MITESD_77S10_lec05

# MITESD_77S10_lec05 - Multidisciplinary System Design...

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1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary System Design Optimization (MSDO) Design Space Exploration Lecture 5 Karen Willcox

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2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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
3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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.

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4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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)
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics 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 1 2 A1 B2 2 3 A2 B1 3 4 A2 B2 4 Here, we have two factors, each of which can take two levels.

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6 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Full-Factorial Experiment Specify levels for each factor Evaluate outputs at every combination of values n factors l levels l n observations complete but expensive!
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MITESD_77S10_lec05 - Multidisciplinary System Design...

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