Joint adaptive parallel annealing source item inversion method for determining nuclear radioactive source
By combining the adaptive parallel annealing method and the enhanced MCMC method, the algorithm convergence difficulty and timeliness issues in the inversion of large-scale unknown location source terms were solved, achieving rapid and accurate localization of nuclear radioactive sources and meeting the needs of nuclear accident emergency response.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA INST FOR RADIATION PROTECTION
- Filing Date
- 2025-12-26
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies suffer from problems such as difficulty in algorithm convergence, complexity in parameter adjustment, difficulty in user operation, and insufficient timeliness in large-scale source term inversion at unknown locations. In particular, they are difficult to quickly and accurately determine nuclear radioactive source information in nuclear accident emergency response.
A joint adaptive parallel annealing method is adopted, combined with the enhanced Markov chain Monte Carlo method (MCMC), and an adaptive inversion model is established through adaptive jump function and parallel annealing algorithm. The diffusion process is reverse-calculated using meteorological data to generate the SRS matrix, thereby quickly and accurately inverting nuclear radioactive source information.
It improves the accuracy and timeliness of large-scale source term inversion at unknown locations, reduces the warm-up period of the sampling process, ensures the effectiveness and consistency of sampling, achieves rapid and accurate nuclear radioactive source localization, and meets the timeliness requirements of nuclear accident emergency response.
Smart Images
Figure CN122019953A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of nuclear accident source term inversion technology, and in particular to a joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources. Background Technology
[0002] Since the 1980s, several nuclear accidents have occurred, raising widespread public concern about the environmental and health problems caused by the atmospheric release of radioactive isotopes. In recent years, several events involving detected anomalous radioactive isotopes have prompted extensive research into the inversion of large-scale, long-distance source terms at unknown locations.
[0003] On the other hand, large-scale inversion methods are needed to estimate the location and amount of radioactive aerosol release to identify potential nuclear tests and threats. While nuclear explosions can be monitored using infrasound, underwater acoustics, and electromagnetic pulses, atmospheric pollutant diffusion inversion is the only effective means to determine the amount of nuclides released.
[0004] Therefore, it is very important to develop techniques for inverting and estimating unknown release source terms based on mesoscale and large-scale data from monitoring stations. These techniques can provide rapid and effective source estimation for large-scale releases of radionuclides caused by accidental releases from nuclear power plants, isotope production plants, and other events. This will enable faster consequence assessment and emergency response plans, which will help protect the lives and property of people living near nuclear accidents.
[0005] Since the detection of anomalous isotopes I-131 in 2011 and Ru-106 in 2017, several countries have conducted research on source term inversion at unknown locations. For example, Tichy et al. proposed a method that performs least-squares calculations at all possible release locations and determines the possible release locations by judging the results of the loss function on each grid. Saunier et al. proposed a method that uses a finite-memory quasi-Newton method solver to calculate the loss function and compares the performance of the integral FAC2 parameter results at different release locations to jointly determine the possible release locations. However, these methods struggle to provide the probability distribution of the inversion results and require traversing the entire discretized solution space. Therefore, in recent years, scholars have focused more on inversion methods based on Bayesian probabilistic models. For example, Dumont et al. used the Metropolis-Hasting (MH) algorithm based on Markov chain Monte Carlo to invert the release location of Ru-106 in 2017, while De Meutter et al. used a multi-chain Markov chain Monte Carlo method to invert the event. To increase the robustness of the model, they used numerical weather prediction ensembles and atmospheric diffusion model ensembles for the inversion study. Although these studies can provide the probability density distribution of the model inversion results, they involve a large number of parameter settings, which need to be adjusted for different cases, making them difficult for users to implement easily.
[0006] There is very little domestic work on source term inversion at unknown locations, and most of the research focuses on small-scale studies. The applicable scenarios are often near the factory area or under ideal simulation experimental conditions at a small scale. The methods used are relatively simple, but they also face the problem that many parameters need to be adjusted according to different cases, which makes it difficult for users to operate.
[0007] Currently, the MCMC (Markov Chain Monte Carlo) method has been widely applied and achieved significant results in the field of large-scale source term inversion at unknown locations. However, existing techniques still present several challenges in practical applications. For example, the selection of the jump function must be suitable for the posterior probability density function of the accident model itself to achieve effective sampling convergence. This requires considerable experience from the designer, ensuring the model can escape local optima to find the global optimum and accurately describe the distribution of local probability density functions. Furthermore, achieving rapid convergence of MCMC in high-dimensional solution spaces to meet emergency response requirements is also a major challenge of this algorithm.
[0008] Both single adaptive jump functions and general parallel multi-chain MCMC have been applied to Bayesian inversion problems. However, both have certain problems. For a single adaptive jump function, although it can solve the problem of jump function design, it generally suffers from ill-conditioned phenomena, does not strictly satisfy the Markov property, cannot achieve the optimal acceptance rate, and may cause bias and inconsistent estimation, requiring consideration of sampling effectiveness. While general multi-chain parallel MCMC methods can effectively increase global search capability, they are still prone to getting trapped in local optima because they do not change the properties of the sampling function. Summary of the Invention
[0009] The purpose of this invention is to address the shortcomings of existing technologies by providing a joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources.
[0010] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources, characterized by comprising the following steps: Obtain measured values of nuclear contaminant concentrations and meteorological data at each monitoring site; The SRS matrix is established by using the adjoint method to calculate the diffusion process in reverse using the meteorological data; An adaptive inversion model is established, including modeling the posterior probability density function of the source term parameters and determining the sampling method. The sampling method adopts the enhanced MCMC method, which combines the MCMC method with a joint adaptive jump function and a parallel annealing algorithm. The joint adaptive jump function is a weighted set including the AM algorithm, the SCAM algorithm, and the DE algorithm. The SRS matrix and the measured values of pollutant concentrations are used as input data for the algorithm and fed into the inversion model for calculation, thereby retrieving and deducing the information of the nuclear radioactive source.
[0011] Furthermore, the posterior probability density function of the source term parameters is modeled using a Bayesian method, namely: ,in For prior functions, Let be the likelihood function. Let be the posterior probability density function.
[0012] Furthermore, the prior function adopts a uniform prior, and the likelihood function adopts a log-Gaussian likelihood function, i.e. Where y is the monitoring vector, x is the source vector, H is the transformation matrix, and yt and cref are hyperparameters. , .
[0013] Furthermore, in the joint adaptive jump function, the weight relationship of the AM algorithm, SCAM algorithm, and DE algorithm is as follows: , where w AM w SCAM w DE The weights of the AM, SCAM, and DE algorithms are respectively, P. AM P SCAM P DE The stable acceptance rates are for the AM algorithm, SCAM algorithm, and DE algorithm, respectively.
[0014] Furthermore, the weight ratio of the AM algorithm, SCAM algorithm, and DE algorithm is 2:2:5.
[0015] Furthermore, the parallel annealing algorithm sets up parallel MCMC sampling chains at different temperatures. The high-temperature chain flattens the probability density function, preventing the jump function from getting trapped in local optima. The probability density function at temperature T... ,in This represents the original probability density distribution.
[0016] Furthermore, the parallel annealing algorithm employs eight MCMC sampling chains at different temperatures, seven of which are annealing chains.
[0017] Furthermore, the temperature scheme of the parallel annealing algorithm adopts an exponential scheme, with the geometric spacing set to e and the maximum temperature set to e. 7 .
[0018] Furthermore, the number of sampling steps in the MCMC sampling chain is set to 20,000, and the average value of the sampling results of the last 5,000 steps is taken as the final result obtained by inversion.
[0019] Furthermore, FLEXPART is used for reverse calculation to establish the SRS matrix.
[0020] Compared with existing technologies, the beneficial effects of this invention are: Based on the Markov chain Monte Carlo method, this method establishes a relatively complete method for inverting large-scale unknown location source terms, improving the robustness of the model converging to the global optimum. Simultaneously, it employs an adaptive jump function, thereby efficiently, quickly, and easily obtaining the relevant parameters of large-scale unknown location source terms, significantly reducing the warm-up period of the sampling process, thus accelerating the sampling process and meeting the timeliness requirements of emergency response. The main advantages are: 1. An adaptive method is introduced to achieve better sampling efficiency for complex probability density functions and reduce user design and usage costs. A joint adaptive algorithm uses multiple adaptive algorithms with different weights, solving the dependence on a single historical sampling path in the case of a single algorithm. The diversity of sampling data sources reduces non-Markovianness, ensuring that the sampling acceptance rate always stays near the optimal acceptance rate, guaranteeing the effectiveness and consistency of sampling, i.e., unbiased convergence to the target distribution.
[0021] 2. The parallel annealing method flattens the probability density function on the high-temperature chain, making the local extrema of the function less steep, which is more conducive to breaking through the limitation of local optima. Then, it is transferred to the low-temperature chain through inter-chain transfer to ensure effective exploration of the overall solution space and thus more conducive to finding the global optimum. Attached Figure Description
[0022] Figure 1 This is a flowchart of an embodiment of the present invention.
[0023] Figure 2 This is a flowchart of the inversion calculation process.
[0024] Figure 3 This is a graph showing the relationship between the acceptance rate and the number of iterations for various adaptive jump suggestion algorithms based on 80 runs.
[0025] Figure 4 The regression curves for the average burn-in period (LOWESS) under different temperature schemes are shown.
[0026] Figure 5 This is a probability density distribution diagram of the MCMC sampling points. Detailed Implementation
[0027] To enhance understanding of the present invention, we will now describe it in further detail with reference to the accompanying drawings. These embodiments are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.
[0028] To address the problems and shortcomings of existing large-scale source term inversion methods for unknown locations, this invention proposes a joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources. This method, based on the Markov Chain Monte Carlo (MCMC) method, creatively establishes a Joint Adaptive Jump Function (JATP), improving the sampling efficiency of the algorithm for high-dimensional and complex posterior probability density functions. Simultaneously, a parallel annealing algorithm (PT) is introduced to improve the global search capability for complex functions. The combination of these two methods enables the original MCMC method to quickly and accurately converge to high-dimensional and complex posterior probability density functions, improving the accuracy of the original MCMC source term inversion method and effectively enhancing the timeliness of the inversion.
[0029] like Figure 1As shown, a specific embodiment of a joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources includes the following steps: The first step is to obtain the measured values of nuclear pollutant concentrations and meteorological data at each monitoring site; The second step involves using the adjoint method to calculate the diffusion process of meteorological data and establish the SRS matrix. The third step is to establish an adaptive inversion model, which includes modeling the posterior probability density function of the source term parameters and determining the sampling method. The sampling method adopts the enhanced MCMC method. The enhanced MCMC method adopts the MCMC method and integrates the joint adaptive jump function (JATP) and the parallel annealing algorithm. The joint adaptive jump function is a weighted set including the AM algorithm, SCAM algorithm and DE algorithm. The fourth step involves using the SRS matrix and measured pollutant concentrations as input data for the algorithm, which are then fed into the inversion model for calculation to deduce the information of the nuclear radioactive source.
[0030] Specifically, in the second step, the adjoint method is used to reverse-calculate the diffusion process and generate the source-receptor sensitive matrix (SRS matrix), in order to reduce the computational time of the Markov chain sampling process during the inversion calculation. Traditional inversion methods calculate the diffusion results of candidate source terms and compare them with actual measurements in each optimization iteration, which is time-consuming and laborious. Therefore, the SRS matrix is established here: in Represents the candidate source term vector, This represents the vector of simulated measurements corresponding to the candidate source term, while This represents the SRS matrix, which is essentially a linear mapping relationship. The general calculation method is as follows: in This represents the amount released per unit time at the position (x, y) with coordinates at time t. This represents the simulated value of the i-th detection point. The parameter is the corresponding position in the SRS matrix.
[0031] After obtaining the SRS matrix, the corresponding parameters of the SRS matrix only need to be interpolated according to the position and time of the candidate source items to quickly calculate the simulated measurement values. However, this method leads to problems such as large computational load and low computational efficiency when applied to large-scale applications because the number of candidate grid points is extremely large.
[0032] To address this issue, this invention employs an adjoint approach, utilizing the inverse calculation method of pollutant diffusion models in the Flexpart open-source software to establish the mapping relationship of the SRS matrix. This involves performing a reverse simulation starting from the detection point, thus requiring only a number of simulations equal to the number of measurements used for the inversion calculation to complete the SRS simulation. This method significantly reduces matrix computation time, ensuring the timeliness of the entire inversion process.
[0033] The third step specifically includes: I. Modeling the posterior probability density function of the source term parameters using Bayesian methods.
[0034] Inversion is based on Bayes' principle, namely: The main technical challenge lies in defining the prior function. and likelihood function These two factors determine the probability density function of the source term vector.
[0035] In this invention, the prior probability density function is defined as a uniform prior, while the likelihood function is defined as a log-Gaussian function: Where y is the monitoring vector, x is the source vector, and H is the transformation matrix. yt and cref are hyperparameters, and their values are determined as follows: Second, after establishing the probability model, the traditional MCMC method is improved by integrating the joint adaptive jump function and the parallel annealing method to achieve fast sampling convergence.
[0036] First, we introduce a joint adaptive jump function: The Metropolis-Hastings algorithm is generally used in MCMC methods, so the choice of jump function is usually arbitrary. Previous works have mostly used random perturbations or Gaussian perturbations. This method is highly dependent on the user's understanding of the data and the algorithm, and during model convergence, we often need relatively large jump steps in the early stages and a more refined representation of the probability density distribution in the later stages. These requirements cannot be met by traditional methods. Therefore, we selected three adaptive jump function methods: AM (Adaptive Metropolis), SCAM (Single Component Adaptive Jump Proposal), and DE (Differential Evolution-Markov Chain) to increase the robustness of the model.
[0037] These three methods all involve selecting candidate vectors during random sampling in the MCMC method. Most are based on historical sampling paths, which can lead to biased posterior estimates if the jump function adjustment relies too heavily on early samples (e.g., variance estimation is affected by initial values). Therefore, this invention does not employ a single adaptive jump function method, but instead performs random sampling based on weighted probabilities, as follows: in Represents the joint adaptive jump function. , , and , , The AM, SCAM, and DE methods and their corresponding weights are described separately. In practice, random numbers are drawn before each sampling to select the corresponding adaptive method for adaptive sampling. This sampling method avoids the inconsistency caused by the accumulation of historical path errors when using a single algorithm by leveraging the differences between different adaptive algorithms, greatly reducing the dependence on single historical sampling information. This method utilizes the adaptability of the adaptive method in selecting jump candidate vectors while mitigating the consistency bias introduced by non-Markov properties, thus achieving fast convergence.
[0038] Weight selection method: Obtain the stable acceptance rate by adaptively sampling the response type function using a single adaptive method. Then, solve the following equation: Where 0.234 is the theoretically optimal acceptance rate derived mathematically, w AM w SCAM w DE The weights of the AM, SCAM, and DE algorithms are respectively, P. AM P SCAM P DE The stable acceptance rates of the AM, SCAM, and DE algorithms are given respectively. Considering the similarity in principle between the AM and SCAM algorithms, the following assumptions are made: This allows us to obtain the weights corresponding to each algorithm and achieve the optimal sampling acceptance rate.
[0039] Stable acceptance rate of each algorithm Figure 3 As shown, the solid line represents the average acceptance rate for each algorithm, the dashed line represents the optimal acceptance rate of 0.234, and the shaded area represents one standard deviation around the average.
[0040] Then, the parallel annealing algorithm is introduced. The core idea of this algorithm is to set up parallel MCMC chains at different temperatures. The high-temperature chain flattens the probability density function, making the jump function less likely to get trapped in local optima. The probability density function at temperature T is: in Representing the original probability density distribution, this method can effectively expand the search range and reduce the probability of getting trapped in local optima.
[0041] In this invention, eight MCMC sampling chains with different temperatures are selected, seven of which are annealing chains. The temperature scheme is an exponential scheme, and the geometric spacing is e. Therefore, the highest temperature is... The specific selection of hyperparameters for the scheme was derived through extensive experimental comparisons. Figure 4 As shown, where, Figure 4 In (a), the geometric distance is fixed as e. Figure 4 In (b), the maximum number of chains is fixed at 3. Figure 4 (c) The highest temperature is set to .
[0042] According to the above Figure 4 (a) It is clear that when the geometric spacing is fixed, the larger the number of chains, the faster the convergence. Figure 4 The optimal geometric spacing can be obtained from (b) as e, while from Figure 4 As shown in (c), when the maximum temperature is fixed, the convergence speed tends to stabilize after the chain spacing meets certain requirements (n>=4). Therefore, we conclude that once the maximum temperature reaches a certain level, as long as the temperature chain spacing meets certain requirements, the sampling performance tends to stabilize. Thus, we selected the above temperature scheme through comparison.
[0043] In the fourth step, the SRS matrix obtained in the preceding steps and its corresponding measurement data are used as input data for the algorithm and substituted into the joint adaptive parallel annealing MCMC method of this invention for inversion calculation. The specific process is as follows: Figure 2 As shown, 1. Given any undetermined source term 2. Calculate the posterior probability 3. Substitute the joint adaptive parallel annealing (MCMC) method of this invention and jump to the next undetermined source item. 4. Calculate the transition probability to determine whether to accept a new undetermined source term; 5. Repeat steps 1-3 until convergence to the target distribution of the posterior probability of the source term; 6. Extract a sample after convergence (after the warm-up period) and determine the inversion source term based on its statistical distribution.
[0044] The following specific cases will be used to further verify and illustrate this point.
[0045] Taking the European Tracer Experiment as an example, this laboratory conducted an atmospheric tracer experiment jointly organized by several European countries from October to November 1994. Its purpose was to provide benchmark experimental data for evaluating the performance of atmospheric diffusion models. In this invention, the first test of this experiment (ETEX-I public data) is used for verification. The release location was Brittany, France (-2.0083°E, 48.058°N), and 58 monitoring stations were established in 17 countries, obtaining a total of 3104 usable measurement data points. Specific source term information is shown in Table 1: Table 1: ETEX-I Source Item Information
[0046] Step 1: Use FLEXPART to perform reverse calculations and build the SRS matrix. To demonstrate that the present invention still exhibits good inversion performance even in the absence of measurement data, only 40 measurement data points (out of a total of 3104) were randomly selected for inverse calculation, and the corresponding SRS matrix was obtained through conversion relationships. The SRS matrix represents the sensitivity relationship between the monitoring point and any point within the spatiotemporal grid. Therefore, its calculation method involves obtaining the sensitivity relationship between the given monitoring point and any point in the spatiotemporal grid through inverse simulation, constructing a four-dimensional matrix of (m,n,t,d), where m and n are the spatial scales of the discrete grid, t is the temporal scale of the discrete grid, and d corresponds to each detection data point.
[0047] Considering the location of the test release point and measurement point, and taking into account both the accuracy and timeliness of the calculation, the final simulation range is selected as shown in Table 2.
[0048] Table 2: Diffusion Simulation Mesh Settings
[0049] The selected data points are shown in Table 3.
[0050] Table 3: List of randomly selected measurement data
[0051] Step 2: Inversion Calculation The SRS matrix obtained in the previous step and its corresponding measurement data are used as input data for the algorithm, and then fed into the joint adaptive parallel annealing MCMC method of this invention for inversion calculation. The specific process is as follows: Figure 2 .
[0052] Step 1: Given any undetermined source item .
[0053] Step 2: Calculate the posterior probability.
[0054] Step 3: Substitute the Joint Adaptive Parallel Annealing (MCMC) method of this invention, and jump to the next undetermined source item. Furthermore, the transition probability is calculated to determine whether to accept a new undetermined source term.
[0055] Step 4: Repeat steps 1-3 until convergence to the target distribution of the posterior probability of the source terms.
[0056] Step 5: Extract the sampled data after convergence (after the warm-up period) and determine the inversion source terms based on its statistical distribution.
[0057] The inversion calculation used eight Markov chains at different temperatures, with the highest chain temperature being... The weight ratio of the three adaptive algorithms is SCAM:AM:DE = 2:2:5.
[0058] Throughout the inversion process, the Markov chain was set to a sampling step count of 20,000. To make the sampling distribution more statistically representative, convergence was actually achieved after 5,000 steps. The average of the sampling results from the last 5,000 steps (according to the law of large numbers: the sampling average is approximately equal to the expectation of the posterior function) was taken as the final inversion result. The inversion results are shown in Table 4 below. Figure 5 As shown.
[0059] Table 4: Source term inversion results (average of 2000 samples after MCMC)
[0060] Figure 5 In the diagram, a pentagram indicates the source term release point, green dots represent non-zero measurement points, and yellow dots represent zero measurement points. Figure 5 (a) Sampling from 1000 to 3000 samples Figure 5 (b) 5000-10000 samplings (the source item identifier is displayed transparently because the sampling points are relatively concentrated at this time).
[0061] As can be seen, the inversion results are very close to the actual values. The longitude error is approximately 0.0037°, the latitude error is approximately 0.012°, and the difference between the actual and predicted positions (0.0126°) is much smaller than the grid resolution of 0.25°. The straight-line distance error is approximately 1.38 kilometers. Within the inversion range at a scale of thousands of kilometers, the errors are almost negligible. The relative error of the release rate is 4.6%. The release time is slightly delayed compared to the actual release time, which may be due to the averaging result of a 1-hour grid density, blurring the time information within the 1-hour resolution.
[0062] The above inversion results show that this method can accurately converge to the vicinity of the true source term location, ensuring the consistency of the MCMC method, thus solving the accuracy problem of the inversion. Furthermore, based on... Figure 4 We can also see that this invention greatly improves convergence efficiency, increasing the convergence speed by 3.3 (8150 / 2470) times. It effectively solves the timeliness problem.
[0063] The above specific embodiments are only for illustrating the technical concept and structural features of the present invention, and are intended to enable those skilled in the art to implement them. However, the above content does not limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit and essence of the present invention should fall within the scope of protection of the present invention.
Claims
1. A joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources, characterized in that, Includes the following steps: Obtain measured values of nuclear contaminant concentrations and meteorological data at each monitoring site; The SRS matrix is established by using the adjoint method to calculate the diffusion process in reverse using the meteorological data; An adaptive inversion model is established, including modeling the posterior probability density function of the source term parameters and determining the sampling method. The sampling method adopts the enhanced MCMC method, which combines the MCMC method with a joint adaptive jump function and a parallel annealing algorithm. The joint adaptive jump function is a weighted set including the AM algorithm, the SCAM algorithm, and the DE algorithm. The SRS matrix and the measured values of pollutant concentrations are used as input data for the algorithm and fed into the inversion model for calculation, thereby retrieving and deducing the information of the nuclear radioactive source.
2. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 1, characterized in that: The posterior probability density function of the source term parameters is modeled using a Bayesian method, namely: ,in For prior functions, Let be the likelihood function. Let be the posterior probability density function.
3. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 2, characterized in that: The prior function adopts a uniform prior, and the likelihood function adopts a log-Gaussian likelihood function, i.e. Where y is the monitoring vector, x is the source vector, H is the transformation matrix, and yt and cref are hyperparameters. , .
4. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 1, characterized in that: In the joint adaptive jump function, the weight relationship between the AM algorithm, SCAM algorithm, and DE algorithm is as follows: , where w AM w SCAM w DE The weights of the AM, SCAM, and DE algorithms are respectively, P. AM P SCAM P DE The stable acceptance rates are for the AM algorithm, SCAM algorithm, and DE algorithm, respectively.
5. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 1, characterized in that: The weight ratio of the AM algorithm, SCAM algorithm, and DE algorithm is 2:2:
5.
6. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 1, characterized in that: The parallel annealing algorithm uses parallel MCMC sampling chains at different temperatures. The high-temperature chain flattens the probability density function, preventing the jump function from getting trapped in local optima. The probability density function at temperature T... ,in This represents the original probability density distribution.
7. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 6, characterized in that: The parallel annealing algorithm uses eight MCMC sampling chains at different temperatures, seven of which are annealing chains.
8. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 7, characterized in that: The parallel annealing algorithm employs an exponential temperature scheme, with the geometric spacing set to e and the maximum temperature set to e. 7 .
9. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 8, characterized in that: The sampling steps of the MCMC sampling chain are set to 20,000, and the average of the sampling results of the last 5,000 steps is taken as the final result obtained by inversion.
10. The joint adaptive parallel annealing source term inversion method for determining nuclear radioactive sources according to claim 1, characterized in that: The SRS matrix is constructed by reverse calculation using FLEXPART.