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

Abstract

The invention discloses a noise determination method disintegrated and assisted by the ensemble average empirical mode. Fast Fourier transform is performed on the white Gaussian noise expressed by randn to acquire the frequency spectrum, the frequency spectrum is multiplied by sine function, the product is expressed asY(f) =A*X(f), fast Fourier transform is performed onY(f), a time series of a noise signal that amplitude is of sinusoidal variation with frequency is acquired, the constructed noise replaces the white Gaussian noise and is added to the original signal for disintegration of the ensemble average empirical mode. According to the invention, the problem of pattern mix caused by adding of the white Gaussian noise, of which the amplitude does not change with frequency, is solved, the effective diagnosis of failures of mechanical equipment is realized, and the analyzing result is relatively correct.

Description

The population mean empirical mode decomposition assists noise to determine method

Technical field

The present invention relates to the mechanical fault diagnosis field, be specifically related to the population mean empirical mode decomposition and assist noise to determine method.

Background technology

Human living standard's raising be unable to do without the development of industrial technology, and the industrial technology level has become one of important indicator of weighing a national comprehensive strength.Mechanical industry have the title of " heart of industry ", and it provides production basis for other economic departments, and all plant equipment are carriers of industrial development, for industrial development provides gordian technique, are bringing into play more and more important effect in industrial development.Simultaneously, also more and more towards maximization, complicated, precise treatment development, the function of equipment is more and more for electromechanical equipment, and structural principle becomes increasingly complex, and performance index are more and more higher, will certainly make the probability that breaks down increase greatly like this.

Because the electromechanical equipment operating mode is complicated and changeable, the mechanical fault feature also becomes increasingly complex, and the fault signature of equipment is non-stationary, nonlinear often.But traditional Trouble Diagnostic Method of Machinery Equipment often only is applicable to stationary signal, and is very poor to non-stationary, nonlinear properties diagnosis effect.Empirical mode decomposition EMD is at non-linear, non-stationary signal and a kind of signal processing method that proposes, it is based on a kind of decomposition method of signal Local Extremum: simulate lower envelope with cubic spline function according to the Local Extremum of signal, ask for the average of lower envelope, again signal is deducted the average of asking for, repeating above-mentioned steps, is the eigenmodes function up to the function that screens; Deduct the eigenmodes function that screens again and continue screening from signal, Cycle Screening like this is less than 3 up to the extreme point number of signal.In empirical mode decomposition, there is the problem of pattern aliasing.Obscure deficiency at empirical mode decomposition EMD pattern, proposed the population mean empirical mode decomposition, this method adds white Gaussian noise to signal, and the extreme point that improves signal distributes, and effectively minimizing pattern is obscured problem.White Gaussian noise has the even distribution character of frequency, and amplitude all equates in whole frequency range, just the high frequency of original signal and low frequency component is all added the noise of identical amplitude size.But, when the noise amplitude that adds is big, its undulatory property is bigger, though the decomposition result to high fdrequency component is better, but because the band center close together of adjacent low frequency eigenmodes function, the noise that undulatory property is big makes the single low frequency mode in the signal decompose in adjacent a plurality of eigenmodes functions easily, pattern occurs and obscures; When the noise amplitude that adds hour, its undulatory property is less, though can avoid the problems referred to above, but because the frequency band of high frequency eigenmodes function is wideer, little noise to the high fdrequency component in the signal " pulling ability " a little less than, cause a plurality of high frequency modes in the signal to decompose in same eigenmodes function, can occur pattern equally and obscure.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, the object of the present invention is to provide the population mean empirical mode decomposition to assist noise to determine method, the pattern that can overcome existing method appearance is obscured problem, obtains the eigenmodes function of explicit physical meaning, effectively realizes the diagnosis of mechanical equipment fault.

In order to achieve the above object, the technical scheme taked of the present invention is:

The population mean empirical mode decomposition assists noise to determine method, 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\left(t\right)=F^{-1}\[Y\left(f\right)\]=F^{-1}\[A\·X\left(f\right)\]=F^{-1}\[a\sin \left(\frac{\mathrm{\π}}{f_s}f\right)\·F\left(\mathrm{randn}\right)\];$

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

Core of the present invention is that the original signal radio-frequency component is added the big noise of amplitude, avoids the function branch of different mode in an eigenmodes function; Low-frequency component adds the less noise of amplitude, avoid a mode component is decomposed in the different eigenmodes functions, overcome owing to add amplitude and do not obscured problem with the pattern that the white Gaussian noise of frequency change brings, realize the efficient diagnosis of mechanical equipment fault, decomposition result is relatively accurate.

Description of drawings

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is that amplitude is with the spectrogram of the noise signal of frequency sinusoidal variations.

Fig. 3 (a) is simulate signal and each ingredient thereof, (b) being the population mean empirical mode decomposition decomposition result that namely adds white Gaussian noise before improving, (c) is the population mean empirical mode decomposition decomposition result that namely replaces white Gaussian noise after improving with amplitude with the noise of frequency sinusoidal variations.

Fig. 4 (a) is actual vibration signal, (b) be the spectrogram of actual vibration signal, (c) being namely to add the population mean empirical mode decomposition of white Gaussian noise to the decomposition result of the vibration signal of reality before improving, (d) is namely to use amplitude to replace the population mean empirical mode decomposition of white Gaussian noise to the decomposition result of the vibration signal of reality with the noise of frequency sinusoidal variations after improving.

Embodiment

Below in conjunction with accompanying drawing the present invention is described in detail.

With reference to Fig. 1, the population mean empirical mode decomposition assists noise to determine method, 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, functional digraph as shown in Figure 2;

(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\left(t\right)=F^{-1}\[Y\left(f\right)\]=F^{-1}\[A\·X\left(f\right)\]=F^{-1}\[a\sin \left(\frac{\mathrm{\π}}{f_s}f\right)\·F\left(\mathrm{randn}\right)\];$

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

In order to verify validity of the present invention, one group of signal of first emulation, simulate signal s is by impact signal c ₁, modulation signal c ₂, high-frequency harmonic c ₃With low-frequency harmonics c ₄Form, shown in (a) among Fig. 3.It is 0.1 white Gaussian noise that composite signal s is added amplitude, and each IMF selects identical screening number of times, and the population mean times N elects 100 as, and decomposition result is shown in Fig. 3 (b); In addition, composite signal is added amplitude with the noise of frequency sinusoidal variations, the amplitude e of noise highest frequency elects 0.1 as, and each eigenmodes function is selected identical screening number of times, and average time is selected 100 times equally, decomposition result such as Fig. 3 (c).As can be seen from the figure, when adding amplitude with the noise of frequency sinusoidal variations, can be with each ingredient c of signal ₁, c ₂, c ₃, c ₄With c ₅Decompose to come out preferably, each mode function does not have the occurrence frequency aliasing; When adding white Gaussian noise, because the simulate signal low-frequency component is added big amplitude noise, low-frequency component decomposes in different eigenmodes functions, pattern occurs and obscures.Therefore the method for invention can be avoided the pattern aliasing.

Said method is applied in the analysis of real data simultaneously.The vibration signal of Fig. 4 (a) for collecting with the vibrating speed sensors that is installed in outside the RFCC machine bearing, Fig. 4 (b) is its spectrogram, comprises three main frequency compositions, is respectively f ₁=25.39Hz, f ₂=97.66Hz, f ₃=193.4Hz.f ₁For the gear case slow-speed shaft changes frequently, f ₂For the gearbox high-speed axle changes frequently, f ₃For high speed shaft changes 2 order harmonic frequency frequently.Be that to be 0.06 amplitude carry out the population mean empirical mode decomposition with the noise of frequency sinusoidal variations for 0.01 white Gaussian noise and highest frequency place amplitude with the adding amplitude respectively, under the screening number of times of the choosing situation identical with average time, the result that decomposition obtains is respectively as Fig. 4 (c) and (d), contrast the decomposition result of the two, as can be seen, the adding amplitude carries out population mean empirical mode decomposition gained result with frequency sinusoidal variations noise and adding white Gaussian noise decomposition result is more accurate, and resulting eigenmodes function has clear physical meaning.Among Fig. 4 (d), decompose the eigenmodes function c that obtains ₁Interval between two impacts is roughly 0.031s, can calculate its frequency of impact

Frequency of impact is that high speed shaft changes f frequently ₂1/3 times, such impact composition characterizes the RFCC machine and exists early stage bearing shell to bump the fault of rubbing.c ₂The commentaries on classics that represents the gearbox high-speed axle equals 97.66Hz, c frequently ₃Representing the gear case slow-speed shaft changes frequently, and frequency is 25.39Hz, and among Fig. 4 (c), c ₁And c ₂Pattern has appearred in two eigenmodes components to be obscured, and their oscillogram all compares chaotic, periodically poor; c ₃In at 0.2s to the waveform between 0.25s disappearance, pattern to a certain extent also occurred and obscured.

Decomposition result contrast by above simulate signal and actual signal, the usefulness amplitude that can obtain inventing replaces the population mean empirical mode decomposition method of white Gaussian noise can reduce the pattern aliasing to a certain extent with the noise of frequency sinusoidal variations, can decomposite the eigenmodes function of explicit physical meaning, can effectively extract fault characteristic information, illustrate that the structure noise replaces the population mean empirical mode decomposition method of white Gaussian noise can better realize the fault diagnosis of plant equipment.

Above content is to further describing that the present invention does in conjunction with concrete preferred implementation; can not assert that the specific embodiment of the present invention only limits to this; for the general technical staff of the technical field of the invention; without departing from the inventive concept of the premise; can also make some simple deduction or replace, all should be considered as belonging to the present invention and determine scope of patent protection by claims of submitting to.

Claims (1)

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\left(t\right)=F^{-1}\[Y\left(f\right)\]=F^{-1}\[A\·X\left(f\right)\]=F^{-1}\[a\sin \left(\frac{\mathrm{\π}}{f_s}f\right)\·F\left(\mathrm{randn}\right)\];$

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

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