method Metamodeling based method (Kriging, Radial Basis Function, moving least square, etc.) Applications Structure Simultaneous structure aerodynamics Manufacturing process Medical Automotive aerospace Military (undersea vehicle, penetration warhead Research Trends/Emerging Topics Future Opportunities Nano-, bio-engineering Incorporating model, data, algorithmic uncertainties From reliability analysis to reliability-based design MDO under uncertainty Integration with rigorous decision making framework (Olson 1997) MDO under Uncertainty Without uncertainty objective function f = V(Y) = V(Y(X)) V - value function, e.g. profit With uncertainty objective function f = E(U) - expected utility. The preferred choice is the alternative (lottery) that has the higher expected utility. * Dr. Wei Chen Integrated Design Automation Laboratory (IDEAL)Department of Mechanical EngineeringNorthwestern University Panel Presentation 7th World Congress on Structural and Multidisciplinary Optimization May 24th, 2007 Moments (mean, variance,…) Reliability Distribution Uncertain