Inversion method of atmospheric radioactive release source term under incomplete data

Abstract

The present invention relates to an atmospheric radioactive release source term inversion method under incomplete data conditions, comprising: S1, inputting and normalizing the transport matrix H m×n and the observation vector y obs m , m represents the amount of data provided by the measurement point during the complete simulation period, and n represents the time step of the simulation; S2, initialize the source term release rate vector σ n ; S3, solve the total variation regularization parameter λ; S4, obtain the cost function expression and its gradient expression; S5, set the constraint boundary of the solution; S6, update the source term release rate σ n ; S7, determine whether the convergence condition is met, if yes, go to S9, otherwise go to S8; S8, determine whether the number of iterations reaches N max If yes, go to S9, otherwise return to S6; S9, solve the release rate σ n Denormalization is performed to obtain the source term inversion results based on incomplete observation data.

Description

Technical Field

[0001] The present invention relates to a method, system, equipment and medium for inverting atmospheric radioactive release source terms under incomplete data conditions, and relates to the field of nuclear application technology. Background Art

[0002] In the event of a nuclear accident or accidental release of radionuclides, the accuracy of source term information directly impacts the outcome of radionuclide release consequence assessments and, in turn, emergency response decisions. The source term refers to the temporal variation of the release rate of radionuclides. Source term inversion is a method for obtaining the source term by solving an inverse problem based on environmental radioactivity monitoring data. For a particular type of source term, the basic principle of release rate inversion is to use the measured values ​​and location information of the monitoring point, meteorological data (such as temperature, wind speed, wind direction, and atmospheric stability), and topographic data as inputs, calculate the source term-site response matrix using an atmospheric diffusion model, and then derive the source term release rate based on this response matrix. Regularization methods, such as the Tikhonov regularization method, are often used to derive such ill-posed inverse problems. These regularization methods require prior information and proceed by minimizing the difference between the atmospheric diffusion model's predictions and actual measurements.

[0003] However, in practical applications, monitoring sites are often sparse, providing limited usable measurement data, and this data is subject to uncertainty. This leads to missing and incomplete valid data, resulting in significant meaningless fluctuations in the source term inversion results. Prior information on the source term is difficult to obtain, and existing atmospheric diffusion models are subject to calculation errors. Factors such as incomplete data and model errors can lead to significant deviations between the solution to the inverse problem of source term inversion and the exact result.

[0004] Incomplete observational data poses numerous challenges for estimating the release rate of atmospheric radioactive source terms, such as exacerbating temporal fluctuations in the release rate and introducing spurious releases into the source term estimate. Some characteristics of the release rate can be incorporated into the inversion process as priors to address the deficiencies in environmental monitoring data. However, these highly constrained priors require expert analysis based on core inventories, accident phenomena, reactor physics, or comprehensive information, making the construction of appropriate prior information difficult. Summary of the Invention

[0005] In response to the above problems, the purpose of the present invention is to provide a method, system, equipment and medium for inverting the source term of atmospheric radioactive release in the case of incomplete data, which can compensate for the information loss caused by insufficient monitoring data and reduce the time series oscillation of the estimated source term.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a method for inverting atmospheric radioactive release source terms in the presence of incomplete data, comprising:

[0008] S1. Input and normalize the transport matrix H m×n and the observation vector y obs m , m represents the amount of data provided by the measurement points during the complete simulation period, and n represents the time step of the simulation;

[0009] S2, initialize the source release rate vector σ n ;

[0010] S3, solve the total variation regularization parameter λ;

[0011] S4. Obtain the cost function expression and its gradient expression;

[0012] S5. Set the constraint boundary of the solution;

[0013] S6, Update source term release rate σ n ;

[0014] S7, determine whether the convergence condition is met, if yes, go to S9, otherwise go to S8;

[0015] S8. Determine whether the number of iterations reaches N max If yes, go to S9, otherwise return to S6;

[0016] S9, the release rate σ obtained by solution n Denormalization is performed to obtain the source term inversion results based on incomplete observation data.

[0017] The atmospheric radioactive release source term inversion method further comprises the following steps:

[0018] The normalized representation of the transport matrix is ​​H m×n / coef;

[0019] The normalized representation of the observation vector is y obs m / coef;

[0020] Among them, the normalization factor coef takes the observation vector y obs m The largest element in absolute value.

[0021] The atmospheric radioactive release source term inversion method further adopts a GCV generalized cross validation method to solve the total variation regularization parameter λ.

[0022] The atmospheric radioactive release source term inversion method further has a cost function expression as follows:

[0023]

[0024] The gradient expression of the cost function is:

[0025]

[0026] The atmospheric radioactive release source term inversion method further adopts the high L-BFGS-B algorithm to solve the cost function and its gradient to update the source term release rate σ n .

[0027] The atmospheric radioactive release source term inversion method further comprises the following steps: determining the projection gradient component ||gcost(k)|| ∞ Whether the convergence condition pgtol is met, pgtol is set to 1e-5.

[0028] The atmospheric radioactive release source term inversion method further includes the release rate σ n The denormalization process is: σ n Multiply by the normalization factor coef.

[0029] In a second aspect, the present invention further provides a system for inverting atmospheric radioactive release source terms in the case of incomplete data, the system comprising:

[0030] Parameter setting unit, used to input and normalize the transport matrix and observation vector and initialize the source term release rate vector;

[0031] Parameter solving unit, used to solve the total variation regularization parameter λ;

[0032] The source release rate update unit is used to obtain the cost function expression and its gradient expression, set the constraint boundary of the solution, and update the source release rate σ n ;

[0033] A convergence condition judgment unit, used to judge whether the convergence condition is met;

[0034] Release rate inversion unit is used to solve the release rate σ n Denormalization is performed to obtain the source term inversion results based on incomplete observation data.

[0035] In a third aspect, the present invention also provides a processing device, which includes at least a processor and a memory, and a computer program is stored on the memory. The device is characterized in that when the processor runs the computer program, it executes the method for inverting the atmospheric radioactive release source term under incomplete data conditions.

[0036] In a fourth aspect, the present invention further provides a computer storage medium having computer-readable instructions stored thereon, wherein the computer-readable instructions can be executed by a processor to implement the atmospheric radioactive release source term inversion method under the aforementioned incomplete data condition.

[0037] The present invention has the following advantages due to the adoption of the above technical solution:

[0038] 1. Since the present invention uses a total variation regularization term, the solution of the regularization parameter is based on the GCV generalized cross-validation algorithm, and the solution of the cost function is based on the L-BFGS-B local minimization algorithm. This can compensate for the information loss caused by insufficient monitoring data and reduce the time series oscillation of the estimated source term;

[0039] 2. The present invention can estimate the release rate of atmospheric radioactive release sources using incomplete observational data. This has been verified using the European tracer experiment scenario. The resulting release rate has significantly reduced temporal oscillations, and the estimation of the initial release time is relatively accurate.

[0040] In summary, the present invention can directly perform an ideal inversion of atmospheric radioactive release source terms from incomplete monitoring data, and can be widely used in the inversion of atmospheric radioactive release source terms. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] 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:

[0042] Figure 1 This is a flow chart of a method for inverting source terms of atmospheric radioactive releases according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0044] It should be understood that the terms used herein are for the purpose of describing specific example embodiments only and are not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms "one", "an" and "said" as used herein may also be meant to include plural forms. The terms "comprise", "include", "contain" and "have" are inclusive and therefore specify the presence of stated features, steps, operations, elements and / or parts, but do not exclude the presence or addition of one or more other features, steps, operations, elements, parts, and / or combinations thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring them to be performed in the specific order described or illustrated, unless the order of execution is clearly indicated. It should also be understood that additional or alternative steps may be used.

[0045] For ease of description, spatially relative terms may be used herein to describe the relationship of one element or feature relative to another element or feature as shown in the figures, such as "inside," "outside," "inner side," "outer side," "lower," "upper," etc. Such spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures.

[0046] The present invention provides a method, system, device and storage medium for inverting atmospheric radioactive release source terms under incomplete data conditions, including: S1, inputting and normalizing the transport matrix H m×n and the observation vector y obs m , m represents the amount of data provided by the measurement point during the complete simulation period, and n represents the time step of the simulation; S2, initialize the source term release rate vector σ n ; S3, solve the total variation regularization parameter λ; S4, obtain the cost function expression and its gradient expression; S5, set the constraint boundary of the solution; S6, update the source term release rate σ n ; S7, determine whether the convergence condition is met, if yes, go to S9, otherwise go to S8; S8, determine whether the number of iterations reaches N max If yes, go to S9, otherwise return to S6; S9, solve the release rate σ n Denormalization is performed to obtain the source term inversion result based on incomplete observation data. This can compensate for information loss caused by insufficient monitoring data and reduce the time series oscillation of the estimated source term. The present invention can obtain the estimated result of the release rate of the atmospheric radioactive release source term based on incomplete observation data.

[0047] Example 1

[0048] like Figure 1 As shown, the inversion method for atmospheric radioactive release source terms under incomplete data provided in this embodiment includes the following contents:

[0049] S1. Input and normalize the transport matrix H m×n and the observation vector y obs m ;

[0050] Specifically, the transport matrix H m×n Produced using an atmospheric diffusion model, m represents the amount of data provided by a measurement point during a complete simulation period, and n represents the simulation time step. If the number of measurement points is num, and the number of measurements at any measurement point during a complete simulation period is f, then m = num*f.

[0051] Observation vector y obs m It is composed of real environment monitoring data. The order of monitoring data in the observation vector should be consistent with the order of data in any column of the transport matrix.

[0052] Normalization processing, the normalization of the transport matrix can be expressed as H m×n / coef, the normalized observation vector can be expressed as y obs m / coef, where the normalization factor coef takes the observation vector y obs m The largest element in absolute value.

[0053] S2, initialize the source release rate vector σ n ;

[0054] Specifically, the source term release rate vector σ n It is composed of the source release rate at n moments, representing the source release in the n time steps. Specifically, the source release rate vector σ is initialized n , that is, all elements in the vector can be set to 0.

[0055] S3, using the GCV generalized cross validation method to solve the total variation regularization parameter λ;

[0056] Specifically, the total variation regularization parameter λ is used to maintain the source release rate vector σ in the iterative solution n The good property of is neither overfitting nor underfitting. The GCV generalized cross validation method is used to obtain the optimal solution of the total variation regularization parameter λ, that is, to solve the following formula:

[0057]

[0058] Where A(λ)=H(H T H+mλI) -1 H T ; m has the same value as in S1, I is the m×m unit matrix, and the tr() operator is used to find the trace of the matrix.

[0059] S4. Obtain the cost function expression and its gradient expression;

[0060] The mathematical problem described by the cost function is the source term inversion problem that needs to be solved. The direction of the minimum value of the cost function gradient is the direction of approach to the solution of the problem.

[0061] Specifically, the cost function expression is:

[0062]

[0063] The gradient expression of the cost function is:

[0064]

[0065] S5. Set the constraint boundary of the solution;

[0066] Specifically, input the number of iterations N max and convergence conditions;

[0067] Maximum number of iterations N max It can be set to 5000, as an example, but not limited to this

[0068] The projected gradient component threshold pgtol is set to 1e-5, which can be expressed as follows, that is, it is used to limit the infinite norm value of the cost function gradient obtained by the k-th iteration:

[0069] pgtol=||gcost (k) || ∞

[0070] The above constraint boundary parameters can be set as needed, and this is an example and is not limited to this.

[0071] S6. Update the source release rate σ using the L-BFGS-B local minimization algorithm n ;

[0072] Specifically, the L-BFGS-B algorithm is used to solve the above cost function and its gradient update source term release rate σ n The L-BFGS-B algorithm is an improvement to the quasi-Newton algorithm. Its basic idea is to only save and use the curvature information from the most recent iterations to construct an approximation of the Heisenberg matrix, thereby updating the solution. This reduces the algorithm's overhead. This example uses the L-BFGS-B integrated package for calculations.

[0073] S7, determine the projected gradient component ||gcost(k)|| ∞ Whether the convergence condition pgtol is met, if yes, go to S9, otherwise go to S8;

[0074] S8. Determine whether the number of iterations reaches N max If yes, go to S9, otherwise return to S6;

[0075] S9, the release rate σ obtained by solution n Perform denormalization, that is, give σ n Multiply by the normalization factor (σ n coef), and obtain the source term inversion results based on incomplete observation data. This source term inversion result can be used to obtain the time-series release rate changes of atmospheric radioactive leakage sources, assess the consequences of atmospheric radioactive releases, and support nuclear emergency decision-making.

[0076] Example 2

[0077] The above-mentioned embodiment 1 provides a method for inverting the source term of atmospheric radioactive release under incomplete data conditions. Correspondingly, this embodiment provides a source term inversion system based on incomplete data conditions. The source term release rate inversion system provided in this embodiment can implement the source term inversion of atmospheric radioactive release under incomplete data conditions based on the total variation regularization process of embodiment 1. The system can be implemented through software, hardware, or a combination of software and hardware. For example, the system can include integrated or separate functional modules or functional units to perform the corresponding steps in each method of embodiment 1. Since the source term release rate inversion system of this embodiment is basically similar to the method embodiment, the process described in this embodiment is relatively simple. For relevant details, please refer to the partial description of embodiment 1. The source term release rate inversion system of this embodiment is merely illustrative.

[0078] Specifically, this embodiment provides a system for inverting atmospheric radioactive release source terms in the case of incomplete data, the system comprising:

[0079] Parameter setting unit, used to input and normalize the transport matrix and observation vector and initialize the source term release rate vector;

[0080] Parameter solving unit, used to solve the total variation regularization parameter λ;

[0081] The source release rate update unit is used to obtain the cost function expression and its gradient expression, set the constraint boundary of the solution, and update the source release rate σ n ;

[0082] A convergence condition judgment unit, used to judge whether the convergence condition is met;

[0083] Release rate inversion unit is used to solve the release rate σ n Perform denormalization to obtain the source term inversion result based on incomplete observation data

[0084] Example 3

[0085] This embodiment provides a processing device for implementing the atmospheric radioactive release source term inversion method provided in the first embodiment under incomplete data conditions. 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 source term release rate inversion method of the first embodiment.

[0086] 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, it executes the method for inverting the source term of atmospheric radioactive releases under incomplete data conditions, as provided in the first embodiment.

[0087] 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.

[0088] 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.

[0089] Example 4

[0090] The method for inverting the source term of atmospheric radioactive release under incomplete data conditions in the first embodiment of the present invention is specifically implemented as a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing the method for inverting the source term of atmospheric radioactive release under incomplete data conditions described in the first embodiment of the present invention.

[0091] 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.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein, and these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for inverting atmospheric radioactive release source terms under incomplete data conditions, characterized by include: S1. Input and normalize the transport matrix H m×n and the observation vector y obs m , m represents the amount of data provided by the measurement points during the complete simulation period, and n represents the time step of the simulation; S2, initialize the source release rate vector σ n ; S3, solving the total variation regularization parameter λ, wherein the total variation regularization parameter λ is solved using the GCV generalized cross validation method; S4. Obtain the cost function expression and its gradient expression, where the cost function expression is: The gradient expression of the cost function is: Where y is the normalized observation vector; S5. Set the constraint boundary of the solution; S6, Update source term release rate σ n , where the L-BFGS-B algorithm is used to solve the cost function and its gradient update source term release rate σ n ; S7, determine whether the convergence condition is met, if yes, go to S9, otherwise go to S8; S8. Determine whether the number of iterations reaches N max If yes, go to S9, otherwise return to S6; S9, the release rate σ obtained by solution n Denormalization is performed to obtain the source term inversion results based on incomplete observation data.

2. The atmospheric radioactive release source term inversion method according to claim 1, characterized in that: The normalization process in S1 includes: The normalized transport matrix is ​​expressed as H = H m×n / coef; The normalized representation of the observation vector is y = y obs m / coef; Among them, the normalization factor coef takes the observation vector y obs m The largest element in absolute value.

3. The atmospheric radioactive release source term inversion method according to claim 1, characterized in that: The convergence condition judgment process is: judge the projected gradient component || gcost under the kth iteration step (k) || ∞ Whether the convergence condition pgtol is met, pgtol is set to 1e-5.

4. The atmospheric radioactive release source term inversion method according to claim 2, characterized in that: Release rate σ n The denormalization process is: σ n Multiply by the normalization factor coef.

5. A system for inverting atmospheric radioactive release source terms under incomplete data conditions, characterized in that: The system includes: Parameter setting unit, used to input and normalize the transport matrix and observation vector and initialize the source term release rate vector; A parameter solving unit is used to solve the total variation regularization parameter λ, wherein the total variation regularization parameter λ is solved using the GCV generalized cross validation method; The source release rate update unit is used to obtain the cost function expression and its gradient expression, set the constraint boundary of the solution, and update the source release rate σ n , where the cost function expression is: The gradient expression of the cost function is: Where y is the normalized observation vector; The L-BFGS-B algorithm is used to solve the cost function and its gradient to update the source term release rate σ n ; A convergence condition judgment unit, used to judge whether the convergence condition is met; Release rate inversion unit is used to solve the release rate σ n Denormalization is performed to obtain the source term inversion results based on incomplete observation data.

6. A processing device, comprising at least a processor and a memory, wherein a computer program is stored in the memory, wherein: When the processor runs the computer program, it is executed to implement the atmospheric radioactive release source term inversion method under incomplete data conditions as described in any one of claims 1 to 4.

7. A computer storage medium, characterized in that Computer-readable instructions are stored thereon, and the computer-readable instructions can be executed by a processor to implement the method for inverting the source term of atmospheric radioactive release under incomplete data conditions as described in any one of claims 1 to 4.

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