cossan training course: optimisazion analysis · optimisation overview optimization maximizing or...
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7th COSSAN TRAINING COURSE - 08-10 April 2019
COSSAN Training Course:Optimisazion Analysis
Edoardo Patelli, Matteo BroggiE: [email protected] W: www.cossan.co.uk T: +44 01517944079
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Optimisation Overview
Outline
1 OptimisationOverviewGradient based andgradient free optimisationStochastic Optimisation
2 Robust and Reliability BasedDesign
Definitions3 Hands-on session
Cantilever Beam
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Optimisation Overview
OptimizationMaximizing or minimizing a real function (Objective Function) bysystematically choosing input values (Design Variables) fromwithin an allowed set (Constrains) and computing the value ofthe function.
ToolsGradient based optimisationGradient free optimisationStochastic and heuristicoptimisation
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Optimisation Gradient based and gradient free optimisation
Outline
1 OptimisationOverviewGradient based andgradient free optimisationStochastic Optimisation
2 Robust and Reliability BasedDesign
Definitions3 Hands-on session
Cantilever Beam
E.Patelli M.Broggi COSSAN Training Course 10 April 2019 4 / 24
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Optimisation Gradient based and gradient free optimisation
Gradient based OptimizationRequires the calculation of the gradient
Generally requires few modelevaluationsNot applicable for noise functions(gradient descent increasingly’zigzags’)Depends of the starting point (canbe trapped on local minima)Example: BFGS,SQP
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Optimisation Gradient based and gradient free optimisation
Gradient free based OptimizationDoes not requires the calculation of the gradient
Robust optimisationalgorithmsDepends of the startingpoint (can be trapped onlocal minima)Can deal with noisefunctionsExample: Simplex,COBYLA, BOBYQA
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Optimisation Stochastic Optimisation
Outline
1 OptimisationOverviewGradient based andgradient free optimisationStochastic Optimisation
2 Robust and Reliability BasedDesign
Definitions3 Hands-on session
Cantilever Beam
E.Patelli M.Broggi COSSAN Training Course 10 April 2019 7 / 24
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Optimisation Stochastic Optimisation
Stochastic Optimization
Robust optimisationIndependent on the starting pointComputationally expensiveExamples: Cross Entropy,Evolution Strategies, GeneticAlgorithms, Simulated Annealing,Stochastic Ranking
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Optimisation Stochastic Optimisation
Stochastic Optimization
Further information and references are available on the TheoryManual
https://cossan.co.uk/wiki/index.php/Simulated_Annealing
https://cossan.co.uk/wiki/index.php/Genetic_Algorithms
https://cossan.co.uk/wiki/index.php/Cross_Entropy
https://cossan.co.uk/wiki/index.php/Evolution_Strategy
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Optimisation Stochastic Optimisation
Optimization in COSSAN Software
Design Variable (Input)Constraint (Evaluator)Objective Function (Evaluator)Optimisation Problem (Model)
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Optimisation Stochastic Optimisation
Optimization in COSSAN SoftwareDesign Variable
Define variables to be”optimised“Continuous ordiscreteBounded orunbounded
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Optimisation Stochastic Optimisation
Optimization in COSSAN SoftwareObjective function
Define function to be”minimised“Define as a matlabscript or functionReturn only 1 output
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Optimisation Stochastic Optimisation
Optimization in COSSAN SoftwareConstraint
Define bounds of theoptimisationDefine as a matlabscript or functionReturn only 1 outputEquality or inequalityconstraints
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Optimisation Stochastic Optimisation
Optimization in COSSAN SoftwareOptimization wizard
Define the optimisationanalysisSet optimisation parameters
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Robust and Reliability Based Design Definitions
Outline
1 OptimisationOverviewGradient based andgradient free optimisationStochastic Optimisation
2 Robust and Reliability BasedDesign
Definitions3 Hands-on session
Cantilever Beam
E.Patelli M.Broggi COSSAN Training Course 10 April 2019 15 / 24
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Robust and Reliability Based Design Definitions
Robust and Reliability Based Optimization
Avoid over-designProvide more robustsolutions
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Robust and Reliability Based Design Definitions
Robust DesignInclude variance of the performance function (due to theunavoidable uncertainty) in the optimisation process
Requires uncertaintyquantificationExample: design bysix-sigma (Taguchi method)Computational veryexpensive (usually requiresa meta-model)
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Robust and Reliability Based Design Definitions
Robust DesignInclude variance of the performance function (due to theunavoidable uncertainty) in the optimisation process
Requires uncertaintyquantificationExample: design bysix-sigma (Taguchi method)Computational veryexpensive (usually requiresa meta-model)
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Robust and Reliability Based Design Definitions
Reliability Based Optimization
Include reliability in theoptimisation process
Requires estimationprobability of failureComputational veryexpensive (usually requiresa meta-model)
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Robust and Reliability Based Design Definitions
RBO in COSSAN software
Optimization model(outer loop)Uncertaintyquantification analysis(inner loop)Dedicated wizard to mapvariables bertween innerand outer loop
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Robust and Reliability Based Design Definitions
RBO in COSSAN software
Optimization model(outer loop)Uncertaintyquantification analysis(inner loop)Dedicated wizard to mapvariables bertween innerand outer loop
E.Patelli M.Broggi COSSAN Training Course 10 April 2019 19 / 24
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Robust and Reliability Based Design Definitions
Mapping variables between inner and outer loolUse failure probability inObjective function orConstraintMapping Design Variable ofthe outer loop with Inputvariables of the inner loop
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Robust and Reliability Based Design Definitions
Mapping variables between inner and outer lool
Use failure probability inObjective function orConstraintMapping Design Variable ofthe outer loop with Inputvariables of the inner loop
E.Patelli M.Broggi COSSAN Training Course 10 April 2019 20 / 24
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Hands-on session
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Hands-on session Cantilever Beam
Outline
1 OptimisationOverviewGradient based andgradient free optimisationStochastic Optimisation
2 Robust and Reliability BasedDesign
Definitions3 Hands-on session
Cantilever Beam
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Hands-on session Cantilever Beam
Analysis of a Cantilever Beam
Design Variables: cross sectionbeam b = [0.010.2] andh = [0.02,0.4]Parameter: Maximum probabilityfailure Maxpf = 0.001
F
H
BL
Increase maximum allowable displacement (wmax )Recompute the probability of failure using advancedsimulation methods
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Hands-on session Transmission Antenna Tower
Transmission Antenna TowerRobust optimization of a 25-bars truss structure, an antenna tower
https://cossan.co.uk/wiki/index.php/Truss_Structure
Define inputs (Random variables,Parameters)Define a model (Evaluator, Matlabsolver)Define Optimisation problem(Design Variable, ObjectiveFunction, Constraints)
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