A high-precision measurement method for Lamb wave phase velocity dispersion curves based on clustering algorithms

Abstract

The present invention discloses a high-precision measurement method for Lamb wave phase velocity dispersion curves based on a clustering algorithm. This method is used to accurately obtain the phase velocity of Lamb waves through experimental means, laying a foundation for the subsequent application of Lamb waves. The frequency contained is obtained from the time of the signal wave peaks and valleys, and then the received signal is filtered using an adaptive band-pass filter to obtain a signal approximated to a single frequency. The time of wave propagation is obtained for the filtered signal using the cross-correlation algorithm, and the phase velocity is calculated therefrom. The corresponding frequencies and phase velocities are combined to obtain a frequency-velocity data set, and then the clustering algorithm is used to cluster the data set to obtain the clustering center points. Finally, the clustering center points are fitted to obtain the phase velocity dispersion curve. This method is simple, practical, and reliable, and an accurate dispersion curve is measured with fewer data points. This method has achieved good results in both isotropic and anisotropic plates, demonstrating the wide applicability of this method.

Description

Technical Field

[0001] The present invention relates to the field of sound velocity measurement, and particularly to a method for measuring the phase velocity dispersion curve of Lamb waves. Background Art

[0002] It has been proved that compared with conventional ultrasonic testing, Lamb waves have the advantages of slow energy attenuation, long propagation distance, sensitivity to hidden and complex damages in structures, high detection efficiency and accuracy, etc., and thus are widely used in non-destructive testing of plate structures and structural health monitoring. The main characteristics of Lamb waves include multimodal characteristics and dispersion characteristics. The dispersion characteristic refers to the phenomenon that the phase velocity and group velocity of guided waves change with the change of frequency. The multimodal characteristic means that in a plate-like structure, there are at least two guided wave modes at any frequency except for echoes caused by geometric structures such as edge reflections. Therefore, before detecting damages, it is necessary to select the excitation frequency and mode for Lamb waves. Thus, the dispersion curve with many modes, which reflects the corresponding relationship between velocity and frequency, is crucial for the signal analysis of Lamb waves and is a key factor affecting the detection accuracy and imaging resolution.

[0003] Generally, if the mechanical parameters and structural dimensions of a material are unknown, it is very difficult to obtain the dispersion curve of Lamb waves through theoretical calculation. For example, in today's industrial production and scientific research fields, composite materials are widely used due to their high strength, corrosion resistance, etc., but their elastic constants are not always known or exact. The reason is that: generally, the measurement of material elastic constants usually adopts the tensile test method, and standard specimens need to be prepared during detection, so the material to be detected needs to have good machining performance. However, composite materials are often not easy to process, so it is difficult to obtain exact elastic constants. In addition, due to the influence of environmental and operating conditions, the mechanical parameters obtained by theoretical solution may also differ from the actual values.

[0004] In addition to theoretical calculation, measurement experiments are also one of the key methods for obtaining the dispersion curve of Lamb waves. It obtains the dispersion curve by directly analyzing and calculating the Lamb wave signals received in the material to be measured. This method is not only convenient for obtaining a relatively accurate dispersion curve, but also can obtain mechanical parameters closer to the actual values than the theoretical calculation results through inversion. Therefore, the measurement of the dispersion curve is of great significance for the practical application of Lamb waves. Summary of the Invention

[0005] The present invention provides a high-precision method for measuring the phase velocity dispersion curve of Lamb waves based on a clustering algorithm. This method is simple, effective, and reliable, and can measure an accurate dispersion curve with fewer data points. The accuracy of this method has been verified on isotropic aluminum plates, and it has also been successfully applied to the measurement of the phase velocity of anisotropic CFRP plates.

[0006] The present invention is implemented through the following technical solutions:

[0007] Step 1: Excite a signal on the plate and receive the signal at a certain distance.

[0008] Step 2: Calculate the approximate frequency using the peak and trough times of the signal.

[0009] Step 3: Filter the received signal using an adaptive band-pass filter to obtain a signal that can be approximated as a single frequency.

[0010] Step 4: Use the cross-correlation algorithm on the single-frequency signal to obtain the exact time of wave propagation, from which the propagation speed, i.e., the phase velocity, can be calculated.

[0011] Step 5: Combine the corresponding frequencies and phase velocities to obtain a frequency-velocity dataset.

[0012] Step 6: Use the K-means++ algorithm to cluster the frequency-velocity dataset to obtain the cluster center points.

[0013] Step 7: Fit the cluster center points to obtain the phase velocity dispersion curve. Description of the Drawings

[0014] Figure 1 is a flowchart of the method involved in the present invention.

[0015] Figure 2 is a schematic diagram of the selection of time points.

[0016] Figure 3 is a schematic diagram of clustering.

[0017] Figure 4 is a diagram of the measurement results of the A0 mode in the aluminum plate.

[0018] Figure 5 is a diagram of the measurement results of the S0 mode in the aluminum plate.

[0019] Figure 6 is a diagram of the calculation results and fitting curves at a 90° braiding angle in the CFRP plate.

[0020] Figure 7 is a comparison diagram of the method of the present invention and the two-dimensional fast Fourier transform method in the CFRP plate.

[0021] Figure 8 is a dispersion curve diagram of the Lamb wave A0 mode corresponding to different braiding angles in the CFRP plate. Detailed Embodiments

[0022] The present invention will be further described in detail below in conjunction with the drawings. The present invention provides a high-precision measurement method for the phase velocity dispersion curve of Lamb waves based on a clustering algorithm. The present invention is implemented through the following technical solutions:

[0023] Step 1: Excite a signal on the board and receive the signal at a certain distance. Excite a vibration signal S(t) on the board. At a position r i away from the signal source, arrange a receiving array. Then the received signal can be expressed as:

[0024] R(t) = [R1(t), R2(t), R3(t)…R n (t)]

[0025] where 1, 2, …, n correspond to the received signals at different positions respectively. Each received signal can be written as:

[0026]

[0027] where S(ω) is the excited signal after Fourier transform, and c p (ω) is the phase velocity. It should be noted that since the cross - correlation method will be used to calculate the propagation time later, the distance between two adjacent receiving points should be as small as possible compared with the wavelengths corresponding to each frequency component.

[0028] Step 2: Calculate the approximate frequency using the peak - valley time of the signal. Record the peak - valley time in the wave packet of each received signal R i (t). The criterion for time - point extraction is that the amplitude is greater than 10% of the maximum amplitude. As Figure 2 shown, the time - points are denoted as t i,j , where i = 1, 2, 3…N represents the i - th position point, and j = 1, 2, 3…M represents the j - th time - point. The signal between two adjacent time - points t i,j and t i,j+1 is approximately a single - frequency signal, and its equivalent frequency is:

[0029]

[0030] where k = 1, 2, 3…m - 1 represents the k - th calculated frequency point. Different sampled signals correspond to different groups of frequency points.

[0031] Step 3: Filter the received signal using an adaptive band - pass filter to obtain a signal that can be approximated as a single frequency. Design a Butterworth band - pass filter B(f i,k ) with an adaptive frequency - response function for each received signal. The center frequency of this filter is f i,k , and the bandwidth is 0.1·f i,k . This adaptive band - pass filter is used to filter the received signals R i (t) and R i+1 (t) at two adjacent positions simultaneously. The filtered results are as follows:

[0032]

[0033] Among them, FT is the Fourier transform and IFT is the inverse Fourier transform.

[0034] Step Four: By using the filtered signal and perform cross-correlation calculation to obtain the delay time τ i,k . Then, at a given distance, the phase velocity can be calculated as:

[0035]

[0036] Step Five: The calculated velocity and frequency correspond to each other. Therefore, combining the calculated f i,k and c i,k together can obtain the frequency-velocity dataset D i,k = [f i,k , c i,k .

[0037] Step Six: Use the K-means++ algorithm to cluster the frequency-velocity dataset to obtain the cluster center points. Generally speaking, the generated dataset D is composed of points around the true value. Therefore, clustering two-dimensional data is beneficial to produce more accurate results. Using the improved K-means++ algorithm for the data in the frequency-velocity dataset D can improve the quality of the final solution of the original clustering algorithm.

[0038] First, the number K of cluster centers (cluster centroids) is set to half of the average value of the calculated number of frequency points. Select K initial cluster centers through the following three steps. The first step is to randomly select a sample from the dataset as the initial cluster center x, and calculate the shortest distance from each sample to the current cluster center, denoted as D(x j ). The second step is to define the probability that each sample is selected as the next cluster center as . Then, according to the calculated probability, use the roulette method to select the next cluster center. The third step is to repeat the previous steps until K cluster centers are selected.

[0039] Secondly, calculate the Euclidean distance from each remaining sample to each cluster center. As Figure 3 shown, each data point is assigned to the nearest center, so that each center has a set of data points:

[0040] label i,k = arg min||D i,k - P q ||

[0041] where q represents the elements of the q-th cluster.

[0042] Next, recalculate the positions of each cluster center so that each center moves closer to the overall centroid P of all points within the cluster. q Closer.

[0043]

[0044] N q represents the number of data points in the cluster. The data points are also reclassified according to the Euclidean distance.

[0045] Finally, perform iterative calculations until the cluster centers no longer change, and record the centroids O of all the final clusters f,v for their frequencies and velocities.

[0046] Step 7: Fit the centroid O f,v to obtain the phase velocity dispersion curve corresponding to the frequency.

[0047] The above method is verified with a specific example below. In this example, an isotropic aluminum plate and an anisotropic carbon fiber reinforced polymer plate (CFRP) will be used for illustration respectively. The specific process is as follows:

[0048] Firstly, experimental verification in the aluminum plate

[0049] Take the Lamb wave experiment in an aluminum plate of 600mm * 600mm * 1mm as an example. The parameters of the plate are: density (ρ = 2700 kg / m 3 ³), Young's modulus (E = 70 GPa), and Poisson's ratio (μ = 0.33). Based on these parameters, the theoretical phase velocity dispersion curve can be obtained through numerical calculation.

[0050] In the aluminum plate, the A0 and S0 mode Lamb waves are excited respectively. Through the above measurement and calculation methods, the experimental setup and experimental results of the aluminum plate are as follows:

[0051] For the A0 mode, chirp signals are excited on transducers with center frequencies of 100 kHz, 200 kHz, and 400 kHz respectively, and corresponding different sampling intervals are selected: 8 mm, 6 mm, and 4 mm (less than the minimum wavelength in each chirp signal of the A0 mode), and the number of sampling points is ten. The laser vibrometer is used to receive the signals. After calculation and processing, the Lamb wave phase velocity data set in the frequency band of 30 - 415 kHz and the corresponding cluster centers are obtained, and the dispersion curve of the A0 mode is fitted according to the cluster centers. The results are as Figure 4 shown. The relative errors and dispersion degrees of the data points in the three frequency bands are both small. The relative errors of each point are calculated at intervals of 10 kHz for the fitted curve, and the average relative error of the curve is 0.53%. The results prove that this method obtains a very accurate dispersion curve.

[0052] For the S0 mode, the signal is received by manually moving the receiving transducer. Chirp signals are excited on transducers with different center frequencies (0.5 MHz, 1 MHz, and 2 MHz), and an appropriate sampling interval and ten sampling points are also used. The calculated and processed results are as Figure 5 shown. Although the inaccurate distance measurement results in a more discrete data set, the clustering algorithm reduces this error, making the relative error of the fitted dispersion curve not exceed 1%. This proves that the method has high fault tolerance and result reliability.

[0053] Second, experimental verification in the CFRP plate

[0054] The plate structure to be measured is a carbon fiber reinforced polymer plate (CFRP) (600 mm * 600 mm * 1 mm). The material parameters of this plate are unavailable. The CFRP plate is an anisotropic material, and different weaving angles correspond to different velocities. Generally, a 0° weaving angle corresponds to the direction parallel to the weaving direction, and a 90° weaving angle corresponds to the direction perpendicular to the weaving direction. Similar to the aluminum plate experiment, a chirp signal is excited on a transducer with a center frequency of 200 kHz, and a sampling interval of 4 mm and ten sampling points are used. The calculated results and the fitted curve at a 90° weaving angle are as Figure 6 shown. Then, this method is compared with the two-dimensional fast Fourier transform method (2D-FFT) in the frequency-wavenumber domain, and it is found that the results of the two methods are basically the same (as Figure 7 , the figure shows the calculation results of the 2D-FFT method). The 2D-FFT method requires 150 sampling points with an interval of 1 mm, but the method proposed in the present invention only requires 10 sampling points with an interval of 4 mm. This proves that under similar results, the method proposed in the present invention requires fewer sampling points.

[0055] Finally, three transducers with center frequencies of 100 kHz, 200 kHz, and 400 kHz are used to measure the CFRP plates with weaving angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90°. All the data are processed to obtain the dispersion curves of the Lamb wave A0 mode corresponding to different weaving angles in the CFRP plate (as Figure 8 ), and the results prove that this method is applicable to the measurement of the dispersion curves of anisotropic materials.

[0056] In summary, the method proposed in the present invention is simple, effective, and reliable, requires fewer data points for calculation, has a shorter required measurement distance, has a higher accuracy and stability of the calculation results.

Claims

1. A high-precision Lamb wave phase velocity dispersion curve measurement method based on a clustering algorithm, characterized in that, Including the following steps: Step 1, exciting a signal on the board and receiving the signal at a certain distance; Step 2, calculating an approximate frequency by using the peak and trough times of the received signal; Step 3, filtering the received signal by using an adaptive band-pass filter to obtain a signal approximated to a single frequency; Step 4, obtaining the accurate time of wave propagation by using the cross-correlation algorithm for the single-frequency signal, and calculating the propagation speed, i.e., the phase velocity, therefrom; Step 5, combining the corresponding frequency and phase velocity to obtain a frequency-velocity data set; Step 6, clustering the frequency-velocity data set by using the K-means++ algorithm to obtain cluster center points; Step 7, fitting the cluster center points to obtain a phase velocity dispersion curve; In Step 2, the approximate frequency is calculated by using the peak and trough times of the signal; wherein the extraction criterion for the peak and trough time points in the wave packet of each received signal is: the amplitude is greater than 10% of the maximum amplitude; In Step 2, the calculation method of the approximate frequency is as follows: Denote the time point as t i,j , where i = 1, 2, 3... N represents the i-th position point, and j = 1, 2, 3... M represents the j-th time point; if the signal between two adjacent time points t i,j is approximately a single-frequency signal, then its approximate frequency is: i,j+1 ​ 2. The high-precision Lamb wave phase velocity dispersion curve measurement method based on a clustering algorithm according to claim 1, characterized in that In step 3, the received signal is filtered using an adaptive band-pass filter, which is a Butterworth band-pass filter B(f i,k ) with an adaptive frequency response function. Its center frequency is f i,k , and the bandwidth is 0.1·f i,k .

3. A high-precision Lamb wave phase velocity dispersion curve measurement method based on a clustering algorithm according to claim 1, characterized in that In step 4, the cross-correlation algorithm is used to calculate the delay time τ for the filtered signal i,k ; then the phase velocity is calculated at a given distance.

4. A high-precision Lamb wave phase velocity dispersion curve measurement method based on a clustering algorithm according to claim 1, characterized in that, In Step 6, the Kmeans++ algorithm is used to cluster the frequency-velocity data set; the frequency-velocity data set is clustered to obtain cluster center points; the number K of the cluster center points is set to be half of the average value of the calculated number of frequency points.

5. A high-precision Lamb wave phase velocity dispersion curve measurement method based on a clustering algorithm according to claim 1, characterized in that In Step 7, the center points obtained by clustering in Step 6 are used to fit the dispersion curve.

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