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To improve the fault identification accuracy of rolling bearing and effectively analyze the fault severity, a novel rolling bearing fault diagnosis and severity analysis method based on the fast sample entropy, the wavelet packet energy entropy, and a multiclass relevance vector machine is proposed in this paper. A fast sample entropy calculation method based on a kd tree is adopted to improve the real-time performance of fault detection in this paper. In view of the non-linearity and non-stationarity of the vibration signals, the vibration signal of the rolling bearing is decomposed into several sub-signals containing fault information by using a wavelet packet. Then, the energy entropy values of the sub-signals decomposed by the wavelet packet are calculated to generate the feature vectors for describing different fault types and severity levels of rolling bearings. The multiclass relevance vector machine modeled by the feature vectors of different fault types and severity levels is used to realize fault type identification and a fault severity analysis of the bearings. The proposed fault diagnosis and severity analysis method is fully evaluated by experiments. The experimental results demonstrate that the fault detection method based on the sample entropy can effectively detect rolling bearing failure. The fault feature extraction method based on the wavelet packet energy entropy can effectively extract the fault features of vibration signals and a multiclass relevance vector machine can identify the fault type and severity by means of the fault features contained in these signals. Compared with some existing bearing rolling fault diagnosis methods, the proposed method is excellent for fault diagnosis and severity analysis and improves the fault identification rate reaching as high as 99.47%.

Because of the low accuracy of the current machine olfactory algorithms in detecting two mixed gases, this study proposes a hybrid gas detection algorithm based on an extreme random tree to greatly improve the classification accuracy and time efficiency. The method mainly uses the dynamic time warping algorithm (DTW) to perform data pre-processing and then extracts the gas characteristics from gas signals at different concentrations by applying a principal component analysis (PCA). Finally, the model is established by using a new extreme random tree algorithm to achieve the target gas classification. The sample data collected by the experiment was verified by comparison experiments with the proposed algorithm. The analysis results show that the proposed DTW algorithm improves the gas classification accuracy by 26.87%. Compared with the random forest algorithm, extreme gradient boosting (XGBoost) algorithm and gradient boosting decision tree (GBDT) algorithm, the accuracy rate increased by 4.53%, 5.11% and 8.10%, respectively, reaching 99.28%. In terms of the time efficiency of the algorithms, the actual runtime of the extreme random tree algorithm is 66.85%, 90.27%, and 81.61% lower than that of the random forest algorithm, XGBoost algorithm, and GBDT algorithm, respectively, reaching 103.2568 s.