CN103336895A

CN103336895A - Noise determination method disintegrated and assisted by ensemble average empirical mode

Info

Publication number: CN103336895A
Application number: CN2013102374194A
Authority: CN
Inventors: 雷亚国; 王思哲; 孔德同; 林京
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2013-06-14
Filing date: 2013-06-14
Publication date: 2013-10-02
Anticipated expiration: 2033-06-14
Also published as: CN103336895B

Abstract

The overall average empirical mode decomposition assists noise determination method, performs fast Fourier transform on Gaussian white noise represented by randn, obtains its spectrum, and multiplies the spectrum by a sine function

The product is expressed as Y(f)=A X(f), and Y(f) is subjected to inverse fast Fourier transform, that is, the time series of the noise signal whose amplitude varies sinusoidally with the frequency is obtained, and the constructed noise is used instead of Gaussian White noise is added to the original signal to decompose the overall average empirical mode. The invention overcomes the mode confusion problem caused by adding Gaussian white noise whose amplitude does not change with frequency, realizes effective diagnosis of mechanical equipment failure, and the decomposition result is relatively accurate.

Description

Population Mean Empirical Mode Decomposition Assisted Noise Determination Method

技术领域technical field

本发明涉及机械设备故障诊断领域，具体涉及总体平均经验模式分解协助噪声确定方法。The invention relates to the field of fault diagnosis of mechanical equipment, in particular to a noise determination method assisted by overall average experience mode decomposition.

背景技术Background technique

人类生活水平的提高离不开工业技术的发展，工业技术水平已经成为衡量一个国家综合实力的重要指标之一。机械工业素有“工业的心脏”之称，它为其他经济部门提供生产基础，一切机械设备是工业发展的载体，为工业发展提供关键技术，在工业发展中发挥着越来越重要的作用。同时，机电设备也越来越朝着大型化、复杂化、精密化发展，设备的功能越来越多，结构原理越来越复杂，性能指标越来越高，这样势必会使得出现故障的概率大大增加。The improvement of human living standards is inseparable from the development of industrial technology, and the level of industrial technology has become one of the important indicators to measure the comprehensive strength of a country. The machinery industry is known as the "heart of industry". It provides the production base for other economic sectors. All machinery and equipment are the carrier of industrial development, providing key technologies for industrial development, and playing an increasingly important role in industrial development. At the same time, electromechanical equipment is becoming more and more large-scale, complex, and sophisticated. The functions of the equipment are increasing, the structural principles are becoming more and more complex, and the performance indicators are getting higher and higher. This will inevitably increase the probability of failure. greatly increase.

由于机电设备工况复杂且多变，机械故障特征也越来越复杂，设备的故障特征往往是非平稳、非线性的。但传统的机械设备故障诊断方法往往只适用于平稳信号，对非平稳、非线性信号诊断效果很差。经验模式分解EMD是针对非线性、非平稳信号而提出的一种信号处理方法，它是基于信号局部极值点的一种分解方法：用三次样条函数根据信号的局部极值点拟合出上下包络，求取上下包络的均值，再将信号减去所求取的均值，重复上述步骤，直到筛选出来的函数是本征模式函数；再从信号中减去筛选出来的本征模式函数继续筛选，如此循环筛选，直到信号的极值点数目少于3。在经验模式分解中，存在模式混叠的问题。针对经验模式分解EMD模式混淆不足，提出了总体平均经验模式分解，该方法对信号加入高斯白噪声，改善信号的极值点分布，可以有效减少模式混淆问题。高斯白噪声具有频率均匀分布特性，在整个频率范围内幅值均相等，也就是对原始信号的高频与低频分量都加入相同幅值大小的噪声。但是，当加入的噪声幅值较大时，其波动性较大，虽然对高频分量的分解结果较好，但由于相邻低频本征模式函数的频带中心距离较近，波动性大的噪声容易使信号中的单一低频模式分解到相邻的多个本征模式函数中，出现模式混淆；当加入的噪声幅值较小时，其波动性较小，虽然可以避免上述问题，但因为高频本征模式函数的频带较宽，小的噪声对信号中的高频分量“拉动能力”较弱，导致信号中的多个高频模式分解在同一个本征模式函数中，同样会出现模式混淆。Due to the complex and changeable working conditions of electromechanical equipment, the mechanical fault characteristics are becoming more and more complex, and the fault characteristics of the equipment are often non-stationary and nonlinear. However, traditional fault diagnosis methods for mechanical equipment are often only suitable for stationary signals, and are poor for non-stationary and nonlinear signals. Empirical mode decomposition EMD is a signal processing method proposed for nonlinear and non-stationary signals. It is a decomposition method based on the local extreme points of the signal: the cubic spline function is used to fit the local extreme points of the signal The upper and lower envelopes, calculate the mean value of the upper and lower envelopes, then subtract the calculated mean value from the signal, and repeat the above steps until the selected function is an eigenmode function; then subtract the filtered eigenmode from the signal The function continues to filter, and so on, until the number of extreme points of the signal is less than 3. In empirical mode decomposition, there is a problem of mode aliasing. Aiming at the deficiency of EMD mode confusion in empirical mode decomposition, an overall average empirical mode decomposition is proposed. This method adds Gaussian white noise to the signal to improve the distribution of extreme points of the signal, which can effectively reduce the mode confusion problem. Gaussian white noise has the characteristic of uniform frequency distribution, and the amplitude is equal in the entire frequency range, that is, noise of the same amplitude is added to the high frequency and low frequency components of the original signal. However, when the amplitude of the added noise is large, its volatility is large. Although the decomposition result of high-frequency components is better, due to the close distance between the frequency band centers of adjacent low-frequency eigenmode functions, the noise with large volatility It is easy to decompose a single low-frequency mode in the signal into multiple adjacent eigenmode functions, resulting in mode confusion; when the added noise amplitude is small, its volatility is small, although the above problems can be avoided, but because the high-frequency The frequency band of the eigenmode function is wide, and the small noise has a weak "pull ability" to the high frequency component in the signal, causing multiple high frequency modes in the signal to be decomposed into the same eigenmode function, and mode confusion will also occur .

发明内容Contents of the invention

为了克服上述现有技术的缺点，本发明的目的在于提供总体平均经验模式分解协助噪声确定方法，可以克服现有方法出现的模式混淆问题，得到物理意义明确的本征模式函数，有效实现机械设备故障的诊断。In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for assisting noise determination by overall average empirical mode decomposition, which can overcome the mode confusion problem in the existing method, obtain eigenmode functions with clear physical meanings, and effectively realize mechanical equipment Diagnosis of faults.

为了达到上述目的，本发明采取的技术方案是：In order to achieve the above object, the technical scheme that the present invention takes is:

总体平均经验模式分解协助噪声确定方法，包括以下步骤：The population averaged empirical mode decomposition assisted noise determination method consists of the following steps:

（1）对用randn表示的高斯白噪声进行快速傅里叶变换，得到其频谱，表示为X(f)＝F(randn)，其中f表示频率，X(f)表示幅值，0＜X(f)＜0.2；(1) Perform fast Fourier transform on Gaussian white noise represented by randn to obtain its spectrum, expressed as X(f)=F(randn), where f represents frequency, X(f) represents amplitude, 0<X (f)<0.2;

（2）对该频谱乘以正弦函数

该乘积表示为Y(f)＝A·X(f)，其中f_s为采样频率；(2) Multiply the spectrum by the sine function

This product is expressed as Y(f)=A·X(f), Where f _s is the sampling frequency;

（3）对Y(f)进行快速傅里叶逆变换，即得到幅值随频率正弦变化的噪声信号的时间序列，表示为y(t)，构造的幅值随频率成正弦变化的噪声信号数学表达式为:(3) Perform inverse fast Fourier transform on Y(f), that is, obtain the time series of the noise signal whose amplitude varies sinusoidally with frequency, expressed as y(t), and construct a noise signal whose amplitude varies sinusoidally with frequency The mathematical expression is:

$y the y ((t t)) = = {F f}^{- - 11} [[Y Y ((f f))]] = = {F f}^{- - 11} [[A A \cdot \cdot X x ((f f))]] = = {F f}^{- - 11} [[a a sin sin ((\frac{π π}{{f f}_{s the s}} f f)) \cdot &Center Dot; F f ((randn rand))]];;$

（4）用构造的噪声代替高斯白噪声加入原始信号，进行总体平均经验模式分解。(4) Replace the Gaussian white noise with the constructed noise and add the original signal to decompose the overall average empirical mode.

本发明的核心是对原始信号高频成分加入幅值较大噪声，避免不同模式的函数分在一个本征模式函数中；低频成分加入幅值较小噪声，避免将一个模式分量分解到不同的本征模式函数中，克服了由于加入幅值不随频率变化的高斯白噪声而带来的模式混淆问题，实现机械设备故障的有效诊断，分解结果相对比较精确。The core of the present invention is to add noise with larger amplitude to the high-frequency component of the original signal, so as to prevent the functions of different modes from being divided into one eigenmode function; to add noise with smaller amplitude to the low-frequency component, to avoid decomposing a mode component into different eigenmode functions. In the eigenmode function, the mode confusion problem caused by the addition of Gaussian white noise whose amplitude does not change with the frequency is overcome, and the effective diagnosis of mechanical equipment faults is realized, and the decomposition results are relatively accurate.

附图说明Description of drawings

图1是本发明的流程图。Fig. 1 is a flow chart of the present invention.

图2是幅值随频率正弦变化的噪声信号的频谱图。Figure 2 is a spectrogram of a noise signal whose amplitude varies sinusoidally with frequency.

图3（a）是仿真信号及其各个组成部分，（b）是改进前即加入高斯白噪声的总体平均经验模式分解分解结果，（c）是改进后即用幅值随频率正弦变化的噪声代替高斯白噪声的总体平均经验模式分解分解结果。Figure 3 (a) is the simulated signal and its various components, (b) is the overall average empirical mode decomposition result of adding Gaussian white noise before improvement, (c) is the noise whose amplitude changes sinusoidally with frequency after improvement Population average empirical mode decomposition decomposition results in place of white Gaussian noise.

图4（a）是实际的振动信号，（b）是实际振动信号的频谱图，（c）是改进前即加入高斯白噪声的总体平均经验模式分解对实际的振动信号的分解结果，（d）是改进后即用幅值随频率正弦变化的噪声代替高斯白噪声的总体平均经验模式分解对实际的振动信号的分解结果。Figure 4 (a) is the actual vibration signal, (b) is the spectrum diagram of the actual vibration signal, (c) is the decomposition result of the overall average empirical mode decomposition of the actual vibration signal by adding Gaussian white noise before improvement, (d ) is the decomposition result of the actual vibration signal by the overall average empirical mode decomposition of Gaussian white noise replaced by noise whose amplitude varies sinusoidally with frequency after improvement.

具体实施方式Detailed ways

下面结合附图对本发明做详细描述。The present invention will be described in detail below in conjunction with the accompanying drawings.

参照图1，总体平均经验模式分解协助噪声确定方法，包括以下步骤：Referring to Figure 1, the overall average empirical mode decomposition assisted noise determination method includes the following steps:

（2）对该频谱乘以正弦函数

该乘积表示为Y(f)＝A·X(f)，其中f_s为采样频率，函数图形如图2所示；(2) Multiply the spectrum by the sine function

This product is expressed as Y(f)=A·X(f), Where f _s is the sampling frequency, and the function graph is shown in Figure 2;

为了验证本发明的有效性，先仿真一组信号，仿真信号s由冲击信号c₁、调制信号c₂、高频谐波c₃和低频谐波c₄组成，如图3中(a)所示。对合成信号s加入幅值为0.1的高斯白噪声，每个IMF选择相同的筛选次数，总体平均次数N选为100，分解结果如图3(b)所示；另外，对合成信号加入幅值随频率正弦变化的噪声，噪声最高频率的幅值e选为0.1，每个本征模式函数选择相同的筛选次数，平均次数同样选择100次，分解结果如图3(c)。从图中可以看出，加入幅值随频率正弦变化的噪声时，能够将信号的各组成部分c₁、c₂、c₃、c₄与c₅较好的分解出来，各个模式函数没有发生频率混叠；加入高斯白噪声时，由于对仿真信号低频成分加入较大幅值噪声，低频成分分解在不同的本征模式函数中，出现模式混淆。因此发明的此方法能够避免模式混叠。In order to verify the effectiveness of the present invention, a group of signals is first simulated, and the simulated signal s is composed of the shock signal c ₁ , the modulation signal c ₂ , the high-frequency harmonic c ₃ and the low-frequency harmonic c ₄ , as shown in (a) in Fig. 3 Show. Gaussian white noise with an amplitude of 0.1 is added to the synthetic signal s, the same screening times are selected for each IMF, and the overall average number N is selected as 100, the decomposition results are shown in Figure 3(b); in addition, the amplitude For noise that varies sinusoidally with frequency, the amplitude e of the highest noise frequency is selected as 0.1, the same number of screenings is selected for each eigenmode function, and the average number of times is also selected to be 100 times. The decomposition results are shown in Figure 3(c). It can be seen from the figure that when noise whose amplitude varies sinusoidally with frequency is added, the components c ₁ , c ₂ , c ₃ , c ₄ and c ₅ of the signal can be better decomposed, and each mode function does not occur Frequency aliasing; when Gaussian white noise is added, due to the addition of large-amplitude noise to the low-frequency component of the simulation signal, the low-frequency component is decomposed into different eigenmode functions, resulting in mode confusion. The method thus invented is able to avoid mode aliasing.

同时将上述方法应用在实际数据的分析中。图4（a）为用安装在重油催化裂化机轴承外的振动速度传感器采集到的振动信号，图4（b）为其频谱图，包含三个主要频率成分，分别为f₁＝25.39Hz，f₂＝97.66Hz，f₃＝193.4Hz。f₁为齿轮箱低速轴转频，f₂为齿轮箱高速轴转频，f₃为高速轴转频的2阶谐波频率。分别用加入幅值为0.01的高斯白噪声和最高频率处幅值为0.06的幅值随频率正弦变化的噪声进行总体平均经验模式分解，在选取的筛选次数和平均次数相同的情况下，分解得到的结果分别如图4（c）与（d）所示，对比二者的分解结果，可以看出，加入幅值随频率正弦变化噪声进行总体平均经验模式分解所得结果与加入高斯白噪声分解结果比较更准确，所得到的本征模式函数具有明确的物理意义。图4（d）中，分解得到的本征模式函数c₁两个冲击之间的间隔大致为0.031s，可以计算其冲击频率

冲击频率为高速轴转频f₂的1/3倍，这样的冲击成分表征重油催化裂化机存在早期轴瓦碰摩故障。c₂代表齿轮箱高速轴的转频等于97.66Hz，c₃代表齿轮箱低速轴转频，频率为25.39Hz，而图4（c）中，c₁和c₂两个本征模式分量出现了模式混淆，它们的波形图都比较混乱，周期性差；c₃中在0.2s到0.25s之间的波形缺失，也出现了一定程度上的模式混淆。At the same time, the above method is applied to the analysis of actual data. Figure 4(a) is the vibration signal collected by the vibration velocity sensor installed outside the bearing of the heavy oil catalytic cracker, and Figure 4(b) is its frequency spectrum, which contains three main frequency components, namely f ₁ =25.39Hz, f ₂ =97.66Hz, f ₃ =193.4Hz. f ₁ is the rotational frequency of the low-speed shaft of the gearbox, f ₂ is the rotational frequency of the high-speed shaft of the gearbox, and f ₃ is the second-order harmonic frequency of the rotational frequency of the high-speed shaft. Gaussian white noise with an amplitude of 0.01 and the noise whose amplitude is 0.06 at the highest frequency that varies sinusoidally with frequency are used to decompose the overall average empirical mode. When the number of screenings and average times selected are the same, the decomposition results in The results are shown in Figure 4(c) and (d), respectively. Comparing the decomposition results of the two, it can be seen that the results obtained by adding the noise whose amplitude varies sinusoidally with frequency and performing the overall average empirical mode decomposition are the same as those obtained by adding Gaussian white noise The comparison is more accurate and the resulting eigenmode functions have a clear physical meaning. In Fig. 4(d), the interval between the two shocks of the decomposed eigenmode function c ₁ is roughly 0.031s, and its shock frequency can be calculated

The impact frequency is 1/3 times of the high-speed shaft rotation frequency f ₂ , such an impact component indicates that the heavy oil catalytic cracker has an early friction failure of the bearing bush. c ₂ represents the rotation frequency of the high-speed shaft of the gearbox is equal to 97.66Hz, c ₃ represents the rotation frequency of the low-speed shaft of the gearbox, the frequency is 25.39Hz, and in Figure 4(c), two eigenmode components of c ₁ and c ₂ appear Mode confusion, their waveforms are chaotic, and the periodicity is poor; the waveform between 0.2s and 0.25s in c ₃ is missing, and there is also a certain degree of mode confusion.

通过以上仿真信号和实际信号的分解结果对比，可以得到所发明的用幅值随频率正弦变化的噪声代替高斯白噪声的总体平均经验模式分解方法能够在一定程度上减少模式混叠，能够分解出物理意义明确的本征模式函数，能有效的提取出故障特征信息，说明构造噪声代替高斯白噪声的总体平均经验模式分解方法可以更好的实现机械设备的故障诊断。Through the comparison of the decomposition results of the above simulated signal and the actual signal, it can be obtained that the invented overall average empirical mode decomposition method that replaces Gaussian white noise with noise whose amplitude varies sinusoidally with frequency can reduce mode aliasing to a certain extent, and can decompose The eigenmode function with clear physical meaning can effectively extract the fault characteristic information, which shows that the overall average empirical mode decomposition method of constructing noise instead of Gaussian white noise can better realize the fault diagnosis of mechanical equipment.

以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明，不能认定本发明的具体实施方式仅限于此，对于本发明所属技术领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干简单的推演或替换，都应当视为属于本发明由所提交的权利要求书确定专利保护范围。The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments. It cannot be determined that the specific embodiments of the present invention are limited thereto. Under the circumstances, some simple deduction or replacement can also be made, all of which should be regarded as belonging to the scope of patent protection determined by the submitted claims of the present invention.

Claims

1. the population mean empirical mode decomposition assists noise to determine method, it is characterized in that, may further comprise the steps:

(1) white Gaussian noise of representing with randn is carried out Fast Fourier Transform (FFT), obtain its frequency spectrum, be expressed as X (f)=F (randn), wherein f represents frequency, and X (f) represents amplitude, 0＜X (f)＜0.2;

(2) this frequency spectrum be multiply by sine function

This product representation is Y (f)=AX (f),

F wherein _sBe sample frequency;

(3) Y (f) is carried out inverse fast Fourier transform, namely obtain amplitude with the time series of the noise signal of frequency sinusoidal variations, be expressed as y (t), the amplitude of structure becomes the noise signal mathematic(al) representation of sinusoidal variations to be with frequency:

y (t) = F^{- 1} [Y (f)] = F^{- 1} [A \cdot X (f)] = F^{- 1} [a \sin (\frac{π}{f_{s}} f) \cdot F (randn)];

(4) noise with structure replaces white Gaussian noise to add original signal, carries out the population mean empirical mode decomposition.