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. You estimate Nonlinear ARX models, use the System Identification app or the nlarx function.

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 (Since R2021a)
`polynomialRegressor`	Specify polynomial regressor for nonlinear ARX model (Since R2021a)
`periodicRegressor`	Specify periodic regressor for nonlinear ARX model (Since R2022a)
`customRegressor`	Specify custom regressor for nonlinear ARX model (Since R2021a)
`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
`idGaussianProcess`	Gaussian process regression mapping function for nonlinear ARX and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox) (Since R2021b)
`idTreeEnsemble`	Decision tree ensemble mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox) (Since R2021b)
`idSupportVectorMachine`	Support vector machine regression mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox) (Since R2022a)
`idNeuralNetwork`	Multilayer neural network mapping function for nonlinear ARX models and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox or Deep Learning Toolbox) (Since R2023b)
`idFeedforwardNetwork`	(Not recommended) Multilayer feedforward neural network mapping function for nonlinear ARX models (requires Deep 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 identified model K-step-ahead output
`predictOptions`	Option set for `predict`
`compare`	Compare identified model output with measured output
`compareOptions`	Option set for `compare`
`forecast`	Forecast time-series values into future
`forecastOptions`	Option set for `forecast`
`nlarxPlot`	Plot nonlinearity of nonlinear ARX model (Since R2023a)
`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

`idnlarx/findop`	Compute operating point for Nonlinear ARX model
`findopOptions`	Option set for `findop`
`idnlarx/operspec`	Construct operating point specification object for `idnlarx` model
`idnlarx/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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Create Black-Box Models of a Robotic Arm System Using Neural Networks

Use neural networks as the nonlinear function when you model nonlinear ARX and Hammerstein-Wiener models. It compares the nonlinear systems estimated using different types of neural networks, activation functions, and number of layers.

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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 using machine learning.

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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 using machine learning.

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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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Nonlinear ARX Model of SI Engine Torque Dynamics

Describes modeling the nonlinear torque dynamics of a spark-ignition (SI) engine as a nonlinear ARX model. The identified model can be used for hardware-in-the-loop (HIL) testing, powertrain control, diagnostic, and training algorithm design. For example, you can use the model for aftertreatment control and diagnostics algorithm development. For more information on nonlinear ARX models, see Nonlinear ARX Models.

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Using idnlarx as a Modern Alternative to narxnet

Generate a NARX network using the idnlarx function from System Identification Toolbox™. To train a neural network for nonlinear systems, you can use the procedure described in this example to replace the use of the narxnet function from Deep Learning Toolbox™ with idnlarx.

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