7th COSSAN TRAINING COURSE - 08-10 April 2019

COSSAN Training Course:Optimisazion Analysis

Edoardo Patelli, Matteo BroggiE: info@cossan.co.uk W: www.cossan.co.uk T: +44 01517944079

Optimisation Overview

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 2 / 24

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

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

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 6 / 24

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

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

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 9 / 24

Optimisation Stochastic Optimisation

Optimization in COSSAN Software

Design Variable (Input)Constraint (Evaluator)Objective Function (Evaluator)Optimisation Problem (Model)

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 10 / 24

Optimisation Stochastic Optimisation

Optimization in COSSAN SoftwareDesign Variable

Define variables to be”optimised“Continuous ordiscreteBounded orunbounded

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 11 / 24

Optimisation Stochastic Optimisation

Optimization in COSSAN SoftwareObjective function

Define function to be”minimised“Define as a matlabscript or functionReturn only 1 output

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 12 / 24

Optimisation Stochastic Optimisation

Optimization in COSSAN SoftwareConstraint

Define bounds of theoptimisationDefine as a matlabscript or functionReturn only 1 outputEquality or inequalityconstraints

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 13 / 24

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

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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)

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 17 / 24

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)

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 17 / 24

Robust and Reliability Based Design Definitions

Reliability Based Optimization

Include reliability in theoptimisation process

Requires estimationprobability of failureComputational veryexpensive (usually requiresa meta-model)

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 18 / 24

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

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

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

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 20 / 24

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

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

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 22 / 24

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

E.Patelli M.Broggi COSSAN Training Course 10 April 2019 23 / 24

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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