sensitivty analysis, optimization and robust design with optislang and ansys workbench 12

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

Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench

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


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


Content

• 1. Model background• 2. ANSYS workbench simulation• 3. optiPlug• 4. Sensitivity analysis• 5. Optimization• 6. Robustness analysis• 7. Summary and conclusion


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.


1. Model background

• Workflow of a robust design optimization

Basic design

Sensitivity analysis

Optimization

Robustness analysis

Robust design

Is the design robust ?

NoYes


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


2.1 CAE Integration within 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

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

2.1 Overview – Parametrization in ANSYS Workbench


2.2 Parametrization of the geometry

• Start a new project in ANSYS Workbench• Create a new „Static Structural (ANSYS)“ analysis



• Attach the geometry file „angle.agdb“ to the project• The geometry is already prepared but not yet parametrized



• To complete the parametrization, right-click on the geometry and select „Edit“


• Mark the single parameters by clicking in the checkbox.• The parameter dialog opens.• Insert a reasonable parameter name.



• Parametrized dimension appear yellowin you model

• After defining the parameter name,a „D“ appears in the checkbox

• Repeat this also for extrusions and blends



• 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



• 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“



• 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.



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.


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.


2.3 Simulation and parametrization of the results

• Set the other Mesh settings like shown below

• Generate the Mesh


2.3 Simulation and parametrization of the results• Now, stet up the static structural analysis settings• Put a fixed support on the 4 holes.


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


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


2.3 Simulation and parametrization of the results

Stress: 133.44 MPa

Deformation: 0.0836 mm


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


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“


2.3 Simulation and parametrization of the results• The parameters are listet like in an Excel Sheet


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.


3. optiPlug

• 1. Model background• 2. ANSYS workbench simulation• 3. optiPlug

• 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


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


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


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 optiSLangruns

• The projectfile *.fgpr


3.2 File system optiSLang - optiPlug

• Files in the folder opti_problems:• Angle_v12_doe.pro:

problemdefinitionIn 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 yourANSYS project file name


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.


• 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, makesure that you have enogh space on your harddrive for storaging a large amount of data



• Default settings:

• Parameter range defaults:• +/- 20% for

Optimizationproblems,(suitable for first basicsimulations)

• Variationcoefficient of 5% for stochastic analysis, standard deviation 1σ

• Update mode:- Warn if the optiSLang files already exist- Update the existing files- Overwrite everything



• 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.

3.4 Export the project bearing angle to optiSLang


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


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 simulationlatin hypercube samplingwith statistics to evaluation for sensitivity calculation:

histogram, anthill plotslinear and quadratic correlation coefficientscorrelation matrix, confidence intervalsprincipal component analysisdetection of most sensitive/relevant input variables

Sensitivity analysis


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“


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“


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.


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 buttonon one parameter and select „Show Dialog“


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.



• Modify the lower and upper bounds of all parameters according to the tabular.

• The variation of the blends will remain on the defaultsetting 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 (150-200)

DS_Blade_thickness_horizontal 20 (15-25)

DS_Blade_length_vertikal 160 (140-170)

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 3 --

DS_Blend_Bore 1 --

DS_Blend_fixing 1 --

DS_Outer_blend 1.5 --



• To close the parametrization, click on „File“ „Exit“• Confirm the following dialogue boxes with „Yes“ and „OK“


• 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.



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 40-50 Samples for a DoE


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



• Choose “Latin hypercube” as samplingmethod

• Definine the desirednumber of designs to calculate (e.g. 40)

• Confirm with “Apply”Then, all of the designswill be created

• Start the DoE with“OK”

40


• 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 greenboxes in the linearcorrelation matrix.

• Start now the DoEby click on “Continue” and confirm with “Yes”



• To start the postprocessing, you have to define a postprocessing workflow

• Double-click on“Result monitoring”

• Browse for the desired“*.bin” file in the relateddirectory

• Select ist and start thepostprocessing with“start”

4.6 Postprocessing


4.6.1 Postprocessing of a sensitivity analysis - overviewThe 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


• First, have a look at the linear correlation matrix

• And the confidence levels for 0.7(-0.05 0.05) and0.5(-0.075 0.075)

• 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

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



• 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



• Strong correlation between the parameter DS_blade_Breadth and the Mass becomes quite clearly regarding the anthill plot.



• 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



• Quadratic correlation becomes also evident regarding the anthill plots.



• 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



• 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



• 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



• Table – most important parameters• These parameters will be optimized now.

Mass Influence

DS_Blade_breadth 53%

DS_Bladethickness_vertical 16%

Stress


DS_Rib_height 33%

Deformation


DS_Rib_height 27%



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.


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


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.


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


• 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”.



• Define the best design of the sensitivity analysis as reference design

• In this case Design 31



• Creating an objective:• Double-click on “Objective section”.• Set a suitable name for the objective and click

on “New”.

• Now insert the name ofthe term(Attention: The namemustn’t be identical toany another name!).

• As a funktion insert the parameter that has to beminimized. In this case itis “Volumenkoerper_mass”Confirm it with “Enter”.

• Close the dialogue with “OK”



• 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 identicalto any other name)

• As a constraint, insertthe following formula:225-Equivalent_Stress…and confirm with Enter.

• Close the dialogue with “OK”



• 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



• 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.



• 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 10-20 iterations.

• So we need60 – 120 FE-Simulations

5.2 Optimization with adaptive response surface methods


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


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“.


5.2.1 Setup the ARSM• You can now make some expert settings.

• Click „OK“ to start the optimization.


5.2.2 Postprocessing ARSM• 1. Iteration History:

• Here you can see the history of your objective for each iteration


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.


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.


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 40 + 57 = 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.


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.


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



• Calculating the results of the initial and optimized design



• Mesh refinement of the optimized design to prove the maximal stress



• Generate the new mesh

• Press solve



• Only a small increasing of the stresses

sensitivty analysis, optimization and robust design with optislang and ansys workbench 12

Documents

ansys workbench2

ansys workbenchmeshing

ansys workbenchcreate

ansys workbenchintroduction

ansys workbench simulation2

ansys workbench simulation3

ansys workbench simulation1

ansys workbenchthe basic