greyestOptions
Option set for greyest
Description
Use an greyestOptions
object to specify options for estimating
greybox models using the greyest
function. You can specify options such
as the handling of initial states, stability enforcement, and the numerical search method to
be used in estimation.
Creation
Properties
InitialState
— Handling of initial states
'auto'
(default)  'model'
 'zero'
 'estimate'
 'backcast'
Handling of initial states during estimation, specified as one of the following values:
'model'
— The initial state is parameterized by the ODE file used by theidgrey
model. The ODE file must return 6 or more output arguments.'zero'
— The initial state is set to zero. Any values returned by the ODE file are ignored.'estimate'
— The initial state is treated as an independent estimation parameter.'backcast'
— The initial state is estimated using the best least squares fit.'auto'
— The software chooses the method to handle initial states based on the estimation data.Vector of doubles — Specify a column vector of length Nx, where Nx is the number of states. For multiexperiment data, specify a matrix with Ne columns, where Ne is the number of experiments. The specified values are treated as fixed values during the estimation process.
DisturbanceModel
— Handling of disturbance component
'auto'
(default)  'model'
 'fixed'
 'none'
 'estimate'
Handling of the disturbance component (K) during estimation, specified as one of the following values:
'model'
— K values are parameterized by the ODE file used by theidgrey
model. The ODE file must return 5 or more output arguments.'fixed'
— The value of theK
property of theidgrey
model is fixed to its original value.'none'
— K is fixed to zero. Any values returned by the ODE file are ignored.'estimate'
— K is treated as an independent estimation parameter.'auto'
— The software chooses the method to handle how the disturbance component is handled during estimation. The software uses the'model'
method if the ODE file returns 5 or more output arguments with a finite value for K. Else, the software uses the'fixed'
method.
Note
Noise model cannot be estimated using frequency domain data.
Focus
— Error to be minimized
'prediction'
(default)  'simulation'
Error to be minimized in the loss function during estimation,
specified as the commaseparated pair consisting of 'Focus'
and
one of the following values:
'prediction'
— The onestep ahead prediction error between measured and predicted outputs is minimized during estimation. As a result, the estimation focuses on producing a good predictor model.'simulation'
— The simulation error between measured and simulated outputs is minimized during estimation. As a result, the estimation focuses on making a good fit for simulation of model response with the current inputs.
The Focus
option can be interpreted as a
weighting filter in the loss function. For more information, see Loss Function and Model Quality Metrics.
WeightingFilter
— Weighting prefilter
[]
(default)  vector  matrix  cell array  linear system
Weighting prefilter applied to the loss function to be minimized
during estimation. To understand the effect of WeightingFilter
on
the loss function, see Loss Function and Model Quality Metrics.
Specify WeightingFilter
as one of the following
values:
[]
— No weighting prefilter is used.Passbands — Specify a row vector or matrix containing frequency values that define desired passbands. You select a frequency band where the fit between estimated model and estimation data is optimized. For example,
[wl,wh]
wherewl
andwh
represent lower and upper limits of a passband. For a matrix with several rows defining frequency passbands,[w1l,w1h;w2l,w2h;w3l,w3h;...]
, the estimation algorithm uses the union of the frequency ranges to define the estimation passband.Passbands are expressed in
rad/TimeUnit
for timedomain data and inFrequencyUnit
for frequencydomain data, whereTimeUnit
andFrequencyUnit
are the time and frequency units of the estimation data.SISO filter — Specify a singleinputsingleoutput (SISO) linear filter in one of the following ways:
A SISO LTI model
{A,B,C,D}
format, which specifies the statespace matrices of a filter with the same sample time as estimation data.{numerator,denominator}
format, which specifies the numerator and denominator of the filter as a transfer function with same sample time as estimation data.This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function.
Weighting vector — Applicable for frequencydomain data only. Specify a column vector of weights. This vector must have the same length as the frequency vector of the data set,
Data.Frequency
. Each input and output response in the data is multiplied by the corresponding weight at that frequency.
EnforceStability
— Control whether to enforce stability of model
false
(default)  true
Control whether to enforce stability of estimated model, specified
as the commaseparated pair consisting of 'EnforceStability'
and
either true
or false
.
EstimateCovariance
— Option to generate parameter covariance data
true
(default)  false
Option to generate parameter covariance data, specified as true
or
false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Option to display estimation progress
'off'
(default)  'on'
Option to display the estimation progress, specified as one of the following values:
'on'
— Information on model structure and estimation results are displayed in a progressviewer window.'off'
— No progress or results information is displayed.
InputInterSample
— Inputchannel intersample behavior
'auto'
 'zoh'
 'foh'
 'bl'
Inputchannel intersample behavior for transformations between discrete time and continuous time, specified as 'auto'
, 'zoh'
,'foh'
, or 'bl'
.
The definitions of the three behavior values are as follows:
'zoh'
— Zeroorder hold maintains a piecewiseconstant input signal between samples.'foh'
— Firstorder hold maintains a piecewiselinear input signal between samples.'bl'
— Bandlimited behavior specifies that the continuoustime input signal has zero power above the Nyquist frequency.
iddata
objects have a similar property,
data.InterSample
, that contains the same behavior value options.
When the InputInterSample
value is 'auto'
and
the estimation data is in an iddata
object data
, the
software uses the data.InterSample
value. When the estimation data
is instead contained in a timetable or a matrix pair, with the 'auto'
option, the software uses 'zoh'
.
The software applies the same option value to all channels and all experiments.
InputOffset
— Removal of offset from timedomain input data during estimation
[]
(default)  vector of positive integers  matrix
Removal of offset from timedomain input data during estimation, specified as one of the following:
A column vector of positive integers of length Nu, where Nu is the number of inputs.
[]
— Indicates no offset.NubyNe matrix — For multiexperiment data, specify
InputOffset
as an NubyNe matrix. Nu is the number of inputs and Ne is the number of experiments.
Each entry specified by InputOffset
is
subtracted from the corresponding input data.
OutputOffset
— Removal of offset from timedomain output data during estimation
[]
(default)  vector  matrix
Removal of offset from timedomain output data during estimation, specified as one of the following:
A column vector of length Ny, where Ny is the number of outputs.
[]
— Indicates no offset.NybyNe matrix — For multiexperiment data, specify
OutputOffset
as a NybyNe matrix. Ny is the number of outputs, and Ne is the number of experiments.
Each entry specified by OutputOffset
is
subtracted from the corresponding output data.
OutputWeight
— Weighting of prediction errors in multioutput estimations
[]
(default)  'noise'
 positive semidefinite symmetric matrix
Weighting of prediction errors in multioutput estimations, specified as one of the following values:
'noise'
— Minimize $$\mathrm{det}(E\text{'}*E/N)$$, where E represents the prediction error andN
is the number of data samples. This choice is optimal in a statistical sense and leads to maximum likelihood estimates if nothing is known about the variance of the noise. It uses the inverse of the estimated noise variance as the weighting function.Note
OutputWeight
must not be'noise'
ifSearchMethod
is'lsqnonlin'
.Positive semidefinite symmetric matrix (
W
) — Minimize the trace of the weighted prediction error matrixtrace(E'*E*W/N)
, where:E is the matrix of prediction errors, with one column for each output, and W is the positive semidefinite symmetric matrix of size equal to the number of outputs. Use W to specify the relative importance of outputs in multipleoutput models, or the reliability of corresponding data.
N
is the number of data samples.
[]
— The software chooses between'noise'
and using the identity matrix forW
.
This option is relevant for only multioutput models.
Regularization
— Options for regularized estimation of model parameters
structure
Options for regularized estimation of model parameters, specified as a structure with the fields in the following table. For more information on regularization, see Regularized Estimates of Model Parameters.
Field Name  Description  Default 

Lambda  Constant that determines the bias versus variance tradeoff. Specify a positive scalar to add the regularization term to the estimation cost. The default value of 0 implies no regularization.  0 
R  Weighting matrix. Specify a vector of nonnegative numbers or a square positive semidefinite matrix. The length must be equal to the number of free parameters of the model. For blackbox models, using the default value is
recommended. For structured and greybox models, you can also
specify a vector of The default value of 1 implies a value of
 1 
Nominal  The nominal value towards which the free parameters are pulled during estimation. The default value of 0 implies that
the parameter values are pulled towards zero. If you are refining a
model, you can set the value to  0 
SearchMethod
— Numerical search method used for iterative parameter estimation
'auto'
(default)  'gn'
 'gna'
 'lm'
 'grad'
 'lsqnonlin'
 'fmincon'
Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.
SearchMethod  Description 

'auto'  Automatic method selection A combination of the
line search algorithms, 
'gn'  Subspace GaussNewton leastsquares search Singular
values of the Jacobian matrix less than

'gna'  Adaptive subspace GaussNewton search Eigenvalues
less than 
'lm'  LevenbergMarquardt least squares search Each
parameter value is 
'grad'  Steepest descent leastsquares search 
'lsqnonlin'  Trustregionreflective algorithm of This algorithm requires Optimization Toolbox™ software. 
'fmincon'  Constrained nonlinear solvers You can use the
sequential quadratic programming (SQP) and trustregionreflective
algorithms of the

SearchOptions
— Option set for search algorithm
search option set
Option set for the search algorithm, specified as a search option set with fields that
depend on the value of SearchMethod
.
SearchOptions
Structure When SearchMethod
is Specified
as 'gn'
, 'gna'
, 'lm'
,
'grad'
, or 'auto'
Field Name  Description  Default  

Tolerance  Minimum percentage difference between the current value
of the loss function and its expected improvement after the next iteration,
specified as a positive scalar. When the percentage of expected improvement
is less than  0.01  
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when Setting
Use
 20  
Advanced  Advanced search settings, specified as a structure with the following fields.

SearchOptions
Structure When SearchMethod
is Specified
as 'lsqnonlin'
Field Name  Description  Default 

FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The
value of  1e5 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of  1e6 
MaxIterations  Maximum number of iterations during lossfunction minimization, specified as a positive
integer. The iterations stop when The value of
 20 
SearchOptions
Structure When SearchMethod
is Specified
as 'fmincon'
Field Name  Description  Default 

Algorithm 
For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).  'sqp' 
FunctionTolerance  Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.  1e6 
StepTolerance  Termination tolerance on the estimated parameter values, specified as a positive scalar.  1e6 
MaxIterations  Maximum number of iterations during loss function minimization, specified as a positive
integer. The iterations stop when  100 
Advanced
— Additional advanced options
structure
Additional advanced options, specified as a structure with the fields in the following table.
Field Name  Description  Default  

ErrorThreshold  Error threshold at which to adjust the weight of large errors from quadratic to linear. Errors larger than
An  0  
MaxSize  Maximum number of elements in a segment when inputoutput data is split into segments.
 250000  
StabilityThreshold  Threshold for stability tests.
 
AutoInitThreshold  Threshold at which to automatically estimate initial conditions. The software estimates the initial conditions when: $$\frac{\Vert {y}_{p,z}{y}_{meas}\Vert}{\Vert {y}_{p,e}{y}_{meas}\Vert}>\text{AutoInitThreshold}$$  1.05 
Examples
Create Default Options Set for Linear Grey Box Estimation
opt = greyestOptions;
Specify Options for Linear Grey Box Estimation
Create an options set for greyest
using the 'backcast'
algorithm to initialize the state. Specify Display
as 'on'
.
opt = greyestOptions('InitialState','backcast','Display','on');
Alternatively, use dot notation to set the values of opt
.
opt = greyestOptions; opt.InitialState = 'backcast'; opt.Display = 'on';
References
[1] Wills, Adrian, B. Ninness, and S. Gibson. "On GradientBased Search for Multivariable System Estimates". Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, July 3–8, 2005. Oxford, UK: Elsevier Ltd., 2005.
[2] Ljung, Lennart. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
Version History
Introduced in R2012aR2022b: InputInterSample
option allows intersample behavior specification for continuous models estimated from timetables or matrices.
iddata
objects contain an InterSample
property that
describes the behavior of the signal between sample points. The
InputInterSample
option implements a version of that property in
greyestOptions
so that intersample behavior can be specified also when
estimation data is stored in timetables or matrices.
R2018a: Renaming of Estimation and Analysis Options
The names of some estimation and analysis options were changed in R2018a. Prior names still work. For details, see the R2018a release note Renaming of Estimation and Analysis Options.
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