A method for measuring damage thickness of composite material based on terahertz time-domain compensation

Abstract

The present application relates to the field of composite material nondestructive testing, in particular to a composite material damage thickness measurement method based on terahertz time domain compensation, which comprises the following steps: S1, preparing a plurality of composite material laminate samples with variable damage thickness and depth, and obtaining terahertz time domain signals of different samples; S2, establishing a theoretical transmission model of a multilayer composite material structure, and defining a reflected terahertz response signal; S3, based on the response characteristics of terahertz waves and the transmission model, proposing a damage thickness measurement idea based on the time-of-flight difference between the damage and non-damage areas; S4, estimating the time-of-flight information of the composite material damage by using terahertz signal reference transformation, alignment and cross-correlation method; S5, establishing a terahertz signal time-of-flight compensation model to realize accurate estimation of the damage thickness. The present application simplifies the time-of-flight of the damage into the transmission time difference of the terahertz wave through the damage and non-damage areas, which can theoretically avoid the influence of human intervention and complex interference.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nondestructive testing of composite materials, and particularly relates to a composite material damage thickness measurement method based on terahertz time domain compensation. BACKGROUND

[0002] Due to the complexity of the service environment and the multi-layer structure of the composite material, the failure mode of the composite material interface damage may occur, which will significantly affect the mechanical properties, therefore, early detection and accurate characterization of damage parameters are crucial for the use of composite materials. Terahertz nondestructive testing technology has great potential in nondestructive testing technology due to its excellent performance, and has been successfully applied in the field of nondestructive evaluation of composite materials.

[0003] In the process of terahertz testing, due to the dielectric discontinuity of depth, the reflected terahertz signal is defined as the superimposed echo from various interfaces in the sample. Generally, the time of flight of the damage is extracted by the time delay between the continuous damage echoes. However, due to the fact that the terahertz signal is easily affected by complex interference such as dispersion, multiple reflections and noise, the performance of time of flight estimation may be reduced in these cases.

[0004] For larger damage thickness, the terahertz wave dispersion caused by the increase of transmission distance will cause the pulse broadening of the damage echo. At the same time, signal attenuation may cause the signal-to-noise ratio of the damage echo from the deeper interface to decrease. These factors make it a major challenge to accurately estimate the time of flight of the damage in complex terahertz signals. Traditional time of flight estimation methods can improve the time of flight estimation performance of complex terahertz signals with signal processing methods, such as wavelet transform, which can analyze both high-frequency fine features and low-frequency features of the signal, and can well suppress noise in the terahertz signal and obtain the reconstructed terahertz signal, but it may fail for complex terahertz signals affected by multiple reflections and overlap. As deconvolution techniques, the terahertz testing process is modeled as a linear time-invariant system, and the reconstructed impulse response may exhibit significant ringing artifacts due to the influence of system and environmental noise. As frequency wavelet domain deconvolution and sparse representation improve deconvolution performance, it can reduce the influence of multiple reflections and effectively solve the problems of terahertz signal dispersion and overlap. But the best performance is usually obtained by optimizing the hyperparameters using manual selection or complex optimization techniques, which is not suitable for processing a large number of terahertz signals and processing complex multi-layer structures or signals with extremely serious overlap and low signal-to-noise ratio. SUMMARY

[0005] The present application aims to solve the problem that the terahertz signal is easily affected by complex conditions and the performance of time domain estimation may be reduced in the background art, and proposes a composite material damage thickness measurement method based on terahertz time domain compensation.

[0006] The technical scheme of the present application: a composite material damage thickness measurement method based on terahertz time domain compensation, comprising the following steps:

[0007] S1, a plurality of composite material laminate samples with variable damage thickness and depth are prepared, and different sample terahertz time domain signals are obtained based on a terahertz time domain spectroscopy system;

[0008] S2, analyze the influence of lifting distance and sample surface uniformity on the terahertz signal, establish a complex multilayer composite material structure theoretical transmission model, and define the reflected terahertz response signal; the lifting distance refers to the distance between the terahertz transmitter and the sample surface;

[0009] S3, based on the response characteristics and transmission model of terahertz waves, a composite material damage thickness measurement idea based on the time of flight difference between damaged and undamaged areas is proposed;

[0010] S4, use terahertz signal reference transformation, alignment, and cross-correlation method to estimate the time of flight information of the composite material damage;

[0011] S5, considering the influence of lifting distance and sample surface uniformity, a terahertz signal time of flight compensation model is established to realize accurate estimation of the composite material damage thickness.

[0012] Preferably, in S1, the terahertz time domain spectroscopy system includes a terahertz source, a control unit, a transmitter, a receiver, and a motion platform, the motion direction of the motion platform includes X and Y directions, the motion platform obtains 2D information from the sample, the transmitter and the receiver are integrated and installed on the motion platform, and the transmitter and the receiver are responsible for transmitting and receiving terahertz signals; the terahertz source includes a femtosecond laser for generating terahertz pulses.

[0013] Preferably, in S1, six 20mmx20mmx2mm composite material laminates with different damage thicknesses are prepared using 3D printing technology, each sample contains 10 layers, the layer thickness is set to 200um, and glass fiber reinforced polymer is used as the printing material; in the damage sample preparation, the test sample is divided into undamaged area and damaged area, a certain thickness of air gap is preset to simulate damage, the damage size is 10mmx10mm, the damage thickness is variable, and is respectively 100um, 200um, 400um, 600um, 800um and 1000um.

[0014] Preferably, in S1, 6 composite laminate samples with a size of 20mmx20mmx1.6mm and different damage depths are prepared, each sample contains 8 layers, each layer is set to a thickness of 200um, adjacent layers are stacked in turn by glass fiber reinforced polymer and polylactic acid printing material, the test sample is divided into an undamaged area and a damaged area, a certain thickness of air gap is preset to simulate damage, the damage size of the damage area is set to 10mmx10mmx0.2mm, the damage depth is set to 200um, 400um, 600um, 800um, 1000um and 1200um, and the damage thickness remains unchanged.

[0015] Preferably, in S2, the reflected terahertz response signal is defined as:

[0016]

[0017] wherein, is the reflected terahertz echo, is the system impulse response function, and represent the number of laminate interface reflectors and the number of damage interface reflectors, respectively, and represent the model parameters corresponding to the th interface reflector and the th damage reflector, respectively, is the Gaussian white noise, is the overall model parameter change of the terahertz signal caused by the lifting distance and surface uniformity change.

[0018] Preferably, in S3, the damage thickness measurement method can be defined as:

[0019]

[0020] wherein is the damage thickness. is the refractive index of air. is the transmission time of the terahertz wave through the thickness of damage. is the refractive index of the sample. is the transmission time of the terahertz wave through the thickness of sample. is the time-of-flight difference, which refers to the transmission time difference of the terahertz wave through the thickness of damage and the thickness of sample, and c is the speed of light.

[0021] Preferably, in S4, the signal reference transform refers to using the terahertz response signal from the same sample non-damaged area as the terahertz reference signal extracted by time of flight of the damaged area, and the signal alignment is to use the unit impulse response function with time shift as the alignment function, move the terahertz damaged signal in the time domain, and accurately align the first pulse of the terahertz reference signal and the damaged signal. The aligned terahertz damaged signal is defined as:

[0022]

[0023] wherein, is the aligned terahertz damaged signal, is a convolution operation, is a time shift value of the terahertz damaged signal, which can be obtained by the time delay corresponding to the first pulse of the terahertz reference signal and the damaged signal.

[0024] Preferably, since the first pulses of the terahertz reference signal and the damaged signal are aligned, the transmission time difference of the terahertz wave can be defined by the time delay difference of the last pulse of the two aligned terahertz signals. The time delay difference of the two signals is determined by the cross-correlation method, specifically: the aligned terahertz signal is subjected to moving average filtering for noise reduction of the terahertz signal. Secondly, the last pulse of the terahertz reference signal and the damaged signal is truncated into new signal vectors and respectively, and the truncation interval can be determined by the signal time domain window, and the cross-correlation coefficient between and is:

[0025]

[0026] wherein, , . is the truncation interval of the signal, and further, the initial damage thickness can be obtained according to the obtained cross-correlation coefficient:

[0027]

[0028] wherein, is the maximum value of the cross-correlation coefficient R and its index, is the length of the signal, is the sampling frequency of the terahertz signal, is the time of flight.

[0029] Preferably, in S5, the positioning parameter : the difference between the transmission distances of the sampling point and the reference point, when When the transmission distance increases, the time delay of the first pulse of the obtained terahertz damage signal is less than the time delay from the reference point, and the transmission time difference between the terahertz reference signal and the damage signal is defined as:

[0030]

[0031] wherein, is the transmission time difference due to the change of the transmission distance of the sampling point and the reference point, is the transmission time difference due to the change of the transmission distance . , is the compensated damage time of flight, is the sample refractive index; when the transmission distance decreases, the time delay of the first pulse of the obtained terahertz damage signal is greater than the time delay from the reference point, and the overall transmission time difference is defined as:

[0032]

[0033] wherein, is the transmission time difference due to the change of the transmission distance of the sampling point and the reference point.

[0034] Preferably, considering the uniformity of the sample surface, the damage thickness is accurately obtained by time of flight compensation, and the overall calculation mode is as follows:

[0035] .

[0036] Compared with the prior art, the present application has the following beneficial technical effects: the time of flight of the damage is simplified as the transmission time difference between the damage area and the non-damage area. In order to better obtain the time of flight of the damage, a time of flight compensation model is established, which considers the influence of the lifting distance of the sample and the uniformity of the surface. In this case, a series of numerical and experimental results, including different damage thicknesses and depths, show the effectiveness of the proposed method for damage thickness estimation. These results highlight the robustness of the method to complex interference and external environment in the terahertz testing process, and can effectively improve the accuracy of damage thickness estimation in different scenarios. Compared with other classic time of flight extraction methods, the proposed method does not require any prior knowledge of the damage and can obtain better damage thickness estimation performance. In future work, since the proposed method is very sensitive to the transmission time difference through the sample, it can not only be used to accurately estimate the damage thickness inside the composite material, but also has great potential to be extended to various thickness estimation fields, such as additive manufacturing, damage formation (TGO in thermal barrier coatings), material wear, etc. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 for the overall flowchart of the present application;

[0038] Figure 2 for the working principle of the experimental equipment of the present application;

[0039] Figure 3 for the illustration of the lifting distance and surface uniformity of the sample of the present application;

[0040] Figure 4 for the sample prepared under different damage thicknesses of the present application;

[0041] Figure 5 for the illustration of the terahertz reference and damage signals obtained under different damage thicknesses of the present application;

[0042] Figure 6 for the damage thickness estimation results under different damage thicknesses of the present application;

[0043] Figure 7 for the sample prepared under different damage depths of the present application;

[0044] Figure 8 for the illustration of the terahertz reference and damage signals obtained under different damage depths of the present application;

[0045] Figure 9 for the damage thickness estimation results under different damage depths of the present application;

[0046] Figure 10 for the influence of the surface uniformity of the sample of the present application on the measured terahertz signals. DETAILED DESCRIPTION

[0047] Example 1, as shown in the present application, a composite material damage thickness measurement method based on terahertz time domain compensation is proposed, which includes the following steps: Figure 1

[0048] S1, prepare a plurality of composite material laminates with variable damage thickness and depth, and obtain terahertz time domain signals of different samples based on a terahertz time domain spectroscopy system;

[0049] S2, analyze the influence of lifting distance and sample surface uniformity on terahertz signals, establish a theoretical transmission model of complex multilayer composite material structure, define the reflected terahertz response signal, and the lifting distance refers to the distance between the terahertz emitter and the sample surface;

[0050] S3, based on the response characteristics and transmission model of terahertz waves, a composite material damage thickness measurement idea based on the time of flight difference between damage and non-damage areas is proposed;

[0051] ​S4, estimating the composite material damage time-of-flight information by using the terahertz signal reference transform, alignment and cross-correlation method;

[0052] S5, considering the influence of the lifting distance and the sample surface uniformity, establishing a terahertz signal time-of-flight compensation model to realize the accurate estimation of the composite material damage thickness.

[0053] In the second embodiment, the present application proposes a composite material damage thickness measurement method based on terahertz time domain compensation. Compared with the first embodiment, the present embodiment details S1.

[0054] As shown in Figure 2 The integrated terahertz time domain spectroscopy system is used to obtain the terahertz signal of the sample. The effective frequency range of the system is from 10GHz to 4.5THz. In order to obtain better depth resolution, the reflection mode is used. The terahertz time domain spectroscopy system is composed of a terahertz source, a control unit, an integrated transmitter and an x-y motion platform. Among them, the terahertz source containing femtosecond laser is used to generate terahertz pulse; the integrated transmitter and receiver are responsible for transmitting and receiving terahertz signal, and are installed on the x-y motion platform; the x-y motion platform obtains 2D information from the sample. In the working process of the terahertz time domain spectroscopy system, the femtosecond laser is first used to generate pump pulse and probe pulse through beam splitter. The pump pulse is used to stimulate the terahertz pulse through the photoconductive antenna, and the probe pulse is used as the coherent femtosecond pulse to detect the terahertz signal reflected by the terahertz receiver. In addition, the optical delay line is used to adjust the time delay of the terahertz signal, the x-y motion platform performs grating scanning, and the full-field terahertz signal of the sample is collected.

[0055] For the actual terahertz test process, the terahertz transmitter is first focused on the polished metal plate to obtain the reference signal. Then, the test sample is placed horizontally on the metal plate. By adjusting the focusing position of the terahertz transmitter, the refocusing process is performed on the test sample. Finally, the terahertz test process is performed by moving the x-y scanning platform through appropriate steps, and the terahertz signal from all sampling points of the sample is collected.

[0056] As shown in Figures 4-5As shown, further, first, the samples to be tested with different damage thicknesses were prepared, and the corresponding terahertz response signals were obtained by the terahertz time-domain spectroscopy system. In order to obtain different terahertz damage signals from different damage thicknesses, six composite laminate samples with different damage thicknesses of 20mmx20mmx2mm were prepared using 3D printing technology. Each sample contains 10 layers, and the layer thickness is set to 200um. Glass fiber reinforced polymer is used as the printing material, and the corresponding refractive index is calibrated to about 1.65. In the preparation of the damaged sample, a certain thickness of air gap is preset to simulate the damage, and the damage size is 10mmx10mm, and the damage thickness is variable, which is 100um, 200um, 400um, 600um, 800um and 1000um. In order to increase the complexity of the terahertz signal, the damage is placed at the bottom of the sample, as Figure 4 shown. Then, the terahertz damage signals from different samples were collected by the terahertz time-domain spectroscopy system. For each test sample, five different terahertz damage signals were obtained from five sampling points in the damage area, and the corresponding non-damage terahertz signal was obtained from the non-damage area of the sample, and the non-damage terahertz signal was used as the comparison signal. Figure 5 The obtained terahertz signals of different samples are shown, it can be found that under different damage thicknesses, the terahertz damage signal and the non-damage signal are similar, and both signals have a zero point shift. The difference is that the time delay of the first pulse of the two signals is different, which is caused by the surface unevenness of the sample. In addition, since the damage occurs at the bottom of the sample, the damage echo component from the lower interface of the damage corresponds to the last pulse in the terahertz signal. When the damage thickness is small, the damage echo component from the upper interface of the damage is submerged in the terahertz signal, increasing the difficulty of damage thickness estimation. With the increase of damage thickness, the damage echo component becomes more obvious, and the time delay of the last pulse between the terahertz damage and non-damage signals gradually increases.

[0057] As shown in Figures 7-8 further, similar to the preparation of test samples with various damage thicknesses, six composite laminate samples with different damage depths of 20mmx20mmx1.6mm were prepared. Each sample contains 8 layers, and the thickness of each layer is set to 200um. The adjacent layers are stacked in turn by glass fiber reinforced polymer and polylactic acid printing materials. The average refractive index of the test sample is about 1.9. As Figure 7As shown, the test sample is divided into an undamaged region and a damaged region, the damage size of the damaged region is set to 10mmx10mmx0.2mm, the damage depth is set to 200um, 400um, 600um, 800um, 1000um and 1200um, and the damage thickness remains unchanged. For each sample, five different sampling points are selected in the damaged region for better evaluation. For the test sample with different damage depths, the measured terahertz damage signals and non-damage signals are as shown in Figure 8 As shown, it can be found that the first pulse of the terahertz signal still has a zero offset and a time delay difference. For terahertz damage signals from different damage depths, the damage echo components overlap, and the corresponding time delay gradually increases with the increase of the damage depth. When the damage depth exceeds 800um, due to the increase of the terahertz wave transmission distance, the dissipation and absorption effect is enhanced, and the damage echo component is submerged in the terahertz signal. This phenomenon is due to the dissipation and absorption effect of the terahertz wave with the increase of the transmission distance, as shown in Figure 8 (f) shown.

[0058] As shown in Figure 9 , the estimated results of the damage thickness under different damage depths are shown. For each sample with a fixed damage depth, 5 tests are performed on 5 different sampling points respectively. Figure 9 (a)-(e) are the estimated damage thickness values of 5 sampling points under different damage depths. It can be seen that the estimated damage thickness values of different sampling points are very close to the true values. In addition, as the damage depth increases, the estimation error does not increase significantly, and for sampling point 5, the worst estimation error is 7.33% when the damage depth is 800um. In addition, Figure 9 (f) shows the average estimation error of 5 different sampling points under different damage depths. The maximum average estimation error is 5.05% for a damage depth of 600um, which further demonstrates the effectiveness of the proposed method in damage estimation performance under different damage depths.

[0059] In Example Three, the present application proposes a composite material damage thickness measurement method based on terahertz time domain compensation. Compared with Example Two, this embodiment details S2.

[0060] As shown in Figure 3 , in terahertz detection, the lifting distance and the sample surface uniformity are two key factors affecting the transmission characteristics of terahertz waves. The lifting distance refers to the distance between the terahertz emitter and the sample surface, which is determined by the focal length of the terahertz lens and the test requirements. The sample surface uniformity refers to the irregularity or fluctuation of the sample surface, which is related to the roughness and surface damage of the sample.

[0061] In terahertz testing, it is usually assumed that the lift-off distance of the terahertz reference signal obtained from a polished metal plate is the same as that of the reflected terahertz response signal obtained from a sample, but it is not the same in actual testing. Due to the error of manual operation, the focusing position of the terahertz transmitter will change, thereby causing the change of the terahertz response signal in the time domain. For all sampling points in a given sample, the reflected terahertz response signal is defined as:

[0062] (1)

[0063] wherein, is the reflected terahertz echo, is the impulse response function in the case of the change of the lift-off distance, and respectively represent the number of laminated board interface reflectors and the number of damage interface reflectors, and respectively represent the model parameters corresponding to the th interface reflector and the th damage reflector, is the Gaussian white noise, is the change of the model parameters caused by the change of the lift-off distance. In particular, in the same measurement, the of all sampling points are the same.

[0064] In addition, the surface uniformity of the sample will also affect the reflected terahertz response signal. For different sampling points in the sample to be tested, the corresponding terahertz signal will change with the change of the surface uniformity. For a sampling point in a given test sample, the corresponding reflected terahertz response signal is represented as:

[0065] (2)

[0066] wherein, is the reflected terahertz echo, is the impulse response function caused by the change of the surface uniformity of the sampling point, and respectively represent the number of laminated board interface reflectors and the number of damage interface reflectors, and respectively represent the model parameters corresponding to the th interface reflector and the th damage reflector, is the Gaussian white noise, is the change of the model parameters caused by the change of the surface uniformity of the sampling point. Generally, for different sampling points, it may be different due to the change of the surface uniformity of the sample.

[0067] Finally, the reflected terahertz response signal of the sampling point can be defined as:

[0068] (3)

[0069] where, is the reflected terahertz echo, is the system impulse response function, and respectively represent the number of laminated board interface reflectors and the number of damage interface reflectors, and respectively represent the model parameters corresponding to the first interface reflector and the first damage reflector, is the Gaussian white noise, is the overall model parameter change of the terahertz signal caused by the lifting distance and the surface uniformity change.

[0070] In example four, the present application proposes a composite material damage thickness measurement method based on terahertz time domain compensation. Compared with example three, this embodiment details S3.

[0071] Traditional terahertz damage thickness measurement methods mainly rely on accurately extracting the time of flight of the damage from the terahertz response signal. However, terahertz waves are easily affected by complex interference during propagation, such as dispersion, overlap, multiple reflections, noise, etc. These interferences will cause the damage echo components in the terahertz signal to overlap. Although some traditional terahertz damage thickness measurement methods have tried to solve this problem, they often need to manually select hyperparameters, and their performance is limited by artificial experience and prior knowledge. Generally, these hyperparameters are very sensitive to changes in terahertz signals, and for terahertz signals from different sampling points, they need to be manually adjusted to obtain optimal performance, which is very time-consuming for samples with a large number of sampling signals. Therefore, a new damage thickness measurement method based on the time of flight difference between damage and non-damage areas is proposed. Specifically, based on the transmission characteristics of terahertz waves in the sample, for a composite layer sample without damage, the transmission time of the terahertz wave through the sample can be defined as the time delay difference between the first pulse (from the upper interface of the sample) and the last pulse (from the lower interface of the sample) of the terahertz response signal. When damage occurs inside the sample, the transmission time of the terahertz wave through the sample will change. The difference in terahertz wave transmission time between the undamaged area and the damaged area is directly related to the damage thickness. In particular, since the energy of the terahertz signal is mainly concentrated in the first and last pulses, while other pulse echoes, including those from the damage, exhibit lower amplitudes, this is due to the high reflectivity of terahertz waves at the upper and lower interfaces of the sample. In this work, the damage thickness is estimated by analyzing the transmission time difference between the undamaged area and the damaged area. Ideally, assuming sample surface uniformity and no changes in test parameters, the proposed damage thickness measurement method can be defined as:

[0072] (4)

[0073] where is the damage thickness. is the refractive index of air. is the transmission time of the terahertz wave through a damage with thickness . is the refractive index of the sample. is the transmission time of the terahertz wave through a sample with thickness . is the time of flight difference, which refers to the transmission time difference of the terahertz wave through a damage with thickness and a sample with thickness , and c is the speed of light.

[0074] As shown in Figure 6 , the damage thickness estimation results under different damage thicknesses. Based on the proposed method, damage thickness estimation was performed, and the estimated damage thicknesses of 5 different sampling points under different damage thicknesses were obtained, as shown inFigure 6 The estimated damage thickness values of different sampling points are very close to the true values as shown in (a)-(e). In addition, the estimation error tends to decrease with the increase of damage thickness, and for sampling point 3, the estimation performance is the worst when the damage thickness is 200 um, the estimated damage thickness is 215.69 um, and the error is as high as 7.84%. Figure 6 (f) shows the average estimation error of 5 different sampling points at different damage thicknesses, and the results show that the average estimation error is less than 5% at all damage thicknesses, which proves the effectiveness of the proposed method in damage thickness estimation at different damage thicknesses.

[0075] In example five, the present application proposes a composite damage thickness measurement method based on terahertz time domain compensation. Compared with example four, this embodiment introduces S4 in detail.

[0076] First, in order to suppress the influence of lifting distance on thickness estimation performance, signal reference transformation is completed. Generally, the terahertz reference signal is obtained by collecting the reflection echo of the metal plate. The conventional thickness estimation method uses this reference signal as the basis for damage time of flight extraction. However, in the terahertz test, the change of lifting distance may cause differences between the reference signal and the sample signal. In this case, the reference signal may not be the best choice for accurately extracting the damage thickness. In order to solve this problem, in the proposed damage thickness measurement method, the terahertz response signal from the non-damage area of the same sample is used as the terahertz reference signal for damage time of flight extraction. In particular, the transformed terahertz reference signal and the terahertz damage signal from the damage area exhibit similar characteristics and change with the change of lifting distance. Therefore, signal reference transformation not only reduces the influence of lifting distance change on thickness estimation performance, but also compensates for the fluctuations or parameter changes of the test environment during the terahertz test.

[0077] Secondly, after completing the signal reference transformation, in order to improve the accuracy of damage thickness measurement, the signal alignment and cross-correlation time of flight extraction process is completed for preliminary estimation of the time of flight of the damage. This method aims to automatically determine the time delay difference between the terahertz reference signal and the damage signal. Initially, the detrend function is used to solve the problem of zero drift occurring in the terahertz test system. Due to the influence of surface uniformity, the first pulse of the terahertz reference signal and the damage signal will appear time shift, which will reduce the accuracy of time of flight estimation. Therefore, the signal alignment operation is completed. Specifically, the unit impulse response function of time shift is used as the alignment function, and the terahertz damage signal is moved in time domain to accurately align the first pulses of the terahertz reference signal and the damage signal.

[0078] (5)

[0079] wherein, are aligned terahertz damage signals, is a convolution operation, is a time shift value of the terahertz damage signal, which can be obtained by the time delay corresponding to the first pulse of the terahertz reference signal and the damage signal.

[0080] Then, after completing the signal alignment, the initial time-of-flight estimation of the damage is realized by calculating the transmission time difference between the terahertz damage signal and the reference signal. In this case, since the first pulses of the terahertz reference signal and the damage signal are aligned, the transmission time difference of the terahertz wave can be defined by the time delay difference of the last pulse of the two aligned terahertz signals. In order to solve the time delay difference of the terahertz signal, the cross-correlation method, as a signal similarity measurement tool, can determine the time delay difference of the two signals by calculating the correlation coefficient, which provides great potential for damage time-of-flight estimation. Specifically, first, the moving average filtering is performed on the aligned terahertz signal, which is used for noise reduction of the terahertz signal. Secondly, the last pulse of the terahertz reference signal and the damage signal is truncated into new signal vectors and respectively, and the cross-correlation coefficient between and can be obtained as follows:

[0081] (6)

[0082] wherein, , . is the truncation interval of the signal.

[0083] Further, the initial damage thickness can be obtained according to the obtained cross-correlation coefficient:

[0084] (7)

[0085] wherein, is the maximum value of the cross-correlation coefficient R and its index, is the length of the signal, is the sampling frequency of the terahertz signal, is the time-of-flight.

[0086] Embodiment six, the present application proposes a composite material damage thickness measurement method based on terahertz time domain compensation, compared with embodiment five, this embodiment introduces S5 in detail.

[0087] As Figure 10As shown, when the sample surface uniformity changes, the damage flight time estimated by formula (7) can be inconsistent with the real transmission time difference between the terahertz reference signal and the damage signal. In order to further improve the estimation accuracy of the damage thickness, a terahertz signal flight time compensation model is established. Specifically, Figure 10 The terahertz wave propagation process of different sampling points of the damage sample to be tested is shown. Point O is the terahertz reference signal sampling point, and points A and B are terahertz damage signal sampling points. It can be found that due to the difference in sample surface uniformity, the terahertz wave transmission distance is different at different sampling points, which will further cause the transmission time of terahertz wave at different sampling points to change. For example, Figure 10 , is the difference between the transmission distances of the sampling point and the reference point. When , that is, sampling point A, the transmission distance increases, and the time delay of the first pulse of the obtained terahertz damage signal is less than that from the reference point O. Therefore, the overall transmission time difference between the terahertz reference signal and the damage signal contains two parts: one is the transmission time difference caused by the change of the transmission distance , which can be defined as , and the other is the transmission time difference caused by the damage, which is related to the damage thickness. For sampling point A ( ), the overall total transmission time difference can be defined as:

[0088] (8)

[0089] wherein can be obtained by formula (7), is the transmission time difference between the sampling point and the reference point caused by the change of the transmission distance , is the compensated damage flight time, is the sample refractive index. On the contrary, when

[0090] , that is, sampling point B, the transmission distance decreases, and the time delay of the first pulse of the obtained terahertz damage signal is greater than that from the reference point O, and the overall transmission time difference is defined as:

[0091] (9) wherein

[0092] is the transmission time difference between the sampling point and the reference point caused by the change of the transmission distance . Finally, considering the sample surface uniformity, the damage thickness

[0093] can be accurately obtained by flight time compensation:

[0094] ​ .

[0095] In summary, a new physical induced terahertz time-of-flight compensation method is proposed to achieve accurate thickness measurement of damage in composite laminates. The core of the proposed method is to simplify the time-of-flight of damage as the transmission time difference between the damage area and the non-damage area. In order to better obtain the time-of-flight of damage, a time-of-flight compensation model is established, which considers the influence of the lifting distance and surface uniformity of the sample. In this case, a series of numerical and experimental results, including different damage thicknesses and depths, demonstrate the effectiveness of the proposed method for damage thickness estimation. These results highlight the robustness of the method to complex interference and external environment during terahertz testing, which can effectively improve the accuracy of damage thickness estimation in different scenarios. Compared with other classic time-of-flight extraction methods, the proposed method does not require any prior knowledge of damage and can achieve better damage thickness estimation performance. In future work, since the proposed method is very sensitive to the transmission time difference through the sample, it not only can be used to accurately estimate the damage thickness inside the composite material, but also has great potential to be extended to various thickness estimation fields, such as additive manufacturing, damage formation (TGO in thermal barrier coatings), material wear, etc.

[0096] The embodiments of the present application are described in detail above with reference to the drawings, but the present application is not limited thereto, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present application.

Claims

1. A method for measuring the damage thickness of composite materials based on terahertz time-domain compensation, characterized in that, Includes the following steps: S1. Prepare multiple composite laminate samples with variable damage thickness and depth, and obtain terahertz time-domain signals of different samples based on a terahertz time-domain spectroscopy system; S2. Analyze the effects of lift distance and sample surface uniformity on terahertz signals, establish a theoretical transmission model for complex multilayer composite material structures, define the reflected terahertz response signal, and the lift distance refers to the distance between the terahertz transmitter and the sample surface. S3. Based on the terahertz wave response characteristics and transmission model, a method for measuring the damage thickness of composite materials based on the difference in flight time between damaged and undamaged regions is proposed. S4. Estimate the time-of-flight information of composite material damage using terahertz signal reference transformation, alignment, and cross-correlation methods; S5. Considering the effects of lifting distance and sample surface uniformity, a terahertz signal time-of-flight compensation model is established to achieve accurate estimation of composite material damage thickness. In S2, the reflected terahertz response signal is defined as: in, It is a reflected terahertz echo. It is the system impulse response function. and These represent the number of reflectors at the laminate interface and the number of reflectors at the damaged interface, respectively. and They respectively represent the corresponding to the first The interface reflector and the first The model parameters corresponding to each damaged reflector. It is Gaussian white noise. The changes in the overall model parameters of the terahertz signal are caused by variations in distance and surface uniformity. In S3, the damage thickness measurement method is defined as follows: in It is the thickness of the damage. It is the refractive index of air. Terahertz waves pass through a thickness of Damage transmission time, It is the refractive index of the sample. Terahertz waves pass through a thickness of Sample transfer time, It is the time difference of flight, which refers to the time that terahertz waves travel through a thickness of [thickness value missing]. The damage and thickness are The time difference in the transmission of the samples, where c is the speed of light; In S4, signal reference transformation refers to using the terahertz response signal from the undamaged region of the same sample as the terahertz reference signal extracted from the time-of-flight of the damaged region. Signal alignment utilizes the time-shifted unit impulse response function as the alignment function to shift the terahertz damage signal in the time domain, precisely aligning the first pulses of the terahertz reference signal and the damage signal. The aligned terahertz damage signal is defined as follows: in, It is an aligned terahertz damage signal. It's a convolution operation. It is the time shift value of the terahertz damage signal, which is obtained by the time delay corresponding to the first pulse of the terahertz reference signal and the damage signal; Since the first pulses of the terahertz reference signal and the damaged signal are aligned, the propagation time difference of the terahertz wave is defined by the time delay difference of the last pulse of the two aligned terahertz signals. The time delay difference between the two signals is determined by the cross-correlation method, specifically: the aligned terahertz signals are subjected to moving average filtering for noise reduction; secondly, the last pulses of the terahertz reference signal and the damaged signal are truncated into new signal vectors. and The truncation interval is determined by the signal time domain window, and then obtained. and The cross-correlation coefficient between them is: in, , ; This refers to the signal cutoff interval. Furthermore, the initial damage thickness is obtained based on the resulting cross-correlation coefficient. in, It is the cross-correlation coefficient R The maximum value and its index, It is the length of the signal. It is the sampling frequency of the terahertz signal. It is flight time; In S5, positioning parameters The difference in transmission distance between the sampling point and the reference point, when As the transmission distance increases, the time delay of the first pulse of the obtained terahertz damage signal is less than the time delay from the reference point. The transmission time difference between the terahertz reference signal and the damage signal is defined as: in, Due to transmission distance The difference in transmission time between the sampling point and the reference point caused by the change Due to transmission distance The transmission time difference caused by the change , It is the compensated damage flight time. It is the sample refractive index; when When the transmission distance decreases, the time delay of the first pulse of the obtained terahertz damage signal is greater than the time delay from the reference point. The overall transmission time difference is defined as: in, Due to transmission distance The difference in transmission time between the sampling point and the reference point caused by the change; Considering the uniformity of the sample surface, the damage thickness is accurately obtained through time-of-flight compensation. The general calculation method is as follows: 。 2. The method for measuring the damage thickness of composite materials based on terahertz time-domain compensation according to claim 1, characterized in that, In S1, the terahertz time-domain spectroscopy system includes a terahertz source, a control unit, a transmitter, a receiver, and a motion platform. The motion platform moves in the X and Y directions and acquires 2D information from the sample. The transmitter and receiver are integrated and mounted on the motion platform and are responsible for transmitting and receiving terahertz signals. The terahertz source contains a femtosecond laser used to generate terahertz pulses.

3. The method for measuring the damage thickness of composite materials based on terahertz time-domain compensation according to claim 1, characterized in that, In S1, six 20mm x 20mm x 2mm composite laminate samples with different damage thicknesses were prepared using 3D printing technology. Each sample contained 10 layers with a layer thickness of 200um, and glass fiber reinforced polymer was used as the printing material. In the preparation of damaged samples, the test samples are divided into undamaged areas and damaged areas. An air gap with a certain thickness is preset to simulate damage. The damage size is 10mm x 10mm, and the damage thickness is variable, namely 100um, 200um, 400um, 600um, 800um and 1000um.

4. The method for measuring the damage thickness of composite materials based on terahertz time-domain compensation according to claim 1, characterized in that, In S1, six composite laminate samples with different damage depths and dimensions of 20mm x 20mm x 1.6mm were prepared. Each sample contained eight layers with a thickness of 200µm. Adjacent layers were made of glass fiber reinforced polymer and polylactic acid printing material stacked sequentially. The test samples were divided into undamaged and damaged areas. An air gap of a certain thickness was preset to simulate damage. The damage size of the damaged area was set to 10mm x 10mm x 0.2mm, and the damage depth was set to 200µm, 400µm, 600µm, 800µm, 1000µm, and 1200µm, while the damage thickness remained constant.

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