Composite multi-scale weighted permutation entropy and extreme learning machine based intelligent fault diagnosis for rolling bearing

•CWMPE is proposed for measuring the complexity and dynamic change of time series.•The influence of data length on CMWPE is studied and compared with MPE and MWPE.•A new fault diagnosis scheme for rolling bearing is proposed based on CMWPE and ELM.•The proposed scheme is applied to experimental data to verify its superiority.•The proposed scheme is compared with existing other methods. Multi-scale permutation entropy (MPE) has been proven to be an effective nonlinear dynamic analysis tool for complexity and irregularity evaluation of rolling bearing. Nevertheless, MPE still has some issues that need to be addressed. First, the coarse grained process used in MPE will shorten the length of time series and result in mode information loss, especially for short time series. Second, different patterns of a symbol cannot be distinguished by permutation entropy and MPE. Inspired by the thought of composite coarse graining and weighted permutation entropy, the composite multi-scale weighted permutation entropy (CMWPE) methodology is proposed in this paper. Compared with MPE, CMWPE preserves much more useful information by adding the weighted factor and using composite coarse graining to optimize the process of coarse-gained time series, where multiple time series information is considered for the same scale factor. The simulation synthetic signals are used to demonstrate the effectiveness of CMWPE and the results show that CMWPE has less dependence on data length and the estimated entropy values are much more stable than the other existing methods. Based on CMWPE, a new intelligent fault diagnosis scheme for rolling bearing is proposed with combination of extreme learning machine. Finally, the proposed fault diagnosis method is applied to two diagnostic cases of rolling bearing and the results verified the effectiveness and superiority of the proposed approach to MPE and MWPE.