CN110542723B - Guided wave signal sparse decomposition and damage positioning-based two-stage damage position identification method - Google Patents
Guided wave signal sparse decomposition and damage positioning-based two-stage damage position identification method Download PDFInfo
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Abstract
A two-stage damage position identification method based on guided wave signal sparse decomposition and damage positioning relates to the field of ultrasonic nondestructive testing. The method aims to solve the problem that a dictionary design method and a signal sparse decomposition algorithm are not complete enough in the ultrasonic guided wave signal overlapped wave packet recognition, and further results obtained by ultrasonic guided wave signal analysis are not accurate enough. The method utilizes the punishment item to make the coefficient vector as sparse as possible, thereby greatly reducing the possibility of matching noise with dictionary atoms; the dictionary matrix is designed by utilizing the propagation model of the guided wave, wherein the problems of frequency dispersion, multi-mode and mode conversion of the guided wave are considered, and the overlapped waveforms are identified in a linear decomposition mode, so that the method has more advantages compared with the conventional signal processing method; the sparse optimization solving algorithm based on the sparse Bayesian learning has unique advantages in the aspect of processing sparse representation such underdetermined linear problems, and has better robustness to noise.
Description
Technical Field
The invention belongs to the field of ultrasonic nondestructive detection.
Background
In the field of civil engineering, ultrasonic nondestructive detection has been widely applied to structural damage detection of building structures, bridges, pipelines and the like. By means of ultrasonic nondestructive detection technology, whether defects or damages exist in the structure can be effectively detected, defect positioning is carried out, and the size of the defects is estimated, so that the safety condition of the structure can be evaluated, and the residual service life can be predicted. Compared with the integral monitoring and a small amount of local monitoring technologies based on vibration in the structural health monitoring, the ultrasonic nondestructive testing technology can better detect the local tiny damage of the structure, and is beneficial supplement to the structural health monitoring technology. The ultrasonic nondestructive detection technology is combined with the structure health monitoring technology, so that full-scale monitoring from local damage to overall damage of the structure can be realized, and the accuracy of structure safety assessment can be effectively improved. The traditional ultrasonic detection method is based on the ultrasonic body wave propagation theory, and has the advantages of small detection range and low detection efficiency. In contrast, the nondestructive testing technology based on the ultrasonic guided wave method has a wide detection range and high efficiency, and in recent years, scientific research gradually goes to practical engineering application. Ultrasonic guided wave can propagate in thin wall members such as board, pipeline, compares traditional ultrasonic wave, and ultrasonic guided wave can propagate longer distance in above-mentioned structure, when meetting structural defect or damage, can take place scattering or reflection, carries out analysis to scattering or reflection wave and can discern structural defect or damage to can further fix a position, ration even formation of image to it.
Due to the characteristics of the ultrasonic guided waves such as frequency dispersion, multi-mode and mode conversion, ultrasonic guided wave signals received by the sensor are usually very complex, so that effective interpretation of the signals becomes extremely difficult, damage information is difficult to accurately acquire, and the effectiveness and the practicability of the ultrasonic guided wave nondestructive testing technology in structure detection are limited. In recent years, digital signal processing technology based on the concept of signal sparse representation has become a focus of research in ultrasonic guided wave signal processing. And under the guided wave signal sparse representation framework, the guided wave signals are subjected to sparse decomposition under a certain overcomplete dictionary matrix to obtain effective information of the guided wave signals. Although the guided wave signal decomposition process is underdetermined, studies have shown that this digital signal processing method has unique advantages in certain applications, such as data compression and noise reduction. On one hand, the signal sparse representation method is more flexible in capturing data features, and only a small number of atoms from the over-complete dictionary need to be selected for characterization for a specific signal. Since each atom describes this data feature, the characterization results are very compact. On the other hand, compared with the conventional signal processing method, the guided wave signal sparse representation has a super-resolution characteristic, and meanwhile, the stability of a noise signal representation result is improved. At present, the signal sparse representation has made a certain progress in the aspect of ultrasonic guided wave signal processing, but has shortcomings in the aspects of dictionary matrix design and signal sparse decomposition algorithm, so that the advantages of guided wave signal sparse representation are not fully exploited. In addition, the application of the method in the aspect of damage positioning has further improved space.
Disclosure of Invention
The invention provides a two-stage damage position identification method based on guided wave signal sparse decomposition and damage positioning, and aims to solve the problem that a dictionary design method and a signal sparse decomposition algorithm existing in ultrasonic guided wave signal overlapped wave packet identification are not complete enough so that the result obtained by ultrasonic guided wave signal analysis is not accurate enough.
A two-stage damage position identification method based on guided wave signal sparse decomposition and damage positioning comprises the following two stages:
the first stage is as follows:
the method comprises the following steps: exciting in a waveguide to be detected to form ultrasonic guided wave signals with two modes, arranging a plurality of acquisition points on the waveguide to be detected, and acquiring the ultrasonic guided wave signals at each acquisition point;
step two: determining the distance propagated by the ultrasonic guided wave signal of each mode at each sampling time according to the sampling frequency of the ultrasonic guided wave signal;
step three: respectively predicting wave packet signals after the ultrasonic guided wave signal propagation distance x at each sampling moment by utilizing a guided wave propagation model considering modal transformation according to the distance obtained in the step two, enabling the predicted wave packet signals at all the sampling moments to jointly form a complete dictionary matrix, and carrying out 2-norm normalization processing on each column vector in the complete dictionary matrix;
step four: performing sparse decomposition on each ultrasonic guided wave signal acquired in the step one by using the complete dictionary matrix normalized by the norm of the step three 2 to obtain a coefficient vector of each ultrasonic guided wave signal, and solving posterior probability distribution of each coefficient vector under sparse constraint conditions by using a sparse Bayesian learning algorithm;
step five: respectively carrying out N times of multivariate Gaussian sampling on the mean value and the covariance of each posterior probability distribution obtained in the step four, taking the propagation distance corresponding to the maximum weight value in each sample as a propagation distance of the corresponding ultrasonic guided wave signal, obtaining N propagation distances for each ultrasonic guided wave signal, wherein N is a positive integer,
forming an ith propagation distance in all ultrasonic guided wave signals into a distance vector, wherein N distance vectors exist, and i is 1,2, … and N;
and a second stage:
step six: forming a dictionary matrix by using the distance from each estimated damage position on the surface of the waveguide to be detected to all acquisition points, and performing 2-norm normalization processing on each vector in the dictionary matrix;
step seven: and respectively carrying out sparse analysis on each distance vector obtained in the fifth step by using the dictionary matrix normalized by the 2 norm in the sixth step to obtain N coefficient vectors related to the estimated damage position, solving posterior probability distribution of each coefficient vector under the sparse constraint condition by using a sparse Bayesian learning algorithm, carrying out one-time multivariate Gaussian sampling on the mean value and covariance of each posterior probability distribution, taking the position coordinate corresponding to the maximum sample value in each sample as an estimated damage position coordinate, obtaining N estimated damage position coordinates in total, and taking the position of the estimated damage position coordinate with the highest repetition rate as the identified damage position.
The invention has the beneficial effects that:
1. because the shape of the noise is greatly different from the wave packet shape of the dictionary matrix atoms, in the sparse Bayesian learning process, the penalty term is utilized to make the coefficient vector as sparse as possible, and the possibility of matching the noise with the dictionary atoms is greatly reduced, so the invention can realize lossless denoising;
2. the invention designs the dictionary matrix by utilizing the propagation model of the guided wave, wherein the problems of frequency dispersion, multi-mode and mode conversion of the guided wave are considered, and the overlapped waveforms are identified in a linear decomposition mode, so that the method has more advantages compared with the conventional signal processing method;
3. the invention adopts a sparse optimization solution algorithm based on sparse Bayesian learning, has unique advantages in the aspect of processing sparse representation such underdetermined linear problems, and has better robustness to noise.
The invention is suitable for the guided wave detection of a transmitting-receiving method and a pulse echo method.
Drawings
Fig. 1 is a schematic structural diagram of an ultrasonic guided wave nondestructive testing system, wherein: 1. any signal generator, 2 signal shielding lines, 3 voltage amplifiers, 4 detected structures, 5 ultrasonic transducers, 6 damages, 7 oscilloscopes, 8 computers;
fig. 2 is a waveform diagram of an acquisition point received signal, wherein: A. all signals received; B. intercepting the signal for analysis;
FIG. 3 is a view at S0And A0A diagram of dictionary primitives at modal propagation distance, wherein: 1. excitation signal, 2.
3.
4.
5.
FIG. 4 is a diagram showing the results of key steps of wave packet identification;
FIG. 5 is a diagram illustrating dictionary element creation at a damaged location;
fig. 6 is a schematic diagram of the lesion localization results.
Detailed Description
According to the structure shown in fig. 1, the device is connected, and then the following damage position identification method is performed based on the device, specifically:
the first embodiment is as follows: specifically, the present embodiment is described with reference to fig. 2 to 6, and the two-stage lesion location identification method based on guided wave signal sparse decomposition and lesion localization according to the present embodiment includes the following two stages:
the first stage is as follows:
the method comprises the following steps: the ultrasonic transducer is excited in the waveguide to be detected to form a waveguide with S0And A0Setting M acquisition points on a to-be-detected waveguide and acquiring ultrasonic guided wave signals at each acquisition point by using a modal Lamb wave;
considering the mode transition at the lesion, there may be the following four Lamb wave packets on the path from the lesion to the acquisition point: directly propagated S0And A0Modality, by S0Converted into A0And from A0Is converted into S0And in the mode, the frequency dispersion effect of the Lamb waves is considered, and the waveform of the wave packet after being transmitted for any distance on the path can be calculated by adopting an ultrasonic guided wave transmission model.
Step two: determining the distance propagated by the ultrasonic guided wave signal of each mode at each sampling time according to the sampling frequency of the ultrasonic guided wave signal; the distance traveled by the ultrasonic guided wave signal includes S0And A0The distance of modal propagation, the distance expressions of two modal propagation are respectively:
wherein the content of the first and second substances,
and
are respectively S0And A0The distance of propagation of the mode shape,
and
are respectively S0And A0Group velocity of mode, fsFor sampling frequency, H is the length of the ultrasonic guided wave signal received at the acquisition point, H0Is the length of the excitation wave packet.
Step three: according to the distance obtained in the second step, respectively predicting the wave packet signals after the ultrasonic guided wave signal propagation distance x at each sampling time by utilizing a guided wave propagation model considering modal transformation, wherein the guided wave propagation model is as follows:
in the above equation, u (x, t) represents a wave packet signal at the sampling time t and the propagation distance x, F (ω) represents fourier transform of the excitation waveform, ω represents angular frequency, j represents an imaginary number,
and
respectively represent S0And A0The wave number of the mode shape is,
and
respectively represent S0And A0The distance of propagation of the ultrasonic guided wave signal of the mode,
using the wave packet waveform predicted at each sampling moment as a dictionary element, combining the wave packet signals predicted at all the sampling moments into a complete dictionary matrix, and performing 2-norm normalization processing on each column vector in the complete dictionary matrix, wherein the dimension of the complete dictionary matrix is Hx [ (H-H)0)×(H-H0)/2]。
Step four: performing sparse decomposition on each ultrasonic guided wave signal acquired in the step one by using the complete dictionary matrix normalized by the norm in the step three 2 to obtain a coefficient vector of each ultrasonic guided wave signal,
the expression for sparse decomposition is:
y＝Φc+ε
in the above formula, y is a decomposed signal, Φ is a complete dictionary matrix, c is a coefficient vector of each ultrasonic guided wave signal, and epsilon is a residual term;
and solving posterior probability distribution of each coefficient vector under the sparse constraint condition by using a sparse Bayesian learning algorithm.
Step five: respectively carrying out N times of multivariate Gaussian sampling on the mean value and the covariance of each posterior probability distribution obtained in the step four, taking the propagation distance corresponding to the maximum weight value in each sample as a propagation distance of the corresponding ultrasonic guided wave signal, obtaining N propagation distances for each ultrasonic guided wave signal, wherein N is a positive integer,
forming a distance vector by the ith propagation distance in all ultrasonic guided wave signals, wherein N distance vectors exist, and the ith distance vector is expressed as:
where i is 1,2, …, N.
And a second stage:
step six: s multiplied by T estimated damage positions are arranged on the surface of the waveguide to be detected and are arranged according to an S multiplied by T rectangular arrayS and T are positive integers, respectively, wherein the coordinates of the estimated lesion position are denoted as (m)s,nt)，s＝1,2,…,S，t＝1,2,…,T；
And forming a dictionary matrix by using the distance from each estimated damage position on the surface of the waveguide to be detected to all acquisition points, and carrying out 2-norm normalization processing on each vector in the dictionary matrix, wherein the dimension of the dictionary matrix is M x (S x T).
Step seven: respectively performing sparse analysis on each distance vector obtained in the fifth step by using the dictionary matrix subjected to 2-norm normalization in the sixth step to obtain N coefficient vectors related to the estimated damage position, wherein the expression of performing sparse analysis on the ith distance vector is as follows:
r(i)＝Dw+ε1
wherein D is a dictionary matrix, w is a coefficient vector for estimating the damage position, epsilon1Is an error;
the posterior probability distribution of each coefficient vector under the sparse constraint condition is solved by using a sparse Bayesian learning algorithm, the mean value and covariance of each posterior probability distribution are subjected to one-time multivariate Gaussian sampling, the position coordinate corresponding to the maximum sample value in each sample is used as an estimated damage position coordinate, N estimated damage position coordinates are obtained in total, and the position of the estimated damage position coordinate with the highest repetition rate is used as the identified damage position.
Claims (9)
1. A two-stage damage position identification method based on guided wave signal sparse decomposition and damage positioning is characterized by comprising the following two stages:
the first stage is as follows:
the method comprises the following steps: exciting in a waveguide to be detected to form ultrasonic guided wave signals with two modes, arranging a plurality of acquisition points on the waveguide to be detected, and acquiring the ultrasonic guided wave signals at each acquisition point;
step two: determining the distance propagated by the ultrasonic guided wave signal of each mode at each sampling time according to the sampling frequency of the ultrasonic guided wave signal;
step three: respectively predicting wave packet signals after the ultrasonic guided wave signal propagation distance x at each sampling moment by utilizing a guided wave propagation model considering modal transformation according to the distance obtained in the step two, enabling the predicted wave packet signals at all the sampling moments to jointly form a complete dictionary matrix, and carrying out 2-norm normalization processing on each column vector in the complete dictionary matrix;
step four: performing sparse decomposition on each ultrasonic guided wave signal acquired in the step one by using the complete dictionary matrix normalized by the norm of the step three 2 to obtain a coefficient vector of each ultrasonic guided wave signal, and solving posterior probability distribution of each coefficient vector under sparse constraint conditions by using a sparse Bayesian learning algorithm;
step five: respectively carrying out N times of multivariate Gaussian sampling on the mean value and the covariance of each posterior probability distribution obtained in the step four, taking the propagation distance corresponding to the maximum weight value in each sample as a propagation distance of the corresponding ultrasonic guided wave signal, obtaining N propagation distances for each ultrasonic guided wave signal, wherein N is a positive integer,
forming an ith propagation distance in all ultrasonic guided wave signals into a distance vector, wherein N distance vectors exist, and i is 1, 2.
And a second stage:
step six: forming a dictionary matrix by using the distance from each estimated damage position on the surface of the waveguide to be detected to all acquisition points, and performing 2-norm normalization processing on each column vector in the dictionary matrix;
step seven: and respectively carrying out sparse analysis on each distance vector obtained in the fifth step by using a dictionary matrix normalized by the 2 norm in the sixth step to obtain N coefficient vectors related to the estimated damage position, solving posterior probability distribution of each coefficient vector under a sparse constraint condition by using a sparse Bayesian learning algorithm, carrying out once multi-element Gaussian sampling on the mean value and covariance of each posterior probability distribution, taking the position coordinate corresponding to the maximum sample value in the once multi-element Gaussian sampling as an estimated damage position coordinate, obtaining N estimated damage position coordinates in total, and taking the position of the estimated damage position coordinate with the highest repetition rate as the identified damage position.
2. The method as claimed in claim 1, wherein the ultrasonic guided wave signal formed by excitation in the step one is S-shaped0And A0The guided wave propagation model in the third step of the modal Lamb wave is:
in the above equation, u (x, t) represents a wave packet signal at the sampling time t and the propagation distance x, F (ω) represents fourier transform of the excitation waveform, ω represents angular frequency, j represents an imaginary number,
and
respectively represent S0And A0The wave number of the mode shape is,
and
respectively represent S0And A0The distance of propagation of the ultrasonic guided wave signal of the mode,
3. the guided wave signal sparse decomposition and damage localization based two-stage damage position identification method according to claim 2, wherein in the second step, the distance traveled by the ultrasonic guided wave signal comprises S0And A0The distance of modal propagation, the distance expressions of two modal propagation are respectively:
wherein the content of the first and second substances,
and
are respectively S0And A0The distance of propagation of the mode shape,
and
are respectively S0And A0Group velocity of mode, fsFor the sampling frequency, H is the number of sampling points in the received signal, H0Is the length of the excitation wave packet.
4. The guided wave signal sparse decomposition and damage positioning-based two-stage damage position identification method according to claim 1,2 or 3, wherein the expression of the sparse decomposition in the fourth step is as follows:
y＝Φc+ε
in the above formula, y is the decomposed signal, Φ is the complete dictionary matrix, c is the coefficient vector of each ultrasonic guided wave signal, and ε is the residual term.
5. The guided wave signal sparse decomposition and damage localization-based two-stage damage position identification method of claim 3, wherein in the third step, after 2-norm normalization processing is performed on each column vector in the complete dictionary matrix, the dimension of the complete dictionary matrix is Hx [ (H-H)0)×(H-H0)/2]。
6. The guided wave signal sparse decomposition and damage localization based two-stage damage position identification method according to claim 3, wherein in the fifth step, the ith distance vector is represented as:
wherein M is the number of collection points on the waveguide to be detected.
7. The guided wave signal sparse decomposition and damage positioning-based two-stage damage position identification method according to claim 3, wherein in the sixth step, S x T estimated damage positions are arranged on the surface of the waveguide to be detected, the S x T estimated damage positions are arranged according to an S x T rectangular array, and S and T are positive integers respectively.
8. The guided wave signal sparse decomposition and damage localization based two-stage damage location identification method according to claim 7, wherein in the sixth step, after 2-norm normalization processing is performed on each column vector in the dictionary matrix, the dimension of the dictionary matrix is mx (sxt).
9. The guided wave signal sparse decomposition and damage localization-based two-stage damage position identification method according to claim 6, wherein the expression for sparse analysis of the ith distance vector is as follows:
r(i)＝Dw+ε1
wherein D is a dictionary matrix, w is a coefficient vector for estimating the damage position, epsilon1Is an error.
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