输入-输出多项式模型

输入-输出多项式模型，包括 ARX、ARMAX、输出-误差和博克斯-詹金斯模型结构

多项式模型使用广义的传递函数概念，通过以下形式的方程表达输入 u(t)、输出 y(t) 和噪声 e(t) 之间的关系：

$A (q) y (t) = \frac{B (q)}{F (q)} u (t - n k) + \frac{C (q)}{D (q)} e (t) .$

A(q)、B(q)、F(q)、C(q) 和 D(q) 是根据时移运算符 q^-1 表示的多项式矩阵。u(t) 是输入，nk 是输入延迟。y(t) 是输出，e(t) 是扰动信号。

每个多项式都有一个独立的阶数，或者说可估计系数的数量。例如，如果 A(q) 的阶数为 2，则 A 多项式的形式为 A(q) = 1 + a₁q^-1 + a₂q^-2。

实际上，并非所有多项式都同时有效。更简单的多项式形式，包括 ARX、ARMAX、输出-误差和博克斯-詹金斯模型，提供了适合特定目标的模型结构，例如处理非平稳扰动或为动态特性和噪声提供完全独立的参数化。有关这些模型类型的详细信息，请参阅What Are Polynomial Models?

App

系统辨识	从测量数据辨识动态系统模型

函数

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创建多项式模型

`idpoly`	Polynomial model with identifiable parameters
`arx`	估计 ARX、ARIX、AR 或 ARI 模型的参数
`armax`	使用时域数据估计 ARMAX、ARIMAX、ARMA 或 ARIMA 模型的参数
`bj`	Estimate Box-Jenkins polynomial model using time-domain data
`iv4`	ARX model estimation using four-stage instrumental variable method
`ivx`	ARX model estimation using instrumental variable method with arbitrary instruments
`oe`	Estimate output-error polynomial model using time-domain or frequency-domain data
`polyest`	Estimate polynomial model using time- or frequency-domain data
`pem`	Prediction error minimization for refining linear and nonlinear models

寻找最佳 ARX 模型-阶数组合

`arxstruc`	Compute loss functions for single-output ARX models
`ivstruc`	Compute loss functions for sets of ARX model structures using instrumental variable method
`selstruc`	Select model order for single-output ARX models
`struc`	为单输出 ARX 模型估计生成模型阶组合

模型初始化和结构参数

`arxRegul`	Determine regularization constants for ARX model estimation
`delayest`	根据数据估计时间延迟（死区时间）
`init`	Set or randomize initial parameter values

提取或设置模型参数

`polydata`	Access polynomial coefficients and uncertainties of identified model
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters
`getpar`	Obtain attributes such as values and bounds of linear model parameters
`setpar`	Set attributes such as values and bounds of linear model parameters
`setPolyFormat`	Specify format for B and F polynomials of multi-input polynomial model

估计选项

`armaxOptions`	Option set for `armax`
`arxOptions`	Option set for `arx`
`arxRegulOptions`	Option set for `arxRegul`
`bjOptions`	Option set for `bj`
`iv4Options`	Option set for `iv4`
`oeOptions`	Option set for `oe`
`polyestOptions`	Option set for `polyest`

主题

多项式模型基础知识

What Are Polynomial Models?
Polynomial model structures including ARX, ARMAX, output-error, and Box-Jenkins.
Data Supported by Polynomial Models
Use time-domain and frequency-domain data to estimate discrete-time and continuous-time models.

估计多项式模型

Preliminary Step – Estimating Model Orders and Input Delays
To estimate polynomial models, you must provide input delays and model orders.
Estimate Polynomial Models in the App
Import data into the app, specify model orders, delays and estimation options.
Estimate Polynomial Models at the Command Line
Specify model orders, delays, and estimation options.
Polynomial Sizes and Orders of Multi-Output Polynomial Models
Size of A, B, C, D, and F polynomials for multi-output models.
Estimate Models Using armax
This example shows how to estimate a linear, polynomial model with an ARMAX structure for a three-input and single-output (MISO) system.

设置多项式模型选项

Specifying Initial States for Iterative Estimation Algorithms
Specify initial conditions of polynomial models for iterative estimation algorithms.
Polynomial Model Estimation Algorithms
Choose between the ARX and IV algorithms for ARX and AR model estimation.

精选示例

Spectrum Estimation Using Complex Data - Marple's Test Case

Perform spectral estimation on time series data. We use Marple's test case (The complex data in L. Marple: S.L. Marple, Jr, Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ 1987.)

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Picking Instrumental Variables for System Identification

Illustration of the meaning and choice of instrumental variables (IVs) for system identification.

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