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

TL;DR

This paper introduces a novel bidirectional transition dispersion entropy-based Lempel-Ziv complexity method that improves nonlinear time series analysis and fault diagnosis by capturing transition patterns and dynamic information.

Contribution

The paper proposes BT-DELZC, a new LZC-based metric combining Markov chain theory and hierarchical decomposition for enhanced feature extraction in nonlinear signals.

Findings

BT-DELZC outperforms existing LZC-based methods in simulated tests.

BT-DELZC achieves higher fault diagnosis accuracy in bearing datasets.

The method effectively captures transition dynamics and frequency components.

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.