CN102393423A - Lamb wave denoising method based on adaptive threshold value orthogonal wavelet transform - Google Patents
Lamb wave denoising method based on adaptive threshold value orthogonal wavelet transform Download PDFInfo
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Abstract
The invention provides a Lamb wave denoising method based on adaptive threshold value orthogonal wavelet transform. In the method, ultrasonic Lamb wave signals are subjected to orthogonal wavelet transform for energy normalization processing to reduce the autocorrelation of the signals, and the ultrasonic Lamb waves are subjected to denoising treatment by an adaptive threshold value method. The method comprises the following steps of: unfolding a noise-containing Lamb wave signal x(t) under a wavelet basis, and performing x(t) orthogonal wavelet transform to obtain an orthogonal wavelet transform coefficient of the x(t); selecting a threshold value and a threshold function, and performing threshold value quantization treatment on the orthogonal wavelet transform coefficient of the x(t) to obtain an orthogonal wavelet transform coefficient subjected to threshold value quantization; and reconstructing the orthogonal wavelet transform coefficient subjected to threshold value quantization to obtain a denoised Lamb wave signal x'(t).
Description
Technical field:
The present invention relates to the ultrasonic Lamb wave signal processing technology field in the Non-Destructive Testing, be specifically related to a kind of Lamb wave denoising method based on the adaptive threshold orthogonal wavelet transformation.
Background technology:
In ultrasonic Lamb wave detects; Because Lamb wave excites with check system flexible; And can produce effectively interaction with plate defect, and carry bulk information, therefore; Can be used as the effective means that plate defect detects, particularly in the Non-Destructive Testing of the tabular structure of large tracts of land, use more extensive.The typical non-stationary signal of ultrasonic Lamb wave signal; Because the influence of factors such as neighbourhood noise; The actual Lamb wave signal that records usually is accompanied by undesired signal, and directly the reliability of influence detection and the accuracy of precision need be carried out denoising to the ultrasonic Lamb wave signal of this type non-stationary.
Can know artificial neural network (Liu Z Q, Zhang H Y. Artificial netural network and its application in ultrasonic testing from domestic and international a large amount of document; Nondestructive Testing, 2001,23:221-225), EMD method (Li G; Shi L H; Wang X W. EMD denosing method and its application in Lamb wave detection, Acta Metrologica Sinica, 2006; 27:149-152) and wavelet transformation (Siqueira M H S; Gatts C E N, Silva R R et al. The use of ultrasonic guided waves and wavelets analysis in pipe inspection, Ultrasonics; 2003,41:785-798) wait and can carry out denoising Lamb wave.Method commonly used in recent years is EMD method and wavelet transformation.Usefulness EMD methods such as Li Gang have been carried out denoising to ultrasonic Lamb wave signal, though the EMD method need can not extracted data according to signal characteristic based on a certain specific function adaptively; But denoising effect is not thorough, has kept the characteristic of a lot of noise signals, can not embody original signal well; Denoising effect is not very desirable (Li G; Shi L H, Wang X W. EMD denosing method and its application in Lamb wave detection, Acta Metrologica Sinica; 2006,27:149-152).Because the advantage of wavelet transformation aspect denoising makes it have in the Non-Destructive Testing field very widely and uses; Employing discrete wavelet transformers such as Siqueir bring handles ultrasonic Lamb wave measured signal, will be made as 0 less than the coefficient of dissociation of given threshold value through the hard-threshold method, yet though this method has been removed noise; But de-noising effect is unsatisfactory; Signal still contains much noise, so reconstruction signal can't accurately embody characteristic (Siqueira M H S, the Gatts C E N of signal; Silva R R et al. The use of ultrasonic guided waves and wavelets analysis in pipe inspection; Ultrasonics, 2003,41:785-798).Employing wavelet transformations such as Lazaro remove noise, carry out denoising respectively through the method for hard-threshold and soft-threshold, because hard-threshold and soft-threshold all have shortcoming separately; Cause removing outstanding (the Lazaro J C of noise signal afterwards; Emeterio J L, Ramos A et al. Influence of thresholding procedures in ultrasonic grain noise reduction using wavelets, Ultrasonics; 2002,40:263 – 267).
Summary of the invention:
In order to overcome the shortcoming of prior art, the present invention proposes a kind of based on the ultrasonic Lamb wave denoising method of adaptive threshold orthogonal wavelet transformation.This method is carried out orthogonal wavelet transformation to ultrasonic Lamb wave signal and is come that signal is carried out energy normalized and handle, and reducing the autocorrelation of signal, and utilizes the adaptive threshold method to come ultrasonic Lamb wave is carried out denoising.
Technical scheme of the present invention is following:
In order to improve the performance of the inventive method, the orthogonal wavelet transformation that will have decorrelation is incorporated in the Lamb wave denoising method its structural principle such as Fig. 1.
x(
t) be the Lamb wave signal of noisy,
r(
t) be through the Lamb wave signal behind the orthogonal wavelet transformation,
y(
t) be through the Lamb wave signal after the adaptive threshold,
X '(
t) be the Lamb wave signal after the denoising.Through the autocorrelation of orthogonal wavelet transformation with reduction Lamb wave signal.Because orthogonal wavelet transformation is linear transformation, so after the input signal process wavelet transformation, it is independent that noise and signal are still added up.Lamb wave signal with noisy
x(
t) under wavelet basis, launch, obtain its orthogonal wavelet transformation coefficient, select threshold value and threshold function table, will
x(
t) the orthogonal wavelet transformation coefficient carry out threshold value quantizing and handle, obtain the orthogonal wavelet transformation coefficient behind the threshold value quantizing, to carrying out reconstruct, obtain the Lamb wave signal after the denoising through the orthogonal wavelet transformation coefficient behind the threshold value quantizing
X '(
t).
Beneficial effect of the present invention is following:
Owing to containing noise in the ultrasonic Lamb wave signal and being non-stationary signal; Utilize orthogonal wavelet transformation to remove the autocorrelation of ultrasonic Lamb wave signal and combine, propose Lamb wave denoising method based on the adaptive threshold orthogonal wavelet transformation with adaptive threshold denoising method.This method has stronger removal noise ability, and signal to noise ratio (S/N ratio) and snr gain are significantly improved, and square error has had obvious reduction, can keep the details of original signal better, and is better than additive method smoothness.
Description of drawings:
Fig. 1: based on orthogonal wavelet transformation adaptive threshold Lamb wave denoising method.
Fig. 2: the present invention tests used original signal.
Fig. 3: the present invention tests used noisy signal.
Fig. 4: with the signal after the denoising of soft-threshold denoising method.
Fig. 5: with the signal after the denoising of EMD method.
Fig. 6: use based on the signal after the denoising of orthogonal wavelet transformation adaptive threshold Lamb wave denoising method.
Embodiment:
The orthogonal wavelet transformation that will have decorrelation is incorporated in the Lamb wave denoising method its structural principle such as Fig. 1.
x(
t) be the Lamb wave signal of noisy,
r(
t) be through the Lamb wave signal behind the orthogonal wavelet transformation,
y(
t) be through the Lamb wave signal after the adaptive threshold,
X '(
t) be the Lamb wave signal after the denoising.Through the autocorrelation of orthogonal wavelet transformation with reduction Lamb wave signal.Because orthogonal wavelet transformation is linear transformation, so after the input signal process wavelet transformation, it is independent that noise and signal are still added up.Lamb wave signal with noisy
x(
t) under wavelet basis, launch, obtain its orthogonal wavelet transformation coefficient, select threshold value and threshold function table, will
x(
t) the orthogonal wavelet transformation coefficient carry out threshold value quantizing and handle, obtain the orthogonal wavelet transformation coefficient behind the threshold value quantizing, to carrying out reconstruct, obtain the Lamb wave signal after the denoising through the orthogonal wavelet transformation coefficient behind the threshold value quantizing
X '(
t).Concrete steps are following:
(1) orthogonal wavelet transformation
Lamb wave signal in any space
is launched under wavelet basis; Claim this wavelet transformation that expands into Lamb wave signal
, its expression formula is:
Wherein
Be wavelet basis function, * representes conjugation,
aBe contraction-expansion factor,
Be shift factor, wavelet basis carried out multiresolution analysis construct Orthogonal Wavelets.Suppose that the sequence of subspaces in
space satisfies: nested property; Approaching property; The scale-of-two retractility, translation invariance.Like this; We claim sequence of subspaces
;
is the multiresolution analysis of function space
; By multiresolution analysis, arbitrary signal
expansion is:
In the MALLAT method;
decomposed once, and its coefficient of dissociation is respectively
The coefficient of dissociation that can be got signal
by two yardstick equations is respectively
(5) formula shows with (6) formula,
jThe scale coefficient of+1 metric space and wavelet coefficient can by
jThe scale coefficient of metric space is through filter coefficient
With
Carrying out weighted sum obtains.The metric space coefficient is further decomposed, can obtain
jThe scale coefficient in+2 spaces and wavelet coefficient, and said process can further continue, and can arrive any metric space.
And in the denoising process, the decomposition number of plies is relevant with signal to noise ratio (S/N ratio), and when signal to noise ratio (S/N ratio) was low, input signal was main with noise mainly, at this moment should decompose the number of plies and select more greatly, is beneficial to noise like this and separates; And when signal to noise ratio (S/N ratio) is higher, be main mainly with signal, at this moment decomposing the number of plies needn't be too big, decompose too many, during reconstruct distortion also relatively more serious, error is also big.In general decomposing the 3-5 layer gets final product.
(2) adaptive threshold denoising
After the Lamb wave signal carries out orthogonal wavelet transformation, signal is carried out the adaptive threshold denoising.Adaptive threshold denoising method is improved on the threshold method basis.Along with people such as Donoho have proposed the wavelet threshold noise-eliminating method and many people have carried out deep research to this field; And obtained a lot of achievements, what Donoho proposed is fixed threshold, and its threshold value is a global threshold; Can not on every grade of yardstick, signal and noise be done maximum separation; Denoising effect is unsatisfactory. when we adopt the soft-threshold de-noising, see that totally effect is better, but it is too smooth when signals and associated noises is very irregular, to seem; When adopting the hard-threshold de-noising, de-noising effect is unsatisfactory, and signal still contains obvious noise.This explanation: when when noise is, becoming, traditional noise-eliminating method effect is very limited.Adopt the adaptive threshold Denoising Method, can overcome above-mentioned defective.For obtaining optimal threshold, realize better denoising effect, the present invention adopts following threshold function table
Wherein
Be sign function,
NBe signal length,
Be the orthogonal wavelet transformation coefficient estimation,
Be the orthogonal wavelet transformation coefficient,
Be noise variance, i decomposes the number of plies during for orthogonal wavelet transformation.In practical application; Noise variance is always unknowable, can get
during denoising.When threshold value
is very little; The effect of this threshold function table is suitable with the hard-threshold function; As
during very near threshold value
;
is approximately equal to
, rather than directly to let
be 0.After calculated threshold
; In its substitution threshold function table; Can realize effectively that useful signal keeps, garbage signal is removed.
(3) wavelet reconstruction
After the Lamb wave signal carried out orthogonal wavelet transformation and adaptive threshold denoising, it is carried out wavelet reconstruction obtain reconstruction signal.The thinking of decomposing through MALLAT can backstepping signal reconstruction process, and fundamental relation is following:
Following formula shows,
j + 1 grade of coefficient process " two interpolation " again through wave filter
,
Just can obtain
jThe level coefficient.Wherein,
and
is the analysis filter coefficient;
and
is respectively scale coefficient and the orthogonal wavelet coefficient under the resolution
,
be that resolution is the scale coefficient under
.If the top of decomposition is
; When the level of carrying out
during reconstruct; Can get
according to following formula; Promptly pass through
successively the level restructuring procedure; Can obtain coefficient of dissociation at different levels, be updated in the formula (2) and can obtain reconstruction signal.
In order to verify the validity of the inventive method, compare research as comparison other with wavelet transformation soft-threshold denoising method (WTSL) and EMD denoising method.The inventive method selects the db8 small echo to decompose, and decomposing the number of plies is 3 layers, and signal length is 1024.Fig. 2 is ultrasonic Lamb wave signal, and its signal center frequency is 0.43MHz, and signal bandwidth is 65kHz.The signal to noise ratio (S/N ratio) of Lamb wave signal denoising front signal is 10 dB behind the adding white noise, and signal waveform is as shown in Figure 3.Denoising result is shown in Fig. 4-6, and table 1 has provided the comparison of these 3 kinds of method signal to noise ratio (snr)s, square error (MSE), snr gain (GSNR), smoothness index (R) four kinds of parameters.
Can know by figure:
When 1, adopting the WTSL method, denoising result is not thorough, has taken away some useful informations, and the flashlight slippery is relatively poor after the denoising, does not have recovering signal characteristic well, and main bang 20-30
μ sBetween have the part signal distortion.
When 2, adopting the EMD method, signal distortion is less, and the goodness of fit of main pulse and original signal has had certain raising than the WTSL method, but smoothness is not fine, and tiny pulse still do not restore well, especially 0-10
μ sAnd 50-70
μ sBetween have many burrs, can not embody the characteristic of original signal well, the effect of denoising is very desirable.
3, adopt the inventive method can well remove noise and the flashlight slippery is better, main pulse and tiny pulse all reduce better and the original signal goodness of fit higher, kept the characteristic of original signal preferably, thereby guaranteed the authenticity of signal after the denoising.
Can be known that by table 1 compare with the WTSL method, the signal to noise ratio (S/N ratio) of the inventive method has improved nearly 9.5dB, square error has reduced nearly 11dB, and snr gain improves nearly 1 than WTSL method; Compare with the EMD method, the signal to noise ratio (S/N ratio) of the inventive method has improved nearly 7dB, and square error has reduced nearly 8.3dB, and snr gain improves nearly 1.7 than EMD method; With regard to the smoothness index, the smoothness index of this method is the highest than other two kinds of methods, and is promptly better than additive method smoothness.The inventive method that hence one can see that is better than the additive method denoising effect.
Parameter relatively after three kinds of method denoisings of table 1
Claims (2)
1. based on the Lamb wave denoising method of adaptive threshold orthogonal wavelet transformation, it is characterized in that: this method may further comprise the steps:
A, orthogonal wavelet transformation: with the Lamb wave signal of noisy
x(
t) under wavelet basis, launch, carry out the Lamb wave signal of noisy
x(
t) wavelet transformation, obtain
x(
t) the orthogonal wavelet transformation coefficient;
B, adaptive threshold denoising: select threshold value and threshold function table, the orthogonal wavelet transformation coefficient is carried out threshold value quantizing handle the orthogonal wavelet transformation coefficient after obtaining handling;
C, wavelet reconstruction: to carrying out reconstruct through the orthogonal wavelet transformation coefficient behind the threshold value quantizing, the Lamb wave signal of noise remove after the acquisition reconstruct
X '(
t).
2. the Lamb wave denoising method based on the adaptive threshold orthogonal wavelet transformation according to claim 1 is characterized in that: said step b adopts following threshold function table right
x(
t) the orthogonal wavelet transformation coefficient quantization:
Wherein
Be sign function, N is a signal length,
Be the orthogonal wavelet transformation coefficient estimation,
Be the orthogonal wavelet transformation coefficient,
Be noise variance,
iDecompose the number of plies during for orthogonal wavelet transformation.
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Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102889896A (en) * | 2012-09-24 | 2013-01-23 | 南京航空航天大学 | Two-stage noise reduction method for impact monitoring digital sequence of composite structure |
| CN103954697A (en) * | 2014-05-20 | 2014-07-30 | 南京信息工程大学 | Fractional differentiation-based lamb wave denoising method |
| CN103971012A (en) * | 2014-05-20 | 2014-08-06 | 南京信息工程大学 | Lamb wave signal denoising method based on John Saris model and fractional differentiation |
| CN105652166A (en) * | 2016-03-01 | 2016-06-08 | 国网江西省电力科学研究院 | Weighted threshold wavelet de-noising method used for local discharge online monitoring |
| CN106646406A (en) * | 2016-12-08 | 2017-05-10 | 南京理工大学 | External trajectory speed-measuring radar power spectrum detection method based on improved wavelet threshold de-noising |
| CN106798554A (en) * | 2017-01-12 | 2017-06-06 | 安徽大学 | A kind of denoising method of noisy IMF components and electrocardiosignal |
| CN107274908A (en) * | 2017-06-13 | 2017-10-20 | 南京邮电大学 | Small echo speech de-noising method based on new threshold function table |
| CN108510459A (en) * | 2018-04-08 | 2018-09-07 | 哈尔滨理工大学 | One kind is based on wavelet adaptive threshold and bilateral filtering image noise reduction algorithm |
| CN108920420A (en) * | 2018-03-23 | 2018-11-30 | 同济大学 | A kind of Wavelet noise-eliminating method suitable for driving evaluation test data processing |
| CN112750090A (en) * | 2020-12-28 | 2021-05-04 | 大连海事大学 | Underwater image denoising method and system for improving wavelet threshold |
| CN114428458A (en) * | 2022-01-18 | 2022-05-03 | 哈尔滨理工大学 | Space distribution process increment modeling method based on space-time data flow |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030139165A1 (en) * | 2002-01-18 | 2003-07-24 | General Instrument Corporation | Adaptive threshold algorithm for real-time wavelet de-noising applications |
| CN101661616A (en) * | 2009-09-29 | 2010-03-03 | 北京科技大学 | Method for enhancing images based on multi-scale edge detection in wavelet reconstruction |
-
2011
- 2011-09-28 CN CN2011102986168A patent/CN102393423A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030139165A1 (en) * | 2002-01-18 | 2003-07-24 | General Instrument Corporation | Adaptive threshold algorithm for real-time wavelet de-noising applications |
| CN101661616A (en) * | 2009-09-29 | 2010-03-03 | 北京科技大学 | Method for enhancing images based on multi-scale edge detection in wavelet reconstruction |
Non-Patent Citations (2)
| Title |
|---|
| W.J. STASZEWSKI: "Intelligent signal processing for damage detection in composite materials", 《COMPOSITES SCIENCE AND TECHNOLOGY》 * |
| 张维强等: "基于一种新的阈值函数的小波域信号去噪", 《西安电子科技大学学报(自然科学版)》 * |
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| CN102889896A (en) * | 2012-09-24 | 2013-01-23 | 南京航空航天大学 | Two-stage noise reduction method for impact monitoring digital sequence of composite structure |
| CN103954697A (en) * | 2014-05-20 | 2014-07-30 | 南京信息工程大学 | Fractional differentiation-based lamb wave denoising method |
| CN103971012A (en) * | 2014-05-20 | 2014-08-06 | 南京信息工程大学 | Lamb wave signal denoising method based on John Saris model and fractional differentiation |
| CN103971012B (en) * | 2014-05-20 | 2017-01-18 | 南京信息工程大学 | Lamb wave signal denoising method based on John Saris model and fractional differentiation |
| CN105652166B (en) * | 2016-03-01 | 2018-04-17 | 国网江西省电力科学研究院 | A kind of Weighted Threshold wavelet de-noising method for partial discharge on-line monitoring |
| CN105652166A (en) * | 2016-03-01 | 2016-06-08 | 国网江西省电力科学研究院 | Weighted threshold wavelet de-noising method used for local discharge online monitoring |
| CN106646406B (en) * | 2016-12-08 | 2019-06-04 | 南京理工大学 | Based on the outer trajectory velocity radar power spectrum detection method for improving wavelet threshold denoising |
| CN106646406A (en) * | 2016-12-08 | 2017-05-10 | 南京理工大学 | External trajectory speed-measuring radar power spectrum detection method based on improved wavelet threshold de-noising |
| CN106798554A (en) * | 2017-01-12 | 2017-06-06 | 安徽大学 | A kind of denoising method of noisy IMF components and electrocardiosignal |
| CN107274908A (en) * | 2017-06-13 | 2017-10-20 | 南京邮电大学 | Small echo speech de-noising method based on new threshold function table |
| CN107274908B (en) * | 2017-06-13 | 2020-07-14 | 南京邮电大学 | Wavelet voice denoising method based on new threshold function |
| CN108920420A (en) * | 2018-03-23 | 2018-11-30 | 同济大学 | A kind of Wavelet noise-eliminating method suitable for driving evaluation test data processing |
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Application publication date: 20120328 |