Bearing fault diagnosis is of significance to ensure the safe and reliable operation of a motor. Deep learning provides a powerful ability to extract the features of raw data automatically. A convolutional deep belief network (CDBN) is an effective deep learning method. In this article, a novel vibration amplitude spectrum imaging feature extraction method using continuous wavelet transform and image conversion is proposed, which can extract the image features with two-dimensional and eliminate the effect of handcrafted features under low signal-to-noise ratio conditions, different operating conditions, and data segmentation. Then, a novel CDBN with Gaussian distribution is constructed to learn the representative features for bearing fault classification. The proposed method is tested on motor bearing dataset with four and ten classifications. The results have been compared with other methods. The experiment results show that the proposed method has achieved significant improvements and is more effective than the traditional methods.

The effective separation of fault characteristic components is the core of compound fault diagnosis of rolling bearings. The intelligent optimization algorithm has better global optimization performance and fast convergence speed. Aiming at the problem of poor diagnosis effect caused by mutual interference between multiple fault responses, a novel compound fault diagnosis method based on optimized maximum correlation kurtosis deconvolution (MCKD) and sparse representation, namely MDSRCFD, is proposed in this article. For the MCKD, because it is very difficult to set reasonable parameter combination values, artificial fish school (AFS) with global search capability and strong robustness is fully utilized to optimize the key parameters of MCKD to achieve the best deconvolution and fault feature separation. Aiming at the problem that orthogonal matching pursuit (OMP) is difficult to be solved in sparse representation, an artificial bee colony (ABC) with global optimization ability and faster convergence speed is employed to solve OMP to obtain the approximate best atom and realize the reconstruction of signal transient components. The envelope demodulation analysis method is applied to realize feature extraction and fault diagnosis. The simulation and practical application results show that the proposed MDSRCFD can effectively separate and extract the compound fault characteristics of rolling bearings, which can realize the accurate compound fault diagnosis.

In recent years, methods for detecting motor bearing faults have attracted increasing attention. However, it is very difficult to detect the faults from weak motor bearing signals under the strong noise. Stochastic resonance (SR) is a popular signal processing method, which can process weak signals with the noise, but the traditional SR is burdensome in determining its parameters. Therefore, in this paper, a new advancing coupled multi-stable stochastic resonance method, with two first-order multi-stable stochastic resonance systems, namely CMSR, is proposed to detect motor bearing faults. Firstly, the effects of the output signal-to-noise ratio (SNR) for system parameters and coupling coefficients are analyzed in-depth by numerical simulation technology. Then, the SNR is considered as the fitness function for the seeker optimization algorithm (SOA), which can adaptively optimize and determine the system parameters of the SR by using the subsampling technique. An advancing coupled multi-stable stochastic resonance method is realized, and the pre-processed signal is input into the CMSR to detect the faults of motor bearings by using Fourier transform. The faults of motor bearings are determined according to the output signal. Finally, the actual vibration data of induction motor bearings are used to prove the effectiveness of the proposed CMSR. The comparison results with the MSR show that the CMSR can obtain a higher output SNR, which is more beneficial to extract weak signal features and realize fault detection. At the same time, this method also has practical application value for engineering rotating machinery.

Parametrized time-frequency analysis (PTFA) can effectively improve time-frequency energy aggregation of non-stationary signal and immunity of cross term interference, but it exists the energy diffusion near the real instantaneous frequency. The improved multi-synchrosqueezing transform (IMSST) can improve the time-frequency energy aggregation, but it still has defects in processing strong FM and AM signals under noise interference. Therefore, in order to make use of their advantages and overcome their disadvantages, a novel parametrized multi-synchrosqueezing transform method based on weighted least square, IMSST and PTFA, namely PMSST is proposed in this paper. In the PMSST, the IMSST is designed to obtain the signal time-frequency representation with high energy aggregation. Then the ridge extraction algorithm is employed to extract the instantaneous frequency ridges of each mono-component signal. The weighted least square method is used to estimate the parameters of parameterized transform kernel. Finally, time-frequency spectrum is superimposed to obtain the time-frequency energy representation of the enhanced signal. The experiment results show that the PMSST can effectively process non-stationary signals with varying instantaneous frequency by the simulated signal and actual fault signals.

In this paper, a new fractional-order (FO) PI^λD^µ controller is designed with the desired gain and phase margin for the automatic rudder of underactuated surface vessels (USVs). The integral order λ and the differential order μ are introduced in the controller, and the two additional adjustable factors make the FO PI^λD^µ controller have better accuracy and robustness. Simulations are carried out for comparison with a ship’s digital PID autopilot. The results show that the FO PI^λD^µ controller has the advantages of a small overshoot, short adjustment time, and precise control. Due to the uncertainty of the model parameters of USVs and two extra parameters, it is difficult to compute the parameters of an FO PI^λD^µ controller. Secondly, this paper proposes a novel particle swarm optimization (PSO) algorithm for dynamic adjustment of the FO PI^λD^µ controller parameters. By dynamically changing the learning factor, the particles carefully search in their own neighborhoods at the early stage of the algorithm to prevent them from missing the global optimum and converging on the local optimum, while at the later stage of evolution, the particles converge on the global optimal solution quickly and accurately to speed up PSO convergence. Finally, comparative experiments of four different controllers under different sailing conditions are carried out, and the results show that the FO PI^λD^µ controller based on the IPSO algorithm has the advantages of a small overshoot, short adjustment time, precise control, and strong anti-disturbance control.