A damage degree identification method based on high-order difference mathematical morphology gradient spectrum entropy (HMGSEDI) is proposed in this paper to solve the problem that fault signal of rolling bearings are weak and difficult to be quantitatively measured. In the HMGSEDI method, on the basis of mathematical morphology gradient spectrum and spectrum entropy, the changing scale influence of structure elements to damage degree identification is thoroughly analyzed to determine its optimal scale range. The high-order difference mathematical morphology gradient spectrum entropy is then defined in order to quantitatively describe the fault damage degree of bearing. The discrimination concept of fault damage degree is defined to quantitatively describe the difference between the high-order differential mathematical entropy and the general mathematical morphology entropy in order to propose a fault damage degree identification method. The vibration signal of motors under no-load and load states are used to testify the effectiveness of the proposed HMGSEDI method. The experiment shows that high-order differential mathematical morphology entropy can more effectively identify the fault damage degree of bearings and the identification accuracy of fault damage degree can be greatly improved. Therefore, the HMGSEDI method is an effective quantitative fault damage degree identification method, and provides a new way to identify fault damage degree and fault prediction of rotating machinery.

Vibration signals are used to diagnosis faults of the rolling bearing which is symmetric structure. Stochastic resonance (SR) has been widely applied in weak signal feature extraction in recent years. It can utilize noise and enhance weak signals. However, the traditional SR method has poor performance, and it is difficult to determine parameters of SR. Therefore, a new second-order tristable SR method (STSR) based on a new potential combining the classical bistable potential with Woods-Saxon potential is proposed in this paper. Firstly, the envelope signal of rolling bearings is the input signal of STSR. Then, the output of signal-to-noise ratio (SNR) is used as the fitness function of the Seeker Optimization Algorithm (SOA) in order to optimize the parameters of SR. Finally, the optimal parameters are used to set the STSR system in order to enhance and extract weak signals of rolling bearings. Simulated and experimental signals are used to demonstrate the effectiveness of STSR. The diagnosis results show that the proposed STSR method can obtain higher output SNR and better filtering performance than the traditional SR methods. It provides a new idea for fault diagnosis of rotating machinery.

The high sampling frequency of traditional Nyquist sampling theory not only puts greater requirements on the sampling equipment, but also generates a large amount of data, which increases the difficulty of information transmission and storage. To this end, this paper proposes a rolling bearing fault signal detection method based on compressed sensing combined with a neural network. Based on the theory of compressed sensing, the observations obtained from compression sampling are divided into two sets of data. Given the one set of data, the predictive ability of the nonlinear time series through the neural network can predict the second set of observed values. The predicted observations are used to reconstruct the signal, thereby reducing the amount of data to be stored and transmitted and realizing secondary compression of the signal.

In mechanical equipment, rolling bearings analyze and monitor their fault based on their vibration signals. Vibration signals obtained are usually weak because the machine works in a noisy background that makes it very difficult to extract its feature. To address this problem, a second-order coupled step-varying stochastic resonance (SCSSR) system is proposed. The system couples two second-order stochastic resonance (SR) systems into a multistable system, one of which is a controlled system and the other of which is a controlling system that uses the output of one system to adjust the output of the other system to enhance the weak signal. In this method, we apply the seeker optimization algorithm (SOA), which uses the output signal-to-noise ratio (SNR) as the estimating function and combines the twice-sampling technology to adaptively select the parameters of the coupled SR system to achieve feature enhancement and collection of the weak periodic signal. The simulation and real fault data of a bearing prove that this method has better results in detecting weak signals, and the system output SNR is higher than the traditional SR method.