Multifractal coupling analysis for state prediction of process complex systems

Abnormal states in complex process industry systems pose significant risks, often leading to serious accidents. This study proposes a multifractal coupling analysis approach to monitor system states by examining the evolving coupling relationships between key variables. The methodology integrates multifractal detrended cross-correlation analysis (MF-DXA) and coupling detrended fluctuation analysis (CDFA) to investigate the multifractal properties of multiple simultaneously recorded time series. The surrogate data method is employed to validate the existence, strength, and source of coupling relations among process variables, while the rolling windows technique is used to analyze their time-varying features. Results demonstrate that evolving coupling relationships are highly sensitive to changes in the system’s state, enabling early detection of abnormal states. The method is validated through a case study using data from a simulated nonlinear model and historical data from an air compressor system in a chemical plant. Findings reveal that unexpected alterations in coupling relationships are closely linked to abnormal system states, which can precede accidents. Based on these insights, Finally, a novel framework for predicting the state of complex process systems is proposed and discussed, offering enhanced safety and operational efficiency in these systems.