CN110207811B - Air floating plate vibration signal processing method based on empirical mode decomposition - Google Patents
Air floating plate vibration signal processing method based on empirical mode decomposition Download PDFInfo
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Abstract
The invention relates to an air floating plate vibration signal processing method based on empirical mode decomposition, which comprises the following steps: acquiring vibration acceleration data of the air floating plate; performing Fourier transformation on the acceleration data to a frequency domain for secondary integration, and performing inverse transformation to a time domain to obtain vibration displacement data; performing empirical mode decomposition to obtain a plurality of intrinsic mode components and residual errors, and screening a first intrinsic mode component as an air floating plate vibration mode component according to characteristics of the air floating plate; performing wavelet threshold denoising on the vibration modal component of the air floating plate; and performing Hilbert spectrum analysis and Hilbert marginal spectrum analysis on the noise-reduced signal. The vibration signal processing method can effectively remove noise and improve the signal-to-noise ratio.
Description
Technical Field
The invention relates to the technical field of vibration signal processing, in particular to an air floating plate vibration signal processing method based on empirical mode decomposition.
Background
In the prior art, there are three main methods for processing vibration signals: the first method is that the collected acceleration signals are amplified and filtered, then Fourier transform is carried out to extract characteristic frequency values, but time components are lost in the Fourier transform process, only frequency amplitude relation can be obtained, time frequency relation cannot be obtained, and instantaneous frequency cannot be known, so that the method is only suitable for a stable random process; the second is wavelet transform developed recently, which is to perform wavelet analysis filtering on the acquired acceleration signals, the wavelet transform can obtain the time-frequency relationship of data and can be adaptively changed according to local analysis of the signals, but due to the instability of vibration signals, the correct selection of wavelet bases is difficult, and the obtained data redundancy is very large; the third is the hilbert-yellow transform, which has no rich theoretical basis compared to the first and second methods, is purely empirical, but is most effective for processing the vibration signal in the experiment because it decomposes the signal directly according to the characteristics of the experimental data without selecting basis functions. Due to the self-adaptability, the obtained eigenmode components have practical physical significance.
However, the screening of the eigenmode component obtained by empirical mode decomposition in the hilbert-yellow transform needs to consider the actual situation, and if the noise in the eigenmode component is not reduced, the time domain result will be directly affected.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in order to overcome the defects in the prior art, the invention provides an air floating plate vibration signal processing method based on empirical mode decomposition, which is used for reducing noise by using a physical vibration mode component obtained by decomposition and improving the signal-to-noise ratio.
The technical scheme adopted by the invention for solving the technical problems is as follows: an air floating plate vibration signal processing method based on empirical mode decomposition comprises the following steps:
a. adhering a sensor to the central position of an air floating plate by using a double-sided adhesive tape, carrying out acceleration calibration at a computer end in a static state, opening a fan, blowing wind in the fan to the air floating plate through a pipeline and a pore plate, enabling the air floating plate to be in an up-and-down floating state, and recording data after the air floating plate is stabilized;
b. processing the vibration signal, and converting the obtained time domain acceleration signal into a time domain displacement signal;
c. performing empirical mode decomposition on the time domain displacement value to obtain a plurality of intrinsic mode components and residual values, and screening vibration mode components of the air outlet floating plate according to the characteristics of the air floating plate;
d. performing wavelet global threshold denoising on the vibration modal component of the air floating plate to obtain a wavelet global threshold denoised result;
e. performing Hilbert transform on the wavelet global threshold denoising result, and then calculating instantaneous frequency to obtain a denoised time-frequency graph;
f. and performing Hilbert marginal spectrum transformation on the denoising result of the wavelet global threshold to obtain a denoising marginal spectrogram.
Preferably, in step a, the sensor is a BWT901CL wireless acceleration sensor, the sensor is attached horizontally, and the double-sided adhesive tape is a hot-melt pressure-sensitive adhesive double-sided adhesive tape.
Specifically, in the step b, the conversion process of converting the time domain acceleration signal into the time domain displacement signal is as follows: and carrying out Fourier transformation on the time domain acceleration signal, carrying out secondary integration in a frequency domain, and carrying out inverse Fourier transformation to obtain a time domain displacement value.
In the step c, the mode of screening the vibration mode of the air floating plate is as follows: and screening the first intrinsic mode component as the vibration mode component of the air floating plate according to the characteristic that the air floating plate is in a suspension state and has no other mechanical vibration interference.
In step d, the specific process of wavelet threshold denoising is as follows: carrying out multi-layer wavelet decomposition on the vibration mode components of the air floating plate, wherein each layer of wavelet decomposition is to decompose the low-frequency components obtained by the previous layer of decomposition into a low-frequency part and a high-frequency part to obtain high-frequency component detail coefficients Dn obtained by the decomposition of each layer; setting a threshold value d, if the detail coefficient Dn of the high-frequency component is greater than d, considering the result of the signal, and keeping the result; if wavelet coefficient DnIf the value is less than d, the value is considered to be caused by noise, and the value is set to zero; and reconstructing the time domain signal.
Further, the value of the threshold in step d is a default threshold:
where σ is the standard deviation of the signal amplitude and N is the sample length.
In step e, the specific process of calculating the instantaneous frequency is as follows: after Hilbert transformation is performed in matlab software, an angle function is used for calculating an instantaneous phase, and the instantaneous phase is differentiated to obtain instantaneous frequency.
In step f, the specific process of the Hilbert marginal spectrum is as follows: and taking the imaginary part after the Hilbert transformation as a frequency domain value after the transformation, and performing cumulative sum on the amplitude of each frequency point to obtain a Hilbert marginal spectrum.
The invention has the beneficial effects that: according to the invention, through screening and wavelet threshold denoising of the physical vibration modal components obtained based on empirical mode decomposition, the influence of noise is effectively removed, a vibration signal which is as real and effective as possible is obtained, and the signal-to-noise ratio is improved.
Drawings
The invention is further illustrated with reference to the following figures and examples.
Fig. 1 is a schematic diagram showing comparison between actually measured acceleration data and processed displacement data.
Fig. 2 is a schematic diagram of seven distributions of intrinsic mode components and residual values obtained by empirical mode decomposition.
Fig. 3 is a schematic diagram of a wavelet three-layer decomposition structure.
Fig. 4 is a schematic diagram of three-layer decomposition approximation, one-layer decomposition detail, two-layer decomposition detail and three-layer decomposition detail obtained by wavelet three-layer decomposition.
FIG. 5 is a time domain contrast diagram before and after wavelet global threshold denoising.
FIG. 6 is a time-frequency contrast diagram obtained by performing Hilbert transform before and after denoising of a wavelet global threshold.
FIG. 7 is a comparison graph of marginal spectra obtained by performing Hilbert transform marginal spectrum transform before and after denoising of a wavelet global threshold.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
As shown in fig. 1 to 7, a method for processing an air floating plate vibration signal based on empirical mode decomposition includes the following steps:
a. a wireless acceleration sensor with the model of BWT901CL is horizontally pasted at the center of an air floating plate by using a hot melt pressure sensitive adhesive double-sided tape, acceleration calibration is carried out at a computer end in a static state, a fan is turned on, wind in the fan blows to the air floating plate through a pipeline and a pore plate, the air floating plate is in an up-and-down floating state, data are recorded after the air floating plate is stabilized, the sampling frequency is 200hz, and the sampling time is 40 s.
b. Actually measuring to obtain an acceleration signal of the air bearing plate, theoretically, performing secondary integration on the acceleration signal in a time domain can obtain displacement, but actually, the method belongs to the category of indefinite integration, placing the acceleration signal in a frequency domain can be simple and more accurate, performing secondary integration in the frequency domain, and performing inverse Fourier transform to obtain a time domain displacement value.
c. Performing empirical mode decomposition on the obtained displacement signal, firstly finding a maximum value point and a minimum value point of the displacement signal X (t), and forming an upper envelope line and a lower envelope line by using a cubic spline function, wherein the average value of the envelope lines is a, and h1 is X-a; because of the non-stationarity of the vibration signal, h1 is still non-linear at this time, the cubic spline function is continuously carried out on h1 to carry out upper and lower envelopes, the average value of the envelope curve is obtained as b, h2 is h1-b,
the above steps are repeated until the highest frequency eigenmode component imf1 is obtained, which satisfies the following two conditions: (1) the number of extreme points and zero-crossing points of the signal are equal or at most one phase difference
(2) The mean value b of the envelope is 0
Subtracting the intrinsic mode component r1 from the original displacement signal, X-imf1, and continuing the above steps until 7 intrinsic mode components from high frequency to low frequency and a residual function are obtained, wherein each intrinsic mode component represents an actual physical vibration mode:
d. on the basis of the step c, because the air floating plate floats up and down without the particularity of physical contact and has no interference of machine vibration, the eigenmode component imf1 of the first highest frequency is screened as the vibration mode component of the air floating plate.
e. The first intrinsic mode component, namely the vibration mode component of the air flotation plate, is subjected to multi-layer wavelet decomposition, the problems of data redundancy and serious signal loss are caused by too many decomposition layers, and noise elimination is not ideal when too few layers are decomposed, so three-layer wavelet decomposition is selected in the example, the basic wavelet base is db1 wavelet, and each layer of wavelet decomposition is that the low-frequency component obtained by the previous layer of decomposition is decomposed into a low-frequency part and a high-frequency part. High-frequency component reconstruction details D1, D2 and D3 and low-frequency component reconstruction approximations A1, A2 and A3 are obtained by decomposition, A3 which is an approximation coefficient reconstruction signal obtained by the third layer of decomposition is directly selected for rough denoising, and wavelet global threshold denoising is needed for further accurate filtering. Because the boundary of the high-frequency component and the low-frequency component obtained by wavelet decomposition is obvious, the basic idea of global threshold denoising is as follows: setting a threshold value D, and if the reconstruction details of the high-frequency components D1, D2 and D3 are greater than D, considering that the signal is caused and keeping; if the reconstruction details of the high frequency component are less than d, the high frequency component is considered to be caused by noise and is set to zero. And then reconstructing the signal through inverse wavelet transform to obtain a denoised signal. In this example, the threshold is selected from a wavelet decomposition default threshold of 0.0025.
f. And performing Hilbert transform on the signal subjected to wavelet global threshold denoising, calculating an instantaneous phase, and differentiating the instantaneous phase to obtain an instantaneous frequency, namely an instantaneous frequency relation.
g. And performing Hilbert marginal spectrum transformation on the signal subjected to wavelet global threshold denoising, taking an imaginary part subjected to Hilbert transformation as a frequency domain value after transformation, and accumulating the amplitude of each sampling point to obtain a Hilbert marginal spectrum.
As shown in fig. 1, a comparison graph of the acceleration data of the vibration signal obtained by actual measurement and the displacement data after processing is obtained at the same time.
As shown in fig. 2, the first eigenmode component is selected as the vibration mode of the air floating plate due to the suspension characteristic of the air floating plate, and seven eigenmode components and residual values obtained by empirical mode decomposition.
As shown in fig. 3, the wavelet tri-layer decomposition yields high frequency component reconstruction details D1, D2, D3 and low frequency component reconstruction approximations a1, a2, A3.
As shown in fig. 4, three-layer decomposition approximation A3, one-layer decomposition detail D1, two-layer decomposition detail D2 and three-layer decomposition detail D3 are obtained by wavelet three-layer decomposition, and coarse denoising directly selects three-layer decomposition approximation A3, and for further precise filtering, wavelet global threshold denoising needs to be performed by using D1, D2 and D3.
As shown in FIG. 5, the time domain comparison of the vibration mode components of the air floating plate before and after denoising results in a smoother curve after denoising.
As shown in fig. 6, the time-frequency contrast of the vibration mode components of the air bearing plate before and after denoising is performed.
As shown in fig. 7, the hubert marginal spectrum of the vibration mode component of the air bearing plate before and after denoising is compared, the amplitude at the peak frequency is kept unchanged, and the amplitude accumulation caused by noise is filtered.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (8)
1. An air floating plate vibration signal processing method based on empirical mode decomposition is characterized by comprising the following steps: comprises the following steps:
a. adhering a sensor to the central position of an air floating plate by using a double-sided adhesive tape, carrying out acceleration calibration at a computer end in a static state, opening a fan, blowing wind in the fan to the air floating plate through a pipeline and a pore plate, enabling the air floating plate to be in an up-and-down floating state, and recording data after the air floating plate is stabilized;
b. processing the vibration signal, and converting the obtained time domain acceleration signal into a time domain displacement signal;
c. performing empirical mode decomposition on the time domain displacement value to obtain a plurality of intrinsic mode components and residual values, and screening vibration mode components of the air outlet floating plate according to the characteristics of the air floating plate;
d. performing wavelet global threshold denoising on the vibration modal component of the air floating plate to obtain a wavelet global threshold denoised result;
e. performing Hilbert transform on the wavelet global threshold denoising result, and then calculating instantaneous frequency to obtain a denoised time-frequency graph;
f. and performing Hilbert marginal spectrum transformation on the denoising result of the wavelet global threshold to obtain a denoising marginal spectrogram.
2. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in the step a, the sensor is a BWT901CL wireless acceleration sensor, the sensor is horizontally adhered, and the double-sided adhesive tape is a hot-melt pressure-sensitive adhesive double-sided adhesive tape.
3. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in step b, the conversion process of converting the time domain acceleration signal into the time domain displacement signal is as follows: and carrying out Fourier transformation on the time domain acceleration signal, carrying out secondary integration in a frequency domain, and carrying out inverse Fourier transformation to obtain a time domain displacement value.
4. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in the step c, the mode of screening the vibration modal components of the air floating plate is as follows: and screening the first intrinsic mode component as the vibration mode component of the air floating plate according to the characteristic that the air floating plate is in a suspension state and has no other mechanical vibration interference.
5. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in step d, the specific process of the wavelet global threshold denoising is as follows: carrying out multi-layer wavelet decomposition on the vibration mode components of the air floating plate, wherein each layer of wavelet decomposition is to decompose the low-frequency components obtained by the previous layer of decomposition into a low-frequency part and a high-frequency part to obtain high-frequency component detail coefficients Dn obtained by the decomposition of each layer; setting a threshold value d, if the detail coefficient Dn of the high-frequency component is greater than d, considering the result of the signal, and keeping the result; if the detail coefficient Dn of the high-frequency component is less than d, the detail coefficient Dn is considered to be caused by noise, and the detail coefficient Dn is set to zero; and reconstructing the time domain signal.
6. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 5, wherein: the value of the threshold in the step d is a default threshold:
where σ is the standard deviation of the signal amplitude and N is the sample length.
7. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in step e, the specific process of calculating the instantaneous frequency is as follows: after Hilbert transformation is performed in matlab software, an angle function is used for calculating an instantaneous phase, and the instantaneous phase is differentiated to obtain instantaneous frequency.
8. The method for processing the vibration signal of the air floating plate based on Empirical Mode Decomposition (EMD) as claimed in claim 1, wherein: in step f, the specific process of the Hilbert marginal spectrum is as follows: and taking the imaginary part after the Hilbert transformation as a frequency domain value after the transformation, and performing cumulative sum on the amplitude of each frequency point to obtain a Hilbert marginal spectrum.
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| CN101769787A (en) * | 2010-01-29 | 2010-07-07 | 浙江大学 | Method for monitoring fault of iron core looseness of power transformer |
| CN102252748A (en) * | 2011-04-08 | 2011-11-23 | 东南大学 | Cavitation noise modulation feature extraction method based on empirical mode |
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