Input–Output Directed Dependency: Driving-Disentangled Dynamic Mode Decomposition for Control System Representation Learning and Monitoring

Process monitoring provides a guarantee for the efficient and safe operation of industrial equipment. However, traditional methods rarely consider the dependency relationship between inputs and outputs in industrial control systems, which can lead to misalignment of process state identification. This study solves the problem based on the following recognitions: 1) the inputs of control systems can drive the changes in the output states, termed input–output directed dependency; 2) both the inputs and the process inertia are related to the dependency, showing the diversity of dependency relationship; and 3) the dependency can be further disentangled into different subspaces, revealing different types of process variations for fine-grained monitoring. Thereupon, a driving-disentangled dynamic mode decomposition with control method is proposed for control systems input–output directed dependency representation learning and monitoring. The process variables are divided into inputs and outputs. The input–output directed dependency is identified, revealing the response of outputs to inputs during adjustment of the process states, which is quite different from common multivariate correlations. A linearly independent vector SelecTion strategy is designed to construct a transformation matrix, which can further disentangle the input–output dependency into external-driving and self-driving subspaces. Three monitoring statistics are developed for process monitoring. The effectiveness is verified through a gas turbine thermal power experimental rig.