Parallel Lempel-Ziv complexity: An efficient computing framework of Lempel-Ziv complexity

Abstract Lempel-Ziv complexity 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 Lempel-Ziv complexity for bearing diagnosis with multipoint signals. Therefore, this paper proposes a parallel computing framework for Lempel-Ziv complexity combined with the parallel computing method. Firstly, the original signal is reconstructed in phase space to transform the one-dimensional signal into the multi-dimensional sub-signal. Then, the independent components of each dimension are calculated. Next, the independent components of all dimensions are integrated and the number of them is counted. Finally, the Lempel-Ziv complexity is calculated according to the number of independent components. The proposed method is verified by three simulated signals, bearing single point fault signal and bearing full-life signal. The changing trend of Lempel-Ziv complexity 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.