Canonical correlation analysis-aided design of Kalman filter-based residual generator for monitoring of industrial control systems

Kalman filters are widely applied for residual generation thanks to the property that the generated residual is white and of minimum covariance. This enables an optimal monitoring. However, the explicit mathematical model is difficult to achieve in a real industrial automation system, and the effect of the feedback has not been explicitly considered in the existing data-driven design method, which degrades the monitoring performance of a Kalman filter-based monitoring system. To deal with such an issue, this paper proposes a purely data-driven realization of the Kalman filter-based residual generator for process monitoring of industrial control systems with a closed-loop configuration. Firstly, a least-mean-square interpretation of canonical correlation analysis (CCA) is introduced, which is helpful to explore the relationships between inputs and outputs of industrial control systems. Then, a CCA-aided Kalman filter-based residual generator is constructed, which is realized by identifying the Kalman gain matrix and the data-driven stable kernel representation. Different from the existing method, the proposed one achieves superior monitoring performance by considering closed-loop dynamics and the correlation between inputs and noises, which is caused by the feedback control structure of systems. The effectiveness of the proposed method is demonstrated and compared through an experimental three-tank system.