Leakage source iterative reconstruction and uncertainty quantification method, system and device based on space prior and medium

Abstract

The invention relates to a leakage source iterative reconstruction and uncertainty quantification method, system, equipment and medium based on spatial prior, and the method comprises the following steps: carrying out the preliminary screening of leakage source positions based on a Spearman coefficient and a source receptor matrix, and obtaining the distribution of spatial prior information; on the basis of space prior information and a Tikhonov regularization method, the release rate of each prior position and a corresponding simulation-observation error index are calculated, and a source position is estimated; according to the estimated source position, based on L1 norm and total variation non-smooth constraint optimization release rate estimation, obtaining a release rate estimation result of time sequence variation; a Bayesian framework is designed, and uncertainty distribution of source positioning and release rate estimation results is obtained through a Monte Carlo sampling mode. The method can be widely applied to the fields of radioactive pollutant traceability and environmental monitoring.

Description

Technical Field

[0001] The present invention relates to a method, system, device and medium for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior, belonging to the field of radioactive pollutant traceability and environmental monitoring. Background Art

[0002] With the implementation of the global nuclear energy tripling plan, nuclear energy is gradually becoming an important part of the energy structure of each country. However, while nuclear power plants provide abundant energy, the widespread use of radioactive substances also brings environmental and health risks that cannot be ignored. Especially in the face of nuclear accidents or radioactive substance leakage incidents, quickly and accurately determining the leakage source location and release rate of radioactive nuclides in the atmosphere is crucial for timely response, assessing radiation risks and ensuring public safety. The current challenge is that leakage source identification is often limited by sparse observation data and unevenly distributed monitoring networks, which restrict the effective constraints of the reconstruction process and make the traceability identification highly complex and uncertain.

[0003] Currently, the most commonly used constraint method is the constant release constraint, which reduces the solution space dimension by assuming a constant release over time and is widely used in Bayesian reconstruction. However, this assumption does not conform to the actual release scenario and is prone to overfitting of the release total and time. This overfitting error will further be transmitted to the source location estimation, resulting in a large difference between the source location and the true location. To avoid this error, the non-constant release constraint stabilizes the solution process of the time-varying release rate by adding a smoothing constraint (such as the L2 norm) to the release rate characteristics. However, the potential smoothing assumption is difficult to distinguish the true peak release from the oscillation caused by the ill-posedness of the reconstruction, because both of them are non-smooth in time. Therefore, the reconstructed release rate may show unrealistic oscillations, which will also be transmitted to the source location estimation, resulting in source localization errors. Therefore, relying solely on time constraints, whether constant release or non-constant release constraints, it is difficult to effectively exclude incorrect source locations, and it is urgent to introduce additional spatial constraints to achieve robust source reconstruction. Summary of the Invention

[0004] In view of the above problems, the object of the present invention is to provide a method, system, device and medium for iterative reconstruction and uncertainty quantification of leakage sources based on spatial prior, which achieves high-precision reconstruction in various applications. This method uses the Spearman correlation coefficient and the source-receptor relationship to constrain the spatial search range, and iteratively optimizes through a cost function within this range to identify the leakage source location. After determining the source location, an error correction matrix is introduced, and a non-smoothing constraint is used to estimate the time-varying release rate, so as to simultaneously reconstruct the peak release and eliminate unreasonable oscillations. Finally, the above process is integrated into a Bayesian framework to evaluate the uncertainty of the leakage source location and release rate reconstruction, providing more reliable technical support for nuclear accident emergency response.

[0005] To achieve the above object, the present invention adopts the following technical solutions: In the first aspect, the present invention provides a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial prior, including the following steps: Based on the Spearman coefficient and the source-receptor matrix, preliminarily screen the leakage source location to obtain the distribution of spatial prior information; Based on the spatial prior information and the Tikhonov regularization method, calculate the release rate of each prior location and the corresponding simulation-observation error index, and estimate the source location; According to the estimated source location, optimize the release rate estimation based on the L1 norm and the total variation non-smoothing constraint to obtain the time-series change release rate estimation result; Design a Bayesian framework to obtain the uncertainty distribution of the source location and release rate estimation results through Monte Carlo sampling.

[0006] Furthermore, the preliminary screening of the leakage source location based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information includes: Based on the obtained source-receptor matrix set and monitoring data, traverse the possible release periods in the time dimension, and calculate the integral source-receptor sensitivity vector corresponding to each location in the monitoring dimension; Based on the integral source-receptor sensitivity vector, summarize the monitoring proportion with an integral sensitivity value greater than 0, and eliminate the source locations below the non-zero monitoring proportion within the initial source location range; On the remaining candidate source locations, calculate the Spearman correlation coefficient between the integral source-receptor sensitivity vector and the monitoring; Retain the source locations with the highest Spearman coefficient in each release period to form a spatial prior region.

[0007] Furthermore, the calculation of the release rate of each prior location and the corresponding simulation-observation error index based on the spatial prior information and the Tikhonov regularization method, and the estimation of the source location include: Traverse the spatial prior locations and extract the source-receptor matrix and update the extracted source-receptor matrix with a matrix scaling factor; Based on the updated source-receptor matrix automatically select a regularization parameter using a cross-validation method and iteratively estimate the release rate corresponding to each source location using the LBFGS algorithm; Search for the source location with the optimal simulation-observation error metric based on the release rate as the source localization result.

[0008] Furthermore, the step of automatically selecting a regularization parameter using a cross-validation method based on the updated source-receptor matrix and iteratively estimating the release rate corresponding to each source location using the LBFGS algorithm includes: Based on the updated source-receptor matrix automatically select a regularization parameter using a cross-validation method ; Based on the selected regularization parameter optimize the L2 regularization cost function using the LBFGS algorithm; Update the release rate according to the gradient information until the iteration termination condition is reached to obtain the optimal release rate corresponding to the source location ;

[0009] Furthermore, the step of automatically selecting a regularization parameter using a cross-validation method based on the updated source-receptor matrix includes: Set the range of the regularization parameter to ; For each candidate regularization parameter divide the source-receptor matrix and the monitoring into 5 subsets, iterate 5 times, and use 4 of the subsets for training in each iteration, with the remaining one subset for validation, and calculate the average cross-validation error of the model; After calculating the average cross-validation error of all candidate regularization parameters select the value that minimizes the average cross-validation error as the final regularization parameter.

[0010] Furthermore, the step of optimizing the release rate estimation based on the L1 norm and total variation non-smoothing constraints according to the estimated source location to obtain the release rate estimation result with temporal variation includes: Extract the corresponding source-receptor matrix according to the source localization result ; ​, and based on the release rate estimated by L2 regularization correct the extracted source-receptor matrix ; Construct a cost function with sparsity and piecewise constant constraints, introduce a simulation-observation error correction matrix, and optimize the release rate.

[0011] Furthermore, design the Bayesian framework, and obtain the uncertainty distributions of the source localization and release rate estimation results through Monte Carlo sampling, including: Incorporate the spatial prior information into the prior distribution, and continuousize the spatial discrete distribution into a probability distribution; Convert the source localization iterative process into Bayesian sampling, and incorporate the simulation-observation error calculation into the likelihood function; Obtain the uncertainty distributions of the source localization and release rate estimation results through Monte Carlo sampling.

[0012] In a second aspect, the present invention provides a leakage source iterative reconstruction and uncertainty quantification system based on spatial prior, including: A spatial prior construction module, configured to preliminarily screen the leakage source position based on the Spearman coefficient and the source-receptor matrix, and obtain the distribution of the spatial prior information; A source localization module, configured to calculate the release rate and the corresponding simulation-observation error index of each prior position based on the spatial prior information and the Tikhonov regularization method, and estimate the source position; A release rate estimation module, configured to optimize the release rate estimation based on the L1 norm and the total variation (TV) non-smoothing constraint according to the estimated source position, and obtain the release rate estimation result with time series variation; An uncertainty quantification module, configured to design a Bayesian framework, and obtain the uncertainty distributions of the source localization and release rate estimation results through Monte Carlo sampling.

[0013] In a third aspect, the present invention provides a computer-readable storage medium storing one or more programs, where the one or more programs include instructions, and when the instructions are executed by a computing device, the computing device is caused to execute any method.

[0014] In a fourth aspect, the present invention provides a computing device, including: one or more processors and a memory, where the memory stores one or more programs and is configured to be executed by the one or more processors, and the one or more programs include instructions for executing any method.

[0015] Due to the above technical solutions, the present invention has the following advantages: The present invention can obtain the reconstruction results of the source location and time-varying release rate with confidence intervals by using sparse monitoring sample information and data-driven spatial prior information. Compared with the traditional constant release constraint method and non-constant release constraint method, the present invention can better solve the following technical problems: 1. Problem of scarce spatial constraints: Traditional leakage source reconstruction methods only rely on time constraints and cannot provide effective spatial constraints, resulting in false source location estimation results. The present invention preliminarily screens the leakage source location based on the Spearman coefficient and the source-receptor matrix to provide a spatial distribution with position-directive information; 2. Problem of missing release timing information: Traditional reconstruction methods based on constant release constraints can only obtain the estimation results of the release time and the total release amount and cannot provide detailed timing release conditions. Traditional reconstruction methods based on non-constant release constraints, due to the use of smooth timing constraints, can only obtain release rate estimation results containing false oscillations. The present invention does not rely on constant release constraints and provides a release timing estimation result with complete and true release timing information through non-smooth timing constraints and model correction methods; 3. Problem of uncertainty quantification: Traditional reconstruction methods based on constant release constraints obtain overfitted release time and total release amount estimation results, often with a very high uncertainty range. Traditional reconstruction methods based on non-constant release constraints can only obtain point estimation results of the release rate and lack uncertainty quantification results. The present invention can provide stable and reliable uncertainty quantification results for the source location and release timing.

[0016] Therefore, the present invention can be widely applied to the fields of radioactive pollutant tracing and environmental monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference numerals are used to represent the same components. In the drawings: Figure 1 is a flowchart of the iterative reconstruction and uncertainty quantification method for leakage sources based on spatial prior provided in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention fall within the scope of protection of the present invention.

[0019] It should be noted that the terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly dictates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of the stated features, steps, operations, devices, components, and / or combinations thereof.

[0020] Current leakage source reconstruction methods generally include the constant release constraint method and the non-constant release constraint method. The constant release constraint method simplifies the source parameters to the source location, release start and end times, and release total amount by imposing unrealistic assumptions on the release characteristics, ignoring the time-varying characteristics of the release in the real leakage scenario, resulting in overfitting of the release total amount and start and end times, and thus causing source localization errors, and there may be an obvious multi-peak phenomenon in the posterior distribution of Bayesian estimation. The non-constant release constraint imposes a smoothing constraint on the release characteristics through regularization to stabilize the solution of the time-varying release rate, but it is prone to cause unreasonable oscillations of the release rate, resulting in source localization errors. Therefore, the existing methods only rely on time constraints and lack spatial constraints, making it difficult to exclude false source locations, provide true and reliable continuous release characteristic information, and increasing the uncertainty of accident consequence assessment.

[0021] In some embodiments of the present invention, a method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior is provided. It preliminarily screens the leakage source location based on the Spearman coefficient and the source-receptor matrix to provide a distribution with spatial prior information; based on the spatial prior information and the Tikhonov regularization method, calculates the release rate at each prior location and the corresponding simulation-observation error index, and estimates the source location; according to the estimated source location, further optimizes the release rate estimation based on the L1 norm and the total variation (TV) non-smoothing constraint to obtain the time-varying release rate estimation result; introduces a Bayesian framework, makes the spatial prior information into a prior distribution, transforms the source localization iterative process into Bayesian sampling, and incorporates the simulation-observation error calculation into the likelihood function to obtain the uncertainty distribution of the source localization and release rate estimation results. Since the present invention introduces spatial constraints on the basis of non-constant release constraints, effectively eliminates false source locations, and then can accurately estimate the source location and the corresponding time-varying release rate through the iterative manner of the cost function, and can quantify the uncertainty of the time-varying source parameter estimation under the Bayesian framework.

[0022] Correspondingly, in some other embodiments of the present invention, a system, device and medium for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior are provided.

[0023] Embodiment 1 As Figure 1 shown, the present invention provides a method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior, which includes the following steps: 1) Construct spatial prior: preliminarily screen the leakage source location based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information; 2) Source localization: based on the spatial prior information and the Tikhonov regularization method, calculate the release rate at each prior location and the corresponding simulation-observation error index, and estimate the source location; 3) Release rate estimation: according to the estimated source location, optimize the release rate estimation based on the L1 norm and the total variation (TV) non-smoothing constraint to obtain the time-varying release rate estimation result; 4) Uncertainty quantification: design a Bayesian framework to obtain the uncertainty distribution of the source localization and release rate estimation results through Monte Carlo sampling.

[0024] Further, in the above step 1), it includes the following steps: 1.1) Based on the obtained input data, traverse the possible release time periods in the time dimension and calculate the integral source-receptor sensitivity vectors corresponding to each location in the monitoring dimension.

[0025] In this embodiment, the obtained input data includes a set of source-receptor matrices and monitoring , where is the number of time steps for the considered release rate, is x the number of grid cells in the is y the number of grid cells in the direction; the source-receptor matrix set is obtained by running the inverse mode of the atmospheric dispersion simulation multiple times, and the number of runs is equal to the number of monitors .

[0026] The calculation method of the integrated source-receptor sensitivity vector corresponding to each position is as follows: (1) In the formula, represents the integrated source-receptor sensitivity vector, ; represents the possible release time period, which can be set according to the earliest sampling start and latest sampling end times of all available non-zero monitors, for example; is the position coordinate. That is, integration is performed in the first time dimension to obtain the integrated source-receptor sensitivity corresponding to each monitor, reflecting the average sensitivity of the source and receptor within the considered time period.

[0027] 1.2) Based on the integrated source-receptor sensitivity vector, summarize the proportion of monitors with an integrated sensitivity value greater than 0, and exclude source positions within the initial source position range that are lower than the proportion of non-zero monitors.

[0028] In this embodiment, the source positions are initially screened using the physical meaning of the source-receptor sensitivity relationship. For the true source positions, the integrated source-receptor sensitivity values corresponding to non-zero monitors must be greater than 0. We relax this restriction and screen the source positions by comparing the proportion of monitors with an integrated sensitivity value greater than 0 with the proportion of non-zero monitors. Among them, the initial source position range can be determined according to conventional experience. For example, if a radioactive leak occurs in Europe, directly set the longitude and latitude range of Europe. If it is completely unclear where it occurred, directly set it to: longitude: 180°W to 180°E; latitude: 90°S to 90°N; The present invention does not elaborate on this.

[0029] 1.3) On the remaining candidate source positions, calculate the Spearman correlation coefficient between the integrated source-receptor sensitivity vector and the monitors.

[0030] In this embodiment, the integrated source-receptor sensitivity vector and the monitor The Spearman correlation coefficient between them is calculated as follows: (2) In the formula, Represents the arithmetic mean over all elements; and respectively represent the vectors composed of the rankings of each element in the monitoring and the vectors composed of the rankings of each element in Represents the proportion of non - zero monitoring. To avoid excessive elimination, this proportion is multiplied by a scaling factor of 0.7.

[0031] 1.4) Retain the source positions with the highest Spearman coefficient in each release period , which constitute the spatial prior region.

[0032] In this embodiment, the spatial prior region is a discontinuous region , which includes the source positions with the highest Spearman coefficient in each release period, expressed as: (3) In the formula, represents the Spearman coefficient calculated for the source position at the release period , represents the spatial calculation domain.

[0033] This embodiment preliminarily screens the leakage source positions based on the Spearman coefficient and the source - receptor matrix, not only providing reliable spatial constraints, but also greatly reducing the space for solving the source position and accelerating the calculation speed of subsequent iterative reconstruction.

[0034] Furthermore, in step 2) above, it includes the following steps: 2.1) Traverse the spatial prior positions, extract the source - receptor matrix , and update the extracted source - receptor matrix through a matrix scaling factor.

[0035] Specifically, it includes the following steps: ① Traverse the spatial prior positions and use the least - squares method to solve the solution between the source - receptor matrix and the monitoring , that is, solve the following equation: (4) In the formula, represents the error vector.

[0036] ② Calculate the matrix scaling factor according to the obtained least - squares solution and update the extracted source - receptor matrix .

[0037] Among them, the least - squares solution is expressed as: (5) Take the largest element in the vector as the matrix scaling factor of the source-receptor matrix to obtain the new source-receptor matrix as follows: (6) 2.2) Based on the updated source-receptor matrix , automatically select the regularization parameter using the cross-validation method, and use the LBFGS algorithm to iteratively estimate the release rate corresponding to each source position.

[0038] Specifically, it includes the following steps: ① Based on the updated source-receptor matrix , automatically select the regularization parameter using the cross-validation method.

[0039] In this embodiment, the method for automatically selecting the regularization parameter using cross-validation is as follows: First, set the range of the regularization parameter to ; Second, for each candidate regularization parameter , divide the source-receptor matrix and the monitoring into 5 subsets, iterate 5 times, and use 4 of the subsets for training each time, and the remaining one subset for validation, and calculate the average cross-validation error of the model; Finally, after calculating the average cross-validation errors of all candidate regularization parameters , select the value that minimizes the average cross-validation error as the final regularization parameter.

[0040] ② Based on the selected regularization parameter , use the LBFGS algorithm to optimize the L2-regularized cost function.

[0041] In this embodiment, the L2-regularized cost function is used as the error cost function between simulation and observation, which consists of two terms. The first term is the squared error term between simulation and observation, and the second term is the L2-regularization term, that is, the two-norm of the release rate vector, that is: (7) In the formula, represents the release rate vector corresponding to the source position .

[0042] Initialize the release rate as a vector of all 1s, and the gradient of the cost function is: (8) ③ Update the release rate according to the gradient information , until the iteration termination condition is reached, the corresponding source position is obtained The optimal release rate .

[0043] 2.3) Search for the source location with the best simulation-observation error index based on the release rate as the source location result .

[0044] In this embodiment, the simulation-observation error index is designed to be , starting from a random grid in the spatial prior area, moving with the minimum spatial resolution as the step size until the simulation-observation error index converges to the minimum value, and the corresponding source position is the positioning result.

[0045] The source localization of this embodiment can provide a stable and accurate release rate estimation, facilitates the distinction between different source locations, and uses a reliable simulation-observation error indicator for evaluation, which is suitable for source localization in various leakage scenarios, especially under sparse monitoring conditions.

[0046] Furthermore, the above step 3) includes the following steps: 3.1) Based on the source positioning results Extract the corresponding source receptor matrix , and the release rate estimated based on L2 regularization Extracted source receptor matrix Make corrections.

[0047] The correction formula is expressed as: (9) 3.2) Construct a cost function with sparsity and piecewise constant constraints, introduce the simulation-observation error correction matrix, and further optimize the release rate solution: (10) . (11) In the formula, is the simulation-observation error correction matrix, which is a diagonal matrix with the initial values ​​of the diagonal elements set to ; is the weight parameter used to balance the error term and the constraint term; is the sparsity constraint of the release rate, is the piecewise constant constraint of the release rate. During the iteration, and , until the two converge.

[0048] The release rate estimation of this embodiment can provide very complete release timing details, which is helpful for conducting reliable nuclear accident consequence assessment.

[0049] Furthermore, in step 4) above, uncertainty quantification can more comprehensively evaluate the reliability of time-varying release source parameters, providing a more solid foundation for decision-making in complex leakage source scenarios.

[0050] Specifically, it includes the following steps: 4.1) Incorporate spatial prior information into the prior distribution to convert the discrete spatial distribution into a probability distribution.

[0051] In this embodiment, the discrete spatial prior region is probabilistically transformed into a prior probability density function by kernel density estimation: (12) In the formula, is the weight at position in space, N is the number of grids in space. According to the previously obtained spatial prior distribution, the weights within the spatial prior region are set to , and the weights outside the region are set to 0.

[0052] 4.2) Convert the source localization iteration process into Bayesian sampling and incorporate the simulation-observation error calculation into the likelihood function.

[0053] During the Bayesian sampling process, the sampling source location is obtained by interpolating the source-receptor matrix. Then the release rate is obtained by monitoring inversion: (13) The likelihood function adopts log Gaussian likelihood, that is: (14) In the formula, is the covariance parameter, is a very small amount used to avoid failure in zero-value logarithm calculation. These two parameters participate in the sampling together with the unknown parameters and the source location; K is the number of monitors. Sampling is performed based on the Markov chain Monte Carlo method, with the number of sampling times set to 5000 times and a total of 5 Markov chains. The first 2500 times of each chain are used as the annealing stage, and the source location sampling results of the last 2500 times are used as the posterior estimate, and the release rates corresponding to these locations are used as the posterior release rates.

[0054] 4.3) Obtain the uncertainty distribution of the source localization and release rate estimation results through Monte Carlo sampling.

[0055] In summary, a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial prior provided by the present invention has the following advantages: (1) Provide effective spatial prior constraints The present invention realizes the preliminary screening of the leakage source location through the Spearman correlation coefficient and the source-receptor sensitivity, and can provide effective prior information on the spatial source location in both the site experiments with rich monitoring data and the real events with sparse and unevenly spatially distributed monitoring data, thereby greatly reducing the computational search space and accelerating the reconstruction process, and being applicable to the rapid response in emergency scenarios.

[0056] (2) Provide accurate source location results The present invention combines the spatial prior information with the Tikhonov regularization method, estimates the scaling factor of the source-receptor matrix by using the least squares method, ensures the stability of the release rate magnitude, and thus realizes the accurate estimation of the release rate at each prior location. By means of the simulation-observation difference index to evaluate the probability of each prior location, the estimation accuracy of the leakage source location and the release rate is significantly improved. The positioning result error in the site experiment is less than one grid accuracy, and the positioning error in the real events under different monitoring conditions is reduced by more than 75% compared with the traditional method, which is suitable for source location in complex leakage scenarios.

[0057] (3) Provide the complete time series information of the time-varying release The present invention adopts the L1 norm and the total variation (TV) non-smoothing constraint to further optimize the release rate, enabling it to capture the peak release while suppressing unreasonable oscillations, improving the estimation accuracy and stability of the release rate in non-constant release scenarios, and having a high degree of agreement with the real or reported release rate in terms of the release time series variation (the size and time of the release peak) and the total release amount, which is helpful for a more reliable consequence assessment.

[0058] (4) Provide the uncertainty quantification of the time-varying release The present invention realizes the statistical analysis of the uncertainty of the source location and the time-varying release rate estimation by converting the spatial prior information into a prior probability distribution, converting the source location iteration process into a Bayesian sampling problem, and converting the evaluation of the simulation-observation error into the calculation of the likelihood function. This method can effectively evaluate the reliability of the estimation results and provides strong support for the uncertainty analysis of the leakage source in complex scenarios.

[0059] Example 2 The above-mentioned Embodiment 1 provides a method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior. Correspondingly, this embodiment provides a system for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior. The system provided in this embodiment can implement the method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior in Embodiment 1, and this system can be implemented in a software, hardware, or a combination of software and hardware manner. For example, this system may include integrated or separate functional modules or functional units to execute the corresponding steps in the methods of Embodiment 1. Since the system in this embodiment is basically similar to the method embodiment, the description process in this embodiment is relatively simple, and the relevant parts can refer to the partial description of Embodiment 1. The embodiments of the system provided in this embodiment are merely illustrative.

[0060] The system for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior provided in this embodiment includes: A spatial prior construction module, configured to preliminarily screen the leakage source positions based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information; A source localization module, configured to calculate the release rate of each prior position and the corresponding simulation-observation error index based on the spatial prior information and the Tikhonov regularization method, and estimate the source position; A release rate estimation module, configured to optimize the release rate estimation based on the L1 norm and the total variation (TV) non-smoothing constraint according to the estimated source position to obtain the time-varying release rate estimation result; An uncertainty quantification module, configured to design a Bayesian framework and obtain the uncertainty distribution of the source localization and release rate estimation results by means of Monte Carlo sampling.

[0061] Embodiment 3 This embodiment provides a processing device corresponding to the method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior provided in Embodiment 1. The processing device may be a processing device for a client, such as a mobile phone, a laptop computer, a tablet computer, a desktop computer, etc., to execute the method of Embodiment 1.

[0062] The processing device includes a processor, a memory, a communication interface, and a bus. The processor, the memory, and the communication interface are connected through the bus to complete communication with each other. The memory stores a computer program that can run on the processor, and when the processor runs the computer program, it executes the method for iterative reconstruction and uncertainty quantification of a leakage source based on spatial prior provided in Embodiment 1.

[0063] Preferably, the memory may be a high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one magnetic disk memory.

[0064] Preferably, the processor may be various types of general-purpose processors such as a central processing unit (CPU) or a digital signal processor (DSP), which is not limited herein.

[0065] Embodiment 4 The method for iterative reconstruction of leakage source and uncertainty quantification based on spatial prior in Embodiment 1 of the present invention can be specifically implemented as a computer program product. The computer program product may include a computer-readable storage medium, on which computer-readable program instructions for executing the method for iterative reconstruction of leakage source and uncertainty quantification based on spatial prior described in Embodiment 1 of the present invention are uploaded.

[0066] The computer-readable storage medium may be a tangible device that holds and stores instructions used by an instruction execution device. The computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination of the above.

[0067] Those skilled in the art should understand that the embodiments of the present invention may be provided as a method, a system, or a computer program product. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program code. The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks. These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to work in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one or more of the processes and / or blocks Figure 1 in one or more of the processes and / or blocks Figure 1 specified in the function. These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the processes and / or blocks Figure 1 in one or more of the processes and / or blocks Figure 1 specified in the function.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific embodiments of the present invention. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors, characterized in that: The following steps are involved: The location of the leakage source is preliminarily screened based on the Spearman coefficient and source receptor matrix to obtain the distribution of spatial prior information; Based on spatial prior information and Tikhonov regularization method, the release rate and corresponding simulation-observation error index of each prior position are calculated, and the source position is estimated; According to the estimated source position, the release rate estimation is optimized based on the L1 norm and total variation non-smooth constraint to obtain the release rate estimation result with time series variation; A Bayesian framework is designed to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.

2. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 1, characterized in that: The leak source location is preliminarily screened based on the Spearman coefficient and the source receptor matrix to obtain the distribution of spatial prior information, including: Based on the acquired source receptor matrix set and monitoring data, possible release periods are traversed in the time dimension, and the integrated source receptor sensitivity vector corresponding to each position is calculated in the monitoring dimension; Based on the integrated source receptor sensitivity vector, the monitoring proportions with integrated sensitivity values ​​greater than 0 are summarized, and source locations with monitoring proportions below non-zero are eliminated within the initial source location range; At the remaining candidate source locations, the Spearman correlation coefficient between the integrated source receptor sensitivity vector and the monitoring is calculated; The source position with the highest Spearman coefficient in each release period is retained to form the spatial prior region.

3. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 1, characterized in that: The method based on spatial prior information and Tikhonov regularization calculates the release rate of each prior position and the corresponding simulation-observation error index, and estimates the source position, including: Traverse the spatial prior positions and extract the source receptor matrix , and update the extracted source receptor matrix by the matrix scaling factor; Based on the updated source receptor matrix , using cross-validation to automatically select the regularization parameter , and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source position; The source position with the best simulation-observation error index is searched based on the release rate as the source localization result.

4. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 3, characterized in that: The updated source receptor matrix , using cross-validation to automatically select the regularization parameter , and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source position, including: Based on the updated source receptor matrix , using cross-validation to automatically select the regularization parameter ; Based on the choice of regularization parameter , the LBFGS algorithm is used to optimize the L2 regularization cost function; Update the release rate based on the gradient information , until the iteration termination condition is reached, the corresponding source position is obtained The optimal release rate .

5. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 4, characterized in that: The updated source receptor matrix , using cross-validation to automatically select the regularization parameter ,include: Set the regularization parameter range to ; For each candidate regularization parameter , the source receptor matrix and monitoring Divide into 5 subsets, iterate 5 times, use 4 subsets for training in each iteration, and use the remaining subset for validation, and calculate the average cross-validation error of the model; After calculating all candidate regularization parameters After the average cross-validation error of The value is used as the final regularization parameter.

6. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 1, characterized in that: The release rate estimation is obtained based on the estimated source position and the L1 norm and the total variation non-smooth constraint optimization to obtain the release rate estimation result of the time series change, including: According to the source positioning results Extract the corresponding source receptor matrix , and the release rate estimated based on L2 regularization Extracted source receptor matrix Make corrections; A cost function with sparsity and piecewise constant constraints is constructed, and a simulation-observation error correction matrix is ​​introduced to optimize the release rate.

7. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 1, characterized in that: The Bayesian framework is designed to obtain the uncertainty distribution of the source location and release rate estimation results through Monte Carlo sampling, including: Integrate spatial prior information into prior distribution and convert spatial discrete distribution into probability distribution; The iterative process of source localization is transformed into Bayesian sampling, and the simulation-observation error calculation is incorporated into the likelihood function; The uncertainty distribution of source location and release rate estimation results is obtained through Monte Carlo sampling.

8. A leakage source iterative reconstruction and uncertainty quantification system based on spatial priors, characterized in that: include: The spatial prior construction module is used to preliminarily screen the leakage source locations based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information; The source localization module is used to calculate the release rate of each prior position and the corresponding simulation-observation error index based on spatial prior information and Tikhonov regularization method, and estimate the source position; The release rate estimation module is used to optimize the release rate estimation based on the estimated source position and the L1 norm and the total variation (TV) non-smooth constraint to obtain the release rate estimation result with time series variation; The uncertainty quantification module is used to design a Bayesian framework to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions, which, when executed by a computing device, cause the computing device to perform any one of the methods of claims 1 to 7.

10. A computing device, characterized in that include: One or more processors and a memory, wherein the memory stores one or more programs and is configured to be executed by the one or more processors, wherein the one or more programs include instructions for executing any one of the methods described in claims 1 to 7.

Images