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# greyestOptions

Option set for greyest

## Syntax

opt = greyestOptions
opt = greyestOptions(Name,Value)

## Description

opt = greyestOptions creates the default options set for greyest.

opt = greyestOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

## Input Arguments

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### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

### 'InitialState' —

Specify how initial states are handled during estimation.

InitialState requires one of the following strings:

• 'model' — The initial state is parameterized by the ODE file used by the idgrey 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' —

Specify how the disturbance component (K) is handled during estimation.

DisturbanceModel requires one of the following strings:

• 'model'K values are parameterized by the ODE file used by the idgrey model. The ODE file must return 5 or more output arguments.

• 'fixed' — The value of the k property of the idgrey 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' —

Defines how the errors e between the measured and the modeled outputs are weighed at specific frequencies during the minimization of the prediction error.

Higher weighting at specific frequencies emphasizes the requirement for a good fit at these frequencies.

Focus can take the following values:

• 'simulation' — Estimates the model using the frequency weighting of the transfer function that is given by the input spectrum. Typically, this method favors the frequency range where the input spectrum has the most power.

This method provides a stable model.

• 'prediction' — Same as 'simulation', except that it does not enforce the stability of the resulting model.

• 'stability' — Same as 'prediction' but with model stability enforced.

• Passbands — Row vector or matrix containing frequency values that define desired passbands. For example:

```[wl,wh]
[w1l,w1h;w2l,w2h;w3l,w3h;...]```

wl and wh represent upper and lower limits of a passband. For a matrix with several rows defining frequency passbands, the algorithm uses union of frequency ranges to define the estimation passband.

• SISO filter — Enter any SISO linear filter in any of the following ways:

• A single-input-single-output (SISO) linear system

• The {A,B,C,D} format, which specifies the state-space matrices of the filter

• The {numerator, denominator} format, which specifies the numerator and denominator of the filter transfer function

This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function. To obtain a good model fit for a specific frequency range, you must choose the filter with a passband in this range. The estimation result is the same if you first prefilter the data using idfilt.

• Weighting vector — For frequency-domain data only, enter a column vector of weights for 'Focus'. This vector must have the same size as length of 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.

### 'EstCovar' — Control whether to generate parameter covariance datatrue (default) | false

Controls whether parameter covariance data is generated, specified as true or false.

If EstCovar 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 strings:

Display requires one of the following strings:

• 'on' — Information on model structure and estimation results are displayed in a progress-viewer window

• 'off' — No progress or results information is displayed

### 'InputOffset' — Remove offset from time-domain input data during estimation[] (default) | vector of positive integers

Removes offset from time-domain input data during estimation, specified as a vector of positive integers.

Specify as a column vector of length Nu, where Nu is the number of inputs.

Use [] to indicate no offset.

For multiexperiment data, specify InputOffset as a Nu-by-Ne 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' — Remove offset from time-domain output data during estimation[] (default) | vector

Removes offset from time domain output data during estimation, specified as a vector of positive integers or [].

Specify as a column vector of length Ny, where Ny is the number of outputs.

Use [] to indicate no offset.

For multiexperiment data, specify OutputOffset as a Ny-by-Ne 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' —

Specifies criterion used during minimization.

OutputWeight can have the following values:

• 'noise' — Minimize $\mathrm{det}\left(E\text{'}*E\right)$, where E represents the prediction error. This choice is optimal in a statistical sense and leads to the maximum likelihood estimates in case nothing is known about the variance of the noise. This option uses the inverse of the estimated noise variance as the weighting function.

• Positive semidefinite symmetric matrix (W) — Minimize the trace of the weighted prediction error matrix trace(E'*E*W). E is the matrix of prediction errors, with one column for each output. 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 multiple-input, multiple-output models, or the reliability of corresponding data.

This option is relevant only for multi-input, multi-output models.

• [] — The software chooses between the 'noise' or using the identity matrix for W.

### 'Regularization' —

Options for regularized estimation of model parameters. For more information on regularization, see Regularized Estimates of Model Parameters.

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 semi-definite matrix. The length must be equal to the number of free parameters of the model.

For black-box models, using the default value is recommended. For structured and grey-box 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), where npfree 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' —

Search method used for iterative parameter estimation.

SearchMethod is a string that can take the following values:

• gn — The subspace Gauss-Newton direction.

• gna — An adaptive version of subspace Gauss-Newton approach, suggested by Wills and Ninness [1].

• lm — Uses the Levenberg-Marquardt method.

• lsqnonlin — Uses the trust region reflective algorithm. Requires Optimization Toolbox™ software.

• auto — The algorithm chooses one of the preceding options. The descent direction is calculated using gn, gna, lm, and grad successively at each iteration. The iterations continue until a sufficient reduction in error is achieved.

### 'SearchOption' —

Advanced is 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 criteria. The standard deviation is estimated robustly as the median of the absolute deviations from the median and divided by 0.7. For more information on robust norm choices, see section 15.2 of [2].

ErrorThreshold = 0 disables robustification and leads to a purely quadratic criterion. When estimating with frequency-domain data, the software sets ErrorThreshold to zero. For time-domain data that contains outliers, try setting ErrorThreshold to 1.6.

Default: 0

• MaxSize — Specifies the maximum number of elements in a segment when input-output 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 right-most pole to test the stability of continuous-time models. A model is considered stable when its right-most pole is to the left of s.

Default: 0

• z — Specifies the maximum distance of all poles from the origin to test stability of discrete-time models. A model is considered stable if all poles are within the distance z from the origin.

Default: 1+sqrt(eps)

• AutoInitThreshold — Specifies when to automatically estimate the initial state.

The initial state is estimated when

$\frac{‖{y}_{p,z}-{y}_{meas}‖}{‖{y}_{p,e}-{y}_{meas}‖}>\text{AutoInitThreshold}$

• ymeas is the measured output.

• yp,z is the predicted output of a model estimated using zero initial states.

• yp,e is the predicted output of a model estimated using estimated initial states.

Applicable when InitialState is 'auto'.

Default: 1.05

## Output Arguments

 opt Option set containing the specified options for greyest.

## Examples

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### 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 Gradient-Based 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: Prentice-Hall PTR, 1999.