Coating structure thickness measuring method based on laser ultrasonic zero group velocity Lamb wave technology

Abstract

The invention relates to a coating structure thickness measuring method based on a laser ultrasonic zero-group velocity Lamb wave technology, which comprises the following steps: acquiring a frequency domain waveform of a simulation signal in a zero-group velocity Lamb wave of a simulation model, extracting a resonance frequency corresponding to a formant in the frequency domain waveform for calculating a zero-group velocity Lamb wave frequency-thickness product, and establishing a multiple linear regression fitting model; and the resonant frequency of the coating structure sample is collected, the resonant frequency and the total thickness are input into the multiple linear regression fitting model, and the coating thickness and the substrate thickness are obtained. According to the method, key parameters of ZGV Lamb waves are extracted, multiple linear regression and a least square method are combined, linear relations between different coating structure thicknesses and corresponding resonant frequencies and multiple linear models between frequency-thickness products and the thicknesses of all the layers are established, and therefore synchronous quantitative measurement of the thicknesses of all the layers of the coatings is achieved; therefore, the overall quality characteristics of the coating structure are reflected.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing and evaluation technology, and in particular to a method for measuring the thickness of coating structures based on laser-ultrasonic zero-group velocity Lamb wave technology. Background Technology

[0002] Coating structures, such as thermal barrier coatings (TBCs), are ceramic material layers commonly used on the surfaces of gas turbine blades, combustion chambers, and similar structural components. They aim to provide oxidation resistance, low thermal conductivity, and corrosion resistance at a relatively low cost. By reducing substrate temperature and inhibiting heat transfer, TBCs can improve the thermal efficiency and service life of components and systems, while also contributing to improved fracture toughness, impact resistance, and wear resistance. Although thermal barrier coatings play a crucial protective role in high-temperature environments, during long-term service, the combined effects of high temperatures, friction, and impact loads can lead to coating thinning, cracking, or peeling, ultimately resulting in coating failure. Therefore, coating thickness is a critical parameter for measuring coating integrity and performance degradation, and is essential for coating performance evaluation and life prediction.

[0003] Currently, the characterization of coating thickness widely employs ultrasonic bulk wave (longitudinal and transverse waves) transmission and reflection measurements, as well as guided wave (mainly Lamb waves) measurements in plate-like structures. Conventional bulk wave methods typically determine thickness based on time-of-flight, but these methods suffer from parameter coupling issues between wave velocity and thickness, and the attenuation of high-frequency signals within the material reduces measurement accuracy. In thin or multilayer structures, incident bulk waves repeatedly reflect and transmit between interfaces, resulting in overlapping wave packets in the received signal, significantly increasing the difficulty of signal processing. Although several algorithms have attempted to decouple multimodal acoustic parameters, contact transducers are limited by transducer size and couplant quality, while immersion ultrasound, although improving coupling conditions, requires complete immersion of the specimen, which is often impractical in actual industrial testing.

[0004] In contrast, guided wave technology is more suitable for non-destructive testing of plate-like structures. Lamb waves are formed by the coupling of longitudinal and transverse waves and propagate through multiple reflections within finite boundaries. They often use lower frequencies, thus limiting spatial resolution and the ability to detect features on the micrometer scale. For typical coating thicknesses (usually ranging from several micrometers to hundreds of micrometers), traditional guided waves struggle to provide sufficient thickness resolution.

[0005] Zero Group Velocity (ZGV) Lamb waves, as a special type of Lamb wave, can effectively overcome the above limitations. ZGV Lamb waves originate from the interference between opposing propagating components, producing highly localized standing wave resonances with relatively concentrated and easily excited energy. Because localized resonance energy is not easily radiated to the far field, ZGV Lamb waves exhibit significant advantages over propagating guided waves in terms of signal-to-noise ratio, sensitivity, and spatial locality. More importantly, the resonant frequency of ZGV Lamb waves is highly sensitive to the geometric scale (especially thickness) of thin-layer structures, thus being considered a promising method for measuring the thickness of thin films and coatings. However, unlike traditional bulk wave or guided wave detection methods, ZGV Lamb wave signals in coated structures do not directly contain resolvable information about each layer. To obtain the structural characteristics of each layer, feature extraction and processing of the signal are required to extract physical information related to interlayer parameters. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to provide a coating structure thickness measurement method based on laser-ultrasonic zero-group velocity (ZGV) Lamb wave technology. This method utilizes the ZGV Lamb wave signal generated by laser-ultrasonic excitation to quantitatively characterize the thickness of each layer of the coating structure. Specifically, by extracting key parameters of the ZGV Lamb wave, a linear relationship is established between different coating structure thicknesses and their corresponding resonant frequencies. Furthermore, by combining multiple linear regression and least squares methods, a multiple linear model is constructed between the frequency-thickness product and the thickness of each layer, thereby achieving synchronous quantitative measurement of the thickness of each coating layer to reflect the overall quality characteristics of the coating structure.

[0007] To achieve the above objectives, the present invention provides the following solution: A method for measuring coating thickness based on laser-ultrasonic zero-group velocity Lamb wave technology includes: The frequency domain waveform of the simulated signal in the zero group velocity Lamb wave of the simulation model is obtained, and the resonant frequency corresponding to the formant peak in the frequency domain waveform is extracted to calculate the frequency-thickness product of the zero group velocity Lamb wave and establish a linear regression fitting model. The resonant frequency of the coated structure sample is collected, and the resonant frequency and the total thickness set in the simulation model are input into the linear regression fitting model to obtain the coating thickness and the substrate thickness.

[0008] Optionally, obtaining the simulated signal in the zero-group velocity Lamb wave of the simulation model includes: Establish simulation models with different combinations of coating and substrate thicknesses, and obtain the simulation signals; During the modeling process, the excitation source is modeled as a Gaussian modulated thermal load to simulate the laser ultrasonic excitation applied to the coating side of the coated structure sample. A receiving source is set on the substrate side to receive the ultrasonic signal, and the ultrasonic signal is used as the simulation signal.

[0009] Optionally, establishing the linear regression fitting model includes: Using the zero-group velocity Lamb frequency product, simple linear regression models and multiple linear regression models are constructed for the thickness parameters of the coating and substrate with respect to the zero-group velocity Lamb frequency product: The simple linear regression model is constructed as follows: the thickness ratio of the coating to the substrate is used as the independent variable, and the zero group velocity Lamb wave frequency-thickness product is used as the dependent variable. The regression coefficient and the coefficient of determination are calculated to obtain the linear regression model. The multiple linear regression model is constructed by using the thickness parameters of the coating and the substrate as multiple independent variables and the zero group velocity Lamb wave-frequency product as the dependent variable, calculating the regression coefficients, and obtaining the multiple linear regression model.

[0010] Optionally, constructing the simple linear regression model includes: ; in, For zero group velocity Lamb frequency thick accumulation, , For regression coefficients, This refers to the thickness ratio.

[0011] Optionally, constructing the multiple linear regression model includes: ; in, For zero group velocity Lamb frequency thick accumulation, , , is the regression coefficient.

[0012] Optionally, the resonant frequencies of the coated structure sample are collected including: A full-laser ultrasonic excitation and detection experimental system was built to acquire the frequency domain waveforms of the coated structure sample; During the system setup process, a laser excitation probe is placed on one side of the coating of the coated structure sample, the laser excitation probe is connected to a pulsed laser, and the pulsed laser is controlled by a laser controller to excite the laser to generate a zero group velocity Lamb wave signal. A laser receiving probe is placed on one side of the substrate of the coated structure sample to receive the zero group velocity Lamb wave signal. The received zero group velocity Lamb wave signal is transmitted to an oscilloscope to acquire the resonant frequency of the coated structure sample.

[0013] Optionally, obtaining the coating thickness and the substrate thickness includes: The resonant frequency and the total thickness are input into the linear regression model to form the first thickness calculation model: ; Solve the first thickness calculation model to obtain the coating thickness and the substrate thickness: ; ; in, The resonant frequency, The total thickness of the coated structure sample is given. For coating thickness, The thickness is the base layer.

[0014] Optionally, obtaining the coating thickness and the substrate thickness further includes: The resonant frequency and the total thickness are input into the multiple linear regression model to form a second thickness calculation model: ; Solve the second thickness calculation model to obtain the coating thickness and the substrate thickness: ; ; in, The resonant frequency, The total thickness of the coated structure sample is given. For coating thickness, The thickness is the base layer.

[0015] The beneficial effects of this invention are as follows: The coating structure model constructed by this invention based on finite element simulation facilitates the extraction of characteristic parameters such as the resonant frequency and frequency-thickness product of zero-group velocity Lamb waves. The signal characteristics are clear and do not require extensive physical pre-experiments. While ensuring comprehensive coverage of thickness combinations, it significantly reduces the cost of physical sample preparation and experimental operation, and lowers the investment in the early stage of detection.

[0016] The all-laser ultrasonic excitation and detection system used in this invention is a non-contact, non-destructive detection method. Both excitation and reception do not require contact with the coating surface, thus avoiding scratches and surface contamination of the brittle coating.

[0017] This invention is based on the detection of zero-group velocity Lamb waves, which is highly sensitive to thickness and enables high-precision measurement of coating structure thickness. Its signal attenuation is low and its energy is high, thereby improving the detection performance in local areas and giving it an advantage in detection in narrow spaces.

[0018] This invention uses the frequency-thickness product of the zero-group velocity Lamb wave signal as the core variable of the model. The linear regression model constructed with the coating structure and its substrate thickness parameters shows significant fitting effect, accurately capturing the mapping relationship between the characteristic parameters of the zero-group velocity Lamb wave signal and the coating and its substrate thickness information. It optimizes the calculation method of the coating structure and its substrate thickness and improves the thickness measurement accuracy. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the finite element simulation model of an embodiment of the present invention; Figure 2 Examples of time-domain and frequency-domain waveforms of the zero-group velocity Lamb wave signal based on finite element simulation in embodiments of the present invention; (a) is an example of the time-domain waveform of the zero-group velocity Lamb wave signal based on finite element simulation, and (b) is an example of the frequency-domain waveform of the zero-group velocity Lamb wave signal based on finite element simulation. Figure 3 This is a schematic diagram of the all-laser ultrasonic excitation and detection experimental system according to an embodiment of the present invention; Figure 4 The coating / substrate thickness ratio in this embodiment of the invention With frequency thick accumulation Example diagram of a simple linear regression fitting model; Figure 5 The coating thickness in this embodiment of the invention , substrate thickness With frequency thick accumulation Example diagram of a multiple linear regression model; Figure 6 Examples of time-domain and frequency-domain waveforms of the zero group velocity Lamb wave signal obtained by experimental measurement in an embodiment of the present invention; (a) is a time-domain waveform of the zero group velocity Lamb wave signal obtained by detecting the thermal barrier coating sample using a full-laser ultrasonic excitation and detection system; (b) is a frequency-domain waveform of the zero group velocity Lamb wave signal obtained by detecting the thermal barrier coating sample using a full-laser ultrasonic excitation and detection system. Figure 7 This is a flowchart of a coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 7 As shown in the figure, this embodiment discloses a method for measuring the thickness of a coating structure based on laser ultrasonic zero-group velocity Lamb wave technology. Specifically, it includes: acquiring the frequency domain waveform of the simulated signal in the zero-group velocity Lamb wave of the simulation model, extracting the resonance frequency corresponding to the resonance peak in the frequency domain waveform, using it to calculate the zero-group velocity Lamb wave frequency-thickness product, and establishing a linear regression fitting model; acquiring the resonance frequency of the coating structure sample, inputting the resonance frequency and total thickness into the linear regression fitting model, and obtaining the coating thickness and substrate thickness.

[0024] Furthermore, obtaining the simulation signal in the zero group velocity Lamb wave of the simulation model includes: establishing simulation models with different combinations of coating and substrate thicknesses and obtaining simulation signals; during the modeling process, the excitation source is modeled as a Gaussian modulated thermal load to simulate the laser ultrasonic excitation applied to the coating side of the coated structure sample, and a receiving source is set on the substrate side to receive the ultrasonic signal, which is then used as the simulation signal.

[0025] Specifically, simulation models with different combinations of coating and substrate thicknesses are established based on finite element simulation: Simulation models with different coating and substrate thickness combinations were established using finite element simulation software, such as... Figure 1 As shown. The excitation source is modeled as a Gaussian-modulated thermal load to simulate laser-ultrasonic excitation applied to the coated sample. A one-excitation-one-receiver mode is adopted, with the laser-ultrasonic excitation source applied to the coating side and a receiving source set at the symmetrical point of the excitation point (the substrate side) to collect out-of-plane displacement.

[0026] Simulated signal time-frequency analysis and zero-group velocity Lamb wave resonance peak-frequency product calculation: The simulation model uses Gaussian-modulated thermal load to simulate the propagation of a laser-ultrasonic signal within a coated structural plate. Transverse and longitudinal waves continuously reflect and couple to form Lamb waves. A receiving source at the same location opposite the excitation source receives the zero-group-velocity Lamb wave as the received ultrasonic signal. For example... Figure 2As shown in (a)-(b), the time-domain and frequency-domain waveforms of the simulated Lamb wave signal with zero group velocity are obtained. A sharp and distinct resonance peak appears in the frequency-domain waveform. The resonance frequency corresponding to the peak value of the resonance peak is extracted. And measure the total thickness of the coating material. Calculate the frequency-thickness layer .

[0027] Furthermore, establishing a linear regression fitting model includes: using the zero-group velocity Lamb wave-frequency product to construct linear regression and multiple linear regression models of the coating and substrate thickness parameters with respect to the zero-group velocity Lamb wave-frequency product: Constructing a linear regression model: using the coating-to-substrate thickness ratio as the independent variable and the zero-group velocity Lamb wave-frequency product as the dependent variable, calculating the regression coefficients and the coefficient of determination to obtain the linear regression model; Constructing a multiple linear regression model: using the coating and substrate thickness parameters as multiple independent variables and the zero-group velocity Lamb wave-frequency product as the dependent variable, calculating the regression coefficients to obtain the multiple linear regression model.

[0028] Specifically, the fitting model is constructed based on linear regression analysis: The simulation data of different coating and substrate thickness combinations were used to perform zero-group velocity Lamb wave-frequency thickness product. Quantitative characterization was performed. A linear regression model was constructed using linear regression analysis, and the model coefficients were solved using the least squares method. This allowed for the construction of the frequency-thickness product of the coating and substrate thickness parameters with the zero-group velocity Lamb wave characteristic parameters. Simple linear regression model and multiple linear regression model. The simple linear regression model uses the thickness ratio of the coating layer to the substrate layer. ( As the independent variable, the zero group velocity Lamb wave-frequency thick product As the dependent variable, the regression coefficient is calculated. , and coefficient of determination To obtain the fitted model The multiple linear regression model uses coating thickness as an example. Base layer thickness As a multivariate independent variable, the zero group velocity Lamb wave frequency thick product As the dependent variable, the regression coefficients are calculated to obtain the fitted model. .

[0029] Furthermore, the acquisition of the resonant frequency of the coated structure sample includes: setting up a full laser ultrasonic excitation and detection experimental system to acquire the frequency domain waveform of the coated structure sample; during the system setup, a laser excitation probe is placed on one side of the coated structure sample, the laser excitation probe is connected to a pulsed laser, and the pulsed laser is controlled by a laser controller to excite the laser to generate a zero group velocity Lamb wave signal; a laser receiving probe is placed on the other side of the coated structure sample to receive the zero group velocity Lamb wave signal, and the received zero group velocity Lamb wave signal is transmitted to an oscilloscope to acquire the resonant frequency of the coated structure sample.

[0030] Specifically, the Lamb wave detection experiment of the zero-group velocity of the coated structure sample using laser ultrasonic technology: Construct an all-laser ultrasonic excitation and detection experimental system, such as Figure 3 As shown. The system includes: 1. a laser controller, 2. a pulsed laser, 3. a laser excitation probe, 4. a laser receiving probe, 5. a coated structure specimen, 6. a laser interferometer, and 7. a digital oscilloscope. The experiment uses a one-excitation-one-receiver mode. A laser excitation probe is placed on the coating side of the coated structure specimen, connected to the pulsed laser to generate a zero-group velocity Lamb wave signal. The pulsed laser is controlled by the laser controller. A laser receiving probe is placed on the substrate side of the coated structure specimen to receive the zero-group velocity Lamb wave signal. The zero-group velocity Lamb wave signal is transmitted to the oscilloscope and acquired by the oscilloscope according to a synchronous trigger signal. The frequency domain waveform of the signal acquired by the oscilloscope is extracted and processed to obtain the zero-group velocity Lamb wave resonant frequency of the coated structure specimen. .

[0031] Furthermore, obtaining the coating thickness and substrate thickness includes: inputting the resonant frequency and total thickness into a linear regression model to form a first thickness calculation model, solving the first thickness calculation model, and obtaining the coating thickness and substrate thickness.

[0032] Obtaining the coating thickness and substrate thickness also includes: inputting the resonant frequency and total thickness into a multiple linear regression model to form a second thickness calculation model, solving the second thickness calculation model, and obtaining the coating thickness and substrate thickness.

[0033] Specifically, quantitative calculations of coating and substrate thickness are based on a linear regression model and the Lamb wave signal of laser-ultrasonic zero-group velocity: Measuring the total thickness of the coated structural specimen This was compared with the Lamb wave resonance frequency obtained from experiments on zero group velocity. Multiplying them together yields the frequency-thickness product of the zero-group velocity Lamb wave. By combining the constructed linear regression model, a system of equations is formed to calculate the coating thickness and substrate thickness. Based on the thickness ratio... Lamb frequency thick product with zero group velocity The simple linear regression model consists of the following system of equations: ; By solving the system of equations, the coating can be calculated. Thickness and substrate thickness : ; ; Based on the coating and its substrate thickness (coating thickness) substrate thickness Lamb frequency thick product with zero group velocity The multiple linear regression model consists of the following equations: ; By solving the system of equations, the coating can be calculated. Thickness and substrate thickness : ; ; The coated structure specimens were ceramic-based thermal barrier coating specimens with a coating thickness of 0.4 mm and a substrate thickness of 2 mm. Figure 4 Demonstrates based on thickness ratio Lamb frequency thick product with zero group velocity The fitting results of the simple linear regression model can be seen from the figure, which shows that the zero group velocity Lamb wave frequency product of the coated plate... With the thickness ratio of the two layers of material They are monotonically increasing, and there is a one-to-one correspondence between them. Figure 5 This demonstrates the effect based on the coating and its substrate thickness (coating thickness) substrate thickness Lamb frequency thick product with zero group velocity The fitting results of the multiple linear regression model can be seen from the figure, which shows that the zero group velocity Lamb wave frequency-thickness product of the coated sample... It exhibits a good linear relationship with the thickness of the two layers of material, frequency-thickness product It increases with increasing coating thickness, while it decreases with increasing substrate thickness. Figure 6 (a) and Figure 6 (b) The time-domain and frequency-domain waveforms of the zero-group velocity Lamb wave signal obtained from the thermal barrier coating sample using a full-laser ultrasonic excitation and detection system are shown respectively. The frequency-thickness product is calculated based on the total thickness of the coating structure sample. ,and Figure 3 and Figure 4The linear regression equations form a system of equations. By calculating and solving the system of equations, the thickness value of the coated structural plate is obtained, realizing the thickness detection of the coating and the substrate. The measurement results and errors of the laser ultrasonic zero-group velocity Lamb wave combining the two linear regression models are shown in Table 1.

[0034] Table 1. Results and errors of laser-ultrasonic zero-group velocity Lamb wave measurement of coating thickness. This invention proposes a coating thickness measurement method based on laser-ultrasonic zero-group velocity Lamb wave technology. It innovatively combines zero-group velocity Lamb wave technology with linear regression methods, constructing two linear regression models for the zero-group velocity Lamb wave frequency-thickness product and coating thickness parameters, thus clarifying the mapping relationship between the zero-group velocity Lamb wave frequency-thickness product and the coating thickness. The proposed method solves the problem of high difficulty in measuring the thickness of each layer in multilayer structures, improves the quantitative evaluation capability of coating thickness, and achieves high-precision measurement of coating and substrate thicknesses in coating structures with different thickness combinations. It overcomes the problems of insufficient accuracy and poor engineering applicability in traditional methods, demonstrating unique capabilities for thickness-related structural measurements.

[0035] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for measuring the thickness of a coating structure based on laser-ultrasonic zero-group velocity Lamb wave technology, characterized in that, include: The frequency domain waveform of the simulated signal in the zero group velocity Lamb wave of the simulation model is obtained, and the resonant frequency corresponding to the formant peak in the frequency domain waveform is extracted to calculate the frequency-thickness product of the zero group velocity Lamb wave and establish a linear regression fitting model. The resonant frequency of the coated structure sample is collected, and the resonant frequency and the total thickness set in the simulation model are input into the linear regression fitting model to obtain the coating thickness and the substrate thickness.

2. The coating structure thickness measurement method based on laser-ultrasonic zero-group velocity Lamb wave technology according to claim 1, characterized in that, Obtaining the simulated signal in the zero-group velocity Lamb wave of the simulation model includes: Establish simulation models with different combinations of coating and substrate thicknesses, and obtain the simulation signals; During the modeling process, the excitation source is modeled as a Gaussian modulated thermal load to simulate the laser ultrasonic excitation applied to the coating side of the coated structure sample. A receiving source is set on the substrate side to receive the ultrasonic signal, and the ultrasonic signal is used as the simulation signal.

3. The coating structure thickness measurement method based on laser-ultrasonic zero-group velocity Lamb wave technology according to claim 2, characterized in that, Establishing the linear regression fitting model includes: Using the zero-group velocity Lamb frequency product, simple linear regression models and multiple linear regression models are constructed for the thickness parameters of the coating and substrate with respect to the zero-group velocity Lamb frequency product: The simple linear regression model is constructed as follows: the thickness ratio of the coating to the substrate is used as the independent variable, and the zero group velocity Lamb wave frequency-thickness product is used as the dependent variable. The regression coefficient and the coefficient of determination are calculated to obtain the linear regression model. The multiple linear regression model is constructed by using the thickness parameters of the coating and the substrate as multiple independent variables and the zero group velocity Lamb wave-frequency product as the dependent variable, calculating the regression coefficients, and obtaining the multiple linear regression model.

4. The coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to claim 3, characterized in that, Constructing the simple linear regression model includes: ； in, For zero group velocity Lamb frequency thick accumulation, , For regression coefficients, This refers to the thickness ratio.

5. The coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to claim 3, characterized in that, Constructing the multiple linear regression model includes: ； in, For zero group velocity Lamb frequency thick accumulation, , , is the regression coefficient.

6. The coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to claim 1, characterized in that, The resonant frequencies of the coated structure specimens were collected including: A full-laser ultrasonic excitation and detection experimental system was built to acquire the frequency domain waveforms of the coated structure sample; During the system setup process, a laser excitation probe is placed on one side of the coating of the coated structure sample, the laser excitation probe is connected to a pulsed laser, and the pulsed laser is controlled by a laser controller to excite the laser to generate a zero group velocity Lamb wave signal. A laser receiving probe is placed on one side of the substrate of the coated structure sample to receive the zero group velocity Lamb wave signal. The received zero group velocity Lamb wave signal is transmitted to an oscilloscope to acquire the resonant frequency of the coated structure sample.

7. The coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to claim 3, characterized in that, Obtaining the coating thickness and the substrate thickness includes: The resonant frequency and the total thickness are input into the linear regression model to form the first thickness calculation model: ； Solve the first thickness calculation model to obtain the coating thickness and the substrate thickness: ； ； in, The resonant frequency, The total thickness of the coated structure sample is given. For coating thickness, The thickness is the base layer.

8. The coating structure thickness measurement method based on laser ultrasonic zero-group velocity Lamb wave technology according to claim 3, characterized in that, Obtaining the coating thickness and the substrate thickness further includes: The resonant frequency and the total thickness are input into the multiple linear regression model to form a second thickness calculation model: ； Solve the second thickness calculation model to obtain the coating thickness and the substrate thickness: ； ； in, The resonant frequency, The total thickness of the coated structure sample is given. For coating thickness, The thickness is the base layer.

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