CN104881567A - Statistical model based bridge health monitoring data wavelet denoising method - Google Patents

Abstract

The invention relates to a statistical model based bridge health monitoring data wavelet denoising method. The method includes the following steps: firstly, establishing a bridge monitoring signal model; secondly, subjecting an obtained structure monitoring signal to wavelet decomposition to obtain two frequency domains, namely a low frequency domain A1 and a high frequency domain D1, continuing performing wavelet decomposition on the low frequency domain A1 to obtain two frequency domains, namely a low frequency domain A2 and a high frequency domain D2, and repeating the step till maximum layers are decomposed; thirdly, subjecting the actual monitoring signal to wavelet decomposition and establishing a statistical model of wavelet decomposition coefficients; fourthly, deducing a wavelet threshold contracting function and subjecting the wavelet coefficients of a high-frequency part (Dj,j=1,2,...J) of each layer to thresholding method contracting processing; fifthly, performing wavelet inverse transformation processing to obtain denoised bridge structure monitoring data. Denoising is performed effectively, quality of the monitoring data is improved, and signal smoothness is improved.

Description

A kind of bridge health monitoring data wavelet de-noising method of Corpus--based Method model

Technical field

The present invention is applied to bridge health monitoring data de-noising field, relates to a kind of Wavelet noise-eliminating method being applicable to the Corpus--based Method model of bridge structure Monitoring Data.

Background technology

China's " highway grow up bridge tunnel operation safety management way (exposure draft) " proposes national highway, the operation safety management of provincial highway grand bridge should implement " safety first, put prevention first " working policy, suggestion Guan Yang unit adopts modern information technologies, progressively set up bridge tunnel safety monitoring system of growing up, set up, sound bridge tunnel safety monitoring appraisal system of growing up, to the working environment of bridge tunnel, configuration state, the response condition of bridge tunnel under all kinds of external loads effect carries out Real-Time Monitoring, timely grasp is grown up the overall technology state of bridge tunnel and operation condition, for bridge tunnel operation management of growing up, maintenance, reliability assessment and related science research provide foundation.By setting up Bridge Structure health monitoring systems, collect effective information to assess bridge state and security, to understand structural safety service state in real time, and implement effective preventive maintenance, maintenance network work, ensure that bridge maintenance and inspection strategy works out pointed, promptness and high efficiency, for maintenance demand, maintenance measure provide the decision-making foundation of science.

Bridge health status monitoring is based on interdisciplinary technology such as building, electronics, computing machines, realizes the new technology of structure control to bridge and assessment.In recent years, although structural states monitoring, the research in assessment and the field of improvement has achieved great progress, but civil engineering structure, especially when it, still happening occasionally without the structural failure example under obvious early warning sign under normal operating conditions is in for bridge structure.Bridge structure health status monitoring is exactly a technology that can make up traditional bridge monitoring deficiency.For forming science, more intelligentized safety monitoring system more, make up the unicity of existing monitoring means, the shortcomings such as the limitation of state estimation object etc. are not enough.Therefore the bridge structural health monitoring quality of data is put forward, for maintenance management department provides more clear muting Monitoring Data to have very important significance.

The signals such as the off normal of cable-stayed bridge pylon and girder, the vibrations of drag-line and bridge crucial welding position STRESS VARIATION, be actually a kind of signal with room and time change, it can be summed up as the analysis to signal.Because monitoring effect quantity is by the impact of Various Complex factor, measurement noises is ubiquitous in data signal acquisition.The source of noise is a kind of is caused by the thermal and magnetic of signals collecting instrument and signal transmission apparatus and electrical effect, and another kind is caused by observational error.These noises all belong to random white noise.When signal is larger by the degree of noise pollution, difficulty can be brought to the Damage Assessment Method of the trend analysis of follow-up Monitoring Data and bridge, therefore effective SNR estimation and compensation technology is used to carry out denoising, from the bridge structure observation time sequence be disturbed, eliminate high frequency noise interference, improving structure monitoring precision is one of gordian technique of bridge structural health monitoring data processing.

Signals and associated noises main manifestations is that data contain a large amount of spike burrs, causes Monitoring Data useful information obviously not embody.Because monitoring effect quantity is by the impact of Various Complex factor, measurement noises is ubiquitous in data signal acquisition.When signal is larger by the degree of noise pollution, can bring difficulty therefore to the analysis and treament of follow-up Monitoring Data, from the angle of automated diagnostic technology, research is needed to remove the method for monitoring noise, for the later stage Intelligent treatment of Monitoring Data provides technical guarantee, promote the development of automatic diagnostics.

In sum, study Loads of Long-span Bridges Monitoring Data denoising method to have very important significance:

(1) improve the quality of Monitoring Data, improve signal smoothing degree;

(2) facilitate Guan Yang department to judge for Monitoring Data more exactly, make pipe in time and support decision-making;

(3) for the subsequent analysis of Monitoring Data and process provide technical guarantee, the development of automatic diagnostics is promoted.

Summary of the invention

There is the poor deficiency of noise, reliability in order to what overcome existing bridge health monitoring data, the invention provides a kind of effective denoising, improve the quality of Monitoring Data, improve the bridge health monitoring data wavelet de-noising method of the Corpus--based Method model of signal smoothing degree.

The technical solution adopted for the present invention to solve the technical problems is:

A bridge health monitoring data wavelet de-noising method for Corpus--based Method model, described method comprises the steps:

Step 1) foundation of bridge monitoring signal model

The model representation of the monitor signal of a Noise becomes following form:

Q(t)＝f(t)+δ(t) (t＝0,1...n-1) (1)

In formula, f (t) is actual signal, and δ (t) is the true Monitoring Data of noise, the signal that Q (t) is Noise and bridge;

Step 2) wavelet decomposition is carried out to the structure monitoring signal obtained, obtain two frequency domains, i.e. low frequency A1, high frequency D1; Proceed wavelet decomposition to lower frequency region A1, then obtain two frequency domains, namely low frequency A2 and high frequency D2, then repeats this step, until decompose maximum number of plies J;

Wavelet coefficient following formula in whole wavelet field is described:

$F_{l,k}^j=D_{l,k}^j+N_{l,k}^j---\left(2\right)$

Wherein, represent the coefficient of dissociation of signals and associated noises, the coefficient of dissociation without noise cancellation signal coefficient of dissociation and noise in wavelet field respectively, wherein subscript l, k coefficient of correspondence position in wavelet field, j is Decomposition order, because wavelet transformation is linear, therefore by above formula obtain jth layer wavelet coefficient variance close be:

${\mathrm{\σ}}_f^2={\mathrm{\σ}}_d^2+{\mathrm{\σ}}_n^2---\left(3\right)$

Wherein, σ _f, σ _d, σ _nbe respectively the variance of signals and associated noises coefficient of dissociation in wavelet field, without noise cancellation signal coefficient of dissociation variance and noise coefficient of dissociation variance.

For discrete monitor signal S, to the step that it carries out discrete multi-scale wavelet decomposition be: first one dimension wavelet decomposition is carried out to monitor signal S, be divided into high fdrequency component D1 and low frequency component A1, again low frequency component A1 is carried out one dimension wavelet decomposition equally, be divided into HFS D2 and low frequency component A2, repeat above-mentioned steps until reach required Decomposition order;

Step 3) wavelet decomposition is carried out to actual monitoring signal and sets up the statistical model of coefficient of wavelet decomposition;

The wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows:

$P_D\left(d\right)=\frac{1}{2b}\exp (-\frac{|d-u|}{b})---\left(5\right)$

Wherein u is location parameter, and b is scale parameter, and d is without noise cancellation signal wavelet coefficient.From above-mentioned statistic histogram, in bridge actual measurement deflection signals coefficient of wavelet decomposition statistical distribution, location parameter u is approximately 0.

The noisy high-frequency wavelet coefficient of bridge monitoring data is approximate obeys zero-mean gaussian distribution:

$P_N\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{2{\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula _nfor the standard deviation of noise in wavelet field, n is without noise cancellation signal wavelet coefficient;

Step 4) derivation wavelet threshold contracting function HFS (D to every one deck _j, j=1,2 ... J) wavelet coefficient carry out threshold method shrink process;

The threshold function table of bridge monitoring data, its formula is as follows

$T={\mathrm{\α}}_j(k\·{\mathrm{\σ}}_n\sqrt{2\log M}+(1-k)\·{\mathrm{\σ}}_n^2/{\mathrm{\σ}}_{d,j})---\left(9\right)$

Wherein, σ _nthe standard deviation of noise, σ _d,jfor the standard deviation without monitor signal jth layer in wavelet field of making an uproar, regulating parameter k is between 0 and 1, and as k=1, threshold formula becomes uniform threshold, and as k=0, threshold formula becomes optimal threshold function, wherein α _j=1/e ^j+1, namely along with the increase threshold value adjustment factor of Decomposition order reduces gradually, namely the larger respective threshold of the higher adjustment factor of sub-bands of frequencies is larger;

Use Bayesian MAP estimation theory, obtain conditional probability function:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}{P}_N(f-d)P_D\left(d\right)---\left(10\right)$

Wherein, d is without noise cancellation signal wavelet coefficient, and f is original signal wavelet coefficient.(5), (6) are substituted in (10), after reduction operation:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}\·\frac{1}{2\sqrt{2\mathrm{\π}}b{\mathrm{\σ}}_n}\·\exp \left(\frac{2{\mathrm{\σ}}_n^2\left|d\right|-b{(f-d)}^2}{2b{\mathrm{\σ}}_n^2}\right)---\left(11\right)$

Wherein, σ _nfor noise criteria is poor, theoretical according to maximum a posteriori probability, make P _d/F(d/f) local derviation is asked to d and zero setting can obtain threshold value shrinkage estimation function:

$\hat{d}=\left\{\begin{array}{c}\mathrm{sgn}\left(f\right)\·(f-\frac{{\mathrm{\σ}}_n^2}{b})\left(\right|f|>T)\\ 0\left(\right|f|\≤T)\end{array}\right.---\left(12\right)$

Wherein parameter b is by following formula gained:

$b={\left[0.5({\mathrm{\σ}}_{f,j}^2-{\mathrm{\σ}}_n^2)\right]}^{0.5}---\left(13\right)$

Wherein, σ _f,jfor the standard deviation of raw monitored signal jth layer in wavelet field, σ _nfor noise criteria is poor.

Step 5) do wavelet inverse transformation process, obtain the bridge structure Monitoring Data after denoising.

Technical conceive of the present invention is: wavelet analysis grows up on the basis of Fourier analysis, there is the feature of multiresolution, solve the contradiction of time domain and frequency domain resolution preferably, make use of the resolution of non-uniform Distribution dexterously, in low-frequency range higher frequency resolution and lower temporal resolution, then adopt lower frequency resolution and higher temporal resolution wavelet transformation can obtain the localization property of signal well at high band, can stress release treatment effectively.[2] and very effectively this also makes it be particularly suitable for processing bridge monitoring data complicated under true environment to the detection of jump signal and non-stationary signal.Donoho and Johnstone proposed the classical soft-threshold based on wavelet analysis and hard-threshold denoising method [3] in 1994.Find that classical soft-threshold and hard-threshold denoising method have following shortcoming by research: hard threshold function has uncontinuity; In soft threshold method, always there is constant deviation in the wavelet coefficient that the wavelet coefficient Sum decomposition after estimation obtains.Due to the existence of these defects, signal after denoising there will be burr in some region, thus seriously hinder follow-up Monitoring Data trend analysis, damage knows on the basis with reference to existing document, propose a kind of new wavelet threshold function in conjunction with bridge Monitoring Data actual conditions according to the characteristic of small echo herein and the threshold value contracting function of small echo improved.Compared with traditional uniform threshold function, new threshold function table weakens wavelet coefficient overall number M to the impact of threshold value, and to the adaptive selection respective threshold of different Decomposition order.And the wavelet threshold contracting function after improving greatly reduces the constant deviation produced in soft threshold method while overcoming the uncontinuity of hard-threshold, make estimation of error wavelet coefficient out more close to actual value.

Beneficial effect of the present invention is mainly manifested in: one aspect of the present invention carries out the statistical modeling of coefficient of wavelet decomposition according to the monitor signal of bridge reality; On the other hand, improve general threshold function table and contraction method, compared with traditional uniform threshold function, new threshold function table weakens wavelet coefficient overall number M to the impact of threshold value, and to the adaptive selection respective threshold of different Decomposition order.To the tiny noise of high-frequency domain, there is very strong noise removal capability.The essence of bridge structure monitoring analysis is signal analysis, build or build up later bridge can passing in time and the change constantly occurred on shape or position.Instance analysis shows, the Wavelet noise-eliminating method based on Bayesian MAP probability can the task of effective settling signal denoising, very effectively processes bridge deformation Monitoring Data, for follow-up data process and trend analysis lay the foundation.

Accompanying drawing explanation

Fig. 1 is monitor signal three grades of wavelet decomposition schematic diagram.

Fig. 2 is three grades of wavelet decomposition schematic diagram of deflection signals.Wherein, (a) is the low frequency general picture coefficient after deflection monitoring signal three layers of wavelet decomposition; B () is the detail coefficients of deflection monitoring signal three layers of wavelet decomposition; C () is the detail coefficients of deflection monitoring signal two layers of wavelet decomposition; D () is the detail coefficients of deflection monitoring signal one deck wavelet decomposition;

Fig. 3 is most high band wavelet coefficient statistical fit figure.

Fig. 4 is the schematic diagram of soft/hard threshold method.Wherein, the contraction factor schematic diagram of (a) Soft thresholding; The contraction factor schematic diagram of (b) hard threshold method; (c) soft-threshold contracting function curve; (d) hard-threshold contracting function curve.

Fig. 5 is the contracting function curve map after improving.

Fig. 6 is original signal and adds the signal after making an uproar.Wherein, (a) is original rope force signal; B () is for adding the rope force signal after making an uproar;

Fig. 7 is three kinds of Threshold Denoising Method comparison diagrams.Wherein, (a) is schematic diagram after Soft thresholding noise reduction; B () is schematic diagram after hard threshold method noise reduction; Schematic diagram after c wavelet de-noising method noise reduction that () is Corpus--based Method model.

Fig. 8 be certain Main Bridge across YB01-YB18 monitoring point vertical deflection variation monitoring data.

Fig. 9 is the deflection monitoring value after noise reduction.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1 ~ Fig. 9, a kind of bridge health monitoring data wavelet de-noising method of Corpus--based Method model, described method comprises the steps:

Step 1) foundation of bridge monitoring signal model

It is generally acknowledged that the envelope signal of bridge health monitoring system collection is made up of two parts, one is true significant bridge structure response signal, and another part is noise signal.Noise Producing reason is a kind of is caused by the thermal and magnetic of signals collecting instrument and signal transmission apparatus and electrical effect, and another kind is caused by observational error.

The model of the monitor signal of a Noise can be expressed as following form:

Q(t)＝f(t)+δ(t) (t＝0,1...n-1) (1)

In formula, f (t) is actual signal, δ (t) is noise, the true Monitoring Data of the signal that Q (t) is Noise and bridge, be usually expressed as low frequency signal or some more stable signals, and noise signal is usually expressed as high-frequency signal.And the object of wavelet transformation is wanted restraint speckle δ (t) to recover original signal f (t) exactly.

Step 2) wavelet decomposition is carried out to the structure monitoring signal obtained, obtain two frequency domains (low frequency A1, high frequency D1).Wavelet decomposition is proceeded to lower frequency region A1, then obtains two frequency domains (A2 and D2).Then this step is repeated, until decompose maximum number of plies J.

Wavelet coefficient in whole wavelet field can be described with following formula:

$F_{l,k}^j=D_{l,k}^j+N_{l,k}^j---\left(2\right)$

represent the coefficient of dissociation of signals and associated noises, the coefficient of dissociation without noise cancellation signal coefficient of dissociation and noise in wavelet field respectively.Wherein subscript l, k coefficient of correspondence position in wavelet field, j is Decomposition order.Because wavelet transformation is linear, therefore the variance pass of jth layer wavelet coefficient is can be obtained fom the above equation:

${\mathrm{\σ}}_f^2={\mathrm{\σ}}_d^2+{\mathrm{\σ}}_n^2---\left(3\right)$

For discrete monitor signal S, to the step that it carries out discrete multi-scale wavelet decomposition be: first one dimension wavelet decomposition is carried out to monitor signal S, be divided into high fdrequency component D1 and low frequency component A1.Again low frequency component A1 is carried out one dimension wavelet decomposition equally, be divided into HFS D2 and low frequency component A2.Repeat above-mentioned steps until reach required Decomposition order.The schematic diagram of three grades of wavelet decomposition is carried out as shown in Figure 1 to monitor signal S.

Signal S can be expressed as:

S＝A3+D3+D2+D1 (4)

In like manner, the schematic diagram that one dimension small echo is reconstructed and Fig. 1 closely similar, namely process according to contrary order, can obtain, therefore repeat no more here.Next by some the sub-band components in Fig. 1, namely corresponding coefficient of wavelet decomposition does simple analysis.S is original signal, and the main information of monitor signal all concentrates on here.Each wavelet decomposition all can obtain two sub-bands, obtains A1 and D1 two sub-bands to S after carrying out one-level wavelet decomposition.

A1 component is the low frequency component obtained after carrying out wavelet decomposition to original signal S, i.e. approximate part after one-level wavelet decomposition, and it contains the maximum low-frequency information of structure monitoring signal.

D1 is the high fdrequency component after a wavelet decomposition, and namely it contains the high-frequency information such as sign mutation, spike burr in monitor signal.

Fig. 2 is three grades of wavelet decomposition schematic diagram of Zhijiang River bridge deflection signals, can find out that the noise of bridge structure monitor signal is mainly distributed in HFS.Low frequency part remains a large amount of tendency information of structure monitoring signal.

Step 3) wavelet decomposition is carried out to actual monitoring signal and sets up the statistical model of coefficient of wavelet decomposition.

The statistic histogram of the wavelet coefficient high-frequency sub-band of bridge monitoring signal presents very long heavily hangover, and at place's appearance at zero point spike sharply.Therefore, this statistical model embodies again certain Lars distribution character to a certain extent except meeting generalized Gaussian distribution.For the Zhijiang River, Hangzhou Main Bridge across the most high frequency coefficient of mid-span deflection measured data three layers of wavelet decomposition, analysis wavelet coefficient of dissociation statistical model distribution situation.We can carry out the foundation of statistical model to the wavelet coefficient under different decomposition yardstick according to this distribution character, and carry out approximate description by these statistical models to signal.

Because in practical application, noise signal belongs to random white noise more, therefore, we suppose that random noise meets Gaussian distribution, meet Lars distribution without noise cancellation signal coefficient of dissociation.Because on each decomposition scale, coefficient of wavelet decomposition statistical distribution is similar, carry out statistics with histogram, to verify the rationality of statistical model with three layers of wavelet decomposition high band wavelet coefficient of Zhijiang River bridge actual measurement deflection signals here.Structure statistical model F (x) is a generalized Gaussian distribution and a laplacian distribution function sum.As shown in Figure 2, wherein loose point is the distribution after the normalization of high band wavelet coefficient statistics, and curve is the matched curve of F (x) to loose point in statistical model matching.

By the analysis to bridge actural deflection Monitoring Data coefficient of wavelet decomposition statistical model, it is considered herein that the wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows:

$P_D\left(d\right)=\frac{1}{2b}\exp (-\frac{|d-u|}{b})---\left(5\right)$

Wherein u is location parameter, and b is scale parameter, and d is the wavelet coefficient without noise cancellation signal.From above-mentioned statistic histogram, in bridge actual measurement deflection signals coefficient of wavelet decomposition statistical distribution, location parameter u is approximately 0.

The noisy high-frequency wavelet coefficient of bridge monitoring data is approximate obeys zero-mean gaussian distribution:

$P_N\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{2{\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula _nfor the standard deviation of noise in wavelet field, n is the wavelet coefficient of noise signal.

Step 4) derivation wavelet threshold contracting function HFS (D to every one deck _j, j=1,2 ... J) wavelet coefficient carry out threshold method shrink process.

In Wavelet noise-eliminating method, the selection of threshold function table directly can have influence on final Monitoring Data denoising result.When Threshold selection is less, the noise figure that a part is greater than this threshold value can be taken as useful signal and remain, and the monitor signal after this just causes denoising still exists much noise; When Threshold selection is larger, the useful information that a lot of coefficient is very little can be used as noise and zero setting, this becomes very level and smooth by making the monitor signal after denoising, loses a lot of detailed information.Therefore select appropriate wavelet threshold function extremely important.

(1) people such as Donoho proposes a kind of typical Research on threshold selection, and demonstrates this threshold value theoretically to the standard deviation of noise and be directly proportional, and changing threshold function table is also called uniform threshold function, and its formula is as follows

$T={\mathrm{\σ}}_n\sqrt{2\log M}---\left(7\right)$

Wherein, namely M is the overall number of wavelet coefficient in corresponding wavelet field, σ _nit is the standard deviation of noise.In this threshold function table, threshold value T affects comparatively large by the number of wavelet coefficient, and namely when M is excessive, larger threshold value may smooth out the less useful information of those coefficients.

(2) people such as Chang proposes a kind of optimal threshold back-and-forth method, and this threshold function table has Bayesian MAP probability to derive to obtain, and its formula is as follows

$T={\mathrm{\α}}_j({\mathrm{\σ}}_n^2/{\mathrm{\σ}}_{g,j})---\left(8\right)$

Wherein, the variance of noise, σ _g,jfor the standard deviation of noise-free signal g jth layer in wavelet field.α _jfor adjustability coefficients, namely at the adjustment factor of wavelet field jth layer, get α under normal circumstances _j=1.

On the basis of formula (7) and formula (8), the present invention proposes a kind of threshold function table being more applicable to bridge monitoring data, its formula is as follows

$T={\mathrm{\α}}_j(k\·{\mathrm{\σ}}_n\sqrt{2\log M}+(1-k)\·{\mathrm{\σ}}_n^2/{\mathrm{\σ}}_{d,j})---\left(9\right)$

Classical uniform threshold combines with optimal threshold method by this threshold value, and chooses different threshold size according to different decomposition dimension self-adaption.Wherein σ _nthe standard deviation of noise, σ _d,jfor the standard deviation without monitor signal jth layer in wavelet field of making an uproar, regulating parameter k is between 0 and 1. and as k=1, threshold formula becomes uniform threshold, and as k=0, threshold formula becomes optimal threshold function.Wherein α _j=1/e ^j+1, namely along with the increase threshold value adjustment factor of Decomposition order reduces gradually, namely the larger respective threshold of the higher adjustment factor of sub-bands of frequencies is larger.Thus more agree with noise and be more distributed in feature in high-frequency sub-band.Formula (9) weakens the impact of formula (7) uniform threshold function on the overall number M of wavelet coefficient on the one hand, refer to the optimal threshold function of formula (8) on the other hand, make choosing of threshold function table more stable like this, namely " robustness " is better.

In Wavelet noise-eliminating method, a first selected given threshold value, then shrinks wavelet coefficient according to certain rule, just completes the denoising to wavelet coefficient.An i.e. given threshold value, the coefficient that all absolute values are less than this threshold value is taken as noise, then does zero setting process to it; Wavelet coefficient absolute value being greater than to threshold value reduces by certain method, then obtains the new value after reducing.

Classical wavelet shrinkage method has Soft thresholding and hard threshold method as Fig. 2, but in Soft thresholding, larger wavelet coefficient is always reduced by threshold value, therefore shrink after signal mathematical expectation with shrink before different, so process after monitor signal relative smooth some.The shortcoming of hard threshold method be wavelet coefficient near null value territory by unexpected zero setting, result in the uncontinuity of wavelet data, denoising result is thorough, easily produces Gibbs vibration at local singular point place.But in actual applications, when particularly noise level is very high, the signal after hard threshold method process can produce concussion around point of discontinuity, affects the denoising effect of signal.

Threshold value contraction method due to classics can not meet the requirement to the denoising of bridge structure Monitoring Data, so the present invention improves contraction method.

Use Bayesian MAP estimation theory, obtain conditional probability function:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}{P}_N(f-d)P_D\left(d\right)---\left(10\right)$

Wherein, d is without noise cancellation signal wavelet coefficient, and f is original signal wavelet coefficient.(5), (6) are substituted in (10), can obtain after reduction operation:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}\·\frac{1}{2\sqrt{2\mathrm{\π}}b{\mathrm{\σ}}_n}\·\exp \left(\frac{2{\mathrm{\σ}}_n^2\left|d\right|-b{(f-d)}^2}{2b{\mathrm{\σ}}_n^2}\right)---\left(11\right)$

Wherein, σ _nfor noise criteria is poor.Theoretical according to maximum a posteriori probability, make P _d/F(d/f) local derviation is asked to d and zero setting can obtain threshold value shrinkage estimation function:

$\hat{d}=\left\{\begin{array}{c}\mathrm{sgn}\left(f\right)\·(f-\frac{{\mathrm{\σ}}_n^2}{b})\left(\right|f|>T)\\ 0\left(\right|f|\≤T)\end{array}\right.---\left(12\right)$

Wherein parameter b can by following formula gained:

$b={\left[0.5({\mathrm{\σ}}_{f,j}^2-{\mathrm{\σ}}_n^2)\right]}^{0.5}---\left(13\right)$

Wherein, σ _f,jfor the standard deviation of raw monitored signal jth layer in wavelet field, σ _nfor noise criteria is poor.

By observing the curve map (Fig. 5) of wavelet shrinkage function, can find out that wavelet shrinkage function that the present invention improves shows on curve image more level and smooth, especially when wavelet coefficient is greater than in the interval range of wavelet threshold.

Step 5) do wavelet inverse transformation process, obtain the bridge structure Monitoring Data after denoising.

The wavelet coefficient after denoising just can be obtained after threshold value shrink process.By to step 4) the monitor signal coefficient of wavelet decomposition that obtains is reconstructed, and can obtain the bridge monitoring signal after denoising.Thus obtain accurately bridge structure Monitoring Data to provide Data support accurately for Guan Yang department.Also demonstrate the present invention by experiment and really can meet requirement for the denoising of bridge structure Monitoring Data.

Experimental verification: evaluate the quality of denoising effect from numerical analysis angle in order to more accurate, according to actual conditions, we simulate bridge cable force vibration signal is here a periodically variable signal in time.And respectively the white noise sequence that variance is 0.2,0.4,0.6 is added to it.Soft-threshold, hard-threshold and proposed method is used to carry out based Denoising respectively by wavelet function feedback, and the signal to noise ratio (S/N ratio) of signal and root-mean-square error under more different noise profile.Fig. 6 is simulation rope force signal and to add variance be signals and associated noises after the white noise of 0.4.

Here as can be seen from figure we, be submerged by useful information a large amount of in the Monitoring Data after noise pollution.Compared with original signal, many useful informations are difficult to differentiate.Under the Orthogonal Wavelets that now employing has near symmetry, compactly support, the wavelet function sym8 of 8 rank vanishing moments generates, carry out three layers of wavelet decomposition of signal.Use traditional soft threshold deniosing, hard-threshold noise reduction and threshold deniosing strategy in this paper to carry out signal de-noising respectively, experimental result is as Fig. 7.

In Fig. 7 respectively to the noisy signal under same noise variance carry out after the denoise algorithm process of soft, hard-threshold and Corpus--based Method model in this paper denoised signal.From figure, we can find out use hard-threshold denoising, and denoising result is thorough, easily produce Gibbs vibration and with the distortion of portion waveshape, the noise cancellation signal at its signal tip is not ideal enough, and after denoising, flashlight slippery is poor at local singular point place.And after soft-threshold de-noising, the high frequency noise of signal is removed substantially, but have some to have periodic information compared with original signal to be removed, to have certain phase distortion and the loss of signal, tip formation keeps not exclusively.And use the noise-eliminating method improving threshold value to have certain improvements relative to above-mentioned two kinds of signals.Signal approximation degree is high and can effectively suppress Gibbs oscillatory occurences, and after signal transacting, waveform is level and smooth, and phase distortion is little with the loss of signal, for unknown signals and associated noises estimation accurately, ensure that the authenticity of signal after denoising.The basis of original signal adds to it white noise sequence that variance is 0.2,0.4,0.6 respectively, uses above-mentioned three kinds of methods to carry out threshold deniosing respectively.And with noise, when root-mean-square error is for index, and comparing result is in table 2.Found by contrast, the method for this improvement threshold function table can obtain denoising effect well really, and after denoising, the signal to noise ratio (S/N ratio) of signal has had significant improvement.Compared with other analytical approachs, bridge deformation monitor signal adopts wavelet multi_resolution analysis method to carry out denoising Processing, can stick signal raw information to the full extent, thus lay the foundation for the carrying out of the work such as subsequent data analysis, trend prediction, the Data support provided.

Table 2

Choose certain Main Bridge across the change of YB01-YB18 monitoring point vertical deflection as research object and Modling model.Studying carefully data set time scope is 1 to 3 Dec in 2014, and accumulative sampling amounts to 1296 times, as shown in Figure 6.Complete and by force seasonal from observation time observation cycle, therefore adopt this Monitoring Data to carry out research as sample representative.

By finding the observation of raw monitored value, due to the impact by the factor such as environment, instrument, actual measurement deflection value contains (as Fig. 8 square frame institute marked regions) such as a large amount of noises, rough error, spike concussions.The existence of these noises, will inevitably produce follow-up bridge structure health early warning and trend analysis and have a strong impact on, thus cause subsequent analysis misalignment.Algorithm of the present invention is used to carry out the denoising effect after amount of deflection measured data as Fig. 9.

Choose typical noisy region in monitor signal and with red boxes mark, contrast denoising before and after deflection monitoring signal, can find to the noise in original signal and the actual denoising effect of rough error obvious.Signal approximation degree is high and can effectively suppress Gibbs oscillatory occurences, and after signal transacting, waveform is level and smooth, and phase distortion and the loss of signal little.In bridge health monitoring system, not de-noising signal is more level and smooth better, but need ensure under the prerequisite that useful information is fully retained, as far as possible smoothly.Research shows that the method is accurate for the estimation of deflection signals in actual condition, and not only denoising effect is desirable but also the accurate information that fully remains in original signal.

By relatively finding that the present invention is in the noise reduction process being applied to bridge monitoring data, denoising effect is significantly improved, and obtained the present invention by emulation experiment and greatly can improve Signal-to-Noise, therefore can be applied greatly in the middle of Real-time System.

Claims (1)

1. a bridge health monitoring data wavelet de-noising method for Corpus--based Method model, is characterized in that: described method comprises the steps:

Step 1) foundation of bridge monitoring signal model

The model representation of the monitor signal of a Noise becomes following form:

Q(t)＝f(t)+δ(t) (t＝0,1...n-1) (1)

In formula, f (t) is actual signal, and δ (t) is the true Monitoring Data of noise, the signal that Q (t) is Noise and bridge;

Step 2) wavelet decomposition is carried out to the structure monitoring signal obtained, obtain two frequency domains, i.e. low frequency A1, high frequency D1; Proceed wavelet decomposition to lower frequency region A1, then obtain two frequency domains, namely low frequency A2 and high frequency D2, then repeats this step, until decompose maximum number of plies J;

Wavelet coefficient following formula in whole wavelet field is described:

$F_{l,k}^j=D_{l,k}^j+N_{l,k}^j---\left(2\right)$

Wherein, represent the coefficient of dissociation of signals and associated noises, the coefficient of dissociation without noise cancellation signal coefficient of dissociation and noise in wavelet field respectively, wherein subscript l, k coefficient of correspondence position in wavelet field, j is Decomposition order, because wavelet transformation is linear, therefore by above formula obtain jth layer wavelet coefficient variance close be:

${\mathrm{\σ}}_f^2={\mathrm{\σ}}_d^2+{\mathrm{\σ}}_n^2---\left(3\right)$

Wherein, σ _f, σ _d, σ _nbe respectively the variance of signals and associated noises coefficient of dissociation in wavelet field, without noise cancellation signal coefficient of dissociation variance and noise coefficient of dissociation variance.

For discrete monitor signal S, to the step that it carries out discrete multi-scale wavelet decomposition be: first one dimension wavelet decomposition is carried out to monitor signal S, be divided into high fdrequency component D1 and low frequency component A1, again low frequency component A1 is carried out one dimension wavelet decomposition equally, be divided into HFS D2 and low frequency component A2, repeat above-mentioned steps until reach required Decomposition order;

Step 3) wavelet decomposition is carried out to actual monitoring signal and sets up the statistical model of coefficient of wavelet decomposition;

The wavelet coefficient without noise cancellation signal after wavelet decomposition obey broad sense laplacian distribution, its probability distribution is as follows:

$P_D\left(d\right)=\frac{1}{2b}\exp (-\frac{|d-u|}{b})---\left(5\right)$

Wherein u is location parameter, and b is scale parameter, and d is without noise cancellation signal wavelet coefficient.From above-mentioned statistic histogram, in bridge actual measurement deflection signals coefficient of wavelet decomposition statistical distribution, location parameter u is approximately 0.

The noisy high-frequency wavelet coefficient of bridge monitoring data is approximate obeys zero-mean gaussian distribution:

$P_N\left(n\right)=\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_n}\exp (-\frac{n^2}{{2\mathrm{\σ}}_n^2})---\left(6\right)$

σ in formula _nfor the standard deviation of noise in wavelet field;

Step 4) derivation wavelet threshold contracting function HFS (D to every one deck _j, j=1,2 ... J) wavelet coefficient carry out threshold method shrink process;

The threshold function table of bridge monitoring data, its formula is as follows

$T={\mathrm{\α}}_j(k\·{\mathrm{\σ}}_n\sqrt{2\log M}+(1-k)\·{\mathrm{\σ}}_n^2/{\mathrm{\σ}}_{d,j})---\left(9\right)$

Wherein, σ _nthe standard deviation of noise, σ _d,jfor the standard deviation without monitor signal jth layer in wavelet field of making an uproar, regulating parameter k is between 0 and 1, and as k=1, threshold formula becomes uniform threshold, and as k=0, threshold formula becomes optimal threshold function, wherein α _j=1/e ^j+1, namely along with the increase threshold value adjustment factor of Decomposition order reduces gradually, namely the larger respective threshold of the higher adjustment factor of sub-bands of frequencies is larger;

Use Bayesian MAP estimation theory, obtain conditional probability function:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}{P}_N(f-d)P_D\left(d\right)---\left(10\right)$

Wherein, d is without noise cancellation signal wavelet coefficient, and f is original signal wavelet coefficient.(5), (6) are substituted in (10), after reduction operation:

$P_{D/F}(d/f)=\frac{1}{P_F\left(f\right)}\·\frac{1}{2\sqrt{2\mathrm{\π}}{\mathrm{b\σ}}_n}\·\exp \left(\frac{{2\mathrm{\σ}}_n^2\left|d\right|-b{(f-d)}^2}{{2\mathrm{b\σ}}_n^2}\right)---\left(11\right)$

Wherein, σ _nfor noise criteria is poor, theoretical according to maximum a posteriori probability, make P _d/F(d/f) local derviation is asked to d and zero setting can obtain threshold value shrinkage estimation function:

$\hat{d}=\left\{\begin{array}{c}\mathrm{sgn}\left(f\right)\·(f-\frac{{\mathrm{\σ}}_n^2}{b})\left(\right|f|>T)\\ 0\left(\right|f|\≤T)\end{array}\right.---\left(12\right)$

Wherein parameter b is by following formula gained:

$b={\left[0.5({\mathrm{\σ}}_{f,j}^2-{\mathrm{\σ}}_n^2)\right]}^{0.5}---\left(13\right)$

Wherein, σ _f,jfor the standard deviation of raw monitored signal jth layer in wavelet field, σ _nfor noise criteria is poor.

Step 5) do wavelet inverse transformation process, obtain the bridge structure Monitoring Data after denoising.