Hierarchical Bidirectional Transition Dispersion Entropy-based Lempel-Ziv Complexity and Its Application in Fault-Bearing Diagnosis

TL;DR

The paper tackles capturing dynamic transitions in nonlinear time series by introducing BT-DELZC, a bidirectional transition network-enhanced LZC-based metric built on dispersion patterns and dispersion-entropy symbolization. It couples this with a hierarchical decomposition to extract multi-frequency features, and validates the approach on simulated signals (including chirp and mix processes) and real fault-bearing datasets (PU and CWRU). BT-DELZC consistently outperforms LZC, PLZC, and DELZC in feature extraction and fault classification across multiple classifiers, demonstrating improved robustness and diagnostic accuracy. The method offers a practical, scalable tool for nonlinear time-series analysis with direct applicability to industrial fault diagnosis and other domains requiring sensitive dynamic-pattern characterization.

Abstract

Lempel-Ziv complexity (LZC) is a key measure for detecting the irregularity and complexity of nonlinear time series and has seen various improvements in recent decades. However, existing LZC-based metrics, such as Permutation Lempel-Ziv complexity (PLZC) and Dispersion-Entropy based Lempel-Ziv complexity (DELZC), focus mainly on patterns of independent embedding vectors, often overlooking the transition patterns within the time series. To address this gap, this paper introduces a novel LZC-based method called Bidirectional Transition Dispersion Entropy-based Lempel-Ziv complexity (BT-DELZC). Leveraging Markov chain theory, this method integrates a bidirectional transition network framework with DELZC to better capture dynamic signal information. Additionally, an improved hierarchical decomposition algorithm is used to extract features from various frequency components of the time series. The proposed BT-DELZC method is first evaluated through four simulated experiments, demonstrating its robustness and effectiveness in characterizing nonlinear time series. Additionally, two fault-bearing diagnosis experiments are conducted by combining the hierarchical BT-DELZC method with various classifiers from the machine learning domain. The results indicate that BT-DELZC achieves the highest accuracy across both datasets, significantly outperforming existing methods such as LZC, PLZC, and DELZC in extracting features related to fault bearings.

Figures (19)

• Figure 1: An example of finding the In-link and Out-link sequences corresponding to the dispersion pattern $\pi_{231}$
• Figure 2: The flow diagram of the procedure for calculating BT-DELZC of a given time series $X$
• Figure 3: The hierarchy diagram of $K=3$.
• Figure 4: The BT-DELZC results for $m=3$ and $m=4$ with varying time series length $N$ and different classification number $c$
• Figure 5: The standard deviations of BT-DELZC and three previous methods (LZC, PLZC, DELZC) with different time series length $N$)