Parallel Lempel–Ziv complexity: an efficient computing framework of Lempel–Ziv complexity

Abstract Lempel–Ziv complexity (LZC) is effectively used in bearing fault diagnosis. However, for bearing vibration signals with a high sampling rate, the traditional calculation method of Lempel–Ziv limits the real-time performance of LZC for bearing diagnosis with multipoint signals. Therefore, this paper proposes a parallel computing framework for LZC combined with the parallel computing method. Firstly, the original signal is reconstructed in phase space to transform the one-dimensional signal into a multi-dimensional sub-signal. Then, the independent components of each dimension are calculated. Next, the independent components of all dimensions are integrated and their number is counted. Finally, the LZC is calculated according to the number of independent components. The proposed method is verified by three simulated signals, bearing a single point fault signal and bearing a full-life signal. The changing trend of LZC calculated by the proposed method is not only consistent with that calculated by the traditional calculation method, but also the computational efficiency has been significantly improved.