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spectrumestOptions

Option set for spectrumest

Since R2022b

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Description

Use a spectrumestOptions object to specify options for estimating spectral transfer function models using the spectrumest function. You can specify options such as the numerical search method to be used in estimation and whether to display estimation progress.

Creation

Syntax

opt = spectrumestOptions
opt = spectrumestOptions(Name=Value)

Description

opt = spectrumestOptions creates the default option set for spectrumest. To modify the properties of this option set for your specific application, use dot notation.

example

opt = spectrumestOptions(Name=Value) creates an option set with the properties specified using one or more name-value arguments.

example

Properties

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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 progress-viewer window.

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

Input-channel 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' — 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.

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.

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.

Weighting prefilter applied to the loss function to be minimized during estimation, specified as one of the values in the following table. To understand the effect of WeightingFilter on the loss function, see Loss Function and Model Quality Metrics.

ValueDescription
[] 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, specify [wl,wh], where wl and wh 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 time-domain data and in FrequencyUnit for frequency-domain data, where TimeUnit and FrequencyUnit are the time and frequency units of the estimation data.

Weighting vector

Specify a column vector of weights. This vector must have the same length as the power spectrum data set. Each input and output response in the data is multiplied by the corresponding weight at that frequency.

'inv'

Use 1.0/sqrt(H) as the weighting filter, where H is the power spectrum data. Use this option for capturing relatively low amplitude dynamics in data or for fitting data with high modal density. This option also makes it easier to specify channel-dependent weighting filters for MIMO frequency-response data.

'invsqrt'

Use 1.0/H^(0.25) as the weighting filter. Use this option for capturing relatively low amplitude dynamics in data, or for fitting data with high modal density. This option also makes it easier to specify channel-dependent weighting filters for MIMO frequency-response data.

Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.

SearchMethodDescription
'auto'

Automatic method selection

A combination of the line search algorithms, 'gn', 'lm', 'gna', and 'grad', is tried in sequence at each iteration. The first descent direction leading to a reduction in estimation cost is used.

'gn'

Subspace Gauss-Newton least-squares search

Singular values of the Jacobian matrix less than GnPinvConstant*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated as JTJ. If this direction shows no improvement, the function tries the gradient direction.

'gna'

Adaptive subspace Gauss-Newton search

Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv contains the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitialGnaTolerance (see Advanced in 'SearchOptions' for more information). This value is increased by the factor LMStep each time the search fails to find a lower value of the criterion in fewer than five bisections. This value is decreased by the factor 2*LMStep each time a search is successful without any bisections.

'lm'

Levenberg-Marquardt least squares search

Each parameter value is -pinv(H+d*I)*grad from the previous value. 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'

Trust-region-reflective algorithm of lsqnonlin (Optimization Toolbox)

This algorithm requires Optimization Toolbox™ software.

'fmincon'

Constrained nonlinear solvers

You can use the sequential quadratic programming (SQP) and trust-region-reflective algorithms of the fmincon (Optimization Toolbox) solver. If you have Optimization Toolbox software, you can also use the interior-point and active-set algorithms of the fmincon solver. Specify the algorithm in the SearchOptions.Algorithm option. The fmincon algorithms might result in improved estimation results in the following scenarios:

  • Constrained minimization problems when bounds are imposed on the model parameters.

  • Model structures where the loss function is a nonlinear or nonsmooth function of the parameters.

  • Multiple-output model estimation. A determinant loss function is minimized by default for multiple-output 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, the fmincon algorithms can offer better efficiency and accuracy for multiple-output model estimations.

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 NameDescriptionDefault
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 Tolerance, the iterations stop. The estimate of the expected loss-function improvement at the next iteration is based on the Gauss-Newton vector computed for the current parameter value.

0.01
MaxIterations

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as Tolerance.

Setting MaxIterations = 0 returns the result of the start-up procedure.

Use sys.Report.Termination.Iterations to get the actual number of iterations during an estimation, where sys is an idtf model.

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Advanced

Advanced search settings, specified as a structure with the following fields.

Field NameDescriptionDefault
GnPinvConstant

Jacobian matrix singular value threshold, specified as a positive scalar. Singular values of the Jacobian matrix that are smaller than GnPinvConstant*max(size(J)*norm(J)*eps) are discarded when computing the search direction. Applicable when SearchMethod is 'gn'.

10000
InitialGnaTolerance

Initial value of gamma, specified as a positive scalar. Applicable when SearchMethod is 'gna'.

0.0001
LMStartValue

Starting value of search-direction length d in the Levenberg-Marquardt method, specified as a positive scalar. Applicable when SearchMethod is 'lm'.

0.001
LMStep

Size of the Levenberg-Marquardt step, specified as a positive integer. The next value of the search-direction length d in the Levenberg-Marquardt method is LMStep times the previous one. Applicable when SearchMethod is 'lm'.

2
MaxBisections

Maximum number of bisections used for line search along the search direction, specified as a positive integer.

25
MaxFunctionEvaluations

Maximum number of calls to the model file, specified as a positive integer. Iterations stop if the number of calls to the model file exceeds this value.

Inf
MinParameterChange

Smallest parameter update allowed per iteration, specified as a nonnegative scalar.

0
RelativeImprovement

Relative improvement threshold, specified as a nonnegative scalar. Iterations stop if the relative improvement of the criterion function is less than this value.

0
StepReduction

Step reduction factor, specified as a positive scalar that is greater than 1. The suggested parameter update is reduced by the factor StepReduction after each try. This reduction continues until MaxBisections tries are completed or a lower value of the criterion function is obtained.

StepReduction is not applicable for a SearchMethod of 'lm' (Levenberg-Marquardt method).

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SearchOptions Structure When SearchMethod Is Specified as 'lsqnonlin'

Field NameDescriptionDefault
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 FunctionTolerance is the same as that of opt.SearchOptions.Advanced.TolFun.

1e-5
StepTolerance

Termination tolerance on the estimated parameter values, specified as a positive scalar.

The value of StepTolerance is the same as that of opt.SearchOptions.Advanced.TolX.

1e-6
MaxIterations

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.

The value of MaxIterations is the same as that of opt.SearchOptions.Advanced.MaxIter.

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SearchOptions Structure When SearchMethod Is Specified as 'fmincon'

Field NameDescriptionDefault
Algorithm

fmincon optimization algorithm, specified as one of the following:

  • 'sqp' — Sequential quadratic programming algorithm. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. It is not a large-scale algorithm. For more information, see Large-Scale vs. Medium-Scale Algorithms (Optimization Toolbox).

  • 'trust-region-reflective' — Subspace trust-region method based on the interior-reflective Newton method. It is a large-scale algorithm.

  • 'interior-point' — Large-scale algorithm that requires Optimization Toolbox software. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results.

  • 'active-set' — Requires Optimization Toolbox software. The algorithm can take large steps, which adds speed. It is not a large-scale 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.

1e-6
StepTolerance

Termination tolerance on the estimated parameter values, specified as a positive scalar.

1e-6
MaxIterations

Maximum number of iterations during loss function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.

100

Additional advanced options, specified as a structure with the fields in the following table.

Field NameDescriptionDefault
MaxSize

Maximum number of elements in a segment when input-output data is split into segments.

MaxSize must be a positive integer value.

250000

Examples

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Open Live Script
opt = spectrumestOptions
Option set for the spectrumest command:

               Display: 'off'
      InputInterSample: 'auto'
    EstimateCovariance: 1
       WeightingFilter: []
          SearchMethod: 'auto'
         SearchOptions: '<Optimization options set>'
              Advanced: [1x1 struct]
Open Live Script

Create an options set for spectrumest using the 'gn' search method, and set the Display to 'on'.

opt = spectrumestOptions(SearchMethod='gn',Display='on');

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

opt = spectrumestOptions;
opt.SearchMethod = 'gn';
opt.Display = 'on';

Version History

Introduced in R2022b

See Also