nlgreyest

Estimate nonlinear grey-box model parameters

Syntax

sys= nlgreyest(data,init_sys)

sys= nlgreyest(data,init_sys,options)

Description

sys= nlgreyest(data,init_sys) estimates the parameters of a nonlinear grey-box model, init_sys, using time-domain data, data.

sys= nlgreyest(data,init_sys,options) specifies additional model estimation options.

Examples

Selectively Estimate Parameters of Nonlinear Grey-Box Model

Load data.

load(fullfile(matlabroot,'toolbox','ident','iddemos','data','twotankdata'));
z = iddata(y,u,0.2,'Name','Two tanks');

The data contains 3000 input-output data samples of a two tank system. The input is the voltage applied to a pump, and the output is the liquid level of the lower tank.

Specify file describing the model structure for a two-tank system. The file specifies the state derivatives and model outputs as a function of time, states, inputs, and model parameters.

FileName = 'twotanks_c';

Specify model orders [ny nu nx].

Order = [1 1 2];

Specify initial parameters (Np = 6).

Parameters = {0.5;0.0035;0.019; ...
    9.81;0.25;0.016};

Specify initial initial states.

InitialStates = [0;0.1];

Specify as continuous system.

Ts = 0;

Create idnlgrey model object.

nlgr = idnlgrey(FileName,Order,Parameters,InitialStates,Ts, ...
    'Name','Two tanks');

Set some parameters as constant.

nlgr.Parameters(1).Fixed = true;
nlgr.Parameters(4).Fixed = true;
nlgr.Parameters(5).Fixed = true;

Estimate the model parameters.

nlgr = nlgreyest(z,nlgr);

Estimate a Nonlinear Grey-Box Model Using Specific Options

Create estimation option set for nlgreyest to view estimation progress, and to set the maximum iteration steps to 50.

opt = nlgreyestOptions;
opt.Display = 'on';
opt.SearchOptions.MaxIterations = 50;

Load data.

load(fullfile(matlabroot,'toolbox','ident','iddemos','data','dcmotordata'));
z = iddata(y,u,0.1,'Name','DC-motor');

The data is from a linear DC motor with one input (voltage), and two outputs (angular position and angular velocity). The structure of the model is specified by dcmotor_m.m file.

Create a nonlinear grey-box model.

file_name = 'dcmotor_m';
Order = [2 1 2];
Parameters = [1;0.28];
InitialStates = [0;0];

init_sys = idnlgrey(file_name,Order,Parameters,InitialStates,0, ...
    'Name','DC-motor');

Estimate the model parameters using the estimation options.

sys = nlgreyest(z,init_sys,opt);

Input Arguments

data — Time domain data

iddata object

Time-domain estimation data, specified as an iddata object. data has the same input and output dimensions as init_sys.

If you specify the InterSample property of data as 'bl'(band-limited) and the model is continuous-time, the software treats data as first-order-hold (foh) interpolated for estimation.

init_sys — Constructed nonlinear grey-box model

idnlgrey object

Constructed nonlinear grey-box model that configures the initial parameterization of sys, specified as an idnlgrey object. init_sys has the same input and output dimensions as data. Create init_sys using idnlgrey.

options — Estimation options

nlgreyestOptions option set

Estimation options for nonlinear grey-box model identification, specified as an nlgreyestOptions option set.

Output Arguments

sys — Estimated nonlinear grey-box model

idnlgrey object

Nonlinear grey-box model with the same structure as init_sys, returned as an idnlgrey object. The parameters of sys are estimated such that the response of sys matches the output signal in the estimation data.

Information about the estimation results and options used is stored in the Report property of the model. Report has the following fields:

Report Field	Description
Status	Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.
Method	Name of the simulation solver and the search method used during estimation.
Fit	Quantitative assessment of the estimation, returned as a structure. See Loss Function and Model Quality Metrics for more information on these quality metrics. The structure has the following fields: Field Description FitPercent Normalized root mean squared error (NRMSE) measure of how well the response of the model fits the estimation data, expressed as the percentage fit = 100(1-NRMSE). LossFcn Value of the loss function when the estimation completes. MSE Mean squared error (MSE) measure of how well the response of the model fits the estimation data. FPE Final prediction error for the model. AIC Raw Akaike Information Criteria (AIC) measure of model quality. AICc Small sample-size corrected AIC. nAIC Normalized AIC. BIC Bayesian Information Criteria (BIC).
Parameters	Estimated values of the model parameters. Structure with the following fields: Field Description InitialValues Structure with values of parameters and initial states before estimation. ParVector Value of parameters after estimation. Free Logical vector specifying the fixed or free status of parameters during estimation FreeParCovariance Covariance of the free parameters. X0 Value of initial states after estimation. X0Covariance Covariance of the initial states.
OptionsUsed	Option set used for estimation. If no custom options were configured, this is a set of default options. See nlgreyestOptions for more information.
RandState	State of the random number stream at the start of estimation. Empty, [], if randomization was not used during estimation. For more information, see rng.
DataUsed	Attributes of the data used for estimation — Structure with the following fields: Field Description Name Name of the data set. Type Data type — For idnlgrey models, this is set to 'Time domain data'. Length Number of data samples. Ts Sample time. This is equivalent to data.Ts. InterSample Input intersample behavior. One of the following values: 'zoh' — Zero-order hold maintains a piecewise-constant input signal between samples. 'foh' — First-order hold maintains a piecewise-linear input signal between samples. 'bl' — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency. The value of Intersample has no effect on estimation results for discrete-time models. InputOffset Empty, [], for nonlinear estimation methods. OutputOffset Empty, [], for nonlinear estimation methods.
Termination	Termination conditions for the iterative search used for prediction error minimization, returned as a structure with the following fields: Field Description WhyStop Reason for terminating the numerical search. Iterations Number of search iterations performed by the estimation algorithm. FirstOrderOptimality $$\infty$$-norm of the gradient search vector when the search algorithm terminates. FcnCount Number of times the objective function was called. UpdateNorm Norm of the gradient search vector in the last iteration. Omitted when the search method is 'lsqnonlin' or 'fmincon'. LastImprovement Criterion improvement in the last iteration, expressed as a percentage. Omitted when the search method is 'lsqnonlin' or 'fmincon'. Algorithm Algorithm used by 'lsqnonlin' or 'fmincon' search method. Omitted when other search methods are used. For estimation methods that do not require numerical search optimization, the Termination field is omitted.

For more information, see Estimation Report.

Extended Capabilities

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

Parallel computing support is available for estimation using the lsqnonlin search method (requires Optimization Toolbox™). To enable parallel computing, use nlgreyestOptions, set SearchMethod to 'lsqnonlin', and set SearchOptions.Advanced.UseParallel to true.

For example:

opt = nlgreyestOptions;
opt.SearchMethod = 'lsqnonlin';
opt.SearchOptions.Advanced.UseParallel = true;