A method for measuring thickness of terahertz coating based on multi-objective function and adaptive niche

Abstract

This invention relates to a terahertz coating thickness measurement method based on multi-objective functions and adaptive niches, belonging to the field of terahertz nondestructive testing. By employing a three-objective collaborative constraint mechanism involving waveform residuals, time-of-flight matching, and reflection peak amplitude, combined with an adaptive niche teaching and learning optimization algorithm, high-precision and high-stability measurement of thermal barrier coating thickness is achieved. First, a theoretical analytical model is established based on the multi-layer propagation law of terahertz waves and coatings, considering the influence of roughness, to obtain simulation signals. Based on the time-domain characteristics of the terahertz reflection signal, a multi-objective optimization function is constructed using waveform residuals, time-of-flight matching, and reflection peak amplitude collaborative constraints. Then, an adaptive niche strategy is integrated into the teaching and learning optimization algorithm to maintain population diversity and improve global optimization ability, forming a teaching and learning optimization algorithm based on multi-objective functions and adaptive niches. Finally, the improved optimization algorithm is applied to solve the terahertz analytical model, achieving high-precision inversion measurement of coating thickness. This method is a nondestructive testing method based on terahertz time-domain spectroscopy, requiring no calibration or damage to the sample under test. Relying on the advantages of multi-objective collaborative constraints, it achieves high-precision and high-stability coating thickness measurement.

Description

Technical Field

[0001] This invention relates to a terahertz coating thickness measurement method based on multi-objective functions and adaptive microenvironment, belonging to the field of terahertz nondestructive testing. Background Technology

[0002] Coatings are functional protective or decorative material layers applied to the surface of a substrate material. They possess key properties such as heat insulation, corrosion resistance, electrical insulation, wear resistance, and sealing, and are widely used in many industrial fields, including aerospace hot-end components, high-end mechanical equipment, electronic components, rail transportation, and marine engineering. Coating thickness is a core technical indicator that directly determines its service performance, service life, and operational reliability. Achieving high-precision, non-destructive testing of coating thickness is a crucial step in ensuring product manufacturing quality and equipment service safety.

[0003] Commonly used techniques for non-destructive testing of coating thickness include ultrasonic testing, infrared testing, eddy current testing, and X-ray testing. These traditional methods all have inherent limitations in practical engineering applications: ultrasonic testing requires a coupling agent, which can easily contaminate the coating surface and has poor adaptability to rough surfaces; eddy current testing is low-cost and requires no coupling agent, but it is only suitable for conductive substrates and cannot directly and effectively test ceramic insulation layers; infrared testing sensitivity decreases significantly with increasing coating thickness and is easily affected by ambient temperature and surface emissivity; X-ray testing has high accuracy and good anti-interference capabilities, but it poses a ionizing radiation hazard, requires specialized protection and dedicated facilities, and has a high barrier to entry and cost.

[0004] Terahertz waves refer to electromagnetic waves with frequencies ranging from 0.1 to 10 THz, falling between microwaves and infrared light. They possess both electronic and photonic characteristics, exhibiting unique advantages such as non-ionizing radiation, non-contact detection, strong penetration of non-metallic coatings, high temporal coherence, and low photon energy. They can penetrate non-metallic materials such as ceramics, polymers, and thermal barrier coatings without damaging the sample, obtaining internal interface information, making them a preferred technology for non-destructive testing of coating thickness. Currently, coating thickness detection methods based on terahertz non-destructive testing technology are mainly divided into three categories: time-of-flight (TOF) methods, machine learning methods, and model inversion methods. The TOF method calculates coating thickness by extracting the time delay of the terahertz reflected echo and combining it with the material's refractive index. It is simple in principle and highly efficient, but requires prior refractive index calibration of the sample. For coatings with inhomogeneous microstructures, refractive index deviations can easily lead to decreased thickness measurement accuracy. Machine learning methods predict thickness by constructing a nonlinear mapping model between terahertz signal characteristics and coating thickness. It has strong adaptability, but relies on massive experimental samples to build datasets, resulting in poor physical interpretability of the model and limited generalization ability. The model inversion method is based on the physical model of terahertz wave propagation and uses an optimization algorithm to invert and solve the coating thickness. It does not require sample calibration, can simultaneously invert multiple physical parameters, and has high thickness measurement accuracy.

[0005] The model inversion method relies on the physical analytical model of terahertz wave propagation. Iteratively solving the optimal parameters of the model through optimization algorithms, thereby realizing the inversion detection of coating thickness. Existing methods (such as patent CN 108519059 A) construct a theoretical analytical model based on the interaction mechanism between terahertz waves and coatings, and use interior point algorithms for iterative solutions. Although this can achieve coating thickness measurement, traditional optimization algorithms are highly dependent on initial values ​​and are prone to getting trapped in local extrema, resulting in large thickness measurement errors. This makes it difficult to meet the high-precision detection requirements of automotive paint coatings, thermal barrier coatings on aero-engine ceramic layers, etc. Cao Binghua's team subsequently proposed an efficient and reliable thickness measurement method for multilayer coatings based on terahertz time-domain spectroscopy (Acta Optica Sinica, 2022, 42(01):127-137.) and (Research on Terahertz Non-destructive Testing Technology for Thermal Barrier Coating Thickness [D]. China University of Mining and Technology, 2022.). The thickness inversion accuracy was improved by a novel swarm intelligence algorithm. However, this method only uses a single waveform residual as the optimization target, and the algorithm population diversity is insufficient. It is easily affected by the deviation between the theoretical model and the actual working conditions. The stability and consistency of the thickness measurement results in practical engineering applications cannot be guaranteed. Subsequently, Cao Binghua's team proposed a terahertz thickness measurement method for thermal barrier coatings based on physical constraints (Research on Terahertz Thickness Detection Method of Thermal Barrier Coating Based on Model Inversion [D]. China University of Mining and Technology, 2024.) and (Physical constraints-based terahertz thickness measurement method of thermal barrier coating [J]. NDT and E International, 2024, 143103058.). Addressing the problem that traditional single-objective optimization lacks physical feature constraints in inversion and is prone to getting trapped in local optima, this method further improves the accuracy of thickness inversion by adding key physical features such as flight time and reflection peak amplitude to the objective function to form collaborative constraints. However, the method is still limited to the field of single-objective optimization, and the introduction of physical feature constraints increases the model inversion time, placing a greater burden on practical engineering applications. This patent proposes a terahertz thermal barrier coating thickness detection method based on multi-objective functions and adaptive microenvironment. This method improves the inversion accuracy and detection stability by constructing a multi-objective optimization function that integrates multiple physical features and introducing an adaptive niche strategy to improve the teaching and learning optimization algorithm, thereby achieving reliable and high-precision measurement of thermal barrier coating thickness. Summary of the Invention

[0006] To address the above problems, this invention proposes a terahertz coating thickness measurement method based on multi-objective functions and adaptive microenvironment. Addressing the issues of existing terahertz thermal barrier coating thickness measurement methods being prone to local optima in single-objective optimization, large parameter coupling interference, and poor measurement stability, this invention achieves high-precision and high-stability measurement of thermal barrier coating thickness by using a three-objective collaborative constraint mechanism involving waveform residuals, time-of-flight matching, and reflection peak amplitude, combined with an adaptive microenvironment teaching and learning optimization algorithm.

[0007] The technical solution of the present invention includes the following steps:

[0008] (1) Prepare the specimen and use a reflective terahertz time-domain spectroscopy system to perform a measurement experiment on the specimen to obtain the terahertz reference signal and the terahertz experimental signal;

[0009] (2) Construct a theoretical analytical model of the interaction between terahertz waves and the coated sample, and substitute the reference signal into the model to obtain the terahertz simulation signal;

[0010] (3) Based on the waveform residuals of the simulated signal and the experimental signal, the algorithm optimization is based on the integration of flight time matching and reflection peak amplitude characteristics to construct a multi-objective constraint term and establish a multi-objective optimization function adapted to terahertz coating thickness measurement.

[0011] The waveform residuals between the terahertz simulation signal and the experimental signal are used as the basic objective for algorithm optimization. The waveform fitting residuals, inter-peak flight time, and amplitude synchronization of the reflection peaks are used as constraint parameters for the inversion parameters. A multi-objective optimization function is constructed to avoid the algorithm getting trapped in local extrema during iterative optimization, forming a multi-objective function adapted for terahertz coating thickness detection. Its expression is: Among them, F R F represents the signal residual term. TOF For flight time matching, F AMP This represents the reflection peak amplitude matching term, and the three-term collaborative constraint inversion process;

[0012] (4) Establish a teaching and learning optimization algorithm based on multi-objective function and adaptive niche strategy. Improve the population distribution characteristics of the standard teaching and learning optimization algorithm through the adaptive niche mechanism, and enhance the algorithm's ability to find global optimization and escape local optima.

[0013] (5) Embed the theoretical analytical model in step (2) into the improved algorithm in step (4), and use the experimental signal obtained in step (1) to solve the multi-objective optimization function constructed in step (3) to obtain the optimized coating thickness value.

[0014] The theoretical analytical model for the interaction between terahertz waves and the coating in step (2) specifically includes:

[0015] According to Fresnel's formula, the reflectance at the air / ceramic layer interface is:

[0016] In the formula, ñ0 and ñ1 represent the complex refractive indices of the air layer and the ceramic layer, respectively, and r 01 This represents the Fresnel reflection coefficient at the air / ceramic layer interface;

[0017] Ceramic layer / metal substrate interface reflectance:

[0018] In the formula, ñ2 represents the complex refractive index of the metal substrate, and r 12 The Fresnel reflection coefficient represents the ceramic layer / metal substrate interface;

[0019] According to the Fresnel formula, the Fresnel transmission coefficients t at the air / ceramic layer interface and the ceramic layer / air interface can also be obtained. 01 , t 10 :

[0020] , ;

[0021] Let the incident terahertz frequency domain signal be E0(ω), then the first three reflected echoes are:

[0022] , , ;

[0023] Where β is the phase factor, and its specific expression is: In the formula, n1 is the complex refractive index of the ceramic layer, ω is the angular frequency of the terahertz signal, d corresponds to the thickness of the ceramic layer, and c is the speed of light in a vacuum.

[0024] From E2(ω) to E n (ω) is a geometric sequence with common ratio r. 10 r 12 e iβ Therefore, the nth reflected echo can be obtained. Summing all the echoes yields the total THz reflected signal E. R (ω), specifically expressed as follows:

[0025] , ;

[0026] According to Stokes' inverse relation, the transmission coefficient and reflection coefficient at the medium interface have the following relationship:

[0027] ;

[0028] Substituting the above relationship into the total reflected signal E R Simplifying the expression for (ω), we get:

[0029] ;

[0030] Since the surfaces of the coating and the metal substrate are not smooth, the surface and interfacial roughness of the coated sample are characterized according to the Kirchhoff approximation method:

[0031] ;in This is the equivalent reflectance after roughness correction. For the ideal interface reflectance, The root mean square roughness is... The wavelength is terahertz; by incorporating the effect of roughness into the total reflected signal, the terahertz simulation signal generated by the theoretical analytical model is: .

[0032] The specific expressions for the three constraints in step (3) are as follows:

[0033] ;

[0034] ;

[0035] ;

[0036] Among them, E sim (t i ,x) is the simulation signal calculated from parameter x using a physical model. The experimental signal Δt is obtained through experimental acquisition. sim With Δt exp These represent the flight times of the simulated signal and the experimental signal, respectively. and These represent the amplitudes of the two reflection peaks in the simulated signal; and The amplitudes of the two reflection peaks in the experimental signal are given.

[0037] Step (4) involves constructing the teaching and learning optimization (MOAN-TLBO) algorithm based on multi-objective function and adaptive niche technology, which includes:

[0038] Class initialization:

[0039] Where i = 1, 2, ..., N, j = 1, 2, ..., D, and Let be the boundary of the j-th dimension variable, and rand(0,1) represent a random number uniformly distributed in the interval (0,1).

[0040] Teacher's instruction:

[0041] , where X teacher X is the optimal individual in the population. i For the i-th student individual; T F M represents the teaching factor; M represents the average parameter of students in the class. The position of the newly generated student. The original student's position;

[0042] Student learning:

[0043] , where X k X is a student individual randomly selected from the population; i For the i-th student individual; The position of the newly generated student. This refers to the original student's position.

[0044] In step (4), a teaching and learning optimization algorithm based on a multi-objective function and an adaptive niche strategy is established. The population is divided into levels using non-dominated sorting, and the shared radius is dynamically adjusted according to the iteration process. In the early stages of iteration, a larger shared radius is used to expand the search range and improve global search capability. In the later stages of iteration, a smaller shared radius is used to shrink the search range and enhance local optimization accuracy. Simultaneously, a shared fitness screening mechanism is used to eliminate similar individuals, concentrating computational resources on high-quality individuals to improve the algorithm's global optimization capability and convergence speed. Step (4) specifically calculates: First, the Euclidean distance between individuals at the same level is calculated:

[0045] ,in, and Individuals belonging to the same non-dominant layer, , These are the upper and lower bounds of the non-dominated layer, respectively.

[0046] Recalculate the shared function:

[0047] In the formula, The parameter used to control the sharing intensity is a set value. The shared radius is a dynamic value, and its specific definition is as follows:

[0048] In the formula, Let λ be the initial maximum shared radius, λ be the decay rate constant controlling the decay rate, t be the current algorithm iteration number, and T be the maximum number of iterations. Then, update the individual shared fitness. ,in, Let be the virtual fitness value of each individual in the P-th non-dominated layer. Finally, the niche sharing radius is dynamically adjusted based on the iteration process. The adaptive niche strategy expands the search range in the early stages of iteration to improve global search capabilities, and shrinks the radius in the later stages of iteration to enhance local optimization accuracy.

[0049] This invention first establishes a theoretical analytical model based on the multilayer propagation law of terahertz waves and coatings, considering the influence of roughness, to obtain simulation signals. Based on the time-domain characteristics of the terahertz reflection signal, a multi-objective optimization function is constructed using waveform residuals, time-of-flight matching, and collaborative constraints of reflection peak amplitude. Then, an adaptive niche strategy is integrated into the teaching and learning optimization algorithm to maintain population diversity and improve global optimization capabilities, forming a teaching and learning optimization algorithm based on the multi-objective function and adaptive niche. Finally, the improved optimization algorithm is applied to solve the terahertz analytical model, achieving high-precision inversion measurement of coating thickness. This method is a non-destructive testing method based on terahertz time-domain spectroscopy, requiring no calibration or damage to the sample. Relying on the advantages of multi-objective collaborative constraints, it can achieve high-precision and high-stability coating thickness measurement. Compared with existing detection methods, this invention has the following advantages:

[0050] First, compared with the traditional time-of-flight method, this invention does not require pre-calibration of the sample refractive index, and will not reduce the thickness measurement accuracy due to material parameter fluctuations caused by the uneven microstructure of the thermal barrier coating, thus making it more applicable to detection. At the same time, compared with machine learning thickness measurement methods, this invention does not require the construction of a large-scale sample dataset, and high-precision inversion can be achieved with a small number of samples.

[0051] II. Based on the propagation and reflection signal characteristics of terahertz waves in thermal barrier coatings, a multi-objective optimization function is constructed that integrates waveform residuals, time-of-flight matching, and reflection peak amplitude. Through the synergistic constraints and mutual checks and balances of these three independent physical features, the pseudo-optimal solution of "good waveform fitting but inaccurate thickness" in single-objective optimization is fundamentally eliminated, effectively avoiding the algorithm iteration getting trapped in local extrema. Experimental results show that the thickness measurement error of this invention is stable at less than 1% with 100mm repeated measurements, far superior to the average error level of about 3% of existing single-objective methods, significantly improving the accuracy and consistency of the thickness measurement results.

[0052] Third, an iterative adaptive niche strategy is used to improve the mutation strategy of the teaching and learning optimization algorithm. By using non-dominated sorting hierarchical layering and adaptive adjustment of shared radius, an optimal balance between global search and local optimization is achieved. This strategy not only dynamically maintains population diversity and avoids premature convergence, further improving convergence accuracy, but also significantly reduces the number of invalid iterations through adaptive search rhythm and similar individual selection mechanism, shortening the single measurement calculation time from 30 seconds in the existing technology to 15 seconds, improving computational efficiency by approximately 50%. Attached Figure Description

[0053] Figure 1 This is a waveform diagram of a terahertz experimental signal.

[0054] Figure 2 This is a schematic diagram of the interaction between terahertz waves and the coating structure.

[0055] Figure 3 This is a flowchart of a teaching and learning optimization algorithm based on multi-objective functions and adaptive niches.

[0056] Figure 4 It is a graph showing the fitting of experimental and simulated signals.

[0057] Figure 5 This is an accuracy evaluation chart of the inversion thickness measurement results. Detailed Implementation

[0058] To clearly illustrate the technical features of the present invention, the present invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings.

[0059] This invention provides a terahertz coating thickness measurement method based on multi-objective functions and adaptive microenvironment, which is particularly suitable for high-precision and rapid detection of thermal barrier coating ceramic layers with a thickness range of 50 μm to 500 μm. The method includes the following steps:

[0060] (1) Prepare experimental samples, use a reflective terahertz time-domain spectroscopy system to measure the samples, obtain terahertz reference signals and terahertz experimental signals, and obtain the actual thickness value of the measured point through a probe profilometer for error comparison.

[0061] (2) Establish a theoretical analytical model for the interaction between terahertz waves and the coated sample, based on Figure 2 The propagation law of terahertz waves inside the coating was investigated, an analytical model was constructed, and a reference signal was introduced into the model to obtain the terahertz simulation signal.

[0062] (3) Using waveform residual, time-of-flight matching error, and reflection peak amplitude error as three sub-objectives, a multi-objective function is constructed to achieve the coordinated constraint of multiple physical characteristics of terahertz signals, thereby improving the stability of thickness inversion results;

[0063] (4) Establish a teaching and learning optimization algorithm based on multi-objective function and adaptive niche. On the basis of the teaching and learning optimization algorithm, introduce an adaptive niche strategy to dynamically adjust the shared radius to maintain population diversity and balance the search ability of the algorithm at different iteration stages.

[0064] (5) The theoretical analytical model is combined with the teaching and learning optimization algorithm based on multi-objective function and adaptive microenvironment, and the terahertz experimental signal is introduced to solve the parameters of the model to obtain the optimized thickness value.

[0065] In this embodiment of the invention, step (2) of the theoretical analytical model for the interaction between the terahertz wave and the coating sample is as follows:

[0066] The reflection and transmission coefficients between different dielectric layers are characterized using Fresnel's law and Rouard's equivalent interface theory:

[0067] , ,in and η0 and η1 represent the reflection and transmission coefficients of the medium interface, respectively, and η0 and η1 represent the complex refractive indices of the air layer and the ceramic layer, respectively.

[0068] The nth reflection echo after the terahertz wave passes through the coating is: ,in Terahertz input radio frequency domain signal, For phase factor, Angular frequency, For coating thickness, The speed of light;

[0069] The total received reflected signal is the sum of all the echoes:

[0070] ;

[0071] The surface and interfacial roughness of the coated sample were characterized using the Kirchhoff approximation method:

[0072] ;

[0073] in This is the equivalent reflectance after roughness correction. For the ideal interface reflectance, The root mean square roughness is... The wavelength is terahertz; by incorporating the effect of roughness into the total reflected signal, the terahertz simulation signal generated by the theoretical analytical model is: .

[0074] In this embodiment of the invention, the establishment of the multi-objective function in step (3) involves the following specific steps:

[0075] The waveform residuals between the terahertz simulation signal and the experimental signal are used as the basic objective for algorithm optimization. Then, the time-domain characteristics of the terahertz reflection signal are analyzed, revealing that its core thickness information is contained in the flight time and reflection peak amplitude. Therefore, the waveform fitting residual, the flight time between reflection peaks, and the synchronization of reflection peak amplitudes are used as constraint parameters for the inversion parameters. A multi-objective optimization function is constructed to avoid the algorithm getting trapped in local extrema during iterative optimization, forming a multi-objective function adapted to terahertz coating thickness detection. Its expression is: A Terahertz Coating Thickness Measurement Method Based on Multi-Objective Function and Adaptive Microenvironment. F R F represents the signal residual term.TOF For flight time matching, F AMP This represents the reflection peak amplitude matching term, and the three-term collaborative constraint inversion process. The specific expression is as follows:

[0076] ;

[0077] ;

[0078] ;

[0079] Among them, E sim (t i ,x) is the simulation signal calculated from parameter x using a physical model, Δt sim With Δt exp These represent the flight times of the simulated signal and the experimental signal, respectively. and These represent the amplitudes of the two reflection peaks in the simulated signal; and The amplitudes of the two reflection peaks in the experimental signal are given.

[0080] like Figure 3 As shown, the flowchart of the teaching and learning optimization algorithm based on multi-objective functions and adaptive niches in this invention includes:

[0081] The teaching and learning optimization algorithm based on multi-objective functions and adaptive niches is constructed, mainly including:

[0082] Class initialization:

[0083] ;

[0084] Where i = 1, 2, ..., N, j = 1, 2, ..., D, and Let be the boundary of the j-th dimension variable, and rand(0,1) represent a random number uniformly distributed in the interval (0,1).

[0085] Teacher's instruction:

[0086] ;

[0087] Among them, X teacher X is the optimal individual in the population. i For the i-th student individual; T F M represents the teaching factor; M is the average parameter of students in the class. The position of the newly generated student. This refers to the original student's position.

[0088] Student learning:

[0089] ;

[0090] Where X k X is a student individual randomly selected from the population. i For the i-th student individual; The position of the newly generated student. This refers to the original student's position.

[0091] A teaching and learning optimization algorithm based on multi-objective functions and adaptive niche strategies is established. The population is divided into levels by non-dominated sorting and the shared radius is dynamically adjusted according to the iteration process. In the early stage of iteration, a larger shared radius is used to expand the search range and improve the global search capability. In the later stage of iteration, a smaller shared radius is used to shrink the search range and enhance the local optimization accuracy. At the same time, a shared fitness screening mechanism is used to eliminate similar individuals and concentrate computing resources on high-quality individuals, thereby improving the algorithm's global optimization capability and convergence speed.

[0092] The specific calculation is as follows: First, calculate the Euclidean distance between individuals at the same level:

[0093] ;

[0094] Recalculate the shared function And update individual shared fitness Dynamically adjust the niche sharing radius according to the iteration process. In the formula, Let λ be the initial maximum shared radius, λ be the decay rate constant controlling the decay rate, t be the current algorithm iteration number, and T be the maximum number of iterations. The adaptive niche strategy expands the search range in the early stages of iteration to improve global search capability, and shrinks the radius in the later stages to enhance local optimization accuracy. Finally, an improved multi-objective function is introduced to form a teaching and learning optimization algorithm based on the multi-objective function and adaptive niche, to improve the thickness detection accuracy of thermal barrier coatings. The algorithm optimization analysis model's simulation signal and experimental signal fitting results are shown in the figure. Figure 4 As shown.

[0095] Fifteen terahertz experimental signals with measured actual thicknesses were applied to an improved algorithm for optimized inversion, in order to evaluate the measurement accuracy of the technical solution proposed in this patent. For example... Figure 5 As shown, the average relative error between the measurement results and the actual values ​​is 0.7%.

[0096] This invention proposes a terahertz thermal barrier coating thickness detection method based on multi-objective functions and adaptive niche optimization. This method eliminates the need for prior refractive index calibration of the specimen and can simultaneously measure multiple parameters such as thickness, refractive index, and roughness. It possesses significant engineering application value for high-precision, high-reliability, non-destructive quantitative detection of thermal barrier coatings.

[0097] There are many specific ways to implement this invention. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates, characterized in that, Includes the following steps: (1) Prepare the specimen and use a reflective terahertz time-domain spectroscopy system to measure the coated specimen and obtain the terahertz reference signal and terahertz experimental signal; (2) Construct a theoretical analytical model of the interaction between terahertz waves and coated specimens, and substitute the reference signal into the model to obtain the terahertz simulation signal; (3) Based on the waveform residuals of the simulated signal and the experimental signal, the algorithm optimization is based on the integration of flight time matching and reflection peak amplitude characteristics to construct a multi-objective constraint term and establish a multi-objective optimization function adapted to terahertz coating thickness measurement. The waveform residuals between the terahertz simulation signal and the experimental signal are used as the basic objective for algorithm optimization. The waveform fitting residuals, inter-peak flight time, and amplitude synchronization of the reflection peaks are used as constraint parameters for the inversion parameters. A multi-objective optimization function is constructed to avoid the algorithm getting trapped in local extrema during iterative optimization, forming a multi-objective function adapted for terahertz coating thickness detection. Its expression is: ; Among them, F R F represents the signal residual term. TOF For flight time matching, F AMP This represents the reflection peak amplitude matching term, and the three-term collaborative constraint inversion process; (4) Establish a teaching and learning optimization algorithm based on multi-objective function and adaptive niche strategy. Improve the population distribution characteristics of the standard teaching and learning optimization algorithm through the adaptive niche mechanism, and enhance the algorithm's ability to find global optimization and escape local optima. (5) Embed the theoretical analytical model in step (2) into the improved algorithm in step (4), and use the experimental signal obtained in step (1) to solve the multi-objective optimization function constructed in step (3) to obtain the optimized coating thickness value.

2. The terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates according to claim 1, characterized in that, The construction of the theoretical analytical model for the interaction between terahertz waves and the coating in step (2) specifically includes: According to Fresnel's formula, the reflectance at the air / ceramic layer interface is: In the formula, ñ0 and ñ1 represent the complex refractive indices of the air layer and the ceramic layer, respectively, and r 01 This represents the Fresnel reflection coefficient at the air / ceramic layer interface; Ceramic layer / metal substrate interface reflectance: In the formula, ñ2 represents the complex refractive index of the metal substrate, and r 12 The Fresnel reflection coefficient represents the ceramic layer / metal substrate interface; According to the Fresnel formula, the Fresnel transmission coefficients t at the air / ceramic layer interface and the ceramic layer / air interface can also be obtained. 01 , t 10 : ， ； Let the incident terahertz frequency domain signal be E0(ω), then the first three reflected echoes are: ， ， ； Where β is the phase factor, and its specific expression is: In the formula, n1 is the complex refractive index of the ceramic layer, ω is the angular frequency of the terahertz signal, d corresponds to the thickness of the ceramic layer, and c is the speed of light in a vacuum. From E2(ω) to E n (ω) is a geometric sequence with common ratio r. 10 r 12 e iβ Therefore, the nth reflected echo can be obtained. Summing all the echoes yields the total THz reflected signal E. R (ω), specifically expressed as follows: ， ； According to Stokes' inverse relation, the transmission coefficient and reflection coefficient at the medium interface have the following relationship: ； Substituting the above relationship into the total reflected signal E R Simplifying the expression for (ω), we get: ； Since the surfaces of the coating and the metal substrate are not smooth, the surface and interfacial roughness of the coated sample are characterized according to the Kirchhoff approximation method: ;in This is the equivalent reflectivity after roughness correction. For the ideal interface reflectance, The root mean square roughness is... The wavelength is terahertz; by incorporating the effect of roughness into the total reflected signal, the terahertz simulation signal generated by the theoretical analytical model is: .

3. The terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates according to claim 1, characterized in that, The specific expressions for the three constraints in step (3) are as follows: ； ； ； Among them, E sim (t i ,x) is the simulation signal calculated from parameter x using a physical model. The experimental signal Δt is obtained through experimental acquisition. sim With Δt exp These represent the flight times of the simulated signal and the experimental signal, respectively. and These represent the amplitudes of the two reflection peaks in the simulated signal; and The amplitudes of the two reflection peaks in the experimental signal are given.

4. The terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates according to claim 1, characterized in that, Step (4) involves constructing a teaching and learning optimization (MOAN-TLBO) algorithm based on multi-objective functions and adaptive niche technology, including: Class initialization: Where i = 1, 2, ..., N, j = 1, 2, ..., D, and Let be the boundary of the j-th dimension variable, and rand(0,1) represent a random number uniformly distributed in the interval (0,1). Teacher's instruction: , where X teacher X is the optimal individual in the population. i For the i-th student individual; T F M represents the teaching factor; M represents the average parameter of students in the class. The position of the newly generated student. The original student's position; Student learning: , where X k X is a student individual randomly selected from the population; i For the i-th student individual; The position of the newly generated student. This refers to the original student's position.

5. The terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates according to claim 4, characterized in that, In step (4), a teaching and learning optimization algorithm based on multi-objective function and adaptive niche strategy is established. The population level is divided by non-dominated sorting and the shared radius is dynamically adjusted according to the iteration process. In the early stage of iteration, a larger shared radius is used to expand the search range and improve the global search capability. In the later stage of iteration, a smaller shared radius is used to shrink the search range and strengthen the local optimization accuracy. At the same time, similar individuals are eliminated through the shared fitness screening mechanism, and computing resources are concentrated on high-quality individuals to improve the global optimization capability and convergence speed of the algorithm.

6. The terahertz coating thickness measurement method based on multi-objective functions and adaptive microclimates according to claim 5, characterized in that, Step (4) is specifically calculated as follows: First, calculate the Euclidean distance between individuals at the same level: ,in, and Individuals belonging to the same non-dominant layer, , These are the upper and lower bounds of the non-dominated layer, respectively. Recalculate the shared function: In the formula, The parameter used to control the sharing intensity is a set value. The shared radius is a dynamic value, and its specific definition is as follows: In the formula, The initial maximum shared radius is given by λ, the decay rate constant controls the decay rate, t is the current algorithm iteration number, and T is the maximum number of iterations; and the individual shared fitness is updated. ,in, Let be the virtual fitness value of each individual in the P-th non-dominated layer. Finally, the niche sharing radius is dynamically adjusted based on the iteration process. The adaptive niche strategy expands the search range in the early stages of iteration to improve global search capabilities, and shrinks the radius in the later stages of iteration to enhance local optimization accuracy.

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