5/16/2018 Types of Surrogate Models 园上活大学 Use of Surrogate in Optimization 国上清大学 o Types of surrogate models Global/local surrogate models Polynomial approximation Update of surrogate models Artificial Neural Network(Radial Basis Functions,RBF) Hybrid surrogate models Intelligent use of surrogate,fo .Gaussian process based methods(Kriging.DACE) 密 Space mapping Hybrid methods ●Procedures: Sampling using design of experiments (DOE) Choosing a type of surrogate Construction of surrogates to fit the data Model validation 包应▣ Model update > o Wenbn Son Sources for Uncertainty and Robust Analysis and Optimization 圈上活大坐 Approaches for Tackling Uncertainty 国上清道大坐 Methodologies that deal with uncertainties will be crucial to Soen EX124S further improve the quality of design Sources for uncertainties Robust analysis and optimization involves identification of .Materials uncertainty sourc es.characterization of uncertainties .Geometry mathematical modeling,analysis methods .Operating conditios .Loads.etc 0 Approaches for tackling uncertainties Monte Carlo 4 Statistical approach,Bayes principle Remdl-0f Erret Optimisation models under An Example Test Function-AM/FM Uncertainties 图上洋大峰 cos Function 国上洋大学 y=f(x,c) Noise (discritsation) Inputs +variations Product Process System drag,PNL Functionplot and a GA search result on the test fiunction (flight conditions) y=f八x+a,e+e)+d 41 75/16/2018 7 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Types of Surrogate Models 37 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Use of Surrogate in Optimization • Global/local surrogate models • Update of surrogate models • Hybrid surrogate models • Intelligent use of surrogate, for example, machine learning… 38 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Robust Analysis and Optimization • Methodologies that deal with uncertainties will be crucial to further improve the quality of design • Robust analysis and optimization involves identification of uncertainty sources, characterization of uncertainties, mathematical modeling, analysis methods Enabling the potential of Non-deterministic Approaches, A joint Industry/Academic/Government Workshop, April, 2000 39 Sources for uncertainties • Materials • Geometry • Operating conditions • Loads, etc Approaches for tackling uncertainties • Monte Carlo • Response surface • Targuchi • Statistical approach, Bayes principle Sources for Uncertainty and Approaches for Tackling Uncertainty 40 y  f (x  δ,c  ε)  Computational model of a physical system with uncertainty y  f (x,c) Computational model of a physical system Optimisation models under Uncertainties 41             n i i f x i f f x 1 2 0.5 cos 2 1 x 5 5cos 2   where and f1  2 f2 10 Function plot and a GA search result on the test function An Example Test Function – AM/FM cos Function 42