An Experimental Method for Measuring the Attenuation Coefficient of Broadband Laser Ultrasonic Lamb Waves in Metal Sheets

Abstract

The present invention discloses a method for actually measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in metal thin plates, belonging to the field of nondestructive testing. Data acquisition stage: Use a nanosecond laser to set a point source excitation on the surface of an aluminum alloy thin plate, and then use a scanning laser Doppler vibrometer (SLDV) to measure the wave field and collect linear wave field data. Data processing stage: Use the time-frequency analysis of continuous complex wavelet transform to obtain the time-frequency spectrum of the one-dimensional wave field signal. Determine the effective analysis range, including the time upper limit and the frequency upper limit. Extract the amplitude data represented by the intercept line. Attenuation characteristic analysis stage: Extract the peaks of the amplitude data at multiple distance points to obtain discrete points of the amplitude change with distance at a specific frequency. The present invention provides a method for actually measuring the attenuation characteristics of broadband laser ultrasonic Lamb waves. The solution of the attenuation coefficient provides an important theoretical reference for the calculation of the effective detection range and the selection of the filtering frequency of damage scattered waves.

Description

Technical Field

[0001] The present invention relates to nondestructive testing technology, and in particular to a method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal thin plate. Background Art

[0002] Laser ultrasonic Lamb waves enable long-distance, non-contact inspection of large plate and shell components, making them particularly suitable for on-site, online inspection of large equipment measuring several meters in diameter. Although laser ultrasonic Lamb wave damage detection technology has been extensively researched, the selection of some specific parameters in various damage imaging algorithms still relies on manual trial and error, and there is still insufficient theoretical support. This requires in-depth research on the propagation of laser ultrasonic Lamb waves in thin metal plates, including characteristics in the time domain, frequency domain, modal conversion, and attenuation. The attenuation characteristics of ultrasonic waves characterize how the energy of a sound wave changes with distance, specifically manifested as a decrease in wave packet amplitude with distance. Studying attenuation characteristics is particularly important for calculating the effective detection range. Analyzing the attenuation characteristics of different frequency components provides an important theoretical basis for selecting the scattered wave filter frequency. Traditional attenuation coefficient calculation methods, primarily for narrowband signals such as ultrasonic body waves, determine the total propagation path based on the time value and sound velocity of the back wave, and calculate the attenuation coefficient using a first-order exponential decay function that combines the path with the change in the back wave amplitude.

[0003] Ultrasonic Lamb waves exhibit dispersion and multimodal effects, manifesting as the width of the wave packet stretching with distance and the aliasing of multiple different wave packets. Ultrasonic Lamb waves excited by nanosecond pulsed lasers are typically broadband signals, exacerbating these dispersion effects. Traditional calculations of attenuation coefficients rely on extracting the arrival time, velocity, and amplitude of the wave packet. These factors necessitate the urgent need for new research methods and theories for evaluating the attenuation characteristics of ultrasonic Lamb waves. Summary of the invention

[0004] In order to provide theoretical support for parameter selection for ultrasonic Lamb wave damage detection technology, the main purpose of the present invention is to calculate the attenuation coefficient at different frequencies based on the actual measurement of laser ultrasonic Lamb waves.

[0005] In order to achieve the purpose of the present invention, the size of the 3 Taking an aluminum alloy sheet as an example, the present invention provides an attenuation coefficient extraction method based on laser ultrasonic Lamb wave line scanning data, comprising the following steps:

[0006] Step S1: After the laser excites an ultrasonic Lamb wave on the surface of the aluminum plate, a scanning laser Doppler vibrometer scans a line starting from the excitation point.

[0007] A nanosecond laser excites a point on the surface of an aluminum alloy sheet. Simultaneously, a synchronous externally triggered SLDV collects out-of-plane vibration displacement data. The excitation point is set as the starting point for the scan, and a total of N discrete points are scanned with a length of D to form a straight line.

[0008] Step S2: performing time-frequency analysis of the collected multiple one-dimensional wave field data using continuous complex wavelet transform to obtain corresponding time-frequency spectra.

[0009] Perform continuous complex wavelet transform (CWT) on the one-dimensional signal and project it onto the two-dimensional time-frequency spectrum. Set 10% of the time-frequency spectrum energy peak as the threshold, and set the area greater than the threshold as the frequency analysis range. At the same time, determine the time analysis range based on the energy distribution of the direct wave, and set the initial frequency, initial distance, and incremental interval.

[0010] Step S3: Set a single frequency, intercept the amplitude data within the direct wave distribution time period in the time-frequency spectrum, and extract the peak value; increase the distance, repeat the above steps, and obtain discrete data of the single frequency peak value changing with distance.

[0011] At a specific frequency, capture the data within the time range of the time spectrum, search for the peak, and save it. Next, perform distance increments and repeat the above steps until the maximum distance is reached. This will obtain the discrete points where the peak value of the frequency changes with distance.

[0012] Step S4: Increment the frequency and repeat step S3; obtain discrete data of how different frequency peaks change with distance; fit the discrete data using a second-order exponential decay function, and finally calculate the double attenuation coefficient of a specific frequency.

[0013] Step S5: Fit the discrete points using a second-order exponential decay function to obtain double attenuation coefficients at different frequencies. Use the coefficient of determination R2 to evaluate the quality of the fit, and select the fit result corresponding to the maximum value.

[0014] In the method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal plate, in step S2, the continuous complex wavelet transform is:

[0015]

[0016] Where t is time, ψ(t) * is the complex conjugate of the Gabor wavelet basis function, τ is the translation factor, and a is the scale factor. The expression of the Gabor wavelet basis function is:

[0017]

[0018] Among them, ω0 is the center frequency, γ is the aspect ratio, and i is the imaginary number. The continuous complex wavelet transform (CWT) decomposes the original time-domain signal into a series of wavelet transform coefficients through the inner product operation of the Gabor wavelet basis, constructing a time-frequency spectrum with good time and frequency domain localization. In the time-frequency spectrum, the horizontal and vertical coordinates represent time and frequency respectively, and the color represents the modulus value of the wavelet coefficient.

[0019] In the method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal plate, in steps S3 and S4, the data within the time range in the time-frequency spectrum is intercepted, the peak value is searched for and saved, and this process is carried out according to the following method:

[0020]

[0021] Among them, is the peak value collected at the distance x from the j-th acquisition point to the excitation point, Δt is the time period in which the direct wave is distributed, and f is the i-th single frequency under study. j

[0022] In the method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal plate, in step S3, the distance is incremented, and the above steps are repeated until the maximum distance. The discrete points of the peak value of this frequency changing with the distance are obtained, and this process is carried out according to the following method:

[0023]

[0024] The peak value data collected at N discrete distance points together form a one-dimensional matrix P.

[0025] In the method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal plate, in step S5, according to the linear least squares method criterion, taking the goodness of fit as the evaluation index of the fitting quality, the second-order exponential decay function is used to fit P, so as to obtain the double attenuation coefficients α1(f) and α2(f) at different frequencies f. Then, the second-order exponential decay function M(x, f) used for fitting is:

[0026]

[0027] Among them, x is the propagation distance, and a and b are the amplitude parameters respectively. The calculation method of the coefficient of determination R2 used to evaluate the fitting quality is:

[0028]

[0029] Among them, M(x i , f) represents the amplitude fitting function when the distance is x i and the frequency is f; ​is the average value of a one-dimensional matrix. The goodness of the model is judged according to the value of R2, and its value range is 0 to 1. The larger the R2, the better the fitting effect of the model. The α1(f) and α2(f) corresponding to the maximum R2 are selected as the double attenuation coefficients of the frequency f.

[0030] As can be seen from the above technical solutions, the present invention has the following beneficial effects:

[0031] (1) Since the traditional first-order exponential decay function has a large error in fitting the amplitude decay characteristic, it cannot characterize the difference in decay characteristics within different distances, nor can it simultaneously characterize the decay characteristics of high frequencies and low frequencies. Therefore, the proposed second-order exponential decay function can uniformly characterize the attenuation characteristics of ultrasonic Lamb waves within different propagation ranges and different frequency bands.

[0032] (2) The attenuation characteristics of broadband laser ultrasonic Lamb waves are obtained based on the measured laser ultrasonic Lamb wave line scan data in an aluminum plate, and this method can be extended to structures of other materials and sizes. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flowchart of a method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a metal plate;

[0034] Figure 2 is a schematic diagram of line scan wave field acquisition based on a laser ultrasonic detection system;

[0035] Figure 3 is a one-dimensional wave field signal collected at a distance of 9.4 cm from the excitation point and its corresponding continuous complex wavelet transform time-frequency spectrum;

[0036] Figure 4 is according to Figure 3 the amplitude data graph at different distances at 200 kHz intercepted by the intercept line;

[0037] Figure 5 is a fitting curve graph of multiple discrete peaks at 200 kHz by a second-order exponential decay function;

[0038] Figure 6 is a discrete point connection graph of double attenuation coefficients at different frequencies calculated according to the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] The following further describes the specific embodiments of the present invention in detail with reference to the attached Figures 1 to 5 drawings. The described embodiments are only used to explain the present invention and are not used to limit the scope of the present invention.

[0040] Refer to Figure 1, which is a flow chart of the method for measuring the attenuation coefficient of broadband Lamb waves in a metal plate using laser ultrasonic technology in this embodiment. The overall process includes data acquisition, initial value setting, time-frequency analysis, peak extraction, data fitting, fit evaluation, and attenuation coefficient calculation.

[0041] Reference Figure 2 , is a schematic diagram of line scanning wave field acquisition based on laser ultrasonic detection system. 3 Ultrasonic Lamb waves are excited by a laser point source in a thin-walled aluminum plate. The SLDV scans a line with a total length D of 25 cm, 85 discrete acquisition points N, and an acquisition interval of approximately 0.3 cm.

[0042] Reference Figure 3 , is the one-dimensional wave field signal collected at 9.4 cm from the excitation point and its corresponding continuous complex wavelet transform time-frequency spectrum. A one-dimensional wave field signal x(t) is stored at each collection point, and a continuous complex wavelet transform based on Gabor wavelet is performed on it:

[0043]

[0044] Where t is time, ψ(t) * is the complex conjugate of the Gabor wavelet basis function, τ is the translation factor, and a is the scale factor. The expression of Gabor wavelet is:

[0045]

[0046] Where ω0 is the center frequency, γ is the aspect ratio, and i is an imaginary number. In the time-frequency spectrum, the horizontal and vertical axes represent time and frequency respectively, and the colors represent the modulus of the wavelet coefficients. According to the distribution characteristics of the direct wave, the time upper limit of the effective analysis range is determined to be 3e -4 s. Take 10% of the peak value of the wavelet coefficient modulus as the threshold, and set the upper and lower limits of the frequency to f m =1MHz and f0=10kHz. The frequency increment interval Δf is 10kHz and 50kHz respectively.

[0047] Reference Figure 4 , in accordance with Figure 3 Amplitude data at different distances at 200kHz captured by the cut line. Figure 3 The horizontal line in the figure is the intercepted amplitude data, which can be expanded as follows: Figure 4 As shown. Extract amplitude data from the time-frequency spectrum collected at multiple distances to obtain multiple amplitude curves, search for peak values and save them:

[0048]

[0049] in, is the distance x from the jth acquisition point to the excitation point j The peak value collected at , Δt is the time period of direct wave distribution, f i is the i-th single frequency under study.

[0050] Reference Figure 5 As shown in FIG, it is a fitting curve diagram of multiple discrete peaks at 200kHz through a second-order exponential decay function. Figure 4 The principle shown is to set the displacement increment interval Δx to 1.47 cm and extract the peak value of the amplitude data of N = 17 discrete points. And form a one-dimensional matrix P:

[0051]

[0052] The one-dimensional matrix P consisting of discrete peak data is fitted using a second-order exponential decay function:

[0053]

[0054] The double attenuation coefficients α1(f) and α2(f) are obtained at different frequencies f. x is the propagation distance, and a and b are the amplitude parameters.

[0055] The coefficient of determination R2 used to evaluate the quality of the fit is calculated as:

[0056]

[0057] Among them, M(x i ,f) indicates the distance x i , the amplitude fitting value when the frequency is f; is the average value of the one-dimensional matrix. The quality of the model is judged by the value of R2, which ranges from 0 to 1. The larger the R2, the better the model fit. α1(f) and α2(f) corresponding to the maximum R2 are selected as the dual attenuation coefficients for frequency f. In this embodiment, the dual attenuation coefficients corresponding to 200 kHz are 39.4 Np / mm and 2.1 Np / mm, respectively, and the R2 value is 0.97.

[0058] Reference Figure 6 As shown, repeat the previous steps to calculate the double attenuation coefficients at different frequencies.

[0059] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for measuring the attenuation coefficient of broadband laser ultrasonic Lamb waves in a thin metal plate, characterized in that, It includes the following steps: Step A: After the laser excites ultrasonic Lamb waves on the surface of the aluminum plate, a line starting from the excitation point is scanned by a scanning laser Doppler vibrometer; Step B: Perform time-frequency analysis of continuous complex wavelet transform on the collected multiple one-dimensional wave field data to obtain the corresponding time-frequency spectra respectively; Step C: Set a single frequency, intercept the amplitude data within the direct wave distribution time period in the time-frequency spectrum, and extract the peak value; increment the distance and repeat the above steps to obtain the discrete data of the single frequency peak value varying with the distance; Step D: Increment the frequency and repeat Step C; obtain the discrete data of different frequency peak values varying with the distance; fit the discrete data with a second-order exponential decay function, and finally calculate the double attenuation coefficient of a specific frequency; Step E, according to the linear least squares criterion, taking the goodness of fit as the evaluation index for the quality of fitting, using the second-order exponential decay function to P perform fitting, thus obtaining the double decay coefficients f at different frequencies , then the second-order exponential decay function used for fitting is: ; Among them, x is the propagation distance, and a and b are amplitude parameters respectively; The coefficient of determination for evaluating the fitting quality is used to judge the goodness of the model according to the value of . Its value range is from 0 to 1. The larger the value, the better the fitting effect of the model. Select when it is the largest as the f double attenuation coefficient of the frequency.

2. The method according to claim 1, characterized in that, In Step B: Take 10% of the time-frequency spectrum energy peak value as the threshold, set the area greater than the threshold as the analysis range of the frequency, and at the same time, determine the analysis range of the time according to the distribution of the direct wave.

3. The method according to claim 1, wherein In Step C: The one-dimensional data intercepted in the time-frequency spectrum is the data intercepted within a certain period of the horizontal axis at a single frequency on the vertical axis of the time-frequency spectrum.

4. The method according to claim 1, wherein In step D: The coefficient of determination is used to evaluate the fitting quality, and the attenuation coefficient corresponding to its maximum value is selected as the optimal coefficient.

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