Nonlinear Model Identification Basics

Identified nonlinear models, black-box modeling, and regularization

Use nonlinear model identification when a linear model does not completely capture your system dynamics. You can identify nonlinear models in the System Identification app or at the command line. System Identification Toolbox™ enables creation and estimation of four nonlinear model structures:

Nonlinear ARX models — Represent nonlinearities in your system using dynamic nonlinear mapping objects such as wavelet networks, tree-partitioning, and sigmoid networks.
Hammerstein-Wiener models — Estimate static nonlinearities in an otherwise linear system.
Nonlinear grey-box models — Represent your nonlinear system using ordinary differential or difference equations (ODEs) with unknown parameters.
Neural state-space models — Use neural networks to represent the functions that define the nonlinear state-space realization of your system.

Topics

Nonlinear Identified Models

About Identified Nonlinear Models
Dynamic models in System Identification Toolbox software are mathematical relationships between the inputs u(t) and outputs y(t) of a system.
Nonlinear Model Structures
Construct model objects for nonlinear model structures, access model properties.
Available Nonlinear Models
The System Identification Toolbox software provides four types of nonlinear model structures:
Black-Box Modeling
Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.
Types of Model Objects
Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.

Model Estimation

Identify Nonlinear Black-Box Models Using System Identification App
Identify nonlinear black-box models from single-input/single-output (SISO) data using the System Identification app.
Modeling Multiple-Output Systems
Use a multiple-output modeling technique that suits the complexity and internal input-output coupling of your system.
Preparing Data for Nonlinear Identification
Estimating nonlinear ARX and Hammerstein-Wiener models requires uniformly sampled time-domain data.
Loss Function and Model Quality Metrics
Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.
Regularized Estimates of Model Parameters
Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.
Estimation Report
The estimation report contains information about the results and options used for a model estimation.
Next Steps After Getting an Accurate Model
How you can work with identified models.

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