Terahertz detection method for thermal barrier coating thickness based on hybrid objective function and mutation strategy

Abstract

The present invention discloses a terahertz detection method for thermal barrier coating thickness based on a hybrid objective function and a mutation strategy, and belongs to the field of terahertz nondestructive testing. By improving the swarm intelligence algorithm to improve the solution accuracy, the characteristics of the terahertz signal are analyzed according to the analytical model, and the characteristic value is introduced into the hybrid objective function, so as to achieve stable and reliable coating thickness detection. The following steps are included: obtaining a terahertz reference signal and a terahertz experimental signal; constructing a theoretical analytical model of the interaction between the terahertz wave and the coating sample; analyzing the characteristics of the terahertz signal and constructing the objective function constraint term, and establishing an improved objective function adapted to terahertz thickness detection; improving the population initialization method of the standard teaching and learning optimization algorithm, and improving the algorithm's search capability; and obtaining the optimized coating thickness value. A teaching and learning optimization algorithm based on an adaptive Cauchy-Gaussian mutation strategy is constructed to achieve high-precision measurement of coating thickness.

Description

Technical Field

[0001] The invention relates to a terahertz detection method for thermal barrier multilayer thickness with improved objective function and variation strategy, belonging to the field of terahertz nondestructive detection. Background Art

[0002] Coatings can be defined as layers of material that cover the surface of bulk materials to achieve specific properties, usually for decorative, functional, or both purposes, such as military applications, marine industry, medical devices, electronic equipment, and daily household appliances. The purpose of the application of functional coatings is usually to protect materials from corrosion, dirt, mechanical wear, etc. The thickness of the coating is an important indicator of its protective performance. Therefore, achieving accurate measurement of coating thickness is crucial to monitor the quality of the coating and ensure that the base material is not damaged.

[0003] Common technologies used in non-destructive testing of coating thickness include ultrasonic testing, infrared testing, eddy current testing, and X-ray testing. However, these methods have certain limitations for testing different materials:

[0004] 1. Ultrasonic testing usually requires the application of coupling agent, and improper operation can easily cause coating contamination. Eddy current testing has low cost and does not require coupling agent, but is not suitable for the detection of non-metallic materials.

[0005] 2. The detection sensitivity of infrared detection will decrease with the increase of coating thickness, and the ambient temperature will also interfere with the detection accuracy.

[0006] 3. The results of X-ray detection are highly accurate and have strong anti-interference capabilities, but corresponding protective measures are required to prevent ionizing radiation from causing harm to the human body.

[0007] It is worth noting that terahertz refers to a range of electromagnetic waves with a frequency of 0.1 to 10 THz, and a wavelength range of 0.03 to 3 mm, which is between the microwave band and infrared light. Terahertz non-destructive testing technology has the advantages of strong penetration, non-ionization, and non-contact, and is suitable for non-destructive testing of non-metallic materials such as composite materials and ceramics. At present, the coating thickness detection methods based on terahertz non-destructive testing technology mainly include: time of flight method, machine learning method and model inversion method.

[0008] However, the time-of-flight method usually requires calibration of the test piece to obtain the refractive index. For coatings with microstructural inhomogeneities due to the manufacturing process, the refractive index at different spatial locations is different from the calibration value, resulting in reduced accuracy in thickness detection. Machine learning often requires a large amount of sample data as a data set.

[0009] As for the model inversion method, it uses an optimization algorithm to solve the theoretical analytical model of terahertz signals, which can realize the simultaneous measurement of the refractive index and thickness of the coating. This method can also achieve high-precision thickness measurement under the condition of uneven coating microstructure.

[0010] The model inversion method is based on the derived physical model, and uses an optimization algorithm to iteratively solve the model to obtain the optimal parameters of the physical model, thereby realizing the thickness detection of the coating. The common method (the method disclosed in patent CN 108519059 A) is to establish a theoretical analytical model based on the mechanism of action between the coating and the terahertz wave, and then use the interior point algorithm to iteratively solve the analytical model to finally measure the thickness of the coating. However, the traditional algorithm used in this method relies on the selection of initial values, and it is easy to fall into local extreme values. The measured coating thickness value has a large error, which is difficult to be competent in occasions such as automotive paint coatings and thermal barrier coating ceramic layers where the thickness detection requirements reach the micron level. On this basis, Cao Binghua's team proposed an efficient and reliable thickness measurement method for multilayer coatings based on terahertz time-domain spectroscopy technology (Acta Optica Sinica, 2022, 42(01): 127-137. Research on terahertz nondestructive testing technology for thickness of thermal barrier coatings [D]. China University of Mining and Technology, 2022.). The accuracy of thickness inversion was improved by using a new swarm intelligence algorithm. However, since the theoretical model cannot be guaranteed to be completely consistent with the actual situation, the stability of the thickness measurement results of this method in practical applications cannot be guaranteed. Summary of the invention

[0011] In view of the above problems, the present invention proposes a terahertz detection method for thermal barrier coating thickness based on a hybrid objective function and a mutation strategy. The swarm intelligence algorithm is improved to improve the solution accuracy. At the same time, the characteristics of the terahertz signal are analyzed according to the analytical model, and the characteristic value is introduced into the hybrid objective function, thereby achieving stable and reliable coating thickness detection.

[0012] The technical solution of the present invention is: comprising the following steps:

[0013] Step (1), using a reflective terahertz time-domain spectroscopy system to perform a measurement experiment on the workpiece to be measured, and obtaining a terahertz reference signal and a terahertz experimental signal;

[0014] Step (2), constructing a theoretical analytical model of the interaction between terahertz waves and coating samples, and introducing a reference signal into the model to obtain a terahertz simulation signal;

[0015] Step (3), using the residual of the simulation signal and the experimental signal as the objective function of the algorithm optimization, analyzing the characteristics of the terahertz signal and constructing the objective function constraint term, and establishing an improved objective function suitable for terahertz thickness detection;

[0016] Step (4), establishing a teaching and learning optimization algorithm based on the objective function and adaptive Cauchy-Gaussian mutation, using piecewise linear chaotic mapping to improve the population initialization method of the standard teaching and learning optimization algorithm, and introducing an adaptive Cauchy-Gaussian mutation strategy into the algorithm to improve the algorithm's search capability;

[0017] Step (5), applying the theoretical analytical model in step (2) to the algorithm in step (4), and introducing the experimental signal obtained in step (1) to solve the improved objective function in step (3) to obtain the optimized coating thickness value.

[0018] The theoretical analytical model of the interaction between the terahertz wave and the coating in step (2) specifically includes:

[0019] The Fresnel formula is used to characterize the reflection coefficient and transmission coefficient between different dielectric layers. where r 01 , r 10 and r 12 is the reflection coefficient, t 01 is the transmission coefficient, and are the complex refractive indices of different dielectric layers respectively; the nth reflected echo after the terahertz wave and the thermal barrier coating is: E n (ω)=t 01 r 10 n-2 r 12 n-1 t 10 e i(n-1)β E i (ω), where E i (ω) is the terahertz incident signal, e is a natural constant, i is an imaginary unit, is the phase factor, ω is the angular frequency, d is the coating thickness, and c is the speed of light; the total reflected signal received is:

[0020] Characterize the rough surface of the coating sample according to Kirchhoff's approximation: Where R r is the effective reflectivity, R s is the sum of total reflection coefficient and diffuse reflection coefficient, δ is the root mean square roughness of the rough surface, λ is the wavelength of light, and e is a natural constant;

[0021] Introducing the influence of roughness into the total reflection signal, the terahertz simulation signal generated by the theoretical analytical model is:

[0022]

[0023] Step (3) establishes an improved objective function adapted to terahertz thickness detection:

[0024] The residual between the terahertz simulation signal and the experimental signal is used as the objective function of the algorithm optimization; then the characteristics of the terahertz reflection signal are analyzed, and its main thickness information is contained in the flight time and the peak value of the reflection peak. Therefore, the peak value of the reflection peak and the flight time between the reflection peaks are used as characteristic parameters to control the inversion parameters. The objective function constraint term is introduced to avoid the algorithm from falling into the local extreme value during the optimization process. An improved objective function suitable for terahertz coating thickness detection is constructed, and its expression is: Where t1 and t2 represent the time from the appearance to the cutoff of the first two reflection peaks, E exp (t) is the measured terahertz signal, E the (t) is the model simulation terahertz signal, t tof and t loc are the flight time from the first reflection peak to the second reflection peak of the experimental signal and the simulation signal, respectively, exp1 and P exp2 are the peak values ​​of the first and second reflection peaks of the experimental signal, P the1 and P the2 are the peak values ​​of the first and second reflection peaks of the simulation signal, and is the weight factor of the control constraint.

[0025] Step (4) constructs a teaching and learning optimization algorithm based on the objective function and the adaptive Cauchy-Gaussian variation, which mainly includes:

[0026] Class initialization: Where j is the subject of each student, i is the student number, are the upper and lower bounds of the control variables for the corresponding subjects, and rand(0,1) is a random number between 0 and 1;

[0027] Teachers’ teaching: x T is the best individual in the population; is the i-th student individual; T i is the teaching factor; x m is the average score of students in the class;

[0028] Students learn: where i≠j, is a student individual randomly selected from the population; the population initialization method of the standard teaching and learning optimization algorithm is improved by using piecewise linear chaotic mapping. The mapping has a uniform distribution characteristic in the range of 0 to 1, thereby improving the population diversity of the algorithm. The specific expression is: where z nis the nth chaotic variable, p∈(0,1); the improved adaptive Cauchy-Gaussian mutation strategy is applied to the optimization algorithm to balance the search capabilities of the algorithm at different stages, thereby improving the convergence ability of the algorithm. Its mathematical model is: in is the adaptive weight factor, t max is the maximum number of iterations of the algorithm, σ is the standard deviation, is the individual with the best fitness, Cauchy(0,σ 2 ) is subject to the mathematical expectation of 0 and the variance of σ 2 The random number of the Cauchy distribution, Gaussian(0,σ 2 ) has a mathematical expectation of 0 and a variance of σ 2 A Gaussian distributed random number is used; depending on whether the iteration situation meets the expectation of the objective function, mutation adjustment is performed in the early and middle stages of the iteration. At the same time, if the objective function has not changed for k consecutive generations in the late stage of the iteration, the weight factor is exchanged for supervision adjustment.

[0029] The present invention overcomes the parameter coupling problem in the process of algorithm optimization to solve the coating thickness, establishes a theoretical analytical model of terahertz signals of thermal barrier coatings for solving inverse problems, and introduces the influence of coating surface roughness into the model. The chaotic mapping population initialization method and the improved Cauchy-Gaussian mutation strategy are introduced into the optimization algorithm, and a teaching and learning optimization algorithm based on the adaptive Cauchy-Gaussian mutation strategy is constructed to achieve high-precision measurement of coating thickness.

[0030] Compared with the existing detection methods, the present invention has the following advantages:

[0031] 1. Compared with the time-of-flight method, the present invention will not cause a decrease in accuracy due to changes in the material parameters of the sample, and does not require calibration of the specimen; at the same time, compared with the machine learning method, the present invention does not require a large number of sample data sets and is suitable for thickness detection of a small number of samples;

[0032] Second, according to the reflection signal characteristics of the interaction between terahertz waves and coatings, the flight time and reflection peak value containing the thickness signal are used as constraints to improve the objective function of the algorithm, reduce local extreme values ​​in the algorithm iteration, and overcome the problem of poor stability of the solution results due to the high randomness of the optimization algorithm.

[0033] 3. Use piecewise chaotic linear mapping to improve the population initialization method of the teaching and learning optimization algorithm and improve the population diversity; at the same time, use the improved adaptive Cauchy-Gaussian mutation strategy to balance the search ability of the algorithm at different iteration stages, thereby improving the convergence ability of the algorithm and obtaining more accurate thickness prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 : Terahertz experimental signal waveform.

[0035] Figure 2 : Schematic diagram of the interaction between terahertz waves and coating structures.

[0036] Figure 3 : Flowchart of the teaching and learning optimization algorithm based on adaptive Cauchy-Gaussian mutation.

[0037] Figure 4 : Fitting diagram of experimental signal and simulation signal.

[0038] Figure 5 : Accuracy assessment diagram of inversion thickness measurement results. DETAILED DESCRIPTION

[0039] In order to clearly illustrate the technical features of this patent, this patent is elaborated in detail below through a specific implementation method and in combination with its accompanying drawings.

[0040] Example:

[0041] The embodiment of the present invention provides a terahertz detection method for thermal barrier coating thickness based on a hybrid objective function and a variation strategy, the method comprising the following steps:

[0042] Step (1), preparing an experimental sample, using a reflective terahertz time-domain spectroscopy system to perform a measurement experiment on the sample, obtaining a terahertz reference signal and a terahertz experimental signal, and obtaining the actual thickness value of the measured point of the sample by metallographic method;

[0043] Step (2), establish a theoretical analytical model of the interaction between terahertz waves and coating samples, according to Figure 2 The propagation law of terahertz waves inside the coating is studied, an analytical model is constructed, and a reference signal is introduced into the model to obtain a terahertz simulation signal;

[0044] Step (3), taking the residual of the simulation signal and the experimental signal as the objective function of the algorithm optimization, analyzing the characteristics of the terahertz signal and constructing the objective function constraint term, and establishing an improved objective function suitable for terahertz thickness detection to avoid the algorithm falling into a local extreme value during iteration, thereby improving the stability of the thickness inversion result;

[0045] Step (4), establishing a teaching and learning optimization algorithm based on objective function optimization and adaptive Cauchy-Gaussian mutation, using piecewise linear chaotic mapping to improve the population initialization method of the standard teaching and learning optimization algorithm, and introducing an adaptive Cauchy-Gaussian mutation strategy into the algorithm to balance the search ability of the algorithm at different iteration stages;

[0046] Step (5), combining the theoretical analytical model with the teaching and learning optimization algorithm based on objective function optimization and adaptive Cauchy-Gaussian variation, and introducing terahertz experimental signals to solve the model parameters to obtain the optimized thickness value.

[0047] In the embodiment of the present invention, the step (2) of establishing the theoretical analytical model of the interaction between the terahertz wave and the coating sample comprises the following specific steps:

[0048] The Fresnel formula is used to characterize the reflection coefficient and transmission coefficient between different dielectric layers. where r 01 , r 10 and r 12 is the reflection coefficient, t 01 is the transmission coefficient, and are the complex refractive indices of different dielectric layers respectively; the nth reflected echo after the terahertz wave and the coating is: E n (ω)=t 01 r 10 n-2 r 12 n-1 t 10 e i(n-1)β E i (ω), where E i (ω) is the terahertz incident signal, e is a natural constant, i is an imaginary unit, is the phase factor, ω is the angular frequency, d is the coating thickness, and c is the speed of light; the total reflected signal received is:

[0049] Characterize the rough surface of the coating sample according to Kirchhoff's approximation: Where R r is the effective reflectivity, R s is the sum of total reflection coefficient and diffuse reflection coefficient, δ is the root mean square roughness of the rough surface, λ is the wavelength of light, and e is a natural constant;

[0050] Introducing the influence of roughness into the total reflection signal, the terahertz simulation signal generated by the theoretical analytical model is:

[0051]

[0052] In the embodiment of the present invention, the establishment of the hybrid objective function in step (3) comprises the following specific steps:

[0053] The residual between the terahertz simulation signal and the experimental signal is used as the objective function of the algorithm optimization; then the characteristics of the terahertz reflection signal are analyzed, and its main thickness information is contained in the flight time and the peak value of the reflection peak. Therefore, the peak value of the reflection peak and the flight time between the reflection peaks are used as characteristic parameters to control the inversion parameters. The objective function constraint term is introduced to avoid the algorithm from falling into the local extreme value during the optimization process. An improved objective function suitable for terahertz coating thickness detection is constructed, and its expression is: Where t1 and t2 represent the time from the appearance to the cutoff of the first two reflection peaks, E exp (t) is the measured terahertz signal, E the (t) is the model simulation terahertz signal, t tof and t loc are the flight time from the first reflection peak to the second reflection peak of the experimental signal and the simulation signal, respectively, exp1 and P exp2 are the peak values ​​of the first and second reflection peaks of the experimental signal, P the1 and P the2 are the peak values ​​of the first and second reflection peaks of the simulation signal, and is the weight factor of the control constraint.

[0054] like Figure 3 As shown, the present invention constructs a flowchart of an embodiment based on a hybrid objective function and an adaptive Cauchy-Gaussian variation teaching and learning optimization algorithm, which specifically includes:

[0055] Construct a teaching and learning optimization algorithm based on a hybrid objective function and adaptive Cauchy-Gaussian variation, which mainly includes:

[0056] Class initialization: Where j is the subject of each student, i is the student number, are the upper and lower bounds of the control variables for the corresponding subjects, and rand(0,1) is a random number between 0 and 1;

[0057] Teachers’ teaching: x T is the best individual in the population, is the i-th student individual, T i is the teaching factor, x m is the average score of students in the class;

[0058] Students learn: where i≠j, are randomly selected student individuals within the population.

[0059] The population initialization method of the standard teaching and learning optimization algorithm is improved by using piecewise linear chaotic mapping. The mapping has a uniform distribution characteristic in the range of 0 to 1, thereby improving the population diversity of the algorithm. The specific expression is: where z n is the nth chaotic variable, p∈(0,1). The improved adaptive Cauchy-Gauss mutation strategy is applied to the optimization algorithm to balance the search capabilities of different stages of the algorithm, thereby improving the convergence ability of the algorithm. Its mathematical model is: in is the adaptive weight factor, tmax is the maximum number of iterations of the algorithm, σ is the standard deviation, is the individual with the best fitness, Cauchy(0,σ 2 ) is subject to the mathematical expectation of 0 and the variance of σ 2 The random number of the Cauchy distribution, Gaussian(0,σ 2 ) has a mathematical expectation of 0 and a variance of σ 2 Gaussian distribution of random numbers; according to whether the iteration situation meets the expectation of the objective function, the mutation adjustment is performed in the early and middle stages of the iteration. At the same time, if the objective function has not changed for k consecutive generations in the late iteration, the weight factor is exchanged for supervision adjustment. Finally, the improved objective function is introduced to form an adaptive Cauchy-Gaussian variation teaching and learning optimization algorithm to improve the thickness detection accuracy of thermal barrier coatings. The algorithm optimizes the fitting of the simulation signal generated by the analytical model and the experimental signal, such as Figure 4 shown.

[0060] 15 terahertz experimental signals with measured actual thickness are applied to the improved algorithm for optimized inversion to evaluate the measurement accuracy of the technical solution proposed in this patent. Figure 5 As shown, the average absolute error between the measured results and the actual values ​​is 1.8μm.

[0061] The present invention proposes a terahertz coating thickness detection method based on swarm intelligence algorithm. This method does not require pre-calibration of the specimen, can measure multiple parameters simultaneously, and has high measurement accuracy and stability; it has important engineering application value for quantitative and accurate non-destructive testing of thermal barrier coating thickness.

[0062] The above only lists preferred embodiments to explain the present invention in detail. The embodiments listed are only illustrative cases and are not intended to limit the applicability of the present invention. Any modifications, equivalent substitutions and improvements made within the essence and principles of the present invention should be included in the protection scope of the present invention.

[0063] There are many specific implementation ways of the present invention. The above is only the preferred implementation mode of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A terahertz detection method for thermal barrier coating thickness based on a hybrid objective function and a variation strategy, characterized in that: The following steps are involved: Step (1), using a reflective terahertz time-domain spectroscopy system to perform a measurement experiment on the workpiece to be measured, and obtaining a terahertz reference signal and a terahertz experimental signal; Step (2), constructing a theoretical analytical model of the interaction between terahertz waves and coating samples, and introducing a reference signal into the model to obtain a terahertz simulation signal; Step (3), using the residual of the simulation signal and the experimental signal as the objective function of the algorithm optimization, analyzing the characteristics of the terahertz signal and constructing the objective function constraint term, and establishing an improved objective function suitable for terahertz thickness detection; Step (4), establishing a teaching and learning optimization algorithm based on the objective function and adaptive Cauchy-Gaussian mutation, using piecewise linear chaotic mapping to improve the population initialization method of the standard teaching and learning optimization algorithm, and introducing an adaptive Cauchy-Gaussian mutation strategy into the algorithm to improve the algorithm's search capability; Step (5), applying the theoretical analytical model in step (2) to the algorithm in step (4), and introducing the experimental signal obtained in step (1) to solve the improved objective function in step (3) to obtain the optimized coating thickness value; The theoretical analytical model of the interaction between the terahertz wave and the coating in step (2) specifically includes: The Fresnel formula is used to characterize the reflection coefficient and transmission coefficient between different dielectric layers. where r 01 、r 10 and r 12 is the reflection coefficient, t 01 ,t 10 is the transmission coefficient, and are the complex refractive indices of different dielectric layers respectively; the nth reflected echo after the terahertz wave and the thermal barrier coating is: E n (ω) = t 01 r 10 n -2 r 12 n -1 t 10 e i(n-1) βE i (ω), where E i (ω) is the terahertz incident signal, e is a natural constant, i is an imaginary unit, is the phase factor, ω is the angular frequency, d is the coating thickness, and c is the speed of light; the total reflected signal received is: Characterize the rough surface of the coating sample according to Kirchhoff's approximation: Where R r is the effective reflectivity, R s is the sum of total reflection coefficient and diffuse reflection coefficient, δ is the root mean square roughness of the rough surface, λ is the wavelength of light, and e is a natural constant; Introducing the influence of roughness into the total reflection signal, the terahertz simulation signal generated by the theoretical analytical model is: Step (3) establishes an improved objective function adapted to terahertz thickness detection: The residual between the terahertz simulation signal and the experimental signal is used as the objective function of the algorithm optimization; then the characteristics of the terahertz reflection signal are analyzed, and its main thickness information is contained in the flight time and the peak value of the reflection peak. Therefore, the peak value of the reflection peak and the flight time between the reflection peaks are used as characteristic parameters to control the inversion parameters. The objective function constraint term is introduced to avoid the algorithm from falling into the local extreme value during the optimization process. An improved objective function suitable for terahertz coating thickness detection is constructed, and its expression is: , Where t1 and t2 represent the time from the appearance to the cutoff of the first two reflection peaks, E exp (t) is the measured terahertz signal, E the (t) is the model simulation terahertz signal, t tof and t loc are the flight time from the first reflection peak to the second reflection peak of the experimental signal and the simulation signal, respectively, exp1 and P exp2 are the peak values ​​of the first and second reflection peaks of the experimental signal, P the1 and P the2 are the peak values ​​of the first and second reflection peaks of the simulation signal, and is the weight factor of the control constraint Step (4) constructs a teaching and learning optimization algorithm based on the objective function and the adaptive Cauchy-Gaussian variation, which mainly includes: Class initialization: Where j is the subject of each student, i is the student number, and are the upper and lower bounds of the control variables for the corresponding subjects, and rand(0,) is a random number between 0 and 1; Teachers’ teaching: x T is the best individual in the population, is the i-th and j-th student individual, T i is the teaching factor, x m is the average score of students in the class; Students learn: where i≠j, is a student individual randomly selected from the population; the population initialization method of the standard teaching and learning optimization algorithm is improved by using piecewise linear chaotic mapping. The mapping has a uniform distribution characteristic in the range of 0 to 1, thereby improving the population diversity of the algorithm. The specific expression is: where z n is the nth chaotic variable, p∈(0,1); the improved adaptive Cauchy-Gaussian mutation strategy is applied to the optimization algorithm to balance the search capabilities of the algorithm at different stages, thereby improving the convergence ability of the algorithm. Its mathematical model is: in is the adaptive weight factor, t max is the maximum number of iterations of the algorithm, σ is the standard deviation, Cauchy(0,σ 2 ) is subject to the mathematical expectation of 0 and the variance of σ 2 The random number of the Cauchy distribution, Gaussian(0,σ 2 ) has a mathematical expectation of 0 and a variance of σ 2 A Gaussian distributed random number is used; depending on whether the iteration situation meets the expectation of the objective function, mutation adjustment is performed in the early and middle stages of the iteration. At the same time, if the objective function has not changed for k consecutive generations in the late stage of the iteration, the weight factor is exchanged for supervision adjustment.

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