A spectral recovery method and system based on a high-order correction equation

Abstract

The present application relates to a kind of energy spectrum recovery method and system based on high-order repair equation, comprising the following steps: the original energy spectrum obtained at each measuring point is preprocessed, obtains the m energy section information corresponding to the original energy spectrum at each measuring point;With the m energy section information corresponding to the original energy spectrum at each measuring point as initial condition, the energy spectrum distribution information under the preset range scene is recovered using the preset high-order repair equation and numerical solution mode.The present application can recover the energy spectrum distribution in a large range of space, and has good recovery effect for complex energy spectrum data with large noise and non-uniformity, solves the problem of weak adaptability of linear interpolation, and can be widely applied in nuclear application technology field.

Description

Technical Field

[0001] The present invention relates to an energy spectrum recovery method and system based on a high-order repair equation, belonging to the field of nuclear application technology. Background Art

[0002] In nuclear power plants, the energy distribution of radiation fields, as described by the energy spectrum, is crucial for nuclear safety. The energy spectrum provides information on the distribution of particle energies, enabling identification and quantitative analysis of nuclides and their concentrations. Furthermore, during nuclear facility operation, energy spectrum analysis helps personnel understand reactor status and determine any anomalies. It also helps nuclear facility operators monitor and assess radiation risks, including personnel radiation doses and environmental radiation levels. Excessive radiation doses can endanger human health, while elevated environmental radiation levels can also harm surrounding organisms and the ecological environment. By analyzing energy spectrum data, abnormal radiation doses and changes in the radiation environment can be detected promptly, enabling timely implementation of appropriate measures to ensure safety. Following a nuclear accident, energy spectrum data can also be used to identify radiation sources, assess radiation doses, infer the extent of contamination, and guide the development of emergency response plans.

[0003] Energy spectrum recovery technology uses a small number of energy spectrum sampling points to predict and calculate the energy spectrum distribution information for an entire region, or even the entire world. Energy spectrum recovery technology is affected by the spatial distribution of the sample points, data resolution, and accuracy. To address these issues, modern scientists have conducted extensive research and innovation to improve energy spectrum recovery technology. Common energy spectrum recovery methods include interpolation and statistical methods, which are briefly introduced below.

[0004] The core idea of ​​interpolation is to treat the spatial energy spectrum as a continuous function and use the energy spectra at known sampling points to infer the missing energy spectrum. This method has become the most commonly used approach for solving inverse problems due to its ease of implementation, low computational complexity, good performance for uniformly distributed samples, and low sensitivity to noise. However, interpolation requires assumptions about the spatial continuity and spatial correlation of the data, and is not suitable for situations where the data is dispersed or contains a large number of outliers and extreme values.

[0005] Statistical methods, on the other hand, recover the energy spectrum by exploring potential regions within multiple disordered, high-dimensional signals. This method can infer data using temporal and spatial relationships in an iterative process, with minimal prior information, and is applicable to different types of data. However, compared to interpolation methods, statistical methods are more complex and require more computational resources and time. Summary of the Invention

[0006] In response to the above problems, the purpose of the present invention is to provide an energy spectrum recovery method and system based on a high-order repair equation. This method is based on the energy spectrum information of a small number of sample points and uses a numerical iterative method with accelerated solution to accurately restore the energy spectrum distribution in a large range of space.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides an energy spectrum recovery method based on a high-order repair equation, comprising the following steps:

[0009] Preprocess the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point;

[0010] Taking the m energy band information corresponding to the original energy spectrum at each measuring point as the initial conditions, the energy spectrum distribution information under the preset range scenario is restored using the preset high-order repair equation and numerical solution method.

[0011] Furthermore, the pre-processing of the original energy spectrum obtained at each measuring point includes normalizing, weighting and accumulating the original energy spectrum.

[0012] Furthermore, the energy spectrum distribution information in a preset range scenario is restored using the m energy band information corresponding to the original energy spectrum at each measuring point as initial conditions and a preset high-order repair equation and a numerical solution method, including:

[0013] ①Establish the initial space matrix u0 of m energy segments respectively;

[0014] ② Determine the high-order repair equation and set the equation parameters and maximum number of iterations N of the high-order repair equation. max Set up;

[0015] ③ Use the initial space matrix u0 of the j-th energy segment to reconstruct and restore the j-th energy segment of all unknown measurement points in the preset large-scale scene;

[0016] ④ Determine whether the set maximum number of iterations has been reached. If not, set i+1 and return to step ③. If so, proceed to step ⑤ to reconstruct the next energy segment.

[0017] ⑤ Determine whether all energy segments have been processed. If not, set j+1 and return to step ③. If so, all energy segments are reconstructed and enter step ⑥;

[0018] ⑥ Process the energy segment data of all unknown measurement points in the preset range scene to obtain the complete energy spectrum distribution of the preset range scene.

[0019] Furthermore, the high-order repair equation adopts TV-H -1 Equation for the TV-H-1 The convex splitting method and the fast Fourier transform method are used to solve the equations.

[0020] Furthermore, the processing of the energy segment data of all unknown measurement points in the preset range scene to obtain the complete energy spectrum distribution of the preset range scene includes:

[0021] The energy band data of all unknown measurement points are denormalized and merged to obtain the complete energy spectrum distribution of the preset large-scale scene.

[0022] In a second aspect, the present invention provides an energy spectrum recovery system based on a high-order repair equation, comprising:

[0023] The data preprocessing module is used to preprocess the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point;

[0024] The energy spectrum recovery module is used to restore the energy spectrum distribution information in a preset range scenario using the m energy band information corresponding to the original energy spectrum at each measuring point as the initial condition, and using the preset high-order repair equation and numerical solution method.

[0025] Furthermore, the energy spectrum recovery module includes:

[0026] The initial space matrix establishment module is used to establish the initial space matrix u0 of the m energy segments of each measuring point;

[0027] The parameter setting module is used to determine the high-order repair equation and set the equation parameters and the maximum number of iterations N of the high-order repair equation. max Set up;

[0028] The energy segment recovery module is used to obtain the energy segments of all unknown measurement points by using the initial space matrix u0 of each energy segment and performing iterative calculations for a preset maximum number of iterations using a determined high-order repair equation;

[0029] The energy segment reconstruction module is used to process the energy segment data of all unknown measurement points in the preset range scene to obtain the complete energy spectrum distribution of the preset range scene.

[0030] 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 of the methods described.

[0031] In a fourth aspect, the present invention provides a computing device comprising: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the methods.

[0032] The present invention has the following advantages due to the adoption of the above technical solution:

[0033] 1. The present invention can restore the energy spectrum distribution in a large range of space, and has a good restoration effect on complex energy spectrum data with large noise and non-uniformity, solving the problem of weak adaptability of linear interpolation;

[0034] 2. The present invention adopts a numerical iterative method to accelerate the solution, which solves the problem of complex calculation and slow speed of statistical methods such as Gaussian process regression;

[0035] 3. The present invention can quickly and accurately restore the energy spectrum distribution information in a large range of space using the energy spectrum information of a small number of samples, solving the problem that existing interpolation methods and statistical methods require a large number of samples to support;

[0036] Therefore, the present invention can be widely applied in the field of nuclear application technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] 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:

[0038] Figure 1 This is a flow chart of an energy spectrum recovery method based on a high-order repair equation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0039] 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.

[0040] 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 application. As used herein, unless the context clearly indicates otherwise, the singular form is also 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.

[0041] Interpolation and statistical methods are currently common approaches for solving inverse problems. Common interpolation methods include linear interpolation, Lagrange interpolation, spline interpolation, kriging interpolation, and inverse distance weighted interpolation. Common statistical methods include Gaussian process regression, support vector regression, neural networks, Bayesian models, and Markov chain Monte Carlo methods.

[0042] The linear interpolation method assumes that the energy spectrum density is continuous and is suitable for relatively smooth energy spectrum data. However, real-world energy spectra often have large variance and noise, and the target energy spectrum may differ significantly from the original energy spectrum data. Therefore, the linear interpolation method is prone to errors and leads to low prediction accuracy. The Gaussian process regression method relies on the spatial correlation of energy spectrum data. It requires calculating the covariance matrix based on known sample points and estimating the energy spectrum of unknown sample points through Bayesian inference. Although this method can theoretically improve the accuracy of energy spectrum recovery, it has high computational complexity and has difficulty handling energy spectra in non-stationary or non-Gaussian conditions.

[0043] Based on the above analysis, in some embodiments of the present invention, a method for energy spectrum recovery based on a high-order repair equation is provided. The method includes two parts: energy spectrum preprocessing and energy spectrum reconstruction based on a high-order repair equation. Based on the energy spectrum information of a small number of sample points, a numerical iterative method with accelerated solution is used to accurately restore the energy spectrum distribution in a large range of space.

[0044] Correspondingly, in other embodiments of the present invention, an energy spectrum recovery system, device and storage medium based on a high-order repair equation are provided.

[0045] Example 1

[0046] like Figure 1 As shown, this embodiment provides an energy spectrum recovery method based on a high-order repair equation, which includes two parts: energy spectrum preprocessing and energy spectrum reconstruction based on a high-order repair equation. Specifically, the method includes the following steps:

[0047] 1) Preprocessing the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point;

[0048] 2) Taking the m energy band information corresponding to the original energy spectrum at each measuring point as the initial condition, the energy spectrum distribution information in the preset large-scale scenario is restored using the preset high-order repair equation and numerical solution method.

[0049] Preferably, in step 1) above, when pre-processing the original energy spectrum at the measuring point, a smoothing accumulation method is used, specifically, including normalizing, weighting, and accumulating the original energy spectrum. Weighting the original energy spectrum can make the peak of the energy spectrum more prominent; accumulating the weighted energy spectrum can remove and reduce the noise added during the weighting process while enhancing the energy spectrum details. The new energy spectrum obtained in this way is wider, has reduced fluctuations, and is easier to analyze and identify. The method of weighting and accumulating is a well-known technology to those skilled in the art, and will not be described in detail in the present invention.

[0050] In fact, compared with the traditional smoothing and truncation method, this preprocessing method emphasizes the role of energy segment accumulation and averaging. It does not directly remove small peaks in the energy spectrum, but achieves a more effective smoothing effect by integrating scattered structures, realizing the functions of balancing peak positions, smoothing energy spectra, and reducing noise. At the same time, since the number of energy segments after accumulation is significantly reduced, the calculation time of subsequent energy spectrum reconstruction is greatly shortened, which is conducive to the realization of rapid energy spectrum recovery function.

[0051] Preferably, the above step 2) includes the following steps:

[0052] 2.1) Establish the initial space matrix u0 of each of the m energy segments;

[0053] 2.2) Determine the high-order repair equation and set the equation parameters and maximum number of iterations N of the high-order repair equation. max Set up;

[0054] 2.3) Using the initial spatial matrix u0 of the j-th energy segment, reconstruct and restore the j-th energy segment of all unknown measurement points in the preset large-scale scene;

[0055] 2.4) Determine whether each energy segment iteration has been completed, that is, determine whether the number of iterations i is less than the maximum number of iterations N. If so, set i + 1 and return to step 2.3); otherwise, proceed to step 2.5);

[0056] 2.5) Determine whether all energy segments have been reconstructed, that is, determine whether the number of reconstructions j is less than the total number of energy segments m. If so, set j + 1 and return to step 2.3); otherwise, proceed to step 2.6);

[0057] 2.6) Process the energy band data of all unknown measurement points in the preset large-scale scene to obtain the complete energy spectrum distribution of the preset large-scale scene.

[0058] Preferably, in the above step 2.3), when the j-th energy segment is reconstructed and restored using the initial space matrix u0 of the j-th energy segment, the following steps are included:

[0059] 2.3.1) Using the initial space matrix u0 of the j-th energy segment as the initial condition, perform repeated iterations based on the predetermined high-order repair equation and numerical solution format;

[0060] 2.3.2) Determine whether the number of iterations N reaches the maximum number of iterations N max If yes, stop the iteration and output the calculation result; otherwise, return to step 2.3.1) to continue the iterative calculation.

[0061] Preferably, in the above step 2.3.1), the high-order restoration equation selected in this embodiment is TV-H which has a good restoration effect in a large range of space. -1 The equation is expressed as:

[0062]

[0063] Transforming the above formula, we get:

[0064]

[0065] Among them, λ(x)(fu) is the fidelity term that ensures that the solution of the equation is consistent with the initial sparse measurement point value at any time, λ(x) is the regularization coefficient, δ is the diffusion parameter, and it is a constant that satisfies 0<δ<<1; λ(x) is a parameter that changes with spatial position and is defined as follows:

[0066]

[0067] Set the equation parameters, including the diffusion parameter δ and the fidelity term coefficient f.

[0068] Specifically, due to the TV-H -1 The equation is a fourth-order partial differential equation. Traditional Lagrange interpolation and Newton interpolation methods have problems such as limited interpolation accuracy and high complexity of coefficient matrix solution when solving high-order partial differential equations. Therefore, the present invention designs a new numerical solution method that combines the convex splitting method and the fast Fourier transform method. Compared with traditional interpolation methods, this method is extremely effective in solving high-order partial differential equations.

[0069] Specifically, the method includes the following steps:

[0070] Firstly, the high-order partial differential equation is decomposed using the convex splitting method to obtain multiple low-order partial differential equations.

[0071] Among them, after convex splitting formula (2), the obtained numerical equation is expressed as:

[0072]

[0073] Where u x 、uy 、u z is the first-order derivative of u in the x, y, and z directions, u xx 、u yy 、u zz 、u xy 、u xz 、u xy is u x 、u y 、u z The derivatives in the x, y, and z directions respectively.

[0074] After discretization, Equation (3) can be calculated using an unconditionally stable numerical stepping scheme, and the solution format is:

[0075]

[0076] Where C1>1 / ε, C2>1 / λ0, Δ is the Laplace operator, U N is the discretized u(x) at the Nth iteration.

[0077] Fast Fourier transform is used to accelerate the solution of the equation. The corresponding numerical solution format obtained from formula (5) is:

[0078]

[0079] Where, is U after fast Fourier transformation, and the eigenvalue is λ i .

[0080] The convex splitting method can decompose high-order partial differential equations into multiple low-order partial differential equations, and the spectral method of fast Fourier transform is used to accelerate the solution of spatial derivative terms. The combination of the two effectively solves the problems of computational efficiency and accuracy when solving high-order partial differential equations.

[0081] Preferably, in the above step 2.5), all reconstructed and restored energy data are processed, including: denormalizing the energy segment data of all unknown measurement points, and merging them to obtain a complete energy spectrum distribution of a preset large-scale scenario.

[0082] Because the energy spectrum restoration method proposed in this paper is based on an image restoration method using high-order partial differential equation models, it possesses various advantages of image restoration, such as the ability to restore large-scale, or even global, information from a small amount of information. In actual nuclear power plant scenarios, where energy spectrum information is very limited, this technology can be effectively used to quickly restore energy spectrum information over a large area. It is applicable to both small amounts of measured energy spectrum information and large amounts of simulated energy spectrum information. Furthermore, this technology is applicable to different radioactive source terms, such as photons and neutrons.

[0083] Example 2

[0084] The above-mentioned embodiment 1 provides an energy spectrum recovery method based on a high-order repair equation. Correspondingly, this embodiment provides an energy spectrum recovery system based on a high-order repair equation. The system provided in this embodiment can implement the energy spectrum recovery method based on a high-order repair equation 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 system of this embodiment is basically similar to the method embodiment, the description process of 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 merely illustrative.

[0085] The energy spectrum recovery system based on the high-order repair equation provided in this embodiment includes:

[0086] The data preprocessing module is used to preprocess the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point;

[0087] The energy spectrum recovery module is used to restore the energy spectrum distribution information in a preset range scenario using the m energy band information corresponding to the original energy spectrum at each measuring point as the initial condition, and using the preset high-order repair equation and numerical solution method.

[0088] Preferably, the energy spectrum recovery module includes:

[0089] The initial space matrix establishment module is used to establish the initial space matrix u0 of the m energy segments of each measuring point;

[0090] The parameter setting module is used to determine the high-order repair equation and set the equation parameters and the maximum number of iterations N of the high-order repair equation. max Set up;

[0091] The energy segment recovery module is used to obtain the energy segments of all unknown measurement points by using the initial space matrix u0 of each energy segment and performing iterative calculations for a preset maximum number of iterations using a determined high-order repair equation;

[0092] The energy segment reconstruction module is used to process the energy segment data of all unknown measurement points in the preset range scene to obtain the complete energy spectrum distribution of the preset range scene.

[0093] Example 3

[0094] This embodiment provides a processing device corresponding to the energy spectrum recovery method based on high-order repair equations 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.

[0095] 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 energy spectrum recovery method based on the high-order repair equation provided in Example 1.

[0096] In some embodiments, 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.

[0097] In other embodiments, the processor may be a central processing unit (CPU), a digital signal processor (DSP), or other general-purpose processors, which are not limited herein.

[0098] Example 4

[0099] The energy spectrum recovery method based on high-order repair equations 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 energy spectrum recovery method based on high-order repair equations described in this embodiment 1 are loaded.

[0100] 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.

[0101] 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 spectrum recovery method based on a high-order repair equation, characterized in that: The following steps are involved: Preprocessing the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point; the preprocessing of the original energy spectrum obtained at each measuring point includes normalizing, weighting and accumulating the original energy spectrum; Taking the m energy band information corresponding to the original energy spectrum at each measuring point as the initial condition, the energy spectrum distribution information under the preset range scenario is restored using the preset high-order repair equation and numerical solution method, including: ① For unknown measurement points, establish the initial space matrix of the m energy segments of the measurement point ; ② Determine the high-order repair equation and adjust the equation parameters and maximum number of iterations of the high-order repair equation Set up; the high-order repair equation uses TV-H -1 Equation for the TV-H -1 When solving the equations, the convex splitting method and the fast Fourier transform method are used; ③ Using the initial space matrix of the jth energy segment Reconstruct and restore the jth energy segment of all unknown measurement points in a preset large-scale scenario; ④ Determine whether the equation iteration is completed. If not, set i+1 and return to step ③. If so, go to step ⑤ to reconstruct the next energy segment. ⑤ Determine whether all energy segments have been processed. If not, set j+1 and return to step ③. If so, all energy segments are reconstructed and enter step ⑥; ⑥ Denormalize the energy band data of all unknown measurement points in the preset range scenario, and merge them to obtain the complete energy spectrum distribution of the preset range scenario.

2. An energy spectrum recovery system based on a high-order repair equation, characterized in that: include: A data preprocessing module is used to preprocess the original energy spectrum obtained at each measuring point to obtain m energy segment information corresponding to the original energy spectrum at each measuring point; the preprocessing of the original energy spectrum obtained at each measuring point includes normalizing, weighting and accumulating the original energy spectrum; The energy spectrum recovery module is used to recover the energy spectrum distribution information in a preset range scenario using the m energy band information corresponding to the original energy spectrum at each measuring point as the initial conditions, and using the preset high-order repair equation and numerical solution method; The initial space matrix establishment module is used to establish the initial space matrix of m energy segments at each measuring point ; Parameter setting module, used to determine the high-order repair equation, and the equation parameters and maximum number of iterations of the high-order repair equation Set up; the high-order repair equation uses TV-H -1 Equation for the TV-H -1 When solving the equations, the convex splitting method and the fast Fourier transform method are used; Energy segment recovery module, used to use the initial space matrix of each energy segment After the iterative calculation of the preset maximum number of iterations for the determined high-order repair equation, the energy segments of all unknown measuring points are obtained; The energy segment reconstruction module is used to denormalize the energy segment data of all unknown measurement points in the preset range scene, and merge them to obtain the complete energy spectrum distribution of the preset range scene.

3. 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 2 .

4. A computing device, characterized in that include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any one of the methods according to claims 1 to 2.

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