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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 IdentificationIdentify models of dynamic systems from measured data

Functions

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idnlarxNonlinear ARX model
nlarxEstimate parameters of nonlinear ARX model
nlarxOptionsOption set for nlarx
isnlarxDetect nonlinearity in estimation data
initSet or randomize initial parameter values
getpvecObtain model parameters and associated uncertainty data
setpvecModify values of model parameters
linearRegressorSpecify linear regressor for nonlinear ARX model
polynomialRegressorSpecify polynomial regressor for nonlinear ARX model
customRegressorSpecify custom regressor for nonlinear ARX model
getregRegressor 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
idWaveletNetworkWavelet network function for nonlinear ARX and Hammerstein-Wiener models
idSigmoidNetworkSigmoid network function for nonlinear ARX and Hammerstein-Wiener models
idTreePartitionTree-partitioned nonlinear function for nonlinear ARX models
idCustomNetworkCustom network function for nonlinear ARX and Hammerstein-Wiener models
idLinearLinear mapping object for nonlinear ARX models
idFeedforwardNetworkMultilayer feedforward neural network mapping function for nonlinear ARX models (requires Deep Learning Toolbox)
idGaussianProcessGaussian process regression mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox)
idTreeEnsembleDecision tree ensemble mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox)
evaluateValue of nonlinearity estimator at given input
simSimulate response of identified model
simOptionsOption set for sim
predictPredict K-step-ahead model output
predictOptionsOption set for predict
compareCompare identified model output and measured output
compareOptionsOption set for compare
forecastForecast identified model output
forecastOptionsOption set for forecast
plotPlot nonlinearity of nonlinear ARX model
evaluateValue of nonlinearity estimator at given input
getDelayInfoGet input/output delay information for idnlarx model structure
findopCompute operating point for Nonlinear ARX model
findopOptionsOption set for findop
operspecConstruct operating point specification object for idnlarx model
linearizeLinearize nonlinear ARX model
linappLinear approximation of nonlinear ARX and Hammerstein-Wiener models for given input

Blocks

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Nonlinear ARX ModelSimulate nonlinear ARX model in Simulink software
Iddata SinkExport simulation data as iddata object to MATLAB workspace
Iddata SourceImport 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

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

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

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

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

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.

Open Live Script

System Identification Toolbox Documentation

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