A method and apparatus for processing physical field reconstruction with tolerance to detector vibrations and noise

Abstract

The present application provides a physical field reconstruction method for handling detector vibration and noise tolerance, which comprises adding random noise in the detector observation data and slightly disturbing the detector position. Through interpolation technology, the processed data is expanded to the same dimension as the physical field to be reconstructed, thereby creating an observation field consistent with the high-resolution physical field. The present application uses residual neural network, and uses the disturbed observation data as input. In the 2D IAEA data verification, the embodiment of the present application shows that when facing 5% noise, the framework of the present application can reduce the relative two norm error from 3.512% to 0.911%, and reduce the infinite norm error from 9.091% to 2.755%. In addition, when the disturbance range is 1 cm, the method of the present application can highly accurately reconstruct the physical field. The relative two norm error of the reconstructed physical field is about 0.1%, and the relative infinite norm error is about 1%, which obviously exceeds the requirement of the industrial standard.

Description

Technical Field

[0001] This invention relates to the field of physical field reconstruction, and more specifically to a physical field reconstruction method and apparatus for handling detector vibration and noise tolerance. Background Technology

[0002] Physical field reconstruction is a key technology widely used in the fields of science, engineering, and technology to acquire and reconstruct the distribution of a target physical field. These physical fields can include radiation fields, electromagnetic fields, temperature fields, pressure fields, and so on. Physical field reconstruction methods aim to estimate or reconstruct the true state of these physical fields using data obtained from detectors or sensors. This technology is crucial for solving problems in many fields, such as medical imaging, environmental monitoring, and industrial process control.

[0003] While physics field reconstruction demonstrates great potential in many applications, it is often affected by external disturbances such as detector vibration and noise in practical applications. These sources of vibration and noise may include mechanical vibration, electronic noise, and environmental noise. Such external disturbances can lead to distortion of detector data, thereby reducing the accuracy and reliability of physics field reconstruction.

[0004] Currently, there are some physical field reconstruction methods for handling vibration and noise tolerance, but they have the following three limitations:

[0005] I. Detector Vibration Issues: Existing physics field reconstruction methods have significant limitations in handling detector vibration issues. Detector vibration is a common phenomenon in practical applications, caused by various factors including mechanical vibration, fluid flow, and electronic equipment operation. This vibration interferes with the data acquired by the detector, thus affecting the accurate reconstruction of the physics field. Existing methods typically perform simple filtering or denoising on the vibration to attempt to mitigate its impact. However, the effectiveness of this approach is limited, especially in high-vibration environments. Vibration can lead to unstable data sampling, causing the detector's position to constantly change, thus introducing uncertainty and errors. This makes it difficult for traditional methods to accurately model and correct vibration data.

[0006] II. Noise in Observational Data: Observational noise is introduced from various sources, including electronic noise from electronic circuits, random errors in sensors, and environmental interference. This noise has a significant impact on the data acquired by the detector, making the reconstruction of the physical field difficult. Existing methods typically assume that the noise is random and attempt to reduce its impact through filtering or statistical methods. However, in some applications, the noise may exhibit non-random characteristics, such as periodic or nonlinear noise, making denoising more complex. The presence of noise also introduces additional requirements for data sampling and signal processing, thereby increasing the complexity and cost of the system.

[0007] Third, computational complexity: Existing physics reconstruction methods typically involve extensive numerical computation and data processing, leading to computational complexity issues. Some methods require high-performance computing resources, including high-speed processors and large amounts of memory, to handle large datasets. This increases hardware requirements and system costs. On the other hand, computational complexity also relates to algorithm runtime. In some real-time applications, physics reconstruction needs to be completed quickly to respond promptly to changing environmental conditions. Existing methods may not be efficient enough in this regard, failing to meet real-time requirements. Summary of the Invention

[0008] This invention aims to address the technical problems existing in the prior art mentioned above, including inaccurate reconstruction results caused by detector vibration and noise in the observation data, and the high computational complexity of traditional reconstruction methods. This invention proposes a neural network framework that is tolerant to detector noise and noise tolerance. This technology, based on residual neural networks, improves the accuracy and robustness of physical field reconstruction. It has achieved excellent reconstruction results on the IAEA-certified 2D IAEA benchmark problem for nuclear reactors and can be applied to multiple fields, including medical imaging, industrial monitoring, weather forecasting, and nuclear reactor operation, to provide a more reliable physical field reconstruction solution.

[0009] The technical solution of the present invention is as follows:

[0010] A physical field reconstruction method for handling detector vibration and noise tolerance is characterized by the following steps:

[0011] S1. Obtain the position and measurement values ​​of each detector in the physical field to be reconstructed. Where n x and n y These are the dimensions of the physical field in the x and y directions, respectively, and the position coordinates of all detectors are r = (r1, r2, ..., r...). M The measurements of all detectors are y = (y1, y2, ..., y...). M );

[0012] S2. Add random noise to the observations from each detector to obtain the observations with added random noise.

[0013] y i '=(1+σε i )y i , where y i It is the measurement value of the i-th detector, ε i It is a random number obtained from the standard normal distribution, and σ is the amplitude of the noise;

[0014] S3. Disturb each detector and record the measured values ​​of the detectors after the disturbance;

[0015] Let the coordinates be r i The detector's vibration range is in the range of r i A square region centered at a point with dimensions of 2δ+1.

[0016] Update the observed value y' to the data of the point after the disturbance, while keeping the coordinates as they were before the disturbance.

[0017] S4. Extend the detector's measurement y' to the physical field to be reconstructed. The same dimensions were used to obtain the expanded measurement values. This allows us to obtain a set of observational data and the real physical field (y”, φ) of the same dimension;

[0018] Preferably, the extension method is the nearest neighbor interpolation method, which first creates a space of size (n x ,n y The matrix is ​​calculated, and for each point, the nearest detector is calculated. The value of that detector is then assigned as its observed value y'. i .

[0019] S5. Determine the operating parameter domain of the physics field to be reconstructed, and randomly sample the stack parameters within this operating parameter domain to obtain multiple sets of physics field sets with different parameters Φ=(φ1,φ2,...,φ N ), where N is the number of samples;

[0020] Iterate through the N samples, add random noise to the observations of the M detectors for each sample, and perturb the positions of the detectors to obtain the perturbed observation data set Y;

[0021] The measurements from each detector in the observation dataset Y are extended to the same dimension (n) of the physics field to be reconstructed. x ,n y This forms a set (Y',Φ) containing multiple samples of measured values ​​and physical field data, where each sample represents a case under different physical field parameter settings;

[0022] S6. Construct and train a residual neural network, using the expanded set of measurements as input and the real physical field as output. By minimizing the mean square error between the real value of the physical field to be reconstructed and the physical field reconstructed by the neural network, obtain the mapping function from the expanded set of measurements Y' to the set of physical fields Φ. During training, the input of the neural network is Y', and the output is the physical field Φ' reconstructed by the neural network. By minimizing the mean square error between Φ' and the real physical field Φ, update the parameters of the residual neural network.

[0023] S7. Using the trained residual neural network, with the newly acquired expanded set of measurements as input, the output is the reconstructed physical field.

[0024] On the other hand, the present invention also provides a physical field reconstruction apparatus for processing detector vibration and noise tolerance, comprising a computer-readable storage medium and a processor, wherein the computer-readable storage medium stores an executable program, characterized in that, when the executable program is executed by the processor, the above-mentioned physical field reconstruction method for processing detector vibration and noise tolerance is implemented.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] 1. Compared to traditional techniques that use filtering methods to mitigate detector vibration, this invention employs a residual neural network, trained using observational data with vibration. This method combines the robustness and strong adaptability of residual neural networks to input data, thus maintaining excellent reconstruction performance even under high vibration conditions.

[0027] 2. This invention considers the impact of noise in observation data from real industrial environments on the reconstruction of physical fields, a factor not addressed by previous numerical reconstruction methods. By taking this into account, this invention exhibits strong robustness, providing high-quality reconstruction results even under severe noise interference.

[0028] 3. The physical field reconstruction method of this invention demonstrates outstanding efficiency in the industrial integration testing phase. The reconstruction of each physical field image requires only microseconds, significantly reducing computational costs compared to traditional methods. This makes this invention highly practical for industrial applications.

[0029] 4. Before using the framework of this invention, the relative L2 error of the reconstructed physical field of the residual neural network was 3.512% and the infinity norm error was 9.091% when facing 5% noise. However, by using the framework of this invention, the relative L2 error was reduced to only 0.911% and the infinity norm error was reduced to 2.755% when facing the same noise.

[0030] 5. The framework proposed in this invention performs excellently in handling detector vibration, maintaining a relative L2 error of 0.1% and a relative infinity L2 error below 1%. In contrast, existing best methods exhibit relative L2 errors as high as 1% and relative infinity L2 errors as high as 10% when dealing with detector vibration.

[0031] 6. The framework proposed in this invention can be easily integrated into industrial systems after the training phase, and its reconstruction process takes only microseconds, fully meeting the requirements for real-time reconstruction. This innovation will provide highly accurate and efficient physical field reconstruction technology support for the industrial field. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of noise with an amplitude of 0.05.

[0033] Figure 2 This is a schematic diagram of the disturbance when the detector disturbance radius is 1.

[0034] Figure 3 This is a diagram showing the observation data before and after dimensionality expansion. 'a' represents the data before expansion, and 'b' represents the data after expansion.

[0035] Figure 4 This is a schematic diagram of the residual neural network structure.

[0036] Figure 5 This is a 2D IAEA diagram.

[0037] Figure 6 This is a comparison of the infinite norm error between using the 2D IAEA power reconstruction of this invention and not using this invention under different noise conditions.

[0038] Figure 7 This is a comparison of the relative L2 error between using the 2D IAEA power reconstruction of this invention and not using this invention under different noise conditions.

[0039] Figure 8 It is a 2D IAEA power distribution.

[0040] Figure 9 It is a reconstructed 2D IAEA power error distribution Detailed Implementation

[0041] The technical solution of the present invention will be further described below with reference to the embodiments and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention.

[0042] A specific implementation scheme for a physical field reconstruction method for handling detector vibration and noise tolerance is as follows:

[0043] 1. First, obtain the positions of all detectors and their actual observations. Plot the detector coordinates as r = (r1, r2, ..., r...). M The observed values ​​are denoted as y = (y1, y2, ..., y3). M ), where M is the number of detectors.

[0044] 2. Adding random noise to the observation data. To simulate the situation where observation data contains noise in real industrial scenarios, the framework of this invention introduces a method for adding random noise to obtain a noise-tolerant model. Specifically, the steps for adding random noise are as follows: For the observation data y of each detector... i First, a random number ε is generated from the standard normal distribution. i Then, this random number is multiplied by a fixed noise amplitude σ. Finally, the resulting noise value is added to the original observation data. This process can be represented by the following formula: y' i =(1+σε i )y i . Figure 1 The example shows a randomly generated noise of size (9,9) when σ = 0.05.

[0045] 3. Simulating detector vibration. By making a small perturbation to the detector's position, this invention can simulate detector vibration that may occur in real industrial scenarios. Specifically, assuming the perturbation range of the detector is a certain value δ (e.g., 1 cm), this range is then considered as relative to the detector's current coordinate r. i Consider a square region centered at a point with sides of length 2δ+1. Within this square region, the detector vibrates to any point with equal probability. For example... Figure 2 As shown, when δ = 1, the possible range of motion of the detector is shown as the white square.

[0046] 4. Record the detector's observations. Record the physical field value y' = (y'1, y'2, ..., y') at the detector's location after the position perturbation in step 3. M The recorded detector coordinates are still r = (r1, r2, ..., r...). M This is because although the detector's position is disturbed in the simulation, in reality, the detector itself cannot sense these vibrations. Therefore, even if the detector's position is slightly disturbed, its coordinates remain unchanged.

[0047] 5. Dimensional Expansion of Observational Data. To facilitate neural network training, this invention employs nearest neighbor interpolation to expand the detector's observations to the same dimension as the physical field to be reconstructed. This expansion process includes the following steps: 1) Create a matrix with the same size as the physical field. 2) Traverse each point in the matrix. 3) For each point, find the nearest detector and set the element value of that point in the matrix to be equal to the observation data of the nearest detector. Through this process, we obtain an expanded observation matrix y”, whose dimension is the same as the physical field. Thus, we create a set of samples (y”, φ) containing the detector observations and the representation of the physical field to be reconstructed in the same dimension. Figure 3 The observation data before and after the dimensionality expansion is shown.

[0048] 6. Sampling for different physical field parameters. To obtain multiple different samples, this invention employs the following steps to randomly sample from the operating range of the physical field parameters, constructing a physical field dataset containing N samples: 1) Random sampling: Random sampling is performed from the operating domain of the physical field parameters to obtain physical field data under different parameter settings. 2) Adding random noise: For each sample, random noise is added to the detector's observation data according to the method in step 2 to simulate noise interference. 3) Position perturbation: For each sample, the detector's position is slightly perturbed according to the method in step 3 to simulate changes in the detector's position. 4) Observation data expansion: According to the process in step 5, the observation data is expanded to the same dimension as the physical field. Through the above steps, this invention generates a set (Y', Φ) of observation data and physical field data containing multiple samples, where each sample represents a situation under different physical field parameter settings. This multi-sample dataset is very valuable for training and testing neural network models, allowing for a more comprehensive evaluation of the model's performance and robustness.

[0049] 7. Training the Neural Network. Training the neural network is a crucial step in this invention. First, a residual neural network is constructed, where the input is the observed data Y', and the output is the physical field Φ' reconstructed by the neural network. The structure of this network is as follows: Figure 4 As shown, the network consists of 10 layers and is centrally symmetric to maintain consistency between the input and output dimensions. Mean squared error is then used to measure the difference between the physical field Φ' output by the neural network and the true physical field Φ. The Adam optimizer is then used to update the network parameters. The Adam optimizer is a commonly used gradient descent algorithm that effectively tunes network parameters to minimize the loss function. During training, observed data is input into the neural network, and the loss function is calculated. Then, backpropagation is used to calculate the gradient, and the Adam optimizer is used to update the network parameters to reduce the loss function. This process is repeated multiple times until the loss function converges to a small value or a predetermined number of training epochs are reached.

[0050] 8. Industrial Integration Testing. In the industrial integration testing phase, the residual neural network trained offline is successfully deployed to the online system. First, the online system needs to be ready to receive measurement data from the detectors. This data will be transmitted to the online system for processing at any given time. For the detector measurement data at each time point, step 5 is executed to expand the observation data to the same dimension as the physical field to be reconstructed. The expanded observation data is then input into the trained residual neural network. The neural network will perform forward propagation to reconstruct the corresponding physical field. This physical field data can be further processed in the online system or used for real-time monitoring and control systems.

[0051] Example:

[0052] The following are examples of 2D IAEA benchmark problems certified by the International Atomic Energy Agency (IAEA), demonstrating the physical field reconstruction process and effects provided by this invention:

[0053] First, the detector locations were determined. In this verification, a detector was installed at the center of each component, and the two groups of neutron diffusion equations were calculated using core physics calculation software (such as CORCA-3D) to obtain accurate data on the flux and power distribution of the core.

[0054] Next, training samples were obtained. In order to obtain a large number of training samples, random sampling was performed within a range of plus or minus 10% according to the given parameters of the 2D IAEA benchmark problem, and core physics calculations were performed to obtain a set Φ of N samples.

[0055] Then, random noise was added. To simulate a real industrial scenario, random noise of σ = 0.05 was added to the detector's observation data to make the model tolerant to noise. Furthermore, the vibration region of the detector in a specific area of ​​δ = 1 was perturbed to construct the observation field Y' corresponding to the physical field Φ.

[0056] A residual neural network was then constructed and trained using the aforementioned sample data. The goal of this neural network is to map the observed data to the physical field, thereby reconstructing the physical field.

[0057] Finally, the model is obtained. Once the model is trained, it has a discrete representation that can reconstruct the corresponding physical field distribution based on any given observation. This model has high accuracy and robustness and can be used for real-time physical field reconstruction and monitoring.

[0058] Figure 5 A schematic diagram of a 2D IAEA is shown. Figure 6In this paper, we compare the infinite norm error of reactor core power reconfiguration before and after using the framework of this invention. The green line represents the framework of this invention, while the blue line represents the case without using the framework of this invention. Figure 7 The comparison of the relative L2 error of nuclear reactor core power reconfiguration before and after using the framework of this invention is shown, where the green line represents the framework of this invention and the blue line represents the non-use of the framework of this invention. Figure 8 The 2D IAEA power distribution is shown, while Figure 9 The reconstructed 2D IAEA power error distribution is shown.

[0059] These charts clearly demonstrate that, when faced with 5% noise, this invention reduces the relative L2 error from 3.512% to 0.911% and the infinity norm error from 9.091% to 2.755%, exhibiting extremely strong robustness. Furthermore, even when the detector vibrates, the framework of this invention still maintains the relative L2 error within 0.1% and the infinity norm error within 1%, far exceeding the requirements for engineering accuracy. Additionally, it is noteworthy that, during the industrial integration testing phase, the reconstruction of each physical field requires only approximately 1 microsecond, meeting the requirements for integration into an online reconstruction system.

[0060] Through the above steps, this invention successfully demonstrates the physics field reconstruction process and effect on a 2D IAEA benchmark problem. This case proves that the present invention can achieve high-precision physics field reconstruction under complex conditions such as detector movement, observation noise, and vibration, far exceeding the performance of traditional methods. This technology has broad industrial application potential and can improve the performance and reliability of fields such as nuclear reactor safety monitoring.

Claims

1. A physical field reconstruction method for handling detector vibration and noise tolerance, characterized in that, The method includes the following steps: Obtain the position and measurement values ​​of each detector in the physical field; Random noise is added to the measurements of each detector; The position of each detector is disturbed, and the measured values ​​of the detectors after the disturbance are recorded; The detector's measurement value Extending to the same dimension as the physical field to be reconstructed, a sample table of detectors and the physical field to be reconstructed in the same dimension is obtained; The operating parameter domain of the physics field to be reconstructed is determined, and the stack parameters are randomly sampled within this domain. Random noise and perturbations are added to each sample, and the detector measurements are extended to the same dimension of the physics field to be reconstructed, forming a set of measurements and physics field data containing multiple samples. Each sample represents a situation under different physical field parameter settings; Construct and train a residual neural network, taking the expanded set of measurements as input and the real physical field as output. By minimizing the mean square error between the real value of the physical field to be reconstructed and the physical field reconstructed by the neural network, obtain the mapping function from the expanded set of measurements to the set of physical fields. By using a trained residual neural network, with the newly acquired expanded set of measurements as input, the output is the reconstructed physical field.

2. The physical field reconstruction method for handling detector vibration and noise tolerance according to claim 1, characterized in that, Random noise is added to the measurements of each detector, specifically including: Generate a random number from a standard normal distribution. ; Multiply the random number With noise amplitude The noise value is obtained; The noise value is added to the measured value, i.e. .

3. The physical field reconstruction method for handling detector vibration and noise tolerance according to claim 2, characterized in that, The noise amplitude The range is 0 to 0.

05.

4. The physical field reconstruction method for handling detector vibration and noise tolerance according to claim 1, characterized in that, The detector's measured values Extending to the same dimension as the physical field to be reconstructed, specifically including: Create a matrix The matrix size The same size as the physical field to be reconstructed; Traverse all points of the matrix to obtain the matrix. The assignment process involves setting the value of each element in the matrix to the measurement value of the detector closest to the point corresponding to that element, resulting in an expanded measurement matrix with the same dimension as the physical field. .

5. A physical field reconstruction apparatus for handling detector vibration and noise tolerance, comprising a computer-readable storage medium and a processor, wherein the computer-readable storage medium stores an executable program, characterized in that, When the executable program is executed by the processor, it implements the physical field reconstruction method for handling detector vibration and noise tolerance as described in any one of claims 1-4.

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