Sensor signals acquired in the industrial process contain rich information which can be analyzed to facilitate effective monitoring of the process, early detection of system anomalies, quick diagnosis of fault root causes, and intelligent system design and control. In many mechatronic systems, multiple signals are acquired by different sensor channels (i.e. multi-channel data) which can be represented by high-order arrays (tensorial data). The multi-channel data has a high-dimensional and complex cross-correlation structure. It is crucial to develop a method that considers the interrelationships between different sensor channels. This paper proposes a new process monitoring approach based on uncorrelated multilinear discriminant analysis that can effectively model the multi-channel data to achieve a superior monitoring and fault diagnosis performance compared to other competing methods. The proposed method is applied directly to the high-dimensional tensorial data. Features are extracted and combined with multivariate control charts to monitor multi-channel data. The effectiveness of the proposed method in quick detection of process changes is demonstrated with both the simulation and a real-world case study.