Attention Lempel-Ziv complexity: an improved Lempel-Ziv complexity with high computational efficiency for bearing early fault detection

• This paper proposes an improved Lempel-Ziv computation framework based on attention entropy. • The information between local peaks in time series is extracted by attention entropy. • The attention Lempel-Ziv complexity is obtained by integrating Lempel-Ziv complexity of different local peaks. • The proposed method can be effectively used for early fault detection of bearings. • The proposed method is validated through four sets of whole life datasets. Lempel-Ziv complexity assesses time series anomalies by quantifying the amount of novel patterns within the time series. It has been effectively utilized in assessing bearing fault severity and classification. Nonetheless, it has the issue of limited applicability in early failure detection and exhibits low computing efficiency. To address this problem, this paper proposes a parameter-free Lempel-Ziv complexity for bearing early fault detection. According to the attention entropy, the local maximum and minimum peak points are extracted from the global signal. Next, the interval between two consecutive peak points is determined and the Lempel-Ziv complexity of these intervals is computed. Finally, the attention Lempel-Ziv complexity is calculated by integrating Lempel-Ziv complexity of different intervals. The four sets of life-cycle data from two life-cycle datasets verify that the method can effectively realize the early fault detection of bearings. And compared with the traditional Lempel-Ziv complexity, it significantly enhances computational efficiency.