A method for material identification

Abstract

An embodiment of the present application provides a material identification method. The identification method first determines the relationship between the standard deviation of the scattering angle distribution generated by muons passing through the material to be measured and the radiation length of the material to be measured; then uses the scattering angle distribution of discrete energy muons to fit to obtain the calibrated muon scattering angle distribution of approximately continuous energy and obtains the scattering angle generated by continuous energy muons passing through the material to be measured, and statistically obtains the standardized scattering angle distribution to get a discrete distribution; couples the discrete distribution with the calibrated muon scattering angle distribution; calculates the radiation length of the material to be measured; and identifies the material to be measured according to the radiation length. The material identification method of the embodiment of the present application introduces the discrete energy information of muons from a statistical perspective, obtains the calibrated muon scattering angle distribution of approximately continuous energy, improves the accuracy of the material identification method, and simplifies the identification method.

Description

Technical Field

[0001] This application relates to the technical field of material identification, and particularly to a method for material identification. Background Art

[0002] Muons are charged particles generated by the interaction of cosmic rays with the atmosphere. They have the characteristics of high energy, strong penetrability, and sensitivity to high-Z materials, and can be used for imaging detection of objects inside the shielding layer. Currently, muon imaging technology has been widely applied in many fields such as nuclear material inspection and reactor core monitoring. The principle of using muons for material identification is based on the multiple Coulomb scattering phenomenon that occurs when muons interact with the material to be measured. When muons pass through the material to be measured, they will undergo continuous small-angle scattering multiple times, and the projection of the scattering angle in the plane follows a Gaussian distribution with a mean of 0 and a standard deviation of σ θ .

[0003] Since the multiple Coulomb scattering effect that occurs when muons interact with the material to be measured is not only related to the type of material but also to the energy of the muons themselves. When using muons for material identification, its accuracy is affected by the energy of the muons. In fact, the muon energy is continuous and it is very difficult to measure in real time.

[0004] In related technologies, the average energy of muons is used to replace the continuous muon energy, which reduces the accuracy of material identification. Summary of the Invention

[0005] In view of this, the embodiments of this application are expected to provide a method for material identification that can improve the identification accuracy.

[0006] To achieve the above object, the embodiments of this application provide a method for material identification, including:

[0007] Determine the relationship between the standard deviation σ of the scattering angle distribution generated when muons pass through the material to be measured θ and the radiation length L of the material to be measured rad ;

[0008] Use the scattering angle distribution of discrete energy muons to fit to obtain the calibrated muon scattering angle distribution f(θ) of approximately continuous energy;

[0009] Obtain the scattering angle generated when continuous energy muons pass through the material to be measured, and statistically obtain the standardized scattering angle distribution to obtain the discrete distribution B;

[0010] Couple the discrete distribution B with the calibrated muon scattering angle distribution f(θ);

[0011] Calculate the radiation length of the material to be measured;

[0012] Identify the material to be measured according to the radiation length.

[0013] In one embodiment, the standard deviation σ of the scattering angle distribution generated when the muons pass through the material to be measured θ and the radiation length L of the material to be measured rad have the following relationship:

[0014]

[0015] In the formula:

[0016] β is the velocity of the muons;

[0017] p is the momentum of the muons;

[0018] L is the thickness of the material to be measured.

[0019] In one embodiment, the method of obtaining the muon scattering angle distribution f(θ) of approximately continuous energy after calibration by fitting the scattering angle distribution of muons with discrete energy includes:

[0020] Selecting monoenergetic muons at n characteristic energy points;

[0021] Using a calibration material to calibrate the weight coefficient A of the scattering angle distribution f(θ) of each monoenergetic muon i ; i Performing calibration;

[0022] According to the calibrated weight coefficients A 1 ,..., A n , obtaining the muon scattering angle distribution f(θ) of approximately continuous energy after calibration.

[0023] In one embodiment, the method of calibrating the weight A of the scattering angle distribution f(θ) of each monoenergetic muon using a calibration material includes: i ; i Performing calibration, including:

[0024] Obtaining the scattering angle distribution f(θ) generated when each monoenergetic muon passes through the calibration material, where f(θ) i is: i In the formula: σ

[0025]

[0026] In the formula: i is the standard deviation of the scattering angle distribution generated when the monoenergetic muons at the i-th characteristic energy point pass through the calibration material;

[0027] Obtaining the muon scattering angle distribution f(θ) of approximately continuous energy, where the muon scattering angle distribution f(θ) is:

[0028]

[0029] Obtain the scattering angle generated by the muons with continuous energy passing through the calibration material, and statistically analyze the standardized scattering angle distribution to obtain the discrete distribution D(θ);

[0030] Fit the scattering angle distribution f(θ) of the muons with approximately continuous energy to the discrete distribution D(θ);

[0031] Calibrate the weight coefficients A 1 ,..., A n .

[0032] In one implementation, the method for obtaining the scattering angle generated by the muons with continuous energy passing through the calibration material and statistically analyzing the standardized scattering angle distribution to obtain the discrete distribution D(θ) includes:

[0033] When defining the incident direction of the muons with continuous energy as the Z-axis, the X-axis orthogonal to the Z-axis, and the Y-axis orthogonal to the Z-axis and orthogonal to the X-axis, measure the planar scattering angles formed by the muons with continuous energy passing through the calibration material with a thickness of L on two orthogonal planes of XZ and YZ;

[0034] Mix the planar scattering angles formed on the two orthogonal planes of XZ and YZ to form a sample set;

[0035] In the range of [-a, a] in the sample set, divide the interval at intervals of b mrad, and statistically analyze the standardized frequency distribution of the planar scattering angles to obtain the discrete distribution D(θ).

[0036] In one implementation, a is 180 mrad - 220 mrad, and b is 0.5 - 2 mrad.

[0037] In one implementation, the calibration material is lead.

[0038] In one implementation, the method for obtaining the radiation length of the material to be measured includes:

[0039] Calculate the frequency value N corresponding to the scattering angle θ = 0 in the discrete distribution B 0 ;

[0040] In the scattering angle distribution f(θ) of the muons with approximately continuous energy after calibration:

[0041]

[0042] Calculate the radiation length of the material to be measured:

[0043]

[0044] In one implementation, the method for selecting mono-energetic muons at n characteristic energy points includes:

[0045] Selecting mono-energetic muons at n characteristic energy points in a log-linear manner within the muon energy range of continuous energy.

[0046] In one implementation, the method for selecting mono-energetic muons at n characteristic energy points includes:

[0047] Selecting nine energy points of 0.25 GeV, 0.5 GeV, 1 GeV, 2 GeV, 4 GeV, 8 GeV, 16 GeV, 32 GeV, and 64 GeV in a log-linear manner within the muon energy range of continuous energy.

[0048] In one implementation, in the step of selecting mono-energetic muons at n characteristic energy points, the value of n is 9.

[0049] In one implementation, the discrimination method includes: verifying the discrimination result using an ROC curve.

[0050] The embodiment of the present application provides a material discrimination method. This discrimination method first determines the relationship between the standard deviation σ of the scattering angle distribution generated when muons pass through the material to be measured θ and the radiation length L of the material to be measured rad ; then uses the scattering angle distribution of discrete-energy muons to fit to obtain the calibrated approximate continuous-energy muon scattering angle distribution f(θ) and obtains the scattering angle generated when continuous-energy muons pass through the material to be measured, and statistically obtains the standardized scattering angle distribution to obtain the discrete distribution B; couples the discrete distribution B with the calibrated muon scattering angle distribution f(θ); calculates the radiation length of the material to be measured; and discriminates the material to be measured based on the radiation length. That is to say, this discrimination method introduces the discrete energy information of muons from a statistical perspective, obtains the calibrated approximate continuous-energy muon scattering angle distribution f(θ), combines the discrete distribution B obtained by measuring the continuous-energy muons passing through the material to be measured, calculates the radiation length of the material to be measured and uses the radiation length as a characteristic quantity to discriminate the material to be measured, improving the accuracy of the material discrimination method. In addition, this discrimination method does not require measuring continuous-energy muons one by one, simplifying the discrimination method while improving the accuracy of the material discrimination method. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the method for the material discrimination method provided by an embodiment of the present application;

[0052] Figure 2Schematic diagram for comparing the accuracy rates of the material identification method according to the embodiments of the present application and the material identification method in the related art. Among them, the dashed line represents the accuracy rate of the material identification method in the related art without introducing muon energy information, and the solid line represents the accuracy rate of the material identification method according to the embodiments of the present application with discrete muon energy information introduced. Detailed implementation manners

[0053] It should be noted that, without conflict, the embodiments in the present application and the technical features in the embodiments may be combined with each other. The detailed description in the detailed implementation manners should be understood as an explanatory illustration of the gist of the present application and should not be regarded as an improper limitation to the present application.

[0054] The embodiments of the present application provide a material identification method. Please refer to Figure 1 , and the identification method includes:

[0055] Step S101: Determine the relationship between the standard deviation σ θ of the scattering angle distribution generated when muons pass through the material to be measured and the radiation length L rad of the material to be measured;

[0056] Step S102: Use the scattering angle distribution of discrete energy muons to fit to obtain the calibrated muon scattering angle distribution f(θ) of approximately continuous energy;

[0057] Step S103: Obtain the scattering angle generated when continuous energy muons pass through the material to be measured, and statistically obtain the standardized scattering angle distribution to obtain the discrete distribution B;

[0058] Step S104: Couple the discrete distribution B with the calibrated muon scattering angle distribution f(θ);

[0059] Step S105: Calculate the radiation length of the material to be measured;

[0060] Step S106: Identify the material to be measured according to the radiation length.

[0061] Among them, steps S102 and S103 are not in a sequential order. That is to say, step S102 can be executed first and then step S103, or step S103 can be executed first and then step S102, or steps S102 and S103 can be executed simultaneously.

[0062] The principle of using muons for material identification is based on the multiple Coulomb scattering phenomenon that occurs when muons interact with the material to be measured. When muons pass through the material to be measured, continuous multiple small-angle scatterings will occur, and the projection of the scattering angle in the plane follows a normal distribution with a mean of 0 and a standard deviation of σ θGaussian distribution. Since the multiple Coulomb scattering of muons with the material to be measured is not only related to the type of material but also to the energy of the muons themselves. When using muons for material identification, its accuracy is affected by the energy of the muons. In fact, the muon energy is continuous and it is very difficult to measure in real time. In related technologies, the average energy of muons is used instead of the continuous muon energy, which reduces the accuracy of material identification. This approximation leads to a reduction in the quality of the imaging image and the accuracy of material identification. Compared with the accurate muon energy, when there is an error of 0.5 GeV in the muon energy, the recognition accuracy between special nuclear materials drops by 11%, and when there is an error of 50% in the muon energy, the imaging result is already very blurred.

[0063] And the embodiment of the present application provides a material identification method. This identification method first determines the standard deviation σ of the scattering angle distribution generated when muons pass through the material to be measured θ and the radiation length L of the material to be measured rad between them; then uses the scattering angle distribution of discrete energy muons to fit to obtain the calibrated approximate continuous energy muon scattering angle distribution f(θ) and obtains the scattering angle generated when continuous energy muons pass through the material to be measured, and statistically obtains the standardized scattering angle distribution to get the discrete distribution B; couples the discrete distribution B with the calibrated muon scattering angle distribution f(θ); calculates the radiation length of the material to be measured; and identifies the material to be measured according to the radiation length. That is to say, this identification method introduces the discrete energy information of muons from a statistical perspective, obtains the calibrated approximate continuous energy muon scattering angle distribution f(θ), combines the discrete distribution B obtained by measuring the continuous energy muons passing through the material to be measured, calculates the radiation length of the material to be measured and uses the radiation length as a characteristic quantity to identify the material to be measured, improving the accuracy of the material identification method. In addition, this identification method does not need to measure continuous energy muons one by one, which simplifies the identification method while improving the accuracy of the material identification method.

[0064] The following will specifically describe the material identification method of the embodiment of the present application in conjunction with specific embodiments.

[0065] In step S101, determine the standard deviation σ of the scattering angle distribution generated when muons pass through the material to be measured θ and the radiation length L of the material to be measured rad between them. The principle of using muons for material identification is based on the multiple Coulomb scattering phenomenon of muons with the material to be measured. When muons pass through the material to be measured, they will undergo continuous small-angle scattering multiple times, and the projection of its scattering angle in the plane follows a Gaussian distribution with a mean of 0 and a standard deviation of σ θ Calculate the radiation length of the material to be measured and use the radiation length as a characteristic quantity to identify the material to be measured

[0066] In one embodiment, the standard deviation σ of the scattering angle distribution generated when muons pass through the material to be measured θ and the radiation length L of the material to be measured rad have the following relationship:

[0067]

[0068] In the formula:

[0069] β is the velocity of the muon;

[0070] p is the momentum of the muon;

[0071] L is the thickness of the material to be measured.

[0072] That is to say, in formula (1), the radiation length L rad is a characteristic quantity of the material. Materials with a specific atomic number correspond to specific radiation length values. Generally, the larger the atomic number of the material, the smaller the radiation length. β is the velocity of the muon, approximately equal to the speed of light, p is the momentum of the muon, and L is the thickness of the material to be measured. By measuring the standard deviation σ of the scattering angle generated when muons pass through the material to be measured θ , and then combining the muon energy information and the thickness of the material to be measured to calculate the radiation length value of the material to be measured, the identification of the material to be measured can be achieved. Formula (1) shows that the muon scattering angle is related to the muon energy. The energy spectrum of natural muons is continuous, and the muon scattering angles measured in experiments are a set of scattering angles generated by muons with different energies.

[0073] In step S102, the method of using the scattering angle distribution of discrete-energy muons to fit and obtain the calibrated approximate continuous-energy muon scattering angle distribution f(θ) includes:

[0074] Step S201: Select monochromatic muons at n characteristic energy points;

[0075] Step S202: Use a calibration material to calibrate the weight coefficient A i of the scattering angle distribution f(θ) i of each monochromatic muon;

[0076] Step S203: According to the calibrated weight coefficients A 1 ,..., A n , obtain the calibrated approximate continuous-energy muon scattering angle distribution f(θ).

[0077] Specifically, the scattering angle of mono - energetic muons passing through the material to be measured follows a Gaussian distribution, and its contribution to the scattering angle distribution of natural continuous - energy muons is the Gaussian probability density function corresponding to its energy. Generalizing this to the entire muon energy range, the distribution satisfied by the scattering angle of continuous - energy muons should be the weighted sum of the scattering angle contributions of muons generated in the full - energy range, with the weight being the probability of muons appearing at each differential energy point. This distribution is theoretically the convolution of the Gaussian distribution and the muon energy spectrum.

[0078] Since the muon energy spectrum is relatively complex, mono - energetic muons at n characteristic energy points are selected, and the n characteristic energy points of muons are used to replace the muon energy spectrum. It should be noted that the value of n is not restricted here. For example, it can be 6, 7, 8, 9, 10, 11, 12, 15, etc. Exemplarily, in one embodiment, for example, the value of n is 9.

[0079] The discrimination method of the embodiment of the present application selects mono - energetic muons at 9 characteristic energy points, and uses the scattering angle distribution of discrete - energy muons to fit and obtain the calibrated approximate continuous - energy muon scattering angle distribution f(θ). It does not require measuring continuous - energy muons one by one, which simplifies the discrimination method while improving the accuracy of the material discrimination method.

[0080] Using the calibration material to calibrate the weight coefficient A i of the scattering angle distribution f(θ) i of each mono - energetic muon, that is, by using a known calibration material, calibrate the weight coefficient A i of the scattering angle distribution f(θ) i of each mono - energetic muon, that is, determine the weight coefficients A 1 ,..., A n at n characteristic energy points, and then according to the calibrated weight coefficients A 1 ,..., A n , obtain the calibrated approximate continuous - energy muon scattering angle distribution f(θ).

[0081] In one embodiment, the method of selecting mono - energetic muons at n characteristic energy points includes: logarithmically linearly selecting mono - energetic muons at n characteristic energy points in the muon energy range of continuous energy. In this way, characteristic energy points covering a sufficiently large range can be selected, so that the span interval of the n characteristic energy points includes as many muons as possible, covering the main interaction energy range of muons, which has theoretical significance, and can make the scattering angle distribution of discrete - energy muons fit to obtain the calibrated muon scattering angle distribution f(θ) closer to the discrete - type distribution D(θ) produced by continuous - energy muons passing through the calibration material.

[0082] In one embodiment, a method for selecting mono-energetic muons at n characteristic energy points includes: logarithmically linearly selecting nine energy points of 0.25 GeV, 0.5 GeV, 1 GeV, 2 GeV, 4 GeV, 8 GeV, 16 GeV, 32 GeV, and 64 GeV in the muon energy range of continuous energy. The span of the nine energy points in the range of 0.25 - 64 GeV contains 94.3% of natural muons, covering the main interaction energy range of muons and having theoretical significance.

[0083] In step S202, the method for calibrating the weight A of the scattering angle distribution f(θ) of each mono-energetic muon using a calibration material includes: i of weight A i is as follows:

[0084] Step S301: Obtain the scattering angle distribution f(θ) generated by each mono-energetic muon passing through the calibration material, where f(θ) i , where f(θ) i is:

[0085]

[0086] In the formula: σ i is the standard deviation of the scattering angle distribution generated by the mono-energetic muon at the i-th characteristic energy point passing through the calibration material;

[0087] Step S302: Obtain the scattering angle distribution f(θ) of muons with approximately continuous energy, where f(θ) is:

[0088]

[0089] Step S303: Obtain the scattering angle generated by muons with continuous energy passing through the calibration material, and statistically obtain the standardized scattering angle distribution to obtain the discrete distribution D(θ);

[0090] Step S304: Fit the scattering angle distribution f(θ) of muons with approximately continuous energy with the discrete distribution D(θ);

[0091] Step S305: Calibrate the weight coefficient A 1 ,..., A n .

[0092] That is to say, first select the n mono-energetic muons and obtain the scattering angle distribution f(θ) generated by each mono-energetic muon passing through the calibration material i . Since the scattering angle generated by the mono-energetic muon passing through the material to be measured follows a Gaussian distribution, that is, equation (2), the contribution of f(θ) i to the scattering angle distribution of natural muons with continuous energy is the Gaussian probability density function corresponding to its energy, that is, the weight coefficient A iThen, the muon scattering angle distributions at n characteristic energy points are weighted and summed to obtain the muon scattering angle distribution f(θ) with approximate continuous energy in Equation (3). Then, the scattering angles of muons with continuous energy passing through the calibration material are obtained, and the normalized scattering angle distribution is statistically obtained to get the discrete distribution D(θ). The muon scattering angle distribution f(θ) with approximate continuous energy is fitted to the discrete distribution D(θ). Among them, Equation (3) is in the form of the weighted sum of Gaussian probability density functions corresponding to n energy points, and the constant term has been incorporated into the undetermined coefficients.

[0093] In one embodiment, when using the calibration material to calibrate the weight coefficients A 1 ,…,A n in the calibration experiment, three lead blocks with thicknesses of 5, 10, and 15 cm respectively and a bottom area of 10×20 cm 2 are simultaneously selected as the standard materials. Since too large a thickness of lead will block low-energy muons, and too small a thickness will make the scattering angles of high-energy muons too small, in this embodiment, the average value of the calibration results of the three lead blocks with different thicknesses is taken as the final weight. The three lead blocks with different thicknesses are simultaneously placed in the cosmic ray muon imaging device, and 90,000 muon scattering angles passing through the lead blocks with the complete thickness are measured each, and the normalized distribution of the measured muon scattering angles is statistically obtained. The measured data points are least-squares fitted using the simplified natural muon scattering angle distribution (Equation (3)), and the weight coefficients A1, A2,…A9 corresponding to each discrete energy point are calculated.

[0094] On the muon energy interval with continuous energy, nine energy points of 0.25 GeV, 0.5 GeV, 1 GeV, 2 GeV, 4 GeV, 8 GeV, 16 GeV, 32 GeV, and 64 GeV are logarithmically linearly selected. The corresponding weight coefficients are: A 1 ,…,A n . The calibration material is used to calibrate the weight coefficients A i of the scattering angle distribution f(θ) i of each of the above monoenergetic muons. The experimental calibration values of the muon discrete energy weight coefficients at the above nine characteristic energy points are shown in Table 1 below:

[0095] Table 1

[0096]

[0097] It should be noted that when using the calibration material to calibrate the weight coefficients A 1 ,…,A n , where the σ i corresponding to each energy point is a known quantity and can be calculated by Equation (1). The weight coefficients A 1 ,…,A n represent the proportion of the number of muons at their respective corresponding energy points. The calibrated weight coefficients A1,…,An Substituting into Equation (3) gives an approximately natural continuous-energy muon scattering angle distribution f(θ). The muon scattering angles of the material to be measured are measured and coupled with the calibrated Equation (3) to deduce the radiation length of the unknown material.

[0098] In step S303, the method for obtaining the scattering angles generated by continuous-energy muons passing through the calibration material and statistically obtaining the discrete distribution D(θ) of the standardized scattering angle distribution includes:

[0099] Step S401: When the incident direction of the continuous-energy muons is defined as the Z-axis, the X-axis orthogonal to the Z-axis, and the Y-axis orthogonal to the Z-axis and orthogonal to the X-axis, measure the planar scattering angles formed by the continuous-energy muons passing through the calibration material with a thickness of L on two orthogonal planes of XZ and YZ;

[0100] Step S402: Mix the planar scattering angles formed on the two orthogonal planes of XZ and YZ to form a sample set;

[0101] Step S403: In the range of [-a, a] in the sample set, divide the intervals at intervals of b mrad, and statistically obtain the standardized frequency distribution of the planar scattering angles to obtain the discrete distribution D(θ).

[0102] Where mrad (milliradian) is the unit of angle, and 1 mrad = 0.001 radian.

[0103] In this embodiment, when the incident direction of the continuous-energy muons is defined as the Z-axis, the X-axis orthogonal to the Z-axis, and the Y-axis orthogonal to the Z-axis and orthogonal to the X-axis, the planar scattering angles formed by the calibration material on two orthogonal planes of XZ and YZ are measured. Here, the calibration material is not limited. For example, the calibration material is a lead block with a thickness of L.

[0104] Mix the planar scattering angles formed on the two orthogonal planes of XZ and YZ to form a sample set. In the range of -a mrad to a mrad, divide the intervals at intervals of b mrad, statistically obtain the normalized frequency of the measured scattering angles, and then make a scatter plot to obtain the discrete distribution D(θ).

[0105] In one embodiment, a is 180 mrad - 220 mrad, and b is 0.5 - 2 mrad. For example, a can be 180 mrad, 190 mrad, 200 mrad, 210 mrad, 220 mrad. Exemplarily, a is 200 mrad. For example, b can be 0.5 mrad, 1 mrad, 1.5 mrad, 2 mrad. Exemplarily, b is 1 mrad. That is, in the range of -200 - 200 mrad, divide the intervals at intervals of 1 mrad, statistically obtain the normalized frequency of the measured scattering angles, and then make a scatter plot to obtain the discrete distribution D(θ).

[0106] In step S105, the method for calculating the radiation length of the material to be measured includes:

[0107] Step S501: Calculate the frequency value N corresponding to the scattering angle θ = 0 in the discrete distribution B 0 ;

[0108] Step S502: In the muon scattering angle distribution f(θ) of the calibrated approximate continuous energy:

[0109]

[0110] Step S503: Calculate the radiation length of the material to be measured:

[0111]

[0112] According to equation (3), it can be seen that the muon scattering angle distribution reaches its maximum value at θ = 0. Calculate the frequency value N corresponding to the scattering angle θ = 0 in the discrete distribution B 0 , let θ = 0 in the muon scattering angle distribution f(θ) of the calibrated approximate continuous energy, and make f(0) ≈ N 0 Obtain equation (4), and the expression for the radiation length is equation (5). Then, the radiation length of the material to be measured can be calculated according to equation (5).

[0113] In one embodiment, for the material identification experiment, cubic samples of C, Al, Fe, Pb, and W with a thickness of 10 cm are selected and placed in the muon imaging device to measure the scattering angle. Similarly, the standardized muon scattering angle distribution is statistically analyzed. Take the probability density value N of the scattering angle distribution of a certain material at θ = 0 0 , and substitute it together with the calibrated weight coefficients A1,..., A of the discrete energy points n into equation (5) to calculate the radiation length of the material.

[0114] Material identification based on discrete energy information is divided into two steps: First, use lead with a known thickness as the calibration material to calibrate the weight coefficients of each energy point. Then, measure the scattering angle of the sample to be identified, calculate the radiation length of each material through the calibrated muon scattering angle distribution, and use this to identify the materials.

[0115] After calculating the radiation length value for the material to be measured, use the radiation length as a characteristic value and use a binary classification method to identify different materials to be measured, and use the ROC curve to evaluate the accuracy of material identification. That is to say, by introducing the ROC curve (Receiver Operating Characteristic curve) to evaluate the accuracy of the identification between two materials, it reflects the overall discrimination ability of each data set.

[0116] In one embodiment, in the material identification experiment of five samples of C, Al, Fe, Pb, and W, the radiation length values of the five materials were calculated. Among them, the radiation lengths of Pb and W only differed from the standard radiation length values provided by Lawrence Berkeley National Laboratory by 4.7% and 9.7%, respectively. The five materials were divided into four experimental groups of C-Al, Al-Fe, Fe-Pb, and Pb-W according to the atomic number for material identification. The results showed that under approximately 1400 muon events, the identification accuracy of Al-Fe was 100%, the identification accuracy of Fe-Pb was 98.3%, the identification accuracy of C-Al was 88.3%, and the identification accuracy of Pb-W was 85%.

[0117] In one embodiment, please refer to Figure 2 , and the material identification method of the embodiment of the present application and the material identification method without introducing energy information were used to identify the materials of the Pb-W experimental group at the same time. When no energy information was introduced, the identification accuracy of Pb-W was 71.7%. After introducing the discrete muon energy information using the material identification method of the embodiment of the present application, the identification accuracy was 85%, which was an increase of 18.5% compared with the former.

[0118] In one embodiment, the five materials were divided into four experimental groups of C-Al, Al-Fe, Fe-Pb, and Pb-W according to the atomic number. Thirty radiation length samples were calculated repeatedly for each material, and the material identification was performed using this sample set. The binary classification method was used in the identification process. The two groups of material samples to be identified were mixed into a total set, and the samples in it were sorted from small to large. The minimum value in the mixed set was selected as the initial threshold to judge all the samples in the mixed set, and the true positive rate (TPR), false positive rate (FPR), and judgment accuracy rate were calculated at the current threshold. Subsequently, the threshold was linearly increased, and the samples in the mixed set were repeatedly judged and identified one by one until the threshold exceeded the maximum value in the mixed set. Finally, the ROC curve of the identification could be drawn according to the TPR and FPR at different thresholds, and the maximum value of the judgment accuracy rate at different thresholds was defined as the identification accuracy rate of the two materials.

[0119] The various embodiments / implementations provided by the present application can be combined with each other without contradiction.

[0120] The above are only the preferred embodiments of the present application and are not used to limit the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application are included in the protection scope of the present application.

Claims

1. A method for material identification, characterized in that, the identification method includes: Determine the standard deviation σ of the scattering angle distribution generated by muons passing through the material to be measured θ and the radiation length L of the material to be measured rad relationship between; obtaining the calibrated muon scattering angle distribution f(θ) of approximate continuous energy by fitting the scattering angle distribution of discrete energy muons; obtaining the scattering angles generated by muons of continuous energy passing through the material to be measured, and statistically obtaining the discrete distribution B of the standardized scattering angle distribution; coupling the discrete distribution B with the calibrated muon scattering angle distribution f(θ); calculating the radiation length of the material to be measured; identifying the material to be measured according to the radiation length; wherein, the standard deviation σ of the scattering angle distribution generated when the muon passes through the material to be measured θ and the radiation length L of the material to be measured rad are related as follows: where: β is the velocity of the muon; p is the momentum of the muon; L is the thickness of the material to be measured; the method for obtaining the calibrated muon scattering angle distribution f(θ) of approximate continuous energy by fitting the scattering angle distribution of discrete energy muons includes: selecting monoenergetic muons at n characteristic energy points; Calibrate the weighting coefficient A i of the scattering angle distribution f(θ) of each of the said mono-energetic muons i ; According to the calibrated weight coefficients A 1 , …, A n , the muon scattering angle distribution f(θ) of the calibrated approximate continuous energy is obtained; The method for calibrating the weight A i of the scattering angle distribution f(θ) of each of the mono-energetic muons i using a calibration material includes: Obtain the scattering angle distribution f(θ) generated by each of the mono-energetic muons passing through the calibration material i , where f(θ) i is defined as: Where: σ i is the standard deviation of the scattering angle distribution generated by the monoenergetic muons at the i-th characteristic energy point passing through the calibration material; obtaining the muon scattering angle distribution f(θ) of approximate continuous energy, where f(θ) is: obtaining the scattering angles generated by muons of continuous energy passing through the calibration material, and statistically obtaining the discrete distribution D(θ) of the standardized scattering angle distribution; fitting the muon scattering angle distribution f(θ) of approximate continuous energy with the discrete distribution D(θ); Calibrate the weight coefficient A 1 ,…,A n .

2. The identification method according to claim 1, characterized in that, the method for obtaining the scattering angles generated by muons of continuous energy passing through the calibration material, and statistically obtaining the discrete distribution D(θ) of the standardized scattering angle distribution includes: when limiting the incident direction of muons of continuous energy as the Z-axis, the X-axis orthogonal to the Z-axis, and the Y-axis orthogonal to the Z-axis and orthogonal to the X-axis, measuring the planar scattering angles formed by muons of continuous energy passing through the calibration material with a thickness of L on two orthogonal planes of XZ and YZ; mixing the planar scattering angles formed on the two orthogonal planes of XZ and YZ to form a sample set; in the range of [-a, a] in the sample set, dividing the interval at intervals of b mrad, and statistically obtaining the standardized frequency distribution of the planar scattering angles to obtain the discrete distribution D(θ).

3. The identification method according to claim 2, characterized in that, a is 180 mrad - 220 mrad, and b is 0.5 - 2 mrad.

4. The identification method according to claim 2, characterized in that, the calibration material is lead.

5. The identification method according to claim 1, characterized in that, the method for obtaining the radiation length of the material to be measured includes: Calculate the frequency value N corresponding to the scattering angle θ = 0 in the discrete distribution B 0 ; in the calibrated muon scattering angle distribution f(θ) of approximate continuous energy: calculating the radiation length of the material to be measured:

6. The identification method according to claim 1, characterized in that, the method for selecting monoenergetic muons at n characteristic energy points includes: selecting monoenergetic muons at n characteristic energy points in a logarithmically linear manner in the muon energy interval of continuous energy.

7. The identification method according to claim 6, characterized in that, the method for selecting monoenergetic muons at n characteristic energy points includes: Nine energy points of 0.25 GeV, 0.5 GeV, 1 GeV, 2 GeV, 4 GeV, 8 GeV, 16 GeV, 32 GeV, and 64 GeV are logarithmically linearly selected in the muon energy range of the continuous energy.

8. The discrimination method according to claim 1, characterized in that in the step of selecting monoenergetic muons at n characteristic energy points, the value of n is 9.

9. The discrimination method according to claim 1, characterized in that the discrimination method includes: using an ROC curve to verify the discrimination result.

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