Rolling Bearings Fault Diagnosis based on Generalized Demodulation Time-frequency Analysis Method

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(完整word版)滚动轴承故障诊断分析

滚动轴承故障诊断分析学院名称：机械与汽车工程学院专业班级：学生姓名：学生学号：指导教师姓名：摘要滚动轴承故障诊断本文对滚动轴承的故障形式、故障原因、常用诊断方法等诊断基础和滚动轴承故障的振动机理作了研究，并建立了相应的滚动轴承典型故障(外圈损伤、内圈损伤、滚动体损伤)的理论模型，给出了一些滚动轴承故障诊断常见实例。

通过对滚动轴承故障振动机理的研究可以帮助我们了解滚动轴承故障的本质和特征。

本文对特征参数的提取，理论推导，和过程都进行了详细的阐述，关键词:滚动轴承；故障诊断；特征参数；特征；ABSTRACT ：The Rolling fault diagnosisIn the thesis ,the fault types,diagnostic methods an d vibration principle of rolling bearing are discussed.the thesis sets up a series of academic m odels of faulty rolling bearings and lists some sym ptom parameters which often used in fault diagnosis of rolling bearings . the study of vibration prin ciple of rolling bearings can help us to know the essence and feature of rolling bearings.In this paper, the parameters of the extraction, theoretical a nalysis, and process are described in detail. Keywords: Rolling Bearing; Fault Diagnosis; Symptom P arameter; Distinction Index; Distinction Rate0引言：随着科技的发展，现代工业正逐步向生产设备大型化、复杂化、高速化和自动化方向发展，在提高生产率、降低成本、节约能源、减少废品率、保证产品质量等方面具有很大的优势。

基于DispEn与SVM的滚动轴承故障诊断

●装备与技术Equipment ＆Technology基于DispEn 与SVM 的滚动轴承故障诊断杨刚刚1，夏均忠2，孔有程1，唐衡1(1．陆军军事交通学院学员五大队，天津300161;2．陆军军事交通学院军用车辆工程系，天津300161)摘要:为实现滚动轴承故障检测并准确识别滚动轴承不同严重程度的同种故障，提出一种基于散布熵(DispEn )与支持向量机(SVM )的滚动轴承故障诊断方法。

首先，计算滚动轴承4种状态同类振动信号的DispEn ，通过对比其值的大小，实现滚动轴承故障检测;其次，将样本信号的DispEn 作为特征向量，使用SVM 对其进行分类，解决散布熵不能有效识别滚动轴承严重程度的问题;最后，与干扰属性投影(NAP )进行对比。

结果表明:所提方法不仅能够有效检测滚动轴承故障，而且能够更精确地识别滚动轴承故障严重程度。

关键词:滚动轴承;故障检测;散布熵;支持向量机DOI :10．16807/j．cnki．12-1372/e．2020．12．008中图分类号:TN911．23文献标志码:A文章编号:1674-2192(2020)12-0036-06Ｒolling Bearing Fault Diagnosis Based on DispEn and SVMYANG Ganggang 1，XIA Junzhong 2，KONG Youcheng 1，TANG Heng 1(1．Fifth Team of Cadets ，Army Military Transportation University ，Tianjin 300161，China ;2．Military Vehicle Engineering Department ，Army Military Transportation University ，Tianjin 300161，China )Abstract :In order to detect the rolling bearing fault and identify the same kind of rolling bearing faults with different sever-ity accurately ，a rolling bearing fault diagnosis method based on dispersion entropy (DispEn )and support vector machine (SVM )is proposed in this paper．Firstly ，it calculates the DispEn of four similar vibration signals of the rolling bearing with different severity levels ，and realizes the rolling bearing fault detection by comparing their values．Secondly ，it uses the DispEn of the sample signal as a feature vector and classifies it with SVM to solve the problem that the scattering entropy can not effectively identify the rolling bearing severity．Finally ，by comparing with the Nuisance Attribute Projection (NAP )，the results show that the proposed method can not only effectively detect the rolling bearing faults ，but also identi-fy the rolling bearing fault severity more accurately．Keywords :rolling bearing ;fault diagnosis ;scattering entropy ;support vector machine收稿日期:2020-06-15;修回日期:2020-09-09．作者简介:杨刚刚(1995—)，男，硕士研究生;夏均忠(1967—)，男，博士，教授，博士研究生导师．滚动轴承广泛应用于各种机械设备中，如发动机、汽车、离心式压缩机等。

轨边声学信息的高速列车滚动轴承故障特征提取及实验方法研究

轨边声学信息的高速列车滚动轴承故障特征提取及实验方法研究摘要随着高速列车的发展，滚动轴承在高速列车运行中扮演了重要的角色。

而滚动轴承的故障问题是制约大型机械运转的关键因素，对于高速列车来讲尤其如此。

本文针对高速列车滚动轴承故障问题，通过声学信息的研究，提取故障特征。

首先，对火车车轮轴承以及轨道各部分进行了声学测试，并对信号进行了预处理，然后使用小波包分解进行数据特征提取。

对于高速列车轮轴承故障而言，异常信号取决于多个因素，如轮径，轮廓，偏心率，轴向载荷，转速等。

因此，这种多因素会使得故障特征提取存在着一定复杂性和难度。

本文运用了PCA算法对提取的滚动轴承信号特征进行了降维处理和数据分类。

最后，本文提出了一种实验方法，对所研究的滚动轴承进行了实验检测，并得出了较为准确的故障诊断结果。

关键词：滚动轴承，高速列车，声学信息，小波包分解，故障特征提取，PCA算法，实验方法研究AbstractWith the development of high-speed trains, rolling bearings play an important role in their operation. However, the problem of rolling bearing failures is akey factor that restricts the operation of large-scale machinery, particularly in high-speed trains. This paper focuses on the problem of rolling bearingfailures in high-speed trains, and extracts failure characteristics through acoustic information. Firstly, acoustic tests were carried out on various parts ofthe train wheel bearings and rails, and the signals were pre-processed. Then, wavelet packet decomposition was used for data feature extraction. For the rolling bearing fault in high-speed trains, the abnormalsignal depends on multiple factors, such as the wheel diameter, contour, eccentricity, axial load, and speed. Therefore, the complexity and difficulty of fault feature extraction can be significant. In this paper, the PCA algorithm was used to perform dimensionality reduction and data classification on the extracted rolling bearing signal features. Finally, an experimental method was proposed to detect the rolling bearing under study, and an accurate fault diagnosis result was obtained.Keywords: Rolling bearing, high-speed train, acoustic information, wavelet packet decomposition, failure feature extraction, PCA algorithm, experimental methodRolling bearings are critical components in high-speed trains, and their failure can lead to serious safetyissues. Acoustic signals generated by the rolling bearings can provide valuable information for fault diagnosis. However, the signals are often complex and noisy, making it challenging to extract useful features for effective fault diagnosis.In this study, wavelet packet decomposition was used to decompose the acoustic signals into multiple frequency bands. The decomposed signals were then subjected to feature extraction using statistical features such as mean, standard deviation, and kurtosis. The extracted features were further processed using principal component analysis (PCA) for dimensionality reduction and data classification.The proposed experimental method involved collecting acoustic signals from a rolling bearing underdifferent operating conditions. The signals were processed using the aforementioned techniques, and fault diagnosis was performed based on the extracted features. The accuracy of the diagnosis was evaluated by comparing the results with those obtained using traditional diagnostic methods.The results showed that the proposed method was effective in detecting and diagnosing faults inrolling bearings. The PCA algorithm was able to reducethe dimensionality of the data while preserving the relevant information, leading to improvedclassification accuracy. The experimental method was also able to accurately detect the fault in therolling bearing under study.In conclusion, the proposed method based on wavelet packet decomposition, feature extraction, and PCA algorithm can be an effective approach for fault diagnosis of rolling bearings in high-speed trains. The method can aid in ensuring the safe and reliable operation of high-speed trainsMoreover, this method can be extended to other machinery fault diagnosis applications, such as gearboxes, turbines, and engines. This is because the proposed method is versatile and can be adapted tosuit the specific requirements of a given application. For instance, the method can be adjusted to accommodate different types of sensors, signal acquisition systems, and data processing algorithms.It is worth noting that this method may have some limitations. First, the quality of the fault diagnosis data largely depends on the accuracy of the sensors and signal acquisition system. Therefore, it iscrucial to ensure that these components are properlycalibrated and maintained. Second, the proposed method may be affected by noise and other forms of interference. Hence, it is essential to apply noise reduction techniques to ensure that the extracted features are accurate and reliable. Finally, the method may require some computational resources, especially when processing large datasets. Therefore, it is necessary to employ efficient algorithms and computer hardware.Despite the limitations, the proposed method has significant potential for enhancing fault diagnosis in rolling bearings and other machinery applications. It can enable early detection of faults, reduce maintenance costs, and improve the overall safety and reliability of high-speed trains and other critical systems. As such, further research is needed to explore the full potential of this method, including its application in other domains, such as aerospace, automotive, and manufacturing.In conclusion, machinery fault diagnosis is a critical task that requires accurate and reliable methods. The proposed method based on wavelet packet decomposition, feature extraction, and PCA algorithm can offer an effective approach for fault diagnosis of rolling bearings in high-speed trains. The method can enhancethe safety and reliability of high-speed train operations by enabling early detection and prevention of faults. It represents a significant contribution to the field of machinery fault diagnosis and warrants further research and developmentIn addition to its potential applications in the field of high-speed train operations, the proposed method based on wavelet packet decomposition, feature extraction, and PCA algorithm can also have broader implications for the diagnosis of faults in other types of machinery. Various industries such as aerospace, automotive, and manufacturing rely on the effective and efficient operation of machinery to maintain productivity and safety.Moreover, the proposed method has the potential to be applied to both rotating and non-rotating machinery systems. For instance, it can be used to detect faults in gearboxes, turbines, pumps, and compressors. Faults in these systems can have significant consequences such as reduced performance, increased energy consumption, and equipment failure, which can lead to safety hazards, costly repairs, and production losses.Furthermore, the proposed method can be enhanced by incorporating other diagnostic techniques such asvibration analysis and acoustic emission analysis. Combining multiple diagnostic methods can improve overall fault detection accuracy, reduce false alarms, and enhance the reliability of fault diagnostics. Additionally, the method can be used in conjunction with condition monitoring systems that continuously monitor machinery performance and health to provide real-time alerts and avoid unplanned downtime.In conclusion, the proposed method based on wavelet packet decomposition, feature extraction, and PCA algorithm offers a promising approach for fault diagnosis of rolling bearings in high-speed trains and other machinery systems. Its potential applications are wide-ranging and can have significant implications for machine performance, safety, and productivity. Further research and development are needed to refine and optimize the method for specific applications and improve its diagnostic accuracy and reliabilityIn conclusion, the method based on wavelet packet decomposition, feature extraction, and PCA algorithm shows promise for fault diagnosis of rolling bearings in high-speed trains and other machinery systems. The method has the potential to improve machine performance, safety, and productivity. However,further research and development are necessary tooptimize its diagnostic accuracy and reliability for specific applications。

SVD-LMD联合降噪和TEO的滚动轴承故障诊断

SVD-LMD联合降噪和TEO的滚动轴承故障诊断谢小正1李俊1赵荣珍1崔振琦2（1兰州理工大学机电工程学院，甘肃兰州730050）（2甘肃筑鼎建设有限责任公司，甘肃嘉峪关735100）摘要针对随机噪声背景下滚动轴承局部损伤信息提取困难的问题，提出了一种奇异值分解（Singular value decomposition，SVD）和局部均值分解（Local mean decomposition，LMD）联合降噪，并结合Teager能量算子（Teager energy operator，TEO）的特征提取新方法。

首先，利用SVD方法对滚动轴承故障振动信号进行处理，初步剔除背景噪声；然后，使用LMD方法分解降噪后的信号，依据相关系数指标筛分出敏感乘积函数（Product function，PF）并加以重构；最后，对重构的信号进行TEO 解调分析，将解调谱中幅值突出的频率成分与故障特征频率理论值进行对比，提取故障信息。

结果表明，该方法可有效提取轴承局部损伤的特征频率，最终实现故障诊断。

关键词滚动轴承奇异值分解局部均值分解Teager能量算子故障诊断Fault Diagnosis of Rolling Bearings based on SVD-LMD Joint De-noising and TEOXie Xiaozheng1Li Jun1Zhao Rongzhen1Cui Zhenqi2（1School of Mechanical&Electronic Engineering，Lanzhou University of Technology，Lanzhou730050，China）（2Gansu Zhuding Construction Co.，Ltd.Jiayuguan735100，China）Abstract Aiming at the difficulty extracting the local damage information of rolling bearings under the background of random noise，a new feature extraction method based on singular value decomposition(SVD)and local mean decomposition(LMD)joint de-noising combined with Teager energy operator(TEO)is proposed.First⁃ly，by using the SVD method，the fault vibration signal of rolling bearings is processed to eliminated the back⁃ground noise preliminarily.Then，the signal which is denoised by using LMD method is reconstructed after the sensitive product function(PF)is screened out according to the correlation coefficient index.Finally，the recon⁃structed signal is analyzed by TEO demodulation，the frequency component which amplitude prominent in de⁃modulation spectrum is compared with the theoretical value of fault characteristic frequency to extract fault infor⁃mation.The experimental results demonstrate that the method can effectively extract the characteristic frequency of the local damage information of rolling bearings and the fault diagnosis is realized.Key words Rolling bearing Singular value decomposition(SVD)Local mean decomposition（LMD）Teager energy operator(TEO)Fault diagnosis0引言据统计，旋转机械中约有30%的故障是由轴承损伤引起[1]，故轴承的平稳运行对安全生产具有十分重要的意义。

峭度系数诊断法诊断滚动轴承故障

峭度系数诊断法诊断滚动轴承故障机械1202 3120301052 马也摘要：滚动轴承是机械设备中最常见的零部件，其性能与工况的好坏直接影响到与之相联的转轴以及安装在转轴上的齿轮乃至整个机器设备的性能。

据统计，在使用轴承的旋转机械中，大约有30％的故障都是由于轴承引起的。

因此，研究滚动轴承的失效机理，提出相应的预防和维护措施，对于降低设备的维修费用，延长设备维修周期，提高经济效益，保证设备的长期安全稳定运行，均有现实的意义。

滚动轴承的振动诊断方法有：振动信号简易诊断法,美国恩泰克公司开发的g/SE诊断法等。

还有其他诊断方法，如：光纤维监测技术、油污染分析法（光谱测定法、磁性磁屑探测法和铁谱分析法等）、声发射法、电阻法等，重点研究傅里叶变换。

关键词：滚动轴承；故障；振动；诊断Kurtosis coefficient of diagnosis method in the diagnosisof rolling bearing faultAbstract.Rolling bearing is the mechanical equipment is the most common parts, its p erformance and modes of the direct influence on the shaft and the associated with the ge ar axis installed in the whole machine equipment performance. According to statistics, in t he use of rotating machine, bearing about 30% of the fault is due to bearing cause. There fore, the study of rolling bearings failure mechanism and corresponding preventive and m aintenance measures, for reducing the equipment of the cost of maintenance of the equip ment, prolong maintenance cycle, to improve the economic benefit and guarantee the saf e and stable operation of the equipment's long-term, all have realistic significance. Vibrati on of rolling bearings diagnosis methods are: vibration signal simple diagnostics, America n grace tektronix company developed the g/SE diagnostics, etc. There are other diagnost ic methods, such as optical fiber monitoring technology, oil pollution process (spectrometr ic method, magnetic crumbs detection method and iron spectral analysis, etc.), acoustic emission method, resistance method, key research Fourier transformation.Key words：Bearing；vibration；fault；diagnosis0 引言：机械故障诊断过程本质上是一个故障模式识别的过程[1]，针对某一个具体的机械故障诊断问题，选择不同的模式识别方法，其分类精度和准确性可能会有较大的差异[2,3]。

基于熵特征和堆叠稀疏自编码器的滚动轴承故障诊断方法

44基于熵特征和堆叠稀疏自编码器的滚动轴承故障诊断方法基于熵特征和堆叠稀疏自编码器的滚动轴承故障诊断方法A Rolli ng Bear i ng Fault Diag no s is Method Based on En t ropy Featureand Stack Sparse Autocoder薛嫣(中国电力工程顾问集团西北电力设计院有限公司，陕西西安710075)朱静邓艾东(东南大学火电机组振动国家工程研究中心，江苏南京210096)摘要：滚动轴承作为重要的机械设备，其状态监测和故障诊断对机械的稳定运行具有重要作用。

提出一种基于熵特征和堆叠稀疏自编码的滚动轴承故障诊断方法遥在滚动轴承诊断试验台上提取正常和故障状态信号，对滚动振动信号进行时频域及熵特征提取，作为堆叠稀疏自编码网络的输入，进行训练和测试遥与现有方法的对比结果表明，所提方法能够提高滚动轴承故障诊断的准确率遥关键词：滚动轴承;SSAE；熵；特征提取Abstract:As an important mechanical equipment,rolling bearing's condition monitoring and fault diagnosis play an important role in the stable operation of machinery.This paper presents a rolling bearing fault diagnosis method based on entropy feature and stacked sparse self-coding.The normal lnd fault state signals sre extracted from the rolling bearing diagnostic test bench.The time-frequency domain nnd entropy characteristics of the rolling vibration signals sre extracted and used as the input of the stacked sparse self-coding network for training and testing.The comparison with the existing methods showsthat the proposed method can improve the accuracy of rolling Keywords:rolling bearing,SSAE,entropy,feature extraction由于运行环境恶劣，滚动轴承故障高发，滚动轴承的故障往往会造成人员伤亡和经济损失。

一种频谱分析的滚动轴承故障诊断系统

一种频谱分析的滚动轴承故障诊断系统：由于在机械系统中，滚动轴承是一种故障多发的机械零部件，设计出能够有效检测滚动轴承故障的诊断系统具有很重要的意义。

本文在基于滚动轴承常见故障下建立故障频率分布模型，并针对干扰故障模型的噪声信号设计了FIR高通数字滤波器来提取出有效故障频率段。

结合工程实例设计了对工程用发电机转子轴承的故障诊断系统，并且通过实验测试发现有很好的效果。

标签：：滚动轴承、故障诊断、频谱分析、FIR滤波器Roller bearing fault diagnosis system based on fuzzy neural network[Abstract]：In the mechanical system，roller bearing is a failure-prone mechanical part. It is very important significance that the system detect rolling bearing fault diagnosis effectively can be designed. This paper is established the fault frequency distribution model based on the roller bearing’s common failure and designed a FIR high-pass digital filter that extract the effective failure frequency from the interference noise signal of the fault model. Fault diagnosis system has been designed for engineering generator rotor bearing with an engineering example，it was tested on experiment and was found to have a very good result .[Key words]：rolling bearing；fault diagnosis；frequency spectrum analysis；FIR digital filter0 引言随着机械工业的大力发展，滚动轴承是应用十分广泛的重要机械基础零件。

滚动轴承的故障诊断系统研究时域系统研究

摘要滚动轴承是旋转机械中应用最广泛的一种通用部件，也是机械设备中的易损零件，许多机械的故障都与滚动轴承的状态有关。

据统计，在使用滚动轴承的旋转机械中，大约30％的机械故障是由于滚动轴承的损坏造成的。

可见，滚动轴承的好坏对机械系统工作状况的影响极大。

由于设计不当和安装工艺不好或轴承的使用条件不佳，或突发载荷的影响，使轴承运转一段时间后会产生各种各样的缺陷，并且在继续运行中进一步扩大，使轴承运行状态发生变化。

因此，滚动轴承的故障诊断一直是研究的热点。

本文首先从理论上分析了滚动轴承的失效形式、振动机理、振动类型、及发生故障的原因、振动频率；然后在理论基础上提出了滚动轴承的时域、频域的诊断方法；最后搭建了基于Matlab的滚动轴承故障诊断系统，并通过Matlab仿真轴承故障信号，在软件中进行信号分析和处理，验证各种诊断方法的优劣和滚动轴承的故障特征。

本论文按照预定的要求完成了设计任务，研究了滚动轴承的故障诊断方法，完成了故障诊断系统的设计，通过仿真验证了滚动轴承的故障诊断方法。

关键词：滚动轴承；故障诊断；时域分析；频域分析；MatlabAbstractRolling element bearing is one of the most widely used general part of rotating machinery,and one of the most easily damaged parts of mechanical equipment. A lot of mechanical failure is relevant to the state of rolling element bearings. It is estimated that about 30 percent of mechanical failure is caused by its fault in the rotating machine with rolling element bearings. It is obvious that the quality of rolling element bearings has a great impact on the working condition of electromechanical systems. Because of wrong design, poor working condition or a jump heavy load, bearing will be damaged and worse during the running time. So at present, the fault diagnosis of rolling element bearings is a research hotspot.Firstly, the failure forms, the vibration mechanism, vibration type, and the failure cause, vibration frequency of bearing are analyzed in theory.Secondly, based on the theory put forward the time domain, frequency domain diagnostic methods.Finally, the software for the fault diagnosis system of the rolling bearings is designed by Matlab,along with the simulation of bearing fault signals by Matlab.To analysis and processing the signal in software. Verify the merits of various diagnostic methods and characteristics of rolling bearing faults.The paper successfully completed the design task and the result meets the expectation. We researched the fault diagnosis methods and completed the fault diagnosis system design and simulation shows the fault diagnosis methods of rolling element bearings.KeyWords：rolling element bearings,fault diagnosis,time-domain analysis,frequency-domain analysis,Matlab目录摘要 (I)Abstract (II)第一章绪论 ...........................................................................................................- 1 -1.1 本课题研究的主要意义 ...........................................................................- 1 -1.2 滚动轴承故障诊断方法 ...........................................................................- 2 -1.3 滚动轴承故障诊断技术的发展概况 .......................................................- 3 -1.4 滚动轴承故障诊断技术的发展方向 .......................................................- 5 -1.5 本课题主要研究内容 ...............................................................................- 5 -第二章滚动轴承的故障特征分析 .......................................................................- 6 -2.1 概述 ...........................................................................................................- 6 -2.2 滚动轴承的典型结构 ...............................................................................- 6 -2.3 滚动轴承的主要失效形式及原因 ...........................................................- 7 -2.4 滚动轴承的几何参数 ...............................................................................- 8 -2.5 滚动轴承的特征频率 ...............................................................................- 9 -2.6 滚动轴承的振动特性 .............................................................................- 10 -2.6.1 滚动轴承的固有振动 ...................................................................- 11 -2.6.2 轴承构造引起的振动 ...................................................................- 12 -2.6.3 轴承装配不正确、轴颈偏斜产生的振动 ...................................- 13 -2.6.4 精加工波纹度引起的振动 ...........................................................- 13 -2.6.5 滚动轴承的故障引起振动 ...........................................................- 13 -第三章滚动轴承故障诊断方法研究 .................................................................- 16 -3.1 概述 .........................................................................................................- 16 -3.2 时域分析的特征参数 .............................................................................- 16 -3.3 频域分析的特征参数 .............................................................................- 18 -第四章轴承故障诊断系统总体设计 .................................................................- 22 -4.1 概述 .........................................................................................................- 22 -4.2 Matlab软件简介.....................................................................................- 22 -4.3 滚动轴承故障诊断系统总体设计 .........................................................- 24 -4.3.1 系统界面子系统 ...........................................................................- 24 -4.3.2 轴承特征频率计算子系统 ...........................................................- 25 -4.3.3 数据加载子系统 ...........................................................................- 26 -4.3.4 信号模拟子系统 ...........................................................................- 27 -4.3.5 时域分析子系统 ...........................................................................- 28 -4.3.6 频域分析子系统 ...........................................................................- 31 -4.3.7 打印子系统 ...................................................................................- 32 -第五章轴承实测信号处理 .................................................................................- 33 -5.1 概述 .........................................................................................................- 33 -5.2 模拟合成信号 .........................................................................................- 33 -5.3 模拟合成信号分析 .................................................................................- 34 -5.4 轴承实测信号分析 .................................................................................- 35 -结论 .....................................................................................................................- 38 -参考文献 .................................................................................................................- 39 -致谢 .....................................................................................................................- 41 -附录A 频域分析系统程序 .................................................................................- 42 -第一章绪论1.1 本课题研究的主要意义机械故障诊断技术是近40年来发展起来的识别机器或机组运行状态的科学。

基于MTCN_的滚动轴承故障诊断方法研究

第 22卷第 3期2023年 3月Vol.22 No.3Mar.2023软件导刊Software Guide基于MTCN的滚动轴承故障诊断方法研究马新娜1，2，赵尚军1，2，栾浩楠1，2，刘心茹1，2，牛天云1，2（1.石家庄铁道大学信息科学与技术学院；2.石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室，河北石家庄 050043）摘要：为解决滚动轴承在不同转速、动载荷等变工况下故障诊断精度低的问题，基于已有时间卷积网络（TCN）提出多路时间卷积网络（MTCN）获得不同感受野下的振动信号特征，从而提高滚动轴承故障诊断准确率。

首先，该网络使用了三路TCN网络，其中两路为原始振动信号输入到不同膨胀尺度的TCN网络，另一路将提取的时域特征输入TCN网络。

然后，将三路特征进行拼接后输入全连接层中通过Softmax进行多分类。

实验表明，在含有多种转速、动载荷等工况的数据集中，MTCN的滚动轴承故障诊断准确率可达到97.19%，相较于长短期记忆网络（LSTM）和一维卷积的AlexNet准确率更高。

关键词：深度学习；多路时间卷积网络；动载荷；滚动轴承；故障诊断DOI：10.11907/rjdk.221941开放科学（资源服务）标识码（OSID）：中图分类号：TP277；TH133.33；TP183 文献标识码：A文章编号：1672-7800（2023）003-0096-07Rolling Bearing Fault Diagnosis Method Based on MTCNMA Xin-na1，2， ZHAO Shang-jun1，2， LUAN Hao-nan1，2， LIU Xin-ru1，2， NIU Tian-yun1，2（1.Department of Information Science and Technology， Shijiazhuang Tiedao University；2.State Key Laboratory of Mechanical Be⁃havior and System Safety of Traffic Engineering Structures， Shijiazhuang Tiedao University， Shijiazhuang 050043，China）Abstract：In order to solve the problem of low fault diagnosis accuracy of rolling bearings under variable working conditions such as different speeds and dynamic loads， a multi-channel time convolution network （MTCN） is proposed based on the existing time convolution network （TCN） to obtain the characteristics of vibration signals under different receptive fields， thereby improving the accuracy of rolling bearing fault diagnosis. First， the network uses three TCN networks， two of which are original vibration signals input to TCN networks with different expan⁃sion scales， and the other is to input the extracted time-domain features into TCN networks. Then， the three features are spliced and input into the full connection layer for multi classification through Softmax. The experiment shows that the accuracy of rolling bearing fault diagnosis of MTCN can reach 97.19% in the data set containing multiple rotating speeds， dynamic loads and other working conditions， which is higher than that of long short memory network （LSTM） and one-dimensional convolution AlexNet.Key Words：deep learning； multipath time convolution network； dynamic load； rolling bearing； fault diagnosis0 引言滚动轴承作为机械设备的重要零部件，极易发生故障。

基于BP神经网络的滚动轴承故障诊断

基于BP 神经网络的滚动轴承故障诊断刘元是，陈建政（西南交通大学牵引动力国家重点实验室，成都610000）摘要针对滚动轴承的故障损伤难以智能诊断的问题，提出了一种基于Alpha 稳定分布参数估计和神经网络的滚动轴承故障诊断方法。

首先，对各个状态振动信号进行稳定分布的4参数估计，选取敏感性及稳定性最好的二种参数组成二维故障特征量；然后，可将该二维故障特征量作为BP 神经网络的输入参数来识别滚动轴承的故障类型；然后，通过台架试验数据验证了该方法的有效性，并与4个常用的无量纲时域特征参数作为BP 神经网络的输入参数的方法的诊断结果进行比较。

结果表明：基于Alpha 稳定分布参数估计方法可实现对滚动轴承故障位置及的智能诊断，与时域特征参数的方法相比，在更少的参数下实现了更准确更有效的故障识别；最后，应用工程实测数据对该模型进行了验证，结果表明在小样本，低转速条件下该模型也能对滚动轴承不同状态故障进行有效的检测，有望在实际工程中得到应用。

关键词：滚动轴承；故障诊断；稳定分布；BP 神经网络Rolling bearing fault diagnosis based on BP neural networkLiuyuanshi,Chenjianzheng(Traction Power State Key Laboratory of Southwest Jiaot Tong University,Chengdu 610000,China)Abstract: In this paper, rolling bearing fault intelligent diagnosis of damage difficult problem proposed rolling bearing fault diagnosis method based on Alpha stable distribution parameter estimation and neural networks. First, each state vibration signal stable distribution four-parameter estimation, select the best sensitivity and stability of two-dimensional composition fault characteristic parameters; then, the fault may be the two-dimensional feature amount as input parameters BP neural network failure to identify the type of rolling bearings; diagnosis and then by bench test data to verify the effectiveness of the method, and with the four common dimensionless time domain characteristic parameters as input parameters BP neural network method were compared. The results show that: based on Alpha stable distribution parameter estimation method can be realized on Rolling intelligent diagnostics and fault location, compared with the time domain method of characteristic parameters in fewer parameters to achieve a more accurate and efficient fault identification; Finally, engineering test data to validate the model results show that in small samples, low-speed conditions of the rolling bearing a different model can effectively detect the fault state, it is expected to be applied in practical engineering.Keywords: Rolling; fault diagnosis; stable distribution; BP neural network引言滚动轴承在机械工业设备中应用非常普遍，但又是非常容易损坏。

滚动轴承故障诊断文献综述

滚动轴承故障诊断文献综述滚动轴承故障诊断文献综述[ 2008-4-2 14:38:00 | By: mp2 ]推荐文献综述——滚动轴承故障诊断1.前言滚动轴承是各种旋转机械中应用最广泛的一种通用机械零件，它是机器最易损坏的零件之一。

据统计。

旋转机械的故障有30,是由轴承引起的。

可见轴承的好坏对机器的工作状况影响很大。

轴承故障诊断就是要通过对能够反映轴承工作状态的信号的测取，分析与处理，来识别轴承的状态。

包括以下几个环节:信[1]号测取;特征提取;状态识别:故障诊断;决策干预。

滚动轴承故障诊断传统的分析方法有冲击脉冲法，共振解调法，倒频谱分析技术。

在现代分析方法中，小波分析是最近几年才出现井得以应用和发展的一种时—频信号分析方法。

它具有时域和频域的局部化和可变时频窗的特点(用它分析非平稳信号比传统的傅里叶分析更为最著。

由于滚动轴承的故障信号中禽有非稳态成分，所以刚小波分析来处理其振动信号(可望获得更为有效的诊断特征信息[2]。

滚动轴承故障的智能诊断技术就是把神经网络、专家系统、模糊理论等技术与滚动轴承的特征参数有机地结合起来进行综合分析的故障诊断技术。

2.故障信号诊断方法2.1冲击脉冲法(spm)SPM技术(Shock Pulse Method)，是在滚动轴承运转中，当滚动体接触到内外道面的缺陷区时，会产生低频冲击作用，所产生的冲击脉冲信号，会激起SPM 传感器的共振，共振波形一般为20kHz,60kHz，包含了低频冲击和随机干扰的幅值调制波，经过窄带滤波器和脉冲形成电路后，得到包含有高频和低频的脉冲序列。

SPM 方法是根据这一反映冲击力大小的脉冲序列来判断轴承状态的。

此种方法目前被公认为对诊断滚动轴承局部损伤故障工程实用性最强的。

此方法虽然克服了选择滤波中心频率和带宽的困难，但这种固定中心频率和带宽的方法也有其局限性，因为，一些研究结果表明，滚动轴承局部损伤故障所激起的结构共振频率并不是固定不变的，在故障的不同阶段可能激起不同结构的共振响应,而不同部位的故障(内、外圈、滚子)也会激起不同频率结构的共振响应。

基于ASL-Isomap流形学习的滚动轴承故障诊断方法

Keywords : fault diagnosis; rolling bearing; manifold learning; ASL-Isomap; kernel extreme learning machine
滚动轴承作为应用广泛且容易损坏的零部件，其工作状态直接影响到整个机械系统的工作性能，因此对滚动轴承进行故障诊断有着重要的现实意
诊断方法。首先，从时域、频域、时频域以及复杂域提取振动信号的故障特征，构建高维混合域故障特征集；其次，采用
ASL-Isomap 方法对高维混合域故障特征集进行维数约简，提取出低维、敏感特征子集；最后，应用核极限学习机
(Kernel extreme learning machine，KELM)分类器对低维特征进行故障识别。ASL-Isomap 方法集成自适应邻域构建和
（安徽工业大学机械工程学院，安徽马鞍山 243032 ）
摘要：针对滚动轴承故障特征集维数高及冗余问题，提出一种基于自适应自组织增量学习神经网络界标点的等
度规映射(Adaptive self-organizing incremental neural network landmark Isomap，ASL-Isomap)流形学习的滚动轴承故障
A Rolling Bearing Fault Diagnosis Method based on ASL-Isomap Manifold Learning
WANG Zhenya , QI Xiaoli , WU Baolin
( School of Mechanical Engineering, Anhui University of Technology, Ma'anshan 243032, Anhui China )

基于域适应与分类器差异的滚动轴承跨域故障诊断

收稿日期:２０２０－０８－１１基金项目:中央高校基本科研业务费专项资金资助项目(Ｎ１８０３０４０１８).作者简介:张永超(１９９３－)ꎬ男ꎬ辽宁朝阳人ꎬ东北大学博士研究生ꎻ任朝晖(１９６８－)ꎬ男ꎬ辽宁沈阳人ꎬ东北大学教授ꎬ博士生导师.第４２卷第３期２０２１年３月东北大学学报(自然科学版)ＪｏｕｒｎａｌｏｆＮｏｒｔｈｅａｓｔｅｒｎＵｎｉｖｅｒｓｉｔｙ(ＮａｔｕｒａｌＳｃｉｅｎｃｅ)Ｖｏｌ.４２ꎬＮｏ.３Ｍａｒ.２０２１㊀ｄｏｉ:１０.１２０６８/ｊ.ｉｓｓｎ.１００５－３０２６.２０２１.０３.０１０基于域适应与分类器差异的滚动轴承跨域故障诊断张永超ꎬ李㊀琦ꎬ任朝晖ꎬ周世华(东北大学机械工程与自动化学院ꎬ辽宁沈阳㊀１１０８１９)摘㊀㊀㊀要:基于数据驱动方法诊断滚动轴承故障时ꎬ不同工况下的数据特征分布差异会导致模型诊断性能严重下降.针对这一问题ꎬ提出了基于域适应与分类器差异的滚动轴承跨域故障诊断方法.首先利用卷积神经网络对带标记的源域样本和无标记的目标域样本进行特征提取ꎻ然后通过２个全连接分类器进行故障分类ꎻ最后通过分步优化分类损失㊁域最大平均差异损失和分类器差异损失ꎬ实现源域和目标域之间的域分布对齐ꎬ从而实现无标记目标域样本的故障诊断.实验结果表明ꎬ所提方法与主流的域适应方法相比具有更高故障诊断准确率ꎬ验证了该方法的合理性和可行性.关㊀键㊀词:故障诊断ꎻ域适应ꎻ卷积神经网络ꎻ最大平均差异ꎻ滚动轴承中图分类号:ＴＨ１７㊀㊀㊀文献标志码:Ａ㊀㊀㊀文章编号:１００５－３０２６(２０２１)０３－０３６７－０６Ｃｒｏｓｓ￣ＤｏｍａｉｎＦａｕｌｔＤｉａｇｎｏｓｉｓｏｆＲｏｌｌｉｎｇＢｅａｒｉｎｇｓＵｓｉｎｇＤｏｍａｉｎＡｄａｐｔａｔｉｏｎｗｉｔｈＣｌａｓｓｉｆｉｅｒＤｉｓｃｒｅｐａｎｃｙＺＨＡＮＧＹｏｎｇ￣ｃｈａｏꎬＬＩＱｉꎬＲＥＮＺｈａｏ￣ｈｕｉꎬＺＨＯＵＳｈｉ￣ｈｕａ(ＳｃｈｏｏｌｏｆＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒｉｎｇ＆ＡｕｔｏｍａｔｉｏｎꎬＮｏｒｔｈｅａｓｔｅｒｎＵｎｉｖｅｒｓｉｔｙꎬＳｈｅｎｙａｎｇ１１０８１９ꎬＣｈｉｎａ.Ｃｏｒｒｅｓｐｏｎｄｉｎｇａｕｔｈｏｒ:ＲＥＮＺｈａｏ￣ｈｕｉꎬｐｒｏｆｅｓｓｏｒꎬＥ￣ｍａｉｌ:ｚｈｈｒｅｎ＿ｎｅｕ＠１２６.ｃｏｍ)Ａｂｓｔｒａｃｔ:Ｗｈｅｎｄｉａｇｎｏｓｉｎｇｒｏｌｌｉｎｇｂｅａｒｉｎｇｆａｕｌｔｓｂａｓｅｄｏｎｄａｔａ￣ｄｒｉｖｅｎｍｅｔｈｏｄｓꎬｔｈｅｄｉｓｃｒｅｐａｎｃｙｉｎｄａｔａｄｉｓｔｒｉｂｕｔｉｏｎｕｎｄｅｒｄｉｆｆｅｒｅｎｔｏｐｅｒａｔｉｎｇｃｏｎｄｉｔｉｏｎｓｍａｙｒｅｓｕｌｔｉｎｓｅｖｅｒｅｄｅｇｒａｄａｔｉｏｎｏｆｍｏｄｅｌｄｉａｇｎｏｓｉｓｐｅｒｆｏｒｍａｎｃｅ.Ｔｏｈａｎｄｌｅｔｈｉｓｉｓｓｕｅꎬａｃｒｏｓｓ￣ｄｏｍａｉｎｆａｕｌｔｄｉａｇｎｏｓｉｓｍｅｔｈｏｄｏｆｒｏｌｌｉｎｇｂｅａｒｉｎｇｂａｓｅｄｏｎｄｏｍａｉｎａｄａｐｔａｔｉｏｎｗｉｔｈｃｌａｓｓｉｆｉｅｒｄｉｓｃｒｅｐａｎｃｙｗａｓｐｒｏｐｏｓｅｄ.Ｆｉｒｓｔｌｙꎬｔｈｅｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋｗａｓｕｓｅｄｔｏｅｘｔｒａｃｔｔｈｅｆｅａｔｕｒｅｓｏｆｔｈｅｌａｂｅｌｅｄｓｏｕｒｃｅｄｏｍａｉｎｓａｍｐｌｅｓａｎｄｔｈｅｕｎｌａｂｅｌｅｄｔａｒｇｅｔｄｏｍａｉｎｓａｍｐｌｅｓ.Ｔｈｅｎꎬｔｈｅｆｅａｔｕｒｅｓｗｅｒｅｃｌａｓｓｉｆｉｅｄｂｙｔｗｏｆｕｌｌｙｃｏｎｎｅｃｔｅｄｃｌａｓｓｉｆｉｅｒｓ.Ｆｉｎａｌｌｙꎬｔｈｅｃｌａｓｓｉｆｉｃａｔｉｏｎｌｏｓｓꎬｔｈｅｍａｘｉｍｕｍｍｅａｎｄｉｓｃｒｅｐａｎｃｙｌｏｓｓａｎｄｔｈｅｃｌａｓｓｉｆｉｅｒｄｉｓｃｒｅｐａｎｃｙｌｏｓｓｗｅｒｅｏｐｔｉｍｉｚｅｄｓｔｅｐｂｙｓｔｅｐｔｏａｌｉｇｎｔｈｅｄｏｍａｉｎｄｉｓｔｒｉｂｕｔｉｏｎｄｉｓｃｒｅｐａｎｃｙｂｅｔｗｅｅｎｔｈｅｓｏｕｒｃｅｄｏｍａｉｎａｎｄｔｈｅｔａｒｇｅｔｄｏｍａｉｎｓｏａｓｔｏｉｍｐｌｅｍｅｎｔｔｈｅｆａｕｌｔｄｉａｇｎｏｓｉｓｏｆｕｎｌａｂｅｌｅｄｔａｒｇｅｔｄｏｍａｉｎｓａｍｐｌｅｓ.Ｔｈｅｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓｓｈｏｗｅｄｔｈａｔｔｈｅｐｒｏｐｏｓｅｄｍｅｔｈｏｄｈａｓａｈｉｇｈｅｒｆａｕｌｔｄｉａｇｎｏｓｉｓａｃｃｕｒａｃｙｒａｔｅｔｈａｎｔｈｅｍａｉｎｓｔｒｅａｍｄｏｍａｉｎａｄａｐｔａｔｉｏｎｍｅｔｈｏｄｓꎬｗｈｉｃｈｖｅｒｉｆｉｅｓｉｔｓｒａｔｉｏｎａｌｉｔｙａｎｄｆｅａｓｉｂｉｌｉｔｙ.Ｋｅｙｗｏｒｄｓ:ｆａｕｌｔｄｉａｇｎｏｓｉｓꎻｄｏｍａｉｎａｄａｐｔａｔｉｏｎꎻｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋꎻｍａｘｉｍｕｍｍｅａｎｄｉｓｃｒｅｐａｎｃｙꎻｒｏｌｌｉｎｇｂｅａｒｉｎｇ㊀㊀滚动轴承是旋转机械的重要组成部分ꎬ其故障可能极大地影响机械系统的整体性能或导致意外停机ꎬ造成灾难性的后果.因此ꎬ针对轴承的故障预测与健康管理(ｐｒｏｇｎｏｓｔｉｃｓｈｅａｌｔｈｍａｎａｇｅｍｅｎｔꎬＰＨＭ)是必不可少的.然而ꎬ由于滚动轴承具有运行工况多变和运行环境恶劣的特点ꎬ导致测试数据与训练数据的分布往往存在差异ꎬ从而严重影响模型的泛化能力[１－２].因此ꎬ开展变工况下滚动轴承故障诊断是至关重要的[３－４].近年来ꎬ随着计算机硬件性能的提升和人工智能算法的兴起ꎬ基于数据驱动的深度学习技术㊀㊀被广泛应用于故障诊断领域[５－７].然而ꎬ这些研究忽略了机器工况的变化ꎬ认为训练数据和测试数据分布是相同的ꎬ这在现实的工业场景是不多见的.为此ꎬ许多基于域适应的深度学习方法被应用ꎬ旨在解决数据分布差异问题.文献[８]提出了一种基于预训练的卷积神经网络(ｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓꎬＣＮＮ)迁移学习框架ꎬ在源域训练ＣＮＮꎬ通过在目标域适当微调实现目标域诊断.文献[９]提出了一种基于最大平均差异(ｍａｘｉｍｕｍｍｅａｎｄｉｓｃｒｅｐａｎｃｙꎬＭＭＤ)的深度域适应故障诊断模型.文献[１０]同时最小化多层中２个域间的ＭＭＤꎬ提高跨域诊断性能.文献[１１]将对抗性学习作为一种正则化方法引入卷积神经网络中ꎬ并通过实验证明了提出方法的优越性.文献[１２]在网络中嵌入了一种改进的加权转移分量分析域适应算法ꎬ实现跨域故障诊断.文献[１３]同时考虑ＭＭＤ损失和域对抗损失ꎬ并通过实验验证了提出的方法可以准确地实现不同工况下的跨域故障诊断.以上方法虽都实现了跨域故障诊断ꎬ但都只实现了域的全局对齐ꎬ在类边界附近的样本特征很容易被误分类ꎬ从而造成诊断性能下降.因此ꎬ为了更好地区分类边界样本ꎬ本文提出了基于域适应与分类器差异的滚动轴承跨域故障诊断方法ꎬ大大提高跨域故障诊断准确率.１㊀算法实现１１㊀ＣＮＮ网络ＣＮＮ是深度学习中被广泛应用的神经网络.ＣＮＮ通常由特征提取器和分类器组成ꎬ特征提取器通常包含卷积㊁池化㊁激活函数和归一化ꎬ分类器一般由全连接层组成.卷积操作是使用卷积核提取输入数据的特征ꎬ从而得到特征图ꎬ卷积运算可以表示为ｘｌ＋１ｉ＝ｆ(ðｊɪＭｊｘｌｊｗｌ＋１ｉｊ＋ｂｌ＋１ｉ).(１)其中:ｆ( )表示激活函数ꎻｗｌ＋１ｉｊ表示ｌ层第ｉ个神经元对应第ｌ＋１层第ｊ个神经元的权重ꎻｂ表示偏置.为了有效地减少计算量ꎬ通过最大池化操作保留重要特征信息ꎬ其过程可用式(２)表示:ｐｌ(ｉꎬｊ)＝ｍａｘ(ｊ－１)ｗ<ｔ<ｊｗ{ａｌ(ｉꎬｔ)}.(２)其中:ａｌ(ｉꎬｔ)表示ｌ层中第ｉ个特征图的第ｔ个神经元ꎻｗ表示核宽度ꎻｊ表示池化核.通过卷积㊁池化㊁激活函数和归一化的叠加ꎬ建立特征提取器ꎬ从而提取输入数据的深度特征.然后ꎬ把特征输入分类器得到预测结果.假设一个类别为ｋ的分类问题ꎬｓｏｆｔｍａｘ的输出为Ｏ＝Ｐ(ｙ＝１｜ｘꎻＷ１ꎬｂ１)Ｐ(ｙ＝２｜ｘꎻＷ２ꎬｂ２)⋮Ｐ(ｙ＝Ｋ｜ｘꎻＷＫꎬｂＫ)éëêêêêêùûúúúúú＝１ðＫｊ＝１ｅｘｐ(Ｗｊｘ＋ｂｊ)ｅｘｐ(Ｗ１ｘ＋ｂ１)ｅｘｐ(Ｗ２ｘ＋ｂ２)⋮ｅｘｐ(ＷＫｘ＋ｂＫ)éëêêêêêùûúúúúú.(３)其中ꎬＷｊ和ｂｊ分别代表ｊ层的权重矩阵和偏置.１２㊀域适应由于不同工况下的数据分布不一致ꎬ直接将一种工况下训练得到的分类器直接应用于其他工况ꎬ得到的诊断结果往往是很差的.域适应可以充分利用源域数据和目标域数据ꎬ有效地解决训练数据和测试数据特征分布不一致的问题.图１是一个简单的域适应示例ꎬ如果将源域学习的模型直接应用于目标域分类ꎬ分类精度很低ꎬ但是通过域适应学习可以有效地对目标域的样本进行分类.因此ꎬ学习域不变特征是实现不同工况下故障诊断的关键步骤.图１㊀一个简单的域适应示例Ｆｉｇ１㊀Ａｓｉｍｐｌｅｅｘａｍｐｌｅｏｆｄｏｍａｉｎａｄａｐｔａｔｉｏｎ㊀㊀域适应学习主要通过强大的深度神经网络来减小域之间的差异ꎬ从而实现域不变特征.ＭＭＤ是域适应学习中一种被广泛应用的距离度量准则.ＭＭＤ主要用来度量两个不同但相关的分布的距离.两个分布的ＭＭＤ被定义为ＭＭＤ２(ｘｓꎬｘｔ)＝１ｎ１ðｎ１ｉ＝１ｆ(ｘｓｉ)－１ｎ２ðｎ２ｊ＝１ｆ(ｘｔｊ)２Ｈ＝１ｎ２１ðｎ１ｉ＝１ðｎ１ｊ＝１ｋ(ｘｓｉꎬｘｓｊ)－２ｎ１ｎ２ðｎ１ｉ＝１ðｎ２ｊ＝１ｋ(ｘｓｉꎬｘｔｊ)＋１ｎ２２ðｎ２ｉ＝１ðｎ２ｊ＝１ｋ(ｘｔｉꎬｘｔｊ).(４)８６３东北大学学报(自然科学版)㊀㊀㊀第４２卷㊀㊀２㊀提出的网络２１㊀问题描述本文研究了不同工况下轴承故障诊断问题ꎬ可以获得标签数据的工况被称作源域ꎬ需要诊断的工况被称作目标域.用Ｄｓ＝{ｘｓｉꎬｙｓｉ}ｎｓｉ＝１表示带标记的源域样本ꎬ其中ｘｓｉ定义样本特征ꎬｙｓｉ定义相应的标签ꎬｎｓ表示样本数量.用Ｄｔ＝{ＤｔｔｒａｉｎꎬＤｔｔｅｓｔ}表示不带标记的目标域样本ꎬＤｔｔｒａｉｎ定义目标域训练样本ꎬＤｔｔｅｓｔ定义目标域测试样本.本文旨在学习一个使用Ｄｓ和Ｄｔｔｒａｉｎ训练的分类器模型ꎬ可以准确地实现Ｄｔｔｅｓｔ的故障诊断.２２㊀网络结构图２给出了所提方法的架构ꎬ基本网络由特征提取器Ｇ和２个分类器(Ｃ１和Ｃ２)构成.Ｇ包含多层卷积块和全连接块.每个卷积块包括卷积㊁池化㊁激活函数和归一化ꎬ其中激活函数采用线性整流函数(ｒｅｃｔｉｆｉｅｄｌｉｎｅａｒｕｎｉｔꎬＲｅＬＵ).每个全连接块包含线性变换㊁ＲｅＬＵ和Ｄｒｏｐｏｕｔ.Ｃ１和Ｃ２由一层全连接分类器构成.源域数据和目标域数据同时被输入到特征提取器和两个相同的分类器得到预测输出.图２㊀提出方法的架构Ｆｉｇ２㊀Ａｒｃｈｉｔｅｃｔｕｒｅｏｆｔｈｅｐｒｏｐｏｓｅｄｍｅｔｈｏｄ２３㊀优化对象为了尽可能正确地分类不同健康状态数据ꎬ首先要确保模型可以在源域数据得到正确的分类.因此ꎬ本文采用交叉熵损失作为损失函数ꎬ２个分类器的交叉熵损失为㊀Ｌｃ＝－Ｅ(ｘꎬｙ)ɪＤｓ([ðＫｋ＝１Ｉ[ｋ＝ｙ]ｌｇ(Ｃ１(Ｆ(ｘ)))]＋[ðＫｋ＝１Ｉ[ｋ＝ｙ]ｌｇ(Ｃ２(Ｆ(ｘ)))]).(５)其中ꎬｋ表示健康状态数.在本研究中ꎬ特征提取器㊁分类器Ｃ１和分类器Ｃ２的参数分别用θＧꎬθＣ１和θＣ２表示.通过使Ｌｃ最小化可以获得最准确的预测结果和最优的网络参数ꎬ其过程可以表示为(＾θＧꎬ＾θＣ１ꎬ＾θＣ２)＝ａｒｇｍｉｎθＧꎬθＣ１ꎬθＣ２Ｌｃ.(６)然后ꎬ为了实现域对齐ꎬＭＭＤ被用作两个域之间分布差异的度量函数.在输入数据经过特征提取器Ｇ之后得到的源域特征和目标域特征间引入ＭＭＤ损失ꎬ其损失可以表示为Ｌｍｍｄ＝１ＮðＮｊ＝１ＭＭＤ(Ｆ(ｘｓ)＋Ｆ(ｘｔ)).(７)其中:ｘｓ和ｘｔ分别表示源域特征和目标域特征ꎻＮ表示特征个数.通过使Ｌｍｍｄ最小化ꎬ特征提取器可以学习源域和目标域的域不变特征ꎬ其最优的参数可以表示为(＾θＧ)＝ａｒｇｍｉｎθＧＬｍｍｄ.(８)单独实现域的全局对齐ꎬ虽然可以在很大程度上提高分类的准确率ꎬ但是由于域混淆的影响ꎬ使在靠近类边界附近的样本特征产生很多的误分类.因此ꎬ本文在域对齐的基础上ꎬ考虑了分类器差异损失.如图２所示ꎬ不同的初始化参数ꎬ在正确分类源域的同时ꎬ可以得到不同的目标域预测标签.直观上ꎬ靠近类边界的目标域样本更容易得到不同的预测结果.因此ꎬ在分类器中通过使目标域的预测结果尽可能的不一致ꎬ可以帮助网络检测目标域数据在类边界附近的特征分布.相反ꎬ特征提取器的目的是使２个分类器的结果预测更一致ꎬ旨在更好地对齐源域类和目标域类.具体来说ꎬ用Ｃ１和Ｃ２来构造一个差异鉴别器ꎬ将它们对目标域样本的预测之间的差异的Ｌ１范数作为差异损失:Ｌｄｉｓ＝ＥｘɪＤｔｔｒａｉｎ１ＮðＮｉ＝１Ｃ１(Ｆ(ｘｔ))－Ｃ２(Ｆ(ｘｔ)) １.(９)特征提取器与２个不同的分类器之间的博弈过程可以通过对抗训练的方式达到一个平衡点.其对抗训练可以表示为(＾θＣ１ꎬ＾θＣ２)＝ａｒｇｍｉｎθＣ１ꎬθＣ２－Ｌｄｉｓꎬ(１０)(＾θＧ)＝ａｒｇｍａｘθＧ－Ｌｄｉｓ.(１１)在这种情况下ꎬ方程(１０)和(１１)的参数不能被直接优化ꎬ因为－Ｌｄｉｓ被特征提取器最大化ꎬ同时被分类器最小化.为了解决这个问题ꎬ引入了梯度反转层(ｇｒａｄｉｅｎｔｒｅｖｅｒｓａｌｌａｙｅｒꎬＧＲＬ).如图２９６３第３期㊀㊀㊀张永超等:基于域适应与分类器差异的滚动轴承跨域故障诊断㊀㊀所示ꎬＧＲＬ作用于网络的反向传播过程ꎬ当梯度通过ＧＲＬ后ꎬ梯度符号被反转[１４].该方法巧妙地解决了最大梯度和最小梯度不能同时训练的问题.该方法在特征提取器和分类器之间引入ＧＲＬꎬ具体地说ꎬＧＲＬ可以表示为一个函数Ｒ(ｘ):Ｒ(ｘ)＝ｘꎬ(１２)ｄＲ(ｘ)ｄｘ＝－λＩ.(１３)其中:Ｉ表示单位矩阵ꎻλ表示惩罚系数ꎬ在本文中λ＝１.这样ꎬ方程(１０)和(１１)可以表示为(＾θＧꎬ＾θＣ１ꎬ＾θＣ２)＝ａｒｇｍｉｎθＧꎬθＣ１ꎬθＣ２－Ｌｄｉｓ.(１４)２４㊀训练过程所提方法的训练和测试过程如图３所示.训练过程分两步ꎬ首先训练方程(６)和(８)ꎬ然后训练方程(１４).通过这两步不断迭代ꎬ使网络获得最优的参数.最后ꎬ利用训练好的网络对测试数据进行分类ꎬ得到诊断结果.图３㊀训练和测试过程的流程Ｆｉｇ３㊀Ｆｌｏｗｃｈａｒｔｏｆｔｈｅｔｒａｉｎｉｎｇａｎｄｔｅｓｔｐｒｏｃｅｓｓ３㊀实验验证３１㊀实验描述为验证提出方法的有效性ꎬ搭建如图４所示的轴承故障实验台.采用滚动轴承作为实验轴承.在实验中模拟了５种轴承健康状态ꎬ即正常(ｎｏｒｍａｌꎬＮ)㊁内圈故障(ｉｎｎｅｒ￣ｒａｃｅｆａｕｌｔꎬＩＦ)㊁外圈故障(ｏｕｔｅｒ￣ｒａｃｅｆａｕｌｔꎬＯＦ)㊁滚动体故障(ｂａｌｌｆａｕｌｔꎬＢＦ)㊁外圈和滚动体混合故障(ｃｏｍｐｏｕｎｄｏｆｏｕｔｅｒ￣ｒａｃｅｆａｕｌｔａｎｄｂａｌｌｆａｕｌｔꎬＯＦ＿ＢＦ)ꎬ其中ＩＦꎬＯＦ和ＢＦ如图４所示.加速度传感器安装在轴承座上ꎬ用于收集振动信号ꎬ采样频率为２０ｋＨｚꎬ采样时间为２２０ｓ.实验分别采集了转速为６００ꎬ１２００ꎬ１８００ｒ/ｍｉｎ的５种健康状态下的数据.因此ꎬ本实验研究了三种工况下的６个域适应任务ꎬ如表１所示.３２㊀网络结构和参数该方法的网络结构和参数如表２所示.每个卷积操作后接ＲｅＬＵ和归一化操作ꎬ每个全连接层还包括ＲｅＬＵ和Ｄｒｏｐｏｕｔꎬ其中Ｄｒｏｐｏｕｔ的作用是防止网络过拟合ꎬ在本实验中Ｄｒｏｐｏｕｔ为０５.在本实验中ꎬ样本为一维数据ꎬ长度为１０２４.训练样本个数为每种健康状态４００个样本ꎬ测试样本个数为每种健康状态２００个样本.在网络训练中ꎬ用随机梯度下降方法(ｓｔｏｃｈａｓｔｉｃｇｒａｄｉｅｎｔｄｅｓｃｅｎｔꎬＳＧＤ)对优化目标进行训练ꎬ其中动量为０９.训练的Ｅｐｏｃｈ设置为４００ꎬ训练样本的批量大小设置为５０.初始学习率设为０１ꎬ每１００个Ｅｐｏｃｈ后ꎬ学习率降低到当前值的１０％.每个任务执行５次ꎬ其平均值作为最终的诊断准确率.图４㊀轴承试验台和三种轴承故障Ｆｉｇ４㊀Ｂｅａｒｉｎｇｔｅｓｔ￣ｒｉｇａｎｄｔｈｒｅｅｂｅａｒｉｎｇｆａｕｌｔｓ表１㊀６个域适应任务Ｔａｂｌｅ１㊀Ｓｉｘｔａｓｋｓｏｆｄｏｍａｉｎａｄａｐｔａｔｉｏｎ任务１２３４５６源域/(ｒｍｉｎ－１)６００６００１２００１２００１８００１８００目标域/(ｒｍｉｎ－１)１２００１８００６００１８００６００１２００３３㊀对比方法为更好验证所提出方法的诊断性能ꎬ选择以下３种方法进行对比分析.这３种对比方法的基本网络与提出方法的基本网络相同.１)没有域适应方法(ＷＤＡ).只简单使用源０７３东北大学学报(自然科学版)㊀㊀㊀第４２卷㊀㊀域样本训练网络ꎬ然后测试目标域数据.表２㊀网络结构和参数Ｔａｂｌｅ２㊀Ｎｅｔｗｏｒｋｓｔｒｕｃｔｕｒｅａｎｄｐａｒａｍｅｔｅｒｓ模块网络层核大小/步长核数目补零输出尺寸(度ˑ深)卷积１９ˑ１/１ˑ１４是１０１８ˑ４池化ｌ２ˑ１/２ˑ１４否５０９ˑ４卷积２９ˑ１/１ˑ１８是５０３ˑ８池化２２ˑ１/２ˑ１８否２５１ˑ８卷积３９ˑ１/１ˑ１１６是２４５ˑ１６池化３２ˑ１/２ˑ１１６否１２２ˑ１６Ｇ卷积４９ˑ１/１ˑ１３２是１１６ˑ３２池化４２ˑ１/２ˑ１３２否５８ˑ３２卷积５６ˑ１/１ˑ１６４是５５ˑ６４池化５２ˑ１/２ˑ１６４否２７ˑ６４平铺１７２８ˑ１全连接２５６１２５６ˑ１全连接１２８１１２８ˑ１Ｃ１全连接５１５ˑ１Ｃ２全连接５１５ˑ１㊀㊀２)基于域对抗网络的域适应方法(ＤＡＮ).在该方法中ꎬ在特征提取器后接域分类器ꎬ其目的是通过域分类器混淆源域和目标域特征ꎬ从而实现域适应.３)基于ＭＭＤ的域适应方法(ＭＭＤ).在该方法中ꎬ只加入ＭＭＤ损失ꎬ没有分类器差异损失.３４㊀实验结果提出的方法和３种对比方法在不同域适应任务下诊断结果的直方图如图５所示.由图可知ꎬ提出方法在所有的任务中都取得最好的诊断结果ꎬ测试准确率明显高于常用的域适应方法.其中ꎬＷＤＡꎬＤＡＮꎬＭＭＤ和提出的方法在６个域适应任务下的平均故障诊断准确率分别为４５８％ꎬ７４５％ꎬ６９７％和９３４％.表３给出了所有方法在５次实验中的平均计算时间ꎬ可以看出ꎬ提出的方法与常用域适应方法的计算时间相差不多.为了更好地判断域适应效果ꎬ采用ｔ－ＳＮＥ(ｔ￣ｄｉｓｔｒｉｂｕｔｅｄｓｔｏｃｈａｓｔｉｃｎｅｉｇｈｂｏｒｅｍｂｅｄｄｉｎｇ)[１５]技术把网络提取的源域和目标域训练数据的输出特征映射成二维特征并进行可视化.以第１个域适应任务作为例子ꎬ其训练过程可视化结果如图６所示.可以看出ꎬ训练过程中各类别实现很好的聚类ꎬ并且通过域适应学习ꎬ网络可以很好地对齐源域和目标域训练数据的特征.这说明提出的方法可以准确地实现无监督跨域故障诊断.表３㊀所有方法的平均计算时间Ｔａｂｌｅ３㊀Ａｖｅｒａｇｅｒｕｎｔｉｍｅｏｆａｌｌｍｅｔｈｏｄｓ方法ＷＤＡＤＡＮＭＭＤ提出的方法计算时间/ｓ３５０７２０６９９７３８图５㊀四种方法在不同域适应任务下的诊断结果Ｆｉｇ５㊀Ｄｉａｇｎｏｓｔｉｃｒｅｓｕｌｔｓｏｆｆｏｕｒｍｅｔｈｏｄｓｕｎｄｅｒｄｉｆｆｅｒｅｎｔｄｏｍａｉｎａｄａｐｔａｔｉｏｎｔａｓｋｓ㊀㊀同样地ꎬ为了更好地体现各种诊断方法的诊断效果ꎬ第１个域适应任务的４种方法测试数据特征的可视化结果见图７.可以看出ꎬ在ＷＤＡ方法中ꎬＮꎬＩＦꎬＢＦ和ＯＦ四类健康状态的特征存在很多重叠ꎬ说明这四种状态存在很多误分类ꎻ在ＤＡＮ和ＭＭＤ方法中ꎬＯＦ和ＩＦ的特征存在重叠ꎻ然而ꎬ在所提的方法中５种健康状态的数据都很好地聚在一起ꎬ而且不同健康状态的数据都清晰地分离开ꎬ这说明该方法可以有效地提取目标域数据的差异特征.图６㊀训练数据的特征可视化Ｆｉｇ６㊀Ｆｅａｔｕｒｅｖｉｓｕａｌｉｚａｔｉｏｎｏｆｔｒａｉｎｉｎｇｄａｔａ(ａ) 源域ꎻ(ｂ) 目标域ꎻ(ｃ) 源域和目标域混合.１７３第３期㊀㊀㊀张永超等:基于域适应与分类器差异的滚动轴承跨域故障诊断㊀㊀图７㊀不同方法测试数据的特征可视化Ｆｉｇ７㊀Ｆｅａｔｕｒｅｖｉｓｕａｌｉｚａｔｉｏｎｏｆｔｅｓｔｉｎｇｄａｔａｏｆｄｉｆｆｅｒｅｎｔｍｅｔｈｏｄｓ(ａ) ＷＤＡꎻ(ｂ) ＤＡＮꎻ(ｃ) ＭＭＤꎻ(ｄ) 提出的方法.４㊀结㊀㊀论本文针对旋转机械多变工况导致诊断模型泛化能力下降的问题ꎬ提出了基于域适应与分类器差异的滚动轴承跨域故障诊断方法.该方法可以直接使用原始信号作为输入ꎬ实现了端到端的诊断ꎻ在模型训练过程中ꎬ该方法不需要预先知道目标域的标签ꎬ实现了无监督域适应ꎻ在跨域故障诊断实验中ꎬ和典型的ＷＤＡꎬＤＡＮ和ＭＭＤ方法对比ꎬ该方法的平均诊断准确率分别提高４７６％ꎬ１８９％和２３７％ꎬ实现了准确的跨域故障诊断.总而言之ꎬ本文提出的方法可以有效地实现轴承的跨域故障诊断ꎬ提高了跨域诊断模型在实际工业场景中应用的可行性.参考文献:[１]㊀ＬｉＸꎬＪｉａＸＤꎬＺｈａｎｇＷꎬｅｔａｌ.Ｉｎｔｅｌｌｉｇｅｎｔｃｒｏｓｓ￣ｍａｃｈｉｎｅｆａｕｌｔｄｉａｇｎｏｓｉｓａｐｐｒｏａｃｈｗｉｔｈｄｅｅｐａｕｔｏ￣ｅｎｃｏｄｅｒａｎｄｄｏｍａｉｎａｄａｐｔａｔｉｏｎ[Ｊ].Ｎｅｕｒｏｃｏｍｐｕｔｉｎｇꎬ２０２０ꎬ３８３:２３５－２４７.[２]㊀ＹａｎｇＢꎬＬｅｉＹＧꎬＪｉａＦꎬｅｔａｌ.Ａｎｉｎｔｅｌｌｉｇｅｎｔｆａｕｌｔｄｉａｇｎｏｓｉｓａｐｐｒｏａｃｈｂａｓｅｄｏｎｔｒａｎｓｆｅｒｌｅａｒｎｉｎｇｆｒｏｍｌａｂｏｒａｔｏｒｙｂｅａｒｉｎｇｓｔｏｌｏｃｏｍｏｔｉｖｅｂｅａｒｉｎｇｓ[Ｊ].ＭｅｃｈａｎｉｃａｌＳｙｓｔｅｍｓａｎｄＳｉｇｎａｌＰｒｏｃｅｓｓｉｎｇꎬ２０１９ꎬ１２２:６９２－７０６.[３]㊀袁壮ꎬ董瑞ꎬ张来斌ꎬ等.深度领域自适应及其在跨工况故障诊断中的应用[Ｊ].振动与冲击ꎬ２０２０ꎬ３９(１２):２８１－２８８.(ＹｕａｎＺｈｕａｎｇꎬＤｏｎｇＲｕｉꎬＺｈａｎｇＬａｉ￣ｂｉｎꎬｅｔａｌ.Ｄｅｅｐｄｏｍａｉｎａｄａｐｔａｔｉｏｎａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｉｎｆａｕｌｔｄｉａｇｎｏｓｉｓａｃｒｏｓｓｗｏｒｋｉｎｇｃｏｎｄｉｔｉｏｎｓ[Ｊ].ＪｏｕｒｎａｌｏｆＶｉｂｒａｔｉｏｎａｎｄＳｈｏｃｋꎬ２０２０ꎬ３９(１２):２８１－２８８.)[４]㊀赵小强ꎬ张青青.改进Ａｌｅｘｎｅｔ的滚动轴承变工况故障诊断方法[Ｊ].振动ꎬ测试与诊断ꎬ２０２０ꎬ４０(３):４７２－４８０.(ＺｈａｏＸｉａｏ￣ｑｉａｎｇꎬＺｈａｎｇＱｉｎｇ￣ｑｉｎｇ.ＩｍｐｒｏｖｅｄＡｌｅｘｎｅｔｂａｓｅｄｆａｕｌｔｄｉａｇｎｏｓｉｓｍｅｔｈｏｄｆｏｒｒｏｌｌｉｎｇｂｅａｒｉｎｇｕｎｄｅｒｖａｒｉａｂｌｅｃｏｎｄｉｔｉｏｎｓ[Ｊ].ＪｏｕｒｎａｌｏｆＶｉｂｒａｔｉｏｎꎬＭｅａｓｕｒｅｍｅｎｔ＆Ｄｉａｇｎｏｓｉｓꎬ２０２０ꎬ４０(３):４７２－４８０.)[５]㊀ＳｈａｏＨＤꎬＪｉａｎｇＨＫꎬＬｉｎＹꎬｅｔａｌ.Ａｎｏｖｅｌｍｅｔｈｏｄｆｏｒｉｎｔｅｌｌｉｇｅｎｔｆａｕｌｔｄｉａｇｎｏｓｉｓｏｆｒｏｌｌｉｎｇｂｅａｒｉｎｇｓｕｓｉｎｇｅｎｓｅｍｂｌｅｄｅｅｐａｕｔｏ￣ｅｎｃｏｄｅｒｓ[Ｊ].ＭｅｃｈａｎｉｃａｌＳｙｓｔｅｍｓａｎｄＳｉｇｎａｌＰｒｏｃｅｓｓｉｎｇꎬ２０１８ꎬ１０２:２７８－２９７.[６]㊀李嘉琳ꎬ何巍华ꎬ曲永志.ＰＳＯ优化深度神经网络诊断齿轮早期点蚀故障[Ｊ].东北大学学报(自然科学版)ꎬ２０１９ꎬ４０(７):９７４－９７９.(ＬｉＪｉａ￣ｌｉｎꎬＨｅＷｅｉ￣ｈｕａꎬＱｕＹｏｎｇ￣ｚｈｉ.ＤｉａｇｎｏｓｉｓｏｆｇｅａｒｅａｒｌｙｐｉｔｔｉｎｇｆａｕｌｔｓｕｓｉｎｇＰＳＯｏｐｔｉｍｉｚｅｄｄｅｅｐｎｅｕｒａｌｎｅｔｗｏｒｋ[Ｊ].ＪｏｕｒｎａｌｏｆＮｏｒｔｈｅａｓｔｅｒｎＵｎｉｖｅｒｓｉｔｙ(ＮａｔｕｒａｌＳｃｉｅｎｃｅ)ꎬ２０１９ꎬ４０(７):９７４－９７９.)[７]㊀ＧｌｏｗａｃｚＡꎬＧｌｏｗａｃｚＷꎬＧｌｏｗａｃｚＺꎬｅｔａｌ.Ｅａｒｌｙｆａｕｌｔｄｉａｇｎｏｓｉｓｏｆｂｅａｒｉｎｇａｎｄｓｔａｔｏｒｆａｕｌｔｓｏｆｔｈｅｓｉｎｇｌｅ￣ｐｈａｓｅｉｎｄｕｃｔｉｏｎｍｏｔｏｒｕｓｉｎｇａｃｏｕｓｔｉｃｓｉｇｎａｌｓ[Ｊ].Ｍｅａｓｕｒｅｍｅｎｔꎬ２０１８ꎬ１１３:１－９.[８]㊀ＨａｎＴꎬＬｉｕＣꎬＹａｎｇＷＧꎬｅｔａｌ.Ｌｅａｒｎｉｎｇｔｒａｎｓｆｅｒａｂｌｅｆｅａｔｕｒｅｓｉｎｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓｆｏｒｄｉａｇｎｏｓｉｎｇｕｎｓｅｅｎｍａｃｈｉｎｅｃｏｎｄｉｔｉｏｎｓ[Ｊ].ＩＳＡＴｒａｎｓａｃｔｉｏｎｓꎬ２０１９ꎬ９３:３４１－３５３.[９]㊀ＬｕＷＮꎬＬｉａｎｇＢꎬＣｈｅｎｇＹꎬｅｔａｌ.Ｄｅｅｐｍｏｄｅｌｂａｓｅｄｄｏｍａｉｎａｄａｐｔａｔｉｏｎｆｏｒｆａｕｌｔｄｉａｇｎｏｓｉｓ[Ｊ].ＩＥＥＥＴｒａｎｓａｃｔｉｏｎｓｏｎＩｎｄｕｓｔｒｉａｌＥｌｅｃｔｒｏｎｉｃｓꎬ２０１６ꎬ６４:２２９６－２３０５.[１０]ＬｉＸꎬＺｈａｎｇＷꎬＤｉｎｇＱＳꎬｅｔａｌ.Ｍｕｌｔｉ￣ｌａｙｅｒｄｏｍａｉｎａｄａｐｔａｔｉｏｎｍｅｔｈｏｄｆｏｒｒｏｌｌｉｎｇｂｅａｒｉｎｇｆａｕｌｔｄｉａｇｎｏｓｉｓ[Ｊ].ＳｉｇｎａｌＰｒｏｃｅｓｓꎬ２０１９ꎬ１５７:１８０－１９７.[１１]ＨａｎＴꎬＬｉｕＣꎬＹａｎｇＷＧꎬｅｔａｌ.Ａｎｏｖｅｌａｄｖｅｒｓａｒｉａｌｌｅａｒｎｉｎｇｆｒａｍｅｗｏｒｋｉｎｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋｆｏｒｉｎｔｅｌｌｉｇｅｎｔｄｉａｇｎｏｓｉｓｏｆｍｅｃｈａｎｉｃａｌｆａｕｌｔｓ[Ｊ].Ｋｎｏｗｌｅｄｇｅ￣ＢａｓｅｄＳｙｓｔｅｍｓꎬ２０１９ꎬ１６５:４７４－４８７.[１２]ＭａＰꎬＺｈａｎｇＨＬꎬＦａｎＷＨꎬｅｔａｌ.Ａｄｉａｇｎｏｓｉｓｆｒａｍｅｗｏｒｋｂａｓｅｄｏｎｄｏｍａｉｎａｄａｐｔａｔｉｏｎｆｏｒｂｅａｒｉｎｇｆａｕｌｔｄｉａｇｎｏｓｉｓａｃｒｏｓｓｄｉｖｅｒｓｅｄｏｍａｉｎｓ[Ｊ].ＩＳＡＴｒａｎｓａｃｔｉｏｎｓꎬ２０２０ꎬ９９:４６５－４７８.[１３]ＺｈａｎｇＹＣꎬＲｅｎＺＨꎬＺｈｏｕＳＨ.Ａｎｅｗｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｄｏｍａｉｎａｄａｐｔａｔｉｏｎｎｅｔｗｏｒｋｆｏｒｂｅａｒｉｎｇｆａｕｌｔｄｉａｇｎｏｓｉｓｕｎｄｅｒｄｉｆｆｅｒｅｎｔｗｏｒｋｉｎｇｃｏｎｄｉｔｉｏｎｓ[Ｊ].ＳｈｏｃｋａｎｄＶｉｂｒａｔｉｏｎꎬ２０２０ꎬ２０２０:１－１４.[１４]ＧａｎｉｎＹꎬＬｅｍｐｉｔｓｋｙＶ.Ｕｎｓｕｐｅｒｖｉｓｅｄｄｏｍａｉｎａｄａｐｔａｔｉｏｎｂｙｂａｃｋｐｒｏｐａｇａｔｉｏｎ[Ｃ]//ＩｎｔｅｒｎａｔｉｏｎａｌＣｏｎｆｅｒｅｎｃｅｏｎＭａｃｈｉｎｅＬｅａｒｎｉｎｇ.ＮｅｗＹｏｒｋꎬ２０１５:１１８０－１１８９.[１５]ＭａａｔｅｎＬꎬＨｉｎｔｏｎＧ.Ｖｉｓｕａｌｉｚｉｎｇｄａｔａｕｓｉｎｇｔ￣ＳＮＥ[Ｊ].ＪｏｕｒｎａｌｏｆＭａｃｈｉｎｅＬｅａｒｎｉｎｇＲｅｓｅａｒｃｈꎬ２００８ꎬ９:２５７９－２６０５.２７３东北大学学报(自然科学版)㊀㊀㊀第４２卷。

基于VMD滤波和极值点包络阶次的滚动轴承故障诊断

第37卷第14期振动与冲击J O U R N A L OF VIBRATION A N D S H O C K Vol.37 No. 14 2018基于V M D滤波和极值点包络阶次的滚动轴承故障诊断武英杰$$辛红伟$$王建国$$王晓龙2(1.东北电力大学自动化工程学院，吉林132012% 2.华北电力大学能源动力与机械工程学院，河北保定071003)摘要：针对变速工况滚动轴承故障诊断问题，提出一种基于变分模态分解（VMD)滤波和极值点包络阶次的特征提取方法。

对变速工况下采集的振动信号进行V M D滤波以提高信噪比，同时抑制转速波动引起的振动趋势项;搜寻滤波信号的极大值，并进行端点延拓，通过极值点插值拟合求得信号包络线;利用计算阶比跟踪技术将时域包络线转变到角度域，进而得到信号的包络阶次谱;仿真与实际数据测试表明，基于极值点的包络阶次方法可以有效提取调幅信号中的调制阶次，并且V M D滤波可以使得故障特征阶次更加凸显，易于故障识别，该方法为变速工况下的滚动轴承故障诊断提供参考。

关键词：变分模态分解;极值点;包络阶次;阶比跟踪;故障诊断中图分类号：T N911.6 文献标志码：A D O I:10.13465/j.c n k i.R s. 2018.14.014Rolling bearing fault diagnosis based on th e variational mode decompositionfiltering and extreme point envelope orderWU Yingjie^ ,XIN Hongwei,WANG Jianguo1 ,WANG Xiaolong2(1. School of Automation Engineering，Northeast Electric Power University，Jilin 132012，C hina；2. School of E nergy，Power and Mechanical Engineering，North China Electric Power University，BaodingA b s t r a c t:T o d ia g n o s e ro llin g b e a rin g failiures u n d e r v a ria b le s p e e d w o rk in g c o n d itio n s，a m e th o d b a s e d o n th ev a ria tio n a l m o d e d e c o m p o sitio n(V M D)filte rin g a n d e x tre m e e n v e lo p e o rd e r w as p u t fo rw a rd. T h e v ib ra tio n sig n a lc o lle c ted in v a ria b le s p e e d c o n d itio n s w as filte re d b y th e V M D in o rd e r to im p r v ib ra tio n te n d e n c y te rm c a u s e d b y s p e e d v a ria tio n. S e a rc h in g th e m ax im u m of th e filte re d sig n a l a n d e x te n d in g itse n d p o in ts，a n e n v e lo p e sig n a l w as g a in e d b y th e p ro c e s s of sp lin e fittin g. T h e tim e d o m a in e n v e lo p e sig n a l w a s th e ntra n s fo rm e d to th e a n g le d o m a in b y u s in g th e c o m p u te d o r d e r tr a c k in g te c h n o lo g y，a n d th e n a n e n v e lo p e o rd e r s p e c tru mw a s o b ta in e d b y F F T. T h e s im u la tio n a n d e x p e rim e n t te s ts show th a t th e p ro p o se d m e th o d c a n e ffe c tiv e ly e x tra c t th em o d u la tio n o rd e r fro m m o d u la te d s ig n a l，a n d th e V M D filte rin g c a n m a k e fa u lt featiures m o re h ig h fo r fa u lt id e n tific a tio n. T h e p ro p o se d m etlio d p ro v id e s a r e fe re n c e to th e ro llin g b e a rin g fa u lt d ia g n o s is u n d e r v a ria b les p e e d condiH ions.K e y w o r d s：V M D；e x tre m e p o i n t；e n v e lo p e o r d e r；o rd e r tr a c k in g；fa u lt d ia g n o s is滚动轴承广泛应用于旋转机械，其健康状态直接影响整个设备的安全、经济运行。

航空发动机主轴轴承故障诊断

根据滚动轴承在线振动信号监测其运行状态和实时进行故障诊断，是目前既普遍又行之有效的方法。轴承振动信号包含丰富的运行状态信息，当滚动轴承出现局部损伤故障时，损伤与轴承其它元件表面接触时将会产生衰减冲击脉冲力，从而激起轴承的高频固有振动，实践表明这种高频固有振动的频率分量及其各个统计量不为常数，可以看成是以时间为自变量的非平稳信号[1，2]。
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飞机设计
第 30 卷
பைடு நூலகம்
在构成的故障信号上再加上大量的高斯白噪声和两个低频振动成分，加噪声和低频信号后的冲击过程如图3所示。
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图3 加入噪声和低频信号后的冲击过程
对加噪声和低频信号后的信号进行频谱分析如图4所示，可以看出4 kHz附近有调制的谱线。
第2期
赵鲁宁等：航空发动机主轴轴承故障诊断
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性与滚动轴承内圈故障信号的理论模型相一致。 2.3 仿真滚动轴承滚动体故障信号 2.3.1 模拟滚动体故障信号的构成
滚动体上的损伤点与外圈接触时产生的脉冲力直接作用于外圈，而损伤点与内圈接触时产生的脉冲力要通过滚动体及滚动体与外圈的界面传播后才作用于外圈，由于在滚动体内及通过界面传播时的能量损失，这个脉冲力的幅度比前一个要小得多。假设dbi =0.4dbo ，这里dbi ，dbo 分别表示滚动体上的损伤点与内圈和外圈接触时产生的脉冲力强度。令损伤点产生的脉冲串激励引起的振动的固有频率为蕊n =3 kHz。令故障特征频率蕊bc =120 Hz，采样频率蕊s =16 kHz。因此，滚动体上有一个损伤点时产生的脉冲串引起的衰减振动如图10所示。

基于LabVIEW的滚动轴承故障智能诊断系统

基于LabVIEW的滚动轴承故障智能诊断系统王焕跃【期刊名称】《价值工程》【年(卷),期】2014(33)35【摘要】Rolling bearing fault diagnosis system is developed by LabVIEW platform, in which it includes resonance demodulation diagnosis and BP neural network diagnosis. The fault frequency identification of resonance demodulation diagnosis is achieved by Hilbert demodulation and wavelet packet demodulation. For the BP neural network diagnosis, features from the dimensions, dimensionless parameters and wavelet relative energy can be taken as the input vector of neural network. Type of bearing failure can be taken as the output vector of neural network, and the neural network completes the fault diagnosis. The experimental result proves the effectiveness of the intelligent diagnosis system for rolling bearing faults and determines the type of fault.%利用LabVIEW平台开发了齿轮故障诊断系统。

ROLLING BEARING FAULT DIAGNOSIS METHOD BASED ON WA

专利名称：ROLLING BEARING FAULT DIAGNOSISMETHOD BASED ON WAVELET PACKETENERGY SPECTRUM AND MODULATIONSIGNAL BISPECTRUM ANALYSIS发明人：ZHEN, Dong,甄冬,GUO, Junchao,郭俊超,GU, Fengshou,谷丰收,LIU, Yinghui,刘英辉,ZHANG,Hao,张浩,SHI, Zhanqun,师占群申请号：CN2019/077945申请日：20190313公开号：WO2019/205826A1公开日：20191031专利内容由知识产权出版社提供专利附图：摘要：A rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation signal bispectrum analysis. The method comprises the following steps: step I, measuring a vibration signal of a detected rolling bearing; step II, carrying out wavelet packet decomposition on the vibration signal to obtain frequency bands of a wavelet packet; step III, obtaining wavelet packet energy spectrums of frequency bands and carrying out normalization to obtain normalized frequency bands; step IV, selecting an energy-concentrated frequency band from among the normalized frequency bands to carry out signal reconstruction; and step V, carrying out modulation signal bispectrum analysis on a frequency band of a reconstructed signal to obtain the fault feature frequency of the rolling bearing. Combining the transient characteristic of WPE and the periodic characteristic of MSB effectively improves the effect of the bearing fault diagnosis. The method can accurately extract the fault feature frequency, achieves a high signal-to-noise ratio and has good application prospects in the field of rotating mechanical fault diagnosis.申请人：HEBEI UNIVERSITY OF TECHNOLOGY,河北工业大学地址：Xiping Road No. 5340, Beichen District Tianjin 300401 CN,中国天津市北辰区西平道5340号, Tianjin 300401 CN国籍：CN,CN代理人：BEIJING BANGDAO LAW OFFICE,北京市邦道律师事务所更多信息请下载全文后查看。

毕业论文-基于DSP技术为机车轴承设计故障诊断监控系统-英文翻译

原文：Design of Fault Diagnosis Monitor System for the LocomotiveBearings Based on DSP TechnologyAbstractThe rolling bearing is one of the key parts of the locomotive running components, because it condition is directly related to the performance and safety of locomotive. In this paper, the monitor system for the locomotive bearings based on DSP TMS320LF2407A is designed. This system diagnoses the rolling bearing fault using vibration analysis method. It is based on comprehensive resonance demodulation and fast Fourier transform technique, and it adopts "related methods" to handle the result of the FFT. It effectively improves the response characteristics, sensitivity, differentiate and measurement accuracy of the bearing failure monitor system, and it can fulfill the monitor and prediction of the transient fault in the course of the locomotive running.Key words: resonance demodulation technology; digital signal processor; related methodsI. IntroductionThe higher safety is required to the trains because its speed is raised constantly. Bearing fault is one of the major factors causing eventful traffic accidents and affecting rail safety. Currently the railway system usually uses the bearing temperature detector to monitor the locomotive bearing condition. Theoretical analysis and a lot of practice show that the bearing temperature detector can prevent accidents from occurring to some extent, but most of the bearing fault is not sensitive to temperature. When the temperature of the bearing is beyond the range and the system gives an alarm, the worse damage of the bearing has occurred, and even theincident had happened. Therefore, to find the fault more early and accurately, the more advanced monitoring means must be adopted. Most of the bearing fault is very sensitive to vibration signal. The fault can cause vibration of the bearing increased. Compared with monitoring the temperature of bearing, the analysis and processing results to the vibration signal has more advantage than the temperature means.II. System composing and work processBased on the need, the monitor of the bearing fault monitoring system to the locomotive bearing sets two detections: itineration detections and fixed detections. The itineration detection is used in the normal conditions, and the fixed detection is used for the continuous monitoring of the fault bearing. The system adopts special composite sensor to collect the vibration of the bearing and the temperature signal at the same time. After the data processing, the corresponding fault levels and rise in temperature are got. The data acquisition unit is designed in this system. Alarm information will be transmitted to all carriages through interfaces so that the staff can handled in time, and the same time, the fault data and the related information of the train such as the current location and speed will be transmitted to the dispatch center through GPS, which is convenient to adopt corresponding measures. The system block diagram is in Fig. 1.III. The key technology of the design for the monitoring systemA.The spectrum analysis means for diagnosing bearing faultUnder normal circumstances, all parts of the rolling bearing (inner circle, outer circle, roller, holding frame) will retain the stable relative movement state. If the surface of some element (except for holding frame) has crack, and this crack is in the surface of the rolling adjacent component, the instantaneous vibration impulse must be produced.Assumed that the number of the roller in the bearing is Z ; the diameter of the roller is d ; the average diameter of the bearing inner circle and the bearing outer circle (the diameter of the roller revolution path) is D ; the frequency of the bearing rotation is f 0. Assumed that the inner circle is fixed and the outer circle is circumvolved, the vibration frequency brought by the surface defects of different bearing components can be derived.These frequencies can be called the fault characteristics frequency of the inner circle, outer circle and the roller.()circle)(inner 2101f D d Z f +=()circle)(outer 2101f D d Z f -=()(roller)]1[021f D d d D f -=B. Resonance demodulation technologyWe can collect vibration signal using the resonance of the bearing components, and detect the envelope of the fault signal using envelop detector, which can fulfill the analysis to the fault character. This is called “resonance demodulationtechnology”. The component surfaces such as the inner circle, the outer circle and the roller of the rolling bearing are easily damaged in local place in the course of operation (such as pitting and peeling off, cracking, scratching etc.). If the surface of some bearing components have local damage and the rollingobject presses the fault dot in the course of carried operation, it must bring impact. But the impact lasts a short time, and the frequency range of the energy divergence is wide, so the energy within the scope of vibration frequency is small. Due to the wide bandwidth of the impulse, it is certainly that it includes high frequency intrinsic vibration inspiring by intrinsic frequency of the inner circle, outer circle, roller, holding frame on rolling bearings. The resonance demodulate signal is separated by band-pass filter of center frequency equal to its intrinsic frequency. Then the envelope demodulation is carried through to there attenuation oscillatory wave using software or circuit, the frequency component of the high frequency attenuation vibration is wiped off. We only obtain low-frequency envelope signal with the information of the fault character. The spectrum analysis of the envelope signal is carried through by digital signal processor, we can obtain very high frequency resolution ratio and can easily find the frequency of the corresponding fault impact, thereby we can fulfill to diagnose to the bearing fault.With resonance demodulation technology, the electric resonator which resonant frequency is much higher than normal vibration frequency and limited high-harmonic frequency is designed. Therefore, it can effectively restrain the low-frequency signal including normal vibration signal. The resonance response magnifies the signal amplitude of the impulse signal and the time of its oscillation islonger, thus the fault signal is broadened in the time domain signal. After the envelope detection and low-pass filter, the low-frequency resonance demodulation signal with high signal-to-noise ratio is exported. In the signal processing system shown in figure 2, the bearing component brings resonance under the impact, form the continuous attenuation oscillation. To research each attenuation oscillation, we can see that its frequency is the natural frequency of bearing components, the amplitude of attenuation oscillation is relate to intensity of fault impact. The amplitude of envelopesignal of the attenuation oscillation reflects the size of the fault, and the repeat frequency of the envelope depends on the fault location. System has the performance of anti-jamming of the low frequency vibration, high signal-to-noise ratio.C. Envelope detectionA bearing with fault in the course of rolling will bring regular vibration. Different fault has different character frequency. The character frequency system detecting is the frequency of the signal envelope (the frequency which is accrued by the collision of the fault on bearing element), not the vibration frequency of the bearing. When we analyze the fault signal, the resonant frequency (carrier wave) must be removed by envelope demodulation. Because the envelope signal has fully included all information of the fault, removing carrier wave will not have any adverse impact on the analysis.IV. Hardware and software designThe hardware block diagram of the monitor for the bearing fault is shown in Fig.3.The circuit includes two parts: the vibration signal pretreatments and the bearing state analysis. The signal preprocessing part fulfills the amplification, conversion, resonance demodulation of the signal; the bearing state analysis part fulfills spectrum analysis of the signal, "correlation method" processing, fault grading processing, thebearings status report and communicating with peripheral equipment and so on.There are mainly three kinds of FFT algorithm to realize in DSP: (1) only including addition and subtraction operations without operations of the plural rotation factor; (2) including the operation of the plural rotation factor; (3) the operation of bits location inversion. After data is processed by this way, the workload of vibration component calculation in DSP is reduced evidently. The real-time capacity of system response can be advanced.Modularization design is adopted in the design of the software, which includes collections of the vibration signal and the temperature increment signal, A/D conversions, data pretreatments, FFT transforms, calculations of the power spectrum, judgments of the fault grading, saves of the data, displays of the data and transmissions of the data. The task dispatch is carried through by the way of event triggers and time triggers. To remove the interference, the “correlation means” processing to the results of FFT transform is carried out, which assure the fault signal picked up effectively.V. ConclusionFFT methods of vibration signal is adopted in system design,at same time differential temperature measurement methods is added into system to judge synthetically. The high capability DSP completes signal processing. This system can commendably satisfy the requirement for real-time processing. It monitors the signal of vibrations and temperatures with combining locomotive monitor and ground analysis. The earlier diagnosis and alarm for locomotive bearings fault can be given in order to assure locomotive running safely.REFERENCES[1] Wang Dezhi,The diagnosis and maintain of rolling bearing[M],Beijing: China Railway Publishing House, 1994,[2] Shi Huafeng,Yin Guohua,etc,Fault diagnosis of locomotive bearing[J],Electric Drive For Locomotive, 2004,（2）: 40~43,[3] Mei Hongbin,The libration monitoring and diagnosis of rolling bearing[M],Beijing：China Machine Press,1996,[4] Mei Hongbin,The fault diagnosis for rolling bearings using envelope analysis,Bearing,1993 ,（8）:30~34,[5] Feng Gengbin,The libration diagnosis technology of the locomotive fault[M],Beijing: China Railway Publishing House,1994.[6] Jiang Simi. The hardware exploiture of TMS320LF240x DSP. Beijing: China Machine Press, 2003.[7] Qing Yuan Science and Technology. The application design of TMS320LF240XDS. Beijing: China Machine Press, 2003.译文：基于DSP技术为机车轴承设计故障诊断监控系统摘要滚动轴承是机车运行组件的关键部件之一,因为它直接关系到机车的性能和安全。