灰盒模型估计

估计线性和非线性微分方程、差分方程和状态空间方程的系数

如果您了解系统的物理特性，并且可以使用带有未知参数的常微分方程或差分方程 (ODE) 来表示系统，则可以使用 System Identification Toolbox™ 命令执行灰盒建模。灰盒模型 ODE 明确指定模型的数学结构，包括参数之间的耦合。当您了解变量之间的关系、模型行为的约束或表示系统动态特性的显式方程时，灰盒建模是很有用的。

函数

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模型估计

`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

模型参数

`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

模型状态

`getinit`	Values of `idnlgrey` model initial states
`setinit`	设置 `idnlgrey` 模型对象的初始状态
`findstates`	Estimate initial states of model
`findstatesOptions`	Option set for `findstates`

仿真

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

主题

灰盒建模基础知识

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.

线性灰盒模型

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.

非线性灰盒模型

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.