There are a lot of interference factors in the operating environment of machinery, which makes it ineffective to use traditional detection methods to judge the fault location and type of fault of the machinery, and even misjudgment of the fault location and type may occur. In order to solve these problems, this paper proposes a bearing fault diagnosis method based on wavelet denoising and machine learning. We use sensors to detect the operating conditions of rolling bearings under different working conditions to obtain datasets of different types of bearing failures. On the basis of using the wavelet denoising algorithm to reduce noise, we comprehensively evaluated five machine learning models, including K-means clustering, decision tree, random forest, and support vector machine to classify bearing faults and compare their results. By designing the fault classification evaluation prediction criteria, the following conclusions are drawn. The model proposed in this paper is significantly better than other traditional diagnostic models for bearing faults. In order to solve the problem of weak signal strength and background noise interference, this paper selects a better noise reduction algorithm under different quantitative evaluation indicators for wavelet denoising, which can better restore the true characteristics of the fault signal. Using unsupervised learning and supervised machine learning classification algorithms, the evaluation indicators before and after denoising are compared to make the classification results more accurate and reliable. This article will help researchers to intelligently diagnose the faults of rolling bearing equipment in rotating machinery.

This paper mainly discusses the asymptotic properties of quantile regression processes. In view of the exponential tightness and convexity argument, we prove the quantile regression estimators satisfy the functional moderate deviation principle. This method can be extended to a fair range of different statistical estimation problems such as quantile regression estimators with bridge penalized functions.

Mortality is one of the most important epidemiological measures and a key indicator of the effectiveness of potential treatments or interventions. In this paper, a permutation test method of variance analysis is proposed to test the null hypothesis that the real-time fatality rates of multiple groups were equal during the epidemic period. In light of large-scale simulation studies, the proposed test method can accurately identify the differences between different groups and display satisfactory performance. We apply the proposed method to the real dataset of the COVID-19 epidemic in mainland China (excluding Hubei), Hubei Province (excluding Wuhan), and Wuhan from 31 January 2020 to 30 March 2020. By comparing the differences in the disease severity for differential cities, we show that the severity of the early disease of COVID-19 may be related to the effectiveness of interventions and the improvement in medical resources.