Neutron spectrum unfolding method based on deep expansion compressed sensing network

Abstract

The invention provides a neutron energy spectrum unfolding method based on a deep expansion compressed sensing network, and belongs to the technical field of neutron energy spectrum unfolding, a plurality of detectors are used for detecting neutrons to obtain a plurality of different response counts, and a compressed sensing model for solving a neutron energy spectrum is constructed according to the response counts and response functions of the detectors; according to a required gradient descent process and a near-end mapping process when the compressed sensing model is solved by an iterative shrinkage threshold algorithm, designing a deep expansion compressed sensing network composed of a CNN branch and a Transform branch, and training the deep expansion compressed sensing network to obtain a trained deep expansion compressed sensing network; and carrying out iterative solution on the compressed sensing model by utilizing the trained depth expansion compressed sensing network to obtain a final neutron energy spectrum. According to the method, a deep expansion compressed sensing network is designed according to a compressed sensing theory, so that spectrum unfolding of the neutron energy spectrum is carried out, and the spectrum unfolding precision of the neutron energy spectrum can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of neutron energy spectrum deconvolution, and particularly relates to a neutron energy spectrum deconvolution method based on a deep unfolded compressive sensing network. Background Technique

[0002] The neutron energy spectrum reflects the relative quantity or intensity distribution of neutrons with different energies in the radiation field. In the radiation field environment, accurately obtaining the full energy range spectrum of neutrons is the basic basis for calculating the neutron ambient dose equivalent in the workplace of nuclear facilities, providing important reference information for radiation protection. In addition, the neutron energy spectrum also has important application values in aerospace, nuclear explosion detection, nuclear arms control, and weapon verification.

[0003] Most existing neutron measurement methods solve the neutron energy spectrum based on the response count of the detector and the energy response function. Since the number of response counts is much smaller than the number of unknowns to be solved in the wide energy range spectrum, it is a typical ill-posed problem. Currently, the commonly used neutron energy spectrum inversion algorithms mainly include the generalized least squares algorithm, the maximum entropy algorithm, and artificial intelligence algorithms, etc. The generalized least squares algorithm and the maximum entropy algorithm appeared earliest and are the most maturely developed, but they have a large dependence on the preset spectrum, and the solution error will increase significantly in an unknown radiation environment. With the in-depth research and continuous progress of technology, artificial intelligence algorithms such as genetic algorithms and neural networks are more and more widely used in the field of neutron energy spectrum solution, but there are still problems in improving the deconvolution accuracy and adapting to complex problems.

[0004] In recent years, researchers have proposed a method to solve the neutron energy spectrum using the compressive sensing theory, which can achieve high-precision reconstruction of the neutron energy spectrum. The compressive sensing theory points out that on the premise that the signal to be reconstructed satisfies sparsity, a small amount of sampling data can be used to accurately recover the signal. Therefore, this theory is particularly suitable for solving highly underdetermined problems. When using the compressive sensing theory to solve problems, its reconstruction algorithms are mainly divided into traditional reconstruction algorithms and deep learning-based reconstruction algorithms. Some scholars have proved that the compressive sensing reconstruction algorithm based on deep learning can significantly improve the reconstruction effect. However, in existing research, there is only a compressive sensing neutron energy spectrum deconvolution method based on traditional reconstruction algorithms, and the compressive sensing reconstruction algorithm based on deep learning has not been applied in the field of neutron deconvolution. There is still a large room for improvement in the deconvolution accuracy and deconvolution speed of using the compressive sensing algorithm to solve the neutron energy spectrum. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a neutron energy spectrum deconvolution method based on a deep unfolded compressive sensing network. The technical problems to be solved by the present invention are realized through the following technical solutions: A neutron energy spectrum deconvolution method based on a deep unfolded compressive sensing network includes: S100. Detect neutrons using multiple detectors to obtain multiple different response counts, and construct a compressive sensing model for solving the neutron energy spectrum based on the response counts and the response function of the detectors; S200. When solving the compressive sensing model according to the iterative shrinkage threshold algorithm, design a deep unfolded compressive sensing network composed of a CNN branch and a Transformer branch based on the required gradient descent process and proximal mapping process, and train it to obtain a trained deep unfolded compressive sensing network; The deep unfolded compressive sensing network includes phases of deep unfolded compressive sensing sub-networks. The structures of the deep unfolded compressive sensing sub-networks in each phase are the same, but the hyperparameters are different; S300. Use the trained deep unfolded compressive sensing network to iteratively solve the compressive sensing model to obtain the final neutron energy spectrum.

[0006] Beneficial effects: The present invention provides a method for solving the neutron energy spectrum based on a deep unfolded compressive sensing network. Detect neutrons using multiple detectors to obtain multiple different response counts, and construct a compressive sensing model for solving the neutron energy spectrum based on the response counts and the response function of the detectors; Design a deep unfolded compressive sensing network composed of a CNN branch and a Transformer branch based on the required gradient descent process and proximal mapping process when solving the compressive sensing model according to the iterative shrinkage threshold algorithm, and train it to obtain a trained deep unfolded compressive sensing network; Use the trained deep unfolded compressive sensing network to iteratively solve the compressive sensing model to obtain the final neutron energy spectrum. The present invention designs a deep unfolded compressive sensing network based on the compressive sensing theory to perform the solution of the neutron energy spectrum, which can improve the solution accuracy of the neutron energy spectrum and has certain theoretical guiding significance and practical engineering application value for the neutron energy spectrum measurement in the field of neutron detection.

[0007] The following will further elaborate on the present invention in conjunction with the drawings and embodiments. Description of the drawings

[0008] Figure 1 is a schematic flowchart of a method for solving the neutron energy spectrum based on a deep unfolded compressive sensing network provided by the present invention.

[0009] Figure 2 is a schematic structural diagram of the deep unfolded compressive sensing network designed by the present invention.

[0010] Figure 3 is a schematic structural diagram of the network of the gradient descent process and the proximal mapping process in each iteration provided by the present invention.

[0011] Figure 4 is a schematic structural diagram of the residual block provided by the present invention.

[0012] Figure 5 It is a schematic diagram of the network structure of the Transformer branch provided by the present invention.

[0013] Figure 6 It is a comparison diagram of the neutron energy spectrum calculated by the present invention and the standard energy spectrum of the fuel storage facility.

[0014] Figure 7 It is a comparison diagram of the neutron energy spectrum calculated by the present invention and the standard energy spectrum of the PWR stray neutron simulation field. Detailed implementation manners

[0015] The present invention will be further described in detail below in conjunction with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0016] As Figure 1 shown, the present invention provides a method for solving the neutron energy spectrum based on a deep unfolding compressive sensing network, including: S100, using a plurality of detectors to detect neutrons to obtain a plurality of different response counts, and constructing a compressive sensing model for solving the neutron energy spectrum according to the response counts and the response function of the detectors; In a specific implementation manner of the present invention, S100 includes: S110, using a plurality of detectors to detect the neutrons in the environment to obtain a plurality of different response counts; S120, constructing a matrix equation using the detected response function and the response counts; For neutron measurement, the relationship between the detector count and the neutron energy spectrum can be represented by a matrix equation, and the matrix equation is expressed by the formula: (1); In the formula, is an -order matrix composed of detector counts, is the number of detectors; represents the energy response function, which is an -order matrix, describing the response of detectors to neutron energy groups; represents the neutron energy spectrum, which is an -order matrix, is the number of neutron energy groups. For the energy spectrum in the same energy range, the larger it is, the finer the description of the neutron energy spectrum.

[0017] S130, transforming the matrix equation according to the compressive sensing theory, and using the norm as a regularization term to obtain a compressive sensing model for solving the neutron energy spectrum.

[0018] Adopt The norm is used as the regularization term. According to the compressive sensing theory, Equation (1) can be transformed into an optimization problem, and thus the compressive sensing model is obtained, which is expressed by the formula as: (2); In the formula, represents the regularization parameter, is the non-linear sparse transformation, represents to find of norm, The norm can be used as a measure of sparsity and ensure the sparsest solution is obtained.

[0019] S200. When solving the compressive sensing model according to the iterative shrinkage threshold algorithm, the required gradient descent process and proximal mapping process are designed to form a deep unfolded compressive sensing network composed of a CNN (deep learning neural network) branch and a Transformer branch, and it is trained to obtain a trained deep unfolded compressive sensing network; the deep unfolded compressive sensing network includes stages of deep unfolded compressive sensing sub-networks. The structures of the deep unfolded compressive sensing sub-networks in each stage are the same, but the hyperparameters are different; It should be noted that the iterative shrinkage threshold algorithm is a popular first-order approximation method. When solving the compressive sensing model by the iterative shrinkage threshold algorithm, the required gradient descent process and proximal mapping process are respectively expressed by the formulas as: (3); (4); In the formula, represents the number of iterations, represents the iteration step size, represents the intermediate reconstruction result (with noise) solved in the th iteration, represents the denoised neutron energy spectrum solved in the th iteration, represents the denoised neutron energy spectrum solved in the th iteration.

[0020] In order to give full play to the respective advantages of the compressive sensing algorithm and deep learning, the present invention maps the update steps of the iterative shrinkage threshold algorithm to a deep learning network architecture composed of a fixed number of layers. Each layer of the network corresponds to an iteration in the algorithm, and a deep unfolded compressive sensing network for neutron energy spectrum deconvolution is obtained. Its network structure is as Figure 2As shown. At the same time, in order to further improve the accuracy and efficiency of reconstruction, the network abandons the manual parameter adjustment method and instead adopts an end-to-end autonomous learning strategy, enabling the network to adaptively learn and optimize the key parameters in the reconstruction process.

[0021] Combined with Figure 2 and Figure 3 , in the iterative process of each stage, the input of the current deep unfolding compressive sensing sub-network is the solution result of the deep unfolding compressive sensing sub-network of the previous stage. Then, the estimated value is updated through the gradient descent process, and finally, the proximal mapping process is used for denoising to regenerate the solution result of the neutron energy spectrum in this stage. The proximal mapping process is designed as a hybrid architecture composed of a CNN branch and a Transformer branch. The CNN branch is used to extract local features to enhance the representation ability of details; the Transformer branch is used to capture long-range global context dependencies to achieve effective fusion of local features and global information.

[0022] Combined with Figure 3 and Figure 4 , the CNN branch consists of two cascaded residual blocks. The CNN branch and the Transformer branch are two parallel branches, and their outputs are connected to the input of the channel concatenation layer. The output of the channel concatenation layer is connected to the input of the first convolutional layer, and the output of the first convolutional layer is the output of the deep unfolding compressive sensing sub-network.

[0023] Referring to Figure 4 , the CNN branch consists of two cascaded residual blocks. By introducing skip connections, the problem of gradient disappearance in the deep layers of the deep unfolding compressive sensing sub-network is effectively alleviated, enabling the deep unfolding compressive sensing sub-network to stack more layers to extract higher-level features. The cascaded structure allows the low-level features extracted by the previous residual block to be fused with the high-level semantic features extracted by the subsequent residual block through the channel concatenation layer to form a hierarchical feature representation, which is suitable for high-precision feature extraction tasks in complex scenarios. The residual block includes a second convolutional layer, a Relu activation function, a third convolutional layer, and a dropout layer connected in sequence. The data obtained after merging the input data of the residual block and the output data of the dropout layer is the output data of the residual block. The dropout layer is used to prevent the model from overfitting.

[0024] Referring to Figure 5, the Transformer branch includes a patch embedding module, a first normalization layer, a multi-head self-attention layer, a second normalization layer, a feed-forward network layer, a third normalization layer, a linear transformation layer, and a positional encoding module; among them, the patch embedding module, the first normalization layer, the multi-head self-attention layer, the second normalization layer, the feed-forward network layer, the third normalization layer, and the linear transformation layer are connected in sequence. The output data of the positional encoding module is merged with the output data of the patch embedding module to obtain the first merged data. The first merged data is input into the first normalization layer. The output data of the multi-head self-attention layer is merged with the first merged data to obtain the second merged data and output to the second normalization layer. The output data of the feed-forward network layer is merged with the second merged data to obtain the third merged data and output to the third normalization layer.

[0025] The Transformer branch of the present invention introduces a Transformer encoder and uses the powerful self-attention mechanism of the Transformer encoder to handle long-range dependencies in the data. The input is the solution result of the neutron energy spectrum in the previous stage. The patch embedding module divides the one-dimensional input data into non-overlapping patches and maps each patch to the embedding space through a convolution operation. The positional encoding module adds learnable position information to the patch sequence. After the input data passes through patch embedding and positional encoding, the multi-head self-attention layer calculates the dependencies between all positions in the input data to capture global context information. The backend of the multi-head self-attention layer is the feed-forward network layer (MLP), which consists of two fully connected layers, a dropout layer, and a GELU activation function to enhance the nonlinear expression ability of the model. The input data of both the multi-head self-attention layer and the feed-forward network layer passes through a normalization layer to accelerate the training speed and improve training stability. In addition, residual connections are introduced in the multi-head self-attention layer and the feed-forward network layer to alleviate the problem of gradient disappearance.

[0026] The reconstruction results after being processed by the CNN branch and the Transformer branch are concatenated along the channel dimension, and then a convolutional layer is used for channel compression to obtain the output result of the depth unfolding compressed sensing sub-network at each stage.

[0027] In a specific embodiment of the present invention, training the depth unfolding compressed sensing network to obtain a trained depth unfolding compressed sensing network includes: a. Obtain a training set composed of standard neutron energy spectrum data; b. Use the training set to iteratively train the deep unfolded compressive sensing network, and during the training process, optimize the hyperparameters of the deep unfolded compressive sensing network in the direction of the decrease of the loss function until the loss function converges, so as to obtain a trained deep unfolded compressive sensing network.

[0028] It should be noted that when using the training set to train the deep unfolded compressive sensing network, during the training process, the loss function gradually decreases with the increase of the number of iterations and finally converges (no longer changes). The hyperparameters of the deep unfolded compressive sensing network are continuously optimized during this process, so as to obtain a trained deep unfolded compressive sensing network.

[0029] Divide the standard energy spectrum released by the International Atomic Energy Agency (IAEA) into a training set and a test set. Use the training set to train the deep unfolded compressive sensing network. The input of the spectral deconvolution network model is the detector count, and the output is the solved neutron energy spectrum. Select the mean square error (MSE) as the loss function. Adjust the hyperparameter combination to observe the spectral deconvolution effect, and select the deep unfolded compressive sensing network with the optimal hyperparameter combination as the trained spectral deconvolution model.

[0030] S300. Use the trained deep unfolded compressive sensing network to iteratively solve the compressive sensing model to obtain the final neutron energy spectrum.

[0031] The trained deep unfolded compressive sensing network in this step includes stages of deep unfolded compressive sensing sub-networks, and the hyperparameters of these sub-networks are the optimal hyperparameters when the loss function converges.

[0032] To verify the effectiveness of the spectral deconvolution method of the present invention, the present invention uses the trained deep unfolded compressive sensing network to verify the spectral deconvolution effect of 40 groups of data in the test set. Figure 6 and Figure 7 are the spectral deconvolution effects on some classic energy spectra. The horizontal axis is the neutron energy, and the vertical axis is the neutron fluence in the unit interval. From the spectral deconvolution results, the neutron energy spectrum solved or reconstructed by the present invention is basically consistent with the trend of the test energy spectrum, and can accurately reflect the energy spectrum peak position. At the same time, the neutron energy spectrum curve solved by the present invention has good smoothness, and there are only oscillations in very few regions, and the overall fitting effect is good. The mean value of MSE of the spectral deconvolution results of 40 groups of test energy spectra is 3.9×10 -4 , and the time for one spectral deconvolution calculation is less than 0.05 s, and both the calculation accuracy and the calculation speed have been greatly improved.

[0033] It should be noted that the terms "first" and "second" in the present invention are only for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality of" means two or more, unless otherwise specifically defined.

[0034] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as falling within the protection scope of the present invention.

Claims

1. A method for neutron energy spectrum deconvolution based on a deep unfolded compressive sensing network, characterized in that, Including: S100: Detect neutrons using multiple detectors to obtain multiple different response counts, and construct a compressive sensing model for solving the neutron energy spectrum according to the response counts and the response function of the detectors; S200. When solving the compressive sensing model according to the iterative shrinkage threshold algorithm, design a deep unfolding compressive sensing network composed of a CNN branch and a Transformer branch according to the required gradient descent process and proximal mapping process, and train it to obtain a trained deep unfolding compressive sensing network; the deep unfolding compressive sensing network includes stages of deep unfolding compressive sensing sub-networks. The structures of the deep unfolding compressive sensing sub-networks in each stage are the same, but the hyperparameters are different. S300: Use the trained deep unfolded compressive sensing network to iteratively solve the compressive sensing model to obtain the final neutron energy spectrum.

2. The method for neutron energy spectrum deconvolution based on a deep unfolding compressive sensing network according to claim 1, wherein S100 includes: S110: Detect neutrons in the environment using multiple detectors to obtain multiple different response counts; S120: Construct a matrix equation using the detected response function and the response counts; S130: Transform the matrix equation according to compressive sensing theory, and use the norm as a regularization term to obtain a compressive sensing model for solving the neutron energy spectrum.

3. The method for neutron energy spectrum deconvolution based on a deep unfolding compressive sensing network according to claim 2, wherein The matrix equation is expressed by the formula: （1）； Wherein, is the matrix composed of detector counts of order ; represents the energy response function, which is a matrix of order and describes the response of detectors to neutron energy groups; represents the neutron energy spectrum, which is a matrix of order ; is the number of neutron energy groups; The compressive sensing model is expressed by the formula: （2）； Wherein, represents a regularization parameter, is a non-linear sparse transform, represents the operation of for norm.

4. The method for neutron energy spectrum deconvolution based on a deep unfolding compressive sensing network according to claim 3, characterized in that, When the iterative shrinkage threshold algorithm solves the compressive sensing model, the required gradient descent process and proximal mapping process are respectively expressed by the formulas: （3）； （4）； In the formula, represents the number of iterations, represents the iteration step size, denotes the intermediate reconstruction result obtained from the -th iteration, denotes the neutron energy spectrum obtained from the -th iteration, denotes the neutron energy spectrum obtained from the -th iteration.

5. The method for neutron energy spectrum deconvolution based on a deep unfolding compressive sensing network according to claim 4, wherein The CNN branch consists of two cascaded residual blocks. The CNN branch and the Transformer branch are two parallel branches. Their outputs are connected to the input of the channel concatenation layer. The output of the channel concatenation layer is connected to the input of the first convolutional layer. The output of the first convolutional layer is the output of the deep unfolded compressive sensing sub-network. The residual block includes a second convolutional layer, a Relu activation function, a third convolutional layer, and a dropout layer connected in sequence. The data obtained after merging the input data of the residual block and the output data of the dropout layer is the output data of the residual block.

6. The method for neutron energy spectrum deconvolution based on a deep unfolding compressive sensing network according to claim 5, wherein The Transformer branch includes a patch embedding module, a first normalization layer, a multi-head self-attention layer, a second normalization layer, a feed-forward network layer, a third normalization layer, a linear transformation layer, and a position encoding module. Among them, the patch embedding module, the first normalization layer, the multi-head self-attention layer, the second normalization layer, the feed-forward network layer, the third normalization layer, and the linear transformation layer are connected in sequence. The output data of the position encoding module is merged with the output data of the patch embedding module to obtain the first merged data. The first merged data is input into the first normalization layer. The output data of the multi-head self-attention layer is merged with the first merged data to obtain the second merged data, and is output to the second normalization layer. The output data of the feed-forward network layer is merged with the second merged data to obtain the third merged data, and is output to the third normalization layer.

7. The method for neutron energy spectrum deconvolution based on the deep unfolding compressive sensing network according to claim 5, characterized in that, Training the deep unfolded compressive sensing network to obtain the trained deep unfolded compressive sensing network includes: a. Obtain a training set composed of standard neutron energy spectrum data; b. Use the training set to iteratively train the deep unfolded compressive sensing network, and optimize the hyperparameters of the deep unfolded compressive sensing network in the direction of the loss function decrease during the training process until the loss function converges, thereby obtaining the trained deep unfolded compressive sensing network.

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