Latent Dynamic Networked System Identification with High-Dimensional Data from Interconnected Process Networks

Networked dynamic systems produce high-dimensional data that reflect the complex interactions among the network nodes with rich sensor measurements. These systems are composed of interconnected nodes with their own dynamics and dynamic interactions with other nodes. The nodes in the networked systems are often equipped with a rich set of sensors that yield high-dimensional time series data. Recent works have dealt with the estimation and system identification problems of these networked models with tremendous progress. However, in dealing with high-dimensional networked systems data, little has been done in extracting low-dimensional latent dynamic networks from the high-dimensional networked data.

In this paper, we propose a novel algorithm for latent dynamic networked system identification that leverages the network structure and performs dimension reduction for each node via dynamic latent variables (DLVs). The algorithm assumes that the DLVs of each node have an auto-regressive model with exogenous input and interactions from other nodes. The DLVs of each node are extracted to capture the most predictable latent variables in the high dimensional data, while the residual factors are not predictable. The advantage of the proposed framework is demonstrated on an industrial process network for system identification and dynamic data analytics and are summarized as follows.
1) To handle co-moving or collinear dynamics, low dimensional dynamics is captured on each individual node system to extract DLVs with a network topology;
2) The DLVs of each node are vector auto-regressive with exogenous input (VARX) and dynamic connections to other nodes following a given topology;
3) The proposed framework extends single-node DLV methods to networked dynamic systems to analyze high-dimensional networked time series data.
4) The identified network model is a networked latent VARX model (Net-LaVARX), which is readily suitable for networked system identification.