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tfestOptions

Options set for tfest

Syntax

opt = tfestOptions
opt = tfestOptions(Name,Value)

Description

opt = tfestOptions creates the default options set for tfest.

opt = tfestOptions(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.

'InitMethod'

Algorithm used to initialize the values of the numerator and denominator of the output of tfest.

Applies only for estimation of continuous-time transfer functions using time domain data.

InitMethod is a string that requires the following values:

  • 'iv' — Instrument Variable approach.

  • 'svf' — State Variable Filters approach.

  • 'gpmf' — Generalized Poisson Moment Functions approach.

  • 'n4sid' — Subspace state-space estimation approach.

  • 'all' — Combination of all of the preceding approaches. The software tries all these methods and selects the method that yields the smallest value of prediction error norm.

'InitOption'

Options associated with the method used to initialize the values of the numerator and denominator of the output of tfest.

InitOption is a structure with the following fields:

  • N4Weight — Calculates the weighting matrices used in the singular-value decomposition step of the 'n4sid' algorithm. Applicable when InitMethod is 'n4sid'.

    N4Weight is a string that requires the following values:

    • 'MOESP' — Uses the MOESP algorithm by Verhaegen.

    • 'CVA' — Uses the canonical variable algorithm (CVA) by Larimore.

    • 'SSARX' — A subspace identification method that uses an ARX estimation based algorithm to compute the weighting.

      Specifying this option allows unbiased estimates when using data that is collected in closed-loop operation. For more information about the algorithm, see [6].

    • 'auto' — The software automatically determines if the MOESP algorithm or the CVA algorithm should be used in the singular-value decomposition step.

    Default: ‘auto'

  • N4Horizon — Determines the forward and backward prediction horizons used by the 'n4sid' algorithm. Applicable when InitMethod is 'n4sid'.

    N4Horizon is a row vector with three elements:  [r sy su], where r is the maximum forward prediction horizon. The algorithm uses up to r step-ahead predictors. sy is the number of past outputs, and su is the number of past inputs that are used for the predictions. See pages 209 and 210 in [1] for more information. These numbers can have a substantial influence on the quality of the resulting model, and there are no simple rules for choosing them. Making 'N4Horizon' a k-by-3 matrix means that each row of 'N4Horizon' is tried, and the value that gives the best (prediction) fit to data is selected. k is the number of guesses of  [r sy su] combinations.

    If N4Horizon = 'auto', the software uses an Akaike Information Criterion (AIC) for the selection of sy and su.

    Default: 'auto'

  • FilterTimeConstant — Time constant of the differentiating filter used by the iv, svf, and gpmf initialization methods (see [4] and [5]).

    FilterTimeConstant specifies the cutoff frequency of the differentiating filter, Fcutoff, as:

    Ts is the sampling time of the estimation data.

    Specify FilterTimeConstant as a positive number, typically less than 1. A good value of FilterTimeConstant is the ratio of Ts to the dominating time constant of the system.

    Default: 0.1

  • MaxIter — Maximum number of iterations. Applicable when InitMethod is 'iv'.

    Default: 30

  • Tolerance — Convergence tolerance. Applicable when InitMethod is 'iv'.

    Default: 0.01

'InitialCondition'

Specifies how initial conditions are handled during estimation.

  • 'zero' — All initial conditions are taken as zero.

  • 'estimate' — The necessary initial conditions are treated as estimation parameters.

  • 'backcast' — The necessary initial conditions are estimated by a backcasting (backward filtering) process, described in [2].

  • 'auto' — An automatic choice among the preceding options is made, guided by the 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 requires one of 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.

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

'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 [3]. 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 the factor 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 only handle the Trace criterion.

  • 'grad' — The steepest descent gradient search method.

  • 'auto' — A choice among the preceding options is made in the algorithm. The descent direction is calculated using 'gn', 'gna', 'lm', and 'grad' successively, at each iteration until a sufficient reduction in error is achieved.

'SearchOption'

Options set for the search algorithm.

 SearchOption structure when SearchMethod is specified as 'gn', 'gna', 'lm', 'grad', or 'auto'

 SearchOption structure when SearchMethod is specified as ‘lsqnonlin'

'Advanced'

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 value.

    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 conditions.

    The initial condition is estimated when

    • 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

'OutputWeight'

Specifies criterion used during minimization.

OutputWeight can have the following values:

  • 'noise' — Minimize , 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, 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 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.

Output Arguments

opt

Option set containing the specified options for tfest.

Examples

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Specify Options for Transfer Function Estimation

Create an options set for tfest using the 'n4sid' initialization algorithm and set the Display to 'on'.

opt = tfestOptions('InitMethod','n4sid','Display','on');

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

opt = tfestOptions;
opt.InitMethod = 'n4sid';
opt.Display = 'on';

References

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

[2] Knudsen, T. "New method for estimating ARMAX models," In Proceedings of 10th IFAC Symposium on System Identification, SYSID'94, Copenhagen, Denmark, July 1994, Vol. 2, pp. 611–617.

[3] 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.

[4] Garnier, H., M. Mensler, and A. Richard. "Continuous-time Model Identification From Sampled Data: Implementation Issues and Performance Evaluation" International Journal of Control, 2003, Vol. 76, Issue 13, pp 1337–1357.

[5] Ljung, L. "Experiments With Identification of Continuous-Time Models." Proceedings of the 15th IFAC Symposium on System Identification. 2009.

[6] Jansson, M. "Subspace identification and ARX modeling." 13th IFAC Symposium on System Identification , Rotterdam, The Netherlands, 2003.

See Also

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