A neutron spectrum decomposition method based on deep unfolding compressed sensing network

Abstract

The present invention provides a neutron spectrum decomposition method based on a deep expansion compressed sensing network, belonging to the technical field of neutron spectrum decomposition. The method uses multiple detectors to detect neutron energy to obtain multiple different response counts, and constructs a compressed sensing model for solving the neutron spectrum based on the response counts and the response function of the detectors; when solving the compressed sensing model according to an iterative shrinkage threshold algorithm, a gradient descent process and a proximal mapping process are required to design a deep expansion compressed sensing network composed of a CNN branch and a Transformer branch, and the network is trained to obtain a trained deep expansion compressed sensing network; the compressed sensing model is iteratively solved using the trained deep expansion compressed sensing network to obtain a final neutron spectrum. The present invention designs a deep expansion compressed sensing network based on compressed sensing theory, thereby decomposing the neutron spectrum and improving the accuracy of neutron spectrum decomposition.

Description

Technical Field

[0001] The present invention belongs to the technical field of neutron energy spectrum decomposition, and in particular relates to a neutron energy spectrum decomposition method based on a deep expansion compressed sensing network. Background Art

[0002] The neutron spectrum reflects the relative number or intensity distribution of neutrons of different energies in a radiation field. Accurately acquiring the full-energy spectrum of neutrons in a radiation field is essential for calculating the neutron dose equivalent around nuclear facility workplaces, providing crucial information for radiation protection. Neutron spectrum also has important applications in aerospace, nuclear explosion detection, nuclear arms control, and weapons verification.

[0003] Most existing neutron measurement methods solve the neutron energy spectrum based on the detector's response counts and energy response functions. Since the number of response counts is far smaller than the number of unknown quantities to be solved in the wide energy spectrum, this is a typical ill-posed problem. Currently, the commonly used neutron spectrum inversion algorithms include generalized least squares algorithms, maximum entropy algorithms, and artificial intelligence algorithms. Generalized least squares algorithms and maximum entropy algorithms appeared the earliest and are the most mature, but they are highly dependent on preset spectra and the solution error will increase significantly in unknown radiation environments. With the deepening of research and continuous advancement of technology, artificial intelligence algorithms such as genetic algorithms and neural networks are becoming more and more widely used in the field of neutron spectrum solution, but they still have problems in improving the accuracy of spectrum solution and adapting to complex problems.

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

[0005] In order to solve the above problems existing in the prior art, the present invention provides a neutron spectrum decomposition method based on a deep expansion compressed sensing network. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] A neutron energy spectrum decomposition method based on a deep expanded compressed sensing network includes:

[0007] S100, detecting neutrons using multiple detectors to obtain multiple different response counts, and constructing a compressed sensing model for solving the neutron energy spectrum based on the response counts and the response functions of the detectors;

[0008] S200, according to the gradient descent process and proximal mapping process required when solving the compressed sensing model by the iterative shrinkage threshold algorithm, designs a deep expanded compressed sensing network composed of CNN branches and Transformer branches, and trains it to obtain a trained deep expanded compressed sensing network; the deep expanded compressed sensing network includes The structure of the depth-expanded compressed sensing sub-network in each stage is the same, but the hyperparameters are different;

[0009] S300: Use the trained deep compressed sensing network to iteratively solve the compressed sensing model to obtain the final neutron energy spectrum.

[0010] Beneficial effects:

[0011] The present invention provides a neutron energy spectrum decomposition method based on a deep expansion compressed sensing network. Multiple detectors are used to detect neutron energy to obtain multiple different response counts, and a compressed sensing model for solving the neutron energy spectrum is constructed based on the response counts and the response function of the detectors. When solving the compressed sensing model according to an iterative shrinkage threshold algorithm, the required gradient descent process and proximal mapping process are used to design a deep expansion compressed sensing network composed of a CNN branch and a Transformer branch, and the network is trained to obtain a trained deep expansion compressed sensing network. The trained deep expansion compressed sensing network is used to iteratively solve the compressed sensing model to obtain a final neutron energy spectrum. The present invention designs a deep expansion compressed sensing network based on compressed sensing theory to decompress the neutron energy spectrum, thereby improving the decomposition accuracy of the neutron energy spectrum and having certain theoretical guidance significance and practical engineering application value for neutron energy spectrum measurement in the field of neutron detection.

[0012] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of a neutron energy spectrum decomposition method based on a deep expanded compressed sensing network provided by the present invention.

[0014] Figure 2 This is a schematic diagram of the deep expansion compressed sensing network structure designed by the present invention.

[0015] Figure 3 It is a schematic diagram of the network structure of the gradient descent process and the proximal mapping process in each iteration process provided by the present invention.

[0016] Figure 4 Schematic diagram of the network structure of the residual block provided by the present invention.

[0017] Figure 5 It is a schematic diagram of the network structure of the Transformer branch provided by the present invention.

[0018] 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.

[0019] Figure 7 It is a comparison diagram of the neutron energy spectrum calculated by the present invention and the standard energy spectrum of the pressurized water reactor stray neutron simulation field. DETAILED DESCRIPTION

[0020] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0021] like Figure 1 As shown, the present invention provides a neutron energy spectrum decomposition method based on a deep expansion compressed sensing network, comprising:

[0022] S100, detecting neutrons using multiple detectors to obtain multiple different response counts, and constructing a compressed sensing model for solving the neutron energy spectrum based on the response counts and the response functions of the detectors;

[0023] In a specific embodiment of the present invention, S100 includes:

[0024] S110, detecting neutrons in the environment using multiple detectors to obtain multiple different response counts;

[0025] S120, constructing a matrix equation using the detected response function and the response count;

[0026] For neutron measurements, the relationship between detector counts and neutron energy spectrum can be expressed by a matrix equation, which is expressed as:

[0027] (1);

[0028] Where, is composed of detector counts rank matrix, is the number of detectors; represents the energy response function, which is The matrix of order, describing detector pairs The response of the neutron energy group; represents the neutron spectrum, rank matrix, is the number of neutron energy groups. For the energy spectrum in the same energy range, The larger the value, the more detailed the characterization of the neutron energy spectrum.

[0029] S130, transforming the matrix equation according to the compressed sensing theory, and using the norm as a regularization term to obtain a compressed sensing model for solving the neutron energy spectrum.

[0030] use The norm is used as a regular term. According to the compressed sensing theory, Equation (1) can be transformed into an optimization problem, thereby obtaining a compressed sensing model, which can be expressed as follows:

[0031] (2);

[0032] Where, represents the regularization parameter, is a nonlinear sparse transformation, Express request of norm, The norm can be used as a measure of sparsity and is guaranteed to yield the sparsest solution.

[0033] S200, when solving the compressed sensing model according to the iterative shrinkage threshold algorithm, the required gradient descent process and proximal mapping process are used to design a deep expanded compressed sensing network composed of a CNN (deep learning neural network) branch and a Transformer branch, and train it to obtain a trained deep expanded compressed sensing network; the deep expanded compressed sensing network includes The structure of the depth-expanded compressed sensing sub-network in each stage is the same, but the hyperparameters are different;

[0034] It is worth noting that the iterative shrinkage threshold algorithm is a popular first-order approximation method. When solving the compressed sensing model, the gradient descent process and proximal mapping process required by the iterative shrinkage threshold algorithm are expressed as follows:

[0035] (3);

[0036] (4);

[0037] Where, represents the number of iterations, represents the iteration step size, Indicates the The intermediate reconstruction result (containing noise) solved by the iteration is Indicates the The denoised neutron energy spectrum obtained by the iteration is Indicates the The denoised neutron energy spectrum obtained by the iteration.

[0038] In order to give full play to the respective advantages of compressed sensing algorithm and deep learning, the present invention maps the update steps of the iterative shrinkage threshold algorithm to a deep learning network architecture consisting of a fixed number of layers. Each layer of the network corresponds to an iteration in the algorithm, and a deep expanded compressed sensing network for neutron energy spectrum decomposition is obtained. Its network structure is as follows Figure 2 At the same time, to further improve the accuracy and efficiency of reconstruction, the network abandons the manual parameter adjustment method and adopts an end-to-end autonomous learning strategy, which enables the network to adaptively learn and optimize the key parameters in the reconstruction process.

[0039] Combine Figure 2 and Figure 3 During each iteration, the input to the current deep-expanded compressed sensing subnetwork is the solution of the previous deep-expanded compressed sensing subnetwork. The estimated value is then updated via gradient descent, and finally denoised via the proximal mapping process to regenerate the neutron spectrum solution from the previous stage. The proximal mapping process is designed as a hybrid architecture consisting of a CNN branch and a Transformer branch. The CNN branch extracts local features to enhance the representation of details, while the Transformer branch captures long-range global contextual dependencies, effectively fusing local features with global information.

[0040] Combine Figure 3 and Figure 4 The CNN branch consists of two residual blocks connected in series. The CNN branch and the Transformer branch are two parallel branches. The outputs of both are connected to the input of the channel splicing layer. The output of the channel splicing layer is connected to the input of the first convolutional layer. The output of the first convolutional layer is the output of the depth-expanded compressed sensing sub-network.

[0041] refer to Figure 4 The CNN branch consists of two residual blocks connected in series. By introducing skip connections, the gradient vanishing problem in the deep layers of the deep expanded compressed sensing sub-network is effectively alleviated, allowing the deep expanded compressed sensing sub-network to stack more layers to extract higher-level features. The serial structure allows the low-level features extracted by the previous residual block to be fused with the high-level semantic features extracted by the next residual block through the channel splicing layer to form a hierarchical feature expression, 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 by merging the input data of the residual block with 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.

[0042] refer 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 feedforward network layer, a third normalization layer, a linear transformation layer and a position encoding module; wherein, the patch embedding module, the first normalization layer, the multi-head self-attention layer, the second normalization layer, the feedforward 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 to 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 feedforward network layer is merged with the second merged data to obtain the third merged data, and is output to the third normalization layer.

[0043] The Transformer branch of this invention introduces a Transformer encoder, leveraging its powerful self-attention mechanism to handle long-range dependencies in the data. The input is the neutron energy spectrum solution from the previous stage. The Patch Embedding module segments the one-dimensional input data into non-overlapping patches and maps each patch into an embedding space through convolution operations. The Positional Embedding module adds learnable position information to the patch sequence. After patch embedding and position encoding, the input data is passed through a multi-head self-attention layer to calculate the dependencies between all positions in the input data, capturing global context. The multi-head self-attention layer is followed by a feedforward network (MLP) consisting of two fully connected layers, a dropout layer, and a GELU activation function to enhance the model's nonlinear representation capabilities. The input data of both the multi-head self-attention layer and the feedforward network layer undergoes normalization to accelerate training and improve training stability. Furthermore, residual connections are introduced in both the multi-head self-attention layer and the feedforward network layer to mitigate the vanishing gradient problem.

[0044] The reconstructed results after processing by the CNN branch and the Transformer branch are spliced along the channel dimension, and then a convolutional layer is used to perform channel compression to obtain the output results of the deeply expanded compressed sensing sub-network at each stage.

[0045] In a specific embodiment of the present invention, training a deep expanded compressed sensing network to obtain a trained deep expanded compressed sensing network includes:

[0046] a. Obtain a training set consisting of standard neutron spectrum data;

[0047] b. Use the training set to iteratively train the deep expanded compressed sensing network, and during the training process, optimize the hyperparameters of the deep expanded compressed sensing network according to the direction of the loss function until the loss function converges, thereby obtaining a trained deep expanded compressed sensing network.

[0048] It is worth noting that the deep unfolded compressed sensing network is trained using the training set. During the training process, the loss function gradually decreases with the increase in the number of iterations and eventually converges (no longer changes). The hyperparameters of the deep unfolded compressed sensing network are continuously optimized in this process, thereby obtaining a trained deep unfolded compressed sensing network.

[0049] The standard energy spectrum published by the International Atomic Energy Agency (IAEA) was divided into a training set and a test set. A deep unfolded compressed sensing network (DCNS) was trained using the training set. The input of the spectral decomposition network model was the detector counts, and the output was the solved neutron energy spectrum. The mean squared error (MSE) was selected as the loss function. The performance of the spectral decomposition was observed by adjusting the hyperparameter combinations. The DCNS with the optimal hyperparameter combination was selected as the trained spectral decomposition model.

[0050] S300: Use the trained deep compressed sensing network to iteratively solve the compressed sensing model to obtain the final neutron energy spectrum.

[0051] The deep unfolded compressed sensing network trained in this step includes The hyperparameters of these sub-networks are the optimal hyperparameters when the loss function converges.

[0052] In order to verify the effectiveness of the spectrum decomposition method of the present invention, the present invention uses a trained deep expansion compressed sensing network to verify the spectrum decomposition effect of 40 groups of test data. Figure 6 and Figure 7 This is the decomposition effect of some classical energy spectra. The horizontal axis is neutron energy, and the vertical axis is neutron flux per unit interval. From the decomposition results, the neutron energy spectrum solved or reconstructed by the present invention is basically consistent with the test energy spectrum trend, 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 only a few areas have oscillation phenomena, and the overall fitting effect is good. The average MSE of the decomposition results of 40 groups of test energy spectra is 3.9×10 -4 The time for performing a spectrum decomposition calculation is less than 0.05s, and the calculation accuracy and speed have been greatly improved.

[0053] It is worth noting that the terms "first" and "second" in this disclosure are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of this disclosure, "plurality" means two or more, unless otherwise specifically defined.

[0054] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A neutron spectrum decomposition method based on a deep expanded compressed sensing network, characterized in that: include: S100, detecting neutrons using multiple detectors to obtain multiple different response counts, and constructing a compressed sensing model for solving the neutron energy spectrum based on the response counts and the response functions of the detectors; S200, according to the gradient descent process and proximal mapping process required when solving the compressed sensing model by the iterative shrinkage threshold algorithm, design a deep expanded compressed sensing network composed of a CNN branch and a Transformer branch, and train it to obtain a trained deep expanded compressed sensing network; the deep expanded compressed sensing network includes The structure of the depth-expanded compressed sensing sub-network in each stage is the same, but the hyperparameters are different; S300, iteratively solving the compressed sensing model using the trained deep expansion compressed sensing network to obtain a final neutron energy spectrum; S100 includes: S110, detecting neutrons in the environment using multiple detectors to obtain multiple different response counts; S120, constructing a matrix equation using the detected response function and the response count; S130, transforming the matrix equation according to compressed sensing theory, and using the norm as a regularization term to obtain a compressed sensing model for solving the neutron energy spectrum; The matrix equation is expressed as follows: （1）； Where, is composed of detector counts rank matrix, is the number of detectors; represents the energy response function, which is The matrix of order, describing detector pairs The response of the neutron energy group; represents the neutron spectrum, rank matrix, is the number of neutron energy groups; The compressed sensing model is expressed as follows: （2）； Where, represents the regularization parameter, is a nonlinear sparse transformation, Express request of norm; When the iterative shrinkage threshold algorithm solves the compressed sensing model, the gradient descent process and the proximal mapping process required are respectively expressed as follows: （3）； （4）； Where, represents the number of iterations, represents the iteration step size, Indicates the The intermediate reconstruction result obtained by the iteration is Indicates the The neutron energy spectrum solved by the iteration is Indicates the The neutron energy spectrum solved by the iteration.

2. The neutron spectrum decomposition method based on deep expansion compressed sensing network according to claim 1 is characterized in that: The CNN branch consists of two residual blocks connected in series. The CNN branch and the Transformer branch are two parallel branches. The outputs of both are connected to the input of the channel splicing layer. The output of the channel splicing layer is connected to the input of the first convolutional layer. The output of the first convolutional layer is the output of the depth-expanded compressed 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 by merging the input data of the residual block and the output data of the dropout layer is the output data of the residual block.

3. The neutron spectrum decomposition method based on deep expansion compressed sensing network according to claim 2 is characterized in that: The Transformer branch includes a patch embedding module, a first normalization layer, a multi-head self-attention layer, a second normalization layer, a feedforward network layer, a third normalization layer, a linear transformation layer and a position encoding module; wherein, the patch embedding module, the first normalization layer, the multi-head self-attention layer, the second normalization layer, the feedforward 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 first merged data, the first merged data is input to the first normalization layer, the output data of the multi-head self-attention layer is merged with the first merged data to obtain second merged data, and output to the second normalization layer, the output data of the feedforward network layer is merged with the second merged data to obtain third merged data, and output to the third normalization layer.

4. The neutron spectrum decomposition method based on a deep expansion compressed sensing network according to claim 2, characterized in that: The deep expansion compressed sensing network is trained to obtain a trained deep expansion compressed sensing network including: a. Obtain a training set consisting of standard neutron spectrum data; b. Iteratively train the deep expanded compressed sensing network using the training set, and optimize the hyperparameters of the deep expanded compressed sensing network in the direction of the decrease of the loss function during the training process until the loss function converges, thereby obtaining a trained deep expanded compressed sensing network.

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