idnlhw - Nonlinear black-box Hammerstein-Wiener model

A structure that specifies the estimation algorithm options, as described in idnlhw Algorithm Properties.

B polynomial as a cell array of Ny-by-Nu elements, where Ny is the number of outputs and Nu is the number of inputs. An element b{i,j} is a row vector representing the numerator polynomial for the j:th input to ith output transfer function. It contains as many leading zeros as there are input delays.

F polynomial as a cell array of Ny-by-Nu elements, where Ny is the number of outputs and Nu is the number of inputs. An element f{i,j} is a row vector representing the denominator polynomial for the j:th input to ith output transfer function.

(Read only) The linear model in the linear block. For single output, represented as an idpoly object. For multiple output, represented as an idss object.

(Read-only) Structure that stores estimation settings and results, as described in idnlhw EstimationInfo Properties.

Nonlinearity estimator object. Assignable values include pwlinear (default), deadzone, wavenet, saturation, customnet, sigmoidnet, poly1d, and unitgain. For more information, see the corresponding reference pages.

For ny outputs, Nonlinearity is an ny-by-1 array, such as [sigmoidnet;wavenet]. However, if you specify a scalar object, this nonlinearity object applies to all outputs.

Same as InputNonlinearity.

Model orders and input delays, where nb is the number of zeros plus 1, nf is the number of poles, and nk is the delay from input to output in terms of the number of samples.

For nu inputs and ny outputs, nb, nf and, nk are ny-by-nu matrices whose i-jth entry specifies the orders and delay of the transfer function from the jth input to the ith output.

A structure that specifies additional estimation algorithm options, as described in idnlhw Advanced Algorithm Properties.

The search method of lsqnonlin supports the Trace criterion only.

Use for multiple-output models only. Criterion can have the following values:

• 'Det': Minimize det(E'*E), where E represents the prediction error. This is the optimal choice in a statistical sense and leads to the maximum likelihood estimates in case nothing is known about the variance of the noise. It uses the inverse of the estimated noise variance as the weighting function. This is the default criterion used for all models, except idnlgrey which uses 'Trace' by default.

• 'Trace': Minimize the trace of the weighted prediction error matrix trace(E'*E*W), where E is the matrix of prediction errors, with one column for each output, and W is a positive semi-definite symmetric matrix of size equal to the number of outputs. By default, W is an identity matrix of size equal to the number of model outputs (so the minimization criterion becomes trace(E'*E), or the traditional least-squares criterion). You can specify the relative weighting of prediction errors for each output using the Weighting field of the Algorithm property. If the model contains neuralnet or treepartition as one of its nonlinearity estimators, weighting is not applied because estimations are independent for each output.

Both the Det and Trace criteria are derived from a general requirement of minimizing a weighted sum of least squares of prediction errors. Det can be interpreted as estimating the covariance matrix of the noise source and using the inverse of that matrix as the weighting. You should specify the weighting when using the Trace criterion.

If you want to achieve better accuracy for a particular channel in MIMO models, use Trace with weighting that favors that channel. Otherwise, use Det. If you use Det, check cond(model.NoiseVariance) after estimation. If the matrix is ill-conditioned, try using the Trace criterion. You can also use compare on validation data to check whether the relative error for different channels corresponds to your needs or expectations. Use the Trace criterion if you need to modify the relative errors, and check model.NoiseVariance to determine what weighting modifications to specify.

(For wavenet nonlinear estimator only)
Implicitly set to perform iterative estimation. Changing this setting does not impact the algorithm.
Default: 'On'.

Robustification criterion that limits the influence of large residuals, specified as a positive real value. Residual values that are larger than 'LimitError' times the estimated residual standard deviation have a linear cost instead of the usual quadratic cost.
Default: 0 (no robustification).

Maximum number of iterations for the estimation algorithm, specified as a positive integer.
Default: 20.

The number of elements (size) of the largest matrix to be formed by the algorithm. Computational loops are used for larger matrices. Use this value for memory/speed trade-off.
MaxSize can be any positive integer. Default: 250000.

Note   The original data matrix of u and y must be smaller than MaxSize.

Method used by the iterative search algorithm.
Assignable values:

• 'Auto' — Automatically chooses from the following methods.

• 'gn' — Gauss-Newton method.

• 'gna' — Adaptive Gauss-Newton method.

• 'grad' — A gradient method.

• 'lm' — Levenberg-Marquardt method.

• 'lsqnonlin' — Nonlinear least-squares method (requires the Optimization Toolbox product). This method handles only the 'Trace' criterion.

Specifies to terminate the iterative search when the expected improvement of the parameter values is less than Tolerance, specified as a positive real value in %.
Default: 0.01.

Toggles displaying or hiding estimation progress information in the MATLAB Command Window.
Default: 'Off'.
Assignable values:

• 'Off' — Hide estimation information.

• 'On' — Display estimation information.

Positive semi-definite matrix W used for weighted trace minimization. When Criterion = 'Trace', trace(E'*E*W) is minimized. Weighting can be used to specify relative importance of outputs in multiple-input multiple-output models (or reliability of corresponding data) when W is a diagonal matrix of nonnegative values. Weighting is not useful in single-output models. By default, Weighting is an identity matrix of size equal to the number of outputs.

When the search direction is computed, the algorithm discards the singular values of the Jacobian that are smaller than GnPinvConst*max(size(J))*norm(J)*eps. Singular values that are closer to 0 are included when GnPinvConst is decreased.
Default: 1e4.
Assign a positive, real value.

(For Levenberg-Marquardt search algorithm) The starting level of regularization when using the Levenberg-Marquardt search method (Algorithm.SearchMethod='lm').
Default: 0.001.
Assign a positive real value.

(For Levenberg-Marquardt search algorithm) Try this next level of regularization to get a lower value of the criterion function. The level of regularization is LMStep times the previous level. At the start of a new iteration, the level of regularization is computed as 1/LMStep times the value from the previous iteration.
Default: 10.
Assign a real value >1.

Maximum number of bisections performed by the line search algorithm along the search direction (number of rotations of search vector for 'lm'). Used by 'gn', 'lm', 'gna' and 'grad' search methods (Algorithm.SearchMethod property).
Default: 10.
Assign a positive integer value.

The iterations are stopped if the number of calls to the model file exceeds this value.
Default: Inf.
Assign a positive integer value.

The smallest parameter update allowed per iteration.
Default: 1e-16.
Assign a positive, real value.

The iterations are stopped if the relative improvement of the criterion function is less than RelImprovement.
Default: 0.
Assign a positive real value.

Note   This does not apply when Algorithm.SearchMethod='lsqnonlin'.

(For line search algorithm) The suggested parameter update is reduced by the factor 'StepReduction' after each try until either 'MaxBisections' tries are completed or a lower value of the criterion function is obtained.
Default: 2.
Assign a positive, real value >1.

Note   This does not apply when Algorithm.SearchMethod='lsqnonlin'.

Shows whether the model parameters were estimated.

Shows the estimation method.

Value of the loss function, equal to det(E'*E/N), where E is the residual error matrix (one column for each output) and N is the total number of samples.

Value of Akaike's Final Prediction Error (see fpe).

Name of the data from which the model is estimated.

Length of the estimation data.

Sampling interval of the estimation data.

'Time' means time domain data. 'Frequency' is not supported.

Intersample behavior of the input estimation data used for interpolation:

• 'zoh' means zero-order-hold, or piecewise constant.

• 'foh' means first-order-hold, or piecewise linear.

Reason for terminating parameter estimation iterations.

Norm of the search vector (gn-vector) in the last iteration. Empty when 'lsqnonlin' is the search method.

Criterion improvement in the last iteration, shown in %. Empty when 'lsqnonlin' is the search method.

Number of iterations performed by the estimation algorithm.

Any warnings encountered during parameter estimation.

The value of randn('state') at the last randomization of the initial parameter vector.

Duration of the estimation.