APPLICATION OF WAVELET TIME—FR EQUENCY ANALYSIS TO INDENTIFICA—TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem ,the corresponding dynamic equation of the cracked rotor is modelled,the numerical simulation solutions of the cracked rotor and the uncracked rotor are obtained,By the continuous wavelet time-frequency transform,the wavelet time-frequecney properties of the uncracked rotor and the cracked rotor are discussed, A new detection algorithm that uses the wavelet time-frequency transform to identify the crack is proposed.The influence of the sampling frequency on the wavelet time-frequency transform is analyzed by the numerical simulation research .The valid sampling frequency is suggested ,Experiments demonstrate the validity and avaliability of the proposed algorithm in identification of the cracked rotor for engi-neering practices.     

基于幅值与相角小波映射的裂纹转子故障诊断

建立了基于简单铰链裂纹模型和局部柔度理论的裂纹转子动力学模型,得到了裂纹转子与无裂纹转子的数值仿真解及其傅里叶变换的相角;利用连续小波变换研究了裂纹转子与无裂纹转子的幅值与相角小波映射特性,提出了利用幅值与相角小波映射识别裂纹的新方法。数值仿真研究了尺度因子对幅值与相角小波映射准确性和有效性的影响,给出了建议的尺度因子。试验研究验证了该方法在工程实际中的有效性和实用性。     

裂纹转子识别中Wigner-Ville分布与小波变换的比较

建立基于简单铰链裂纹模型的裂纹转子瞬态响应的动力学模型，得到裂纹转子与无裂纹转子的数值仿真解，比较裂纹转子与无裂纹转子Wigner-Ville分布和小波变换时频特性的不同。数值仿真进一步对比研究Wigner-Ville分布和小波变换对刚度变化的敏感性，并讨论质量偏心和质量偏心角对Wigner-Ville时频特性与小波时频特性的影响，为工程实际中裂纹转子的识别提供依据。     

SIMULATION OF CRACK DIAGNOSIS OF ROTOR BASED ON MULTI-SCALE SINGUUR-SPECTRUM ANALYSIS

In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis (MS-SSA) is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response (signals). Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.     

基于小波脊提取的扭转振动测试方法研究

针对工程中转子的扭转振动提取对硬件要求严格的情况,提出了一种基于小波脊提取的扭转振动测试方法。首先,通过小波变换获得齿信号的时频信息;其次,对时频信息进行脊提取得到齿信号的瞬时频率,获得转子的瞬时转速;然后,对瞬时转速进行参数估计获得最终的扭转振动参数;最后,通过仿真与试验分别对所提出的方法进行了验证。结果表明,与传统的扭转振动测试方法相比,所提出的方法不但具有较高的精度,且对硬件的要求相对较低,所需采样频率和储存空间远远小于传统的测齿法。     

基于有限元模型单一开裂纹转子的振动分析与无损估计

基于局部柔度理论和传递矩阵分析,给出一种简化的裂纹转子有限元模型。数值仿真研究了转子的长径比、裂纹位置以及裂纹深度对停机状态单一开裂纹转子的特征频率和振型的影响。提出一种借助裂纹转子前两阶特征频率和一阶振型对转子进行无损估计的新方法,仿真算例验证了该方法的有效性和可行性。     

Crack identification in a rotor with an open crack

A finite element (FE) model, which is based on a transfer matrix analysis and local flexibility theorem, is introduced for crack identification of a static (non-rotating) rotor with an open crack. Through numerical simulation, the effects of crack location and crack depth on the mode shapes and the changes in the eigenfrequencies of the cracked rotor are investigated. A crack identification algorithm that makes use of the translations of the first mode at two symmetric points and the contour diagram of crack location versus crack depth for the first two given normalized eigenfrequencies is proposed to estimate the crack location and depth in the rotor. Two illustrative examples are demonstrated and compared for availability and validity of the proposed algorithm.     

Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform

There are significant changes in the vibration responses of cracked structures when the crack depth is significant in comparison to the depth of the structure. This fact enables the identification of cracks in structures from their vibration response data. However when the crack is relatively small, it is difficult to identify the presence of the crack by a mere observation of the vibration response data. A new approach for crack detection in beam-like structures is presented and applied to cracked simply supported beams in this paper. The approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. These two sets of mode shape data, which constitute two new signal series, are obtained and reconstructed from the modal displacement data of a cracked simply supported beam. They represent the left half and the modified right half of the modal data of the simply supported beam. SWT is a redundant transform that doubles the number of input samples at each iteration. It provides a more accurate estimate of the variances at each scale and facilitates the identification of salient features in a signal, especially for recognising noise or signal rupture. It is well known that the mode shape of a beam containing a small crack is apparently a single smooth curve like that of an uncracked beam. However, the mode shape of the cracked beam actually exhibits a local peak or discontinuity in the region of damage. Therefore, the mode shape ‘signal’ of a cracked beam can be approximately considered as that of the uncracked beam contaminated by ‘noise’, which consists of response noise and the additional response due to the crack. Thus, the modal data can be decomposed by SWT into a smooth curve, called the approximation coefficient, and a detail coefficient. The difference of the detail coefficients of the two new signal series includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams used are computed using the finite element method. For real cases, mode shape data are affected by experimental noise. Therefore, mode shape data with a normally distributed random noise are also studied. The results show that the proposed method has great potential in crack detection of beam-like structures as it does not require the modal parameters of an uncracked beam as a baseline for crack detection. The effects of crack size, depth and location, and the effects of sampling interval are examined.     

旋转机械轴心轨迹信号的复数小波分析

提出了一种利用复数小波变换分析转子振动轴心轨迹信号的方法,通过分析小波尺度与振动倍频间的关系,使得观察某一尺度上的小波幅值就相当于考察一定频率范围的周期谱图,对典型非线性故障轴心轨迹信号的分析揭示出,摩擦故障时高频振动地时－频域上呈现出非均匀间歇现象,而轴裂纹时的高频振动是均匀间歇地出现,且周期与旋转基频相同,因此该方法可以直观地识别故障的细节性特征,有望形成一种新的、有效地监测诊断技术。     

基于区间B样条小波有限元的转子裂纹定量识别

研究一种基于区间B样条小波有限元的转子横向裂纹定量识别方法.构造包含转动惯量影响的区间B样条小波Rayleigh梁单元,高精度求解裂纹转子前三阶固有频率,获得裂纹相对位置和相对深度作为变量的固有频率解曲面.然后将实测的裂纹转子前三阶固有频率作为裂纹识别问题的输入,利用三条等高线的交点定量识别出裂纹存在的相对位置和相对深度.数值仿真和试验研究结果表明,该方法鲁棒性强,单元数量少,辨识精度和效率高,为转子系统裂纹定量识别提供了新方法.     

单盘含裂纹转子系统的非线性响应分析与实验研究

建立含裂纹Jeffcott转子的动力学运动方程。针对裂纹深度对转子系统动态响应的影响及转子盘摆振响应的特点进行仿真计算和试验研究。数值仿真表明，对于较浅的裂纹，系统响应为周期性运动，在某些转速下会出现倍周期运动，同时还出现各种倍频分量。此时的摆振运动常包含激振频率的倍频成分。当裂纹较深时，盘的摆振运动与横向振动都会出现各种非协调响应。试验结果表明，当轴上存在裂纹时，盘的横向振动响应和摆振响应中都会出现高次谐波分量，这些分量虽然从频率成分上讲是相同的，但各分量的大小有明显差异。这些结论对于转子裂纹故障的监测与诊断具有新的意义。     

Mallat算法的光学实现方法

现有的光学小波变换方法均基于连续小波变换,基于离散信号的小波变换算法（Mallat算法）的光学小波变换还没有出现,这阻碍了光学小波变换应用的发展。针对这一问题,分析利用光学4f系统实现Mallat算法的基本原理,提出Mallat算法的光学实现方法。针对空间光调制器只能实现非负的实函数,且CCD只能记录光的强度,给出一种应用于光学4f系统的光学小波滤波器的设计方法。使用该种光学小波滤波器,利用光学4f系统实现Mallat算法的小波分解部分,并通过数值计算实现Mallat算法的小波重构部分。仿真分析和光学实验结果验证了方法的正确性。     

基于小波分析的裂纹梁的损伤识别

阐述了一种基于小波变换的含裂纹梁的损伤识别方法,利用含裂纹梁的一阶模态阵型作为小波分析的力学特征信号,识别损伤的位置和大小.利用小波分析系数的模极大值随分析尺度的传播定位损伤的位置,计算针对于损伤频率信号的能量判断损伤的大小.与以前的小波分析方法相比,此方法确定损伤位置的可靠性高,能识别微小的损伤.利用能量守恒定理和小波分析频段细化的能力,裂纹的定量分辨率高.     

小波包熵在设备性能退化评估中的应用

开展设备性能退化评估研究,是制定主动设备维护策略、降低设备维护费用的基础。在设备性能退化过程中,信号成份会逐渐复杂化。本文提出利用小波包熵监测信号的复杂性变化,从而为设备性能退化评估提供可靠的特征向量。为了研究性能退化过程中振动信号的小波包熵的变化规律,使用裂纹转子动力学模型模拟了转子裂纹逐渐增加的过程,并使用仿真数据计算了各个状态下的小波包能量熵和小波包奇异值熵值。分析结果表明,随着转子性能退化程度的加深,小波包熵值逐渐增加,且对于性能恶化的突变较为敏感。     

小波分析识别裂纹参数中的噪声影响

鉴于信号和噪声进行多尺度小波变换时,其小波系数模极大值在多尺度上表现出截然不同的性质,直接将悬臂梁含噪声的前四阶模态进行小波分析,从小波系数模极大值在多尺度上的特性可以定位损伤,讨论高阶模态在损伤识别中的优缺点.定义一个和小波系数直接相关的集中因子,建立其与裂纹深度之间的关系,并分析模态中的噪声对裂纹深度识别的影响规律.研究可对实测环境中小波分析识别损伤提供一定的参考.     

基于改进同步挤压小波变换识别信号瞬时频率

提出了改进同步挤压小波变换。首先,采用解析模态分解定理将非平稳响应信号分解为多个单分量信号;其次,通过频率转换将分解后的单分量信号从低频区域转换到高频区域以提高时间分辨率;然后,对频率重点关注区域的时频代表值进行局部挤压,提高时频曲线的频率精度;最后,通过两个数值算例和一个拉索试验验证了改进同步挤压小波变换方法的有效性和准确性。研究结果表明,改进同步挤压小波变换能够提高信号在特定区域内的瞬时频率识别精度,是一种可行的时变结构参数识别方法。     

RESEARCH OF PROBLEMS ON REALIZING DIRECT ALGORITHM OF WAVELET TRANSFORM

Direct algorithm of wavelet transform (WT) is the numerical algorithm obtained from the integral formula of WT by directly digitization. Some problems on realizing the algorithm are studied. Some conclusions on the direct algorithm of discrete wavelet transform (DWT), such as discrete convolution operation formula of wavelet coefficients and wavelet components, sampling principle and technology to wavelets, deciding method for scale range of wavelets, measures to solve edge effect problem, etc, are obtained. The realization of direct algorithm of continuous wavelet transform (CWT) is also studied. The computing cost of direct algorithm and Mallat algorithm of DWT are still studied, and the computing formulae are obtained. These works are beneficial to deeply understand WT and Mallat algorithm. Examples in the end show that direct algorithm can also be applied widely.     

含横向裂纹的Jeffcott转子刚度分析

根据断裂力学理论和转子动力学理论,考虑沿3个坐标轴方向6个载荷的作用,推导出了含裂纹的转轴刚度。裂纹的开闭状态由裂纹面的应力决定。通过数值仿真计算发现:刚度在3个坐标轴方向上随着裂纹深度的变化幅度有很大差异,轴向刚度变化以及小裂纹情况下垂直于裂纹方向的刚度变化可以不考虑;随着细长比的增大,裂纹轴的刚度减小。     

EMD方法基于径向基神经网络预测的数据延拓与应用

把基于径向基神经网络(radbas function,RBF)预测的数据延拓技术引入经验模态分解(empirical mode decomposition,EMD)时频分析领域,论述基于RBF神经网络预测的数据延拓技术原理,通过对非线性仿真信号基于RBF神经网络预测延拓研究表明,该延拓技术是有效的,并且把该延拓技术应用于转子横向裂纹的时频分析,获得良好的效果.该研究成果能广泛用于信号时频分析领域.     

基于小波分析的旋转机械故障诊断技术及其试验研究

通过把转子试验台裂纹故障信号与小波变换的多分辨率方法以及奇异性理论相结合进行研究,发现小波分析便于对信号的总体和局部进行刻画;利用小波变换对信号的分解和重构特性,可有针对性地选取有关频带的信息以及降低噪声干扰,通过对重构信号的频谱分析能更有效地提取裂纹故障的典型特征,为计算机自动识别或专家系统的建立奠定了基础,从而达到了诊断的目的。结果表明,对于旋转机械的非平稳信号来说,利用小波变换方法进行故障诊断是行之有效的。