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Simulate System Model Sensitivities—Wolfram Documentation

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• See Also
  • SystemModelSimulate
  • SystemModelSimulationData
  • SystemModelExamples
  • SystemModelParametricSimulate
  • ParametricNDSolveValue
• Related Guides
  • System Model Simulation
  • System Model Analytics & Design

• SystemModelSimulateSensitivity is used to estimate the variations in simulation results when changing parameter values in system models.
• The model can have the following forms:
• SystemModelSimulateSensitivity returns a SystemModelSimulationData object.
• For a SystemModel model, SystemModelSimulateSensitivity generates solutions for all variables , as well as derivatives , , … for all states , for .
• For other types of models, SystemModelSimulateSensitivity generates solutions for all variables , as well as derivatives , , …, for .
• Sensitivities can be listed in a SystemModelSimulationData object sd with sd["SensitivityNames"].
• The stored simulation variables vars can have the following values:
• Automatic automatically choose what to store {v₁,v₂,…} store only variables v_i All store all variables
• SystemModelSimulateSensitivity[…,spec] uses Association spec for initial values, parameters and inputs:
• "ParameterValues" {p₁val₁,…} parameter p_i has value val_i "InitialValues" {v₁val₁,…} variable v_i has initial value val_i "Inputs" {in₁fun₁,…} input in_i has value fun_i[t] at time t
• Setting "ParameterValues" or "InitialValues" to {p_i->{c₁,c₂,…},…} runs simulations in parallel, with p_i taking values c_j.
• "InitialValues" corresponds to the start property in the Modelica model.
• The following options can be given:
• The option setting Automatic normally means that the setting is taken from model or its experiment setting.
• For a SystemModel model, 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" 10^-6 tolerance for adaptive step size

Study sensitivity of a parameter over the time interval in model experiment settings:

Extract sensitivity names and plot them:

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:

Compute variables and sensitivities when simulating a NonlinearStateSpaceModel:

Extract sensitivity names and plot them:

Plot bounds for a state when varying a by 40%:

Compute sensitivities in a parameter sweep for an AffineStateSpaceModel:

Plot bounds for a state when varying a by 50%:

Compute sensitivities for a DiscreteInputOutputModel:

Plot bounds for the output when varying a by 5%:

Simulate with settings from the model:

Simulate from time 0 to 5:

Simulate for an explicit time interval:

Study the sensitivity of one parameter:

Simulate with sensitivity to parameter a:

Get the sensitivity names:

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 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 0.05:

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 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:

Plot the variation of y when parameter a varies by ±0.1:

Change the initial values of a simulation:

Compare the changes in a plot:

Change the parameter values of a simulation:

Compare the two in a plot:

Give an input function for a variable and study the sensitivity of the output to a gain parameter:

Plot the sensitivity of the output to the gain parameter:

Store only selected variables:

Only the given variables and parameters are saved:

Simulate with interpolation orders 1 and 3, and 3 interpolation points:

Show the sensitivity variable:

Simulate a SystemModel and compute sensitivities with the number of interpolation points set by the model:

Simulate and compute sensitivities with a custom number of interpolation points:

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 frequency parameter:

A 10% sensitivity bound shows that "integrator3.y" is most sensitive to the parameter:

Simulate a rolling wheel:

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 SystemModelSimulateSensitivity to get gradients:

Plot the result of the simulation for specific parameter values:

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 SystemModelPlot 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 SystemModelParametricSimulate for a function that can be evaluated for different values:

Compute solutions for different values of the frequency parameter:

Plot the solutions over time:

Show sensitivity bounds for the and axes in the Rabinovich–Fabrikant equations:

Show the sensitivity bounds in 3D:

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