Fault diagnosis of rolling bearings is important for ensuring the safe operation of industrial machinery. How to effectively extract the fault features and select a classifier with high precision is the key to realizing the fault recognition of bearings. Accordingly, a new fault diagnosis method of rolling bearings based on improved fast spectral correlation and optimized random forest (i.e., particle swarm optimization-random forest (PSO-RF)) is proposed in this paper. The main contributions of this study are made from two aspects. One is that an improved fast spectral correlation approach was developed to extract the fault features of bearings and form the feature vector more effectively. The other is that an optimized random forest classifier was developed to achieve highly accurate identification by exploiting particle swarm optimization to select the best parameters of random forest (RF). In the presented method, improved fast spectral correlation was first utilized to analyze the raw vibration signal caused by a faulty bearing to obtain the enhanced envelope spectrum. Then, the amplitudes of the four characteristic cyclic frequencies (i.e., the rotating frequency, the characteristic frequency of outer-race fault, the characteristic frequency of inner-race fault, and the characteristic frequency of rolling element fault) exhibited in the enhanced envelope spectrum were selected to form the feature vector. Finally, the PSO-RF method was introduced for identifying and classifying bearing faults. The experimental investigations demonstrate the proposed method can accurately identify bearing faults and outperform other state-of-art techniques considered.

Rotor is a widely used and easily defected mechanical component. Thus, it is significant to develop effective techniques for rotor fault diagnosis. Fault signature extraction and state classification of the extracted signatures are two key steps for diagnosing rotor faults. To complete the accurate recognition of rotor states, a novel evaluation index named characteristic frequency band energy entropy (CFBEE) was proposed to extract the defective features of rotors, and support vector machine (SVM) was employed to automatically identify the rotor fault types. Specifically, the raw vibration signal of rotor was first analyzed by a joint time–frequency method based on improved singular spectrum decomposition (ISSD) and Hilbert transform (HT) to derive its time–frequency spectrum (TFS), which is named ISSD-HT TFS in this paper. Then, the CFBEE of the ISSD-HT TFS was calculated as the fault feature vector. Finally, SVM was used to complete the automatic identification of rotor faults. Simulated processing results indicate that ISSD improves the end effects of singular spectrum decomposition (SSD) and is superior to empirical mode decomposition (EMD) in extracting the sub-components of rotor vibration signal. The ISSD-HT TFS can more accurately reflect the time–frequency information compared to the EMD-HT TFS. Experimental verification demonstrates that the proposed method can accurately identify rotor defect types and outperform some other methods.

Compound fault diagnosis is challenging due to the complexity, diversity and non-stationary characteristics of mechanical complex faults. In this paper, a novel compound fault separation method based on singular negentropy difference spectrum (SNDS) and integrated fast spectral correlation (IFSC) is proposed. Firstly, the original signal was de-noised by SNDS which improved the noise reduction effect of singular difference spectrum by introducing negative entropy. Secondly, the de-noised signal was analyzed by fast spectral correlation. Finally, IFSC took the fourth-order energy as the index to determine the resonance band and separate the fault features of different single fault. The proposed method is applied to analyze the simulated compound signals and the experimental vibration signals, the results show that the proposed method has excellent performance in the separation of rolling bearing composite faults.

The impulsive fault feature signal of rolling bearings at the early failure stage is easily contaminated by the fundamental frequency (i.e., the rotation frequency of the shaft) signal and background noise. To address this problem, this paper puts forward a rolling bearing weak fault diagnosis method with the combination of optimal notch filter and enhanced singular value decomposition. Firstly, in order to eliminate the interference of the fundamental frequency signal, the original signal was processed by the notch filter with the fundamental frequency as the center frequency and with a varying bandwidth to get a series of corresponding notch filter signals. Secondly, the Teager energy entropy index was adopted to adaptively determine the optimal bandwidth to complete the optimal notch filter analysis on the raw vibration signal and obtain the corresponding optimal notch filter signal. Thirdly, an enhanced singular value decomposition de-nosing method was employed to de-noise the optimal notch filter signal. Finally, the envelope spectrum analysis was conducted on the de-noised signal to extract the fault characteristic frequencies. The effectiveness of the presented method was demonstrated via simulation and experiment verifications. In addition, the minimum entropy deconvolution, Kurtogram and Infogram methods were employed for comparisons to show the advantages of the presented method.

The accurate fault diagnosis of gearboxes is of great significance for ensuring safe and efficient operation of rotating machinery. This paper develops a novel fault diagnosis method based on hierarchical instantaneous energy density dispersion entropy (HIEDDE) and dynamic time warping (DTW). Specifically, the instantaneous energy density (IED) analysis based on singular spectrum decomposition (SSD) and Hilbert transform (HT) is first applied to the vibration signal of gearbox to acquire the IED signal, which is designed to reinforce the fault feature of the signal. Then, the hierarchical dispersion entropy (HDE) algorithm developed in this paper is used to quantify the complexity of the IED signal to obtain the HIEDDE as fault features. Finally, the DTW algorithm is employed to recognize the fault types automatically. The validity of the two parts that make up the HIEDDE algorithm, i.e., the IED analysis for fault features enhancement and the HDE algorithm for quantifying the information of signals, is numerically verified. The proposed method recognizes the fault patterns of the experimental data of gearbox accurately and exhibits advantages over the existing methods such as multi-scale dispersion entropy (MDE) and refined composite MDE (RCMDE).

Fast kurtogram (FK) is an efficient method for processing non-stationary signals, widely recognized by scholars as a rapid and effective approach for fault diagnosis. However, it has limitations in distinguishing between periodic pulse and random interference pulses due to the drawbacks in its frequency band segmentation methods and the inherent shortcomings of the kurtosis index itself. To address this, this paper proposes a fault feature extraction method based on the maximum envelope spectrum power function-based Gini indices (PFGI2) and empirical wavelet transform. This method, inspired by the concept of FK, constructs a series of band-pass filters following the principles of empirical wavelet decomposition. It applies envelope spectrum analysis to a series of sub-bands and calculates the PFGI2 value for each, to identify the optimal sub-band. The effectiveness of the proposed method is validated through simulations of vibration signals and experimental data.