Nonlinear ARX Models

Nonlinear behavior modeled using dynamic networks such as sigmoid and wavelet

Use nonlinear ARX models to represent nonlinearities in your system using dynamic nonlinearity estimators such as wavelet networks, tree-partitioning, and sigmoid networks. In the toolbox, these models are represented as idnlarx objects. You can estimate Nonlinear ARX models in the System Identification app, or at the command line using the nlarx command.

Apps

System Identification

Identify models of dynamic systems from measured data

Functions

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Model Estimation

`idnlarx`	Nonlinear ARX model
`nlarx`	Estimate parameters of nonlinear ARX model
`nlarxOptions`	Option set for `nlarx`
`isnlarx`	Detect nonlinearity in estimation data
`init`	Set or randomize initial parameter values
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters

Model Regressors

`linearRegressor`	Specify linear regressor for nonlinear ARX model
`polynomialRegressor`	Specify polynomial regressor for nonlinear ARX model
`periodicRegressor`	Specify periodic regressor for nonlinear ARX model
`customRegressor`	Specify custom regressor for nonlinear ARX model
`getreg`	Regressor expressions and numerical values in nonlinear ARX model
`polyreg`	(Not recommended) Powers and products of standard regressors
`customreg`	(Not recommended) Custom regressor for nonlinear ARX models
`addreg`	(Not recommended) Add custom regressors to nonlinear ARX model

Nonlinear and Linear Mapping Objects

`idWaveletNetwork`	Wavelet network function for nonlinear ARX and Hammerstein-Wiener models
`idSigmoidNetwork`	Sigmoid network function for nonlinear ARX and Hammerstein-Wiener models
`idTreePartition`	Tree-partitioned nonlinear function for nonlinear ARX models
`idCustomNetwork`	Custom network function for nonlinear ARX and Hammerstein-Wiener models
`idLinear`	Linear mapping object for nonlinear ARX models
`idFeedforwardNetwork`	Multilayer feedforward neural network mapping function for nonlinear ARX models (requires Deep Learning Toolbox)
`idGaussianProcess`	Gaussian process regression mapping function for nonlinear ARX and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox)
`idTreeEnsemble`	Decision tree ensemble mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox)
`idSupportVectorMachine`	Support vector machine regression mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox)
`evaluate`	Evaluate output values of `idnlarx` or `idnlhw` mapping object array for given set of input values

Simulation, Prediction, and Validation

`sim`	Simulate response of identified model
`simOptions`	Option set for `sim`
`predict`	Predict K-step-ahead model output
`predictOptions`	Option set for `predict`
`compare`	Compare identified model output and measured output
`compareOptions`	Option set for `compare`
`forecast`	Forecast identified model output
`forecastOptions`	Option set for `forecast`
`plot`	Plot nonlinearity of nonlinear ARX model
`evaluate`	Evaluate output values of `idnlarx` or `idnlhw` mapping object array for given set of input values
`getDelayInfo`	Get input/output delay information for `idnlarx` model structure

Linearization

`findop`	Compute operating point for Nonlinear ARX model
`findopOptions`	Option set for `findop`
`operspec`	Construct operating point specification object for `idnlarx` model
`linearize`	Linearize nonlinear ARX model
`linapp`	Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input

Blocks

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Simulation

Nonlinear ARX Model	Simulate nonlinear ARX model in Simulink software
Iddata Sink	Export simulation data as `iddata` object to MATLAB workspace
Iddata Source	Import time-domain data stored in `iddata` object in MATLAB workspace

Topics

What are Nonlinear ARX Models?
Understand the structure of a nonlinear ARX model.
Available Mapping Functions for Nonlinear ARX Models
Choose from sigmoid, wavelet, tree partition, linear, neural, and custom network nonlinearities.
Identifying Nonlinear ARX Models

Specify the Nonlinear ARX structure, and configure the estimation algorithm.
Validate Nonlinear ARX Models
Plot model nonlinearities, analyze residuals, and simulate and predict model output.
Using Nonlinear ARX Models
Simulate, predict, and forecast model output, linearize nonlinear ARX models, and import estimated models into the Simulink^® software.
Linear Approximation of Nonlinear Black-Box Models
Choose the approach for computing linear approximations, compute operating points for linearization, and linearize your model.
How the Software Computes Nonlinear ARX Model Output
How the software evaluates the output of nonlinearity estimators and uses this output to compute the model response.

Featured Examples

A Tutorial on Identification of Nonlinear ARX and Hammerstein-Wiener Models

Identify single-input-single-output (SISO) nonlinear black box models using measured input-output data.

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Building Nonlinear ARX Models with Nonlinear and Custom Regressors

Use custom regressors in SISO and MIMO nonlinear ARX (IDNLARX) models.

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Machine-Learning-Based Identification of Two-Tank System

Identify a black-box dynamic model of a nonlinear two-tank system.

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Machine-Learning-Based Identification of Nonlinear Magneto-Rheological Fluid Damper

Estimate a black-box dynamic model of a nonlinear magneto-rheological (MR) fluid damper. Magneto-rheological dampers are used to reduce structural vibrations by applying a controlled force, which depends on the input voltage and current of the device. A nonlinear ARX model with a regression tree ensemble mapping function is used to model the MR damper.

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Surrogate Modeling Using Gaussian Process-Based NLARX Model

In this example, you replace a hydraulic cavitation cycle model in Simulink® with a surrogate nonlinear ARX (NLARX) model to facilitate faster simulation.

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Piezoelectric Actuator Model Identification Using Machine Learning

Identify a piezoelectric actuator nonlinear model using machine-learning-based techniques that include support vector machines and Gaussian process functions.

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