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ARX、ARMAX、出力誤差、Box-Jenkins の各モデル構造を含む入出力多項式モデル

多項式モデルでは、伝達関数の一般化概念を使用して、入力 u(t)、出力 y(t)、およびノイズ e(t) の関係を次の形式の式を使用して表現します。


A(q)、B(q)、F(q)、C(q) および D(q) は、時間シフト演算子 q-1 に関する多項式行列です。u(t) は入力、nk は入力遅延です。y(t) は出力、e(t) は外乱信号です。

各多項式は、独立した "次数"、つまり推定可能な係数の数をもちます。たとえば、A(q) の次数が 2 である場合、A 多項式の形式は A(q) = 1 + a1q-1 + a2q-2 になります。

実際には、すべての多項式が同時にアクティブになるわけではありません。ARX、ARMAX、出力誤差、Box-Jenkins などのよりシンプルな形式の多項式では、非定常外乱の処理やダイナミクスとノイズの完全に独立したパラメーター化の提供といった特定の目的に適したモデル構造が得られます。これらのモデル タイプの詳細については、What Are Polynomial Models?を参照してください。


System IdentificationIdentify models of dynamic systems from measured data



idpolyPolynomial model with identifiable parameters
arxEstimate parameters of ARX, ARIX, AR, or ARI model
armaxEstimate parameters of ARMAX, ARIMAX, ARMA, or ARIMA model using time-domain data
bjEstimate Box-Jenkins polynomial model using time domain data
iv4ARX model estimation using four-stage instrumental variable method
ivxARX model estimation using instrumental variable method with arbitrary instruments
oeEstimate output-error polynomial model using time-domain or frequency-domain data
polyestEstimate polynomial model using time- or frequency-domain data
pemPrediction error minimization for refining linear and nonlinear models
arxstrucCompute loss functions for single-output ARX models
ivstrucCompute loss functions for sets of ARX model structures using instrumental variable method
selstrucSelect model order for single-output ARX models
strucGenerate model-order combinations for single-output ARX model estimation
arxRegulDetermine regularization constants for ARX model estimation
delayestEstimate time delay (dead time) from data
initSet or randomize initial parameter values
polydataAccess polynomial coefficients and uncertainties of identified model
getpvecObtain model parameters and associated uncertainty data
setpvecModify values of model parameters
getparObtain attributes such as values and bounds of linear model parameters
setparSet attributes such as values and bounds of linear model parameters
setPolyFormatSpecify format for B and F polynomials of multi-input polynomial model
armaxOptionsOption set for armax
arxOptionsOption set for arx
arxRegulOptionsOption set for arxRegul
bjOptionsOption set for bj
iv4OptionsOption set for iv4
oeOptionsOption set for oe
polyestOptionsOption set for polyest



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.


Preliminary Step – Estimating Model Orders and Input Delays

To estimate polynomial models, you must provide input delays and model orders. If you already have insight into the physics of your system, you can specify the number of poles and zeros.

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 using the iterative estimation method armax. For a summary of all available estimation commands in the toolbox, see Model Estimation Commands.


Specifying Initial States for Iterative Estimation Algorithms

When you use the pem or polyest functions to estimate ARMAX, Box-Jenkins (BJ), Output-Error (OE), you must specify how the algorithm treats initial conditions.

Polynomial Model Estimation Algorithms

Choose between the ARX and IV algorithms for ARX and AR model estimation.