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双语推荐：Morlet小波变换

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针对Morlet小波变换结果中的特征提取问题，对连续小波变换得到的小波系数矩阵进行奇异值分解（ SVD），分析了所获得的奇异值与Morlet小波变换结果中的特征信号以及噪声的对应关系。基于这种关系，通过选择合适的奇异值进行重构，清晰地提取到Morlet小波分解结果中的有效特征信息；进一步计算得到频率-能量谱，根据峰值位置能够提取冲击特征。将该方法应用于轴承振动信号的故障特征提取，并与其他方法进行了比较。结果表明，文中方法所获得的故障波形非常清晰，在低信噪比时具有较好的故障特征提取效果。
Aiming at the feature extraction of Morlet wavelet transform results , the wavelet coefficient matrix obtained by the continuous Morlet wavelet transform is decomposed by singular value decomposition ( SVD ) .The relationship among the singular value , the feature signal and the noise in the Morlet wavelet transform results is analyzed .Based on this relationship , the effective feature information of wavelet transform results can be clearly extracted by selecting appropriate singular values for SVD reconstruction .Further calculation is carried out to obtain the frequency-energy spectrum , and the shock feature can be extracted according to the peak position of this spec -trum.Finally, the proposed method is applied to the fault feature extraction of bearing vibration signals and is com-pared with other methods .The results show that the proposed method can extarct the distinct fault waveforms and achieve a very good effect on fault feature extraction at a low signal-to-nois

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用Morlet小波变换方法对时变振动系统和典型非线性振动系统进行参数识别。首先,通过Morlet小波变换提取振动响应的小波脊线,从而获得瞬时频率和瞬时幅值,然后,通过最小二乘曲线拟合即可估计系统的非线性阻尼和刚度系数。分别以时变阻尼自由振动系统、达芬有阻尼非线性简谐振动系统和范德波尔非线性自由振动系统为例子来说明小波变换方法对识别时变振动系统和非线性振动系统的有效性。
The parameter identifications of time-varying vibration system and typical nonlinear vibration system were conducted by using Morlet wavelet transform method.The wavelet ridge of vibration response was extracted by Morlet wavelet transform,and then the instantaneous frequency and instantaneous amplitude were obtained.The nonlinear damping and stiffness coefficients were estimated by using the least squares curve fitting.The time-varying damping free vibration system,the Duffing damped nonlinear harmonic vibration system,and the Van der Pol nonlinear free vibration system were taken as examples to show the effectiveness of wavelet transform method in identifying time-varying vibration system and nonlinear vibration system.

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首先介绍利用复Morlet小波变换进行结构非线性振动模型参数识别的原理,进而分析了因小波变换过程中的边端效应以及在采样点较少情况下复Morlet小波变换对非线性模型参数识别准确性的影响。然后提出了利用BP神经网络对非线性模型参数识别的信号进行预测延拓,并基于预测后的信号进行参数识别。最后通过对两种非线性振动模型进行数值仿真,验证了该方法能很好的提高非线性模型参数识别的准确性,并且具有一定的抗噪能力。
Here,the principle of parametric identification of structural nonlinear vibration model based on the complex Morlet wavelet transformation was introduced firstly.The influence of the complex Morlet wavelet transformation on the identification accuracy of nonlinear model parameters was analyzed under different cases of edge-effect of wavelet transformation and less sampling points.Then,a BP neural network was used for the prediction extension of nonlinear vibration signals and a novel parametric identification method was proposed based on the prediction results.Finally, through the numerical simulation of two nonlinear vibration models,the method was proved to be effective in ability identification of nonlinear model parameters and have a certain anti-noise ability.

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为准确识别电力变压器绕组模态参数,据某10 kV实体变压器绕组轴向激振实验结果,采用复Morlet小波对自由振动信号进行时频变换;使用改进的Crazy Climber算法提取时频图中小波脊线,获得变压器绕组前四阶固有频率及阻尼比,并将计算结果与PolyMax频域识别方法结果对比验证。结果表明,该方法能准确识别出变压器绕组前四阶固有频率,能更清晰显示信号能量随时间频率分布。基于复Morlet小波变换的模态参数识别方法抗干扰性能力较强,适合识别变压器绕组类复杂结构模态参数。
The complex Morlet wavelet was applied to analyze the free vibration signals in an axial excitation experiment of some 10kV power transformer winding.An improved Crazy Climber algorithm was designed and presented to extract the wavelet ridge of time-frequency spectrogram.Then the first four natural frequencies and its corresponding damping ratios were obtained successfully.The calculated results were also compared with the identification results calculated by the widely used frequency domain identification method of PolyMAX to illustrate the effectiveness of the proposed method.It is shown that the proposed method can accurately identify the first four natural frequencies,and the distribution of signal energy with time and frequency can be displayed more clearly.Furthermore,It is illustrated that the proposed method has strong anti-interference feature and can be applied effectively to identify the modal parameters of power transformer winding.

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与短时傅里叶变换、连续小波变换、广义S变换等时频分析方法相比，匹配追踪方法具有更高的时频分辨率，但传统的贪婪迭代算法计算效率较低。以Morlet小波作为时频原子进行匹配追踪，通过分析尺度因子不同时Morlet小波时频原子在时间域的形态，比较信号向频率、相位和延时相同，仅尺度因子不同的不同时频原子投影的投影值，认为尺度因子对时频原子的形态具有较强的控制作用，因而对时频原子和信号局部特征的匹配性能具有较强的控制作用。基于以上分析，在利用复地震道计算信号的瞬时信息作为时频原子频率、相位和时延等参数的基础上，对Morlet小波时频原子的尺度参数首先进行一维寻优，在得到最佳尺度因子基础上对时频原子参数进行微调，提高了计算效率。针对模型测试了算法的有效性及在去除噪声和薄层厚度求取等方面的应用前景。
Matching pursuit time-frequency analysis has better time-frequency resolution compared to short-time Fourier transform,continuous wavelet transform,and generalized S transform,but the tradi-tional greed iterative algorithm has lower computation efficiency.The Morlet wavelet is chosen as time-frequency atoms to achieve the matching pursuit due to the good property of scale parameter.The scale parameter has strong control action on the form of time-frequency atom,thus has strong control action on the matching character between signal and time-frequency atom,through comparing and analyzing the forms of time-frequency atoms based on different scale parameters and the projection values of signal onto different time-frequency atoms with the same frequency,phase and time-delay parameters but different scale parameters.The 1 D optimization for scale parameter is done with the frequency,phase and time-de-lay parameters calculated by Hilbert transform as the parameters of time-frequenc

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利用小波变换法反演边界层高度时，不同小波母函数的选取可能得到不同的边界层高度。因此，对构造的白天及夜间激光雷达后向散射信号理想廓线进行Haar小波协方差变换，并对后向散射信号梯度廓线进行Morlet与Mexican Hat小波变换反演边界层高度。结果表明，宜采用Haar函数与Mexican Hat函数作为小波母函数，其中Haar函数准确性优于Mexican Hat函数，而Mexican Hat函数更易稳定。同时为了进一步检验3种小波变换法的反演结果对小波振幅的敏感性，通过改变小波母函数的小波振幅，发现无论是理想廓线还是叠加扰动的廓线，较大的小波振幅易得到比较稳定准确的白天边界层高度与夜间混合层高度。
When applying wavelet transformation method in the retrieval of the boundary layer height by using lidar backscatter signals, the different selection of wavelet generating function may get different results. Therefore,the idealized lidar signal profiles during the daytime and nighttime have been built to explore which wavelet generating function will get the best performance. In this study,Haar wavelet covariance transformation has been used for the profiles of lidar backscatter signal,and Morlet and Mexican Hat wavelet trans-formation have been utilized for the gradient profiles of lidar backscatter signal,respectively. The results showed that the Haar function and the Mexican Hat function should be used as wavelet generating functions:the Haar function is more accurate and the Mexican Hat function is more stable. Furthermore,the changed wavelet dilation of the wavelet generating function also has been researched in order to test the sensitivity of the three different wavele

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针对电机电流信号特征分析(motor current signature analysis,MCSA)诊断早期转子断条故障时存在的频谱泄露阻碍故障特征频率识别的问题,提出一种基于定子电流Morlet小波解调制信号分析的故障诊断方法。首先选择合适的参数对Morlet小波性能进行优化,继而利用优化后的Morlet小波提取鼠笼电机定子电流信号包络线以消除基频和噪声干扰的影响,然后对提取到的包络线作快速傅里叶变换(fast Fourier transform,FFT)分析,并根据FFT频谱中是否存在特征频率成分2sfs判断转子断条故障发生与否。所提方法在电机工频或变频供电方式、不同负载运行状况下都能够消除噪声干扰和频谱泄露影响,因而便于故障特征提取并实现早期转子断条故障诊断。理论分析和实验结果表明了所提方法的正确性和有效性。
Spectrum leakages make it difficult to identify fault feature during early diagnostics of squirrel cage induction motor broken rotor bars with motor current signature analysis ( MCSA) method. A diagnosis method based on Morlet wavelet demodulated current signal was proposed to overcome this problem. The fast Fourier transform ( FFT) spectrum of the envelope of stator current was investigated and the conclusion of failure or not was drawn depending on the situation that characteristic frequency of 2sfs could be found in obtained spectrum. The envelope extraction was performed by Morlet wavelet demodulation algorithm with proper selected wavelet parameters and used to remove the strong fundamental frequency and additional components outside the frequency region of interest. For main-fed or inverter-fed motor operating under dif-ferent load conditions, the proposed method can all eliminate noises and fundamental frequency, which make feature extraction easier for the purpose of incipient

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传统的Canny边缘检测方法提取遥感图像边缘视觉特征在设定不变矩阈值采用经验模式,导致视觉提取分辨率不好,特征提取不准。提出采用Morlet小波变换对遥感图像边缘特征进行不变矩阈值函数构建,提出一种基于Morlet小波Canny边缘检测算法的遥感图像视觉特征提取。将图像数据经过Canny边缘检测和标记分水岭分割,实现遥感图像视觉提取。仿真实验表明,该方法在遥感图像视觉特征提取上比传统的Canny边缘检测方法效果明显,提取正确率最高可以达到94.20%,算法将在远距离遥感目标识别和监测等领域具有很好的应用价值。
Traditional Canny edge detection methods for feature extraction of remote sensing image edge vision in the set-ting of moment invariant threshold is taken by using empirical mode, resulting in visual resolution is not good. The remote sensing image edge features are invariant threshold function constructed by Morlet wavelet transform, and we propose a kind of remote sensing image feature visual Morlet wavelet edge detection algorithm based on the extraction of Canny. Re-mote sensing image extraction is obtained. Simulation results show that, the method in remote sensing image visual feature extraction than conventional Canny edge detection methods and obvious effect, extraction accuracy can reach 94.20% of the maximum, the algorithm will have good application value in the field of remote sensing target identification and monitor-ing.

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为了从柴油机缸盖振动信号中获取缸内燃烧响应信号,提出了基于连续小波时间—能量分布提取柴油机燃烧响应信号的方法:选择Morlet小波对原信号做连续小波变换,在尺度上积分求出信号的时间—能量分布;然后,根据柴油机的工作相位截取燃烧响应信号。用该方法对实测缸盖振动信号进行分析,结果表明:该方法可以比较准确地提取柴油机缸内燃烧响应信号,为进一步依据燃烧响应信号分析柴油机的工作状况提供了条件。
In order to obtain the combustion signal from diesel cylinder head vibration , this paper presents a method of extracting diesel combustion signal based on time-wavelet energy distribution .Firstly,do continuous wavelet transforma-tion applying morlet wavelet and obtain the time-wavelet energy distribution of signal;then intercept combustion response signal according to the diesel ’ s working principles .Using this method , vibration signals of the cylinder head were ana-lyzed .The result showed that this method could accurately extract signals of diesel combustion from the diesel cylinder head vibration signals .This provided conditions for further analyzing the working state of diesel based on combustion sig -nals .

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压扭应力场环境下形成的走滑断层一般具有断面陡立,在剖面上呈花状等特点,其构造特征复杂,剖面解释和空间组合难度较大。同一地震剖面的浅、中、深层的资料品质有差异,断点、断面的清晰度也不同。以地质背景为基础,针对不同层段采用不同主频的地震资料进行断层解释,能够增强其可靠性。三参数小波变换具有比傅里叶变换、Morlet小波变换更好的时频聚焦性,可以使断层在不同主频的地震剖面上取得最佳的成像效果,有利于人工解释并提高其可信度。南堡凹陷走滑断层发育,这里采用三参数小波分频处理技术,针对该区块的地震资料进行处理并用于断层解释,取得了较好的效果。
Generally,strike-slip fault formed under pressure torsion stress field has the characteristics of steep section,flower structure,etc.Its structural feature is complex,and it is difficult to accomplish fault interpretation.The data quality of the same seismic profile at shallow,middle and deep segment has great difference.Therefore,the definition of breakpoints and fault section is also different.Based on the geological background,the Reliability of fault interpretation can be improved by u-sing seismic data with different dominant frequency at different interval.Three parameter wavelet transform is much better than Fourier transform and Morlet wavelet transform in time-frequency focusing.The best effect of fault imaging can be obtained by this method in different dominant frequency of seismic profiles,and it is also convenient for manual interpretation and credibility enhancement.There are large amount of strike-slip faults in Nanpu Sag.Three parameter wavelet frequency processing tech

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