1 / 40

Tutorial 2, Part 1: Optimization of a damped oscillator

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.

almira
Download Presentation

Tutorial 2, Part 1: Optimization of a damped oscillator

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Tutorial 2, Part 1: Optimization of a damped oscillator

  2. 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 Tutorial 2, Part 1: Optimization

  3. Damped oscillator • Time-dependent displacement function • Optimization goal: Minimize maximum amplitude after 5s free vibration • Optimization constraint: • Optimization parameter bounds & constant parameters: Tutorial 2, Part 1: Optimization

  4. 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 Tutorial 2, Part 1: Optimization

  5. Project manager 1. 2. 3. • Open the project manager • Define project name • Create a new project directory • Copy optiSLang examples/Oscillator into project director Tutorial 2, Part 1: Optimization

  6. Parameterization of the problem 1. 2. 3. 4. 5. • Start a new parametrize workflow • Define workflow name • Create a new problem specification • Enter problem file name Tutorial 2, Part 1: Optimization

  7. Parameterization of the problem 1. 2. 3. • Click “open file” icon in parametrize editor • Browse for the SLang input file oscillator.s • Choose file type as INPUT Tutorial 2, Part 1: Optimization

  8. Parameterization of the problem 2. 1. 3. • Mark value of m in the input file • Define m as input parameter • Define parameter name Tutorial 2, Part 1: Optimization

  9. Parameterization of the problem 1. 2. • Open parameter in parameter tree • Enter lower and upper bounds (0.1 … 5.0) Tutorial 2, Part 1: Optimization

  10. Parameterization of the inputs • Repeat procedure for k Tutorial 2, Part 1: Optimization

  11. Parameterization of the output signal 1. 2. 3. • Click “open file” icon in parametrize editor • Browse for the SLang output file oscillator_solution.txt • Choose file type as OUTPUT Tutorial 2, Part 1: Optimization

  12. Parameterization of the problem 2. 1. 3. • Mark output value in editor • Define omega as output parameter • Repeat for x_max and x_max_env Tutorial 2, Part 1: Optimization

  13. Parameterization of the problem 2. 1. • Create new objective function • Define objective as x_max Tutorial 2, Part 1: Optimization

  14. Parameterization of the problem 2. 1. • Create new constraint equation • Define inequality constraint 0≤8-omega Tutorial 2, Part 1: Optimization

  15. Parameterization of the problem 1. 2. • Check overview for inputs • Check overview for outputs Tutorial 2, Part 1: Optimization

  16. Parameterization of the problem 1. 2. • Check overview for objectives • Check overview for constraints Tutorial 2, Part 1: Optimization

  17. Design Of Experiments (DOE) 2. 1. 2. 3. • Start a new DOE workflow • Define workflow name and workflow identifier • Enter problem file name • Enter solver call (slang –b oscillator.s) • Start DOE evaluation with 100 LHS samples Tutorial 2, Part 1: Optimization

  18. Meta-Model of Optimal Prognosis (MOP) 2. 1. 3. 4. • Start a new MOP workflow • Define workflow name and workflow identifier • Choose DOE result file • Choose optional problem file Tutorial 2, Part 1: Optimization

  19. Meta-Model of Optimal Prognosis (MOP) 1. 4. 2. 3. 5. • CoP settings (sample splitting or cross validation) • Investigated approximation models • DCoP - accepted reduction in prediction quality to simplify model • Filter settings • Selection of inputs and outputs Tutorial 2, Part 1: Optimization

  20. Meta-Model of Optimal Prognosis (MOP) • Check approximation quality to identify solver problems and for a possible use of MOP for the optimization task Tutorial 2, Part 1: Optimization

  21. Gradient-based optimization 2. 1. 2. 3. 4. • Start a new Gradient-based workflow • Define workflow name and workflow identifier • Enter problem file name • Choose optimization method • Enter solver call (slang –b oscillator.s) • Start gradient workflow Tutorial 2, Part 1: Optimization

  22. Gradient-based optimization 1. • Keep default settings and start optimization task • Differentiation interval is too small for noisy objective • Optimizer runs into local optimum • Change differentiation interval to 5% • Slow convergence but global optimum is found Tutorial 2, Part 1: Optimization

  23. Gradient-based optimization 1. 3. 2. 4. • Objective history • Best design input parameters • Best design response data • Objective and constraints data • Parameter history 5. Tutorial 2, Part 1: Optimization

  24. Gradient-based optimization using MOP 3a. 3b. 4. • Start a new Gradient-based workflow • Define workflow name, workflow identifier and problem file name • Use MOP as solver and choose MOP data file • Enter solver call (slang –b oscillator.s) to verify best design • Start gradient workflow Tutorial 2, Part 1: Optimization

  25. Gradient-based optimization using MOP 1. • Keep default settings and start optimization task Tutorial 2, Part 1: Optimization

  26. Gradient-based optimization using MOP 1. 3. 2. 4. • Objective history • Best design input parameters (MOP and calculated) • Best design response data (MOP and calculated) • Objective and constraints data (MOP and calculated) Tutorial 2, Part 1: Optimization

  27. Adaptive response surface (local) 2. 1. 2. 3. • Start a new ARSM workflow • Define workflow name and workflow identifier • Enter problem file name • Enter solver call (slang –b oscillator.s) • Start ARSM workflow Tutorial 2, Part 1: Optimization

  28. Adaptive response surface (local) 2. 1. 2. 3. • NLPQL as optimization method • Approximation settings: keep polynomial regression • Advanced settings: no recycle of previous support points Tutorial 2, Part 1: Optimization

  29. Adaptive response surface (local) 1. 3. 2. 4. 5. • Objective history for each iteration step • Best design input parameters (ARSM and original) • Best design response data (ARSM and original) • Objective and constraints data (ARSM and original) • Parameter history for each iteration step Tutorial 2, Part 1: Optimization

  30. Adaptive response surface (global) 2. 1. 2. • GA & NLPQL as optimization method • Approximation settings: choose Moving Least Squares Tutorial 2, Part 1: Optimization

  31. Adaptive response surface (global) 2. 1. • Increase stopping criteria to 0.1% • Advanced settings: choose recycle previous support points Tutorial 2, Part 1: Optimization

  32. Adaptive response surface (global) Tutorial 2, Part 1: Optimization

  33. Evolutionary algorithm (EA) 2. 1. 2. 3. 4. • Start a new NOA workflow • Define workflow name and workflow identifier • Enter problem file name • Choose optimization algorithm (EA with global search is default) • Enter solver call (slang –b oscillator.s) and start workflow Tutorial 2, Part 1: Optimization

  34. Evolutionary algorithm (EA) 1. • Choose start population size • Keep defaults for Selection, Crossover and Mutation Tutorial 2, Part 1: Optimization

  35. Evolutionary algorithm (EA) 1. 3. 2. 4. 5. • Objective history for each design • Best design input parameters • Best design response data • Penalized objective and constraints data • Parameter history for each design, new generations are marked Tutorial 2, Part 1: Optimization

  36. Parameterization of second objective 2. 3. 4. • Start a new parametrize workflow • Define workflow name • Create a copy and modify it • Open Tutorial_Oscillator.pro and enter new problem file name Tutorial 2, Part 1: Optimization

  37. Parameterization of second objective 2. 4. 1. 3. • Create a new objective • Enter name, activate and enter function obj2= omega • Delete omega constraint • Close editor and check objectives Tutorial 2, Part 1: Optimization

  38. Pareto optimization with EA 2. 1. 2. 3. 4. • Start a new Pareto workflow • Define workflow name and workflow identifier • Enter problem file name • Choose EA as optimization algorithm • Enter solver call (slang –b oscillator.s) and start workflow Tutorial 2, Part 1: Optimization

  39. Pareto optimization with EA 1. • Choose start population size • Keep defaults for Selection, Crossover and Mutation Tutorial 2, Part 1: Optimization

  40. Pareto optimization with EA 2. 3. 1. 5. 4. • Plot of objective values of designs including Pareto front • Best design input parameters • Best design response data • Objectives data • Parameter history for each design, new generations are marked Tutorial 2, Part 1: Optimization

More Related