Sensitivty Analysis, Optimization
and Robust Design with optiSLang and
ANSYS Workbench (ANSYS v13)
Optimization of a bearing angle
Dipl.-Ing. (FH) Andreas Veiz
Dynamic Software and Engineering GmbH, Weimar, Germany
Seminar 23.-24.5.2011, Weimar
Agenda
• 1. Model background
• 2. 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
Agenda
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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. The Metamodel of optimal prognosis (MoP)
6. 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
7. Basics of a robustness analysis
• Stochastic scatter of parameters
• Write out a new robustness task with optiPlug
• Update the parametrization for a robustness analysis
8. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
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
2. ANSYS Workbench simulation
• 1. Model background
• 2. 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. optiPlug
• 4. Sensitivity analysis
• 5. Optimization
• 6. Robustness analysis
• 7. Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
2.1 CAE Integration within ANSYS Workbench
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
2.3 Simulation and parametrization of the results
Stress: 133.44 MPa
Deformation: 0.0836 mm
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
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
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
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
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
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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 v12/13),
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
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
3.2 File system optiSLang - optiPlug
• optiPlug saves the files into a
subdirectory of your ANSYSproject 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
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
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
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 project
• 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
3.3 Export an ANSYS project to optiSLang
• Default settings:
• Parameter range defaults:
• +/- 20% for
Optimizationproblems,
(suitable for first basic
simulations)
• Coefficient of variation 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
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
4. Sensitivity analysis
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Model background
ANSYS workbench simulation
optiPlug
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
Optimization
Robustness analysis
Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
4.1 Introduction – Sensitivity analysis
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
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
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
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
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
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
4.3 Modification of the parameter settings
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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
Reference
value
Variation
space
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
--
Parametername
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
4.3 Modification of the parameter settings
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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
4.3 Modification of the parameter settings
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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
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 5075 Samples for
a DoE
• Because of the
future meta
modeling, we’ll
choose 75
designs
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
4.5 Performing a sensitivity analysis
• Choose “advanced latin
hypercube” as sampling
method
• Definine the desired
number of designs to
calculate (e.g. 75)
• Confirm with “Apply”
Then, all of the designs
will be created
75
• Start the DoE with
“OK”
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
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
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
4.6.2 Postprocessing – Evaluation of the results
• First, have a look at the linear
correlation matrix
• And the confidence levels for
0.7(-0.04 0.03) and
0.5(-0.06 0.05)
• 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
4.6.2 Postprocessing – Evaluation of the results
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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
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
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
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
4.6.2 Postprocessing – Evaluation of the results
• A Quadratic correlation becomes also evident regarding the anthill
plots of the stress.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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.
• The COI will increase.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
4.6.2 Postprocessing – Evaluation of the results
• Coefficient of Importance (R²) is also quite 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
4.6.2 Postprocessing – Evaluation of the results
Mass
Influence
DS_Blade_breadth
54%
DS_Bladethickness_vertical
17%
Stress
DS_Bladethickness_vertical
42%
DS_Rib_height
34%
Deformation
DS_Bladethickness_vertical
42%
DS_Rib_height
22%
• Table – most important parameters
• These parameters will be optimized now.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
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
• As a result, we can apply an effective direct 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
6. Metamodel of optimal Prognosis – MoP and CoP
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Background
The ANSYS Workbench Simulation
Using the Workbench plug-in optiPlug
Getting started in optiSLang
The sensitivity analysis
Metamodel of optimal Prognosis – MoP and CoP
6.1 Metamodeling
6.2 The Coefficient of Prognosis
6.3 The Approximation Window
6.4 Summary and conclusion of Meta-Modeling with CoP
Introduction into optimization Methods
The Robustness analysis
Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5 Metamodeling – the Metamodel of optimal Prognosis
• A meta model uses the pre-calculated designs of a sensitivity
analysis.
• A defined part of these support points will be used to describe a
global response surface.
• This surface is fixed with the latest methods of Moving Least
Squares to fit the whole variation space as good as possible.
• Usually 2/3 of the support points is used to generate the response
surface – the other third of support points is uses to test the
approximaztion regarding the fitness.
• As a result, you will get a Coefficient of Prognosis that will give
you a overview how good your model is to describe it
• Furthermore, you can start an optimization run on this meta
model that is much more fast than FE-solver runs.
• Be aware that a meta model is only a fitness. There are some
highly non-linear problems that cannot be optimized with meta
models.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.1 The MoP Workflow
• Start a Metamodel of optimal Prognosis Workflow.
• As Sample File, choose the Save*.bin file of the DoE
• As Problem File, use the DoE Problem file.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.1 The MoP Workflow
• Keep the standard settings for this run
• Start the analysis by clicking on „OK“ – it will only take a few
seconds.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.2 The Coefficient of Prognosis
• The Postprocessing is the looking the same like after the DoE
• Click on an output file to have a look at the CoP
• You see here that the order of the important parameters is the
same as in the CoI
• A CoP Value of 98% is an excellent value
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.2 The Coefficient of Prognosis
• Now, take a look at the CoP of the stress.
• You see here that the order of the important parameters is similar
to the CoI.
• A CoP Value of 94% is an very good value
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.2 The Coefficient of Prognosis
• Now, take a look at the CoP of the deformation.
• You see here that the order of the important parameters is similar
to the CoI.
• A CoP Value of 97% is an excellent value
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.3 The Approximation window
• Reload the postprocessing as „Approximation“
• Have a look at the approximation window of the output parameter
„mass“ vs. their two most influating inputs.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
5.4 Summary and conclusion of Meta-Modeling with CoP
• The CoP of our model shows that in this case we can get excellent
results by having a Moving Least Squares approximation in the
design space.
• The precondition is that we have a good sampling with fulfilled
confidence cirteria.
• In this case we can save a lot of time by performing an
optimization run on the meta model.
• An optimization on a meta model may give you some first hints of
you possible optimization space.
• Be aware that a meta model cannot replace the FE-runs in every
application. Optimization on meta models can be very quick in
some applications but a calculated best design can be quite
different from the result of a meta model. So handle optimization
runs with care.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6. Optimization
•
•
•
•
•
•
1.
2.
3.
4.
5.
6.
•
•
•
•
•
• 6.
• 7.
Modelbackground
ANSYS workbench simulation
optiPlug
Sensitivity analysis – Design of Experiments (DoE)
Metamodel of optimal prognosis (MoP)
Optimization
6.1 Definition of objectives and constraints
6.2 Optimization using the Metamodel of optimal prognosis
6.3 Direct optimization using FE solver calls
6.4 Read-in the optimized model in ANSYS Workbench
6.5 Summary
Robustness analysis
Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6. Multidisciplinary Optimization with optiSLang
CAD and CAE
Parameter definition
Sensitivity study – identify the
most important parameters
and check variation/COD
of response values
minimize
Validate optimized
design in CAE and CAD
Define optimization goal
and optimize
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6. 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
6.1 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 XX
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.1 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
6.1 Definition of objectives and constraints
• Define the best
design of the
sensitivity analysis
as reference design
• In this case:
Design 13
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.1 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
6.1 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
6.1 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
6.1 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
6.2 Optimization using the MoP
•
If a sensitivity Analysis is performed before and a Metamodel of
optimal Prognosis was done, it is recommended to do the first
optimization on this meta model.
•
The reason is quite simple – if the response surface is good
enough (take a look at the Coefficient of Prognosis) an optimal
performance can be expected.
•
The big advantage is that no solver run is done during the
optimization – the only solver run is the recalculation of the best
design in the end.
•
Be aware, that the MoP as a solver does not work properly for the
extreme values of the parameters nearby the lower or upper
bound.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2.1 Evolutionary algorithm (EA) using MoP
2a.
1.
2b.
2c.
3.
1. Start a new Nature inspired optimization workflow
2. Define workflow name, workflow identifier and problem file name
3. Select Evolutionary Algorithm (EA) – global search as algorithm
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2.1 Evolutionary algorithm (EA) using MoP
1.
2.
3.
1. Use MoP as solver and choose the MoP data file from sensitivity
2. Enter solver call (Maxwell_Batch.bat) to verify best design
3. Start NOA workflow
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2.1 Evolutionary algorithm (EA) using MoP
1.
1. Choose start population size
2. Keep defaults for Selection, Crossover and Mutation
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2.1 Evolutionary algorithm (EA) using MoP
2.
1.
3.
5.
4.
1.
2.
3.
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
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2.1 Evolutionary algorithm (EA) using MoP
3.
1.
3.
2.
1. Objective history and response data shows again a quite large
difference between the approximated and the real values.
2. Input Data shows, that the parameters touched their borders.
3. The Stress constraint is violated by 2,8%
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.2 Optimization using the MoP - Summary
• Using the MoP as a base for the Solver, optiSLang was able to
generate better designs than the sensitivity analysis in each
different way but because of the violation of the stress constraint,
these designs can only be taken as a starting point of a design
improvement.
Analysis
Type
Initial Design
Sensitivity
Analysis
Evolutionary
Algorithm
(EA) on MoP
Simple Design
Improvement
(SDI) on MoP
Stress
141.014 MPa
182.918
MPa
231.355 MPa
236.406 MPa
Mass
4.89 Kg
3.181 kg
2.5772 kg
2.577 kg
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3 Direct optimization
• The other way of optimizing a Model is using the direct
optimization – that means that each desing is calculated in a
solver run.
• The advantage is that the final performance of the best design
is often better than using the MoP response surface.
• It is necessary to use it when the MoP shows only a weak quality
of prognosis.
• It is recommended if you are working with signals because the
optimization on MoP does not deal with signals.
• Be aware that the total calculation time is much longer.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3 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 10-20 iterations.
So we need
100 – 200
FE-Simulations
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3.1 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
6.3.1 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
6.3.1 Setup the ARSM
• You can now make some expert settings.
• It is recommended to set the option „recycle previous support
points“ to make the optimization more robust at the parameter
bounds.
• Click „OK“ to start the optimization.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3.2 Postprocessing ARSM
2.
1.
4.
1.
2.
3.
4.
5.
5.
Objective history for each design
Best design input parameters
Best design response data
Penalized objective and constraints data
Parameter history for each design
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
3.
6.3.2 Postprocessing ARSM
• 1. Iteration History:
• Here you can see the history of your objective for each iteration
• As it is indicated there are soe occurances of failed designs.
This longers the whole optimization process.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3.2 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.
• The stress constraint is not violated!
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.3.2 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
6.3.2 Summary ARSM
• Performing an optimization with ARSM, a significant design
improvement could be achieved.
• The mass was reduced by 48 % from 4.89 to 2.57 kg
• The stress increased by um 69 % to 225 MPa.
• The stress remains in the given constraints
• Therefore we can say that regarding the boundary conditions, the
part has now been optimized as good as possible.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.4 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
6.4 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 219 (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
6.4 Read-in the optimized model in ANSYS Workbench
• Calculating the results of the optimized design
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.5 Summary optimization
1. In optiSLang, you have always two different approaches to
optimize your task.
2. If you did a sensitivity analysis including a Meta Model it is
recommended to use this Meta Model for a first optimization run.
You may not get the absolute best design but it is usually better
that your start design.
3. One of the big advantages is the minimal time that is used. You
only have to recalculate 1 design – the best design instead of
several hundreds.
4. The quality of the MoP optimization depends directly on the
quality of the basic meta model. That means – the higher the
Coefficient of Prognosis of the meta model – the better the
optimization result will be.
5. Parallel to that it is possible to use a direct approach for
optimizing. There, the direct outputs of a FEA are used. So the
quality of the optimization is usually better but takes much more
time because you have to calculate each design.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.5 Summary optimization
•
•
•
•
Overview of the different optimization approaches.
It becomes evident that using the MoP solver, it is possible to reach a quite
good design, but you have to check the constraint fullfillment
The combination of sensitivity analysis, MoP and Optimization on the
generated response surface shows an optimal relation of performance and
calculation time.
The ARSM optimization leads to the absolute best design in an affordable
period of time.
Initial Design
Sensitivity
Analysis
EA (MoP)
ARSM (direct)
Max Stress
141 MPa
182.9 MPa
231.4 MPa
222.3 MPa
Mass
4.89 Kg
3.181 kg
2.5772 kg
2.57 kg
Calculated
designs
1
75
75 + 1
(Σ=76)
75 + 250
(Σ=325)
Calculation
time
1.3 min
95 min
97 min
420 min
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
6.5 Summary Optimization
• The different optimization approaches on their response surfaces:
ARSM (global)
EA (MoP)
• A very large area
on the response
surface is used
for the EA on MoP.
• This depends also
on the start values
given from sensitivty.
• The used area
on the global response
surface for the direct optimization
is much smaller. This depends
on the ARSM start setting of the
start range
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7. The robustness analysis
•
•
•
•
•
•
•
1.
2.
3.
4.
5.
6.
7.
•
•
•
•
• 8.
Background
The ANSYS Workbench Simulation
Using the Workbench plug-in optiPlug
Getting started in optiSLang
The sensitivity analysis
Metamodel of optimal Prognosis – MoP and CoP
The robustness analysis
7.1 Introduction into robust design / design for six sigma
7.2 Exporting the files for a robustness analysis
7.3 Performing a robustness analysis
7.4 Postprocessing of a robustness analysis
Summary and conclusion
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.1 Introduction into robust design / design for six sigma
•
The product robustness is one of the most
important tasks for “optimizing” the performance
of a product.
•
The proof of robustness with variation or
probability measurements requires a probabilistic
analysis.
•
It determines Safety and reliability for 1 & 2 (3)
Sigma levels and identifies the most sensitive
stochastic variables. A higher sigma level is also
possible by performing a reliability analysis
•
State of the art, possible with high number of
stochastic variables can be analyzed by a
relatively small number of necessary FEsimulations due to sophisticated sampling.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.1 Introduction into robust design / design for six sigma
• Six Sigma is a concept to optimize the manufacturing processes
such that automatically parts conforming to six sigma quality are
produced
• Design for Six Sigma is a concept to optimize the design such
that the parts conform to six sigma quality, i.e. quality and
reliability are explicit optimization goals
• Because not only 6 Sigma values have to be used as measurement
for a robust design, we use the more general classification Robust
Design Optimization
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.2 Exporting the files for a robustness analysis
• We have to add the material parameters and a the force as
additional parameters for the robustness analysis
• First open the engineering data to parametrize the material:
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.2 Exporting the files for a robustness analysis
• Now, open the simulation and parametrize the force
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.2 Exporting the files for a robustness analysis
•
•
•
•
•
Save the ANSYS Project (e.g. as Angle_robust)
Click on the optiPlug export button
This time, choose „Stochastic problem“
Set the Coefficient of variation to 2.5 and click OK
The robustness workflow and
parametrization is automatically
added to the existing project
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.3 Performing a robustness analysis
• Open the predefined robustness workflow.
• Set the number of designs to 75 and the Sampling method to
„Advanced LHS: minimal linear correlation“
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4 Postprocessing of a robustness analysis
• Start the calculations.
• Open the generated resultfile after the analysis has finished.
• Click on the outputvalue of the maximum stress. This will be our
indicator for a robust design.
• We will add now a limit to see, how
robust the optimum design regarding
a maximum stress will be.
• Click on the Marker „Set limit“ in
the main Window of the postprocessing
and type a 250 (that is the maximum
tensile stress of strutural steel: 250 MPa)
as a limit.
• We will now get the probability that a
design has a larger maximum stress than
the limit.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4 Postprocessing of a robust analysis
• Taking a look at the
histogramm, we see
that we have a probability of 56% that
the maximum stress
is below the desired
limit of 250 MPa
• That means, a probability of failure of
44%
• To achieve a much
lower probability of
failure, it is necessary
to re-run an optimization
with a lower max-stress
condition!
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4 Postprocessing of a robust analysis
• Another Information, we
get from the result of a
robustness analysis is
the variation of the
output variable in
correlation to the input
variables.
• In this case, we see that
the maximum stress
varies +/- 13.2%
• As in the sensitivity
analysis, we also get the
most important
parameters
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4 Postprocessing of a robust analysis
• Take a look at the Histogramm
of the mass
• The mass varies between 2.3
and 2.85 kg, that means 4,2%
• So the variation of the mass is
double than the variation of
each input (2.5%)
• The highest mass is still lower
than of the best design of the
sensitivity analysis in the
beginning.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4 Postprocessing of a robust analysis
• Take a look at the Histogramm
of the deformation
• The mass varies between 0.3
and 0.55 kg, that means 12%!
• So the variation of the mass is
four times higher than the
variation of each input (2.5%)
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.4.1 MoP after a robust analysis
• Run a MoP Analysis on the robustness result
• Get the CoP and the response surface of the critical value „Stress“.
• The rather low CoP of 74% indicates noise effects of the solver to the
result or maybe mesh influence.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.5 Conclusion of the first robust analysis
• The robustness analysis gives us the possibility to analyse the
variation of the output variables in correlation to small input
variation.
• The more stable the structure is after an optimization or in the
beginning, the smaller these variations of the output variables are.
• The variation of the responses is two or four times higher than of
the input variables. This indicates that with a variation of 2.5%, we
will have to high variations of the responses.
• We also get to know, how many of the designs would fail by setting
a limit. Because of a rather small number of designs, this
probability is more an overview.
• To get a robust design, it is now necessary to re-run another
optimization.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.6 Roust Design Optimization Iteration II
• To achieve a design that is either optimized and also robust, it was
now necessary to start another optimization run.
• Set the output constraint for the stress now to 200 MPa and start
an ARSM optimization run with this edited problem definition.
• The total mass was reduced by 29% to 3.07 kg.
• The maximum stress is now 200 MPa.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
7.6 Roust Design Optimization Iteration II
• Take the new optimized Design now into a robustness analysis.
• We will now get a more robust design
• The percentage of Designs that will fail is now ~12% instead of
>44%.
• To get a design that will cause no failure, it would be necessary to
start more iterations.
• The rather low CoP of 76% indicates noise effects of the solver to
the result or maybe mesh influence.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench
8 Summary
• During this seminar, we got the basic analyisis settings in
optiSLang.
• The Workflow of a simple robust design optimization was shown
here.
• In the beginning, the most important parameters are determined.
• Then, an optimization run was set-up and we got an optimum.
• In a robustness analysis, we saw that we got several designs, that
violat the material limit and we got a rather large variaton of the
output variable „max-stress“
• Next step was to re-run the optimization and robustness flow until
the robust criterias are fullfilled.
Sensitivity analysis, optimization and robust design with optiSLang and ANSYS Workbench