CN103076028A - Wavelet de-noising method of optical-phase vibration - Google Patents

Wavelet de-noising method of optical-phase vibration Download PDF

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CN103076028A
CN103076028A CN2013100211050A CN201310021105A CN103076028A CN 103076028 A CN103076028 A CN 103076028A CN 2013100211050 A CN2013100211050 A CN 2013100211050A CN 201310021105 A CN201310021105 A CN 201310021105A CN 103076028 A CN103076028 A CN 103076028A
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wavelet
signal
noise
coefficient
threshold
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罗广迪
司崇杰
王文伟
蒋海军
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XINJIANG MEITE INTELLIGENT SECURITY ENGINEERING Co Ltd
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XINJIANG MEITE INTELLIGENT SECURITY ENGINEERING Co Ltd
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Abstract

The invention discloses a wavelet de-noising method of optical-phase vibration. In a localized time-frequency analyzing method of which the size of a window (i.e. the area of the window) is fixed, but the shape of the window can be changed, and a time window and a frequency window can both be changed, a low-frequency part is provided with a wider time window and higher frequency resolution, and a high-frequency part is provided with a wider frequency window and higher time resolution, so that wavelet transformation has self-adaptability for signals so as to achieve the purposes of accurate de-noising and strong self-adaptability. Therefore, optical fibers can be accurately transmitted in a complicated electromagnetic environment.

Description

The Methods for Wavelet Denoising Used of light phase vibration
Technical field
The present invention relates to the signal process field, particularly, relate to a kind of Methods for Wavelet Denoising Used of light phase vibration.
Background technology
Optical fiber sensing technology is along with the development of Fibre Optical Communication Technology and light signal treatment technology develops the technology that becomes engineering application the supreme arrogance of a person with great power rapidly, because its light wave is not afraid of electromagnetic interference (EMI), easily be that various light-detecting devices receive, can carry out easily the conversion of photoelectricity or electric light, modern electronics and computing machine easy and high development are complementary.Be widely used in the fields such as buildings deformation, monitoring temperature, airport circumference, monitoring leak from oil gas pipe.Situation of change according to the physical features parameter of the light wave of being modulated by outer signals can be divided into the modulation of light wave five types of light intensity modulation, light frequency modulation, optical wavelength modulation, light phase modulation and Polarization Modulation etc.
In many light modulating methods, phase-modulation with respect to the most obvious characteristics of other modulator approaches is: utilize light phase modulation to realize that the measurement of some physical quantitys can obtain high sensitivity.What therefore, generally use at present is the phase modulation-type Fibre Optical Sensor.
Because sensor fibre usually is distributed under the complicated physical environment, (such as linked network, buried) faces wind, drenches with rain, the impact of snow, the environment such as freezing, produces environmental background noise, brought great impact for sensitivity and the degree of accuracy of Fibre Optical Sensor.
Usually signal denoising is to utilize noise to carry out in the different principle of frequency domain distribution with signal.In the existing signal antinoise method based on Fourier transform so that the band overlapping of signal and noise part is as far as possible little, like this at frequency domain by filtering, just signal and noise range are separated.The wave filter denoising is the most a kind of method of practical application, but the time caused the distortion of useful signal when being everlasting filtering noise, it is should eliminate noise in which frequency range from the angle analysis of pure frequency domain.If when signal and noise band overlapping region are very large, just can't realize the effect of denoising.
Summary of the invention
The object of the invention is to, for the problems referred to above, propose a kind of Methods for Wavelet Denoising Used of light phase vibration, to realize accurate denoising, the advantage that self-adaptation is strong.
For achieving the above object, the technical solution used in the present invention is:
A kind of Methods for Wavelet Denoising Used of light phase vibration may further comprise the steps:
A, data are made wavelet decomposition change: its concrete formula is as follows:
Wherein
Figure 2013100211050100002DEST_PATH_IMAGE002
Expression contains hot-tempered signal, can be expressed as data vector
Figure 2013100211050100002DEST_PATH_IMAGE003
,
Figure 2013100211050100002DEST_PATH_IMAGE004
,
Figure 2013100211050100002DEST_PATH_IMAGE005
,
Figure 2013100211050100002DEST_PATH_IMAGE006
It is the actual signal vector
Figure DEST_PATH_IMAGE007
,
Figure 2013100211050100002DEST_PATH_IMAGE008
,
Figure DEST_PATH_IMAGE009
,
Figure 2013100211050100002DEST_PATH_IMAGE010
It is Gaussian random vector
Figure DEST_PATH_IMAGE011
,
Figure 2013100211050100002DEST_PATH_IMAGE012
,
Figure DEST_PATH_IMAGE013
, wherein the wavelet decomposition conversion is linear transformation,
Figure 2013100211050100002DEST_PATH_IMAGE014
The expression wavelet coefficient,
Figure DEST_PATH_IMAGE015
Be noise level;
B, at wavelet frequency domain, its mould value of the wavelet coefficient that useful signal produces is larger; (white Gaussian noise is through wavelet transformation and noise has albefaction trend through wavelet transformation, still show as very strong randomness at wavelet frequency domain, think Gaussian distribution), its wavelet frequency domain coefficient of correspondence mould value is very little, and useful signal is usually expressed as more stably signal of low frequency signal or some, noise signal then is usually expressed as high-frequency signal, so we can carry out wavelet decomposition (as carrying out three layers of decomposition) to signals and associated noises first:
Figure 2013100211050100002DEST_PATH_IMAGE016
Y is noise signal, wherein
Figure DEST_PATH_IMAGE017
Be the approximate part of decomposing,
Figure 2013100211050100002DEST_PATH_IMAGE018
Be the detail section that decomposes,
Figure DEST_PATH_IMAGE019
, then noise section is generally comprised within
Figure 2013100211050100002DEST_PATH_IMAGE020
,
Figure DEST_PATH_IMAGE021
,
Figure 2013100211050100002DEST_PATH_IMAGE022
In, with threshold value wavelet coefficient is processed (less than the coefficient zero setting of threshold value), last reconstruction signal can reach the purpose of de-noising;
Select the threshold values formula to above-mentioned wavelet coefficient
Figure 636288DEST_PATH_IMAGE014
Make threshold value and process,
Threshold value is processed and can be expressed as
Figure DEST_PATH_IMAGE023
, n representation signal length is used the threshold value formula that wavelet coefficient is made threshold process when n is tending towards infinity and can be removed noise; Wherein
Figure 2013100211050100002DEST_PATH_IMAGE024
Threshold function table, desirable hard-threshold function and soft-threshold function;
C, the wavelet coefficient of above-mentioned processing is done inverse transformation
Figure DEST_PATH_IMAGE025
Reconstruction signal: the signal after the de-noising that can be eliminated; Its formula is as follows:
Figure 2013100211050100002DEST_PATH_IMAGE026
Wherein d is coefficient of dissociation vector, i.e. d=(D1, and D2 ... Dn).
Further, described hard threshold values belongs to fixedly threshold values, and the hard-threshold function expression is as follows:
Wherein t represents the time, and unit is s.
Further, described soft threshold values belongs to the variable threshold values, and the soft-threshold function expression is as follows:
Figure 2013100211050100002DEST_PATH_IMAGE028
Wherein t represents the time, and unit is s.
Further, above-mentioned threshold values formula is as follows:
Figure DEST_PATH_IMAGE029
。
Technical scheme of the present invention has following beneficial effect:
Technical scheme of the present invention, than traditional Fourier transform, that fixing but its shape of a kind of window size (being window area) can change, time window and frequency window be changeable Time-Frequency Localization analytical approach all, it has wider time window and higher frequency resolution in low frequency part, has wider frequency window and higher temporal resolution at HFS.Make wavelet transformation have adaptivity to signal.Thereby reach accurate denoising, purpose that self-adaptation is strong.The transmission that the optical fiber that makes can be prepared under the electromagnetic environment of complexity.
Below by drawings and Examples, technical scheme of the present invention is described in further detail.
Description of drawings
Fig. 1 is the process flow diagram of the Methods for Wavelet Denoising Used of the described light phase vibration of the embodiment of the invention;
Embodiment
Below in conjunction with accompanying drawing the preferred embodiments of the present invention are described, should be appreciated that preferred embodiment described herein only is used for description and interpretation the present invention, is not intended to limit the present invention.
As shown in Figure 1, a kind of Methods for Wavelet Denoising Used of light phase vibration may further comprise the steps:
A, data are made wavelet decomposition change: its concrete formula is as follows:
Figure 241844DEST_PATH_IMAGE001
Wherein
Figure 21581DEST_PATH_IMAGE002
Expression contains hot-tempered signal, can be expressed as data vector ,
Figure DEST_PATH_IMAGE031
,
Figure 2013100211050100002DEST_PATH_IMAGE032
,
Figure 541424DEST_PATH_IMAGE006
It is the actual signal vector
Figure 355796DEST_PATH_IMAGE007
,
Figure 178259DEST_PATH_IMAGE008
,
Figure DEST_PATH_IMAGE033
,
Figure 2013100211050100002DEST_PATH_IMAGE034
It is Gaussian random vector
Figure 9074DEST_PATH_IMAGE011
,
Figure DEST_PATH_IMAGE035
,
Figure 2013100211050100002DEST_PATH_IMAGE036
, wherein the wavelet decomposition conversion is linear transformation, The expression wavelet coefficient,
Figure 939170DEST_PATH_IMAGE015
Be noise level;
B, at wavelet frequency domain, its mould value of the wavelet coefficient that useful signal produces is larger; (white Gaussian noise is through wavelet transformation and noise has albefaction trend through wavelet transformation, still show as very strong randomness at wavelet frequency domain, think Gaussian distribution), its wavelet frequency domain coefficient of correspondence mould value is very little, and useful signal is usually expressed as more stably signal of low frequency signal or some, noise signal then is usually expressed as high-frequency signal, so we can carry out wavelet decomposition (as carrying out three layers of decomposition) to signals and associated noises first:
Figure 994850DEST_PATH_IMAGE016
Y is noise signal, wherein Be the approximate part of decomposing,
Figure 486192DEST_PATH_IMAGE018
Be the detail section that decomposes,
Figure 71894DEST_PATH_IMAGE019
, then noise section is generally comprised within
Figure 501738DEST_PATH_IMAGE020
,
Figure 743363DEST_PATH_IMAGE021
,
Figure 582269DEST_PATH_IMAGE022
In, with threshold value wavelet coefficient is processed (less than the coefficient zero setting of threshold value), last reconstruction signal can reach the purpose of de-noising;
Select the threshold values formula to above-mentioned wavelet coefficient
Figure 225740DEST_PATH_IMAGE014
Make threshold value and process,
Threshold value is processed and can be expressed as
Figure 560906DEST_PATH_IMAGE023
, n representation signal length is used the threshold value formula that wavelet coefficient is made threshold process when n is tending towards infinity and can be removed noise; Wherein
Figure 352145DEST_PATH_IMAGE024
Threshold function table, desirable hard-threshold function and soft-threshold function;
C, the wavelet coefficient of above-mentioned processing is done inverse transformation
Figure 430959DEST_PATH_IMAGE025
Reconstruction signal: the signal after the de-noising that can be eliminated; Its formula is as follows:
，
Wherein d is coefficient of dissociation vector, i.e. d=(D1, and D2 ... Dn).
Wherein: hard threshold values belongs to fixedly threshold values, and the hard-threshold function expression is as follows:
Figure DEST_PATH_IMAGE037
Wherein t represents the time, and unit is s.
Soft threshold values also can belong to the variable threshold values, and the soft-threshold function expression is as follows:
Figure 2013100211050100002DEST_PATH_IMAGE038
Wherein t represents the time, and unit is s.
The threshold values formula is as follows:
Figure 825217DEST_PATH_IMAGE029
。
Because it is transducing signal that vibration optical fiber adopts light, has effectively avoided electromagnetic interference (EMI), but be subject to the impact of thermonoise and environment dither, reduced the degree of accuracy of vibration optical fiber.The present invention is directed to this Noise Design based on Wavelet noise-eliminating method.We can say that above-mentioned noise regards additive noise as, are expressed as:
Figure 2013100211050100002DEST_PATH_IMAGE040
Wherein y is the Noise signal,
Figure DEST_PATH_IMAGE041
Be " pure " vibration signal,
Figure 2013100211050100002DEST_PATH_IMAGE042
Be independent identically distributed white Gaussian noise
Figure DEST_PATH_IMAGE043
,
Figure 339637DEST_PATH_IMAGE015
Be noise level, signal length is
Figure 2013100211050100002DEST_PATH_IMAGE044
. for from signals and associated noises
Figure DEST_PATH_IMAGE045
In restore actual signal
Figure 2013100211050100002DEST_PATH_IMAGE046
, can utilize signal and the different characteristic of noise under wavelet transformation, by coefficient of wavelet decomposition being processed to reach the purpose of signal and noise separation.In wavelet field, its mould value of the wavelet coefficient that useful signal produces is often larger; And noise has albefaction trend (white Gaussian noise still shows as very strong randomness through wavelet transformation in wavelet field, usually still thinks Gaussian distribution) through wavelet transformation, and its wavelet field coefficient of correspondence mould value is very little.And useful signal is usually expressed as more stably signal of low frequency signal or some, and noise signal then is usually expressed as high-frequency signal, so we can carry out wavelet decomposition (as carrying out three layers of decomposition) to signals and associated noises first:
Wherein Be the approximate part of decomposing,
Figure 2013100211050100002DEST_PATH_IMAGE048
Be the detail section that decomposes,
Figure DEST_PATH_IMAGE049
, then noise section is generally comprised within
Figure 761577DEST_PATH_IMAGE020
,
Figure 704126DEST_PATH_IMAGE021
,
Figure 705842DEST_PATH_IMAGE022
In, with threshold value wavelet coefficient is processed (less than the coefficient zero setting of threshold value), last reconstruction signal can reach the purpose of de-noising.
Suppose the additive signal that vibration signal that the light phase detector monitors arrives is comprised of pure vibration signal and independent identically distributed white Gaussian noise.Adopt wavelet transformation that the light phase vibration signal that detects is decomposed, by coefficient of wavelet decomposition being processed to reach the purpose of signal and noise separation.Adopt the mould value of coefficient of wavelet decomposition as the standard of burbling noise and actual signal.
Data are vibration signal in the technical solution of the present invention, and this vibration signal is the additive signal that is comprised of pure vibration signal and independent identically distributed white Gaussian noise.Adopt wavelet transformation that this vibration signal is decomposed, by coefficient of wavelet decomposition being processed to reach the purpose of signal and noise separation.Wherein the mould value of coefficient of wavelet decomposition is as the standard of burbling noise and actual signal.
It should be noted that at last: the above only is the preferred embodiments of the present invention, be not limited to the present invention, although with reference to previous embodiment the present invention is had been described in detail, for a person skilled in the art, it still can be made amendment to the technical scheme that aforementioned each embodiment puts down in writing, and perhaps part technical characterictic wherein is equal to replacement.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1. the Methods for Wavelet Denoising Used of a light phase vibration is characterized in that, may further comprise the steps:
A, data are made wavelet decomposition change: its concrete formula is as follows:
Figure 286862DEST_PATH_IMAGE002
Wherein
Figure 407264DEST_PATH_IMAGE004
Expression contains hot-tempered signal, can be expressed as data vector
Figure 187002DEST_PATH_IMAGE006
,
Figure 582211DEST_PATH_IMAGE008
,
Figure 396583DEST_PATH_IMAGE010
,
Figure 405996DEST_PATH_IMAGE012
It is the actual signal vector
Figure 673029DEST_PATH_IMAGE014
,
Figure 871930DEST_PATH_IMAGE016
,
Figure 540808DEST_PATH_IMAGE018
,
Figure 206276DEST_PATH_IMAGE020
It is Gaussian random vector
Figure 960605DEST_PATH_IMAGE022
, ,
Figure 221003DEST_PATH_IMAGE026
, wherein the wavelet decomposition conversion is linear transformation,
Figure 103377DEST_PATH_IMAGE028
The expression wavelet coefficient, Be noise level;
B, at wavelet frequency domain, its mould value of the wavelet coefficient that useful signal produces is larger; (white Gaussian noise is through wavelet transformation and noise has albefaction trend through wavelet transformation, still show as very strong randomness at wavelet frequency domain, think Gaussian distribution), its wavelet frequency domain coefficient of correspondence mould value is very little, and useful signal is usually expressed as more stably signal of low frequency signal or some, noise signal then is usually expressed as high-frequency signal, so we can carry out wavelet decomposition (as carrying out three layers of decomposition) to signals and associated noises first:
Y is noise signal, wherein Be the approximate part of decomposing,
Figure 598763DEST_PATH_IMAGE036
Be the detail section that decomposes, , then noise section is generally comprised within
Figure 78603DEST_PATH_IMAGE040
,
Figure 576580DEST_PATH_IMAGE042
, In, with threshold value wavelet coefficient is processed (less than the coefficient zero setting of threshold value), last reconstruction signal can reach the purpose of de-noising;
Select the threshold values formula to above-mentioned wavelet coefficient Make threshold value and process,
Threshold value is processed and can be expressed as , n representation signal length is used the threshold value formula that wavelet coefficient is made threshold process when n is tending towards infinity and can be removed noise; Wherein Threshold function table, desirable hard-threshold function and soft-threshold function;
C, the wavelet coefficient of above-mentioned processing is done inverse transformation
Figure 928933DEST_PATH_IMAGE050
Reconstruction signal: the signal after the de-noising that can be eliminated; Its formula is as follows:
Figure 304551DEST_PATH_IMAGE052
，
Wherein d is coefficient of dissociation vector, i.e. d=(D1, and D2 ... Dn).
2. the Methods for Wavelet Denoising Used of light phase vibration according to claim 1 is characterized in that, described hard threshold values belongs to fixedly threshold values, and the hard-threshold function expression is as follows:
Figure 725168DEST_PATH_IMAGE054
Wherein t represents the time, and unit is s.
3. the Methods for Wavelet Denoising Used of light phase vibration according to claim 1 is characterized in that, described soft threshold values belongs to the variable threshold values, and the soft-threshold function expression is as follows:
Figure 197738DEST_PATH_IMAGE056
Wherein t represents the time, and unit is s.
4. according to claim 1 to the Methods for Wavelet Denoising Used of 3 arbitrary described light phase vibrations, it is characterized in that, above-mentioned threshold values formula is as follows:
Figure 311187DEST_PATH_IMAGE058
。
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CN107941733A (en) * 2017-12-21 2018-04-20 苏州汉策能源设备有限公司 Super low concentration multicomponent ultraviolet spectra flue gas analysis method based on Wavelet Denoising Method
CN108446440A (en) * 2018-02-11 2018-08-24 上海理工大学 The method for improving particle temperature measurement accuracy
CN113188461A (en) * 2021-05-06 2021-07-30 山东大学 OFDR large strain measurement method under high spatial resolution
CN113432709A (en) * 2021-06-25 2021-09-24 湖南工业大学 Visualization mechanical fault diagnosis method based on graphics

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
CN107941733A (en) * 2017-12-21 2018-04-20 苏州汉策能源设备有限公司 Super low concentration multicomponent ultraviolet spectra flue gas analysis method based on Wavelet Denoising Method
CN108446440A (en) * 2018-02-11 2018-08-24 上海理工大学 The method for improving particle temperature measurement accuracy
CN113188461A (en) * 2021-05-06 2021-07-30 山东大学 OFDR large strain measurement method under high spatial resolution
CN113188461B (en) * 2021-05-06 2022-05-17 山东大学 OFDR large strain measurement method under high spatial resolution
CN113432709A (en) * 2021-06-25 2021-09-24 湖南工业大学 Visualization mechanical fault diagnosis method based on graphics
CN113432709B (en) * 2021-06-25 2023-08-08 湖南工业大学 Visual mechanical fault diagnosis method based on graphics

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