CN103336895B - Population mean empirical mode decomposition is assisted noise determining method - Google Patents

Abstract

Population mean empirical mode decomposition is assisted noise determining method, and the white Gaussian noise representing with randn is carried out to Fast Fourier Transform (FFT), obtains its frequency spectrum, and this frequency spectrum is multiplied by SIN functionThis product representation is Y (f)=AX (f), Y (f) is carried out to inverse fast Fourier transform, obtain the time series of amplitude with the noise signal of frequency sinusoidal variations, with structure noise replace white Gaussian noise add primary signal, carry out population mean empirical mode decomposition, the present invention has overcome because the pattern that adds amplitude not bring with the white Gaussian noise of change of frequency is obscured problem, realize the efficient diagnosis of mechanical equipment fault, decomposition result is relatively accurate.

Description

Population mean empirical mode decomposition is assisted noise determining method

Technical field

The present invention relates to mechanical fault diagnosis field, be specifically related to population mean empirical mode decomposition and assistNoise determining method.

Background technology

Human living standard's raising be unable to do without the development of industrial technology, and industrial technology level has become weighing apparatusOne of important indicator of a national comprehensive strength of amount. Mechanical industry have the title of " heart of industry ",It provides production basis for other economic departments, and all plant equipment are carriers of industrial development, are industryDevelopment provides key technology, is bringing into play more and more important effect in industrial development. Meanwhile, electromechanics is establishedStandby also more and more towards maximization, complicated, precise treatment development, the function of equipment is more and more, structurePrinciple becomes increasingly complex, and performance indications are more and more higher, will certainly make like this probability that breaks down greatlyIncrease.

Because electromechanical equipment operating mode is complicated and changeable, mechanical breakdown feature also becomes increasingly complex, the event of equipmentBarrier feature non-stationary, nonlinear often. But traditional Trouble Diagnostic Method of Machinery Equipment is often only suitableFor stationary signal, very poor to non-stationary, nonlinear properties diagnosis effect. Empirical mode decomposition EMDBe for non-linear, non-stationary signal and a kind of signal processing method proposing, it is based on signal partA kind of decomposition method of extreme point: simulate up and down according to the Local Extremum of signal with cubic spline functionEnvelope, asks for the average of lower envelope, then signal is deducted to asked for average, repeats above-mentioned steps,Until the function screening is intrinsic mode function; From signal, deduct again the eigen mode screeningFunction continues screening, and so Cycle Screening, until the extreme point number of signal is less than 3. In empirical modeIn decomposition, there is the problem of mode mixing. Obscure deficiency for empirical mode decomposition EMD pattern, carryGone out population mean empirical mode decomposition, the method adds white Gaussian noise to signal, improves the utmost point of signalValue point distributes, and effectively minimizing pattern is obscured problem. White Gaussian noise has frequency and is uniformly distributed characteristic,In whole frequency range, amplitude all equates, namely the High-frequency and low-frequency component of primary signal is all addedThe noise of identical amplitude size. But in the time that the noise amplitude adding is larger, its fluctuation is larger, thoughSo better to the decomposition result of high fdrequency component, but due to the band center distance of adjacent low frequency intrinsic mode functionClose to, the noise that fluctuation is large easily makes the single low frequency mode in signal decompose adjacent multipleLevy in mode function, occur that pattern obscures; When the noise amplitude adding hour, its fluctuation is less,Although can avoid the problems referred to above, because wider, the little noise pair of frequency band of high frequency intrinsic mode functionHigh fdrequency component in signal " pull ability " a little less than, cause multiple high frequency modes in signal decompose withIn an intrinsic mode function, there will be equally pattern to 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 population mean Empirical ModeFormula is decomposed assistance noise determining method, and the pattern that can overcome existing method appearance is obscured problem, obtains thingManage univocal intrinsic mode function, effectively realize the diagnosis of mechanical equipment fault.

In order to achieve the above object, the technical scheme that the present invention takes is:

Population mean empirical mode decomposition is assisted noise determining method, comprises the following steps:

(1) white Gaussian noise representing with randn is carried out to Fast Fourier Transform (FFT), obtains 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 is multiplied by SIN functionThis product representation is Y (f)=AX (f),Wherein f_sFor sample frequency;

(3) Y (f) is carried out to inverse fast Fourier transform, obtain the noise of amplitude with frequency sinusoidal variationsThe time series of signal, is expressed as y (t), and the amplitude of structure becomes the noise signal number of sinusoidal variations with frequencyExpression formula is:

$y\left(t\right)=F^{-1}\&lsqb;Y\left(f\right)\&rsqb;=F^{-1}\&lsqb;A\&CenterDot;X\left(f\right)\&rsqb;=F^{-1}\&lsqb;sin\left(\frac{\mathrm{\&pi;}}{f_s}f\right)\&CenterDot;F\left(randn\right)\&rsqb;;$

(4) replace white Gaussian noise to add primary signal with the noise of structure, carry out population mean Empirical ModeFormula is decomposed.

Core of the present invention is that primary signal radio-frequency component is added to the larger noise of amplitude, avoids different modeFunction divide in an intrinsic mode function; Low-frequency component adds the less noise of amplitude, avoids oneMode component decomposes in different intrinsic mode functions, has overcome owing to adding amplitude not with change of frequencyWhite Gaussian noise and the pattern brought is obscured problem, realize the efficient diagnosis of mechanical equipment fault, decomposeResult is relatively accurate.

Brief description of the drawings

Fig. 1 is flow chart of the present invention.

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

Fig. 3 (a) is simulate signal and each part thereof, is (b) to add Gauss's white noise before improvingThe population mean empirical mode decomposition decomposition result of sound is (c) to become with frequency is sinusoidal by amplitude after improvingThe noise of changing replaces the population mean empirical mode decomposition decomposition result of white Gaussian noise.

Fig. 4 (a) is actual vibration signal, is (b) spectrogram of actual vibration signal, is (c) to changeBefore entering, add the population mean empirical mode decomposition of white Gaussian noise to unhitching dividing of actual vibration signalReally, (d) be the overall flat that replaces white Gaussian noise after improving by amplitude with the noise of frequency sinusoidal variationsThe all decomposition result of empirical mode decomposition to actual vibration signal.

Detailed description of the invention

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

With reference to Fig. 1, population mean empirical mode decomposition is assisted noise determining method, comprises the following steps:

(1) white Gaussian noise representing with randn is carried out to Fast Fourier Transform (FFT), obtains 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 is multiplied by SIN functionThis product representation is Y (f)=AX (f),Wherein f_sFor sample frequency, functional digraph as shown in Figure 2;

(3) Y (f) is carried out to inverse fast Fourier transform, obtain the noise of amplitude with frequency sinusoidal variationsThe time series of signal, is expressed as y (t), and the amplitude of structure becomes the noise signal number of sinusoidal variations with frequencyExpression formula is:

$y\left(t\right)=F^{-1}\&lsqb;Y\left(f\right)\&rsqb;=F^{-1}\&lsqb;A\&CenterDot;X\left(f\right)\&rsqb;=F^{-1}\&lsqb;sin\left(\frac{\mathrm{\&pi;}}{f_s}f\right)\&CenterDot;F\left(randn\right)\&rsqb;;$

(4) replace white Gaussian noise to add primary signal with the noise of structure, carry out population mean Empirical ModeFormula is decomposed.

In order to verify validity of the present invention, one group of signal of first emulation, simulate signal s is by impact signal c₁、Modulation signal c₂, high-frequency harmonic c₃With low-frequency harmonics c₄Composition, as shown in (a) in Fig. 3. To composite signal sAdding amplitude is 0.1 white Gaussian noise, and each IMF selects identical screening number of times, population meanNumber N elects 100 as, and decomposition result is as shown in Fig. 3 (b); In addition, add amplitude with frequency to composite signalThe noise of sinusoidal variations, the amplitude e of noise highest frequency elects 0.1 as, and each intrinsic mode function is selected phaseSame screening number of times, average time is selected 100 times equally, and decomposition result is as Fig. 3 (c). Can from figureFind out, while adding amplitude with the noise of frequency sinusoidal variations, can be by each part c of signal₁、c₂、c₃、c₄With c₅Decompose out preferably, each mode function does not have occurrence frequency aliasing; Add white GaussianWhen noise, due to simulate signal low-frequency component is added compared with amplitude noise, low-frequency component decomposes in differenceIntrinsic mode function in, occur that pattern obscures. Therefore the method for invention can be avoided mode mixing.

Said method is applied in the analysis of real data simultaneously. Fig. 4 (a) is for to urge with being arranged on heavy oilChange the vibration signal that the vibrating speed sensors outside cracking machine bearing collects, Fig. 4 (b) is its spectrogram,Comprise three main frequency compositions, be respectively f₁＝25.39Hz，f₂＝97.66Hz，f₃＝193.4Hz。f₁ForGear-box slow-speed shaft turns frequently, f₂For high speed shaft of gearbox turns frequently, f₃For high speed shaft turns 2 order harmonicses frequencies frequentlyRate. Respectively with to add amplitude be 0.01 white Gaussian noise and the highest frequency place amplitude amplitude that is 0.06 withThe noise of frequency sinusoidal variations carries out population mean empirical mode decomposition, at the screening number of times of choosing and averageIn the identical situation of number of times, decompose the result that obtains respectively as Fig. 4 (c) with (d) as shown in, contrast twoPerson's decomposition result, can find out, adds amplitude to carry out population mean experience with frequency sinusoidal variations noiseMode Decomposition acquired results with add white Gaussian noise decomposition result more accurate, the eigen mode obtainingFormula function has clear and definite physical significance. In Fig. 4 (d), decompose the intrinsic mode function c obtaining₁TwoInterval between impact is roughly 0.031s, can calculate its frequency of impactImpactFrequency is that high speed shaft turns f frequently₂1/3 times, such impact composition characterizes RFCC machine and exists earlyPhase bearing shell touches the fault of rubbing. c₂Represent that turning of high speed shaft of gearbox equals 97.66Hz, c frequently₃Represent that gear-box is lowSpeed axle turns frequently, and frequency is 25.39Hz, and in Fig. 4 (c), c₁And c₂Two eigen mode components have occurredPattern is obscured, and their oscillogram is all more chaotic, periodically poor; c₃In at 0.2s between 0.25sWaveform disappearance, also occurred that pattern to a certain extent obscures.

By the decomposition result contrast of above simulate signal and actual signal, can obtain the invented width of usingValue can with the population mean empirical mode decomposition method of the noise replacement white Gaussian noise of frequency sinusoidal variationsReduce to a certain extent mode mixing, can decomposite the intrinsic mode function of explicit physical meaning, energyEffectively extract fault characteristic information, illustrate that structure noise replaces the population mean experience of white Gaussian noiseMode Decomposition method can better realize the fault diagnosis of plant equipment.

Above content is in conjunction with concrete preferred embodiment further description made for the present invention,Can not assert that the specific embodiment of the present invention only limits to this, common for the technical field of the inventionTechnical staff, without departing from the inventive concept of the premise, can also make some simple deductionsOr replace, all should be considered as belonging to the present invention and determine scope of patent protection by submitted to claims.

Claims (1)

1. the population mean empirical mode decomposition in mechanical fault diagnosis is assisted a noise determining method, itsBe characterised in that, comprise the following steps:

(1) white Gaussian noise representing with randn is carried out to Fast Fourier Transform (FFT), obtains 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 is multiplied by SIN functionThis product representation is Y (f)=AX (f),Wherein f_sFor sample frequency;

(3) Y (f) is carried out to inverse fast Fourier transform, obtain the noise of amplitude with frequency sinusoidal variationsThe time series of signal, is expressed as y (t), and the amplitude of structure becomes the noise signal number of sinusoidal variations with frequencyExpression formula is:

$y\left(t\right)=F^{-1}\&lsqb;Y\left(f\right)\&rsqb;=F^{-1}\&lsqb;A\&CenterDot;X\left(f\right)\&rsqb;=F^{-1}\&lsqb;sin\left(\frac{\mathrm{\&pi;}}{f_s}f\right)\&CenterDot;F\left(randn\right)\&rsqb;;$

(4) replace white Gaussian noise to add primary signal with the noise of structure, carry out population mean Empirical ModeFormula is decomposed.