1. Dynamic Software and Engineering GmbH, Weimar, Germany
Sensitivty Analysis, Optimization and Robust Design with optiSLang and ANSYS Workbench 12
- Part II -
Optimization of a bearing angle
Dynamic Software and Engineering GmbH, Weimar, Germany

2. Agenda 1. Model background 2. Set-up of the ANSYS workbench simulation
Parametrization of the Geometry Values
Setting boundary conditions in ANSYS Workbench
Meshing in ANSYS Workbench
Solver settings in ANSYS Workbench
Parametrization of simulation results
ANSYS Parameter Manager
3. Introduction in optiPlug
Workaround optiPlug and optiSLang
File system in optiSLang created by optiPlug
Exporting the simulation to optiSLang
Default settings
Special features of optiPlug
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

3. Agenda 4. Performing of a sensitivity analysis (DoE)
Checking the parametrization in optiSLang
Updating the parameter range
Starting a new Design of Experiments
Postprocessing of the sensitivity study
5. Optimization of the model
Reducing the number of necessary parameters
Defining an suitable obective function
Optimization of the model with the method of adaptive response surfaces
Read-in the best design in ANSYS Workbench
Introduction in other optimization algorithms
6. Basics of a robustness analysis
Stochastic scatter of parameters
Write out a new robustness task with optiPlug
Update the parametrization for a robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

4. Content 1. Model background 2. ANSYS workbench simulation 3. optiPlug
4. Sensitivity analysis
5. Optimization
6. Robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

5. 1. Model background
The bearing angle is part of a test bench for chains.
In this test bench, a load of 12.6 kN is set on chains.
The load is set in longitudinal direction.
A load cell is fixed to the angle. This measures the load and send it to the computer system
Therefore the whole load of 12.6 kN is set on the winding, where the load cell is fixed to the bearing angle
Thus, the problematic variables are the v.Mises stress in the whole structure and especially at the connection between the rib and the angle short below the winding.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

6. 1. Model background Workflow of a robust design optimization
Basic design
Sensitivity analysis
Optimization
Robustness analysis
Is the design robust ? No
Yes
Robust design
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

7. 2. ANSYS Workbench simulation
1. Model background
2. ANSYS workbench simulation
2.1 Overview – Parametrisation in ANSYS Workbench
2.2 Parametrization of the geometry
2.3 Simulation and parametrization of the results
2.4 Summary - simulation
3. optiPlug
4. Sensitivity analysis
5. Optimization
6. Robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

8. 2.1 CAE Integration within ANSYS Workbench
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

9. 2.1 Overview – Parametrization in ANSYS Workbench
The basic of the parametrization in ANSYS is the Parameter Set on the project page:
Geometryparameters (from CAD or Design Modeler)
Materialparameters/ Simulationparameters
Simulationresults
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

10. 2.1 Overview – Parametrization in ANSYS Workbench
The Parameter section summarizes the Parameters of each component
CAD Parameters: CAD System (external) or ANSYS Design Modeler
Material Parameter: Engineering Data
Simulation results: Simulation
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

11. 2.2 Parametrization of the geometry
Start a new project in ANSYS Workbench
Create a new „Static Structural (ANSYS)“ analysis
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

12. 2.2 Parametrization of the geometry
Attach the geometry file „angle.agdb“ to the project
The geometry is already prepared but not yet parametrized
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

13. 2.2 Parametrization of the geometry
To complete the parametrization, right-click on the geometry and select „Edit“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

14. 2.2 Parametrization of the geometry
Mark the single parameters by clicking in the checkbox.
The parameter dialog opens.
Insert a reasonable parameter name.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

15. 2.2 Parametrization of the geometry
Parametrized dimension appear yellow in you model
After defining the parameter name, a „D“ appears in the checkbox
Repeat this also for extrusions and blends
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

16. 2.2 Parametrization of the geometry
Repeat this procedure for all of your desired parameters:
XY_plane sketch 2:
H14: DS_Rib_length
H5: DS_Blade_thickness_vertical
H6: DS_Blade_length_horizontal
V7: DS_Blade_thickness_horizontal
V8: DS_Blade_length_vertical
XY_plane sketch 3:
V12: DS_Rib_height
Extrude1: DS_Blade_breadth
Extrude2: DS_Rib_breadth
Outer_blend: DS_Outer_Blend
Blend_Fixing: DS_Blend_Fixing
Blend_Bore: DS_Blend_Bore
Rib_Blend: DS_Rib_Blend
Edge_Blend: DS_Edge_Blend
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

17. 2.2 Parametrization of the geometry
For the blade and Rib-breadth we have to do a modification, because of symmetry
1. Open the parameter section of the Design Modeler
2. Double the value of the parameter „ DS_Blade_breadth“ and „ DS_Rib_breadth“ in „Design Parameters“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

18. 2.2 Parametrization of the geometry
3. Now click on „Parameter/Dimension Assignments“:
Here, you can modify each of the parameters so that they depend another parameters. You may also insert formulas here.
4. Modifiy the dimension assignment so that the value of the parameter is divided by 2.
5. You can check your parametrization easily by clicking on „Check“.
Save the project as Angle_v12 locate in a local directory.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

19. 2.3 Simulation and parametrization of the results
Close the design modeler and start a new simulation by click RMB on „Model“ and select „Edit“.
See the „Parameter Set“ Box. This indicates that you are working with parameters in ANSYS Workbench.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

20. 2.3 Simulation and parametrization of the results
Make sure that the units are switched to „mm, kg, N, °C, s“
Insert a Refinement with a ratio of 2 on the shown faces.
The highest stress level is expected here.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

21. 2.3 Simulation and parametrization of the results
Set the other Mesh settings like shown below
Generate the Mesh
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

22. 2.3 Simulation and parametrization of the results
Now, stet up the static structural analysis settings
Put a fixed support on the 4 holes.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

23. 2.3 Simulation and parametrization of the results
In addition to that set a displacement of „0“ in Y-Direction on the ground plate. This prevents the structure to lift from the imaginary bearing
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

24. 2.3 Simulation and parametrization of the results
Set a force in negative X-direction with a magnitude of 12.6 kN on the winding
As results, we need the total deformation and the equivalent Stress click solve
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

25. 2.3 Simulation and parametrization of the results
Stress: MPa
Deformation: mm
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

26. 2.3 Simulation and parametrization of the results
For the following analysis we need 3 simulations parameters:
Mass (material: structural steel)
Maximum deformation
Maximum equivalent stress
Parametrization just by clicking in the checkbox in the outline tree. A „P“ indicates a successful parametrization
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

27. 2.3 Simulation and parametrization of the results
Save the project and close the mechanical simulation.
Check the parametrization by opening the parameter section by doubleclicking on „Parameter Set“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

28. 2.3 Simulation and parametrization of the results
The parameters are listet like in an Excel Sheet
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

29. 2.4 Summary Simulation The geometrie has been opened and parametrized
Static-structural analysis with parametrized results
Calculation time is about 1.5 min
Check of the parametrization in the parameter set
Save now the project.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

30. 3. optiPlug 1. Model background 2. ANSYS workbench simulation
3.1. Introduction
3.2. File system optiPlug - optiSLang
3.3. Export an ANSYS project to optiSLang
3.4. Export the project bearing angle to optiSLang
4. Sensitivity analysis
5. Optimization
6. Robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

31. 3.1 Introduction
Bidirektional Interface between optiSLang and ANYS Workbench.
Extraction of results and input of external input-parameters to the ANSYS parametermanager
Starting of the Workbench using Python-skripts (ANSYS v12), former by Java-scripting (ANSYS v11)
optiPlug is now located on the project page in ANSYS Workbench, therefore it is now possible to cope with different simulation types in one optiSLang project!
Basic feature is to write the optiSLang input and output file and generates pre-defined basic workflows.
optiPlug generates the complicated starting script for starting the workbench automatically by optiSLang
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

32. 3.1 Introduction Preparings in ANSYS workbench:
Definition of all parameters (design-, material-, simulation parameters) in ANSYS Workbench
Save your project.
Settings in optiPlug
Choose the analysis type (optimization / stochastic)
Default settings
optiSLang
Modification of the variation space
Definition of objectives and constraints
Execution of the desired optimization / analysis runs
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

33. 3.2 File system optiSLang - optiPlug
optiPlug saves the files into a subdirectory of your ANSYS-project directory:
bin – folder: here is the starting script located
opti_problems: here is the input and output file and the problem file located
workflows: here you can find all the executed workflows in XML format
logfiles: logfiles of optiSLang runs
The projectfile *.fgpr
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

34. 3.2 File system optiSLang - optiPlug
Files in the folder opti_problems:
Angle_v12_doe.pro: problemdefinition
In the subfolder:
Angle_v12_doe.dat : all input variables are saved in an ASCII format text file
Angle_v12_doe.dat : all output variables are saved in an ASCII format text file
The name is according to your ANSYS project file name
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

35. 3.3 Export an ANSYS project to optiSLang
Start optiPlug by clicking on the „optiPlug“ Button on the project page.
Then, the optiPlug dialogue opens.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

36. 3.3 Export an ANSYS project to optiSLang
Overview optiPlug Dialogue:
Write or read
Problem type
Stochastic
Optimization
Start Variations space
Modify/overwrite of an existing optiSLang pro- ject
Save ANSYS Data*
Show ANSYS GUI
* If you choose this option, make sure that you have enogh space on your harddrive for storaging a large amount of data
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

37. 3.3 Export an ANSYS project to optiSLang
Default settings:
Parameter range defaults:
+/- 20% for Optimizationproblems, (suitable for first basic simulations)
Variationcoefficient of 5% for stochastic analysis, standard deviation 1σ
Update mode: - Warn if the optiSLang files already exist - Update the existing files - Overwrite everything
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

38. 3.4 Export the project bearing angle to optiSLang
Click on the optiPlug Button to export the project.
The export dialogue opens.
You do not need to make any changes here.
Confirm the export with OK.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

39. 4. Sensitivity analysis 1. Model background
2. ANSYS workbench simulation
3. optiPlug
4. Sensitivity analysis – Design of Experiments (DoE)
4.1 Introduction – Sensitivity analysis
4.2 Import the project bearing angle
4.3 Modification of the parameter settings
4.4 Sampling
4.5 Performing a sensitivity analysis
4.6 Postprocessing of a sensitivity analysis
4.7 Summary
5. Optimization
6. Robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

40. 4.1 Introduction – Sensitivity analysis
Analysis of parameter sensitivity means investigating the effect of variability of certain parameters on the variability of design-relevant response quantities. Using stochastic sampling methods such as plain Monte Carlo simulation latin hypercube sampling with statistics to evaluation for sensitivity calculation: histogram, anthill plots linear and quadratic correlation coefficients correlation matrix, confidence intervals principal component analysis detection of most sensitive/relevant input variables
… continuation from previous slide:
First: If the input parameters do scatter then we want to know how large is the scatter of the output parameters. In other words we want to quantify the uncertainty of the output parameters.
Second: If the output parameters are uncertain then we want to know how large the probability is that an output parameter by chance does not meet some design criteria. I. e. we want to know how reliable the component is.
Third: If the output parameters are uncertain then we want to know which parameters on the input side contribute the most to the uncertainty of the output parameter. Knowing this we will be able to tackle the “evil” drivers efficiently and improve the reliability of the component.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

41. 4.2 Import the project bearing angle
Start optiSLang
To import the project that you created with optiPlug, click on „flowGuide“ and choose the „Project manager“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

42. 4.2 Import the project bearing angle
Now, choose „Import project“
Browsen for the project by clicking on the button
Choose the flowGuide project file xyz.fgpr in the defined directory and confirm the selection with „Select“
Conform the creation of the project with „Apply“ and close the Project Manager with „Close“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

43. 4.3 Modification of the parameter settings
Now, we have to modify the variation space of each Parameter.
To do this, choose the current project and double-click on „Parametrize_problem“ then choose the predefined „…_modify_1“ workflow.
Confirm with „Start“ to start the parametrization.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

44. 4.3 Modification of the parameter settings
Unfold the parameter tree by clicking „Tree“  „Unfold Tree“
To modify a parameter, double-click on it in the unfolded parameter tree
Alternative: right mouse button on one parameter and select „Show Dialog“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

45. 4.3 Modification of the parameter settings
In the „Parameter Settings“-dialogue all of parameter settings are listed
Modify at „Optimization“ the lower and upper bounds for the parameter as shown below
Format type and parameter type are already correctly predefined.
Click on „OK“ to close the „Parameter Settings“-dialogue.
„Go to parameter“ causes a jump of a marker to the parameter in the input / output file.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

46. 4.3 Modification of the parameter settings
Modify the lower and upper bounds of all parameters according to the tabular.
The variation of the blends will remain on the default setting of +/- 10% as predefined with optiPlug
We have got 13 design paramters to deal with in our sensitivity analysis
Parametername
Ref.Wert
Wertebereich
DS_Blade_thickness_vertical 24
(15-30)
DS_Blade_length_horizontal
180
( )
DS_Blade_thickness_horizontal 20
(15-25)
DS_Blade_length_vertikal
160
( )
DS_Rib_height 90
(50-90)
DS_Blade_breadth 80
(60-100)
DS_Rib_breadth 15
(7-20)
DS_Rib_length 40
(10-100)
DS_Blend_Edge 3 --
DS_Blend_Rib
DS_Blend_Bore 1
DS_Blend_fixing
DS_Outer_blend
1.5
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

47. 4.3 Modification of the parameter settings
To close the parametrization, click on „File“  „Exit“
Confirm the following dialogue boxes with „Yes“ and „OK“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

48. 4.3 Modification of the parameter settings
Finally, you get a table of all you parameters and lower and upper bounds.
Please check your parametrization carefully.
You can also make final changes here
Close the table with „OK“.
Now the parametrization is finished.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

49. In our case, we have about 40-50 Samples for a DoE
4.4.3 Sampling Summary
State-of-the-art of today is to generate the samples by Latin Hypercube Sampling in a DoE!
In our case, we have about Samples for a DoE
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

50. 4.5 Performing a sensitivity analysis
The Workflow of a sensitivity analysis has been predefined by optiPlug
Already filled in:
Worflow Identificator (Name)
Problem specification file (Parametrization)
Start script (by optiPlug)
Start the DoE by clicking on “Start”
Now the DoE dialogue opens
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

51. 4.5 Performing a sensitivity analysis
Choose “Latin hypercube” as sampling method
Definine the desired number of designs to calculate (e.g. 40)
Confirm with “Apply” Then, all of the designs will be created
Start the DoE with “OK” 40
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

52. 4.5 Performing a sensitivity analysis
The sampling overview window opens. In this design overview, you can determine correlations between input parameters and check the distribution of the parameters.
In a good sampling, you will only see green boxes in the linear correlation matrix.
Start now the DoE by click on “Continue” and confirm with “Yes”
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

53. 4.6 Postprocessing
To start the postprocessing, you have to define a postprocessing workflow
Double-click on “Result monitoring”
Browse for the desired “*.bin” file in the related directory
Select ist and start the postprocessing with “start”
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

54. 4.6.1 Postprocessing of a sensitivity analysis - overview
The postprocessing of a DoE gives us the following results:
Correlation matrix – linear and quadratic:
Shows correlations (strong and weak) between: Input-Input, Input-Output und Output-Output
Coefficients:
Coefficient of Determination (CoD)
Coefficient of Importance (CoI) – Importance of a parameter
Regarding the CoD / CoI also leads us to reduce the parameter space by determining and deactivating unimportant parameters
Linear correlationcoefficient – correlation between parameters
Principal Component Analysis:
Another way to display the relation between inputs and outputs
Histograms:
Scatter of the parameters. It is also possible to determine areas of failed designs / critical areas
Anthill plots:
Graphical illustration of the design space of two (2D) or three (3D) parameters
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

55. 4.6.2 Postprocessing – Evaluation of the results
First, have a look at the linear correlation matrix
And the confidence levels for 0.7( ) and 0.5( )
Green stands for few / no correlation
Orange - red: strong positive correlation
Light-blue – darkblue: strong negative correlation
The first impression, we got from here is that we have only few but strong correlations between some input parameters and the output parameters
Now we have a detailed look at the Coefficients of Importance
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

56. 4.6.2 Postprocessing – Evaluation of the results
Coefficient of determination (R²) is excellent
The model can be described completely with linear relations
2 parameters a large influence on the mass
Dominating parameter: DS_Blade_breadth
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

57. 4.6.2 Postprocessing – Evaluation of the results
Have a look at this correlation in the anthill plot:
Click in the linear correlationmatrix on the box which indicates the highest correlation between input and output
Alternative: Select the parameters in the pull-down menu
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

58. 4.6.2 Postprocessing – Evaluation of the results
Strong correlation between the parameter DS_blade_Breadth and the Mass becomes quite clearly regarding the anthill plot.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

59. 4.6.2 Postprocessing – Evaluation of the results
Coefficient of determination (R²) is very good
We can determine 2 parameters with a large influence on the stress
Most important parameter here is: DS_Blade_thickness_vertical
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

60. 4.6.2 Postprocessing – Evaluation of the results
Quadratic correlation becomes also evident regarding the anthill plots.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

61. 4.6.2 Postprocessing – Evaluation of the results
To calculate the COI with respect to this monotonic nonlinear behavior we use the rank order transformation via Spearman correlation.
COI is larger
DS_Rib_height is the most important parameter now
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

62. 4.6.2 Postprocessing – Evaluation of the results
Coefficient of Importance (R²) is also very good
2 Parameters have a large influence on the deformation
Most important parameter here also is: DS_Blade_thickness_vertical
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

63. 4.6.2 Postprocessing – Evaluation of the results
Coefficient of Importance (R²) is also very good
2 Parameters have a large influence on the mass
Most important parameter here also is: DS_Blade_breadth
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

64. 4.6.2 Postprocessing – Evaluation of the results
Mass
Influence 
DS_Blade_breadth
53%
DS_Bladethickness_vertical
16%
Stress
41%
DS_Rib_height
33%
Deformation
27%
Table – most important parameters
These parameters will be optimized now.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

65. 4.7 Sensitivity analysis - summary
A sensitivity analysis leads us to a better understanding of the correlations in our model.
We could specify the connections between the parameters in a detailed way.
We were able to determine the most important parameters in our model.
Therefore, the number of parameters could be reduced to three:
DS_Blade_breadth
DS_Bladethickness_vertical
DS_Rib_height
Therefore we can apply an effective optimization method that can deal perfectly with a limited number of parameters – the adaptive response surface method.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

66. 5. Optimization 1. Modelbackground 2. ANSYS workbench simulation
3. optiPlug
4. Sensitivity analysis – Design of Experiments (DoE)
5. Optimization
5.1 Definition of objectives and constraints
5.2 Optimization with adaptive response surfaces
5.3 Read-in the optimized model in ANSYS Workbench
5.4 Optimization with evolutionary algorithms
5.5 Other optimization algorithms
5.6 Summary
6. Robustness analysis
7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

67. 5. Optimization
After performing a sensitivity analysis we take the won knowledge to optimize our model.
The optimization improves a model due to defined objectives.
If you choose the right end conditions, you always get a better model during an optimization.
According to the desired optimization aim, you can choose the suitable algorithm.
An optimization can include several objectives, some even can deal with conflicting objectives
After optimizing a model, it has usually be checked concerning its robustness against small variations, e.g. tolerances.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

68. 5.1 Definition of objectives and constraints
You can use the predefined problem file of the sensitivity analysis for the optimization
Necessary modifications:
Deaktivate the unimportant parameters
Define a suitable Objective
Include Constraints if necessary
Our optimization should follow the following aim:
Reduce the mass
The equivalent stress should not exceed 225 MPa.
We use a compromise result as start solution for optimization
In this case design 31
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

69. 5.1 Definition of objectives and constraints
To adapt the problem-files chose “Parametrize Problem” in optiSLang and click on “create a copy and modify it”.
Browse for the predefined File of the sensitivity with and insert a new name (without path!) and
Choose reference design
confirm with “Start”.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

70. 5.1 Definition of objectives and constraints
Define the best design of the sensitivity analysis as reference design
In this case Design 31
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

71. 5.1 Definition of objectives and constraints
Creating an objective:
Double-click on “Objective section”.
Set a suitable name for the objective and click on “New”.
Now insert the name of the term (Attention: The name mustn’t be identical to any another name!).
As a funktion insert the parameter that has to be minimized. In this case it is “Volumenkoerper_mass” Confirm it with “Enter”.
Close the dialogue with “OK”
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

72. 5.1 Definition of objectives and constraints
Creating a boundary condition – a stress-constraint:
double-click on “Constraint section”
click on “New” at “Inequality 0<=“
The formula of the constraint is: 0<= 225 – Equivalent_Stress_Maximum
Insert the name (Attention: not identical to any other name)
As a constraint, insert the following formula: 225-Equivalent_Stress… and confirm with Enter.
Close the dialogue with “OK”
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

73. 5.1 Definition of objectives and constraints
Save the tree and exit the parametrization.
In the overview table, set the unimportant parameters as constant by clicking in the constant checkbox.
Set the parameters shown right as constant.
3 parameters remain active:
DS_Bladethickness_vertikal
DS_Blade_breadth
DS_Rib_height
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

74. 5.1 Definition of objectives and constraints
Now we have:
Deactivated the unimportant parameters
Defined a suitable objective
Defined a necessary constraint
Click through the different cards to check you settings
Close the Parametrization with “OK” and confirm any changings.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

75. 5.2 Optimization with adaptive response surface methods
ARSM provides a local linearization (local DoE) in the design space.
Therefore for each subspace of our 3 Parameters, only 6 design points are necessary if we choose the D-optimal linear scheme for the local DoE
Usually, the ARSM converges after iterations.
So we need 60 – 120 FE-Simulations
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

76. 5.2.1 Setup the ARSM
Start the ARSM Workflow by a double-click on Adaptive_...
Set a Workflow Identificator (Name)
Browse for the adapted problem file with
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

77. 5.2.1 Setup the ARSM
Choose „Run a script file“ and browsen with for the start script in the \bin folder of your project or copy it from the DoE dialogue.
Choose the number of parallel runs and idle time according to your hardware.
Start the ARSM with „Start“.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

78. 5.2.1 Setup the ARSM You can now make some expert settings.
Click „OK“ to start the optimization.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

79. 5.2.2 Postprocessing ARSM 1. Iteration History:
Here you can see the history of your objective for each iteration
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

80. 5.2.2 Postprocessing ARSM 2. Response Data:
Here you can see the results (outputs) of your design.
As default the best design is chosen, so that you can now get an information how much the algorithm could improve your model.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

81. 5.2.2 Postprocessing ARSM 3. Design Parameter:
These are the CAD parameter values of your optimization.
The default setting is also the best design.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

82. 5.2.3 Summary ARSM
Performing an optimization with ARSM, a significant design improvement could be achieved.
The mass was reduced by 36 % from 4,89 to 3,11 kg
The stress increased by um 69 % to 225 MPa.
The number of design evaluation is = 97
The stress remains in the given constraints
Therefore we can say that regarding the boundary conditions, the part has been optimized as good as possible.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

83. 5.3 Read-in the optimized model in ANSYS Workbench
Now we want to read in our best design in Workbench to have a look at the geometry and for further analysis.
To do this, just open the project and simulation in workbench again.
The geometry read-in will be done by clicking on the optiPlug button on the project page.
Now, the optiPlug dialogue opens again.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

84. 5.3 Read-in the optimized model in ANSYS Workbench
Select „Read calculated design“
Browse for the correct best design
In our case it is the Design 57 (this is different usually for each optimization run!) and confirm your selection.
If you want to calculate your model again, just update the results
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

85. 5.3 Read-in the optimized model in ANSYS Workbench
Calculating the results of the initial and optimized design
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

86. 5.3 Read-in the optimized model in ANSYS Workbench
Mesh refinement of the optimized design to prove the maximal stress
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

87. 5.3 Read-in the optimized model in ANSYS Workbench
Generate the new mesh
Press solve
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

88. 5.3 Read-in the optimized model in ANSYS Workbench
Only a small increasing of the stresses
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench