Grey-Box Model Estimation

Estimate coefficients of linear and nonlinear differential, difference and state-space equations

If you understand the physics of your system and you can represent the system using ordinary differential or difference equations (ODEs) with unknown parameters, then you can use System Identification Toolbox™ commands to perform grey-box modeling. Grey-box model ODEs specify the mathematical structure of the model explicitly, including couplings between parameters. Grey-box modeling is useful when you know the relationships between variables, constraints on model behavior, or explicit equations representing system dynamics.

Functions

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Model Estimation

`greyest`	Estimate ODE parameters of linear grey-box model
`greyestOptions`	Option set for `greyest`
`nlgreyestOptions`	Option set for `nlgreyest`
`nlgreyest`	Estimate nonlinear grey-box model parameters
`idgrey`	Linear ODE (grey-box model) with identifiable parameters
`idnlgrey`	Nonlinear grey-box model
`pem`	Prediction error minimization for refining linear and nonlinear models

Model Parameters

`init`	Set or randomize initial parameter values
`getpar`	Parameter values and properties of `idnlgrey` model parameters
`setpar`	Set initial parameter values of `idnlgrey` model object
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters

Model States

`getinit`	Values of `idnlgrey` model initial states
`setinit`	Set initial states of `idnlgrey` model object
`findstates`	Estimate initial states of model
`findstatesOptions`	Option set for `findstates`

Simulation

`sim`	Simulate response of identified model
`simOptions`	Option set for `sim`

Topics

Grey-Box Modeling Basics

Linear and Nonlinear Grey-Box Modeling
If you understand the physics of your system, you can estimate linear or nonlinear grey-box models.
Identifying State-Space Models with Separate Process and Measurement Noise Descriptions
An identified linear model is used to simulate and predict system outputs for given input and noise signals.
Loss Function and Model Quality Metrics
Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.
Estimation Report
The estimation report contains information about the results and options used for a model estimation.
Regularized Estimates of Model Parameters
Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.
Estimate Coefficients of ODEs to Fit Given Solution
Estimate model parameters using linear and nonlinear grey-box modeling.
Building Structured and User-Defined Models Using System Identification Toolbox
This example shows how to estimate parameters in user-defined model structures.

Linear Grey-Box Models

Estimate Linear Grey-Box Models
How to define and estimate linear grey-box models at the command line.
Estimate Continuous-Time Grey-Box Model for Heat Diffusion
This example shows how to estimate the heat conductivity and the heat-transfer coefficient of a continuous-time grey-box model for a heated-rod system.
Estimate Discrete-Time Grey-Box Model with Parameterized Disturbance
This example shows how to create a single-input and single-output grey-box model structure when you know the variance of the measurement noise.
Estimate Model Using Zero/Pole/Gain Parameters
This example shows how to estimate a model that is parameterized by poles, zeros, and gains.
Estimate State-Space Models with Structured Parameterization
Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.

Nonlinear Grey-Box Models

Estimate Nonlinear Grey-Box Models
How to define and estimate nonlinear grey-box models at the command line.
Creating IDNLGREY Model Files
This example shows how to write ODE files for nonlinear grey-box models as MATLAB® and C MEX files.