In view of the problems in traditional fault diagnosis method, such as small samples and nonlinear relations, a fault diagnosis method based on improved multi-class classification algorithm and relevance vector machine (RVM) is proposed in the paper. Through improving the majority-vote strategy of traditional One-Against-One (OAO) algorithm and combining the features of OAO and One-Against-Rest (OAR) algorithms, the k-class classification problem is transformed into k(k-1)/2 three-class classification problems based on the proposed majority-vote strategy of double-layer and thereby an improved multi-class classification algorithm of One-Against-One-Against-Rest (OAOAR) is presented. And on each three-class classification issue, OAO and RVM as the binary classifier are adopted to achieve the multi-class classification of RVM. Numerical simulations of UCI datasets and fault diagnostic experiments results of power transformers both demonstrate that the proposed method performs significantly better than other traditional methods in terms of increasing the diagnostic accuracy, optimizing the voting results, strengthening the diagnostic confidence and identifying the hidden classes, and has more practical value in engineering.

Stochastic resonance is like a nonlinear filter to detect the weak bearing fault-induced impulses that submerged in strong noises. Signal-to-noise ratio (SNR) is often used as the index to evaluate the SR output, but the fault characteristic frequency (FCF) must be known in order to calculate SNR. A novel bearing fault diagnosis method called synthetic quantitative index-based adaptive underdamped stochastic resonance (SQI-AUSR) is proposed. The synthetic quantitative index (SQI) is composed of power spectrum kurtosis, kurtosis, margin index, and correlation coefficient. The SQI is independent of FCF, which avoids the limitation that the calculation of SNR must know the FCF. Numeric simulations and two case studies of bearing faults are carried out. The results show that (1) the SQI is more effective than other proposed indexes such as correlation coefficient and weight power spectrum kurtosis and (2) the proposed SQI-AUSR is effective for bearing fault diagnosis and is better than SNR-AOSR.

Effective filtering and noise reduction, feature extraction and fault diagnosis, and prognostics technology are important to Prognostics and Health Management (PHM) of equipment. Therefore, a multifeature fusion fault diagnosis method based on the combination of quadratic filtering and QPSO-KELM algorithm is proposed. In the quadratic filtering, stable filtering can reduce the impact of noise and fast-kurtogram can filtrate fault frequency bands with rich fault information. Then, the time-domain, frequency-domain, and time-frequency parameters of the secondary filter signal are extracted. MSSST was used to analyze the filtered signal, and the time-frequency image was obtained. The time-frequency parameter was extracted from the time-frequency image by 2DPCA, and all the extracted parameters are taken as the fusion fault feature of the gearbox. Finally, the fault feature parameters are taken as the training sample and testing sample of QPSO-KELM for training and testing to achieve the purpose of fault diagnosis. The experimental results show that the proposed method can effectively filter the noise, complete the fault mode identification of gearbox, and improve the fault diagnosis accuracy better than other methods.

It is difficult to estimate the parameters of Weibull mixtures precisely when using these distributions to analyze the reliability of equipment parts. As to this problem, an optimization model of the Weibull mixtures based on the Bayes theorem is proposed, and the cuckoo search is used to solve the optimization model. An case makes the diesel injector as the object of study and the two-component Weibull distribution as the life distribution. Three algorithms including cuckoo search (CS), particle swarm optimization (PSO) and genetic algorithm (GA) are used to solve the optimization model, and their solving results are compared. The result shows that the cuckoo search is the best algorithm of the three in solution efficiency and convergence performance.