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WSMSimulateSensitivity


simulates a model and sensitivities to parameters a, b, ... from to .
  • The refers to the fully qualified Modelica name.
  • 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 following options can be given:
WSMInitialValuesAutomaticoverriding initial values
WSMInputFunctionsAutomaticoverriding input values
InterpolationOrderAutomaticcontinuity degree of output between events
WSMParameterValuesAutomaticoverriding parameter values
  • uses the CVODES solver.
  • The CVODES solver can be controlled with Method with possible values:
"InterpolationPoints"Automaticnumber of interpolation points
"Tolerance"106tolerance for adaptive step size
Load Wolfram SystemModeler Link:
Study the sensitivity of one parameter:
Study the sensitivities from one parameter:
Plot one of the sensitivities:
Load Wolfram SystemModeler Link:
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Study the sensitivity of one parameter:
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Study the sensitivities from one parameter:
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Plot one of the sensitivities:
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Simulate with sensitivity to parameter a:
Get the sensitivity names:
Get the sensitivity y has to changes in a:
Show the sensitivity of a signal to a parameter:
Simulate with sensitivity to a:
Get the sensitivity names:
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 :
Show the sensitivity of a signal to relative changes in a parameter:
Get the sensitivity names:
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 :
Plot the variation of y when parameter a varies by :
The symbols returned from WSMModelData can be used as sensitivity parameters:
Change the initial values of a simulation:
Compare the changes in a plot:
Give an input function for a variable and study the sensitivity of the output:
Simulate the model that integrates the input after applying a gain:
Plot the sensitivity of the output to the gain parameter:
Simulate with interpolation orders 1 and 3, and 3 interpolation points:
Show the sensitivity variable:
Change the parameter values of a simulation:
Compare the two in a plot:
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 is most sensitive to the parameter:
Calibrate parameters in a model by comparing to measurement data:
Set up caching for simulation:
Use to get gradients:
Fit parameters to the measurement data:
Not using gradients takes 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:
Show a 5% sensitivity bound:
Simulate with a maximal variation of 5%:
Get the trajectories:
Show that the trajectories are mostly contained in the approximated sensitivity bounds:
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, we see that a 10% variation gives trajectories outside computed bounds:
Show sensitivity bounds for the and axes in the Rabinovich-Fabrikant equations:
Show the sensitivity bounds in 3D: