Identifying Edge Changes in Networks from Input and Output Covariance Data

We study the problem of identifying changes in network systems, encompassing changes such as the addition or removal of edges and their various combinations. We focus on the systems that obey conservation laws and balance equations (e.g., Kirchoff's laws) in which the nodal injections (inputs) are linearly related to potentials (outputs). For finite-dimensional networks, this relationship is given by the weighted Laplacian matrix, where the non-zero entries correspond to the edges. Assuming that inputs are zero-mean random vectors, we present spectral and algebraic methods to identify edge changes from the output covariance data. The spectral method requires the knowledge of input covariance data, whereas the algebraic method does not require this knowledge. Finally, we validate the performance of our proposed method on many numerical examples, including the IEEE 14 bus power system.