Mest 16888 ES077 Multidisciplinary System Design Optimization(MSDO) Design Space Exploration Lecture 5 18 February 2004 Karen willcox C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary System Multidisciplinary System Design Optimization (MSDO) Design Optimization (MSDO) Design Space Exploration Lecture 5 18 February 2004 Karen Willcox
Mest Today's Topics 16888 ESD.J7 Design of Experiments Overview Full Factorial Design · Parameter stud One at a time Latin Hypercubes Orthogonal Arrays Effects DoE Paper Airplane Experiment C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Today’s Topics Today’s Topics • Design of Experiments Overview • Full Factorial Design • Parameter Study • One at a Time • Latin Hypercubes • Orthogonal Arrays • Effects • DoE Paper Airplane Experiment
Mlsd Design of Experiments 16888 E77 A collection of statistical techniques providing a systematic way to sample the design space Useful when tackling a new problem for which you know very little about the design space Study the effects of multiple input variables on one or more output parameters Often used before setting up a formal optimization problem Identify key drivers among potential design variables Identify appropriate design variable ranges Identify achievable objective function values Often, DOE is used in the context of robust design. Today we will just talk about it for design space exploration C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design of Experiments Design of Experiments • A collection of statistical techniques providing a systematic way to sample the design space • Useful when tackling a new problem for which you know very little about the design space. • Study the effects of multiple input variables on one or more output parameters • Often used before setting up a formal optimization problem – Identify key drivers among potential design variables – Identify appropriate design variable ranges – Identify achievable objective function values • Often, DOE is used in the context of robust design. Today we will just talk about it for design space exploration
Mlsd Design of Experiments 16888 E77 Design variables= factors Values of design variables levels noise factors variables over which we have no control e.g. manufacturing variation in blade thickness Control factors variables we can control e.g. nominal blade thickness Outputs =observations objective functions Factors +—“ Experiment Observation Levels Often an analysis code C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Design of Experiments Design of Experiments Design variables = factors Values of design variables = levels Noise factors = variables over which we have no control e.g. manufacturing variation in blade thickness Control factors = variables we can control e.g. nominal blade thickness Outputs = observations (= objective functions) Factors + Levels “Experiment” Observation (Often an analysis code)
Mest Matrix Experiments 16888 E77 Each row of the matrix corresponds to one experiment Each column of the matrix corresponds to one factor Each experiment corresponds to a different combination of factor levels and provides one observation Expt Ne Factora Factorb Observation A1 B1 n1 A1 B2 A2 B1 n A2 B2 n4 Here, we have two factors each of which can take two levels C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Matrix Experiments Matrix Experiments • Each row of the matrix corresponds to one experiment. • Each column of the matrix corresponds to one factor. • Each experiment corresponds to a different combination of factor levels and provides one observation. Expt No. Factor A Factor B Observation 1 A1 B1 K1 2 A1 B2 K 2 3 A2 B1 K 3 4 A2 B2 K 4 Here, we have two factors, each of which can take two levels