Import.
line source
+ − % CSD2TF Input cross spectral density matrix and output stable transfer function
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − %
+ − % DESCRIPTION:
+ − %
+ − % Input cross spectral density (csd) and output corresponding
+ − % stable functions. Identification can be performed for a simple system
+ − % (one psd) or for a N dimensional system. Discrete transfer functions are
+ − % output in partial fraction expansion:
+ − %
+ − % r1 rN
+ − % f(z) = ----------- + ... + ----------- + d
+ − % 1-p1*z^{-1} 1-pN*z^{-1}
+ − %
+ − % System identification is performed in frequency domain, the order of
+ − % the model function is automatically chosen by the algorithm on the
+ − % base of the input tolerance condition.
+ − % In the case of simple systems the square root of the psd is fitted
+ − % and then the model is stabilized by the application of an all-pass
+ − % function.
+ − % In the case of two dimensional systems, transfer functions frequency
+ − % response is calculated by the eigendecomposition of the
+ − % cross-spectral matrix. Then models are identified by fitting
+ − % in frequency domain.
+ − %
+ − % CALL:
+ − % out = csd2tf(csd,f,params)
+ − %
+ − % INPUT:
+ − %
+ − % - csd is the cross spectral density matrix. It is in general a
+ − % [n,n,m] dimensional matrix. Where n is the dimension of the system
+ − % and m is the number of frequencies
+ − % - f: is the corresponding frequencies vector in Hz (of length m)
+ − % - params: is a struct of identification options, the possible values
+ − % are:
+ − %
+ − % params.fullauto = 0 --> Perform a fitting loop as far as the number
+ − % of iteration reach Nmaxiter. The order of the fitting function will
+ − % be that specified in params.minorder. If params.dterm is setted to
+ − % 1 the function will fit only with direct term.
+ − % params.fullauto = 1 --> Parform a full automatic search for the
+ − % transfer function order. The fitting procedure will stop when the
+ − % stopping condition defined in params.ctp is satisfied. Default
+ − % value.
+ − %
+ − % - params.Nmaxiter = # set the maximum number of fitting steps
+ − % performed for each trial function order. Default is 50
+ − %
+ − % - params.minorder = # set the minimum possible function order.
+ − % Default is 2
+ − %
+ − % - params.maxorder = # set the maximum possible function order.
+ − % Default is 25
+ − %
+ − % params.spolesopt = 1 --> use real starting poles
+ − % params.spolesopt = 2 --> generates complex conjugates poles of the
+ − % type \alfa e^{j\pi\theta} with \theta = linspace(0,pi,N/2+1).
+ − % params.spolesopt = 3 --> generates complex conjugates poles of the
+ − % type \alfa e^{j\pi\theta} with \theta = linspace(0,pi,N/2+2).
+ − % Default option.
+ − %
+ − % - params.weightparam = 0 --> use external weights
+ − % - params.weightparam = 1 equal weights (one) for each point
+ − % - params.weightparam = 2 weight with the inverse of absolute value
+ − % of fitting data
+ − % - params.weightparam = 3 weight with square root of the inverse of
+ − % absolute value of fitting data
+ − % - params.weightparam = 4 weight with the inverse of the square mean
+ − % spread
+ − %
+ − % params.extweights = [] --> A vector of externally provided weights.
+ − % It has to be of the same size of input data.
+ − %
+ − % - params.plot = 0 --> no plot during fit iteration
+ − % - params.plot = 1 --> plot results at each fitting steps. default
+ − % value.
+ − %
+ − % - params.ctp = 'chival' --> check if the value of the Mean Squared
+ − % Error is lower than 10^(-1*lsrcond).
+ − % - params.ctp = 'chivar' --> check if the value of the Mean Squared
+ − % Error is lower than 10^(-1*lsrcond) and if the relative variation of mean
+ − % squared error is lower than 10^(-1*msevar).
+ − % - params.ctp = 'lrs' --> check if the log difference between data and
+ − % residuals is point by point larger than the value indicated in
+ − % lsrcond. This mean that residuals are lsrcond order of magnitudes
+ − % lower than data.
+ − % - params.ctp = 'lrsmse' --> check if the log difference between data
+ − % and residuals is larger than the value indicated in lsrcond and if
+ − % the relative variation of mean squared error is lower than
+ − % 10^(-1*msevar).
+ − %
+ − % - params.lrscond = # --> set conditioning value for point to point
+ − % log residuals difference (params.ctp = 'lsr') and mean log residual
+ − % difference (params.ctp = 'mlsrvar'). Default is 2. See help for
+ − % stopfit.m for further remarks.
+ − %
+ − % - params.msevar = # --> set conditioning value for root mean squared
+ − % error variation. This allow to check that the relative variation of
+ − % mean squared error is lower than 10^(-1*msevar).Default is 7. See
+ − % help for stopfit.m for further remarks.
+ − %
+ − % - params.fs set the sampling frequency (Hz). Default is 1 Hz
+ − %
+ − % params.dterm = 0 --> Try to fit without direct term
+ − % params.dterm = 1 --> Try to fit with and without direct term
+ − %
+ − % params.spy = 0 --> Do not display the iteration progression
+ − % params.spy = 1 --> Display the iteration progression
+ − %
+ − %
+ − % OUTPUT:
+ − %
+ − % - ostruct is a struct with the fields:
+ − % - ostruct(n).res --> is the vector of residues.
+ − % - ostruct(n).poles --> is the vector of poles.
+ − % - ostruct(n).dterm --> is the vector of direct terms.
+ − % - ostruct(n).mresp --> is the vector of tfs models responses.
+ − % - ostruct(n).rdl --> is the vector of fit residuals.
+ − % - ostruct(n).mse --> is the vector of mean squared errors.
+ − %
+ − %
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − %
+ − % VERSION: $Id: csd2tf.m,v 1.1 2009/04/23 09:56:28 luigi Exp $
+ − %
+ − % HISTORY: 22-04-2009 L Ferraioli
+ − % Creation
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − function ostruct = csd2tf(csd,f,params)
+ −
+ − utils.helper.msg(utils.const.msg.MNAME, 'running %s/%s', mfilename('class'), mfilename);
+ −
+ − % Collect inputs
+ −
+ − % Default input struct
+ − defaultparams = struct('Nmaxiter',50, 'minorder',2,...
+ − 'maxorder',25, 'spolesopt',2, 'weightparam',1, 'plot',0,...
+ − 'ctp','chival','lrscond',2,'msevar',2,...
+ − 'fs',1,'dterm',0, 'spy',0, 'fullauto',1,...
+ − 'extweights', []);
+ −
+ − names = {'Nmaxiter','minorder','maxorder','spolesopt',...
+ − 'weightparam','plot','stopfitcond',...
+ − 'ctp','lrscond','msevar',...
+ − 'fs','dterm','spy','fullauto','extweights'};
+ −
+ − % collecting input and default params
+ − if ~isempty(params)
+ − for jj=1:length(names)
+ − if isfield(params, names(jj)) && ~isempty(params.(names{1,jj}))
+ − defaultparams.(names{1,jj}) = params.(names{1,jj});
+ − end
+ − end
+ − end
+ −
+ − % default values for input variables
+ − Nmaxiter = defaultparams.Nmaxiter; % Number of max iteration in the fitting loop
+ − minorder = defaultparams.minorder; % Minimum model order
+ − maxorder = defaultparams.maxorder; % Maximum model order
+ − spolesopt = defaultparams.spolesopt; % 0, Fit with no complex starting poles (complex poles can be found as fit output). 1 fit with comples starting poles
+ − weightparam = defaultparams.weightparam; % Weight 1./abs(y). Admitted values are 0, 1, 2, 3
+ − checking = defaultparams.plot; % Never polt. Admitted values are 0 (No polt ever), 1 (plot at the end), 2 (plot at each step)
+ − ctp = defaultparams.ctp;
+ − lrscond = defaultparams.lrscond;
+ − msevar = defaultparams.msevar;
+ − fs = defaultparams.fs; % sampling frequency
+ − idt = defaultparams.dterm;
+ − spy = defaultparams.spy;
+ − autosearch = defaultparams.fullauto;
+ − extweights = defaultparams.extweights;
+ −
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − % Checking inputs
+ −
+ − [a,b] = size(f);
+ − if a < b % shifting to column
+ − f = f.';
+ − end
+ −
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − % switching between inputs
+ −
+ − clear dim
+ − % cecking for dimensionality
+ − [nn,mm,kk] = size(csd);
+ − if kk == 1
+ − dim = '1dim';
+ − utils.helper.msg(utils.const.msg.PROC1, ' Performing one dimesional identification on psd ')
+ − if nn < mm % shift to column
+ − csd = csd.';
+ − end
+ − else
+ − dim ='ndim';
+ − utils.helper.msg(utils.const.msg.PROC1, ' Performing N dimesional identification on csd ')
+ − end
+ −
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − % system identification
+ −
+ − switch dim
+ − case '1dim'
+ −
+ − utils.helper.msg(utils.const.msg.PROC1, ' Performing z-domain identification ')
+ − itf = abs(sqrt(csd)); % input data
+ −
+ − % Fitting params
+ − params = struct('spolesopt',spolesopt, 'Nmaxiter',Nmaxiter, 'minorder',minorder,...
+ − 'maxorder',maxorder, 'weightparam',weightparam, 'plot',checking,...
+ − 'ctp',ctp,'lrscond',lrscond,'msevar',msevar,...
+ − 'stabfit',0,'dterm',idt,'spy',spy,'fullauto',autosearch,'extweights',extweights);
+ −
+ − % Fitting
+ − utils.helper.msg(utils.const.msg.PROC1, ' Fitting absolute TF value with unstable model ')
+ − [res,poles,dterm,mresp,rdl,msei] = utils.math.autodfit(itf,f,fs,params);
+ −
+ − % all pass filtering for poles stabilization
+ − [ntf,np] = utils.math.pfallpz(res,poles,dterm,mresp,f,fs,false);
+ −
+ − % Fitting params
+ − params = struct('spolesopt',0,'extpoles', np,...
+ − 'Nmaxiter',Nmaxiter,'minorder',minorder,'maxorder',maxorder,...
+ − 'weightparam',weightparam,'plot',checking,...
+ − 'ctp',ctp,'lrscond',lrscond,'msevar',msevar,...
+ − 'stabfit',1,...
+ − 'dterm',idt,'spy',spy,'fullauto',autosearch,...
+ − 'extweights',extweights);
+ −
+ − utils.helper.msg(utils.const.msg.PROC1, ' Fitting TF with stable model ')
+ − [res,poles,dterm,mresp,rdl,msef] = utils.math.autodfit(ntf,f,fs,params);
+ −
+ − % Output data switching between output type
+ − utils.helper.msg(utils.const.msg.PROC1, ' Output z-domain model ')
+ −
+ − ostruct = struct();
+ −
+ − ostruct.res = res;
+ − ostruct.poles = poles;
+ − ostruct.dterm = dterm;
+ − ostruct.mresp = mresp;
+ − ostruct.rdl = rdl;
+ − ostruct.mse = msei;
+ −
+ − case 'ndim'
+ − % switching between continuous and discrete type identification
+ −
+ − % utils.helper.msg(utils.const.msg.PROC1, ' Performing z-domain identification on 2dim system, z-domain output ')
+ − tf = utils.math.ndeigcsd(csd,'OTP','TF','MTD','KAY'); % input data
+ −
+ − [nn,mm,kk] = size(tf);
+ −
+ − % % Shifting to columns
+ − % [a,b] = size(tf11);
+ − % if a<b
+ − % tf11 = tf11.';
+ − % end
+ − % [a,b] = size(tf12);
+ − % if a<b
+ − % tf12 = tf12.';
+ − % end
+ − % [a,b] = size(tf21);
+ − % if a<b
+ − % tf21 = tf21.';
+ − % end
+ − % [a,b] = size(tf22);
+ − % if a<b
+ − % tf22 = tf22.';
+ − % end
+ − %
+ − % % Collecting tfs
+ − % f1 = [tf11 tf21];
+ − % f2 = [tf12 tf22];
+ −
+ − %%% System identification
+ −
+ − % init output
+ − ostruct = struct();
+ −
+ − for dd = 1:mm
+ − fun = squeeze(tf(1,dd,:));
+ − % willing to work with columns
+ − [a,b] = size(fun);
+ − if a<b
+ − fun = fun.';
+ − end
+ − for ff = 2:nn
+ − tfun = squeeze(tf(ff,dd,:));
+ − % willing to work with columns
+ − [a,b] = size(tfun);
+ − if a<b
+ − tfun = tfun.';
+ − end
+ − fun = [fun tfun];
+ − end
+ −
+ − % Fitting with unstable poles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − params = struct('spolesopt',spolesopt, 'Nmaxiter',Nmaxiter, 'minorder',minorder,...
+ − 'maxorder',maxorder, 'weightparam',weightparam, 'plot',checking,...
+ − 'ctp',ctp,'lrscond',lrscond,'msevar',msevar,...
+ − 'stabfit',0,'dterm',idt,'spy',spy,'fullauto',autosearch,'extweights',extweights);
+ −
+ − % Fitting
+ − utils.helper.msg(utils.const.msg.PROC1, ' Fitting with unstable common poles ')
+ − [res,poles,dterm,mresp,rdl,msei] = utils.math.autodfit(fun,f,fs,params);
+ −
+ − % Poles stabilization %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − utils.helper.msg(utils.const.msg.PROC1, ' All pass filtering')
+ − [nfun,np] = utils.math.pfallpz(res,poles,dterm,mresp,f,fs,false);
+ − np = np(:,1);
+ −
+ − % Fitting with stable poles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ −
+ − % Fitting params
+ − params = struct('spolesopt',0,'Nmaxiter',Nmaxiter,...
+ − 'minorder',minorder,'maxorder',maxorder,...
+ − 'weightparam',weightparam,'plot',checking,...
+ − 'ctp',ctp,'lrscond',lrscond,'msevar',msevar,...
+ − 'stabfit',1,...
+ − 'dterm',idt,'spy',spy,'fullauto',autosearch,...
+ − 'extweights',extweights,'extpoles', np);
+ −
+ − % Fitting
+ − utils.helper.msg(utils.const.msg.PROC1, ' Fitting with stable common poles ')
+ − [res,poles,dterm,mresp,rdl,msef] = utils.math.autodfit(nfun,f,fs,params);
+ −
+ −
+ − % Output stable model %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ −
+ − ostruct(dd).res = res;
+ − ostruct(dd).poles = poles;
+ − ostruct(dd).dterm = dterm;
+ − ostruct(dd).mresp = mresp;
+ − ostruct(dd).rdl = rdl;
+ − ostruct(dd).mse = msei;
+ −
+ − end
+ −
+ − end
+ − end
+ −
+ − % END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%