tutorial 2, part 1: optimization of a damped oscillator

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Tutorial 2, Part 1: Optimization of a damped oscillator. Damped oscillator. Mass m , damping c , stiffness k and initial kinetic energy Equation of motion:. Undamped eigen-frequency: Lehr's damping ratio D Damped eigen-frequency. Damped oscillator. - PowerPoint PPT Presentation

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Tutorial 2, Part 1: Optimization of a damped oscillator

2 Tutorial 2, Part 1: Optimization

Damped oscillator

• Mass m, damping c, stiffness k and initial kinetic energy

• Equation of motion:

• Undamped eigen-frequency:

• Lehr's damping ratio D

• Damped eigen-frequency

3 Tutorial 2, Part 1: Optimization

Damped oscillator

• Time-dependent displacement function

• Optimization goal: Minimize maximum amplitude after 5s free vibration

• Optimization constraint:

• Optimization parameter bounds & constant parameters:

4 Tutorial 2, Part 1: Optimization

Task description

• Parameterization of the problem

• Definition and evaluation of DOE scheme

• Definition and evaluation of MOP

• Single objective, constraint optimization

• Gradient based optimization

• Global response surface method

• Adaptive response surface method

• Evolutionary algorithm

• Multi objective optimization

• Pareto optimization with evolutionary algorithm

5 Tutorial 2, Part 1: Optimization

Project manager

1. Open the project manager2. Define project name3. Create a new project directory4. Copy optiSLang examples/Oscillator into project director

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6 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Start a new parametrize workflow2. Define workflow name3. Create a new problem specification4. Enter problem file name

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7 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Click “open file” icon in parametrize editor2. Browse for the SLang input file oscillator.s 3. Choose file type as INPUT

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8 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Mark value of m in the input file2. Define m as input parameter3. Define parameter name

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9 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Open parameter in parameter tree2. Enter lower and upper bounds

(0.1 … 5.0)

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10 Tutorial 2, Part 1: Optimization

Parameterization of the inputs

1. Repeat procedure for k

11 Tutorial 2, Part 1: Optimization

1. Click “open file” icon in parametrize editor2. Browse for the SLang output file oscillator_solution.txt 3. Choose file type as OUTPUT

Parameterization of the output signal

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12 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Mark output value in editor2. Define omega as output parameter3. Repeat for x_max and x_max_env

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13 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Create new objective function2. Define objective as x_max

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14 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Create new constraint equation2. Define inequality constraint 0≤8-omega

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15 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Check overview for inputs2. Check overview for outputs

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16 Tutorial 2, Part 1: Optimization

Parameterization of the problem

1. Check overview for objectives2. Check overview for constraints

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17 Tutorial 2, Part 1: Optimization

Design Of Experiments (DOE)

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1. Start a new DOE workflow2. Define workflow name and workflow identifier3. Enter problem file name4. Enter solver call (slang –b oscillator.s)5. Start DOE evaluation with 100 LHS samples

18 Tutorial 2, Part 1: Optimization

Meta-Model of Optimal Prognosis (MOP)

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1. Start a new MOP workflow2. Define workflow name and workflow identifier3. Choose DOE result file4. Choose optional problem file

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19 Tutorial 2, Part 1: Optimization

Meta-Model of Optimal Prognosis (MOP)

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1. CoP settings (sample splitting or cross validation)2. Investigated approximation models3. CoP - accepted reduction in prediction quality to simplify model4. Filter settings5. Selection of inputs and outputs

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20 Tutorial 2, Part 1: Optimization

Meta-Model of Optimal Prognosis (MOP)

• Check approximation quality to identify solver problems and for a possible use of MOP for the optimization task

21 Tutorial 2, Part 1: Optimization

Gradient-based optimization

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1. Start a new Gradient-based workflow2. Define workflow name and workflow identifier3. Enter problem file name4. Choose optimization method5. Enter solver call (slang –b oscillator.s)6. Start gradient workflow

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22 Tutorial 2, Part 1: Optimization

Gradient-based optimization

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1. Keep default settings and start optimization task Differentiation interval is too small for noisy objective Optimizer runs into local optimum

2. Change differentiation interval to 5% Slow convergence but global optimum is found

23 Tutorial 2, Part 1: Optimization

Gradient-based optimization

1. Objective history 2. Best design input parameters3. Best design response data4. Objective and constraints data5. Parameter history

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24 Tutorial 2, Part 1: Optimization

Gradient-based optimization using MOP

3b.

1. Start a new Gradient-based workflow2. Define workflow name, workflow identifier and problem file name3. Use MOP as solver and choose MOP data file4. Enter solver call (slang –b oscillator.s) to verify best design5. Start gradient workflow

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25 Tutorial 2, Part 1: Optimization

Gradient-based optimization using MOP

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1. Keep default settings and start optimization task

26 Tutorial 2, Part 1: Optimization

Gradient-based optimization using MOP

1. Objective history 2. Best design input parameters (MOP and calculated)3. Best design response data (MOP and calculated)4. Objective and constraints data (MOP and calculated)

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27 Tutorial 2, Part 1: Optimization

Adaptive response surface (local)

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1. Start a new ARSM workflow2. Define workflow name and workflow identifier3. Enter problem file name4. Enter solver call (slang –b oscillator.s)5. Start ARSM workflow

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28 Tutorial 2, Part 1: Optimization

Adaptive response surface (local)

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1. NLPQL as optimization method2. Approximation settings:

keep polynomial regression3. Advanced settings: no recycle

of previous support points

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29 Tutorial 2, Part 1: Optimization

Adaptive response surface (local)

1. Objective history for each iteration step 2. Best design input parameters (ARSM and original)3. Best design response data (ARSM and original)4. Objective and constraints data (ARSM and original)5. Parameter history for each iteration step

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30 Tutorial 2, Part 1: Optimization

Adaptive response surface (global)

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1. GA & NLPQL as optimization method2. Approximation settings: choose Moving Least Squares

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31 Tutorial 2, Part 1: Optimization

Adaptive response surface (global)

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1. Increase stopping criteria to 0.1%2. Advanced settings: choose recycle previous support points

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32 Tutorial 2, Part 1: Optimization

Adaptive response surface (global)

33 Tutorial 2, Part 1: Optimization

Evolutionary algorithm (EA)

1. Start a new NOA workflow2. Define workflow name and workflow identifier 3. Enter problem file name4. Choose optimization algorithm (EA with global search is default)5. Enter solver call (slang –b oscillator.s) and start workflow

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34 Tutorial 2, Part 1: Optimization

Evolutionary algorithm (EA)

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1. Choose start population size2. Keep defaults for Selection,

Crossover and Mutation

35 Tutorial 2, Part 1: Optimization

Evolutionary algorithm (EA)

1. Objective history for each design2. Best design input parameters 3. Best design response data 4. Penalized objective and constraints data5. Parameter history for each design,

new generations are marked

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36 Tutorial 2, Part 1: Optimization

Parameterization of second objective

1. Start a new parametrize workflow2. Define workflow name3. Create a copy and modify it4. Open Tutorial_Oscillator.pro and enter new problem file name

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37 Tutorial 2, Part 1: Optimization

Parameterization of second objective

1. Create a new objective2. Enter name, activate and enter function obj2 = omega3. Delete omega constraint4. Close editor and check objectives

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38 Tutorial 2, Part 1: Optimization

Pareto optimization with EA

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1. Start a new Pareto workflow2. Define workflow name and workflow identifier 3. Enter problem file name4. Choose EA as optimization algorithm 5. Enter solver call (slang –b oscillator.s) and start workflow

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39 Tutorial 2, Part 1: Optimization

Pareto optimization with EA

1. Choose start population size2. Keep defaults for Selection, Crossover and Mutation

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40 Tutorial 2, Part 1: Optimization

Pareto optimization with EA

1. Plot of objective values of designs including Pareto front 2. Best design input parameters 3. Best design response data 4. Objectives data5. Parameter history for each design, new generations are marked

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