PEM algorithm for single module/full network identification

Identification of a single target module is performed on the basis of a selected predictor model and measurement data of the node signals and external excitation signals that appear in this predictor model. The applied method is the local direct method, i.e. a direct method directed towards estimating a single module. The applied model structure is given by

$w_Y(t) = G(q) w_D(t) + T(q) r(t) + H(q) e(t)$

With $Y$ and $D$ selected sets of predictor outputs and inputs.
A non-convex optimization is performed to a quadratic cost function of the one-step-ahead prediction errors. In the predictor model it is indicated which entries in the predictor model ($G$,$T$,$H$) are fixed or parametrized. In this way topological prior information is exploited in the identification. The consistency conditions for the predictor model can be checked, prior to identification, in the Predictor Model Window of the SYSDYNET app, or through the m-file predmodel_analysis_dm.m.

This algorithm is applicable for both single module identification, as well as full network identification.

Implementation aspects:

• Modules in the network are allowed to have direct feedthrough terms.
• It is assumed that the noise process has full rank, i.e. $H$ is square, monic, stable and stably invertible.

References

1. K.R. Ramaswamy and P.M.J. Van den Hof (2021). A local direct method for module identification in dynamic networks with correlated noise. IEEE Trans. Automatic Control, Vol. 66, no. 11, pp. 3237-3252, November 2021.
2. K.R. Ramaswamy (2022). A guide to learning modules in a dynamic network. Dr. Dissertation, Eindhoven University of Technology, 2022.