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

Abstract

The present invention relates to a method, system, device, and medium for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors. The method comprises the following steps: preliminarily screening the leakage source locations based on the Spearman coefficient and source-receptor matrix to obtain the distribution of spatial prior information; calculating the release rate and corresponding simulation-observation error index for each prior location based on the spatial prior information and the Tikhonov regularization method, and estimating the source location; optimizing the release rate estimation based on the estimated source location using the L1 norm and total variation non-smooth constraint to obtain a time-series release rate estimation result; and designing a Bayesian framework to obtain the uncertainty distribution of the source location and release rate estimation results through Monte Carlo sampling. The present invention can be widely applied in the fields of radioactive pollutant tracing and environmental monitoring.

Description

Technical Field

[0001] The present invention relates to a method, system, equipment and medium for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priori, and belongs to the field of radioactive pollutant tracing and environmental monitoring. Background Art

[0002] With the implementation of the plan to triple global nuclear energy production capacity, nuclear energy is gradually becoming an important component of the energy structure of various countries. However, while nuclear power plants provide abundant energy, the widespread use of radioactive materials also brings environmental and health risks that cannot be ignored. Especially in the face of nuclear accidents or radioactive material leaks, quickly and accurately determining the location of the leakage source of radioactive nuclides in the atmosphere and their release rate is crucial for timely response, radiation risk assessment, and public safety. The current challenge is that leakage source identification is often limited by sparse observation data and unevenly distributed monitoring networks. These factors limit the effective constraints of the reconstruction process and make source identification highly complex and uncertain.

[0003] Currently, the most commonly used constraint method is the constant release constraint, which reduces the spatial dimensionality of the solution by assuming a constant release in time and is widely used in Bayesian reconstruction. However, this assumption is inconsistent with real-world release scenarios and can easily lead to overfitting of the total release amount and time. This overfitting error is further propagated to the source position estimate, causing the source position to deviate significantly from the true location. To avoid this error, the non-constant release constraint stabilizes the solution of the time-varying release rate by adding smoothness constraints (such as the L2 norm) to the release rate characteristics. However, the underlying smoothness assumption makes it difficult to distinguish true peak release from oscillations caused by reconstruction ill-posedness, as both exhibit temporal non-smoothness. As a result, the reconstructed release rate may exhibit unrealistic oscillations, which can also propagate to the source position estimate, leading to source localization errors. Therefore, relying solely on temporal constraints, whether constant or non-constant release constraints, is difficult to effectively eliminate erroneous source positions. Therefore, the introduction of additional spatial constraints is urgently needed to achieve robust source reconstruction. Summary of the Invention

[0004] In response to the above problems, the purpose 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 priors, which achieves high-precision reconstruction in a variety of applications. The method uses the Spearman correlation coefficient and the source-receptor relationship to constrain the spatial search range, and identifies the leakage source location within this range through iterative optimization of the cost function. After determining the source location, an error correction matrix is ​​introduced, and the time-varying release rate is estimated using non-smooth constraints, thereby simultaneously reconstructing the peak release and eliminating 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:

[0006] In a first aspect, the present invention provides a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors, comprising the following steps:

[0007] 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;

[0008] Based on spatial prior information and the Tikhonov regularization method, the release rate and the corresponding simulation-observation error index of each prior position are calculated, and the source position is estimated;

[0009] 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 time-series release rate estimation result;

[0010] A Bayesian framework is designed to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling.

[0011] Furthermore, 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:

[0012] 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;

[0013] 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;

[0014] At the remaining candidate source locations, the Spearman correlation coefficient between the integrated source receptor sensitivity vector and the monitoring is calculated;

[0015] The source position with the highest Spearman coefficient in each release period is retained to form the spatial prior region.

[0016] Furthermore, the release rate of each prior position and the corresponding simulation-observation error index are calculated based on the spatial prior information and the Tikhonov regularization method, and the source position is estimated, including:

[0017] Traverse the spatial prior positions and extract the source receptor matrix , and update the extracted source receptor matrix by the matrix scaling factor;

[0018] 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;

[0019] The source position with the optimal simulation-observation error index is searched based on the release rate as the source localization result.

[0020] Further, the source receptor matrix based on the update , 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:

[0021] Based on the updated source-receptor matrix , using cross-validation to automatically select the regularization parameter ;

[0022] Based on the selected regularization parameter , the LBFGS algorithm is used to optimize the L2 regularization cost function;

[0023] 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 .

[0024] Further, the source receptor matrix based on the update , using cross-validation to automatically select the regularization parameter ,include:

[0025] Set the regularization parameter range to ;

[0026] 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;

[0027] After calculating all candidate regularization parameters After the average cross-validation error of The value is used as the final regularization parameter.

[0028] Furthermore, the release rate estimation is optimized based on the L1 norm and the total variation non-smooth constraint according to the estimated source position to obtain a release rate estimation result of time series variation, including:

[0029] 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;

[0030] 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.

[0031] Furthermore, the Bayesian framework is designed to obtain the uncertainty distribution of the source location and release rate estimation results through Monte Carlo sampling, including:

[0032] Integrate spatial prior information into prior distribution and convert spatial discrete distribution into continuous probability distribution;

[0033] The iterative process of source localization is transformed into Bayesian sampling, and the simulation-observation error calculation is incorporated into the likelihood function;

[0034] The uncertainty distribution of source location and release rate estimation results is obtained through Monte Carlo sampling.

[0035] In a second aspect, the present invention provides a leakage source iterative reconstruction and uncertainty quantification system based on spatial prior, comprising:

[0036] The spatial prior construction module is used to preliminarily screen the leakage source location based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information;

[0037] 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 the Tikhonov regularization method, and estimate the source position;

[0038] The release rate estimation module is used to optimize the release rate estimation based on the estimated source position and the L1 norm and total variation (TV) non-smooth constraint to obtain the release rate estimation result with time series variation;

[0039] 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.

[0040] In a third aspect, the present invention provides a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any method.

[0041] In a fourth aspect, the present invention provides 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, and the one or more programs include instructions for executing any method.

[0042] Due to the adoption of the above technical solution, the present invention has the following advantages: the present invention can use sparse monitoring sample information and data-driven spatial prior information to obtain source position and time-varying release rate reconstruction results with confidence intervals. Compared with traditional constant release constraint methods and non-constant release constraint methods, the present invention can better solve the following technical problems:

[0043] 1. Scarcity of spatial constraints: Traditional leakage source reconstruction methods rely solely on temporal constraints and cannot provide effective spatial constraints, resulting in false source location estimates. This invention uses the Spearman coefficient and source-receptor matrix to perform a preliminary screening of leakage source locations to provide a spatial distribution with positional directivity information.

[0044] 2. Missing release timing information: Traditional reconstruction methods based on constant release constraints can only obtain release time and total release amount estimates, but cannot provide detailed release timing information. Traditional reconstruction methods based on non-constant release constraints, due to the use of smooth timing constraints, can only obtain release rate estimates containing false oscillations. The present invention does not rely on constant release constraints, and provides complete and true release timing estimation results through non-smooth timing constraints and model correction methods;

[0045] 3. Uncertainty Quantification: Traditional reconstruction methods based on constant release constraints produce overfitted estimates of release time and total release volume, often with extremely high uncertainty ranges. Traditional reconstruction methods based on non-constant release constraints can only produce point estimates of release rates, lacking uncertainty quantification. This invention provides stable and reliable uncertainty quantification of source location and release timing.

[0046] Therefore, the present invention can be widely used in the fields of radioactive pollutant tracing and environmental monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. Throughout the drawings, the same reference numerals are used to denote the same components. In the drawings:

[0048] Figure 1 This is a flow chart of a method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field are within the scope of protection of the present invention.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] Current leak source reconstruction methods typically include constant release constraint methods and non-constant release constraint methods. The constant release constraint method imposes unrealistic assumptions on the release characteristics, simplifying the source parameters to source location, release start and end times, and total release volume. This ignores the time-varying characteristics of release in real leak scenarios, leading to overfitting of the total release volume and start and end times, which in turn causes source location errors and may result in significant multimodal phenomena in the posterior distribution of the Bayesian estimate. The non-constant release constraint imposes smoothing constraints on the release characteristics through regularization, thereby stabilizing the solution of the time-varying release rate. However, it is easy to cause unreasonable oscillations in the release rate, leading to source location errors. Therefore, existing methods rely only on time constraints and lack spatial constraints. It is difficult to exclude false source locations and provide true and reliable continuous release characteristic information, which increases the uncertainty of accident consequence assessment.

[0052] In some embodiments of the present invention, a method for iterative reconstruction and uncertainty quantification of leak sources based on spatial priors is provided. The method preliminarily screens leak source locations based on the Spearman coefficient and source-receptor matrix to provide a distribution with spatial prior information. The method then calculates the release rate and corresponding simulation-observation error index for each prior location based on the spatial prior information and the Tikhonov regularization method to estimate the source location. Based on the estimated source location, the release rate estimate is further optimized using the L1 norm and total variation (TV) non-smooth constraints to obtain a time-varying release rate estimate. A Bayesian framework is introduced to convert the spatial prior information into a prior distribution, transform the iterative source localization process into Bayesian sampling, and incorporate the simulation-observation error calculation into the likelihood function to obtain an uncertainty distribution for the source localization and release rate estimation results. Because the present invention introduces spatial constraints based on non-constant release constraints, false source locations are effectively eliminated. Subsequently, the source location and corresponding time-varying release rate can be accurately estimated through cost function iteration. Furthermore, the uncertainty of the time-varying source parameter estimate can be quantified within the Bayesian framework.

[0053] Correspondingly, in some other embodiments of the present invention, a system, device and medium for iterative reconstruction and uncertainty quantification of leakage sources based on spatial prior are provided.

[0054] Example 1

[0055] like Figure 1 As shown, the present invention provides a leakage source iterative reconstruction and uncertainty quantification method based on spatial prior, which includes the following steps:

[0056] 1) Constructing spatial priors: Preliminary screening of the leakage source locations is performed based on the Spearman coefficient and source-receptor matrix to obtain the distribution of spatial prior information;

[0057] 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 position are calculated, and the source position is estimated;

[0058] 3) Release rate estimation: Based on the estimated source position, the release rate estimation is optimized based on the L1 norm and total variation (TV) non-smooth constraints to obtain the time-varying release rate estimation result;

[0059] 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.

[0060] Furthermore, the above step 1) includes the following steps:

[0061] 1.1) Based on the acquired input 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.

[0062] In this embodiment, the input data obtained includes a source receptor matrix set and monitoring ,in, is the number of release rate time steps considered, for x The number of grids in the direction, for y The number of grids in the direction, is the number of monitoring; source receptor matrix set Obtained by running the atmospheric dispersion simulation in reverse mode multiple times, with the number of runs equal to the number of monitoring .

[0063] The integrated source-receptor sensitivity vector corresponding to each position is calculated as:

[0064] (1)

[0065] Where, represents the integrated source-receptor sensitivity vector, ; Indicates a possible release period, which can be set, for example, based on the earliest sampling start time and the latest sampling end time of all available non-zero monitoring; is the position coordinate. That is, integration is performed in the first time dimension to obtain the integrated source-receptor sensitivity corresponding to each monitoring, which reflects the average sensitivity of the source and receptor in the considered time period.

[0066] 1.2) Based on the integrated source receptor sensitivity vector, summarize the monitoring proportions with integrated sensitivity values ​​greater than 0, and eliminate source locations with monitoring proportions below non-zero within the initial source location range.

[0067] In this embodiment, the physical meaning of the source-receptor sensitivity relationship is used to preliminarily screen the source location. For the actual source location, the integrated source-receptor sensitivity value corresponding to the non-zero monitoring must be greater than 0. We relax this restriction and screen the source location 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 a radioactive leak occurs in Europe, the longitude and latitude range of Europe can be directly set. If it is completely unclear where the leak occurred, the longitude and latitude range can be directly set to: longitude: 180°W to 180°E; latitude: 90°S to 90°N. This invention will not be described in detail.

[0068] 1.3) Calculate the Spearman correlation coefficient between the integrated source-receptor sensitivity vector and the monitoring at the remaining candidate source locations.

[0069] In this embodiment, the integrated source receptor sensitivity vector and monitoring The Spearman correlation coefficient between The calculation formula is:

[0070] (2)

[0071] Where, Represents the arithmetic mean of all elements; and Respectively indicate monitoring The vector and the order of each element in A vector consisting of the sort of each element in ; Indicates the proportion of non-zero monitoring. To avoid excessive elimination, this proportion is multiplied by a scaling factor of 0.7.

[0072] 1.4) Keep the source position with the highest Spearman coefficient in each release period , constituting a spatial prior region.

[0073] In this embodiment, the spatial prior region is a discontinuous region , which includes the source location with the highest Spearman coefficient at each release period, expressed as:

[0074] (3)

[0075] Where, Indicates the source location During the release period The Spearman coefficient calculated below is, Represents the spatial computational domain.

[0076] This embodiment performs preliminary screening of the leakage source location based on the Spearman coefficient and the source receptor matrix, which not only provides reliable spatial constraints but also greatly reduces the space for solving the source location and accelerates the calculation speed of subsequent iterative reconstruction.

[0077] Furthermore, the above step 2) includes the following steps:

[0078] 2.1) Traverse the spatial prior positions and extract the source receptor matrix , and the extracted source-receptor matrix is ​​updated by the matrix scaling factor.

[0079] Specifically, the method includes the following steps:

[0080] ① Traverse the spatial prior positions and use the least squares method to solve the source receptor matrix and monitoring The solution between , that is, to solve the following equation:

[0081] (4)

[0082] Where, represents the error vector.

[0083] ② Calculate the matrix scaling factor based on the obtained least squares solution and apply it to the extracted source receptor matrix to update.

[0084] The least squares solution is expressed as:

[0085] (5)

[0086] The vector The largest element in the source-receptor matrix The matrix scaling factor is , and the new source receptor matrix is:

[0087] (6)

[0088] 2.2) 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.

[0089] Specifically, the method includes the following steps:

[0090] ① Based on the updated source-receptor matrix , using cross-validation to automatically select the regularization parameter .

[0091] In this embodiment, cross validation is used to automatically select the regularization parameter The method is: First, set the regularization parameter range to ; Secondly, 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 verification, and calculate the average cross-validation error of the model; finally, calculate all candidate regularization parameters After the average cross-validation error of The value is used as the final regularization parameter.

[0092] ② Based on the selected regularization parameter , the LBFGS algorithm is used to optimize the L2 regularization cost function.

[0093] In this embodiment, the L2 regularization cost function is used as the error cost function between simulation and observation. It consists of two terms. The first term is the square error term between simulation and observation, and the second term is the L2 regularization term, that is, the second norm of the release rate vector, that is:

[0094] (7)

[0095] Where, Indicates the source location The release rate vector.

[0096] Initial release rate is a full 1 vector, the gradient of the cost function is:

[0097] (8)

[0098] ③ Update the release rate based on gradient information , until the iteration termination condition is reached, the corresponding source position is obtained The optimal release rate .

[0099] 2.3) Search for the source location with the best simulation-observation error index based on the release rate, and use it as the source location result .

[0100] 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.

[0101] The source localization of this embodiment can provide 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.

[0102] Furthermore, the above step 3) includes the following steps:

[0103] 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.

[0104] The correction formula is expressed as:

[0105] (9)

[0106] 3.2) Construct a cost function with sparsity and piecewise constant constraints, introduce a simulation-observation error correction matrix, and further optimize the release rate solution:

[0107] (10)

[0108] . (11)

[0109] Where, 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.

[0110] The release rate estimation of this embodiment can provide very complete release timing details, which is helpful for conducting reliable nuclear accident consequence assessment.

[0111] Furthermore, in step 4) above, uncertainty quantification can more comprehensively evaluate the reliability of time-varying release source parameters, providing a more solid basis for decision-making in complex leakage source scenarios.

[0112] Specifically, the method includes the following steps:

[0113] 4.1) Incorporate spatial prior information into the prior distribution and convert the spatial discrete distribution into a continuous probability distribution.

[0114] In this embodiment, the discrete spatial prior region is probabilized into a priori probability density function by kernel density estimation:

[0115] (12)

[0116] Where, is the position in space The weight of N is the number of grids in the space. According to the spatial prior distribution obtained previously, the weights belonging to the spatial prior area are set to , the weight outside the region is set to 0.

[0117] 4.2) The iterative process of source localization is transformed into Bayesian sampling, and the simulation-observation error calculation is incorporated into the likelihood function.

[0118] In the Bayesian sampling process, the sampling source location , obtained by interpolating the source-receptor matrix The release rate Through monitoring inversion, we can get:

[0119] (13)

[0120] The likelihood function uses the log-Gaussian likelihood, that is:

[0121] (14)

[0122] Where, is the covariance parameter, is a very small quantity used to avoid failure in zero-value logarithm calculations. These two parameters are sampled together with the source location as unknown parameters; K is the number of monitoring points. Sampling is performed based on the Markov Monte Carlo method, with a set number of sampling times of 5000, and a total of five Markov chains. The first 2500 sampling cycles of each chain serve as the annealing phase, and the last 2500 sampling results of the source location are used as the posterior estimate. The release rates corresponding to these locations are used as the posterior release rates.

[0123] 4.3) The uncertainty distribution of source location and release rate estimation results is obtained through Monte Carlo sampling.

[0124] In summary, the present invention provides a leakage source iterative reconstruction and uncertainty quantification method based on spatial priors, which has the following advantages:

[0125] (1) Providing effective spatial prior constraints

[0126] The present invention achieves preliminary screening of the leakage source location through the Spearman correlation coefficient and source-receptor sensitivity. It can provide effective prior information on the spatial source location in both field experiments with rich monitoring data and real events with sparse monitoring data and uneven spatial distribution, thereby greatly reducing the computational search space and accelerating the reconstruction process, making it suitable for rapid response in emergency scenarios.

[0127] (2) Providing accurate source positioning results

[0128] The present invention 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 magnitude is ensured, thereby achieving accurate estimation of the release rate at each prior position. The probability of each prior position is evaluated with the help of the simulation-observation difference index, which significantly improves the estimation accuracy of the leakage source position and release rate. The positioning result error in the field experiment is less than one grid accuracy, and the positioning error in real events under different monitoring conditions is reduced by more than 75% compared with traditional methods, which is suitable for source positioning in complex leakage scenarios.

[0129] (3) Provide complete timing information of time-varying release

[0130] The present invention adopts L1 norm and total variation (TV) non-smooth constraints to further optimize the release rate, so that it can capture peak release while suppressing unreasonable oscillations, improving the release rate estimation accuracy and stability in non-constant release scenarios, and has a high degree of consistency with the actual or reported release rate in terms of release timing changes (release peak size and peak time) and total release amount, which contributes to more reliable consequence assessment.

[0131] (4) Provide uncertainty quantification of time-varying release

[0132] This method transforms spatial prior information into a prior probability distribution, transforms the iterative source localization process into a Bayesian sampling problem, and transforms the evaluation of simulation-observation error into a likelihood function calculation. This method enables statistical analysis of the uncertainty in the estimation of source location and time-varying release rate. This method effectively assesses the reliability of the estimation results and provides strong support for uncertainty analysis of leak sources in complex scenarios.

[0133] Example 2

[0134] The above-mentioned embodiment 1 provides a leakage source iterative reconstruction and uncertainty quantification method based on spatial prior. Correspondingly, this embodiment provides a leakage source iterative reconstruction and uncertainty quantification system based on spatial prior. The system provided by this embodiment can implement the leakage source iterative reconstruction and uncertainty quantification method based on spatial prior of embodiment 1. The system can be implemented by software, hardware, or a combination of software and hardware. For example, the system can include integrated or separate functional modules or functional units to execute the corresponding steps in each method of embodiment 1. Since the system of this embodiment is basically similar to the method embodiment, the process described in this embodiment is relatively simple. For relevant points, please refer to the partial description of embodiment 1. The embodiment of the system provided in this embodiment is only illustrative.

[0135] The leakage source iterative reconstruction and uncertainty quantification system provided in this embodiment based on spatial priors includes:

[0136] The spatial prior construction module is used to preliminarily screen the leakage source location based on the Spearman coefficient and the source-receptor matrix to obtain the distribution of spatial prior information;

[0137] 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 the Tikhonov regularization method, and estimate the source position;

[0138] The release rate estimation module is used to optimize the release rate estimation based on the estimated source position and the L1 norm and total variation (TV) non-smooth constraint to obtain the release rate estimation result with time series variation;

[0139] 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.

[0140] Example 3

[0141] This embodiment provides a processing device corresponding to the iterative reconstruction and uncertainty quantification method of leakage sources based on spatial prior provided in this embodiment 1. The processing device can 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.

[0142] 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 facilitate communication between them. The memory stores a computer program executable on the processor. When the processor executes the computer program, iterative reconstruction and uncertainty quantification method for leakage sources based on spatial priors provided in Example 1 is performed.

[0143] Preferably, the memory may be a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory.

[0144] Preferably, the processor may be a central processing unit (CPU), a digital signal processor (DSP), or other general-purpose processors of various types, which are not limited here.

[0145] Example 4

[0146] The iterative reconstruction and uncertainty quantification method of leakage sources based on spatial prior in this embodiment 1 can be specifically implemented as a computer program product, which may include a computer-readable storage medium carrying computer-readable program instructions for executing the iterative reconstruction and uncertainty quantification method of leakage sources based on spatial prior in this embodiment 1.

[0147] Computer readable storage media can be tangible devices that hold and store instructions used by instruction execution devices. Computer readable storage media can be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof.

[0148] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, 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 storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0149] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes 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 a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0150] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0151] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0152] 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 it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection 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 the Tikhonov regularization method, the release rate and the 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 time-series release rate estimation result; A Bayesian framework is designed to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling. 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, the release period is 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; 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 result r e Extract the corresponding source-receptor matrix And based on the release rate estimated by 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.

2. 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 of each prior position and the corresponding simulation-observation error index are calculated based on the spatial prior information and the Tikhonov regularization method, and the source position is estimated, including: Traverse the spatial prior positions and extract the source receptor matrix The extracted source-receptor matrix is ​​updated by the matrix scaling factor; Based on the updated source-receptor matrix The regularization parameter λ is automatically selected using the cross-validation method, and the LBFGS algorithm is used to iteratively estimate the release rate corresponding to each source position; The source position with the optimal simulation-observation error index is searched based on the release rate as the source localization result.

3. The method for iterative reconstruction and uncertainty quantification of leakage sources based on spatial priors according to claim 2, wherein: The updated source receptor matrix The regularization parameter λ is automatically selected using the cross-validation method, 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 The regularization parameter λ is automatically selected using the cross-validation method; 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 the gradient information Until the iteration termination condition is reached, the corresponding source position is obtained The optimal release rate 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 The regularization parameter λ is automatically selected using a cross-validation method, including: Set the regularization parameter range to λ∈[1e-6,1]; For each candidate regularization parameter λ, the source-receptor matrix The monitoring data f 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. 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.

5. 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 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 continuous 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.

6. 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 location 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 the 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 total variation non-smooth constraint to obtain the release rate estimation result of time series variation; Uncertainty quantification module, used to design a Bayesian framework to obtain the uncertainty distribution of source location and release rate estimation results through Monte Carlo sampling; 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, the release period is 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; 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 result r e Extract the corresponding source-receptor matrix And based on the release rate estimated by 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. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any one of the methods of claims 1 to 5 .

8. 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 according to claims 1 to 5.

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