Spatial-prior-based iterative reconstruction and uncertainty quantification method and system for leakage source, and device and medium
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2026-02-04
- Publication Date
- 2026-08-13
Smart Images
Figure CN2026076940_13082026_PF_FP_ABST
Abstract
Description
Methods, systems, devices, and media for iterative reconstruction of leakage sources and uncertainty quantification based on spatial priors.
[0001] Cross-references to related applications
[0002] This application claims priority to Chinese patent application 202510139952.X, filed on February 8, 2025, entitled “Iterative Reconstruction and Uncertainty Quantification Method, System, Device and Medium for Leakage Sources Based on Spatial Priorities,” the entire contents of which are incorporated herein by reference. Technical Field
[0003] This application relates to a method, system, device, and medium for iterative reconstruction of leakage sources and uncertainty quantification based on spatial priors, belonging to the field of radioactive pollutant tracing and environmental monitoring. Background Technology
[0004] With the implementation of the global plan to triple nuclear energy capacity, nuclear energy is gradually becoming an important component of the energy structure of various countries. However, while providing abundant energy, the widespread use of radioactive materials by nuclear power plants also brings significant environmental and health risks. Especially in the face of nuclear accidents or radioactive material leaks, rapidly and accurately determining the location and release rate of radioactive nuclides in the atmosphere is crucial for timely response, radiation risk assessment, and ensuring public safety. The current challenge lies in the fact that leak source identification is often limited by sparse observational data and unevenly distributed monitoring networks. These factors restrict the effective constraints of the reconstruction process, making source identification highly complex and uncertain.
[0005] Currently, the most commonly used constraint method is the constant release constraint. This method reduces the spatial dimension of the solution by assuming constant release over time and is widely used in Bayesian reconstruction. However, this assumption does not conform to the real release scenario and can easily lead to overfitting of the total release amount and time. This overfitting error will further propagate to the source location estimation, resulting in a significant difference between the source location and the true location. To avoid this error, the non-constant release constraint adds a smoothing constraint (such as the L2 norm) to the release rate feature to stabilize the solution process of the time-varying release rate. However, the potential smoothing assumption is difficult to distinguish between the real peak release and the oscillations caused by ill-posed reconstruction, as both are non-smooth over time. Therefore, the reconstructed release rate may exhibit unrealistic oscillations, which will also propagate to the source location estimation, leading to source localization errors. Therefore, relying solely on time constraints, whether constant or non-constant release constraints, is insufficient to effectively eliminate erroneous source locations, and there is an urgent need to introduce additional spatial constraints to achieve robust source reconstruction. Summary of the Invention
[0006] To address the aforementioned issues, one objective of this application is to provide a method, system, device, and medium for iterative reconstruction and uncertainty quantification of leak sources based on spatial priors, achieving high-precision reconstruction in various applications. This method utilizes the Spearman correlation coefficient and source-receptor relationship to constrain the spatial search range, and identifies the leak source location within this range through iterative optimization of a cost function. 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, thereby simultaneously reconstructing the peak release and eliminating unreasonable oscillations. Finally, the above process is integrated into a Bayesian framework to assess the uncertainty of the leak source location and release rate reconstruction, providing more reliable technical support for nuclear accident emergency response.
[0007] To achieve the above objectives, this application adopts the following technical solution:
[0008] Firstly, this application provides a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors, comprising the following steps:
[0009] Based on the Spearman coefficient and the source-receptor matrix, the location of the leakage source was initially screened to obtain the distribution of spatial prior information.
[0010] Based on spatial prior information and the Tikhonov regularization method, the release rate and corresponding simulation-observation error index of each prior location are calculated, and the source location is estimated.
[0011] Based on the estimated source location, the release rate estimation is optimized using the L1 norm and total variational nonsmoothing constraints to obtain the time-varying release rate estimation results;
[0012] We designed a Bayesian framework to obtain the uncertainty distribution of source localization and release rate estimation results through Monte Carlo sampling.
[0013] Furthermore, the preliminary screening of leakage source locations based on Spearman coefficients and the source-receptor matrix to obtain the distribution of spatial prior information includes:
[0014] Based on the acquired source receptor matrix set and monitoring data, the possible release periods are traversed in the time dimension, and the integral source receptor sensitivity vector corresponding to each location is calculated in the monitoring dimension.
[0015] Based on the proportion of monitoring with an integrated sensitivity value greater than 0 by summarizing the integrated source-receptor sensitivity vector, source locations with a monitoring proportion lower than non-zero are removed within the initial source location range;
[0016] At the remaining candidate source locations, calculate the Spearman correlation coefficient between the integrated source receptor sensitivity vector and the monitoring;
[0017] The source locations with the highest Spearman coefficients during each release period are retained to form the spatial prior region.
[0018] Furthermore, the calculation of the release rate and corresponding simulation-observation error index for each prior location based on spatial prior information and the Tikhonov regularization method, and the estimation of the source location, includes:
[0019] Traverse the prior spatial locations to extract the source-receptor matrix. The extracted source receptor matrix is then updated using a matrix scaling factor.
[0020] Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source location.
[0021] The source location that is optimal based on the release rate search simulation-observation error index is used as the source localization result.
[0022] Furthermore, the updated source-receptor matrix... Cross-validation is used to automatically select the regularization parameter λ, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source location, including:
[0023] Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ;
[0024] Based on the selected regularization parameter λ, the LBFGS algorithm is used to optimize the L2 regularization cost function;
[0025] Update the release rate based on gradient information. Until the iteration termination condition is met, the result corresponding to the source position is obtained. Optimal release rate
[0026] Furthermore, the updated source-receptor matrix... The regularization parameter λ is automatically selected using cross-validation, including:
[0027] Set the regularization parameter range to λ∈[1e-6,1];
[0028] For each candidate regularization parameter λ, the source-receptor matrix The monitoring f is divided into 5 subsets, and the process is iterated 5 times. In each iteration, 4 subsets are used for training and the remaining subset is used for validation. The average cross-validation error of the model is calculated.
[0029] After calculating the average cross-validation error of all candidate regularization parameters λ, the λ value that minimizes the average cross-validation error is selected as the final regularization parameter.
[0030] Furthermore, the step of optimizing the release rate estimation based on the estimated source location, using the L1 norm and total variational nonsmoothness constraints, to obtain a time-varying release rate estimation result includes:
[0031] Based on the source localization result r e Extract the corresponding source receptor matrix The release rate was estimated based on L2 regularization. For the extracted source receptor matrix Perform correction;
[0032] We construct a cost function with sparsity and piecewise constant constraints, introduce a simulation-observation error correction matrix, and optimize the release rate.
[0033] Furthermore, the proposed Bayesian framework, through Monte Carlo sampling, obtains the uncertainty distribution of the source localization and release rate estimation results, including:
[0034] Integrate spatial prior information into the prior distribution, and transform the spatial discrete distribution into a probability distribution;
[0035] The source localization iterative process is transformed into Bayesian sampling, and the simulation-observation error calculation is incorporated into the likelihood function;
[0036] The uncertainty distribution of source location and release rate estimation results was obtained through Monte Carlo sampling.
[0037] Secondly, this application provides a system for iterative reconstruction of leakage sources and quantification of uncertainty based on spatial priors, including:
[0038] The spatial prior construction module is used to initially screen the location of leakage sources based on the Spearman coefficient and the source-receptor matrix, and obtain the distribution of spatial prior information.
[0039] The source localization module is used to calculate the release rate and corresponding simulation-observation error index of each prior location based on spatial prior information and the Tikhonov regularization method, and to estimate the source location.
[0040] The release rate estimation module is used to optimize the release rate estimation based on the estimated source location, the L1 norm and the total variation (TV) non-smoothing constraint, and obtain the time-varying release rate estimation result.
[0041] The uncertainty quantification module is used to design a Bayesian framework and obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.
[0042] Thirdly, this application provides a computer-readable storage medium for storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the above-described spatial prior leakage source iterative reconstruction and uncertainty quantification methods.
[0043] Fourthly, this application provides a computing device, including: 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, and the one or more programs include instructions for performing any of the above-described spatial prior leakage source iterative reconstruction and uncertainty quantification methods.
[0044] This application, by adopting the above technical solution, has the following advantages: It can utilize sparse monitoring sample information and data-driven spatial prior information to obtain source location and time-varying release rate reconstruction results with confidence intervals. Compared with traditional constant release constraint methods and non-constant release constraint methods, this application can better solve the following technical problems:
[0045] 1. Spatial Constraint Scarcity Problem: Traditional leakage source reconstruction methods rely solely on temporal constraints and cannot provide effective spatial constraints, leading to spurious source location estimation results. This application uses Spearman coefficients and source-receptor matrices to perform preliminary screening of leakage source locations, providing spatial distributions with location-oriented information;
[0046] 2. Problem of missing release timing information: Traditional reconstruction methods based on constant release constraints can only obtain estimates of release time and total release amount, but cannot provide detailed timing information on release. Traditional reconstruction methods based on non-constant release constraints, due to the use of smooth timing constraints, can only obtain release rate estimates containing spurious oscillations. This application does not rely on constant release constraints and provides complete and accurate release timing estimates through non-smooth timing constraints and model correction methods.
[0047] 3. Uncertainty Quantification Issue: Traditional reconstruction methods based on constant release constraints often result in overfitted estimates of release time and total release volume, leading to extremely high uncertainty. Traditional reconstruction methods based on non-constant release constraints can only provide point estimates of the release rate, lacking uncertainty quantification results. This application provides stable and reliable uncertainty quantification results for both source location and release timing.
[0048] Therefore, this application can be widely used in the fields of radioactive pollutant tracing and environmental monitoring. Attached Figure Description
[0049] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Throughout the drawings, the same reference numerals denote the same parts. In the drawings:
[0050] Figure 1 is a flowchart of the leakage source iterative reconstruction and uncertainty quantification method based on spatial priors provided in the embodiments of this application. Detailed Implementation
[0051] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the described embodiments of this application are within the scope of protection of this application.
[0052] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0053] Current methods for leak source reconstruction typically include constant release constraint methods and non-constant release constraint methods. Constant release constraint methods simplify source parameters to source location, release start and end times, and total release amount by imposing unrealistic assumptions on release characteristics, ignoring the time-varying characteristics of release in real leak scenarios. This leads to overfitting of the total release amount and start and end times, resulting in source location errors and potentially exhibiting significant multimodal phenomena in the Bayesian estimated posterior distribution. Non-constant release constraints apply smoothing constraints to release characteristics through regularization, thereby stabilizing the solution for time-varying release rates. However, this can easily lead to unreasonable oscillations in the release rate, resulting in source location errors. Therefore, existing methods rely only on time constraints, lacking spatial constraints, making it difficult to eliminate false source locations and provide truly reliable continuous release characteristic information, thus increasing the uncertainty in accident consequence assessment.
[0054] In some embodiments of this application, a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors is provided. This method initially screens leakage source locations based on Spearman coefficients and source-receptor matrices to provide a distribution with spatial prior information. Based on the spatial prior information and the Tikhonov regularization method, the release rate and corresponding simulation-observation error index for each prior location are calculated to estimate the source location. Based on the estimated source location, the release rate estimation is further optimized using the L1 norm and total variational (TV) non-smoothing constraints to obtain a time-varying release rate estimation result. A Bayesian framework is introduced to construct a prior distribution from the spatial prior information, transform the source localization iteration process into Bayesian sampling, and incorporate the simulation-observation error calculation into the likelihood function to obtain the uncertainty distribution of the source localization and release rate estimation results. Because this application introduces spatial constraints on top of non-constant release constraints, spurious source locations are effectively eliminated. Subsequently, the source location and corresponding time-varying release rate can be accurately estimated through cost function iteration, and the uncertainty of time-varying source parameter estimation can be quantified within the Bayesian framework.
[0055] Correspondingly, in other embodiments of this application, a system, device, and medium for iterative reconstruction of leakage sources and quantification of uncertainty based on spatial priors are provided.
[0056] Example 1
[0057] As shown in Figure 1, this application provides an iterative reconstruction and uncertainty quantification method for leakage sources based on spatial priors, which includes the following steps:
[0058] 1) Constructing spatial priors: Based on the Spearman coefficients and the source-receptor matrix, the leakage source locations are initially screened to obtain the distribution of spatial prior information;
[0059] 2) Source localization: Based on spatial prior information and the Tikhonov regularization method, the release rate and corresponding simulation-observation error index of each prior location are calculated, and the source location is estimated;
[0060] 3) Release rate estimation: Based on the estimated source location, the release rate estimation is optimized based on the L1 norm and the total variation (TV) non-smoothing constraint to obtain the time-varying release rate estimation result;
[0061] 4) Uncertainty quantification: A Bayesian framework is designed to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.
[0062] Furthermore, step 1) above includes the following steps:
[0063] 1.1) Based on the acquired input data, the possible release periods are traversed in the time dimension, and the integral source receptor sensitivity vector corresponding to each location is calculated in the monitoring dimension.
[0064] In this embodiment, the acquired input data includes a source-receptor matrix set. and monitoring Where T is the number of time steps for the release rate considered (i.e., T in Figure 1: time dimension), M is the number of grids in the x direction (i.e., M in Figure 1: x-direction dimension), N is the number of grids in the y direction (i.e., N in Figure 1: y-direction dimension), and K is the number of monitoring units (i.e., K in Figure 1: monitoring dimension); the source-receptor matrix set H is obtained by running the inverse mode of atmospheric diffusion simulation multiple times, and the number of runs is equal to the number of monitoring units K.
[0065] The integral source-receptor sensitivity vector corresponding to each location is calculated as follows:
[0066] In the formula, f xy Represents the integral source-receptor sensitivity vector. [t1,t2] represents the possible release periods, which can be set, for example, based on the earliest sampling start and latest sampling end times of all available non-zero monitors; r = (x,y) are the location coordinates. That is, integration is performed on 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.
[0067] 1.2) Based on the integrated source-receptor sensitivity vector, the proportion of monitoring with an integrated sensitivity value greater than 0 is summarized, and source locations with a monitoring proportion lower than non-zero are removed within the initial source location range.
[0068] In this embodiment, the physical meaning of the source-receptor sensitivity relationship is used to initially screen source locations. For true source locations, the integrated source-receptor sensitivity value corresponding to non-zero monitoring must be greater than 0. We relax this restriction and screen source locations by comparing the proportion of monitoring with an integrated sensitivity value greater than 0 with the proportion of non-zero monitoring. The initial source location range can be determined based on conventional experience. For example, if the radioactive leak occurred in Europe, the latitude and longitude range of Europe can be directly set. If the location is completely unknown, it can be set as: longitude: 180°W to 180°E; latitude: 90°S to 90°N. This application will not elaborate further on this.
[0069] 1.3) At the remaining candidate source locations, calculate the Spearman correlation coefficient between the integrated source receptor sensitivity vector and the monitoring.
[0070] In this embodiment, the integral source-receptor sensitivity vector f xy Spearman correlation coefficient S with monitoring f xy The calculation formula is:
[0071] In the formula, <·> represents the arithmetic mean over all elements; R and R H Let f represent the vector composed of the sorted order of each element in f and f, respectively. xy The vector is composed of the sorted order of each element; P represents the proportion of non-zero monitoring, which is multiplied by a scaling factor of 0.7 to avoid over-elimination.
[0072] 1.4) Retain the source location with the highest Spearman coefficient during each release period. This constitutes the spatial prior region (i.e., the spatial prior information in Figure 1).
[0073] In this embodiment, the spatial prior region is a discontinuous region. It includes the source locations with the highest Spearman coefficients during each release period, denoted as:
[0074] In the formula, S xy (t1,t2) represents the Spearman coefficients calculated at the source location (x,y) during the release period [t1,t2], and Ω represents the spatial computational domain.
[0075] This embodiment uses Spearman coefficients and source-receptor matrices to initially screen the leakage source location, which not only provides reliable spatial constraints but also greatly reduces the space required to solve for the source location and accelerates the calculation speed of subsequent iterative reconstruction.
[0076] Furthermore, step 2) above includes the following steps:
[0077] 2.1) Traverse the prior spatial locations to extract the source-receptor matrix. The extracted source receptor matrix is then updated using a matrix scaling factor.
[0078] Specifically, it includes the following steps:
[0079] ① Traverse the prior spatial locations and solve the source-receptor matrix using the least squares method. The solution between and monitoring f is to solve the following equation:
[0080] In the formula, This represents the error vector.
[0081] ② Calculate the matrix scaling factor based on the obtained least-squares solution, and apply it to the extracted source-receptor matrix. Update.
[0082] The least squares solution is expressed as:
[0083] The largest element in vector q is taken as the source-receptor matrix. By adjusting the matrix scaling factor, the new source-receptor matrix is obtained as follows:
[0084] 2.2) Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source location.
[0085] Specifically, it includes the following steps:
[0086] ①Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ.
[0087] In this embodiment, the method for automatically selecting the regularization parameter λ using cross-validation is as follows: First, the range of the regularization parameter is set to λ∈[1e-6,1]; second, for each candidate regularization parameter λ, the source-receptor matrix is... The model is divided into 5 subsets and iterated 5 times. In each iteration, 4 subsets are used for training and the remaining subset is used for validation. The average cross-validation error of the model is calculated. Finally, after calculating the average cross-validation error of all candidate regularization parameters λ, the λ value that minimizes the average cross-validation error is selected as the final regularization parameter.
[0088] ②Based on the selected regularization parameter λ, the LBFGS algorithm is used to optimize the L2 regularization cost function.
[0089] In this embodiment, the L2 regularized cost function is used as the error cost function between simulation and observation. It 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, which is the L2 norm of the release rate vector.
[0090] In the formula, Indicates the corresponding source location The release rate vector.
[0091] The initial release rate q0 is an all-one vector, and the gradient of the cost function is:
[0092] ③ Update the release rate based on gradient information Until the iteration termination condition is met, the result corresponding to the source position is obtained. Optimal release rate
[0093] 2.3) The source location with the optimal simulation-observation error index based on the release rate is used as the source localization result r. e =(x e ,y e ).
[0094] In this embodiment, the simulation-observation error index is designed as follows: Starting from a random grid in the prior spatial region, move the simulation-observation error index to its minimum value until the simulation-observation error index converges to its minimum value. The corresponding source location is the positioning result.
[0095] The source localization in this embodiment can provide a stable and accurate release rate estimate, making it easy to distinguish different source locations. It also uses a reliable simulation-observation error index for evaluation, making it suitable for source localization in various leakage scenarios, especially under sparse monitoring conditions.
[0096] Furthermore, step 3) above includes the following steps:
[0097] 3.1) Based on the source localization result r e Extract the corresponding source receptor matrix The release rate was estimated based on L2 regularization. For the extracted source receptor matrix Perform corrections.
[0098] The correction formula is expressed as follows:
[0099] 3.2) Construct a cost function with sparsity and piecewise constant constraints, introduce the simulation-observation error correction matrix (i.e., the error correction matrix in Figure 1), and further optimize the release rate solution: stP≥0,center(diag(P))=0.2. (11)
[0100] In the formula, P is the simulation-observation error correction matrix, which is a diagonal matrix, and the initial values of the diagonal elements are set to... τ is a weighting parameter used to balance the error term and the constraint term; ||q||1 is the sparsity constraint on the release rate. A piecewise constant constraint is applied to the release rate to add a time non-smooth constraint to the release rate; during the iteration, P and P are updated simultaneously. Until both converge.
[0101] The release rate estimation in this embodiment can provide very complete details of the release timing, which helps to conduct reliable assessments of the consequences of nuclear accidents.
[0102] Furthermore, in step 4) above, uncertainty quantification can more comprehensively assess the reliability of time-varying release source parameters, providing a more solid foundation for decision-making in complex leakage source scenarios.
[0103] Specifically, it includes the following steps:
[0104] 4.1) Incorporate spatial prior information into the prior distribution to transform the spatial discrete distribution into a probability distribution.
[0105] In this embodiment, the discrete spatial prior regions are probabilistically transformed into prior probability density functions using kernel density estimation:
[0106] In the formula, ω i is the weight of position i in space, and N is the number of grids in space. Based on the previously obtained spatial prior distribution, the weight of the position i within the spatial prior region is set to 1 / N, and the weight of the position i outside the region is set to 0.
[0107] 4.2) The source localization iteration process is transformed into Bayesian sampling, and the simulation-observation error calculation is incorporated into the likelihood function.
[0108] In Bayesian sampling, the sampling source location r s =(x s ,y s (This is obtained by interpolating the source-receptor matrix.) Release rate The following was obtained through monitoring and inversion:
[0109] The likelihood function uses the log-Gaussian likelihood, i.e.:
[0110] In the formula, b is the covariance parameter, δ is a minimum value used to avoid failure in zero-value logarithm calculation, and these two parameters are included in the sampling as unknown parameters along with the source locations; K is the number of monitoring points. Sampling is performed based on the Markov Monte Carlo method, with 5000 sampling times and a total of 5 Markov chains. The first 2500 sampling times of each chain are used as the annealing stage, and the source location sampling results of the last 2500 sampling times are used as the posterior estimate. The release rates corresponding to these locations are used as the posterior release rates.
[0111] 4.3) The uncertainty distribution of source location and release rate estimation results is obtained through Monte Carlo sampling.
[0112] In summary, the iterative reconstruction and uncertainty quantification method for leakage sources based on spatial priors provided in this application has the following advantages:
[0113] (1) Provide effective spatial prior constraints
[0114] This application achieves preliminary screening of leakage source locations through Spearman correlation coefficient and source receptor sensitivity. It can provide effective prior information on spatial source locations in both field experiments with abundant monitoring data and real events with sparse and unevenly distributed monitoring data, thereby greatly reducing the computational search space and accelerating the reconstruction process, making it suitable for rapid response in emergency scenarios.
[0115] (2) Provides accurate source localization results
[0116] This application combines spatial prior information with the Tikhonov regularization method. By using the least squares method to estimate the scaling factor of the source-receptor matrix, the stability of the release rate order of magnitude is ensured, thereby achieving accurate estimation of the release rate at each prior location. The probability of each prior location is evaluated by using the simulation-observation difference index, which significantly improves the estimation accuracy of the leakage source location and release rate. The positioning error in the field experiment is less than one grid precision, and the positioning error in real events under different monitoring conditions is reduced by more than 75% compared with traditional methods, making it suitable for source positioning in complex leakage scenarios.
[0117] (3) Provide complete timing information for time-varying release
[0118] This application employs L1 norm and total variation (TV) nonsmoothing constraints to further optimize the release rate, enabling it to capture peak release while suppressing unreasonable oscillations. This improves the accuracy and stability of release rate estimation in non-constant release scenarios and shows high agreement with the actual or reported release rate in terms of release timing variations (peak size and peak time) and total release amount, thus contributing to more reliable consequence assessment.
[0119] (4) Provides uncertainty quantification for time-varying release
[0120] This application achieves statistical analysis of the uncertainty in estimating source location and time-varying release rate by transforming spatial prior information into a prior probability distribution, converting the source localization iteration process into a Bayesian sampling problem, and transforming the evaluation of simulation-observation error into likelihood function calculation. This method effectively assesses the reliability of the estimation results and provides strong support for uncertainty analysis of leakage sources in complex scenarios.
[0121] Example 2
[0122] The above-described embodiment 1 provides a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors. Correspondingly, this embodiment provides a system for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors. The system provided in this embodiment can implement the method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors of embodiment 1. This system can be implemented through software, hardware, or a combination of both. For example, the system may include integrated or separate functional modules or 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. For relevant details, please refer to the description of embodiment 1. The system embodiment provided in this embodiment is merely illustrative.
[0123] The leakage source iterative reconstruction and uncertainty quantification system based on spatial priors provided in this embodiment includes:
[0124] The spatial prior construction module is used to initially screen the location of leakage sources based on the Spearman coefficient and the source-receptor matrix, and obtain the distribution of spatial prior information.
[0125] The source localization module is used to calculate the release rate and corresponding simulation-observation error index of each prior location based on spatial prior information and the Tikhonov regularization method, and to estimate the source location.
[0126] The release rate estimation module is used to optimize the release rate estimation based on the estimated source location, the L1 norm and the total variation (TV) non-smoothing constraint, and obtain the time-varying release rate estimation result.
[0127] The uncertainty quantification module is used to design a Bayesian framework and obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.
[0128] Example 3
[0129] This embodiment provides a processing device corresponding to the spatial prior-based leakage source iterative reconstruction and uncertainty quantification method provided in Embodiment 1. The processing device can be a client-side processing device, such as a mobile phone, laptop, tablet computer, desktop computer, etc., to execute the method of Embodiment 1.
[0130] The processing device includes a processor, a memory, a communication interface, and a bus. The processor, memory, and communication interface are connected via the bus to enable communication between them. The memory stores a computer program that can run on the processor. When the processor runs the computer program, it executes the leakage source iterative reconstruction and uncertainty quantification method based on spatial priors provided in Embodiment 1.
[0131] Optionally, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.
[0132] Optionally, the processor can be any type of general-purpose processor such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation on this.
[0133] Example 4
[0134] The spatial prior-based leak source iterative reconstruction and uncertainty quantification method of this embodiment 1 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 spatial prior-based leak source iterative reconstruction and uncertainty quantification method of this embodiment 1 are loaded.
[0135] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can 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 thereof.
[0136] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0137] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams.
[0138] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.
[0139] These computer program instructions may 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, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.
[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.
Claims
1. A method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors, comprising the following steps: Based on the Spearman coefficient and the source-receptor matrix, the location of the leakage source was initially screened to obtain the distribution of spatial prior information. Based on spatial prior information and the Tikhonov regularization method, the release rate and corresponding simulation-observation error index of each prior location are calculated, and the source location is estimated. Based on the estimated source location, the release rate estimation is optimized using the L1 norm and total variational nonsmoothing constraints to obtain the time-varying release rate estimation results; We designed a Bayesian framework to obtain the uncertainty distribution of source localization 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 as described in claim 1, wherein, The preliminary screening of leakage source locations based on Spearman coefficients and source-receptor matrices yields the distribution of spatial prior information, including: Based on the acquired source receptor matrix set and monitoring data, the release period is traversed in the time dimension, and the integral source receptor sensitivity vector corresponding to each location is calculated in the monitoring dimension. Based on the proportion of monitoring with an integrated sensitivity value greater than 0 by summarizing the integrated source-receptor sensitivity vector, source locations with a monitoring proportion lower than non-zero are removed within the initial source location range; At the remaining candidate source locations, calculate the Spearman correlation coefficient between the integrated source receptor sensitivity vector and the monitoring; The source locations with the highest Spearman coefficients during each release period are retained to form the spatial prior region.
3. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors as described in claim 1, wherein, The method, based on spatial prior information and Tikhonov regularization, calculates the release rate and corresponding simulation-observation error index for each prior location, and estimates the source location, including: Traverse the prior spatial locations to extract the source-receptor matrix. The extracted source receptor matrix is then updated using a matrix scaling factor. Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source location. The source location that is optimal based on the release rate search simulation-observation error index is used as the source localization result.
4. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors as described in claim 3, wherein, The updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source location, including: Based on the updated source-receptor matrix Cross-validation is used to automatically select the regularization parameter λ; Based on the selected regularization parameter λ, the LBFGS algorithm is used to optimize the L2 regularization cost function; Update the release rate based on gradient information. Until the iteration termination condition is met, the result corresponding to the source position is obtained. Optimal release rate 5. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors as described in claim 4, wherein, The updated source-receptor matrix The regularization parameter λ is automatically selected using cross-validation, including: Set the regularization parameter range to λ∈[1e-6,1]; For each candidate regularization parameter λ, the source-receptor matrix The monitoring f is divided into 5 subsets, and the process is iterated 5 times. In each iteration, 4 subsets are used for training and the remaining subset is used for validation. The average cross-validation error of the model is calculated. After calculating the average cross-validation error of all candidate regularization parameters λ, the λ value that minimizes the average cross-validation error is selected as the final regularization parameter.
6. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors as described in claim 1, wherein, The process of optimizing the release rate estimation based on the estimated source location, using the L1 norm and total variational nonsmoothness constraints, yields a time-varying release rate estimation result, including: Based on the source localization result r e Extract the corresponding source receptor matrix The release rate was estimated based on L2 regularization. For the extracted source receptor matrix Perform correction; We construct a cost function with sparsity and piecewise constant constraints, introduce a simulation-observation error correction matrix, and optimize the release rate.
7. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors as described in claim 1, wherein, The proposed Bayesian framework obtains the uncertainty distribution of source localization and release rate estimation results through Monte Carlo sampling, including: Integrate spatial prior information into the prior distribution, and transform the spatial discrete distribution into a probability distribution; The source localization iterative process 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 was obtained through Monte Carlo sampling.
8. A system for iterative reconstruction of leakage sources and quantification of uncertainty based on spatial priors, comprising: The spatial prior construction module is used to initially screen the location of leakage sources based on the Spearman coefficient and the source-receptor matrix, and obtain the distribution of spatial prior information. The source localization module is used to calculate the release rate and corresponding simulation-observation error index of each prior location based on spatial prior information and the Tikhonov regularization method, and to estimate the source location. The release rate estimation module is used to optimize the release rate estimation based on the estimated source location, the L1 norm, and the total variational nonsmoothing constraint, to obtain the time-varying release rate estimation result. The uncertainty quantification module is used to design a Bayesian framework and 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, said one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any one of the methods claimed in claims 1 to 7.
10. A computing device, comprising: 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, the one or more programs including instructions for performing any of the methods described in claims 1 to 7.