Terahertz inversion method and system based on fuzzy reasoning and teaching optimization algorithm

Abstract

The present invention proposes a terahertz inversion method and system based on fuzzy reasoning and teaching optimization algorithm, which belongs to the field of terahertz inversion. The method includes: using a terahertz time-domain spectrometer to collect time-domain signals and obtain frequency-domain signals through Fourier transform, and performing preprocessing; constructing a transmission propagation model of terahertz waves in the sample to be measured, and obtaining a model terahertz frequency-domain signal based on the model; establishing a composite objective function based on the measured terahertz frequency-domain signal and the model terahertz frequency-domain signal; performing parameter inversion on the composite objective function based on fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; the present invention realizes accurate matching of key features of terahertz signals by constructing a composite objective function that integrates the overall frequency domain error, peak frequency error and peak amplitude error. By introducing the fuzzy reasoning mechanism, the problem of premature convergence of the algorithm or falling into local optimum is effectively avoided, the convergence speed is improved, and the inversion process is made more efficient and stable.

Description

Technical Field

[0001] The present invention belongs to the technical field of terahertz inversion, and in particular relates to a terahertz inversion method and system based on fuzzy reasoning and teaching optimization algorithm. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Terahertz waves, an electromagnetic wave band between microwaves and infrared, offer broad application prospects in nondestructive testing, biomedical imaging, and material characterization due to their unique advantages, including strong penetration, low photon energy, and high spectral resolution. With the rapid development of terahertz technology, accurately obtaining the physical parameters of materials has become a key prerequisite for its engineering applications. Theoretical modeling of the interaction between terahertz waves and matter, as well as parameter inversion, have become research hotspots in this field.

[0004] In the study of terahertz wave interactions with matter, transmission detection, one of the most fundamental measurement methods, focuses on analyzing the electric field distribution, phase change, and amplitude attenuation of terahertz waves after they pass through a sample, thereby inverting the material's microscopic physical parameters. Existing research indicates that terahertz waves undergo complex refraction, reflection, and absorption processes within a medium, and their frequency-domain signal characteristics are closely related to the material's thickness and dielectric constant.

[0005] However, the traditional method uses the terahertz signal residual obtained from actual measurement and model calculation as the objective function, without considering factors such as sample surface roughness, noise interference and dispersion effect, resulting in difficulty in matching the measured signal with the theoretical model, reduced algorithm solution accuracy, and failure to take into account the differences in terahertz wave absorption and scattering by samples of different thicknesses, resulting in insufficient model adaptability. The teaching and learning optimization algorithm is prone to falling into local optimality when processing terahertz multi-parameter inversion due to its fixed teaching factor and learning step size, and cannot dynamically adjust according to the population fitness variance and the optimal fitness change rate. It has insufficient convergence accuracy and poor adaptability to multiple parameters. Summary of the Invention

[0006] To overcome the shortcomings of the aforementioned prior art, the present invention provides a terahertz inversion method and system based on fuzzy reasoning and a teaching optimization algorithm. This method establishes a theoretical expression for the reflection and transmission coefficients using Fresnel's law, and combines the multiple reflection and refraction processes of terahertz waves within a sample to derive a theoretical model of the frequency-domain signal. On this basis, an innovative fuzzy reasoning and teaching optimization algorithm is proposed. By introducing the population fitness variance and the optimal fitness change rate as fuzzy inputs, the teaching factor and learning step size are dynamically adjusted, effectively improving the algorithm's global search capability and convergence accuracy in multi-parameter inversion.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] The first aspect of the present invention provides a terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm;

[0009] Terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm, including:

[0010] The terahertz time-domain spectroscopy instrument is used to collect the measured terahertz time-domain signal of the sample to be measured, the time-domain signal is Fourier transformed to obtain the frequency-domain signal, and the frequency-domain signal is preprocessed;

[0011] Constructing a transmission propagation model of terahertz waves in a sample to be tested, and obtaining a model terahertz frequency domain signal based on the model;

[0012] A composite objective function is established based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, which integrates the overall frequency domain error, the peak frequency error, and the peak amplitude error. The composite objective function adjusts the weight of the error term by a normalized weighting factor.

[0013] The composite objective function is subjected to parameter inversion based on fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; wherein, the population is initialized based on the composite objective function; the teaching factor and learning step of the population individuals are dynamically adjusted by introducing fuzzy logic; the population is updated in the teacher stage and the student stage based on the adjusted teaching factor and learning step, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

[0014] As a further technical solution, the preprocessing includes: using the Savitzky-Golay method to smooth and denoise the collected measured terahertz frequency domain signal.

[0015] As a further technical solution, the transmission propagation model is:

[0016]

[0017] in, is the received terahertz wave; is the incident wave; is the air-sample transmission coefficient; is the sample-air transmission coefficient; is the reflection coefficient of air-sample; is the reflection coefficient of sample-air; Represents the displacement caused by the propagation of terahertz waves inside the sample.

[0018] As a further technical solution, the composite objective function is:

[0019]

[0020] in, is the objective function, and are the lower and upper limits of the angular frequency, represents the frequency domain experimental signal, is the model simulation signal, and are the frequencies at which the measured signal and the simulated signal reach their peak points, and are the amplitudes of the measured signal and the simulated signal reaching the peak point, and is the normalized weighting factor, is the maximum value of the analog signal, is the peak frequency of the analog signal, Peak amplitude of the analog signal.

[0021] As a further technical solution, the normalized weighting factor is:

[0022]

[0023]

[0024] Where, and is the normalized weighting factor.

[0025] As a further technical solution, the method of dynamically adjusting the teaching factors and learning steps of individuals in the population by introducing fuzzy logic includes:

[0026] The population fitness variance and the optimal fitness change rate are selected as input variables, and the teaching factor and learning step size are selected as output variables;

[0027] The membership function is used to extract the fuzzy features of input and output variables;

[0028] The updated teaching factors and learning steps are obtained through fuzzy reasoning and defuzzification.

[0029] As a further technical solution, the updated teaching factor and learning step size obtained through fuzzy reasoning and defuzzification include:

[0030] constructing a fuzzy rule base according to the population fitness variance and the current optimal fitness change rate, and formulating inference rules based on the fuzzy rule base;

[0031] The centroid method is used to defuzzify the fuzzy reasoning results obtained through the rule base, and the adjustment amount of teaching factor, the adjustment amount of learning step length in the teaching stage and the adjustment amount of learning step length in the student stage are obtained;

[0032] The teaching factor and the learning step are updated based on the teaching factor adjustment amount, the teaching stage learning step adjustment amount and the student stage learning step adjustment amount.

[0033] A second aspect of the present invention provides a terahertz inversion system based on fuzzy reasoning and teaching optimization algorithm.

[0034] The terahertz inversion system based on fuzzy reasoning and teaching optimization algorithm includes:

[0035] The measured terahertz frequency domain signal acquisition module is configured to: collect the measured terahertz time domain signal of the sample to be measured using a terahertz time domain spectrometer, perform Fourier transform on the time domain signal to obtain a frequency domain signal, and perform preprocessing;

[0036] The model terahertz frequency domain signal acquisition module is configured to: construct a transmission propagation model of the terahertz wave in the sample to be tested, and acquire the model terahertz frequency domain signal based on the model;

[0037] An objective function construction module is configured to: establish a composite objective function that integrates the overall frequency domain error, the peak frequency error, and the peak amplitude error based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, wherein the composite objective function adjusts the weight of the error term by a normalized weighting factor;

[0038] The optimal individual generation module is configured to: perform parameter inversion on the composite objective function using a fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; wherein, the population is initialized based on the composite objective function; the teaching factor and learning step of the population individuals are dynamically adjusted by introducing fuzzy logic; the population is updated in the teacher stage and the student stage based on the adjusted teaching factor and learning step, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

[0039] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in the first aspect of the present invention.

[0040] The fourth aspect of the present invention provides an electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in the first aspect of the present invention are implemented.

[0041] One or more of the above technical solutions have the following beneficial effects:

[0042] (1) The present invention achieves precise matching of key features of terahertz signals by constructing a composite objective function that integrates the overall frequency domain error, peak frequency error, and peak amplitude error. Compared with traditional methods, the present invention can more accurately capture the influence of sample thickness and dielectric constant on terahertz wave propagation, thereby significantly improving the reliability of the inversion results. In addition, the improved objective function optimizes the contribution of different error terms through normalized weighting factors, avoiding the problem of a single error dominating the optimization process, making the inversion results more consistent with actual physical laws.

[0043] (2) This invention introduces a fuzzy inference mechanism (FI-TLBO) to adjust algorithm parameters in real time based on the population fitness variance and the optimal fitness change rate, enabling the optimization process to strike a balance between global search and local convergence. This effectively avoids the problem of premature convergence or falling into local optimality, ensuring that the algorithm approaches the global optimal solution in a complex multi-parameter space. At the same time, it improves the convergence speed, making the inversion process more efficient and stable.

[0044] (3) In practical applications, terahertz signals are susceptible to interference from factors such as noise, sample surface roughness, and dispersion effects, resulting in reduced inversion accuracy. This invention preprocesses the original signal by combining Savitzky-Golay smoothing filtering to effectively suppress high-frequency noise and improve data quality. In addition, the improved transmission propagation model fully considers the multiple reflection and refraction effects of terahertz waves inside the sample, and can more accurately simulate the propagation behavior of electromagnetic waves in complex media.

[0045] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0047] Figure 1 This is a flow chart of the method of the first embodiment.

[0048] Figure 2 Schematic diagram of electromagnetic wave propagation through a material with a thickness of in the first embodiment.

[0049] Figure 3 This is a frequency domain diagram of polyethylene samples with different parameters in the first embodiment.

[0050] Figure 4This is a framework diagram of the FI-TLBO algorithm used in the first embodiment.

[0051] Figure 5 This is a comparison diagram of the experimental and theoretical frequency domains of sample 1 in the first embodiment.

[0052] Figure 6 1 is the experimental and theoretical frequency domain residual diagram of sample 1 in the first embodiment.

[0053] Figure 7 This is the convergence diagram of the TLBO algorithm in the first embodiment.

[0054] Figure 8 This is the convergence diagram of the FI-TLBO algorithm in the first embodiment.

[0055] Figure 9 This is a system structure diagram of the second embodiment. DETAILED DESCRIPTION

[0056] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0057] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0058] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0059] Example 1

[0060] This embodiment discloses a terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm;

[0061] like Figure 1 As shown, the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm includes:

[0062] Step S1, using a terahertz time-domain spectrometer to collect a measured terahertz time-domain signal of a sample to be measured, performing Fourier transform on the time-domain signal to obtain a frequency-domain signal, and performing preprocessing;

[0063] Step S2, constructing a transmission propagation model of a terahertz wave in a sample to be tested, and obtaining a model terahertz frequency domain signal based on the model;

[0064] Step S3, establishing a composite objective function that integrates the overall frequency domain error, the peak frequency error, and the peak amplitude error based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, wherein the composite objective function adjusts the weight of the error term by a normalized weighting factor;

[0065] Step S4, performing parameter inversion on the composite objective function using a fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; wherein, the population is initialized based on the composite objective function; the teaching factor and learning step of the population individuals are dynamically adjusted by introducing fuzzy logic; the population is updated in the teacher stage and the student stage based on the adjusted teaching factor and learning step, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

[0066] Specifically, it also includes the following:

[0067] In step S1, the terahertz time-domain spectrometer scans each sample point by point with a specific step size, obtains the terahertz time-domain spectrum signal at each acquisition point, and performs a Fourier transform on the acquired terahertz time-domain spectrum signal to obtain a frequency domain signal. The Savitzky-Golay smoothing denoising method is used to reduce noise interference generated by the instrument or environment, thereby improving the accuracy and reliability of the classification model. The formula for Savitzky-Golay smoothing denoising is:

[0068]

[0069] in yes The smoothed value at is the point of the original data, is the offset within the window, are the coefficients of the filter, is the half-width of the window.

[0070] In step S2, assuming that a terahertz wave is input into a uniform medium under transmission, the incident wave interacts with the material at one end of the sample medium, and the detector at the other end receives the sample wave, the electric field distribution inside the sample medium is as follows:

[0071]

[0072] in, express Time position The electric field strength (signal value) at is the speed of light in a vacuum, is the magnetic permeability, is the dielectric constant, Represents the total received electric field strength (time domain sample signal), Indicates the The transmitted electric field strength, and denote the electric field strength in medium 1 and medium 2 respectively, is the unit normal vector of the interface (pointing from medium 1 to medium 2), and denote the normal components of the electric field intensities in medium 1 and medium 2, respectively, and represent the dielectric constants of medium 1 and medium 2 respectively.

[0073] Generally, the sample signal in the time domain is obtained by terahertz time-domain spectroscopy. , and then perform Fourier transform on the time domain signal to obtain the sample signal in the frequency domain In this embodiment, by analyzing the interaction between materials and combining with Fresnel's law, the reflection coefficient and transmission coefficient can be obtained, and then the relative displacement generated can be obtained. Finally, combined with the physical changes of multiple reflections and refractions inside the sample, the total terahertz frequency domain signal can be obtained, such as Figure 2 shown.

[0074] Specifically: When the terahertz incident is vertical, the thickness of the sample to be tested is known to be , complex refractive index and relative dielectric constant for:

[0075]

[0076]

[0077] in, represents the complex refractive index of the medium, represents the refractive index of the medium, represents the extinction coefficient.

[0078] The reflection coefficient and transmission coefficient can be obtained by Fresnel's law, that is,

[0079]

[0080]

[0081]

[0082] in, and denote the reflection coefficients of air-sample and sample-air, respectively. and are the transmission coefficients of air-sample and sample-air, and are the complex refractive indices of the sample and air, respectively.

[0083] When the terahertz wave propagates within the sample for a distance of , the resulting phase shift is

[0084]

[0085] in, represents the displacement caused by the propagation of the terahertz wave inside the sample, represents the complex refractive index of the sample, represents the angular frequency of the terahertz wave, Represents the speed of light.

[0086] After multiple reflections and refractions, the transmission propagation model of the terahertz wave in the sample to be tested is finally constructed as follows:

[0087]

[0088] in, is the received terahertz wave (frequency domain signal); is the incident wave; is the air-sample transmission coefficient; is the sample-air transmission coefficient; is the reflection coefficient of air-sample; is the reflection coefficient of sample-air; Represents the displacement caused by the propagation of terahertz waves inside the sample.

[0089] In step S3, in the actual scenario of model inversion, due to factors such as sample surface roughness, noise interference, and dispersion effects, it is difficult to achieve complete consistency between the measured terahertz signal and the terahertz signal calculated by the theoretical model. This error can easily cause the algorithm to have reduced accuracy during the solution process.

[0090] By deducing the terahertz transmission model formula, it can be seen that samples with different thicknesses and dielectric constants have different peak frequency delays and amplitude attenuations, such as Figure 3As shown. Each color in the figure is sample 1 to sample 6 composed of different thicknesses and different dielectric constants. Taking sample 1 as an example, its actual thickness is 0.92mm and its actual dielectric constant is 2.2313. When other parameters remain unchanged, the spectrum analysis selects the spectrum range of 0.1 to 2.5THz to clearly see that when terahertz passes through samples of different thicknesses or dielectric constants, the propagation phase changes due to the difference in refractive index, which is manifested as a position shift of the peak frequency in the frequency domain. When the thickness or dielectric constant increases, the refractive index increases, the propagation path of the terahertz wave becomes longer, the phase delay increases, the peak frequency moves to a lower frequency, and the peak frequency delay becomes more obvious. The increase in sample thickness or dielectric constant will enhance the absorption and scattering of terahertz waves, resulting in attenuation of the frequency domain signal amplitude. Therefore, incorporating the frequency and amplitude errors of the peak point into the objective function can more comprehensively and deeply capture the intrinsic connection between the terahertz signal and the material parameters, and provide a richer information dimension for accurate inversion. The normalization parameter is used in the objective function and To control the weight of the frequency and amplitude of the peak point, the objective function changes as follows:

[0091]

[0092]

[0093]

[0094] in, and are the lower and upper limits of the angular frequency, represents the frequency domain experimental signal, is the model simulation signal, and are the frequencies at which the measured signal and the simulated signal reach their peak points, and are the amplitudes of the measured signal and the simulated signal reaching the peak point, and is the normalized weighting factor, is the maximum value of the analog signal, is the peak frequency of the analog signal, Peak amplitude of the analog signal.

[0095] By modifying the objective function , combining the overall frequency domain error, peak frequency error, and peak amplitude error, and adjusting and The weights allow the theoretical model to be close to the experiment in the full frequency domain and accurately match the key features (frequency and amplitude) of the peak point.

[0096] In step S4, the Teaching and Learning Optimization (TLBO) algorithm is a swarm intelligence-based optimization algorithm inspired by classroom teaching. In this algorithm, the solution to the optimization problem is considered a student, and the quality of the solution (the objective function value) corresponds to the student's learning performance. The algorithm primarily consists of a teacher phase and a student phase. The teacher phase transfers the knowledge of the best individual in the current swarm (the teacher) to other individuals (the students), bringing the swarm's average level closer to that of the teacher. The output is the student's individual solution, updated under the teacher's guidance. The student phase involves mutual learning among students. Each student compares their fitness values ​​with those of other students and learns from the more advanced students. The output is the student's individual solution, further optimized through inter-student communication and learning. Through continuous iteration of the teacher and student phases, the optimal solution that meets stopping criteria (such as reaching the maximum number of iterations or finding a satisfactory solution) is ultimately output.

[0097] The fixed teaching factor and learning step size of the traditional TLBO algorithm easily lead to the algorithm falling into local optimality and cannot adapt to the strong nonlinear characteristics of multi-parameter inversion. Therefore, fuzzy logic is introduced to dynamically adjust the teaching factor and learning step size. The framework of the FI-TLBO algorithm is as follows Figure 4 shown.

[0098] Step S41: randomly generate a certain number of individuals, and randomly initialize the parameters of each individual within a reasonable value range to determine the possible value range of the dielectric constant. The thickness range is , randomly generate initial values ​​within these intervals to construct individual , calculate the objective function value of each individual , the smaller the value, the higher the fitness. Specifically, in the teacher phase, an initial teacher individual and student individual are randomly selected. In the student phase, two different initial student individuals are randomly selected.

[0099] Step S42, dynamically adjust the teaching factor and learning step size by introducing fuzzy logic. In step S42, the following contents are included:

[0100] Step S421, create input variables and output variables. Among them, the fuzzy input variable selects the population fitness variance ( ) and the current optimal fitness change rate ( ).in, Measuring the dispersion of individual fitness in a population can reflect population diversity. The calculation formula is as follows:

[0101]

[0102]

[0103] in, represents the population fitness variance, Indicates the number of populations, Indicates the The objective function value, Indicates the average moderation value.

[0104] Current optimal fitness change rate ( ) can reflect the convergence speed of the algorithm, and the calculation formula is as follows

[0105]

[0106] in, represents the current optimal fitness change rate, Indicates the fitness value before updating, Indicates the updated fitness value.

[0107] The output variable is the teaching factor adjustment and learning step size , . Used to adjust The value of learning step Used to adjust The value of Used to adjust value.

[0108] Step S422: To extract the fuzzy features of the input information, the input information needs to be fuzzified by using the membership function. In this embodiment, the input variables and Select Gaussian membership function and output variable teaching factor , learning step size , A triangular membership function is selected.

[0109] Defining input variables Fuzzy sets are divided into "small, medium, and large". Fuzzy sets are divided into "slow, medium, and fast", and the formula of their Gaussian membership function is as follows:

[0110]

[0111] in, is the membership value, is the input variable, is the center parameter, is the width parameter.

[0112] Define output variable teaching factors , learning step size , The triangle membership function is selected, and the triangle membership function formula is as follows:

[0113]

[0114] In step S423, in order to perform fuzzy inference, inference rules need to be formulated. This paper formulates nine inference rules based on a complete fuzzy rule base constructed based on the input variables, the population fitness variance (small, medium, large), and the current optimal fitness change rate (slow, medium, fast). They are shown in Table 1:

[0115] Table 1 Fuzzy rule base

[0116]

[0117] In step S424, in order to obtain an accurate output result, the centroid method is used for defuzzification. The formula of the centroid method is as follows:

[0118]

[0119] in represents the adjustment amount of the teaching factor, represents the adjustment amount of the learning step size in the teaching phase, Represents the adjustment amount for the learning step size of the student stage, represents the discrete sampling points in the output fuzzy set universe, Indicates that at the sampling point The membership value of the fuzzy set is output at Represents the number of discrete sampling points of the output fuzzy set universe.

[0120] Step S425: Update the teaching factor and the learning step length based on the teaching factor adjustment amount, the teaching stage learning step length adjustment amount, and the student stage learning step length adjustment amount. renew:

[0121]

[0122] Learning step size , Updated to:

[0123]

[0124]

[0125] In step S43, the parameters of individual students are updated based on the updated teaching factor and learning step size. This process is called the teacher phase. During the teacher phase, the algorithm simulates the process of a teacher imparting knowledge to students. Assume that there is a teacher, which represents the optimal solution in the current population. The individual with the best fitness is selected from the population as the "teacher," which will transfer knowledge to other students. For each individual student, its parameters are updated according to the following formula:

[0126]

[0127] in, and Respectively represent Students updated before and after The value of the parameter, represents a random number in [0,1], Is the teacher's individual The value of the parameter, The teaching factor is 1 or 2, is the number of individuals in the current population The average value of the parameters.

[0128] Step S44: After the teacher phase, students further optimize their own parameters by learning from each other. For each student, a different student is randomly selected for learning. The parameters are updated according to the following formula:

[0129]

[0130] in, and Respectively represent Students updated before and after The value of the parameter, Indicates the randomly selected Student No. The value of the parameter, represents a random number in [0,1], and They are and The objective function value of each student.

[0131] Step S45, evaluate the updated population and calculate the The objective function value of , which is the difference between the terahertz electric field intensity obtained by the theoretical model and the actual measured terahertz electric field intensity. A check is performed to determine whether the maximum number of iterations has been reached. If the termination condition is met, the optimal individual is output, i.e., the inverted dielectric constant and thickness parameters are obtained. If the termination condition is not met, the optimization returns to the teacher stage and iterative optimization continues.

[0132] Furthermore, six polyethylene sheet samples of varying thicknesses were prepared, designated Samples 1-6. These samples were 60 mm long, 60 mm wide, and had thicknesses of 0.92 mm, 1.94 mm, 2.88 mm, 3.85 mm, 4.97 mm, and 5.67 mm, respectively. Due to their nonpolar structure, high crystallinity, and low polarization loss, the imaginary part of the dielectric constant of polyethylene samples is extremely small. Therefore, in practical analysis, only the real part is often ignored. Using a terahertz time-domain spectroscopy instrument, transmission scans were performed on each sample with a 5 mm step size, resulting in the actual dielectric constants of 2.3612, 2.2313, 2.2561, 2.2646, 2.2658, and 2.2682, respectively.

[0133] The Savitzky-Golay smoothing denoising method is used to obtain the terahertz time domain spectrum signal of each acquisition point to reduce the noise interference generated by the instrument or environment, so as to improve the accuracy and reliability of the classification model. Taking sample 1 as an example, the frequency domain comparison diagram between theory and practice is as follows: Figure 5 shown.

[0134] pass Figure 5 From the experimental and theoretical frequency domain comparison chart, it can be seen that the simulated signal output by the algorithm is consistent with the actual measured terahertz signal, both have a transmission peak point, and the residual between the actual and theoretical is small. Figure 6 is the experimental and theoretical frequency domain residual diagram of sample 1, Figure 6 It shows that the theoretical model can accurately simulate the interaction between terahertz and the sample, and the algorithm can produce ideal thickness results.

[0135] The inversion of six samples of different thicknesses using the teaching and learning optimization combined with fuzzy reasoning algorithm yields the thicknesses shown in the table. The table shows that the method of the present invention has a smaller error than the traditional teaching optimization algorithm.

[0136] Table 2 Comparison of thickness obtained by the method of the present invention and the teaching and learning optimization

[0137]

[0138] The dielectric constants of the six samples were inverted by combining the teaching and learning optimization algorithm with fuzzy reasoning. The dielectric constants were shown in Table 3, and the error was reduced to about 1%.

[0139] Table 3 Comparison of dielectric constants obtained by the present invention and teaching and learning optimization

[0140]

[0141] Furthermore, in order to verify the performance of the algorithm, the convergence of the algorithm is calculated, such as Figure 7 and Figure 8 shown. Figure 7 represents the traditional teaching and learning optimization algorithm, Figure 8 The fuzzy reasoning combined with the teaching and learning optimization algorithm adopted by the present invention is compared Figure 7 and Figure 8 The algorithm convergence curve of the present invention not only has the fast convergence characteristics of the traditional TLBO algorithm, but also has better performance in the problem of multi-parameter inversion according to the characteristics of the terahertz signal.

[0142] Example 2

[0143] This embodiment discloses a terahertz inversion system based on fuzzy reasoning and teaching optimization algorithm;

[0144] like Figure 9 As shown, the terahertz inversion system based on fuzzy reasoning and teaching optimization algorithm includes:

[0145] The measured terahertz frequency domain signal acquisition module is configured to: collect the measured terahertz time domain signal of the sample to be measured using a terahertz time domain spectrometer, perform Fourier transform on the time domain signal to obtain a frequency domain signal, and perform preprocessing;

[0146] The model terahertz frequency domain signal acquisition module is configured to: construct a transmission propagation model of terahertz waves in the sample to be measured, and obtain the model terahertz frequency domain signal based on the model; the objective function construction module is configured to: establish a composite objective function that integrates the overall frequency domain error, peak frequency error, and peak amplitude error based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, and the composite objective function adjusts the weight of the error term through a normalized weighting factor;

[0147] The optimal individual generation module is configured to: perform parameter inversion on the composite objective function using a fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; wherein, the population is initialized based on the composite objective function; the teaching factor and learning step of the population individuals are dynamically adjusted by introducing fuzzy logic; the population is updated in the teacher stage and the student stage based on the adjusted teaching factor and learning step, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

[0148] Example 3

[0149] The purpose of this embodiment is to provide a computer-readable storage medium.

[0150] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in Example 1.

[0151] Example 4

[0152] The purpose of this embodiment is to provide an electronic device.

[0153] An electronic device comprises a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in Example 1 are implemented.

[0154] The steps involved in the apparatuses of Examples 2, 3, and 4 above correspond to those of Method Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and causing the processor to perform any method of the present invention.

[0155] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0156] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm, characterized in that: include: The terahertz time-domain spectroscopy instrument is used to collect the measured terahertz time-domain signal of the sample to be measured, the time-domain signal is Fourier transformed to obtain the frequency-domain signal, and the frequency-domain signal is preprocessed; Constructing a transmission propagation model of terahertz waves in a sample to be tested, and obtaining a model terahertz frequency domain signal based on the model; A composite objective function is established based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, which integrates the overall frequency domain error, the peak frequency error, and the peak amplitude error. The composite objective function adjusts the weight of the error term by a normalized weighting factor. The composite objective function is subjected to parameter inversion based on fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; wherein, the population is initialized based on the composite objective function; and the teaching factor and learning step size of the population individuals are dynamically adjusted by introducing fuzzy logic, including: The population fitness variance and the optimal fitness change rate are selected as input variables, and the teaching factor and learning step size are selected as output variables; The membership function is used to extract the fuzzy features of input and output variables; Obtaining an updated teaching factor and learning step size through fuzzy reasoning and defuzzification, including: constructing a fuzzy rule base according to the population fitness variance and the current optimal fitness change rate, and formulating inference rules based on the fuzzy rule base; defuzzifying the output result using a centroid method to obtain a teaching factor adjustment amount, a teaching stage learning step size adjustment amount, and a student stage learning step size adjustment amount; and updating the teaching factor and learning step size based on the teaching factor adjustment amount, the teaching stage learning step size adjustment amount, and the student stage learning step size adjustment amount; Based on the adjusted teaching factor and learning step size, the population is updated in the teacher stage and the student stage, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

2. The terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm according to claim 1, characterized in that: The preprocessing includes: using the Savitzky-Golay method to smooth and denoise the obtained measured terahertz frequency domain signal.

3. The terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm according to claim 1, characterized in that: The transmission propagation model is: in, is the received terahertz wave; is the incident wave; is the air-sample transmission coefficient; is the sample-air transmission coefficient; is the reflection coefficient of air-sample; is the reflection coefficient of sample-air; Represents the displacement caused by the propagation of terahertz waves inside the sample.

4. The terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm according to claim 1, characterized in that: The composite objective function is: in, is the objective function, and are the lower and upper limits of the angular frequency, represents the frequency domain experimental signal, is the model simulation signal, and are the frequencies at which the measured signal and the simulated signal reach their peak points, and are the amplitudes of the measured signal and the simulated signal reaching the peak point, and is the normalized weighting factor, is the maximum value of the analog signal, is the peak frequency of the analog signal, Peak amplitude of the analog signal.

5. The terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm according to claim 4, characterized in that: The normalized weighting factor is: Where, and is the normalized weighting factor.

6. A terahertz inversion system based on fuzzy reasoning and teaching optimization algorithm, characterized in that: include: The measured terahertz frequency domain signal acquisition module is configured to: collect the measured terahertz time domain signal of the sample to be measured using a terahertz time domain spectrometer, perform Fourier transform on the time domain signal to obtain a frequency domain signal, and perform preprocessing; The model terahertz frequency domain signal acquisition module is configured to: construct a transmission propagation model of the terahertz wave in the sample to be tested, and acquire the model terahertz frequency domain signal based on the model; An objective function construction module is configured to: establish a composite objective function that integrates the overall frequency domain error, the peak frequency error, and the peak amplitude error based on the measured terahertz frequency domain signal and the model terahertz frequency domain signal, wherein the composite objective function adjusts the weight of the error term by a normalized weighting factor; The optimal individual generation module is configured to: perform parameter inversion on the composite objective function using a fuzzy reasoning and teaching optimization algorithm to obtain the optimal individual; initialize the population based on the composite objective function; and dynamically adjust the teaching factor and learning step size of the population individuals by introducing fuzzy logic, including: The population fitness variance and the optimal fitness change rate are selected as input variables, and the teaching factor and learning step size are selected as output variables; The membership function is used to extract the fuzzy features of input and output variables; Obtaining an updated teaching factor and learning step size through fuzzy reasoning and defuzzification, including: constructing a fuzzy rule base according to the population fitness variance and the current optimal fitness change rate, and formulating inference rules based on the fuzzy rule base; defuzzifying the output result using a centroid method to obtain a teaching factor adjustment amount, a teaching stage learning step size adjustment amount, and a student stage learning step size adjustment amount; and updating the teaching factor and learning step size based on the teaching factor adjustment amount, the teaching stage learning step size adjustment amount, and the student stage learning step size adjustment amount; Based on the adjusted teaching factor and learning step size, the population is updated in the teacher stage and the student stage, the updated population is evaluated, and the objective function value of each individual is calculated; the above process is iterated, and the optimal individual is output when the maximum number of iterations is reached or the termination condition is met.

7. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in any one of claims 1 to 5 are implemented.

8. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the terahertz inversion method based on fuzzy reasoning and teaching optimization algorithm as described in any one of claims 1 to 5 are implemented.

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