Sensitivity Analysis, Feasibility and Optimization Studies
About
the Sensitivity Analysis
Sensitivity analysis
allows you to analyze how various measured quantities (parameters) vary when a model
dimension or an independent model parameter is varied within a specified range.
The result is a graph for each selected parameter showing the value of the
parameter as a function of the dimension.
To access a sensitivity
analysis, click Analysis – Sensitivity Analysis.
To create the analysis,
you define the following attributes:
·
A
model dimension or parameter to vary.
·
The
range of values within which the dimension will vary.
·
The
number of steps (computations in the range).
·
Parameters
that have been created as the results of analysis features.
To generate the
sensitivity analysis, the system does the following:
·
Varies
the selected dimension or parameter within the range
·
Regenerates
the model at each step.
·
Computes
the selected parameters.
·
Generates
a graph.
To Perform a
Sensitivity Analysis
1.
From the menu
bar, click Analysis – Sensitivity Analysis.
The Sensitivity dialog box opens.
2.
Create a new
or open an existing study.
o
To create a new
study, click 
. Accept a default name or type a name for
the study.
o
To open an existing
study, click 
. Select the name of the study from a list.
3. Under Variable Selection,
select design variables as follows:
o
To select a
variable dimension, click Dimension and select a
dimension in the model.
Note: You
cannot select driven dimensions. They appear on the left side of a relation.
o
To select an
independent model parameter, click Parameter. An independent
model parameter is a parameter on the right hand side of a relation.
4. Specify the range for design variables by typing the
minimum and maximum values in the respective fields in the dialog box.
5. Under Parameters to Plot,
click the selection arrow button and choose any of the previously created
analysis feature parameters from the Parameters dialog box.
6. Click OK to return to
the Sensitivity dialog box.
Note:
o
If you have a
license for Pro/MECHANICA, Pro/MECHANICA parameters and analyses that have been
previously defined also appear in the Parameters list
box. After you select Pro/MECHANICA parameters or analyses and click Compute, the system starts running multiple Pro/MECHANICA
analyses.
o
If you have a
license for Mechanism Dynamics, dynamics measures created in Mechanism Dynamics
are available under Goals and Design Constraints.
7. Under Steps, enter the
number of calculations you want to make between the minimum and maximum values.
8. (Optional) To see the model change as each value is
calculated, click Options
– Preferences and click Animate model.
Click OK to return to the Sensitivity dialog box.
9. (Optional) To set the default range for design
variables, click Options
– Default Range.
10. Click Compute or click 
. For each selected parameter, a graph window
opens to display the calculations.
11. To save the study, click 
.
Click Close.
Example:
Sensitivity Analysis
Summary: This example shows how to create a sensitivity
study to investigate the relationship between two model parameters.
Problem: Need to analyze how the part mass changes as
you change the number of teeth in the gear.
Solution: Create an analysis feature to measure the mass
of the gear. After the MASS parameter is created, you can conduct a sensitivity
study to investigate how the mass changes as you change another parameter, the
number of teeth in the gear.
The following basic steps outline this example:
1.
Create an analysis feature to measure the mass of the gear. Choose Insert – Model Datum – Analysis.
In the ANALYSIS dialog box, do the following:
o
Enter
the name of the analysis, gear_mass.
o
Choose
Model Analysis as the type of the
analysis.
o
Click
Next.
o
Choose
Model Mass Properties
as the type
of measure.
o
Click
Compute.
o
Click
Close.
o
Under
Result params, choose the parameter MASS and select Yes to create this
parameter.
o
Click
OK.
2.
Create a sensitivity analysis by choosing Analysis
> Sensitivity Analysis. In the Sensitivity
dialog box, specify the following:
o
Click
Parameter.
o
Choose
the number of teeth (N) as the parameter to vary and
click OK.
o
Set
the range to 10 – 20 teeth.
o
Select
a parameter to plot (MASS) and choose OK.
o
Select
the number of passes, 11.
o
Choose
Compute.
3.
Inspect the graph produced by the analysis. Choose Close.
The following graph
shows the output of the sensitivity study. The graph shows how the mass of the
gear (y-axis) changes as you change the number of teeth (x-axis). The number of
points in the resulting curve corresponds to the number of computations within
the selected range.
About Feasibility and
Optimization Studies
Feasibility and optimization studies allow you to have
the system compute dimension values that cause the model to satisfy certain
user-specified constraints. To access a feasibility or optimization study,
click Analysis – Feasibility/Optimization and choose the type of study from the dialog box.
Optimization Study
An optimization study seeks a solution to an objective
(minimization or maximization of an analysis feature parameter) while being
constrained by a set of rules specified in the form of allowable ranges for
model dimensions and other analysis feature parameters. If a solution exists
for the objective given the set of constraints, the model is optimized and
changed to the new configuration.
With an
optimization study, you can specify the goal function in addition to the
parameters for a feasibility study.
For an
optimization study, you define the following attributes:
·
A set of
dimensions to vary
·
A range within
which each dimension can vary
·
A set of
constraints that you want the design to satisfy
·
A goal function
to be optimized (maximized or minimized)– a goal function is created as the
result of an analysis feature
For an
optimization study, the system does the following actions:
·
Looks for
feasible solutions
·
Out of feasible
solutions, selects the solution that optimizes the goal function
Feasibility Study
For a
feasibility study, you define the following attributes:
·
A set of model
dimensions to vary
·
A range within
which each dimension can vary
·
A set of
constraints that you want the design to satisfy
The
analysis constraints are defined as equalities or inequalities that use parameters
(which are the result of an analysis feature) and constant values. A sample
constraint may appear as follows:
length
< 6.3 or distance = 11
For a
feasibility study, the system performs the following actions:
·
Attempts to find
a set of dimension values within the specified ranges that satisfies all of the
constraints.
·
If a solution is
found, changes the model display to show the dimensions modified to the new
values.
You can
either accept these new dimensions or undo the changes and revert the model to
its state before the feasibility study. There can be many solutions in a
feasibility study that satisfy all constraints. The system converges to one of
the solutions.
To Perform an
Optimization Study
If you
have a license for Mechanism Dynamics, the dynamics measures created in
Mechanism Dynamics are available under Goals and Design Constraints.
Note: You cannot specify an integer parameter to be used in
the optimization or feasibility study.
1.
From the menu
bar, click Analysis
– Feasibility/Optimization. The Feasibility/Optimization dialog
box opens with the Optimization button selected.
2.
Under Goal, select the objective of the optimization to be
applied to a given analysis feature parameter.
3. From the list of available analysis feature parameters
on the right, choose the parameter to optimize.
4.
To create a
design constraint, click Add under Design Constraints. The Design Constraints dialog box opens.
a.
Select an
analysis feature parameter and an operator.
b.
Under Value, click Current to accept the
current value, or click Set to type the value for the
constraint.
c.
Click OK in the Design
Constraints dialog box to return to the Feasibility/Optimization dialog
box.
The names and values for the selected constraints
appear under Parameter, Operator, and Value. You can edit these entries directly by clicking the
cell.
5. To delete a design constraint, select a constraint and
click Delete.
6. To set design variables, click one of these buttons
under Design Variables:
o
Add Dimension—Select a
dimension to vary and enter its minimum and maximum values. You can add several
variable dimensions.
o
Add Parameter—From the Parameter Selection dialog box, select an existing independent model
parameter and enter its minimum and maximum values.
7. To edit an entry, click the cell and enter a new
value.
8. To delete a design variable, select a variable and
click Delete.
9. (Optional) Set display preferences for the study by
clicking Options –
Preferences. In the Graphs tab, you can set the following options:
o
Graph goal—Show in a graph the
convergence between the selected goal parameter and the chosen constraints
after the computation is made.
o
Graph constraints—Show in a
graph the constraint parameter values during the computation.
o
Graph variables—Show in a graph
the variable values during the computation.
In the Run tab, you can
set the following options:
o
Convergence %—Use the default
or type a value for the convergence criterion. Computation stops when the
difference between the parameter values for the current and previous iteration
is less than the Convergence %. The lower the value, the longer the calculation
takes and, if there is a feasible solution, the more accurate the results.
o
Max Iterations—Use the default
or type in a value for the maximum number of iterations for the computation.
The higher the value, the longer the calculation takes and the more specific
the results.
o
Animate model—Animate changes
in the model for the computed results.
Under the Method tab, you
can select the optimization method:
o
GDP—Use the standard algorithm
to optimize the model using the current model conditions as the starting point.
o
MDS—Use the multi-objective
design studies algorithm to determine the optimum starting point for the
optimization. You can specify the number of starting points to compute in the Max
Iterations field. This method has a higher chance of finding the
overall optimum design within the design parameters and dimensions.
Click Close to close the
Preferences dialog box.
10.
To create an Optimization feature, click File – Make Feature and enter the name of the feature.
11.
To save the
study, click File –
Save.
12.
Click Compute. Pro/ENGINEER calculates and displays the results.
13.
Click Close.
To Perform a
Feasibility Study
Note: You cannot specify an integer parameter to be used in
the optimization or feasibility study.
1.
From the menu
bar, choose Analysis
– Feasibility/Optimization. The Feasibility/Optimization dialog box opens.
2.
Under Study Type/ Name, select Feasibility.
3.
Accept the
default name or type the name for the study.
4.
To create a
design constraint, click Add under Design Constraints. The Design Constraint
dialog box opens.
a.
Select an
analysis feature parameter and an operator (=, <, or >=).
b.
Under Value, click Current to accept
the current value or click Set to type the value for the constraint.
c.
Click OK in the Design
Constraints dialog box to return to
the Feasibility/Optimization dialog box.
The names
and values for the selected constraints appear under the headings Parameter,
Operator, and Value. You can edit these entries directly by clicking on the
cell.
5. To delete a design constraint, select a constraint and
click Delete.
6. To set a design variable, choose one of these buttons
under Design Variables:
o
Add Dimension—Select a
dimension to vary. Enter its minimum and maximum values. You can add several
variable dimensions.
o
Add Parameter—From the Parameter Selection dialog box, select an existing independent model
parameter and enter its minimum and maximum values.
7. To edit an entry, click the cell and enter a new
value.
8. To delete a design variable, select a variable and
click Delete.
9. Optionally, you can set preferences for the study by
choosing Options –
Preferences. In the Graphs tab, you can set the following options:
o
Graph goal—Show in a graph
convergence between the selected goal parameter and the chosen constraints
after the computation is made.
o
Graph constraints—Show in a
graph constraint parameter values during the computation.
o
Graph variables—Show in a
graph variable values during the computation.
In the Run tab, you can set the following options:
o
Convergence %—Use the default
or type in a value for the convergence criterion. Computation stops when the
difference between the parameter values for the current and previous iteration
is less than the Convergence %. The lower the value, the longer the calculation
takes and, if there is a feasible solution, the more accurate the results are.
o
Max Iterations—Use the default
or type in a value for the maximum number of iterations for the computation.
The higher the value, the longer the calculation takes and the more specific
the results are.
o
Animate model—Animate changes
in the model for the computed results.
10. Choose Close to close the
Preferences dialog box.
11. To create an Optimization
feature, choose File
– Make Feature and enter the name of the feature.
12. Click Compute.
Pro/ENGINEER calculates and displays the results.
13. To save the study, choose File – Save.
14. Choose Close to close the dialog box.
Example:
Sensitivity, Feasibility, and Optimization Studies
Summary: This example shows how you can achieve a
design goal by using a sensitivity analysis, feasibility study, and an
optimization study.
Problem: For optimal balance, the center of gravity of a
crankshaft part must be coincident with its axis of rotation. The axis of
rotation of the crank cannot be altered, but other design conditions, such as
the width of the crank, can vary. In this part, you want to minimize the
distance between the axis and the center of mass while achieving the minimum
part mass.
Solution: You can find the center of gravity and create
an analysis feature to measure the distance between the axis of rotation and
the center of gravity. Then you can perform a sensitivity analysis to
investigate which dimensions have the most effect on the location of the center
of gravity. Finally, you can perform a feasibility study to investigate if it
is feasible to set the distance between the center of gravity and the axis of
rotation to zero. If a solution exists, you can then perform an optimization
study to minimize the mass of the crank while maintaining the center of gravity
on the crank axis.
|
|
1. Create an analysis
feature to perform a model analysis to determine the mass properties. Compute
the mass and create a coordinate system and a datum point at the center of
gravity as well as the MASS parameter. |
|
|
2. Create an analysis
feature to measure the distance from the datum point at the center of gravity
to the axis of rotation. As a result of the measurement, create a parameter
for this distance. |
|
|
3. Perform a sensitivity
analysis to determine how varying the width dimension affects the
location of the center of gravity. |
|
|
4. Perform a sensitivity
analysis to determine how varying the height dimension affects the
location of the center of gravity. |
|
|
5. Create an analysis
feature to measure the distance between the shaft and the outer edge of the
profile of the part. You can use this measurement to define the constraints
in a feasibility study. Create datum points at the beginning and end of the
distance line. In the next figure, this measurement is shown as E-E distance. |
6.
Perform a feasibility study to determine if it is feasible
to make the center of gravity coincident with the axis of rotation. In the
study, you vary the width, height, and radius dimensions while maintaining some
distance between the shaft of the part and the outer edge of the profile of the
part (E-E distance).
7.
Perform an optimization study to minimize the mass (goal
function) while maintaining the same constraints as outlined in Step 6.