Multivariate multiscale dispersion Lempel–Ziv complexity for fault diagnosis of machinery with multiple channels

Lempel–Ziv complexity (LZC), as a nonlinear feature in information science, has shown great promise in detecting correlations and capturing dynamic changes in single-channel time series. However, its application to multichannel data has been largely unexplored, while the complexity of real-world systems demands the utilization of data collected from multiple sensors or channels so as to extract distinguishable fault features for fault diagnosis. This paper proposes a novel method called multivariate multiscale dispersion Lempel–Ziv complexity (mvMDLZC) to extract the fault features hidden in multi-source information. First, multivariate embedding theory is applied to obtain multivariate embedded vectors and multivariate dispersion patterns, which can reflect the inherent relationships in the multichannel series. Second, by assigning labels to these patterns, the original multichannel time series can be transformed into a symbolic sequence with multiple symbols instead of the original binary conversion, enabling the accurate recovery of the system dynamics. Finally, the complexity counter value and normalized LZC are calculated for the complexity measure. Experimental results using synthetic and real-world datasets demonstrate that mvMDLZC outperforms existing LZC-based methods and multivariate dispersion entropy in recognizing different states of mechanical systems. Additionally, mvMDLZC exhibits robustness in handling challenges such as small sample datasets and noise interference, making it suitable for real industrial applications. These findings highlight the potential of mvMDLZC as a valuable approach for dissecting multichannel systems across various real-world scenarios.