greyestOptions
Option set for greyest
Syntax
opt = greyestOptions
opt = greyestOptions(Name,Value)
Description
creates
the default options set for opt
= greyestOptionsgreyest
.
creates
an option set with the options specified by one or more opt
= greyestOptions(Name,Value
)Name,Value
pair
arguments.
Input Arguments
NameValue Arguments
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
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
.
Data Types: logical
EstimateCovariance
— Control whether to generate parameter covariance data
true
(default)  false
Controls whether parameter covariance data is generated, specified as
true
or false
.
If EstimateCovariance
is true
, then use
getcov
to fetch the covariance matrix
from the estimated model.
Display
— Specify whether to display the estimation progress
'off'
(default)  'on'
Specify whether 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.
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 the commaseparated pair consisting of 'InputOffset'
and
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 the commaseparated pair consisting of 'OutputOffset'
and
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 the'noise'
or 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. For more information on regularization, see Regularized Estimates of Model Parameters.
Regularization
is a structure with the following
fields:
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 zero implies no regularization.
Default: 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
np
positive numbers such that each entry denotes the confidence in the value of the associated parameter.The default value of 1 implies a value of
eye(npfree)
, wherenpfree
is the number of free parameters.Default: 1
Nominal
— The nominal value towards which the free parameters are pulled during estimation.The default value of zero implies that the parameter values are pulled towards zero. If you are refining a model, you can set the value to
'model'
to pull the parameters towards the parameter values of the initial model. The initial parameter values must be finite for this setting to work.Default: 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 commaseparated pair consisting of 'SearchMethod'
and
one of the following:
'auto'
— A combination of the line search algorithms,'gn'
,'lm'
,'gna'
, and'grad'
methods is tried in sequence at each iteration. The first descent direction leading to a reduction in estimation cost is used.'gn'
— Subspace GaussNewton least squares search. Singular values of the Jacobian matrix less thanGnPinvConstant*eps*max(size(J))*norm(J)
are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated as J^{T}J. If there is no improvement in this direction, the function tries the gradient direction.'gna'
— Adaptive subspace GaussNewton search. Eigenvalues less thangamma*max(sv)
of the Hessian are ignored, where sv contains the singular values of the Hessian. The GaussNewton direction is computed in the remaining subspace. gamma has the initial valueInitialGnaTolerance
(seeAdvanced
in'SearchOptions'
for more information). This value is increased by the factorLMStep
each time the search fails to find a lower value of the criterion in fewer than five bisections. This value is decreased by the factor2*LMStep
each time a search is successful without any bisections.'lm'
— LevenbergMarquardt least squares search, where the next parameter value ispinv(H+d*I)*grad
from the previous one. H is the Hessian, I is the identity matrix, and grad is the gradient. d is a number that is increased until a lower value of the criterion is found.'grad'
— Steepest descent least squares search.'lsqnonlin'
— Trustregionreflective algorithm oflsqnonlin
(Optimization Toolbox). Requires Optimization Toolbox™ software.'fmincon'
— Constrained nonlinear solvers. You can use the sequential quadratic programming (SQP) and trustregionreflective algorithms of thefmincon
(Optimization Toolbox) solver. If you have Optimization Toolbox software, you can also use the interiorpoint and activeset algorithms of thefmincon
solver. Specify the algorithm in theSearchOptions.Algorithm
option. Thefmincon
algorithms may result in improved estimation results in the following scenarios:Constrained minimization problems when there are bounds imposed on the model parameters.
Model structures where the loss function is a nonlinear or non smooth function of the parameters.
Multioutput model estimation. A determinant loss function is minimized by default for multioutput model estimation.
fmincon
algorithms are able to minimize such loss functions directly. The other search methods such as'lm'
and'gn'
minimize the determinant loss function by alternately estimating the noise variance and reducing the loss value for a given noise variance value. Hence, thefmincon
algorithms can offer better efficiency and accuracy for multioutput model estimations.
SearchOptions
— Option set for the search algorithm
search option set
Option set for the search algorithm, specified as the commaseparated pair consisting
of 'SearchOptions'
and 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 
Advanced  Advanced search settings, specified as an option set
for For more information, see the Optimization Options table in Optimization Options (Optimization Toolbox).  Use optimset('lsqnonlin') to create a default
option set. 
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 following fields:
ErrorThreshold
— Specifies when to adjust the weight of large errors from quadratic to linear.Errors larger than
ErrorThreshold
times the estimated standard deviation have a linear weight in the loss function. The standard deviation is estimated robustly as the median of the absolute deviations from the median of the prediction errors, divided by0.7
. For more information on robust norm choices, see section 15.2 of [2].ErrorThreshold = 0
disables robustification and leads to a purely quadratic loss function. When estimating with frequencydomain data, the software setsErrorThreshold
to zero. For timedomain data that contains outliers, try settingErrorThreshold
to1.6
.Default: 0
MaxSize
— Specifies the maximum number of elements in a segment when inputoutput data is split into segments.MaxSize
must be a positive integer.Default: 250000
StabilityThreshold
— Specifies thresholds for stability tests.StabilityThreshold
is a structure with the following fields:s
— Specifies the location of the rightmost pole to test the stability of continuoustime models. A model is considered stable when its rightmost pole is to the left ofs
.Default: 0
z
— Specifies the maximum distance of all poles from the origin to test stability of discretetime models. A model is considered stable if all poles are within the distancez
from the origin.Default:
1+sqrt(eps)
AutoInitThreshold
— Specifies when to automatically estimate the initial state.The initial state is estimated when
$$\frac{\Vert {y}_{p,z}{y}_{meas}\Vert}{\Vert {y}_{p,e}{y}_{meas}\Vert}>\text{AutoInitThreshold}$$
y_{meas} is the measured output.
y_{p,z} is the predicted output of a model estimated using zero initial states.
y_{p,e} is the predicted output of a model estimated using estimated initial states.
Applicable when
InitialState
is'auto'
.Default:
1.05
Output Arguments
opt
— Options set for greyest
greyestOptions
option set
Option set for greyest
,
returned as an greyestOptions
option set.
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';
Compatibility Considerations
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.
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, L. System Identification: Theory for the User. Upper Saddle River, NJ: PrenticeHall PTR, 1999.
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