WSMSimulateSensitivity
WSMSimulateSensitivity["mmodel",{p1,p2,…}]
simulates "mmodel" and sensitivities to parameters pi following experiment settings.
WSMSimulateSensitivity["mmodel",tmax,{p1,p2,…}]
simulates from 0 to tmax.
WSMSimulateSensitivity["mmodel",{tmin,tmax},{p1,p2,…}]
simulates from tmin to tmax.
WSMSimulateSensitivity["mmodel",vars,{tmin,tmax},{p1,p2,…}]
stores only simulation data for the variables vars.
Details and Options
- WSMSimulateSensitivity returns a WSMSimulationData object.
- The "mmodel" refers to the fully qualified Modelica name.
- WSMSimulateSensitivity generates solutions
for all variables 
, as well as derivatives 
, 
, … for all states 
, for 
. - Sensitivities can be listed in a WSMSimulationData object sd with sd["SensitivityNames"].
- The shortest unique model name mmodel can be used where WSMNames["*.mmodel"] gives a unique match.
- The stored simulation variables vars can have the following values:
-
Automatic automatically choose what to store {v1,v2,…} store only variables vi All store all variables - The following options can be given:
-
InterpolationOrder Automatic continuity degree of output between events WSMInitialValues Automatic overriding initial values WSMInputFunctions Automatic overriding input values WSMParameterValues Automatic overriding parameter values WSMProgressMonitor Automatic control display of progress - The option setting Automatic normally means that the setting is taken from "mmodel" or its experiment setting.
- Setting WSMParameterValues or WSMInitialValues to {pi->{c1,c2,…},…} runs simulations in parallel, with pi taking values cj.
- WSMInitialValues corresponds to the start property in the Modelica model.
- WSMInputFunctions->{"var1"->fun1,…} uses funi[t] as the input value for vari at time t.
- The CVODES solver used can be controlled with Method->{"opt1"->val1}.
- Possible suboptions for the CVODES method include:
-
"InterpolationPoints" Automatic number of interpolation points "Tolerance" 106 tolerance for adaptive step size
Examples
open all close allBasic Examples (4)
Load Wolfram System Modeler Link:
Study sensitivity of a parameter over the time interval in model experiment settings:
Show the sensitivity of a signal to relative changes in a parameter:
Plot bounds for y and z when varying a by 10%:
Use the diagram representation of a model as input:
Copy and paste the output above:
Scope (10)
Simulation Time (3)
Sensitivity Results (6)
Study the sensitivity of one parameter:
Simulate with sensitivity to parameter a:
Get the sensitivity y has to changes in a:
Study the sensitivities from one parameter:
Plot one of the sensitivities:
Show the sensitivity of a signal to a parameter:
Simulate with sensitivity to a:
Get the sensitivity y has to changes in a, as well as the nominal trajectory for y:
Plot y with original parameter a, and with parameter a increased by 0.05:
Show the sensitivity of a signal to relative changes in a parameter:
Get the sensitivity y and z have to changes in a, as well as nominal trajectories and value:
Plot bounds for y and z when varying a by 10% of the sensitivity:
Show the sensitivity of a signal to absolute changes in a parameter:
Simulate with sensitivity to a:
Get the sensitivity y has to changes in a, as well as the trajectory for y:
Compute the change in y when parameter a changes with absolute value 0.1:
Generalizations & Extensions (1)
Options (5)
InterpolationOrder (1)
WSMInputFunctions (1)
WSMProgressMonitor (1)
Turn off the progress dialog with WSMProgressMonitor:
Applications (5)
Study the sensitivity of a model:
Get the value of the parameter:
Find the peak deviation when varying the parameter:
Show a 5% sensitivity bound and the peak deviation time:
Find out which variable is most sensitive to a parameter:
Simulate with sensitivities to a frequency parameter:
A 10% sensitivity bound shows that "integrator3.y" is most sensitive to the parameter:
Select the position of the wheel and its sensitivities to different parameters:
Show the path of the wheel with 4% variation of the wheel radius and mass, respectively:
Calibrate parameters in a model by comparing to measurement data:
Set up caching for simulation:
Use WSMSimulateSensitivity to get gradients:
Fit parameters to the measurement data:
Not using gradients may take longer:
Simulate with the fitted parameters:
Show the test data and the calibrated model together:
Plot a solution with its sensitivity bounds:
Get the nominal value of the parameter:
Simulate with a maximal variation of 5%:
Show that the trajectories are mostly contained in the approximated sensitivity bounds:
Properties & Relations (4)
Compare a sensitivity simulation with the sensitivity of the corresponding differential equation:
Plot bounds for a relative parameter change:
Get the sensitivity y has to changes in a, as well as y and the value for a:
Plot bounds for y when varying a by 10% of the sensitivity:
Use WSMPlot instead:
Sensitivities are valid for small changes in the parameter:
Get sensitivities to a parameter:
Simulate with 
variation of the parameter:
Comparing in a plot, a 10% variation gives trajectories outside computed bounds:
Use WSMParametricSimulate for a function that can be evaluated for different values:
Compute solutions for different values of the frequency parameter:
