In order to separate the sub-signals and extract the feature frequency in the signal accurately, we proposed a parameter-adaptive time-varying filtering empirical mode decomposition (TVF-EMD) feature extraction method based on the improved grasshopper optimization algorithm (IGOA). The method not only improved the local optimal problem of GOA, but could also determine the bandwidth threshold and B-spline order of TVF-EMD adaptively. Firstly, a nonlinear decreasing strategy was introduced in this paper to adjust the decreasing coefficient of GOA dynamically. Then, energy entropy mutual information (EEMI) was introduced to comprehensively consider the energy distribution of the modes and the dependence between the modes and the original signal, and the EEMI was used as the objective function. In addition, TVF-EMD was optimized by IGOA and the optimal parameters matching the input signal were obtained. Finally, the feature frequency of the signal was extracted by analyzing the sensitive mode with larger kurtosis. The optimization experiments of 23 sets of benchmark functions showed that IGOA not only enhanced the balance between exploration and development, but also improved the global and local search ability and stability of the algorithm. The analysis of the simulation signal and bearing signal shows that the parameter-adaptive TVF-EMD method can separate the modes with specific physical meanings accurately. Compared with ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), TVF-EMD with fixed parameters and GOA-TVF-EMD, the decomposition performance of the proposed method is better. The proposed method not only improved the under-decomposition, over-decomposition and modal aliasing problems of TVF-EMD, but could also accurately separate the frequency components of the signal and extract the included feature information, so it has practical significance in mechanical fault diagnosis.

Aiming at the problem that fault feature extraction is susceptible to background noises and burrs, we proposed a new feature extraction method based on a new decomposition method and an effective intrinsic mode function (IMF) selection method. Firstly, pairs of white noises with opposite signs were introduced to neutralize the residual noises in ensemble empirical mode decomposition (EEMD) and suppress mode mixing. Both the reconstruction error (1.8445 × 10⁻¹⁷) and decomposition time (0.01 s) were greatly reduced through fast, complementary ensemble empirical mode decomposition (FCEEMD). Secondly, we integrated the energy and kurtosis of the IMF and proposed an effective IMF selection method based on energy kurtosis mean filtering, and the background noise of the signal was greatly suppressed. Finally, the periodic impacts were extracted from the IMF reconstruction signal by multipoint optimal minimum entropy deconvolution adjusted (MOMEDA). The fault frequencies were extracted from the periodic impacts through Hilbert demodulation, and the relative errors between the measured values and the theoretical values were all less than 0.05. The experimental results show that the proposed method can extract fault features more efficiently and provide a novel method for the fault diagnosis of rotating machinery.

Aiming at the disadvantages of low trend, poor characterization performance, and poor anti-noise performance of traditional degradation features such as dispersion entropy (DE), a fault detection method based on sliding dispersion entropy (SDE) is proposed. Firstly, a sliding window is added to the signal before extracting the DE feature, and the root mean square of the signal inside the sliding window is used to replace the signal in the window to realize down sampling, which enhances the trend of DE. Secondly, the hyperbolic tangent sigmoid function (TANSIG) is introduced to map the signals to different categories when extracting the DE feature, which is more in line with the signal distribution of mechanical parts and the monotonicity of the degradation feature is improved. For noisy signal, the introduction of locally weighted scatterplot smoothing (LOWESS) can remove the burrs and fluctuations of the SDE curve, and the anti-noise performance of SDE is improved. Finally, the SDE state warning line is constructed based on the 2σ criterion, which can determine the fault warning point in time and effectively. The state detection results of bearing and check valve show that the proposed SDE improves the trend, monotonicity, and robustness of the state tracking curve, and provides a new method for fault state detection of mechanical parts.