A method for detecting internal substances in fruits based on terahertz signal delay

Abstract

The present invention discloses a method for detecting internal substances of fruits based on terahertz signal delay. The method can be applied to a scenario where the internal substances to be detected have an influence on the delay time of terahertz signals from the perspective of time domain. A square weighted sum objective function of the signal difference between the actual delay time and the fitted delay time is established by fitting the power exponential relationship between the delay time characteristics and the internal substance conditions, and the function is minimized to obtain the weight coefficients of the main frequency feature points, the power exponential coefficients of the fitting relationship, the power exponential base and the constant term, thereby completing the detection of internal substances in fruits.

Description

Technical Field

[0001] The invention belongs to the technical field of fruit quality detection, and in particular relates to a method for detecting internal substances of fruits by analyzing the fitting relationship between terahertz signal delay and detection results of internal substances of fruits. Background Art

[0002] Terahertz waves refer to coherent electromagnetic radiation between microwaves and infrared waves, with a frequency range of 0.1 to 10 THz. They belong to the far-infrared band and occupy a very special position in the electromagnetic spectrum. They are in the transition zone from electronics to photonics. They have very important academic value and application prospects. Therefore, terahertz technology has received more and more attention. Terahertz time-domain spectroscopy (THz-TDS) technology is a spectral measurement technology based on femtosecond laser technology. It analyzes the structure and composition of materials based on the absorption characteristics of materials to terahertz radiation, and has become a research hotspot in the field of terahertz. Compared with traditional Fourier transform infrared spectroscopy, THz-TDS is a synchronous coherent detection technology that is not very sensitive to thermal background noise, can obtain a high signal-to-noise ratio, and does not require a thermal radiation detector. A large number of studies have shown that the low-frequency collective vibration and rotation modes of many molecules (such as intermolecular vibration, lattice vibration, hydrogen bonding, and intramolecular vibration, etc.) are in the terahertz band. This collective vibration mode mainly reflects the overall structural information of the molecule, and its distribution and intensity provide a basis for judging the composition and state of the substance. For a transmission terahertz time-domain spectroscopy system, the signal of the terahertz wave radiated by the photoconductive antenna before irradiating the sample surface is called the reference signal. When the terahertz signal passes through the sample, the signal is called the sample signal. Relative to the reference signal, the peak amplitude of the sample signal passing through the sample decreases, and the position of the peak amplitude moves backward. The time difference between the two delays is called the delay time. It can be seen that the peak amplitude moves backward due to the delay time because of the influence of the sample to be tested on the terahertz pulse. Summary of the invention

[0003] The purpose of the present invention is to analyze the influence of the internal substance to be tested on the delay time of the terahertz signal from the time domain perspective when detecting the internal substances of the fruit through the terahertz signal, thereby establishing a fitting relationship between the delay time characteristics and the internal substance conditions, so as to realize the detection of the internal substances of the fruit.

[0004] In order to achieve the above object, the present invention includes Figure 1 The following steps are shown in :

[0005] Step 1: When a certain internal substance of a fruit sample set Γ = {j|1≤j≤J} is detected by terahertz signal, the detection result of the internal substance of fruit j (j∈Γ) is It can be obtained by the main frequency feature point set Ω={λ i|1≤i≤I} the main frequency feature point λ i Signal delay time T i,j The existing fitting relationship expression It is represented by i,j is the main frequency feature point λ corresponding to fruit j i Indication of internal matter, μ i Corresponding to the main frequency characteristic point λ i The weight coefficient, J is the number of fruit sample sets, I is the number of main frequency feature points after screening, α i ,β i ,γ i They correspond to the main frequency characteristic points λ i The power exponential coefficient, power exponential base and constant term of the fitting relationship, is the main frequency feature point λ corresponding to fruit j i The terahertz signal phase is then the actual delay time T i,j and fitting delay time The weighted sum of squared signal differences between The following objective function F(μ) with the Lagrangian constant ξ can be established: i ,α i ,β i ,γ i ,ξ), and minimize it:

[0006]

[0007] Step 2: Transform the objective function F(μ i ,α i ,β i ,γ i ,ξ) to μ i As well as the power exponential coefficient, power exponential base and constant term α of the fitting relationship i ,β i ,γ i By calculating the first-order derivative and the second-order derivative respectively, we can get the corresponding first-order derivative and second-order derivative expressions:

[0008]

[0009]

[0010] It is obvious that the second-order derivative Greater than 0, when the first-order derivative When it is 0, we can optimize μ i F(w i ,α i ,β i ,γ i,ξ) satisfies the extreme value condition and is a minimum value.

[0011] Depend on and The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression:

[0012]

[0013] Considering And in the case of fitting Should be close to T i,j , which can meet the situation that sina≈a when a→0, so we can get:

[0014]

[0015]

[0016] The objective function F(μ i ,α i ,β i ,γ i ,ξ) for the power exponential coefficient, power exponential base and constant term α of the fitting relationship i ,β i ,γ i Calculate the first-order derivative and the second-order derivative respectively, then the corresponding first-order derivative and second-order derivative expressions can be expressed as follows:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] Second Derivative and Obviously greater than 0, when the first-order derivative and When it is 0, the power exponential coefficient, power exponential base and constant term α of the fitting relationship expression i ,β i ,γi The objective function F(μ i ,α i ,β i ,γ i ,ξ) satisfies the minimum condition.

[0024] make According to the first-order derivative and Take 0 and list the system of equations:

[0025]

[0026] Arranging the equations, we can obtain the power coefficient, power base and constant term α including the fitting relationship expression. i ,β i ,γ i The system of equations:

[0027]

[0028] Step 3: The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression (1) and the power exponent coefficient, power exponent base and constant term α containing the fitting relationship expression i ,β i ,γ i Substitute equations (2), (3), and (4) into the following iterative process from ① to ⑤ to generate the actual value of the weight coefficient μ i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i ', the iterative process is specifically expressed as follows:

[0029] ① Initialization process, set the number of iterations k to 0, and the power exponent base β i (k=0) is set to the natural number e which is usually used as the base, the main frequency feature point λ i The weight coefficient μ i (k=0) is set as the inverse of the number of main frequency feature points after screening, and the main frequency feature point set Ω and the main frequency feature point λ in the set Ω are statistically obtained through testing. i The terahertz signal delay time T i,j , terahertz signal phase And the main frequency feature point λ corresponding to fruit j in the fruit sample set Γ i Internal material indication τ i,j , and set the weight coefficient fluctuation threshold δ μ , power exponential coefficient fluctuation threshold δ α , Power exponential base fluctuation threshold δ β and constant term fluctuation threshold δ γ ;

[0030] ② β i (k) and μ i Substitute (k) into equation (2) and equation (3), and assume From equations (2) and (3), we know that Aα i +Bγ i =C and Available and Thus, the number of iterations k is set to k+1, and the output is and

[0031] ③ α i (k), β i (k-1),γ i Substituting (k) into equation (1), the output is

[0032]

[0033] ④ Select J′ sample fruits with consistent internal substance test results from the fruit sample set Γ as the sample set Γ′. It can be seen that for the J′ sample fruits in the sample set Γ′, ε i,j′ With τ i,j′ are basically the same, so we can set and Then from formula (4) we can get This can be output

[0034]

[0035] ⑤If satisfied and Then the output μ i (k), α i (k), β i (k) and γ i (k) is the actual value of the weight coefficient μ i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i', then the iteration process can be ended. If the above process is not satisfied, the iteration process will enter ②.

[0036] Step 4: The M fruits of the same kind to be tested are grouped into a test set Θ = {m|1≤m≤M}, and the delay time of the terahertz signal of the main frequency feature points in the test set Θ is tested and counted. At the same time, the actual value μ of the weight coefficient generated by the iterative process in step 3 is i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i 'For the internal material detection of the test set Θ, the fitting relationship expression is It can be seen that the internal substance detection result of fruit m is τ m It can be expressed as BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 : Flowchart of fruit internal substance detection based on terahertz signal delay. DETAILED DESCRIPTION

[0038] The following is a specific example of using the delay of the position of the amplitude peak in the terahertz signal to move backward to detect the content of the fungicide pesticide thiabendazole in bananas to describe the technical solution provided by the present invention in detail. Figure 1 As shown, the method for detecting the internal substances of fruits based on terahertz signal delay includes the following steps:

[0039] Step 1: When the thiabendazole in the banana sample set Γ={j|1≤j≤J} is detected by terahertz signal, its characteristic absorption peak positions are 1.111, 1.184, 1.257, 1.331 and 1.478 THz, then the above five frequencies constitute the main frequency feature point set after screening Ω={λ i |1≤i≤I}, let the test result of thiabendazole content of banana j (j∈Γ) It can be obtained by the main frequency feature point set Ω={λ i |1≤i≤I} the main frequency feature point λ i Signal delay time T i,j The existing fitting relationship expression It is represented by i,j is the main frequency feature point λ corresponding to banana j i Indication of internal matter, μ i Corresponding to the main frequency characteristic point λ i The weight coefficient, the number of banana sample sets J = 200, the number of main frequency feature points after screening I is 5, α i ,βi ,γ i They correspond to the main frequency characteristic points λ i The power exponential coefficient, power exponential base and constant term of the fitting relationship, is the main frequency feature point λ corresponding to banana j i The terahertz signal phase is then the actual delay time T i,j and fitting delay time The weighted sum of squared signal differences between The following objective function F(μ) with the Lagrangian constant ξ can be established: i ,α i ,β i ,γ i ,ξ), and minimize it:

[0040]

[0041] Step 2: Transform the objective function F(μ i ,α i ,β i ,γ i ,ξ) to μ i Finding the first-order derivative and the second-order derivative, we can get the corresponding first-order derivative and second-order derivative expressions:

[0042]

[0043]

[0044] It is obvious that the second-order derivative Greater than 0, when the first-order derivative When it is 0, we can optimize μ i F(w i ,α i ,β i ,γ i ,ξ) satisfies the extreme value condition and is a minimum value.

[0045] Depend on and The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression:

[0046]

[0047] The objective function F(μ i ,α i ,βi ,γ i ,ξ) for the power exponential coefficient, power exponential base and constant term α of the fitting relationship i ,β i ,γ i Calculate the first-order derivative and the second-order derivative respectively, then the corresponding first-order derivative and second-order derivative expressions can be expressed as follows:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Second Derivative and Obviously greater than 0, when the first-order derivative and When it is 0, the power exponential coefficient, power exponential base and constant term α of the fitting relationship expression i ,β i ,γ i The objective function F(μ i ,α i ,β i ,γ i ,ξ) satisfies the minimum condition.

[0056] According to the first-order derivative and Taking 0 can list the equation system:

[0057]

[0058] Step 3: The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression (1) and the power exponent coefficient, power exponent base and constant term α containing the fitting relationship expression i ,β i ,γ iSubstitute equations (2), (3), and (4) into the following iterative process from ① to ⑤ to generate the actual value of the weight coefficient μ i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i ', the iterative process is specifically expressed as follows:

[0059] ① Initialization process, set the number of iterations k to 0, and the power exponent base β i (k=0) Set e, main frequency feature point λ i The weight coefficient μ i (k=0) is set to 0.2, and the main frequency feature point set Ω and the main frequency feature point λ in the set Ω are statistically obtained through testing. i The terahertz signal delay time T i,j , terahertz signal phase And the main frequency feature point λ corresponding to banana j in the sample set Γ i Thiabendazole indications i,j , and set the weight coefficient fluctuation threshold δ μ , power exponential coefficient fluctuation threshold δ α , Power exponential base fluctuation threshold δ β and constant term fluctuation threshold δ γ All are 1%;

[0060] ② β i (k) and μ i Substitute (k) into equation (2) and equation (3), set the number of iterations k to k+1, and output and

[0061] ③ α i (k), β i (k-1),γ i Substituting (k) into equation (1), the output is

[0062]

[0063] ④ Select J′=10 sample fruits with consistent thiabendazole content test results from the banana sample set Γ as the sample set Γ′. It can be seen that for J′ bananas in the sample set Γ′, ε i,j′ With τ i,j′ are basically the same, and can be output

[0064] ⑤If satisfied and Then the output μ i (k), α i (k), βi (k) and γ i (k) is the actual value of the weight coefficient μ i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i ', then the iteration process can be ended. If the above process is not satisfied, the iteration process will enter ②.

[0065] Step 4: The M=50 bananas to be tested are grouped into a test set Θ={m|1≤m≤M}, and the terahertz signal delay time of the main frequency feature points in the test set Θ is tested and counted. At the same time, the actual value μ of the weight coefficient generated by the iterative process in step 3 is i ', Actual value of the power exponential coefficient of the fitting relationship expression α i ', Actual value of the power exponent base β i ' and the actual value of the constant term of the fitting relationship expression γ i 'For the detection of thiabendazole in the test set Θ, the fitted relation expression It can be seen that the test results of thiabendazole content in banana m are τ m It can be expressed as The detection data of the banana sample set showed that the characteristic absorption peaks of the banana samples containing thiabendazole were located at 1.111, 1.184, 1.257, 1.331 and 1.478 THz. In the 0.2-1.5 THz band, the band showed obvious fluctuations when the thiabendazole content in the banana increased from 0.1% to 5%. The absorption spectrum increased and the intensity changed significantly. It can be seen that the different content of the components caused the difference in the backward movement of the characteristic peaks in the absorption spectrum of the banana samples. After comparing the thiabendazole content in the banana given by the fitting relationship expression with the actual detected thiabendazole content result, it was found that the relative error was less than 2%, and the maximum deviation error did not exceed 3%, which can meet the detection needs of the thiabendazole content in bananas.

Claims

1. A method for detecting internal substances in fruits based on terahertz signal delay, characterized in that: The following steps are involved: Step 1: When a certain internal substance of a fruit sample set Γ = {j|1≤j≤J} is detected by terahertz signal, the detection result of the internal substance of fruit j (j∈Γ) is It can be obtained by the main frequency feature point set Ω={λ i |1≤i≤I} the main frequency feature point λ i Signal delay time T i,j The existing fitting relationship expression It is represented by i,j is the main frequency feature point λ corresponding to fruit j i Indication of internal matter, μ i Corresponding to the main frequency characteristic point λ i The weight coefficient, J is the number of fruit sample sets, I is the number of main frequency feature points after screening, α i ,β i ,γ i They correspond to the main frequency characteristic points λ i The power exponential coefficient, power exponential base and constant term of the fitting relationship, is the main frequency feature point λ corresponding to fruit j i The terahertz signal phase is then the actual delay time T i,j and fitting delay time The weighted sum of squared signal differences between The following objective function F(μ) with the Lagrangian constant ξ can be established: i ,α i ,β i ,γ i ,ξ), and minimize it: Step 2: Transform the objective function F(μ i ,α i ,β i ,γ i ,ξ) to μ i Finding the first-order derivative and the second-order derivative, we can get the corresponding first-order derivative and second-order derivative expressions: It is obvious that the second-order derivative Greater than 0, when the first-order derivative When it is 0, we can optimize μ i F(w i ,α i ,β i ,γ i ,ξ) satisfies the extreme value condition and is a minimum value. At this time, and The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression of ; The objective function F(μ i ,α i ,β i ,γ i ,ξ) for the power exponential coefficient, power exponential base and constant term α of the fitting relationship i ,β i ,γ i Calculate the first-order derivative and the second-order derivative respectively, then the corresponding first-order derivative and second-order derivative expressions can be expressed as follows: Second Derivative and Obviously greater than 0, when the first-order derivative and When it is 0, the power exponential coefficient, power exponential base and constant term α of the fitting relationship expression i ,β i ,γ i The objective function F(μ i ,α i ,β i ,γ i ,ξ) satisfies the minimum condition; let According to the first-order derivative and Take 0 to list the power exponent coefficient, power exponent base and constant term α of the fitting relationship expression i ,β i ,γ i The system of equations; Step 3: The objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i Theoretical value expression (1) and the power exponent coefficient, power exponent base and constant term α containing the fitting relationship expression i ,β i ,γ i Substitute equations (2), (3), and (4) into the following iterative process from ① to ⑤ to generate the actual value of the weight coefficient μ′ i , the actual value of the power exponential coefficient of the fitting relationship expression α′ i , the actual value of the power exponent base β′ i The actual value of the constant term γ′ in the fitting relationship expression i , the iterative process is specifically expressed as follows: ① Initialization process, set the number of iterations k to 0, and the power exponent base β i (k=0) is set to the natural number e which is usually used as the base, the main frequency feature point λ i The weight coefficient μ i (k=0) is set as the inverse of the number of main frequency feature points after screening, and the main frequency feature point set Ω and the main frequency feature point λ in the set Ω are statistically obtained through testing. i The terahertz signal delay time T i,j , terahertz signal phase And the main frequency feature point λ corresponding to fruit j in the fruit sample set Γ i Internal material indication τ i,j , and set the weight coefficient fluctuation threshold δ μ , power exponential coefficient fluctuation threshold δ α , Power exponential base fluctuation threshold δ β and constant term fluctuation threshold δ γ ; ② β i (k) and μ i (k) Substitute the power coefficient, power base and constant term α into the expression containing the fitting relationship i ,β i ,γ i In the equations (2) and (3) of the system, the number of iterations k is set to k+1, which can be obtained by α i (k) and γ i (k) is output; ③ α i (k), β i (k-1),γ i (k) Substitute the weight coefficient μ i The theoretical value expression of μ is output i (k); ④ Select J′ sample fruits with consistent internal substance test results from the fruit sample set Γ as the sample set Γ′. It can be seen that for the J′ sample fruits in the sample set Γ′, ε i,j′ With τ i,j′ are basically the same, so we can output in ⑤If satisfied and Then the output μ i (k), α i (k), β i (k) and γ i (k) is the actual value of the weight coefficient μ′ i , the actual value of the power exponential coefficient of the fitting relationship expression α′ i , the actual value of the power exponent base β′ i The actual value of the constant term γ′ in the fitting relationship expression i , the iteration process can be ended at this time. If the above process is not satisfied, the iteration process will enter ②; Step 4: The M fruits of the same kind to be tested are grouped into a test set Θ = {m|1≤m≤M}, and the delay time of the terahertz signal of the main frequency feature points in the test set Θ is tested and counted. At the same time, the actual value μ′ of the weight coefficient generated by the iterative process in step 3 is i , the actual value of the power exponential coefficient of the fitting relationship expression α′ i , the actual value of the power exponent base β′ i The actual value of the constant term γ′ in the fitting relationship expression i The internal substance detection of the test set Θ is expressed by the fitting relationship It can be seen that the internal substance detection result of fruit m is τ m It can be expressed as In step 2, the objective function F(μ i ,α i ,β i ,γ i ,ξ) when the main frequency characteristic point λ meets the minimum condition i The weight coefficient μ i The theoretical value expression can be expressed as: Step 3 contains the power exponential coefficient, power exponential base and constant term α of the fitting relationship expression i ,β i ,γ i The system of equations can be expressed as: In the iterative process of step 2②, α i (k) and γ i The expressions of (k) are respectively expressed as: in,

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