Accelerating the pace of engineering and science

# procestOptions

Options set for procest

## Syntax

opt = procestOptions
opt = procestOptions(Name,Value)

## Description

opt = procestOptions creates the default options set for procest.

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

## Input Arguments

expand all

### 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.

### 'InitialCondition' —

Specify how initial conditions are handled during estimation.

InitialCondition requires one of the following values:

• 'zero' — The initial condition is set to zero.

• 'estimate' — The initial condition is treated as an independent estimation parameter.

• 'backcast' — The initial condition is estimated using the best least squares fit.

• 'auto' — The software chooses the method to handle initial condition based on the estimation data.

### 'DisturbanceModel' —

Specify how the handling of additive noise (H) during estimation for the model

$y=G\left(s\right)u+H\left(s\right)e$

e is white noise, u is the input and y is the output.

H(s) is stored in the NoiseTF property of the numerator and denominator of idproc models.

DisturbanceModel requires one of the following strings:

• 'none'H is fixed to one.

• 'estimate'H is treated as an estimation parameter. The software uses the value of the NoiseTF property as the initial guess.

• 'ARMA1' — The software estimates H as a first-order ARMA model

$\frac{1+cs}{1+ds}$

• 'ARMA2' — The software estimates H as a second-order ARMA model

$\frac{1+{c}_{1}s+{c}_{2}{s}^{2}}{1+{d}_{1}s+{d}_{2}{s}^{2}}$

• 'fixed' — The software fixes the value of the NoiseTF property of the idproc model as the value of H.

 Note:   A 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 — Automatically calculates the weighting function as a product of the input spectrum and the inverse of the noise model. The weighting function minimizes the one-step-ahead prediction. This approach typically favors fitting small time intervals (higher frequency range). From a statistical-variance point of view, this weighting function is optimal. However, this method neglects the approximation aspects (bias) of the fit. Use 'stability' when you want to ensure a stable model.

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

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

where 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. You receive an estimation result that is the same as if you had first prefiltered using idfilt.

• Weighting vector — For frequency-domain data only, enter a column vector of weights for 'Focus'. 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.

### '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' —

Removes offset from time domain input data during estimation.

Specify InputOffset as one of the following:

• 'estimate' — The software treats the input offsets as an estimation parameter.

• 'auto' — The software chooses the method to handle input offsets based on the estimation data and the model structure. The estimation either assumes zero input offset or estimates the input offset.

For example, the software estimates the input offset for a model that contains an integrator.

• A column vector of length Nu, where Nu is the number of inputs.

Use [] to specify no offsets.

In case of multi-experiment 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.

• A parameter object, constructed using param.Continuous, that imposes constraints on how the software estimates the input offset.

For example, create a parameter object for a 2-input model estimation. Specify the first input offset as fixed to zero and the second input offset as an estimation parameter.

```opt = procestOptions;
u0 = param.Continuous('u0',[0;NaN]);
u0.Free(1) = false;
opt.Inputoffset = u0;```

### '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 when nothing is known about the variance of the noise. It 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 requires one of the following values:

• 'gn' — The subspace Gauss-Newton direction. Singular values of the Jacobian matrix less than GnPinvConst*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated by JTJ. If there is no improvement in this direction, the function tries the gradient direction.

• 'gna' — An adaptive version of subspace Gauss-Newton approach, suggested by Wills and Ninness [2]. Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv are the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitGnaTol (see Advanced for more information). gamma is increased by the factor LMStep each time the search fails to find a lower value of the criterion in less than 5 bisections. gamma is decreased by a factor of 2*LMStep each time a search is successful without any bisections.

• 'lm' — Uses the Levenberg-Marquardt method so that the next parameter value is -pinv(H+d*I)*grad from the previous one, where 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.

• 'lsqnonlin' — Uses lsqnonlin optimizer from Optimization Toolbox™ software. This search method can handle only the Trace criterion.

• '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 [1].

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 condition.

The initial condition 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 InitialCondition is 'auto'.

Default: 1.05

## Output Arguments

 opt Option set containing the specified options for procest.

## Examples

expand all

### Create Default Options Set for Process Model Estimation

`opt = procestOptions;`

### Specify Options for Process Model Estimation

Create an options set for procest using the 'stability' for Focus and set the Display to 'on'.

`opt = procestOptions('Focus','stability','Display','on');`

Alternatively, use dot notation to set the values of opt.

```opt = procestOptions;
opt.Focus = 'stability';
opt.Display = 'on';```

## References

[1] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.

[2] 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.