Thermal barrier coating thermal resistance inversion method based on terahertz technology

Abstract

The invention relates to a thermal barrier coating thermal resistance inversion method and device based on a terahertz technology, computer equipment, a computer readable storage medium and a computer program product. The method comprises the following steps: acquiring a terahertz time-domain spectrum of a to-be-detected area of the thermal barrier coating, and performing transformation processing on the terahertz time-domain spectrum to obtain a terahertz frequency-domain spectrum; determining a candidate complex refractive index corresponding to each coating thickness candidate value according to the terahertz frequency domain spectrum in combination with a plurality of coating thickness candidate values and a terahertz wave theoretical transmission function model; determining a target complex refractive index corresponding to a coating thickness target value according to the candidate complex refractive index corresponding to each coating thickness candidate value; and determining the thermal resistance of the coating according to the coating thickness target value, the target complex refractive index and the cross sectional area of the to-be-measured area. Therefore, nondestructive evaluation of the heat insulation performance of the thermal barrier coating is realized, and accuracy and reliability of heat insulation performance evaluation are improved at the same time.

Description

Technical Field

[0001] This application relates to the field of terahertz technology, and in particular to a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for inverting the thermal resistance of thermal barrier coatings based on terahertz technology. Background Technology

[0002] Currently, the operating temperature of hot-end components in high-temperature equipment such as aero-engines and gas turbines often far exceeds the heat resistance limit of metal materials. Thermal barrier coatings applied to metal surfaces have become an indispensable means of heat insulation and protection. These thermal barrier coatings are usually ceramic matrix composites with a thickness ranging from tens to hundreds of micrometers. They can establish an effective thermal barrier, and their heat insulation performance is crucial for the safe and reliable operation of high-temperature equipment.

[0003] In related technologies, the assessment of thermal insulation performance mainly relies on indirect measurement of the temperature difference between the upper and lower surfaces of the coating. For example, embedded thermocouples can be used, but these thermocouples need to be embedded in a metal substrate, which is complex to manufacture and involves lead wire issues. Alternatively, temperature measurement can be performed by doping with phosphorescent particles, but this method alters the original properties of the coating and also carries the risk of high-temperature annihilation. Therefore, the above-mentioned indirect measurement methods are prone to damaging the thermal barrier coating during the testing process and will also lead to insufficient accuracy in the thermal insulation performance test. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for inverting the thermal resistance of thermal barrier coatings based on terahertz technology to address the above-mentioned technical problems.

[0005] In a first aspect, this application provides a method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology, including:

[0006] The terahertz time-domain spectrum of the thermal barrier coating under test area is obtained, and the terahertz time-domain spectrum is transformed to obtain the terahertz frequency-domain spectrum.

[0007] Based on the terahertz frequency domain spectrum, and combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined;

[0008] Based on the candidate complex refractive index corresponding to each candidate coating thickness value, determine the target complex refractive index corresponding to the target coating thickness value;

[0009] The thermal resistance of the coating is determined based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be tested.

[0010] In one embodiment, determining the candidate complex refractive index corresponding to each of the terahertz frequency domain spectra, combined with multiple candidate coating thickness values ​​and a terahertz wave theoretical transfer function model, includes:

[0011] Select multiple candidate coating thickness values ​​from the candidate coating thickness range;

[0012] Based on the terahertz wave theoretical transfer function model and the initial complex refractive index, the theoretical amplitude and phase values ​​of each candidate coating thickness are determined at each frequency point, and the frequency points are determined by the terahertz frequency domain spectrum.

[0013] Based on the true amplitude and true phase values ​​at each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude and theoretical phase values ​​at each frequency point, determine the total error value of each candidate coating thickness at each frequency point;

[0014] The initial complex refractive index is updated based on the total error value of each candidate coating thickness at each frequency point;

[0015] Using the updated initial complex refractive index, return to the steps described above for determining the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point until the iteration stop condition is met, and determine the complex refractive index of each current candidate coating thickness at each frequency point as the corresponding candidate complex refractive index.

[0016] In one embodiment, determining the total error value of each candidate coating thickness at each frequency point based on the true amplitude and true phase values ​​at each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude and theoretical phase values ​​at each frequency point, includes:

[0017] Determine the amplitude error value between the actual amplitude value and the theoretical amplitude value, and the phase error value between the actual phase value and the theoretical phase value, for each candidate coating thickness value at each frequency point;

[0018] Based on the amplitude error and phase error of each candidate coating thickness value at each frequency point, the total error value of each candidate coating thickness value at each frequency point is determined.

[0019] In one embodiment, determining the target complex refractive index corresponding to the target coating thickness value based on the candidate complex refractive index corresponding to each candidate coating thickness value includes:

[0020] The cost function value for each candidate coating thickness is determined based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value.

[0021] The candidate coating thickness value corresponding to the minimum cost function value is determined as the target coating thickness value, and the candidate complex refractive index of each frequency point of the minimum cost function value is determined as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

[0022] In one embodiment, determining the cost function value of each candidate coating thickness value based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value includes:

[0023] For each candidate coating thickness value, calculate the first rate of change of the real part of the candidate complex refractive index between adjacent frequency points and the second rate of change of the imaginary extinction coefficient between adjacent frequency points;

[0024] The sum of the squares of the first rate of change and the sum of the squares of the second rate of change are superimposed to obtain the cost function value corresponding to the candidate coating thickness value.

[0025] In one embodiment, determining the coating thermal resistance based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be measured includes:

[0026] The equivalent dielectric constant of the region to be measured is determined based on the target complex refractive index.

[0027] The porosity of the coating in the test area is determined based on the equivalent dielectric constant, the dielectric constant of the dense coating, and the dielectric constant of air.

[0028] The thermal conductivity of the area to be tested is determined based on the thermal conductivity of the dense coating and the porosity of the coating.

[0029] The thermal resistance of the coating is determined based on the target coating thickness, the thermal conductivity of the area to be tested, and the cross-sectional area of ​​the area to be tested.

[0030] Secondly, this application also provides a thermal barrier coating thermal resistance inversion device based on terahertz technology, comprising:

[0031] The acquisition module is used to acquire the terahertz time-domain spectrum of the thermal barrier coating under test area, and to transform the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum.

[0032] The first determining module is used to determine the candidate complex refractive index corresponding to each of the terahertz frequency domain spectra, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model.

[0033] The second determining module is used to determine the target complex refractive index corresponding to the target coating thickness based on the candidate complex refractive index corresponding to each candidate coating thickness value;

[0034] The third determining module is used to determine the thermal resistance of the coating based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be measured.

[0035] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0036] The terahertz time-domain spectrum of the thermal barrier coating under test area is obtained, and the terahertz time-domain spectrum is transformed to obtain the terahertz frequency-domain spectrum.

[0037] Based on the terahertz frequency domain spectrum, and combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined;

[0038] Based on the candidate complex refractive index corresponding to each candidate coating thickness value, determine the target complex refractive index corresponding to the target coating thickness value;

[0039] The thermal resistance of the coating is determined based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be tested.

[0040] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0041] The terahertz time-domain spectrum of the thermal barrier coating under test area is obtained, and the terahertz time-domain spectrum is transformed to obtain the terahertz frequency-domain spectrum.

[0042] Based on the terahertz frequency domain spectrum, and combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined;

[0043] Based on the candidate complex refractive index corresponding to each candidate coating thickness value, determine the target complex refractive index corresponding to the target coating thickness value;

[0044] The thermal resistance of the coating is determined based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be tested.

[0045] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0046] The terahertz time-domain spectrum of the thermal barrier coating under test area is obtained, and the terahertz time-domain spectrum is transformed to obtain the terahertz frequency-domain spectrum.

[0047] Based on the terahertz frequency domain spectrum, and combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined;

[0048] Based on the candidate complex refractive index corresponding to each candidate coating thickness value, determine the target complex refractive index corresponding to the target coating thickness value;

[0049] The thermal resistance of the coating is determined based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be tested.

[0050] The aforementioned method, apparatus, computer equipment, computer-readable storage medium, and computer program product for inverting the thermal resistance of thermal barrier coatings based on terahertz technology can first acquire the terahertz time-domain spectrum of the thermal barrier coating under test, and then transform the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum. Subsequently, based on the terahertz frequency-domain spectrum, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined. Then, based on the candidate complex refractive index corresponding to each candidate coating thickness value, the target complex refractive index corresponding to the target coating thickness value is determined. Finally, based on the target coating thickness value, the target complex refractive index, and the cross-sectional area of ​​the test area, the coating thermal resistance is determined. Thus, by acquiring the terahertz time-domain spectrum and performing frequency-domain transformation, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value can be determined, thereby selecting the target coating thickness value and its corresponding target complex refractive index. Finally, the thermal resistance of the thermal barrier coating is calculated, thus achieving a non-destructive evaluation of the thermal insulation performance of the thermal barrier coating, while also improving the accuracy and reliability of the thermal insulation performance evaluation. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart illustrating a thermal resistance inversion method for thermal barrier coatings based on terahertz technology in one embodiment.

[0053] Figure 2 This is a flowchart illustrating a method for determining candidate complex refractive index values ​​for coating thickness in one embodiment.

[0054] Figure 3 This is a flowchart illustrating a method for determining the target complex refractive index of a coating thickness target value in one embodiment;

[0055] Figure 4 This is a flowchart illustrating the thermal resistance inversion method for thermal barrier coatings based on terahertz technology in another embodiment.

[0056] Figure 5 This is a structural block diagram of a thermal barrier coating thermal resistance inversion device based on terahertz technology in one embodiment.

[0057] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0059] It should be noted that the terms "first," "second," etc., used in this application can be used to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish the first element from the second element. The terms "comprising" and "having," and any variations thereof, used in this application, are intended to cover non-exclusive inclusion. The term "multiple" used in this application refers to two or more. The term "and / or" used in this application refers to one of the embodiments, or any combination of multiple embodiments.

[0060] In one embodiment, such as Figure 1 As shown, a method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and further to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0061] Step 102: Obtain the terahertz time-domain spectrum of the thermal barrier coating area to be tested, and transform the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum.

[0062] Thermal barrier coatings are materials typically applied to the metal surfaces of hot-end components in high-temperature equipment such as aero engines and gas turbines. They can ensure the safe and reliable operation of high-temperature equipment by establishing an effective thermal barrier.

[0063] Furthermore, since the thermal barrier coating has a large coverage area and size, it can be divided into multiple independent cells to facilitate the evaluation of its thermal insulation performance. The test area can be one or more specified cells in the thermal barrier coating, or it can be all cells covering the entire thermal barrier coating, etc., and this application does not limit it in this way.

[0064] In addition, terahertz (THz) waves refer to electromagnetic waves with frequencies in the range of 0.1 to 10 THz, corresponding to wavelengths of 3000 to 3000 Hz. It lies between millimeter waves and infrared light, possessing excellent penetration and frequency domain resolution.

[0065] Typically, thermal barrier coatings exhibit a multi-layered structure consisting of an air-ceramic top layer and a metal bonding layer. In this application, the coating refers to the ceramic top layer, which is the thermal insulation layer of the coating. Terahertz waves can be partially reflected and transmitted at the interface between the air and the ceramic top layer. The transmitted wave propagates into the interior of the ceramic top layer. Because the metal bonding layer exhibits high reflectivity in the terahertz band, the transmitted wave is almost completely reflected at the interface between the ceramic and the metal bonding layer and returns, undergoing partial transmission and reflection again at the air-ceramic interface. This forms a series of time-delayed multi-level reflected echoes. These multi-level reflected echoes are superimposed in the time domain to constitute the acquired terahertz time-domain reflection signal, i.e., the terahertz time-domain spectrum.

[0066] Performing a Fourier transform on the terahertz time-domain signal yields the corresponding frequency-domain signal, i.e., the terahertz frequency spectrum, from which the phase difference and amplitude attenuation characteristics at each frequency point can be extracted. Since the refractive index of air is a known constant, and the equivalent refractive index of the metal bonding layer can be considered a known quantity, the unknown variables determining the aforementioned phase and amplitude characteristics are the thickness of the ceramic top layer itself and its complex refractive index.

[0067] Based on this, by establishing a terahertz wave reflection and transmission model based on Fresnel's formula, the complex refractive index of the ceramic top layer can be obtained by combining the measured time-domain spectrum and frequency-domain spectrum inversion. The real part of the complex refractive index can characterize the wave propagation speed and determine the phase, while the imaginary part characterizes the absorption and scattering characteristics of the material and determines the amplitude attenuation, thereby determining the coating thickness and related performance parameters.

[0068] Optionally, to avoid the impact of phase shift on the calculation results, the time-domain signals of the first two reflection peaks can be extracted from the terahertz time-domain reflection signals actually collected from the coating's test area. The first reflection peak corresponds to the reflection signal of the terahertz wave at the interface between the air and the coating surface, and the second reflection peak corresponds to the reflection signal of the terahertz wave at the interface between the coating and the bottom surface of the metal adhesive layer. The first two reflection peaks can contain all the amplitude, phase, and time delay information required to calculate the coating thickness and complex refractive index. Subsequent reflection peaks are prone to introducing additional errors due to energy attenuation and low signal-to-noise ratio; therefore, only the time-domain signals of the first two reflection peaks are extracted. The extracted time-domain signals are then transformed to the frequency domain using a Fourier transform to obtain a set of terahertz frequency domain spectra containing amplitude and phase, providing a stable and reliable data foundation for subsequent parameter inversion based on the transfer function model.

[0069] Therefore, in this embodiment, the corresponding terahertz time-domain spectrum of the thermal barrier coating under test can be obtained, and then a Fourier transform can be performed to obtain the terahertz frequency-domain spectrum of the test area. By acquiring signals on a per-region basis, independent detection can be achieved, which is highly targeted at large-area thermal barrier coatings with uneven thickness. By acquiring the time-domain spectrum of each test area separately and transforming it to the frequency domain, the amplitude and phase characteristics of the corresponding area can be accurately extracted, avoiding mutual interference between signals from different areas and providing a reliable data foundation for subsequent processing.

[0070] Step 104: Based on the terahertz frequency domain spectrum, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, determine the candidate complex refractive index corresponding to each candidate coating thickness value.

[0071] The candidate values ​​for coating thickness can be a range of possible values ​​for coating thickness that are pre-set based on historical experience or prior knowledge. For example, the coating thickness is roughly between 100 and 300 micrometers, and multiple candidate values ​​for coating thickness can be obtained in increments of 1 micrometer. This application does not limit this.

[0072] Furthermore, the terahertz wave theory transfer function model can be a physical mathematical model based on Fresnel's formula, which can be expressed as follows:

[0073] ;

[0074] Where, r 12 and t 12 The r represents the reflection and transmission coefficients of terahertz waves from medium 1 (air) to medium 2 (ceramic coating). 23 t represents the reflection coefficient of terahertz waves from medium 2 (ceramic coating) to medium 3 (metal bonding layer). 21 This represents the transmission coefficient of terahertz waves from medium 2 (ceramic coating) to medium 1 (air). denoted as angular frequency of the terahertz wave, and d as the thickness of the ceramic coating. denoted as the complex refractive index of the ceramic coating, and c as the speed of light.

[0075] Wherein, the reflection coefficient r 12 With transmission coefficient t 12 It can be represented as follows:

[0076] ;

[0077] ;

[0078] in, Let be the complex refractive index of medium 1 (air). Let be the complex refractive index of medium 2 (ceramic coating). The angle of incidence at the air-ceramic coating interface in medium 1 (air). The angle of refraction at the air-ceramic coating interface in medium 2 (ceramic coating).

[0079] In addition, the refractive index t 21 It can be represented as follows:

[0080] ;

[0081] in, Let be the complex refractive index of medium 1 (air). Let be the complex refractive index of medium 2 (ceramic coating). Let be the angle of refraction at the air-ceramic coating interface in medium 1 (air). The angle of incidence at the air-ceramic coating interface in medium 2 (ceramic coating).

[0082] In addition, the reflection coefficient r 23 It can be represented as follows:

[0083] ;

[0084] in, Let be the complex refractive index of medium 2 (ceramic coating). Let be the complex refractive index of medium 3 (metallic bonding layer). The angle of incidence of medium 2 (ceramic coating) at the interface between the ceramic coating and the metal adhesive layer. The angle of refraction at the ceramic coating-metal adhesive layer interface in medium 3 (metal adhesive layer).

[0085] The above angle and , and , and The relationship between them follows Snell's Law:

[0086] .

[0087] For ease of description, the complex refractive index of the ceramic coating is... Abbreviated as .

[0088] Furthermore, the candidate complex refractive index can be the complex refractive index corresponding to each frequency point for a given candidate coating thickness, where each frequency point is included in the terahertz frequency domain spectrum. For each candidate coating thickness, it can be substituted into the terahertz wave theoretical transfer function model, using the amplitude and phase of the measured terahertz frequency domain spectrum as the fitting target. The value of the complex refractive index is optimized for each frequency point. When the error between the theoretical transfer function and the measured frequency domain spectrum at each frequency point is minimized, the complex refractive index corresponding to each frequency point is the candidate complex refractive index corresponding to that candidate coating thickness.

[0089] Therefore, in this embodiment of the application, by combining the terahertz frequency domain spectrum, multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, a corresponding candidate complex refractive index is matched for each candidate coating thickness value. This enables synchronous fitting of coating optical parameters even when the thickness is unknown, making full use of the amplitude and phase information at each frequency point, and improving the stability and reliability of parameter solving.

[0090] Step 106: Determine the target complex refractive index corresponding to the target coating thickness value based on the candidate complex refractive index corresponding to each candidate coating thickness value.

[0091] The target coating thickness value can be the thickness value that best conforms to physical smoothness and has the smallest error, selected from multiple candidate thickness values. The target complex refractive index can be the complex refractive index corresponding to the target coating thickness value, which is ultimately used for subsequent calculations.

[0092] Understandably, each candidate coating thickness value corresponds to a set of candidate complex refractive indices, which include the fitted complex refractive index values ​​at each frequency point. After obtaining the candidate complex refractive indices for all candidate coating thickness values, the optimal result, i.e., the target complex refractive index, can be selected based on the stability of the changes in these candidate complex refractive indices. For each set of candidate complex refractive indices, the amplitude of its change between different frequency points is calculated. A cost function is constructed using the amplitude of change to measure the smoothness of the curve; the more stable the change and the smoother the curve, the smaller the corresponding cost function value. Subsequently, the cost function values ​​corresponding to all candidate coating thickness values ​​are compared, and the candidate coating thickness value with the smallest cost function value is taken as the target coating thickness value. The candidate complex refractive indices corresponding to each frequency point within this set are then determined as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

[0093] Step 108: Determine the thermal resistance of the coating based on the target coating thickness, target complex refractive index, and cross-sectional area of ​​the area to be measured.

[0094] Among them, the cross-sectional area of ​​the area to be tested is the effective heat transfer area when the heat flows through the coating. The thermal resistance of the coating can be used to characterize the coating's ability to impede heat transfer and directly reflect the quality of its heat insulation performance. Generally, the greater the thermal resistance, the better the heat insulation effect of the coating.

[0095] One approach is to first determine the equivalent dielectric constant of the region to be measured based on the target complex refractive index.

[0096] Optionally, the target frequency point can be determined from the frequency points in the terahertz frequency domain spectrum based on the detection frequency, and the sum of the squares of the target complex refractive index corresponding to the target frequency point can be determined as the equivalent dielectric constant of the region to be measured.

[0097] The detection frequency can be a frequency commonly used in the field. It can be the target frequency point from the corresponding frequency point in the terahertz frequency domain spectrum, and then the equivalent dielectric constant can be calculated based on the target complex refractive index corresponding to that target frequency point. If there is no frequency point in the terahertz frequency domain spectrum that matches the detection frequency, the frequency point closest to the detection frequency can be selected as the target frequency point, etc. This application does not impose any limitations on this.

[0098] Typically, the target complex refractive index can be expressed as:

[0099] ;

[0100] in, Let n be the target complex refractive index, and n be the real part of the complex refractive index, i.e., the refractive index itself. This is the imaginary part of the complex refractive index, also known as the extinction coefficient.

[0101] The equivalent dielectric constant of the region under test can be expressed as follows:

[0102] ;

[0103] in, The sum of squares of the target complex refractive index. is the equivalent dielectric constant of the region to be measured.

[0104] The porosity of the coating in the test area can then be determined based on the equivalent dielectric constant, the dielectric constant of the dense coating, and the dielectric constant of air.

[0105] Optionally, the coating porosity can be calculated using the Bruggeman effective medium model, and the coating porosity can satisfy the following relationship:

[0106] ;

[0107] in, For coating porosity, The real part of the equivalent dielectric constant. For the real part of the dielectric constant of a dense, non-porous coating, is the real part of the air dielectric constant.

[0108] Then, the thermal conductivity of the area to be tested can be determined based on the thermal conductivity and porosity of the dense coating. This thermal conductivity can satisfy the following relationship:

[0109] ;

[0110] in, The thermal conductivity of the region to be measured is P represents the thermal conductivity of the dense, non-porous coating material, and P represents the porosity of the coating.

[0111] Then, based on the target coating thickness, the thermal conductivity of the area to be measured, and the cross-sectional area of ​​the area to be measured, the thermal resistance of the coating is determined. This thermal resistance of the coating can satisfy the following relationship:

[0112] ;

[0113] Where R is the thermal resistance of the coating, and d is the target value of the coating thickness. Let be the thermal conductivity of the region to be measured, and A be the cross-sectional area of ​​the region to be measured.

[0114] Therefore, in this embodiment, the equivalent dielectric constant, coating porosity, and thermal conductivity are determined sequentially from the target complex refractive index, and the coating thermal resistance is finally calculated, rather than the thermal resistance and thermal properties of the coating plus the substrate. This can be directly used to evaluate the thermal insulation performance of the coating, realizing the mapping from the material's optical properties to its thermal properties. By utilizing the optical parameters obtained from terahertz non-destructive testing, the internal pore structure and thermal conductivity of the coating can be indirectly inverted, reflecting the thermal insulation level of the coating in a single point area. This eliminates the need for destructive testing, additional heating, or contact measurement, enabling non-contact evaluation of thermal insulation performance. This effectively improves the accuracy and reliability of thermal insulation performance evaluation, providing a basis for the quality evaluation and safety assessment of thermal barrier coatings for aero-engines.

[0115] In the aforementioned method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology, the terahertz time-domain spectrum of the thermal barrier coating under test is first obtained, and then transformed to obtain the terahertz frequency-domain spectrum. Subsequently, based on the terahertz frequency-domain spectrum, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined. Then, based on the candidate complex refractive index corresponding to each candidate coating thickness value, the target complex refractive index corresponding to the target coating thickness value is determined. Finally, based on the target coating thickness value, the target complex refractive index, and the cross-sectional area of ​​the test region, the thermal resistance of the coating is determined. Thus, by acquiring the terahertz time-domain spectrum and performing frequency-domain transformation, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value can be determined. This allows for the selection of the target coating thickness value and its corresponding target complex refractive index, ultimately calculating the thermal resistance of the thermal barrier coating. This achieves a non-destructive evaluation of the thermal insulation performance of the thermal barrier coating, while also improving the accuracy and reliability of the thermal insulation performance evaluation.

[0116] In one exemplary embodiment, such as Figure 2 As shown, step 104 includes steps 202 to 210. Wherein:

[0117] Step 202: Select multiple candidate values ​​for coating thickness from the candidate range of coating thickness.

[0118] The candidate range for coating thickness can be a reasonable range of thickness set based on prior knowledge or engineering experience of thermal barrier coatings, such as process range and historical data. The candidate value for coating thickness can be a coating thickness value selected uniformly or non-uniformly within this candidate range, and this application does not limit it in this regard.

[0119] For example, when the candidate range for coating thickness is [100, 300] micrometers, multiple candidate values ​​for coating thickness can be selected uniformly in steps of 1 micrometer, etc. This application does not limit this.

[0120] Therefore, in this embodiment of the application, by pre-setting the candidate range of coating thickness and selecting multiple candidate values ​​of coating thickness from it, the thickness range can be limited to a reasonable range that conforms to engineering reality, avoiding invalid calculations and unreasonable numerical interference. At the same time, the multi-point candidate traversal method can ensure that the true thickness is effectively covered, improve the accuracy and completeness of subsequent thickness and optical parameter inversion, and provide a reliable basis for subsequent determination of the true coating thickness.

[0121] Step 204: Based on the terahertz wave theoretical transfer function model and the initial complex refractive index, determine the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point. The frequency points are determined by the terahertz frequency domain spectrum.

[0122] The initial complex refractive index can be a pre-set complex refractive index, such as one set based on experience, literature values, or similar materials, or it can be a randomly set complex refractive index, etc. This application does not limit this.

[0123] In addition, the frequency points can be a series of discrete frequency points obtained after the Fourier transform of the terahertz time domain spectrum, that is, all the frequencies contained in the terahertz frequency domain spectrum.

[0124] In addition, the theoretical amplitude and phase values ​​can be calculated using the terahertz wave theory transfer function model, and are used to compare with the measured amplitude and phase to determine the fitting performance.

[0125] Understandably, the theoretical amplitude and phase values ​​can be calculated for each candidate coating thickness at each frequency point in the terahertz frequency spectrum, based on the theoretical transfer function of the terahertz wave theory and the initial given complex refractive index. This provides a theoretical basis for subsequent comparison with measured values ​​and optimization of the complex refractive index.

[0126] Step 206: Based on the true amplitude and true phase values ​​of each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude and theoretical phase values ​​of each frequency point, determine the total error value of each candidate coating thickness at each frequency point.

[0127] Among them, the true amplitude value and the true phase value can be the signal amplitude and phase of each frequency point extracted from the terahertz frequency domain spectrum and obtained by actual measurement, which can characterize the true reflection and transmission characteristics of the coating.

[0128] In addition, the total error value can be understood as the error obtained by comprehensively calculating the difference between the actual amplitude value and the theoretical amplitude value, and the difference between the actual phase value and the theoretical phase value at the same frequency point for each candidate coating thickness value. It can be used to characterize the degree of closeness between the theoretical simulation results and the actual measurement results.

[0129] Optionally, the amplitude error between the actual amplitude value and the theoretical amplitude value, and the phase error between the actual phase value and the theoretical phase value of each candidate coating thickness value at each frequency point can be determined first. Then, based on the amplitude error value and phase error value of each candidate coating thickness value at each frequency point, the total error value of each candidate coating thickness value at each frequency point can be determined.

[0130] Among them, the amplitude error value can be used to characterize the fitting deviation in the amplitude direction, the phase error value can characterize the fitting deviation in the phase direction, and the total error value can be understood as the overall deviation of the amplitude error and phase error at each frequency point for each candidate coating thickness value, which is used to characterize the degree of difference between the theoretical calculation value and the actual measured value.

[0131] For example, for each discrete frequency point f in the measured terahertz frequency domain spectrum i The true amplitude value determined from this frequency domain spectrum can be expressed as: The true value of the phase can be expressed as The theoretical amplitude value determined based on the terahertz wave theory transfer function model can be expressed as: The theoretical value of the phase can be expressed as .

[0132] For a single frequency point, the amplitude error value can be The phase error value can be The total error value can be .

[0133] Optionally, the amplitude error and phase error values ​​can be normalized to avoid excessively large differences in magnitude that could affect subsequent processing. When calculating the phase error value, the phase difference can be reduced to the principal value range; this application does not impose any limitations on this.

[0134] It is understandable that, for each candidate coating thickness value, the above operation is performed sequentially at each frequency point, and finally the total error value of each candidate coating thickness value at each frequency point is obtained.

[0135] Therefore, in this embodiment of the application, by calculating the amplitude error and the phase error separately and then combining them to obtain the total error value, the deviation contribution of amplitude information and phase information can be taken into account at the same time. This avoids the one-sidedness caused by using only a single error. Calculating each frequency point separately can make full use of the spectrum information of the entire frequency band, making the error evaluation more comprehensive and accurate, providing a reliable basis for subsequent iterative optimization of complex refractive index, and thus improving the fitting accuracy and stability of candidate complex refractive index.

[0136] Step 208: Update the initial complex refractive index based on the total error value of each candidate coating thickness at each frequency point.

[0137] For each candidate coating thickness value, calculations can be performed based on each frequency point to obtain the total error value corresponding to each frequency point, and the initial complex refractive index can be corrected. For example, the real and imaginary parts of the initial complex refractive index can be adjusted to achieve the update and optimization of the complex refractive index.

[0138] For example, iterative optimization algorithms such as gradient descent can be used to adjust the real part of the initial complex refractive index (i.e., refractive index n) and the imaginary extinction coefficient κ) based on the magnitude and direction of the total error at each frequency point. For instance, if the total error at a certain frequency point is positive, it can be assumed that the theoretical value deviates significantly from the measured value, and the values ​​of the real and imaginary parts of the complex refractive index can be appropriately increased or decreased; if the error is negative, the direction of increase or decrease of the real and imaginary parts can be adjusted in the opposite direction; or weights can be allocated according to the magnitude of the error at each frequency point to adjust the correction range of the corresponding complex refractive index, thereby completing the update and optimization of the complex refractive index and obtaining the candidate complex refractive index corresponding to each thickness candidate value, etc. This application does not limit this.

[0139] Optionally, during the process of updating the initial complex refractive index based on the total error value at each frequency point for each candidate coating thickness value, any acceptable method, such as nonlinear least squares optimization or the Levenberg-Marquardt algorithm, can be used to calculate the optimal adjustment amount of the real and imaginary parts of the complex refractive index at each frequency point in each iteration step, thereby realizing the updating and optimization of the complex refractive index spectrum. This application does not limit this.

[0140] Step 210: Using the updated initial complex refractive index, return to the steps above for determining the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point until the iteration stop condition is met, and determine the complex refractive index of each candidate coating thickness at each frequency point as the corresponding candidate complex refractive index.

[0141] There are various iteration stopping conditions, such as the total error value being less than the error threshold, the number of iterations reaching a preset number, or the change in complex refractive index between two adjacent iterations being less than a preset threshold. This application does not limit these conditions.

[0142] Understandably, iterative optimization is performed for each candidate coating thickness value. Based on the total error value calculated for the current candidate thickness at that frequency point, the goal is to reduce the total error and make the theoretical value closer to the measured value. Targeted adjustments and corrections are made to the real and imaginary parts of the initial complex refractive index, continuously bringing the theoretical amplitude and phase values ​​closer to the true amplitude and phase values, resulting in a complex refractive index closer to reality at that frequency point. This achieves one round of complex refractive index update optimization. Then, using the updated initial complex refractive index, the theoretical amplitude and phase values ​​for the current candidate coating thickness at that frequency point are determined again based on the terahertz wave theory transfer function model. The total error value for the current candidate coating thickness at that frequency point is then calculated again, and the initial complex refractive index is updated again. This process is repeated until the iteration stops, and the final complex refractive index is determined as the candidate complex refractive index for the current candidate coating thickness at that frequency point.

[0143] Then, following the above method, iterative optimization can be performed on each frequency point for the current candidate coating thickness value to obtain the candidate complex refractive index of the candidate coating thickness value at each frequency point. Then, the same operation can be performed on all candidate coating thickness values ​​to finally obtain the candidate complex refractive index corresponding to each candidate coating thickness value at each frequency point.

[0144] For each frequency point f i Given a candidate coating thickness value d guess In this case, by minimizing the squared error modulus between the theoretical transfer function model of terahertz waves and the measured results of the terahertz frequency domain spectrum, the optimal refractive index n corresponding to the current frequency point can be obtained through optimization. i With extinction coefficient That is, satisfying:

[0145] ;

[0146] Among them, H model For the terahertz wave theory transfer function model, H measured Extracted from the terahertz frequency domain spectrum at frequency point f i The complex reflection coefficient at point (including the true amplitude and true phase values), argmin represents the parameter n that minimizes the target error function. .

[0147] Therefore, in this embodiment, the frequency-point independent optimization method can be adopted to solve the error minimization problem separately for the spectral characteristics of each frequency point. This can fully adapt to the signal differences and material dispersion characteristics at different frequency points, avoid the mutual influence of signal interference and errors between different frequencies, and obtain the optimal optical parameters independently for each frequency point. The fitting accuracy is higher, and it is more sensitive to local spectral details. It can more realistically reflect the variation law of complex refractive index with frequency and improve the accuracy of parameter inversion.

[0148] Optionally, for each candidate coating thickness value, a global joint optimization method across the entire frequency band can be used to iteratively solve for the complex refractive index.

[0149] For example, for each candidate coating thickness value, the total error across all frequency points can be accumulated to obtain the global total error corresponding to the current candidate coating thickness value. With the goal of minimizing the global total error, the real and imaginary parts of the initial complex refractive index are globally adjusted and corrected. Then, using the updated complex refractive index, the theoretical amplitude and phase values ​​of the current candidate coating thickness value at each frequency point are re-determined based on the terahertz wave theory transfer function model. The total error value at each frequency point is then recalculated to update the global total error value, resulting in a new round of updates to the complex refractive index. This iterative process is repeated until the iteration termination condition is met. Upon iteration termination, the complex refractive index corresponding to each frequency point is determined as the candidate complex refractive index of the current candidate coating thickness value at that frequency point. Following this method, global iterative optimization is performed for each candidate coating thickness value, ultimately yielding the candidate complex refractive index corresponding to each candidate coating thickness value at each frequency point.

[0150] It should be noted that the above examples are merely illustrative and should not be construed as limiting the methods for determining candidate complex refractive indices in the embodiments of this application.

[0151] Therefore, in this embodiment of the application, the global joint optimization method of the whole frequency band is adopted to comprehensively accumulate the errors of all frequency points and minimize them as a whole. This can balance the deviation of each frequency point at the global level, avoid the excessive influence of signal noise or local anomalies of a single frequency point on the optimization results, and make the optimization results smoother, more stable, and better anti-interference ability by adjusting the complex refractive index globally, thus effectively improving the consistency of the overall fitting of the complex refractive index.

[0152] In this embodiment, multiple candidate coating thickness values ​​can be selected within a preset candidate coating thickness range, effectively narrowing the parameter search range and improving computational efficiency. Based on the terahertz wave theory transfer function model and the initial complex refractive index, the theoretical amplitude and phase values ​​of each candidate thickness value at each frequency point are calculated. Then, the total error value at each frequency point is obtained by combining the actual amplitude and phase values. This can comprehensively reflect the difference between the theoretical calculation results and the measured signal. The complex refractive index is iteratively updated based on the total error value. After the iteration converges, the candidate complex refractive index corresponding to each candidate coating thickness value at each frequency point is obtained, thereby improving the accuracy and reliability of the candidate complex refractive index and laying a solid foundation for accurately determining the actual coating thickness and optical parameters in the future.

[0153] In one exemplary embodiment, a method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology is provided, such as... Figure 3 As shown, step 106 includes steps 302 to 304. Wherein:

[0154] Step 302: Determine the cost function value for each candidate coating thickness based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value.

[0155] Among them, the rate of change of candidate complex refractive index can be the degree of change of the real and imaginary parts of complex refractive index with frequency, and can be its derivative or difference, reflecting the smoothness and continuity of the change of complex refractive index with frequency. The larger the rate of change, the less smooth it can be considered.

[0156] In addition, the cost function value can be calculated based on the rate of change of the candidate complex refractive index. The smaller the cost function value, the smoother the corresponding candidate complex refractive index can be considered.

[0157] Understandably, the correct coating thickness can precisely counteract the oscillations caused by phase delay in terahertz frequency domain spectral measurements, and the calculated... and The curve is also smooth, while the incorrect coating thickness is calculated due to incomplete phase compensation. and The curve exhibits obvious oscillations. Since the optical constants of a real, homogeneous material change smoothly with frequency, the candidate coating thickness with the minimum cost function value corresponds to the most physically reasonable material optical properties, and this candidate coating thickness is most likely to be close to the true coating thickness.

[0158] Optionally, for each candidate coating thickness value, the first rate of change of the real part of the candidate complex refractive index between adjacent frequency points and the second rate of change of the imaginary extinction coefficient between adjacent frequency points can be calculated. The sum of the squares of the first rate of change and the sum of the squares of the second rate of change are then superimposed to obtain the cost function value corresponding to the candidate coating thickness value.

[0159] The first rate of change can be the rate of change of the real part of the candidate complex refractive index between adjacent frequency points, reflecting the degree of change of the real part parameter with frequency. The second rate of change can be the rate of change of the imaginary part of the candidate complex refractive index, i.e., the extinction coefficient, between adjacent frequency points, reflecting the degree of change of the imaginary part parameter with frequency.

[0160] Based on the first rate of change and the second rate of change, the sum of squares of the first rate of change and the sum of squares of the second rate of change are calculated, and the two are superimposed to obtain the cost function value of the corresponding candidate coating thickness value.

[0161] The cost function can be expressed as:

[0162] ;

[0163] in, Candidate value for coating thickness d guess The cost function value, n i and n i+1 Let be the real part of the candidate complex refractive index at adjacent frequency points. and This represents the imaginary part of the candidate complex refractive index at adjacent frequency points, i.e., the extinction coefficient. This represents the interval between adjacent frequency points.

[0164] Therefore, in this embodiment, the constructed cost function can quantify the degree of change of the real and imaginary parts of the candidate complex refractive index with frequency, and objectively reflect the smoothness of the optical parameter curve by the sum of squares of the rate of change between adjacent frequency points. At the same time, by superimposing the degree of change of the real and imaginary parts, the parameter oscillation problem caused by improper phase compensation can be effectively identified and eliminated.

[0165] Step 304: Determine the candidate coating thickness value corresponding to the minimum cost function value as the target coating thickness value, and determine the candidate complex refractive index of each frequency point of the minimum cost function value as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

[0166] Understandably, all candidate coating thickness values ​​can be iterated through, and the cost function value corresponding to each candidate coating thickness value can be calculated. By comparing all cost function values, the candidate coating thickness value corresponding to the minimum cost function value is selected as the target coating thickness value. The candidate complex refractive index obtained by iterative optimization of this candidate coating thickness value at each frequency point is determined as the target complex refractive index of the target coating thickness value at each corresponding frequency point. Thus, the cost function constructed in the above manner can quantify the degree of change of the real and imaginary parts of the complex refractive index. By summing the squares, it reflects the smoothness of the optical parameter curve. By globally comparing the cost function values ​​of all candidate coating thickness values ​​and selecting the minimum value, the thickness and optical parameters that best match the real material properties can be screened from the perspective of physical smoothness. This effectively eliminates the oscillation anomaly caused by incomplete phase compensation, thereby ensuring that the selected target coating thickness value and target complex refractive index conform to the material's physical properties. This can effectively improve the accuracy and reliability of thickness inversion and provide precise support for subsequent coating characteristic analysis and quality inspection.

[0167] In this embodiment, the cost function value of each candidate coating thickness can be determined based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value. The candidate coating thickness value corresponding to the minimum cost function value is determined as the target coating thickness value, and the candidate complex refractive index of each frequency point of the minimum cost function value is determined as the target complex refractive index of the target coating thickness value at the corresponding frequency point. This allows for the selection of parameters that conform to the physical properties of the material, effectively eliminating parameter anomalies caused by improper phase compensation, ensuring that the selected coating thickness and optical parameters match the actual situation, improving the accuracy and reliability of parameter inversion, and providing precise parameter support for subsequent coating characteristic analysis and quality inspection.

[0168] In one exemplary embodiment, such as Figure 4As shown, a method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology is provided. In this embodiment, the method includes the following steps:

[0169] Step 401: Obtain the terahertz time-domain spectrum of the thermal barrier coating area to be tested, and perform transformation processing on the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum.

[0170] Step 402: Based on the terahertz wave theoretical transfer function model and the initial complex refractive index, determine the theoretical amplitude and phase values ​​of each layer thickness candidate value at each frequency point. The frequency points are determined by the terahertz frequency domain spectrum.

[0171] Step 403: Based on the amplitude error between the actual amplitude value and the theoretical amplitude value, and the phase error between the actual phase value and the theoretical phase value, for each candidate coating thickness value at each frequency point, determine the total error value of each candidate coating thickness value at each frequency point.

[0172] Step 404: Update the initial complex refractive index based on the total error value of each candidate coating thickness at each frequency point.

[0173] Step 405: Using the updated initial complex refractive index, return to the steps above for determining the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point until the iteration stop condition is met, and determine the complex refractive index of each candidate coating thickness at each frequency point as the corresponding candidate complex refractive index.

[0174] Step 406: For each candidate coating thickness value, determine the cost function value corresponding to the candidate coating thickness value based on the first rate of change of the real part of the candidate complex refractive index between adjacent frequency points and the second rate of change of the imaginary extinction coefficient between adjacent frequency points.

[0175] Step 407: Determine the candidate coating thickness value corresponding to the minimum cost function value as the target coating thickness value, and determine the candidate complex refractive index of each frequency point of the minimum cost function value as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

[0176] Step 408: Determine the thermal resistance of the coating based on the target coating thickness, target complex refractive index, and cross-sectional area of ​​the area to be measured.

[0177] Step 409: Determine the equivalent dielectric constant of the region to be measured based on the target complex refractive index.

[0178] Step 410: Determine the porosity of the coating in the area to be tested based on the equivalent dielectric constant, the dielectric constant of the dense coating, and the dielectric constant of air.

[0179] Step 411: Determine the thermal conductivity of the area to be tested based on the thermal conductivity and porosity of the dense coating.

[0180] Step 412: Determine the thermal resistance of the coating based on the target coating thickness, the thermal conductivity of the area to be tested, and the cross-sectional area of ​​the area to be tested.

[0181] It should be noted that the specific content and implementation method of each step can be referred to the description of the various embodiments of this application, and will not be repeated here.

[0182] In this embodiment, terahertz wave detection technology enables non-destructive testing of parameters related to the thermal insulation performance of thermal barrier coatings without requiring any destructive manipulation of the samples. This preserves sample integrity and avoids sample loss and testing bias associated with destructive testing. The thermal insulation performance testing process begins by iteratively updating the complex refractive index to ensure the theoretical and measured signals closely match, reducing data fitting errors. Then, a cost function is used to screen target thicknesses and complex refractive indices that conform to the material's physical properties. By comparing the smoothness of material properties derived under different thickness assumptions, rationality is ensured. Finally, based on the selected target coating thickness and target complex refractive index, a series of calculations yield the coating's thermal increase, effectively mitigating the impact of parameter deviations on thermal insulation performance evaluation. Through multi-step iterative optimization and screening, the accuracy and reliability of thermal insulation performance testing are significantly improved, providing comprehensive and reliable support for the evaluation and quality control of thermal barrier coating thermal insulation performance.

[0183] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages in other steps. It is understood that the steps in different embodiments can be freely combined as needed, and all non-contradictory solutions formed by such combinations are within the scope of protection of this application.

[0184] Based on the same inventive concept, this application also provides a terahertz-based thermal barrier coating thermal resistance inversion device for implementing the aforementioned terahertz-based thermal barrier coating thermal resistance inversion method. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations of one or more terahertz-based thermal barrier coating thermal resistance inversion device embodiments provided below can be found in the above-described limitations of the terahertz-based thermal barrier coating thermal resistance inversion method, and will not be repeated here.

[0185] In one exemplary embodiment, such as Figure 5 As shown, a thermal barrier coating thermal resistance inversion device 500 based on terahertz technology is provided, comprising: an acquisition module 510, a first determination module 520, a second determination module 530, and a third determination module 540, wherein:

[0186] The acquisition module 510 is used to acquire the terahertz time-domain spectrum of the thermal barrier coating under test area, and to transform the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum.

[0187] The first determining module 520 is used to determine the candidate complex refractive index corresponding to each of the terahertz thickness candidate values ​​based on the terahertz frequency domain spectrum, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model.

[0188] The second determining module 530 is used to determine the target complex refractive index corresponding to the target coating thickness value based on the candidate complex refractive index corresponding to each candidate coating thickness value.

[0189] The third determining module 540 is used to determine the thermal resistance of the coating based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be measured.

[0190] In one embodiment, the first determining module 520 includes:

[0191] The selection unit is used to select multiple candidate values ​​for coating thickness from the candidate range of coating thickness.

[0192] The first determining unit is used to determine the theoretical amplitude and theoretical phase values ​​of each candidate coating thickness at each frequency point based on the terahertz wave theoretical transfer function model and the initial complex refractive index, wherein the frequency point is determined by the terahertz frequency domain spectrum.

[0193] The second determining unit is used to determine the total error value of each candidate coating thickness at each frequency point based on the true amplitude value and the true phase value of each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude value and the theoretical phase value of each frequency point.

[0194] An update unit is configured to update the initial complex refractive index based on the total error value of each candidate coating thickness at each frequency point;

[0195] The third determining unit is used to return to the above steps of determining the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point using the updated initial complex refractive index, until the iteration stop condition is met, and to determine the complex refractive index of each candidate coating thickness at each frequency point as the corresponding candidate complex refractive index.

[0196] In one embodiment, the second determining unit is specifically used for:

[0197] Determine the amplitude error value between the actual amplitude value and the theoretical amplitude value, and the phase error value between the actual phase value and the theoretical phase value, for each candidate coating thickness value at each frequency point;

[0198] Based on the amplitude error and phase error of each candidate coating thickness value at each frequency point, the total error value of each candidate coating thickness value at each frequency point is determined.

[0199] In one embodiment, the second determining module 530 includes:

[0200] The fourth determining unit is used to determine the cost function value of each candidate coating thickness based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value;

[0201] The fifth determining unit is used to determine the candidate coating thickness value corresponding to the minimum cost function value as the target coating thickness value, and to determine the candidate complex refractive index of each frequency point of the minimum cost function value as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

[0202] In one embodiment, the fourth determining unit is specifically used for:

[0203] For each candidate coating thickness value, calculate the first rate of change of the real part of the candidate complex refractive index between adjacent frequency points and the second rate of change of the imaginary extinction coefficient between adjacent frequency points;

[0204] The sum of the squares of the first rate of change and the sum of the squares of the second rate of change are superimposed to obtain the cost function value corresponding to the candidate coating thickness value.

[0205] In one embodiment, the third determining module 540 is specifically used for:

[0206] The equivalent dielectric constant of the region to be measured is determined based on the target complex refractive index.

[0207] The porosity of the coating in the test area is determined based on the equivalent dielectric constant, the dielectric constant of the dense coating, and the dielectric constant of air.

[0208] The thermal conductivity of the area to be tested is determined based on the thermal conductivity of the dense coating and the porosity of the coating.

[0209] The thermal resistance of the coating is determined based on the target coating thickness, the thermal conductivity of the area to be tested, and the cross-sectional area of ​​the area to be tested.

[0210] Each module in the aforementioned thermal barrier coating thermal resistance inversion device based on terahertz technology can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0211] In one exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6 As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides the environment for the operation of the operating system and computer programs in the non-volatile storage medium. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When executed by the processor, the computer program implements a thermal barrier coating thermal resistance inversion method based on terahertz technology.

[0212] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0213] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.

[0214] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0215] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0216] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0217] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0218] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for inverting the thermal resistance of thermal barrier coatings based on terahertz technology, characterized in that, The method includes: The terahertz time-domain spectrum of the thermal barrier coating under test area is obtained, and the terahertz time-domain spectrum is transformed to obtain the terahertz frequency-domain spectrum. Based on the terahertz frequency domain spectrum, and combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, the candidate complex refractive index corresponding to each candidate coating thickness value is determined; Based on the candidate complex refractive index corresponding to each candidate coating thickness value, determine the target complex refractive index corresponding to the target coating thickness value; The thermal resistance of the coating is determined based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be tested.

2. The method according to claim 1, characterized in that, The step of determining the candidate complex refractive index corresponding to each of the terahertz frequency domain spectra, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model, includes: Select multiple candidate coating thickness values ​​from the candidate coating thickness range; Based on the terahertz wave theoretical transfer function model and the initial complex refractive index, the theoretical amplitude and phase values ​​of each candidate coating thickness are determined at each frequency point, and the frequency points are determined by the terahertz frequency domain spectrum. Based on the true amplitude and true phase values ​​at each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude and theoretical phase values ​​at each frequency point, determine the total error value of each candidate coating thickness at each frequency point; The initial complex refractive index is updated based on the total error value of each candidate coating thickness at each frequency point; Using the updated initial complex refractive index, return to the steps described above for determining the theoretical amplitude and phase values ​​of each candidate coating thickness at each frequency point until the iteration stop condition is met, and determine the complex refractive index of each current candidate coating thickness at each frequency point as the corresponding candidate complex refractive index.

3. The method according to claim 2, characterized in that, The step of determining the total error value of each candidate coating thickness at each frequency point based on the true amplitude and true phase values ​​at each frequency point in the terahertz frequency domain spectrum, and the theoretical amplitude and theoretical phase values ​​at each frequency point, includes: Determine the amplitude error value between the actual amplitude value and the theoretical amplitude value, and the phase error value between the actual phase value and the theoretical phase value, for each candidate coating thickness value at each frequency point; Based on the amplitude error and phase error of each candidate coating thickness value at each frequency point, the total error value of each candidate coating thickness value at each frequency point is determined.

4. The method according to claim 1, characterized in that, The step of determining the target complex refractive index corresponding to the target coating thickness value based on the candidate complex refractive index corresponding to each candidate coating thickness value includes: The cost function value for each candidate coating thickness is determined based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness value. The candidate coating thickness value corresponding to the minimum cost function value is determined as the target coating thickness value, and the candidate complex refractive index of each frequency point of the minimum cost function value is determined as the target complex refractive index of the target coating thickness value at the corresponding frequency point.

5. The method according to claim 4, characterized in that, The step of determining the cost function value for each candidate coating thickness based on the rate of change of the candidate complex refractive index corresponding to each candidate coating thickness includes: For each candidate coating thickness value, calculate the first rate of change of the real part of the candidate complex refractive index between adjacent frequency points and the second rate of change of the imaginary extinction coefficient between adjacent frequency points; The sum of the squares of the first rate of change and the sum of the squares of the second rate of change are superimposed to obtain the cost function value corresponding to the candidate coating thickness value.

6. The method according to claim 1, characterized in that, The step of determining the coating thermal resistance based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be measured includes: The equivalent dielectric constant of the region to be measured is determined based on the target complex refractive index. The porosity of the coating in the test area is determined based on the equivalent dielectric constant, the dielectric constant of the dense coating, and the dielectric constant of air. The thermal conductivity of the area to be tested is determined based on the thermal conductivity of the dense coating and the porosity of the coating. The thermal resistance of the coating is determined based on the target coating thickness, the thermal conductivity of the area to be tested, and the cross-sectional area of ​​the area to be tested.

7. A thermal barrier coating thermal resistance inversion device based on terahertz technology, characterized in that, The device includes: The acquisition module is used to acquire the terahertz time-domain spectrum of the thermal barrier coating under test area, and to transform the terahertz time-domain spectrum to obtain the terahertz frequency-domain spectrum. The first determining module is used to determine the candidate complex refractive index corresponding to each of the terahertz frequency domain spectra, combined with multiple candidate coating thickness values ​​and the terahertz wave theoretical transfer function model. The second determining module is used to determine the target complex refractive index corresponding to the target coating thickness based on the candidate complex refractive index corresponding to each candidate coating thickness value; The third determining module is used to determine the thermal resistance of the coating based on the target coating thickness, the target complex refractive index, and the cross-sectional area of ​​the region to be measured.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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