Full Decoupling High-Order Dynamic Mode Decomposition for Advanced Static and Dynamic Synergetic Fault Detection and Isolation

Real industrial processes often present coupled static and dynamic characteristics, leading to significant challenges for fault detection and isolation. However, traditional dynamic modeling methods may lead to the coupling problem of statics and dynamics, which provide ambiguous process status descriptions and incorrect fault isolation results. In this work, a novel full decoupling high-order dynamic mode decomposition (FDHODMD) method is developed for fault detection and isolation of dynamic processes. Different from the existing dynamic methods, the proposed FDHODMD can separate the high-order dynamic information from static information. First, the static characteristics are separated by discarding the decomposed features corresponding to smaller singular values. Then, a high-order dynamic model is established to present the temporal relationships between variables. In this way, the effect of static characteristics on dynamics analysis can be eliminated. Accordingly, from both static and dynamic perspectives, multiple statistics are designed to comprehensively detect the anomalies and provide an explicit status identification. In addition to the static fault isolation strategy, a dynamic fault isolation strategy is designed to recognize the fault variables after detecting the deviation, which divides the complex dynamic system into several individual dynamic modes to avoid the interaction of dynamic characteristics. Thereupon, the contributions of different variables to each dynamic mode can be clearly presented to recognize the fault variables. Finally, the validity of the proposed method is illustrated through both a numerical case and a real industrial process. Note to Practitioners-In industrial processes, the static and dynamic characteristics of data are often coupled. This work presents a FDHODMD method, which can be considered the high-order version of DMD, to achieve the decoupling of dynamics and statics while extracting high-order dynamic characteristics. Then the proposed fault detection strategy designs multiple statistics for monitoring the process from both dynamic and static perspectives, which ensures the safe operation of industrial processes. After detecting the anomaly, the proposed fault isolation strategy can recognize the fault variables separately dominating the dynamic and static deviation, which may help engineers locate the fault source.