LTPDA Toolbox™

contents

Method ao/sDomainFit

  sDomainFit performs a fitting loop to identify model order and
  parameters.
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  DESCRIPTION: sDomainFit fit a partial fraction model to frequency
      response data using  the function utils.math.vcfit.
 
      The function performs a fitting loop to automatically identify model
      order and parameters in s-domain. Output is a s-domain model expanded
      in partial fractions:
 
               r1              rN
      f(s) = ------- + ... + ------- + d
             s - p1          s - pN
 
      The function attempt to perform first the identification of a model
      with d = 0, then if the operation do not succeed, it try the
      identification with d different from zero.
      %     Identification loop stop when the stop condition is reached.
      Stop criterion is based on three different approachs:
 
      1) Mean Squared Error and variation
      Check if the normalized mean squared error is lower than the value specified in
      FITTOL and if the relative variation of the mean squared error is lower
      than the value specified in MSEVARTOL.
      E.g. FITTOL = 1e-3, MSEVARTOL = 1e-2 search for a fit with
      normalized magnitude error lower than 1e-3 and and MSE relative
      variation lower than 1e-2.
 
      1) Log residuals difference and root mean squared error
      Log Residuals difference
      Check if the minimum of the logarithmic difference between data and
      residuals is larger than a specified value. ie. if the conditioning
      value is 2, the function ensures that the difference between data and
      residuals is at lest 2 order of magnitude lower than data itsleves.
      Root Mean Squared Error
      Check that the variation of the root mean squared error is lower than
      10^(-1*value).
 
      2) Residuals spectral flatness and root mean squared error
      Residuals Spectral Flatness
      In case of a fit on noisy data, the residuals from a good fit are
      expected to be as much as possible similar to a white noise. This
      property can be used to test the accuracy of a fit procedure. In
      particular it can be tested that the spectral flatness coefficient of
      the residuals is larger than a certain qiantity sf such that 0<sf<1.
      Root Mean Squared Error
      Check that the variation of the root mean squared error is lower than
      10^(-1*value).
 
      Both in the first and second approach the fitting loop stops when the
      two stopping conditions are satisfied.
      The output are AOs containing the frequency response of the fitted
      model, while the Model parameters are output as a parfrac model
      in the output AOs procinfo filed.
 
      The function can also perform a single loop without taking care of
      the stop conditions. This happens when 'AutoSearch' parameter is
      setted to 'off'.
 
      If you provide more than one AO as input, they will be fitted
      together with a common set of poles.
 
  CALL:         mod = sDomainFit(a, pl)
 
  INPUTS:      a  - input AOs to fit to. If you provide more than one AO as
                    input, they will be fitted together with a common set
                    of poles. Only frequency domain (fsdata) data can be
                    fitted. Each non fsdata object will be ignored. Input
                    objects must have the same number of elements.
               pl - parameter list (see below)
 
  OUTPUTS:
                mod - matrix of one parfrac object for each input AO.
                      Usseful fit information are stored in the procinfoi
                      field:
                      FIT_RESP  - model frequency response.
                      FIT_RESIDUALS - analysis object containing the fit
                      residuals.
                      FIT_MSE - analysis object containing the mean squared
                      error progression during the fitting loop.
 
 
  Note: all the input objects are assumed to caontain the same X
  (frequencies) values
 
 
  EXAMPLES:
 
  1) Fit to a frequency-series using Mean Squared Error and variation stop
  criterion
 
    % Create a frequency-series AO
    pl_data = plist('fsfcn', '0.01./(0.0001+f)', 'f1', 1e-5, 'f2', 5, 'nf', 1000);
    a = ao(pl_data);
 
    % Fitting parameter list
    pl_fit = plist('AutoSearch','on',...
    'StartPoles',[],...
    'StartPolesOpt','clog',...
    'maxiter',5,...
    'minorder',2,...
    'maxorder',20,...
    'weights',[],...
    'CONDTYPE','MSE',...
    'FITTOL',1e-3,...
    'MSEVARTOL',1e-2,...
    'Plot','off',...
    'ForceStability','off',...
    'direct term','off',...
    'CheckProgress','off');
 
    % Do fit
    b = sDomainFit(a, pl_fit);
 
  2) Fit to a frequency-series using Log residuals difference and mean
  squared error variation stop criterion
 
    % Create a frequency-series AO
    pl_data = plist('fsfcn', '0.01./(0.0001+f)', 'f1', 1e-5, 'f2', 5, 'nf', 1000);
    a = ao(pl_data);
 
    % Fitting parameter list
    pl_fit = plist('FS',[],...
    'AutoSearch','on',...
    'StartPoles',[],...
    'StartPolesOpt','clog',...
    'maxiter',5,...
    'minorder',2,...
    'maxorder',20,...
    'weights',[],...
    'weightparam','abs',...
    'CONDTYPE','RLD',...
    'FITTOL',1e-3,...
    'MSEVARTOL',1e-2,...
    'Plot','off',...
    'ForceStability','off',...
    'CheckProgress','off');
 
    % Do fit
    b = sDomainFit(a, pl_fit);
 
  3) Fit to a frequency-series using Residuals spectral flatness and mean
  squared error variation stop criterion
 
    % Create a frequency-series AO
    pl_data = plist('fsfcn', '0.01./(0.0001+f)', 'f1', 1e-5, 'f2', 5, 'nf', 1000);
    a = ao(pl_data);
 
    % Fitting parameter list
    pl_fit = plist('FS',[],...
    'AutoSearch','on',...
    'StartPoles',[],...
    'StartPolesOpt','clog',...
    'maxiter',5,...
    'minorder',2,...
    'maxorder',20,...
    'weights',[],...
    'weightparam','abs',...
    'CONDTYPE','RSF',...
    'FITTOL',0.5,...
    'MSEVARTOL',1e-2,...
    'Plot','off',...
    'ForceStability','off',...
    'CheckProgress','off');
 
    % Do fit
    b = sDomainFit(a, pl_fit);
 
 
  Parameters Description
 
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Parameter Description

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Method: ao/rms

Method: ao/select

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