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グレーボックス モデルの推定

線形および非線形の微分方程式、差分方程式、状態空間方程式の係数の推定

関数

greyestLinear grey-box model estimation
nlgreyestEstimate nonlinear grey-box model parameters
idgreyLinear ODE (grey-box model) with identifiable parameters
idnlgreyNonlinear grey-box model
pemPrediction error estimate for linear and nonlinear model
findstatesEstimate initial states of model
initSet or randomize initial parameter values
getinitValues of idnlgrey model initial states
setinitSet initial states of idnlgrey model object
getparParameter values and properties of idnlgrey model parameters
setparSet initial parameter values of idnlgrey model object
getpvecModel parameters and associated uncertainty data
setpvecModify value of model parameters
simSimulate response of identified model
greyestOptionsOption set for greyest
nlgreyestOptionsOption set for nlgreyest
findstatesOptionsOption set for findstates
simOptionsOption set for sim

例および操作のヒント

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. The code in this example uses the Control System Toolbox™ command kalman for computing the Kalman gain from the known and estimated noise variance.

Estimate Coefficients of ODEs to Fit Given Solution

This example shows how to estimate model parameters using linear and nonlinear grey-box modeling.

Estimate Model Using Zero/Pole/Gain Parameters

This example shows how to estimate a model that is parameterized by poles, zeros, and gains. The example requires Control System Toolbox™ software.

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.

Estimate State-Space Models with Structured Parameterization

Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values. This approach is useful when you can derive state-space matrices from physical principles and provide initial parameter values based on physical insight. You can use this approach to discover what happens if you fix specific parameter values or if you free certain parameters.

概念

Supported Grey-Box Models

Types of supported grey-box models.

Data Supported by Grey-Box Models

Types of supported data for estimating grey-box models.

Choosing idgrey or idnlgrey Model Object

Difference between idgrey and idnlgrey model objects for representing grey-box model objects.

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. The input signals are measured while the noise signals are only known via their statistical mean and variance. The general form of the state-space model, often associated with Kalman filtering, is an example of such a model, and is defined as:

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. This report is stored in the Report property of the estimated model. The exact contents of the report depend on the estimator function you use to obtain the model.

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.