A Bayesian characteristic peak identification method for gamma spectroscopy data

Abstract

The present invention discloses a Bayesian characteristic peak recognition method for gamma energy spectrum data, comprising the following steps: step S1, establishing a distribution model of energy measurement values ​​within a characteristic peak interest interval; step S2, selecting a priori distribution and designing a model parameter inference algorithm, specifically: using a Bayesian parameter estimation method to infer model parameters, and the model parameters w m and b m The posterior distribution of is defined as #imgabs0# and #imgabs1#. Step S3, multi-characteristic peak recognition method design. In the present invention, by using a linear function to approximate the background energy distribution for gamma spectrum analysis with low counting rate under short measurement time, and designing a related parameter inference algorithm, a near-real-time low misjudgment rate and a high characteristic peak recognition rate can be achieved, thereby improving the qualitative analysis capability of gamma spectrum data in this type of application and improving the detection limit of qualitative measurement of characteristic peaks.

Description

Technical Field

[0001] The invention belongs to the technical field of radiation environment monitoring, and in particular relates to a Bayesian characteristic peak recognition method for gamma energy spectrum data. Background Art

[0002] UAV-mounted and vehicle-mounted environmental radiation monitoring systems have a wide range of application scenarios in environmental monitoring and radiation emergency response, and are an important means of ensuring nuclear safety. However, due to the changing environmental background radiation level, unpredictable types and distances of radioactive sources, and limited detector volume and energy resolution, the detector system can usually only collect energy spectrum data with low count rates, large statistical fluctuations, and weak characteristic peaks in a short measurement time. The processing of this type of energy spectrum data, especially the reliable identification of characteristic gamma rays of interest in the energy spectrum data, is an urgent problem to be solved in this type of application.

[0003] Traditional qualitative analysis methods for energy spectrum data mainly use energy spectrum data peak finding algorithms based on derivatives or symmetric zero-area methods. Such algorithms are simple and efficient to implement, but the energy spectrum data to be processed must meet the requirements of smooth distribution. Usually, they can only process energy spectrum data with high counting rates and long measurement times. For gamma energy spectrum data with low counting rates and short measurement times, such methods usually have no practical value.

[0004] In recent years, the qualitative analysis of gamma energy spectrum data based on artificial intelligence algorithms has made certain breakthroughs. Among them, the model training-based method usually constructs a training sample set artificially, and extracts feature data from the measured energy spectrum data through analytical methods such as discrete cosine transform or wavelet transform, which is used to train a classifier to realize the identification of characteristic peaks. In addition, the Bayesian model-based method integrates the physical knowledge in the gamma detection process to establish a corresponding probability model for the measured energy spectrum data, and estimates the model parameters through measured data to complete the qualitative analysis of the characteristic peaks. Both have the potential to overcome the problem of gamma energy spectrum characteristic peak identification under low counting rate and short measurement time, but the former usually has high complexity and high model training and deployment costs, while the latter has good interpretability and flexible modeling, but the parameter inference process also has certain computational complexity. In summary, through the appropriate optimization of the Bayesian model, it is expected to develop a method with high recognition rate and practical ability. Summary of the invention

[0005] The purpose of the present invention is to provide a Bayesian characteristic peak recognition method for gamma spectrum data to solve the problems of long model training time and complex parameter inference process calculation in the prior art for characteristic peak recognition.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A Bayesian characteristic peak identification method for gamma spectral data comprises the following steps:

[0008] Step S1, establishing a distribution model of energy measurement values ​​within the characteristic peak interest interval; the distribution model is specifically:

[0009]

[0010] Where, the particle event set Events measured in the mth characteristic peak energy interval of interest is m The probability distribution of the neutrino event energy e is Depend on and The weighted sum is obtained, and the weighted coefficient is w m , is the energy probability distribution of the photoelectric event, which has a mean value of e m , the standard deviation is , the value range is arrive The phase Gaussian distribution of is, k is the confidence coefficient, For Gaussian distribution The cumulative distribution function value at is the energy probability distribution of the Compton event, which has a linear function form and its intercept parameter is ;

[0011] Step S2, prior distribution selection and model parameter inference algorithm design, specifically: use Bayesian parameter estimation method to infer model parameters, model parameters w m and b m The posterior distribution of is defined as and , the following formula is obtained by Bayes formula:

[0012]

[0013] In the formula, is the model parameter and Given the posterior probability distribution of the observed outcome Eventsm, is the model parameter and The prior distribution of is the likelihood function;

[0014] Step S3, design of a multi-feature peak recognition method.

[0015] According to the above technical solution, in step S1, The specific calculation process is:

[0016] Step S101, defining the characteristic peaks to be identified as a set of peaks; the set of peaks is shown in the following formula:

[0017]

[0018] In the formula, is the attribute value characteristic energy, is the standard deviation, m represents the sequence number of the characteristic peak in the set, and M is the number of information of the characteristic peak;

[0019] Step S102, defining the particle event sequence recorded by the gamma radiation detector as a set Events, and the set Events is shown in the following formula:

[0020]

[0021] Where N is the number of particle events, is the energy of the measured particle event, is the arrival time, where i is the particle event number;

[0022] Step S103: for the mth characteristic peak, specify an energy interval of interest, and define the set of particle events in the energy interval as Events m ; Particle event collection Events m As shown below:

[0023]

[0024] In the formula, represents the number of particle events included, and k is the confidence coefficient;

[0025] Step S104, defining the energy probability distribution of the photoelectric event as ; Specifically:

[0026]

[0027] In the formula, Indicates support for , the mean is em, and the standard deviation is The probability density value of the truncated Gaussian distribution at e, For Gaussian distribution The cumulative distribution function value at .

[0028] According to the above technical solution, in step S1, The specific calculation process is:

[0029] Step S105: Distribute the energy Use linear function expression, specifically:

[0030]

[0031] In the formula, and are the slope and intercept of the linear function respectively;

[0032] Step S106, performing algebraic operations on the formula of step S105, and obtaining and The conversion relationship is as follows:

[0033]

[0034] In the formula, and are the slope and intercept, is the half-width of the energy interval of interest, where is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient;

[0035] Step S107, the conversion relationship calculated in step S106 is then substituted into the formula of step S105 to obtain :

[0036]

[0037] In the formula, is the intercept, is the half-width of the energy interval of interest, where is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient.

[0038] According to the above technical solution, in step S2, the posterior distribution samples of the parameters are sampled by the Markov chain-Monte Carlo sampling method, and the mean of all samples is taken as the point estimate of the posterior distribution of the parameters, as follows:

[0039]

[0040] In the formula, and are the model parameters and The prior distribution of is the posterior distribution of the model parameters given the observation Eventsm, and is the i-th sample sampled from the posterior distribution of the model. The sampled samples are averaged to obtain the posterior distribution point estimate of the model parameters. and .

[0041] According to the above technical solution, in step S3, the multi-feature peak recognition method is specifically designed as follows:

[0042] Step S301, firstly, a database is established for the characteristic peaks to be identified. The characteristic energy of each characteristic peak is queried by the nuclide information, and the standard deviation is calculated by the energy calibration coefficient, specifically:

[0043]

[0044] In the formula, is the standard deviation of the Gaussian distribution obeyed by the m-th characteristic peak energy, The energy resolution of the detector system to measure the 661keV characteristic gamma ray;

[0045] Step S302: Secondly, for each characteristic peak in each characteristic peak database, an identification pipeline is established, and each pipeline works in an independent thread and has a unified workflow.

[0046] According to the above technical solution, in step S302, the specific workflow is:

[0047] Step S3021, setting a corresponding characteristic peak energy interval of interest according to the database, and filtering the collected data to obtain radiation particle events within the interval of interest;

[0048] Step S3022, initializing model parameters, including characteristic peak parameters, parameter prior distribution and recognition threshold;

[0049] Step S3023, updating the model posterior parameters based on the measurement data;

[0050] Step S3024, determining whether a characteristic peak exists based on a recognition threshold.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] In the present invention, a probability model of the energy distribution of radiation particle events in the characteristic peak interest interval based on a physical model is proposed for gamma energy spectrum analysis with low counting rate under short measurement time, in which a linear function is used to approximate the background energy distribution, and a related parameter inference algorithm is designed, which can achieve a near real-time low misjudgment rate and a high characteristic peak recognition rate, improve the qualitative analysis capability of gamma energy spectrum data in this type of application, and improve the detection limit of qualitative measurement of characteristic peaks. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The radiation particle event (left) and the corresponding energy spectrum data (right) of the present invention are shown;

[0054] Figure 2It is a model diagram of particle event energy probability distribution within the characteristic peak interest interval of the present invention;

[0055] Figure 3 It is a block diagram of the multi-feature peak recognition system of the present invention;

[0056] Figure 4 A schematic diagram of a gamma detector system and a radiation source of the present invention;

[0057] Figure 5 It is the MCMC sampling result in parameter inference of the present invention;

[0058] Figure 6 It is the typical energy spectrum data of the airborne ionizing radiation monitoring system of the present invention within 1s measurement time;

[0059] Figure 7 This is a posterior estimation thermodynamic diagram of the 661keV characteristic peak-to-peak ratio of the airborne ionizing radiation monitoring system of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Embodiment 1

[0062] A Bayesian characteristic peak identification method for gamma spectral data comprises the following steps:

[0063] Step S1, establishing a distribution model of energy measurement values ​​within the characteristic peak interest interval; the distribution model is specifically:

[0064]

[0065] Where, the particle event set Events measured in the mth characteristic peak energy interval of interest is m The probability distribution of the neutrino event energy e is , Depend on and The weighted sum is obtained, and the weighted coefficient is , The energy probability distribution of photoelectric events follows a mean of , the standard deviation is , the value range is arrive The phase Gaussian distribution of is, k is the confidence coefficient, For Gaussian distribution The cumulative distribution function value at is the energy probability distribution of the Compton event, which has a linear function form and its intercept parameter is ;

[0066] Step S2, prior distribution selection and model parameter inference algorithm design, specifically: use Bayesian parameter estimation method to infer model parameters, model parameters and The posterior distribution of is defined as and , the following formula is obtained by Bayes formula:

[0067]

[0068] In the formula, is the model parameter and Given the posterior probability distribution of the observed outcome Eventsm, is the model parameter and The prior distribution of is the likelihood function;

[0069] Step S3, design of a multi-feature peak recognition method.

[0070] In the present invention, a probability model of the energy distribution of radiation particle events in the characteristic peak interest interval based on a physical model is proposed for gamma energy spectrum analysis with low counting rate under short measurement time, in which a linear function is used to approximate the background energy distribution, and a related parameter inference algorithm is designed, which can achieve a near real-time low misjudgment rate and a high characteristic peak recognition rate, improve the qualitative analysis capability of gamma energy spectrum data in this type of application, and improve the detection limit of qualitative measurement of characteristic peaks.

[0071] Embodiment 2

[0072] This embodiment is a further refinement of the first embodiment.

[0073] In step S1, The specific calculation process is:

[0074] Step S101, defining the characteristic peaks to be identified as a set of peaks; the set of peaks is shown in the following formula:

[0075]

[0076] In the formula, is the attribute value characteristic energy, is the standard deviation, m represents the sequence number of the characteristic peak in the set, and M is the number of information of the characteristic peak;

[0077] Step S102, defining the particle event sequence recorded by the gamma radiation detector as a set Events, and the set Events is shown in the following formula:

[0078]

[0079] Where N is the number of particle events, is the energy of the measured particle event, is the arrival time, where i is the particle event number;

[0080] Step S103: for the mth characteristic peak, specify an energy interval of interest, and define the set of particle events in the energy interval as Events m ; Particle event collection Events m As shown below:

[0081]

[0082] In the formula, represents the number of particle events included, and k is the confidence coefficient;

[0083] Step S104, defining the energy probability distribution of the photoelectric event as ; Specifically:

[0084]

[0085] In the formula, Indicates support for , the mean is em, and the standard deviation is The probability density value of the truncated Gaussian distribution at e, For Gaussian distribution The cumulative distribution function value at .

[0086] In step S1, The specific calculation process is:

[0087] Step S105: Distribute the energy Use linear function expression, specifically:

[0088]

[0089] In the formula, and are the slope and intercept of the linear function respectively;

[0090] Step S106, performing algebraic operations on the formula of step S105, and obtaining and The conversion relationship is as follows:

[0091]

[0092] In the formula, and are the slope and intercept, is the half-width of the energy interval of interest, where is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient;

[0093] Step S107, the conversion relationship calculated in step S106 is then substituted into the formula of step S105 to obtain :

[0094]

[0095] In the formula, is the intercept, is the half-width of the energy interval of interest, where is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient.

[0096] In step S2, the posterior distribution samples of the parameters are obtained by Markov chain-Monte Carlo sampling method, and the mean of all samples is taken as the point estimate of the posterior distribution of the parameters, as follows:

[0097]

[0098] In the formula, and are the model parameters and The prior distribution of is the posterior distribution of the model parameters given the observation Eventsm, and is the i-th sample sampled from the posterior distribution of the model. The sampled samples are averaged to obtain the posterior distribution point estimate of the model parameters. and .

[0099] In step S3, the multi-feature peak recognition method is specifically designed as follows:

[0100] Step S301, firstly, a database is established for the characteristic peaks to be identified. The characteristic energy of each characteristic peak is queried by the nuclide information, and the standard deviation is calculated by the energy calibration coefficient, specifically:

[0101]

[0102] In the formula, is the standard deviation of the Gaussian distribution obeyed by the m-th characteristic peak energy, The energy resolution of the detector system to measure the 661keV characteristic gamma ray;

[0103] Step S302: Secondly, for each characteristic peak in each characteristic peak database, an identification pipeline is established, and each pipeline works in an independent thread and has a unified workflow.

[0104] In step S302, the specific workflow is:

[0105] Step S3021, setting a corresponding characteristic peak energy interval of interest according to the database, and filtering the collected data to obtain radiation particle events within the interval of interest;

[0106] Step S3022, initializing model parameters, including characteristic peak parameters, parameter prior distribution and recognition threshold;

[0107] Step S3023, updating the model posterior parameters based on the measurement data;

[0108] Step S3024, determining whether a characteristic peak exists based on a recognition threshold.

[0109] Embodiment 3

[0110] The inventive concept of the present invention is:

[0111] The method of the present invention mainly includes the following three features: establishment of energy measurement value distribution model in the characteristic peak interest interval, design of prior distribution selection and model parameter inference method, and design of multi-characteristic peak recognition program under multi-core CPU architecture.

[0112] 1. Establishment of energy measurement value distribution model within the characteristic peak interest interval

[0113] The characteristic peaks to be identified are defined as a set of peaks, as shown in formula (1), which contains information of a total of M characteristic peaks, each of which has two attribute values ​​and characteristic energy. and standard deviation , where m represents the sequence number of the characteristic peak in the set.

[0114]

[0115] The particle event sequence recorded by the gamma radiation detector is defined as a set Events, as shown in formula (2), which contains a total of N particle events. Each particle event has two properties: the measured energy and arrival time , where i is the particle event number.

[0116]

[0117] For the mth characteristic peak, specify an energy interval of interest and define the set of particle events in the energy interval as Events m , as shown in formula (3), which contains particle events, where k is the confidence coefficient.

[0118]

[0119] According to the interaction process between gamma rays and matter, Events m It is considered to be composed of two types of particle events. The first type is defined as a photoelectric event. This type of particle event is observed when a characteristic gamma ray is incident on the detector and the energy is completely deposited in the detector. Due to the limited energy resolution of the detector, the observed energy value follows a truncated Gaussian distribution within the characteristic peak energy interval of interest. The energy probability distribution of the photoelectric event is defined as , as shown in formula (4). Indicates support for , the mean is em, and the standard deviation is The probability density value of the truncated Gaussian distribution at e.

[0120]

[0121] The second type of particle event is defined as a Compton event, which is caused by other high-energy gamma rays incident on the detector, and part of the energy is deposited in the detector and observed. Its energy distribution Continuous smoothing within the characteristic peak interval of interest can be approximately expressed as a linear function, as shown in formula (5). and are the slope and intercept of the linear function respectively.

[0122]

[0123] Performing algebraic operations on formula (5), we can obtain and The conversion relationship is shown in formula (6).

[0124]

[0125] Substituting equation (6) into equation (5), we obtain equation (7).

[0126]

[0127] Events m The probability distribution of the neutrino event energy is defined as , as shown in formula (8), for and The weighted sum of , whose physical meaning corresponds to the peak-to-total ratio in the interval of interest.

[0128]

[0129] 2. Prior distribution selection and model parameter inference algorithm design

[0130] because Medium Parameters The maximum likelihood estimation of does not have an analytical solution, and it is difficult to design a maximum likelihood estimation algorithm for a mixed probability model. The present invention uses a Bayesian parameter estimation method to infer model parameters. and The posterior distribution of is defined as and , we get formula (9) by using the Bayesian formula.

[0131]

[0132] In order to reduce the computational complexity of parameter inference, the present invention is and All specify discrete type prior distributions, as shown in Table 1, where It obeys geometric distribution. Due to the location of the emission source information in the radiation field, the prior assumption is that within the characteristic peak interest interval, the probability of the characteristic peak existing or not is 0.5. For the case where the characteristic peak exists, the peak has a higher probability when it is at a lower ratio. On the contrary, it has a lower probability value. It obeys the discrete uniform distribution, and its value range is from 0 to The posterior distribution samples of the parameters are obtained by the Markov chain-Monte Carlo sampling method as in formula (10), and the mean of all samples is taken as the point estimate of the posterior distribution of the parameters.

[0133]

[0134] Table 1 Parameter prior distribution

[0135]

[0136] In a radiation field environment that does not contain the radioactive source to be detected, use a detector to perform repeated sampling 50 times at a specified measurement time t. Using the above model and parameter estimation method, calculate the estimated peak-to-total ratio of a characteristic peak to be identified in each data acquisition. Set the detection threshold from 0 to 1.0 with a step size of 0.01, calculate the false positive rate under the given threshold, and record the detection threshold when the false positive rate is less than a certain value as the identification parameter in the actual application process.

[0137] 3. Multi-feature peak recognition program design under multi-core CPU architecture

[0138] First, a database is established for the characteristic peaks to be identified. The characteristic energy of each characteristic peak can be queried by the nuclide information provided by the IAEA. The standard deviation is determined by the detector system. This value can be obtained from the test report provided by the manufacturer or calculated by the energy calibration coefficient, as shown in formula (11).

[0139]

[0140] Secondly, for each characteristic peak in each characteristic peak database, an identification pipeline is established. Each pipeline works in an independent thread with a unified workflow:

[0141] 1) Set the energy interval of interest of the corresponding characteristic peak according to the database, and filter the radiation particle events within the interval of interest from the collected data;

[0142] 2) Initialize model parameters, including characteristic peak parameters, parameter prior distribution and recognition threshold;

[0143] 3) Update the model posterior parameters based on the measured data;

[0144] 4) Determine whether the characteristic peak exists based on the recognition threshold.

[0145] Embodiment 4

[0146] This embodiment provides a specific implementation of the method of the present invention.

[0147] Building a gamma radiation detection system in a laboratory environment, such as Figure 4 As shown in the figure, the experiment uses 137Cs and 60Co radioactive sources with activities of 80000Bq and 300000Bq respectively. The detector used is φ3''*3''NaI(Tl). Each radioactive source is placed separately next to the detector for measurement. The measurement time of the multi-channel analyzer is set to 1200 seconds, and the accumulated energy spectrum data is recorded. The accumulated energy spectrum data collected when the two radioactive sources are placed separately are used to calibrate the energy of the detector system, and the energy resolution of the detector system is calculated using the collected 137Cs source energy spectrum data. The result is 7.2%@661keV. According to the calibration information of the detector system, a database of characteristic peaks to be detected is established, as shown in Table 2.

[0148] Table 2 Characteristic peak database to be detected

[0149]

[0150] According to the characteristic peak database, initialize the characteristic peak recognition algorithm, such as Figure 3As shown in the figure, an independent recognition channel is established for each characteristic peak. Each recognition channel works in an independent thread. The characteristic peak to be detected, characteristic peak parameters, energy interest interval, prior distribution parameters, Markov chain-Monte Carlo sampling algorithm parameters (sampling number 2000 and burn-in sample size 1000), detection time and corresponding detection threshold are specified for the channel.

[0151] The detector system is placed in the environment to be detected, and the multi-analyzer is set to a fixed detection time for data sampling. After a data collection is completed, the characteristic peak recognition algorithm is used to process the data. Each recognition channel first intercepts the data in the interval of interest from the measured data, and obtains the posterior estimation of the model parameters through the parameter inference algorithm. The result is as follows: Figure 5 As shown in the figure, the left side of the figure shows the result of MCMC sampling algorithm sampling from the posterior distribution of model parameters, and the right side shows the statistical histogram of the sampling results. The mean of the model parameters is calculated as the posterior estimation result of the model parameters and compared with the preset detection threshold. If w m If the detection threshold is exceeded, it is determined that the characteristic peak exists; otherwise, it is determined that the characteristic peak does not exist.

[0152] Embodiment 5

[0153] This embodiment provides a specific implementation of the method of the present invention.

[0154] Without placing any radioactive source, the detector was exposed to the measurement environment to measure the environmental background radiation. The measurement time of the multi-channel analyzer was set to 1800 seconds, and the energy spectrum data was recorded at a frequency of 1 Hz. According to the aforementioned characteristic peak database, the relevant parameters of the 661 keV characteristic peak were queried, a detection channel was established for the 661 keV characteristic peak, the corresponding model parameters were initialized, 50 groups of radiation particle events within 1s, 5s, 10s, 15s and 20s were randomly selected, and the parameters of each group of measurement data were estimated to obtain the corresponding peak-to-total ratio posterior estimation mean. The discrimination threshold was selected from the value interval of [0,1.0] with a step size of 0.02, and the error rate of different detection thresholds at different measurement times was tested. The detection thresholds when the error rate was less than 5% and 2% were recorded, as shown in Table 3. The measurement time and detection threshold in the table were used as reference values ​​for all characteristic peak identification. When establishing the detection algorithm, the peak-to-total ratio posterior estimation detection threshold used under different measurement times and a given error rate upper limit was obtained by looking up the table.

[0155] Table 2 Detection thresholds for given measurement time and upper limit of false detection rate

[0156]

[0157] Embodiment 6

[0158] This embodiment provides a specific implementation of the method of the present invention.

[0159] In the airborne environmental radiation monitoring application, a quad-rotor drone is used to mount a φ2*2-inch CeBr3 detector (energy resolution of 4%@661keV) and a multi-channel analyzer at a flight altitude of 5m. 137 Cs radioactive source, activity is 200mCi, the UAV flies along the Z trajectory in the airspace above the radioactive source, the flight speed is 1m / s, the multi-channel analyzer cumulative energy spectrum data recording frequency is set to 1Hz, the UAV sends the energy spectrum data and the GPS data at the sampling time to the ground computer through wireless communication, the ground computer runs the characteristic peak recognition algorithm proposed by the present invention, sets the left and right energy boundaries of the 661keV characteristic peak to [638.49keV, 683.5keV], and by querying Table 2, according to the 5% error rate, takes 0.24 as the model peak-to-background ratio posterior estimation detection threshold. The ground station computer processes the energy spectrum data recorded every second, identifies whether there is a characteristic peak at the sampling point, and renders the peak-to-total ratio posterior estimation result in the form of a heat map on the map, as shown in Figure 7 As shown. In contrast, the traditional energy spectrum data qualitative method cannot process the energy spectrum data with short measurement time and low count rate, which effectively improves the detection limit of characteristic peak identification in such applications and improves the spatial resolution of abnormal identification in environmental radiation monitoring. The recognition algorithm processes the data per second in an average of less than 2 seconds, achieving a near real-time processing speed, which is of practical value for airborne environmental radiation monitoring applications.

[0160] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0161] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A Bayesian characteristic peak identification method for gamma spectral data, characterized in that: The following steps are involved: Step S1, establishing a distribution model of energy measurement values ​​within the characteristic peak interest interval; the distribution model is specifically: Where, the particle event set Events measured in the mth characteristic peak energy interval of interest is m The probability distribution of the particle event energy e is P m (e), P m (e) By and The weighted sum is obtained, and the weighted coefficient is w m , is the energy probability distribution of the photoelectric event, which has a mean value of e m , with standard deviation σ m , the value interval is e m -kσ m To e m +kσ m The phase Gaussian distribution, k is the confidence coefficient, Φ(e m -kσ m |e m ,σ m ) is a Gaussian distribution in e m -kσ m The cumulative distribution function value at is the energy probability distribution of the Compton event, which has a linear function form and its intercept parameter is b m ; Step S2, prior distribution selection and model parameter inference algorithm design, specifically: use Bayesian parameter estimation method to infer model parameters, model parameters w m and b m The posterior distribution of is defined as and The following formula is obtained from the Bayesian formula: In the formula, is the model parameter w m and b m Given the posterior probability distribution of the observed outcome Eventsm, P(w m ,b m ) is the model parameter w m and b m The prior distribution of m (Events m |w m ,b m ) is the likelihood function; Step S3, designing a multi-feature peak recognition method; In step S3, the multi-feature peak recognition method is specifically designed as follows: Step S301, firstly, a database is established for the characteristic peaks to be identified. The characteristic energy of each characteristic peak is queried by the nuclide information, and the standard deviation is calculated by the energy calibration coefficient, specifically: In the formula, σ m is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, resolution 661keV The energy resolution of the detector system to measure the 661keV characteristic gamma ray; Step S302, establishing a recognition pipeline for each characteristic peak in each characteristic peak database, each pipeline working in an independent thread; In step S302, the specific workflow is: Step S3021, setting a corresponding characteristic peak energy interval of interest according to the database, and filtering the collected data to obtain radiation particle events within the interval of interest; Step S3022, initializing model parameters, including characteristic peak parameters, parameter prior distribution and recognition threshold; Step S3023, updating the model posterior parameters based on the measurement data; Step S3024, determining whether a characteristic peak exists based on a recognition threshold.

2. A Bayesian characteristic peak identification method for gamma spectrum data according to claim 1, characterized in that: In step S1, The specific calculation process is: Step S101, defining the characteristic peaks to be identified as a set of peaks; the set of peaks is shown in the following formula: peaks={[e m ,σ m ]},m=1,...,M In the formula, e m is the attribute value characteristic energy, σ m is the standard deviation, m represents the sequence number of the characteristic peak in the set, and M is the number of information of the characteristic peak; Step S102, defining the particle event sequence recorded by the gamma radiation detector as a set Events, and the set Events is shown in the following formula: Events={[e(i),t(i)]},i=1,...,N Where N is the number of particle events, e(i) is the energy of the measured particle event, t(i) is the arrival time, and i is the particle event number; Step S103: for the mth characteristic peak, specify an energy interval of interest, and define the set of particle events in the energy interval as Events m ; Particle event collection Events m As shown below: Events m ={[e m (i),t m (i),i=1,...,N m ]} e m -kσ m ≤e m (i)≤e m +kσ m ,i=1,...,N m Where N m represents the number of particle events included, and k is the confidence coefficient; Step S104, defining the energy probability distribution of the photoelectric event as Specifically: In the formula, Ψ(e|e m , σ m , e m -kσ m , e m +kσ m ) indicates that the support is [e m -kσ m ,e m +kσ m ], with mean em and standard deviation σ m The probability density value of the truncated Gaussian distribution at e, Φ(e m -kσ m |e m ,σ m ) is a Gaussian distribution in e m -kσ m The cumulative distribution function value at .

3. A Bayesian characteristic peak identification method for gamma spectrum data according to claim 1, characterized in that: In step S1, The specific calculation process is: Step S105: Distribute the energy Use linear function expression, specifically: In the formula, a m and b m are the slope and intercept of the linear function respectively; Step S106, performing algebraic operations on the formula of step S105 to obtain a m and b m The conversion relationship is as follows: In the formula, a m With b m are the slope and intercept, kσ m is the half-width of the energy interval of interest, where σ m is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient; Step S107, the conversion relationship calculated in step S106 is then substituted into the formula of step S105 to obtain e m -kσ m ≤e≤e m +kσ m Where b m is the intercept, kσ m is the half-width of the energy interval of interest, where σ m is the standard deviation of the Gaussian distribution obeyed by the energy of the mth characteristic peak, and k is the confidence coefficient.

4. The Bayesian characteristic peak identification method for gamma spectrum data according to claim 1, characterized in that: In step S2, the posterior distribution samples of the parameters are obtained by Markov chain-Monte Carlo sampling method, and the mean of all samples is taken as the point estimate of the posterior distribution of the parameters, as follows: w m ~P(w m ),b m ~P(b m ) In the formula, P(w m ) and P(b m ) are the model parameters w m With b m The prior distribution of is the posterior distribution of the model parameters given the observation Eventsm, and is the i-th sample sampled from the posterior distribution of the model. The sampled samples are averaged to obtain the posterior distribution point estimate of the model parameters. and

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