Topology estimation
On the basis of a set of measured node variables, an interconnection structure is estimated for a module dynamic network. The interconnection structure is provided in the form of an adjacency matrix for the network matrix , indicating which nodes are causally connected to which other nodes.
For each single node considered as output, a MISO (multi-input single-output) model is estimated, by parametrizing each potential module by a Gaussian kernel. An EM (expectation maximization) algorithm is implemented to find the (hyper)parameters that optimize the marginal likelihood of the data for a fully connected network. Subsequently, a search algorithm finds the optimal topology, by stepwise adding and removing links, while evaluating the consequences for the marginal likelihood.
For large data sets, the marginal likelihood calculations can be split as a sum over different data segments, for computational efficiency.
An "Evaluate" function is available that evaluates the detection of a particular link for all possible interconnection structures in the network. It delivers a percentage of situations for which the considered link is detected. Since this includes an exhaustive search over all possible network topologies, this procedure can be computationally heavy.
Current implementation restrictions:
- No use is made of possible excitation signals .
- Not available yet for diffusively coupled networks (DCN's)
- The possible effect of correlations between the disturbances is not taken into account.
Reference
- S. Shi, G. Bottegal and P.M.J. Van den Hof. Bayesian topology identification of linear dynamic networks. Proc. 2019 European Control Conference, Napels, Italy, June 25-28, 2019, pp. 2814-2819.