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1、基于小波分析的旋转机械振动信号定量特征研究 国家自然科学基金项目（50105004）侯敬宏 黄树红 申 弢 张燕平（华中科技大学能源与动力工程学院 武汉 430074）摘要： 通过对机械振动信号的连续小波变换，利用小波滤波器良好的时频特性，研究了振动信号经过连续小波变换后的统计特征。在信号的特征提取中， 引入“灰度矩”并把一阶矩作为定量指标。对8种典型故障信号的研究表明，这种方法能够简单有效地提取信号的特征，区分振动故障。关键词: 小波变换；故障诊断；信号处理；特征提取中图分类号 TH165.3 文献标识码 A现有的旋转机械振动信号的分析方法多只是定性指出机组可能存在的故障，而现实中并不是设备
2、存在隐患就立即停机处理，而是希望根据定量评价故障的危害程度以及发展趋势而作决定，从而有效避免“维修不足”和“过剩维修”所带来的经济损失。 小波滤波器是一个具有恒(品质因子，定义为滤波器的中心频率与带宽之比)特性的滤波器，因此，其可以随信号频率增高而减小时窗宽度并相应增加频窗宽度，即具有”变焦”分析的特性。故而小波分析在信号的时频分析中具有特殊的地位和性能。从数学上看，对机械振动信号进行小波分析，是将一维信号在二维空间进行分解，使得在一维空间中无法提取的特征在二维空间中得到很好的反映。从物理上看，对振动信号进行连续小波变换和分析，实际上就是将无法从一维时域或者频域中体现的信号特征，在具有良好滤波
3、器特性的小波时频窗中得以体现，以获得信号所包含的特征信息3。因此，分析机械振动信号的连续小波系数，从中提取特征，可以更好地反映信号的本质。利用连续小波分析信号时，一般用每个尺度下小波能谱图提取信号的定性特征。这在很大程度上依赖于人的主观判断。如果要实现自主式的状态诊断，则必须要提取能反映信号特征的定量指标。本文引入一种“灰度矩”的统计量，对8种故障信号波形经连续小波变换后的系数矩阵进行处理，提出区分这些故障的定量指标。所选取的8种故障信号为2：不平衡，不对中，油膜振荡，轴裂纹，支座松动的轴振动信号，支座松动的支座振动信号，碰摩故障的轴振动信号，碰摩故障的支座振动信号。本文所采用的所有故障信号均
4、为本单位模拟试验台的实验数据。一 连续小波变换一般所讨论的小波，是指一个被称之为母小波或基本小波的函数，经伸缩和平移所产生的函数簇a，b（t），式中a0是尺度因子，b反映位移，其值可正可负。定义满足“容许条件”1： 的函数（t）为基本小波函数，简称小波函数。若函数f(t)是平方可积函数，即，定义： WTx(a，b)= 为f(t)的小波变换。上标*代表共轭，代表内积。要实现WTx(a，b)所定义的内积，除少数情况可做解析计算外，大多数情况只能通过计算机做近似数值计算。按数字信号处理的习惯可将式变成：WTx(a，k)= 对每一个固定a值，依次求不同k值下的乘积和，便得到该a值下一组WT系数。f(t
5、)如果是由512个离散点组成的时间序列，每一个给定的a值（尺度），有512个系数值，N个尺度下经小波变换后便组成一个N512的系数矩阵。二 小波系数矩阵的“灰度矩”信号经连续小波变换后的小波系数往往以灰度图的形式呈现出来。对于旋转机械的振动信号来讲，其故障特征周期出现，可用灰度图表示，如图1所示。显然，从灰度图上可直观分辨不同的故障，但实际故障诊断时，人为判断会存在模糊性和个体差异。那么，能否用一种定量指标来区分灰度图之间的总体差异呢？本文定 义 一 个 mn 矩阵的k阶“灰度矩”来定量描述小波灰度图的差异： Mk= 图2 用morl小波分析8种故障的Mk(k=150)分布油膜振荡碰摩-支座松
6、动-支座轴裂纹不对中碰摩-轴不平衡松动-轴这里的权值表示元素aij与a11之间的“距离”，相当于灰度图中某一个像素点与参考点之间的几何长度。式不直接采用灰度图中的几何距离，是为了不受灰度图几何尺寸的影响。图2是对应8种振动故障信号morl小波系数矩阵的灰度矩，其中灰度矩的阶数为k=150。可以看出，高阶矩与低阶矩对故障的区分度相差不大，因此可以采用一阶灰度矩M1来区分故障的灰度图，以减少计算量，有利于实时诊断。三 故障信号灰度矩M1的处理方法 图2同时给出了另外一个结果，即morl 小波的灰度矩可以很好地区分8种振动故障。显然，这对于定量故障诊断是极有吸引力的。如果能找到几种故障区分性很好的小
7、波，就有可能从多个角度进行定量故障诊断，减少由于信号畸变而导致某一个小波灰度矩不稳定造成的误诊断。为此，本文进行了以下工作：对采集到的故障信号(假设由512个离散点组成)进行归一化处理，若处理后的序列为x1，x2，x512，有成立；1. 选择8种常用的连续小波db4、 sym3、 coif4、 bior6.8、 rbio6.8、 dmey、 meyr、 morl分别对每一种故障进行N尺度连续小波变换，得到小波系数矩阵coefs(N512矩阵)，本文采用MATLAB进行计算；2. 对小波系数求绝对值；3. 依式求得coefs矩阵的1阶“灰度矩” M1。之所以对故障信号进行归一化处理，是因为故障的
8、原始波形振幅差异较大，经归一化处理以后，相当于在保证能量守恒的前提下，把不同波形限制在一定的范围内，增强不同波形之间的可比性，使研究的结果具有普遍意义。图3 8种故障经3种小波分析后的64尺度M1分布线油膜振荡碰摩-支座松动-支座轴裂纹不对中碰摩-轴不平衡松动-轴油膜振荡碰摩-支座松动-支座轴裂纹不对中碰摩-轴不平衡松动-轴图4 8种故障经3种小波分析后的128尺度M1分布线如果以8种小波为横轴，M1的大小为纵轴，把每一种故障的8 M1个用线连起来，便得到对应故障的灰度矩分布线。图3是64尺度的灰度矩分布线。由图3可以看出，8种故障被灰度矩分布线很好的区分开了，只有轴裂纹和碰摩-轴2种故障基本
9、重合在一起。而且db4， sym3， dmey， meyr， morl小波区分度较好。在以下的分析中，将采用dmey、meyr、morl三种小波。如将尺度再增加1倍，改为128尺度，只用dmey， meyr， morl小波进行分析，M1的分布线如图4所示。从图4中可以看出，从上到下8种故障线的相对位置没有发生改变，说明尺度的变化对灰度矩影响不大，这个结果非常有利于故障识别。四. 典型故障小波灰度矩M1的分布在实际情况下，同一种典型故障会有不同的时域波形，比如，同一台设备在不同转速下的波形是不同的，二台相同故障的设备的时域波形也可能是不同的。这是因为影响振动的还有其他因素。但是对应同一种故障，不
10、同时刻或位置采集的振动波形应有反映故障的共性特征。那么，在固定尺度的情况下，一定故障是否有一定的灰度矩数值区间呢？如果不同故障的灰度矩区间互不重叠，则可以用信号的小波灰度矩准确识别故障。1. 不平衡故障 分别提取3种不同转速下的不平衡故障曲线如图5图7。1/2X1X图10 3组不同转速下油膜振荡故障的M1分布线图8 3组不同转速下不平衡故障的M1分布线M1456944964439 图8 3组不同转速不平衡故障的M1分布线dmeymeyrmorl456M1102030977297519730图10 3组不同转速油膜振荡信号的M1分布线dmeymeyrmorl图9 转速9730rpm下的油膜振荡波
11、形及频谱图7 转速4569rpm下的不平衡故障波形及频谱1X1X图6 转速4496rpm下的不平衡故障波形及频谱图5 转速4439rpm下的不平衡故障波形及频谱经dmey、meyr、morl这3种小波分析后，对应的灰度矩分布如图8所示。M1的大小大约在46的范围内。2. 油膜振荡提取转速分别为9730rpm、9751rpm、9772rpm下的油膜振荡的波形，其中9730rpm的波形及频谱如图9所示。它们经上述3种小波分析后，灰度矩M1的分布如图10。由图10可以看出油膜振荡故障在三种转速下M1的大小集中在1832之间。3. 8种故障信号的灰度矩分布经过相同的计算，8种故障利用上述小变换及频谱后
12、M1的变化区间如表-1所示。 将表-1数据绘成灰度矩分布图，参见图11、图12。图11是几种故障的轴振动信号的M1分布区间图。可以看出，几种故障一阶灰度矩的区间并不重合。如果振动信号的灰度矩落入某故障区间，即可初步判断其故障类型。 图12上方两条灰度矩分布线分别是碰摩和松动故障的轴承座振动信号灰度矩，它们也有很好的区分度。图12下方的阴影区是不对中故障的轴振动信号灰度矩。可以看出不对中故障的M1区域覆盖了图11中碰摩-轴、不平衡、松动-轴以及轴裂纹的大部分区域，说明这几种故障具有与不对中故障相似的信号特征。可见，还需进一步提取有关征兆和改进分析方法，将这几种故障与不对中故障再区分。这正是作者下
13、一步拟开展的工作。不对中松动-支座摩碰-支座M1dmeymeyrmorlM1322824201612840M1322824201612840图12 支座振动信号及不对中故障的M1分布区间图11 轴振动信号的M1分布区间 表-1 8种典型故障在不同情况下的M1值典型故障转速统计指标M1值dmeymeyrmorl油膜振荡973032312897512322209772202018碰摩支座346225242235182524223618252422松动支座459615151346521515134683151513轴裂纹3041141413317010.810.21032698.68.27.8不对中
14、2419121211.532744.243.741995.35.24.8碰摩-轴34628.387.335188.387.336188.387.3不平衡443965.95.244965.35.24.84569554.4松动轴45964.34.23.846524.34.23.846834.34.23.8 五 .结论为了对机械振动信号连续小波系数进行总体定量刻画，并从中提取信号特征，引入了小波系数矩阵的k阶“灰度矩”的概念。研究表明，小波系数矩阵的一阶“灰度矩”能够很好地表征机械振动信号的特征，并且能定量地描述旋转机械的故障，有望成为新的、有效的故障诊断工具，其意义是重大的，在机械故障诊断中有良好
15、的应用前景。参 考 文 献1 杨福生. 小波变换的工程分析与应用. 科学出版社 ，20002 申 弢. 大型旋转机械智能监测诊断中信息融合理论与技术的研究. 华中理工大学博士学位论文， 19993 刘刚，屈梁生. 机械信号连续小波系数的统计特性研究. 西安交通大学学报. 第36卷第3期，20024 张志涌. 精通MATLAB5.3版. 北京航空航天大学出版社，2000A wavelet-based quantitative analysis of vibration signal of rotary machinesHou Jinghong Huang Shuhong Shen Tao Zha
16、ng Yanping（Huazhong University of Science and Technology，430074）Abstract: Wavelet has very good time-frequency domain features， so in this paper ， the continuous wavelet coefficients of mechanical vibration signal has been studied. From the aspect of feature extracting， this paper puts forward a new
17、 statistics and proved that this kind of one-order moment is very effective. 8 kinds of fault analysis results are given in detail. Research show that this quantitative analysis method could be used for extracting features of vibration siganl. Key words: wavelet transform， fault diagnosis， signal pr
18、ocessing， feature extracting Hou Jinghong Master Candidate; School of Energy & Power Eng.， Huazhong University of Science and Technology， Wuhan 430074， China.作者简介：侯敬宏，男，1974年生，华中科技大学能源与动力工程学院硕士研究生，主要研究方向为动力机械的故障诊断。Editors note: Judson Jones is a meteorologist, journalist and photographer. He has fre
19、elanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sput
20、nik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatize
21、d space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a
22、crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at w
23、ork glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also
24、a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his
25、 pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded superso
26、nic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent co
27、uld happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the
28、atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary l
29、ayer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Ol
30、ympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver
31、 preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goe
32、s too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute suc
33、cessfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parach
34、ute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
