To intelligently identify gear fault types on the basis of gear vibration signals, due to the non-linear and non-stationary characteristics of gear vibration signals, a fuzzy function is used to represent the gear vibration signals in different states as two-dimensional time-frequency images. To solve the problem that the recognition effect of discontinuity area in the image by traditional Hu invariant moments is not ideal, improved Hu invariant moments are proposed, and the feature parameters of time-frequency images of gear vibration signals are extracted based on the improved Hu invariant moments. Different intelligent classifiers are used to recognize the gear vibration signals in different states. The recognition accuracy is higher by improved Hu invariant moments than by traditional Hu invariant moments, which shows that the method of gear fault feature extraction based on a fuzzy function and improved Hu invariant moments is quite ideal, and can be used in intelligent diagnosis of gear faults.

Bearing fault signal analysis is an important means of bearing fault diagnosis. To effectively eliminate noise in a fault signal, an adaptive multiscale combined morphological filter is proposed based on the theory of mathematical morphology. Both simulation and experimental results show that the adaptive multiscale combined morphological filter can remove noise more thoroughly and retain details of the fault signal better than the dual-tree complex wavelet filter, traditional morphological filter, adaptive singular value decomposition method (ASVD), and improved switching Kalman filter (ISKF). The adaptive multiscale combined morphological filter considers both positive and negative impulses in the signal; therefore, it has strong adaptability to complex noise in the environment, making it an effective new method for bearing fault diagnosis.

In order to solve the problem that the accuracy is not high when the traditional fuzzy morphological associative memories network (FMAM) is used to classify samples, based on quantum superposition and collapse, the quantum fuzzy morphological associative memories network (QFMAM) is proposed. In QFMAM, the structural element is constructed by the qubit system and the qubit probability represents corresponding membership degree to obtain adaptive structural elements. The samples are preprocessed first and then classified to ensure high classification accuracy. QFMAM, FMAM, support vector machine (SVM) and naive Bayes classifier (NBC) are used to classify simulation data and experimental signals of rolling bearings respectively. Comparing the performance of the four classifiers, it is obvious that the training time of QFMAM is far less than SVM and NBC, and the classification accuracy of the test samples by QFMAM is higher than that by the other three classifiers. QFMAM is very suitable for intelligent diagnosis of rolling bearing fault.