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nlgreyest

Estimate nonlinear grey-box model parameters

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Syntax

sys= nlgreyest(data,init_sys)
sys= nlgreyest(data,init_sys,options)

Description

example

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

example

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

Examples

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Open Live Script

Load data.

load(fullfile(matlabroot,'toolbox','ident','iddemos','data','twotankdata')); z = iddata(y,u,0.2,'Name','两个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;

Createidnlgreymodel object.

nlgr = idnlgrey(FileName,Order,Parameters,InitialStates,Ts,...'Name','两个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);
Open Live Script

Create estimation option set fornlgreyestto 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 bydcmotor_m.m文件。

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

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Time-domain estimation data, specified as aniddataobject.datahas the same input and output dimensions asinit_sys.

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

Constructed nonlinear grey-box model that configures the initial parameterization ofsys, specified as anidnlgreyobject.init_syshas the same input and output dimensions asdata. Createinit_sysusingidnlgrey.

Estimation options for nonlinear grey-box model identification, specified as annlgreyestOptions选项设置。

Output Arguments

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Nonlinear grey-box model with the same structure asinit_sys, returned as anidnlgreyobject. The parameters ofsysare estimated such that the response ofsysmatches the output signal in the estimation data.

Information about the estimation results and options used is stored in theReportproperty of the model.Report有以下字段:

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. SeeLoss Function and Model Quality Metricsfor 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 percentagefitpercent= 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. SeenlgreyestOptionsfor 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, seerng.
DataUsed

Attributes of the data used for estimation — Structure with the following fields:

Field Description
Name

Name of the data set.
Type

Data type — Foridnlgreymodels, this is set to时间域数据的.
Length

Number of data samples.
Ts

Sample time. This is equivalent todata.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 ofIntersamplehas 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

∞ -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, theTerminationfield is omitted.

For more information, seeEstimation Report.

Extended Capabilities

Version History

Introduced in R2015a

See Also

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