Synthetic minority oversampling (SMOTE) has been widely used in dealing with the imbalance classification in the mechanical fault diagnosis field. However, the classical SMOTE model generates poor quality data, which leads to a low diagnostic accuracy of the classification model. This article proposes an oversampling generation model based on the Gaussian mixture model (GMM) and boundary joint optimization (BDOP-GMM-SMOTE). First, GMM is utilized to cluster minority class bearing fault data, and weights of different classes should be distributed according to the cluster density distribution function. Then, the minority classes should be resampled to balance intraclass. Third, the data boundary is established by calculating intraclass and interclass distances between the minority class and other failure-class samples. And penalty coefficient is introduced to optimize data generation boundary by minimizing intraclass and maximizing interclass principle. Afterward, a generated fault dataset satisfied intraclass and interclass balance is obtained. Finally, the generation effectiveness and robustness of the proposed method are verified by bearing experiment data, especially in diagnostic accuracy and processing speed.

Recently, the enhanced frequency band entropy (EFBE) was proposed based on the replacement of short-time Fourier transform with wavelet packet transform. In view of the shortcomings of EFBE, a feasible solution is provided, namely modified frequency band envelope kurtosis (MFBEK), which can be described as follows: First, the modified adaptive resonance bandwidth (MARB) based on the bearing inner-race fault frequency is proposed. The kurtosis of the envelope signal as an available indicator and the MARB are used to determine the optimal depth of MFBEK. Second, this special case, that is, the resonant frequency occurs at the junction of two adjacent subbands is considered, and a corresponding effective solution is provided to determine the optimal subband(s). Then, the reconstructed signal can be obtained. And then, if necessary, a band-pass filter is designed to process the reconstructed signal to enhance the noise reduction performance. Finally, envelope power spectrum analysis is performed on the reconstructed signal or the filtered signal to extract the fault characteristic frequency. In addition, a modified indicator is proposed to measure the analysis results. Analysis results on simulated and vibration signals measured from actual bearing have revealed that the MFBEK can obtain more robust performance.

The singular value decomposition (SVD) based on the Hankel matrix is commonly used in signal processing and fault diagnosis. The noise reduction performance of SVD based on the Hankel matrix is affected by three factors: the reconstruction component(s), the structure of the Hankel matrix, and the point number of the analysis data. In this article, the three influencing factors are systematically studied, and a method based on correlated SVD (C-SVD) is proposed and successfully applied to bearing fault diagnosis. First, perform SVD analysis on the collected original signal. Then, the reconstructed component(s) determination method of SVD based on the combination of singular value ratio (SVR) and correlation coefficient is proposed. Then, based on the SVR, using the envelope kurtosis as the indicator, the optimal structure of the Hankel matrix (number of rows and columns) is studied. Then, the number of data points of the analysis signal is discussed, and the constraint range is given. Finally, the envelope power spectrum analysis is performed on the reconstructed signal to extract the fault features. The proposed C-SVD method is compared with the existing typical methods and applied to the simulated signal and the actual bearing fault signal, and its superiority is verified.

A reliable, efficient, and simple control is presented and validated for a quarter-car active suspension system equipped with an electro-hydraulic actuator. Unlike the existing techniques, this control does not use any function approximation, e.g., neural networks (NNs) or fuzzy-logic systems (FLSs), while the unmolded dynamics, including the hydraulic actuator behavior, can be accommodated effectively. Hence, the heavy computational costs and tedious parameter tuning phase can be remedied. Moreover, both the transient and steady-state suspension performance can be retained by incorporating prescribed performance functions (PPFs) into the control implementation. This guaranteed performance is particularly useful for guaranteeing the safe operation of suspension systems. Apart from theoretical studies, some practical considerations of control implementation and several parameter tuning guidelines are suggested. Experimental results based on a practical quarter-car active suspension test-rig demonstrate that this control can obtain a superior performance and has better computational efficiency over several other control methods.

For the two shortcomings of singular value decomposition (SVD), the determination of the reconstruction order and the poor noise reduction ability, an enhanced SVD is introduced in this article. The core ideas include: first, an efficient method to determine the reconstructed order of SVD and the relative-change rate of the singular envelope kurtosis is presented, composed of improved SVD (ISVD). Then, the method to select the optimal node of wavelet packet transform (WPT) by the criterion of envelope kurtosis maximum is presented, composed of improved WPT (IWPT). The flexible filter design and superior noise reduction abilities of the IWPT and the passband denoise ability of the ISVD are organicly combined to form enhanced singular value decomposition (E-SVD) method. In addition, an indicator is introduced to evaluate the performance of the results. First, the reconstructed signal is obtained by performing ISVD on the original signal. Second, IWPT is executed on the reconstructed signal to achieve the optimal node. Finally, the filtered signal is combined with the envelope power spectrum to extract the bearing fault characteristic frequency. The method's validity and superiority are verified by the analysis of simulated data and actual cases of rolling bearing.

This paper presents a new adaptive fuzzy control scheme for active suspension systems subject to control input time delay and unknown nonlinear dynamics. First, a predictor-based compensation scheme is constructed to address the effect of input delay in the closed-loop system. Then, a fuzzy logic system (FLS) is employed as the function approximator to address the unknown nonlinearities. Finally, to enhance the transient suspension response, a novel parameter estimation error-based finite-time (FT) adaptive algorithm is developed to online update the unknown FLS weights, which differs from traditional estimation methods, for example, gradient algorithm with e -modification or σ -modification. In this framework, both the suspension and estimation errors can achieve convergence in FT. A Lyapunov-Krasovskii functional is constructed to prove the closed-loop system stability. Comparative simulation results based on a dynamic simulator built in a professional vehicle simulation software, Carsim, are provided to demonstrate the validity of the proposed control approach, and show its effectiveness to operate active suspension systems safely and reliably in various road conditions.

Frequency band entropy (FBE) has been proved usable in the fault diagnosis of rolling bearings, but its performance is poor in the presence of non-Gaussian noise and a low signal-to-noise ratio. In order to extract the transient impulsive signals more effectively, wavelet packet transform (WPT) is considered as an alternative method for signal decomposition. Therefore, by introducing WPT into FBE, this article introduces an enhanced FBE (EFBE) adopting WPT as the filter of FBE to overcome the shortcomings of the original FBE. Then, the depth of EFBE is optimized using adaptive resonance bandwidth and power amplitude spectrum entropy (PASE). Third, a novel method based on the indicator PASE is introduced to select the optimal node of EFBE. Finally, the filtered signal is combined with the envelope power spectrum to extract the fault feature frequency. In addition, an evaluation indicator is proposed to evaluate the performance of the EFBE. The simulation and cases are used to demonstrate the effectiveness and improved performance of the EFBE compared with the original FBE and other typical methods. The results show that the EFBE can detect various rolling bearing failures and implement its fault diagnosis effectively.