A core power distribution reconstruction method for handling detector movement

Abstract

The present invention proposes a method for reconstructing the core power distribution that handles detector movement. By dividing the effective domain with the detector position as the core, the observation values ​​of the detector are distributed in the space belonging to the same area, and then constructing an observation field with the same resolution as the high-resolution physical field. Based on a large number of samples of the observation field and the high-dimensional observation field, a convolutional neural network is used for training, and finally a neural network that infers the physical field from the observation is obtained. Based on this neural network, the problem of physical field reconstruction under small movements of the detector position can be handled, and a core power distribution reconstruction system that handles detector movement can be constructed. Based on the test of 2D IAEA, the present invention found that when the detector movement position is limited to 5cm, the mean square error of the reconstructed fast thermal group flux and power distribution is within 5%, which meets the engineering accuracy requirements.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor core operation and safety technology, and in particular to an online reconstruction method for core power distribution based on a deep machine learning method. Background Art

[0002] Online monitoring of nuclear reactor core power distribution is crucial for ensuring reactor core safety and improving the economic efficiency of nuclear power plants. However, core power distribution is not a directly monitored variable; rather, it is measured indirectly through neutron flux density. To measure core neutron flux density in real time, neutron detectors are installed inside or outside the reactor. However, these detectors are located at specific locations and are limited in number. Therefore, to achieve spatially continuous real-time monitoring of power distribution, it is essential to develop online reconstruction methods for core power distribution.

[0003] One of the core technologies of the core monitoring system is the core physical field reconstruction algorithm, specifically how to reconstruct the full reactor power distribution from limited internal and external detector readings. Scholars at home and abroad have conducted extensive research on this issue, with a key branch focusing on reconstruction methods based on the background physical field distribution.

[0004] This type of physical field reconstruction method uses a given background physical field distribution and, using measured values ​​from internal and external detectors, corrects or fits the background to obtain the measured core power distribution. The background physical field is typically derived from theoretical calculations or measured distributions from a previous moment, and there is a certain deviation from the current actual power distribution. Key methods for this type of physical field reconstruction include interpolation fitting, coupling coefficient methods, and data assimilation.

[0005] 1) Interpolation Fitting Methods: The BEACON system developed by Westinghouse uses spline function interpolation to reconstruct the physical field based on the deviation between the measured and theoretically calculated physical fields at the measured points. Other methods include the weight coefficient method and the ordinary Kriging method, which were developed earlier.

[0006] 2) Coupling Coefficient Method: The coupling coefficient method (CECOR) developed by Combustion Engineering has a simple calculation process and is widely used in engineering. Its core concept is to assume that the theoretical distribution is not much different from the actual distribution, which can basically describe the characteristics of the physical field. Small deviations between the theoretical and actual physical fields are corrected by combining field measurements with the coupling coefficient. Webb improved the coupling coefficient method and developed the Lagrange multiplier method, which has a calculation concept and accuracy similar to CECOR.

[0007] 3) Data assimilation: Data assimilation is a method that aims to integrate new observational data into the dynamic operation of the numerical model, taking into account the temporal and spatial distribution of data and the errors in the observation field and background field. It is a method that automatically adjusts the model trajectory by continuously integrating direct or indirect observation information with different sources and different resolutions of discrete temporal and spatial distributions through data assimilation algorithms within the dynamic framework of the process model, so as to improve the estimation accuracy of the dynamic model state and enhance the model's predictive ability. Data assimilation is particularly widely used in meteorology, weather forecasting, oceanography, environment and other fields to reconstruct physical fields by combining limited measured values ​​and theoretical values. Bryson first attempted to apply the Kalman filter method to the reconstruction of core power distribution; in recent years, research teams represented by Electricité de France (EDF) have conducted extensive research on the application of different data assimilation methods to core flux and power reconstruction.

[0008] According to data released by the International Atomic Energy Agency, over 60% of the world's nuclear power plants have been operating for more than 30 years, leading to the aging of these plants. The aging of nuclear power plant components causes vibrations within the reactor core, which in turn causes vibrations in the neutron detectors installed within the core. However, almost all of the aforementioned methods lack the ability to reconstruct the physical fields in the presence of detector movement or vibration. Summary of the Invention

[0009] In response to the problem of inaccurate physical field reconstruction caused by the vibration of the core neutron detector due to the vibration of the internal components of the reactor core, the present invention proposes a set of core physical field reconstruction methods for processing the displacement of the detector relative to the original position. This method can reconstruct the core physical field distribution when the detector has a certain displacement, meeting the engineering accuracy requirements. The method provided by the present invention can be integrated into the existing nuclear power plant core online monitoring system to expand the functions of the core online monitoring system, especially to expand the ability to process the physical field reconstruction under the condition of detector vibration, and provide guarantees for the safe and economical operation of nuclear reactors. The method described in the present invention can be implemented on existing pressurized water reactors, and can also be used to expand the application to any other type of reactor with an in-core measurement system.

[0010] The present invention is achieved through the following technical solutions:

[0011] A method for reconstructing core power distribution by processing detector movement is characterized in that it comprises the following steps:

[0012] S1. Regularize the core geometry and expand it into a two-dimensional or three-dimensional rectangle Ω. The grid points are grouped into n x ×n y The total number of grid points is N, N = n x ×n y, the discrete representation of the physical field f(r) is

[0013] S2. Determine the distribution of core detector positions:

[0014] Assume that there are M detectors in the core, with positions r s =(r1,r2,…,r M ) T , for a given physical field f, at each detector location r i The observed value y i (f), the total observation vector is y(f) = (y1(f),y2(f),…,y M (f)) T , the superscript “T” indicates transpose;

[0015] S3. Determine the disturbance interval δ of the core detector at the nominal position, that is, the detector can be i For any activity in a square area with a length and width of 2δ as the center, the signal detected by the detector is the signal of the physical field at the current position of the square area;

[0016] S4. Divide the effective range of detector position:

[0017] Calculate the relationship between all grid points in the two-dimensional or three-dimensional rectangular Ω area and each detector position. k , calculated with r s The distance between the points in the i If point r is closest, k Classified into group i, we get a segmentation g1,g2,…,g in Ω M , regarded as detector r s Segmentation, each region g i Included in r i The i-th detector at ;

[0018] S5. Construct an observation field consistent with the structure of the physical field F

[0019] For each point Y(r k ), if r k In the split g i , then take the detector y i (f) The value of, that is, Y contains the detection values ​​and detector position information of M detectors;

[0020] S6. Based on S1-S5, a set of representations of the detector and the physical field in the same network structure is obtained, namely (Y, F);

[0021] S7. Determine the reactor operating parameter domain And in the running parameter domain Random sampling heap parameters in the formation of N sample The physical field F set of samples;

[0022] S8. Based on the detector vibration interval 2δ determined in S3, perform joint random sampling on specific positions within the vibration interval of the M detectors, and obtain a detector random position sample Y for a given physical field F;

[0023] S9. According to S7 and S8, obtain samples of detectors and physical fields under the same network structure

[0024] S10. Using deep convolutional neural network (CNN), Train to obtain the mapping relationship from Y to F, that is, the neural network model

[0025] S11. Physical field reconstruction:

[0026] After getting the trained neural network For the core detector configuration at any time, obtain the measurement value, repeat S5 according to the preparations of S1.-S4., and obtain the current observation field Y according to the detector's observation value y, and input it into the trained neural network model Obtain the reconstructed physical field distribution F.

[0027] Furthermore, the step S7 determines the reactor operating parameter domain And in the running parameter domain Random sampling heap parameters in the formation of N sample The physical field F set of samples includes:

[0028] S7.1 Assume that the nuclear reactor state parameters μ that affect the distribution of the physical field F are μ = (μ1, μ2, …, μ p ) T , μ i The operating parameters of the nuclear reactor are reactor power level, control rod position, burnup level, boron concentration and coolant inlet temperature.

[0029] S7.2 is the state parameter μ for each dimension (μ i ,i=1,2,…,p) determine a local interval [μ i -Δμ i ,μ i +Δμ i ], where Δμ i μ iThe domain formed by the offset values ​​of all p dimensions of the state parameter μ is called the operating parameter domain of the state parameter μ.

[0030] S7.3 in the operating parameter field The heap parameters are randomly sampled according to the sampling parameters μ sample , perform core physics calculations and obtain the corresponding physical field F, including power distribution P(r), fast group flux distribution φ1(r) and hot group flux distribution φ2(r), forming N sample A collection of physical fields F of samples.

[0031] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0032] 1. The present invention realizes the reconstruction of multiple physical fields of the reactor core, especially the rapid reconstruction of power distribution, fast group flux and thermal group flux.

[0033] 2. Compared with other conventional physical field reconstruction methods, the present invention has the ability to handle physical field reconstruction when the detector moves, which has never been achieved in previous technical solutions.

[0034] 3. The physical field reconstruction method provided by the present invention is fast. After the CNN is trained, the time required for physical field reconstruction for any new observation parameters is less than 0.1 second, which provides convenience for online power reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a schematic diagram of the regularized completion of the core geometry.

[0036] Figure 2 Schematic diagram of the detector vibrating near its nominal position

[0037] Figure 3 This is a schematic diagram of reconstructing fast group flux, hot group flux and power distribution based on hot group flux training.

[0038] Figure 4 This is the core layout of the 2D IAEA benchmark example.

[0039] Figure 5 is the 2D IAEA fast group flux distribution

[0040] Figure 6 is the reconstructed 2D IAEA fast group flux distribution, the detector is active within 1cm

[0041] Figure 7 is the 2D IAEA heat cluster flux distribution

[0042] Figure 8is the reconstructed 2D IAEA thermal cluster flux distribution, with the detector moving within 1 cm

[0043] Figure 9 is the 2D IAEA power distribution

[0044] Figure 10 is the reconstructed 2D IAEA power distribution, with the detector active within 1cm DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described below in conjunction with embodiments and drawings, but this should not limit the scope of protection of the present invention.

[0046] A method for reconstructing core power distribution by processing detector movement includes the following steps:

[0047] (1) Determine the canonical geometric representation of the core. To facilitate subsequent implementation, the given reactor core is expanded into a normal two-dimensional rectangle or three-dimensional cuboid Ω. For traditional pressurized water reactors, especially Figure 1 The core shown is padded into a normal cuboid (three-dimensional core) or rectangle (two-dimensional core). For ease of description, the following description is based on the two-dimensional case.

[0048] (2) Divide the reactor core grid point set into n x ×n y The total number of points is recorded as N = n x ×n y , the corresponding physical field f(r) (such as power distribution P(r), fast group flux distribution φ1(r) and hot group flux distribution φ2(r)) is expressed as For areas where core blanks are filled, the relevant value can be set to 0.

[0049] (3) Determine the nominal position distribution of the core detectors. Assume that there are M detectors in the core, with positions r s =(r1,r2,…,r M ) T , for a given physical field f, at each detector location r i The observed value is y i (f), the total observation vector is recorded as y(f) = (y1(f),y2(f),…,y M (f)) T The superscript “T” indicates transpose.

[0050] (4) Determine the perturbation interval of the core detector at the nominal position. The perturbation interval of the detector at the nominal position is δ, which means that the detector can be iFor any activity in a square area with a length and width of 2δ as the center, the signal detected by the detector is also the signal of the physical field at the current position of the square area.

[0051] (5) Divide the effective range of the detector position. According to the detector position r s , calculate N=n in the total area Ω x ×n y Position point to r s The relationship between the points, for the midpoint r k , calculated with r s The distance between the points in the i Click the nearest one, and r k Classified into group i, we get a segmentation g1,g2,…,g in Ω M , regarded as detector r s Each region g i Included in r i The i-th detector at .

[0052] (6) Construct an observation field consistent with the structure of the physical field F The construction method is as follows: For each point Y(r k ), if r k In the split g i , then take the detector y i (f) Thus, Y contains the detection values ​​of M detectors and also includes the segmentation information determined by the location of the detector, that is, the location information of the detector.

[0053] Based on steps (1) to (6), a set of representations of the detector and the physical field in the same network structure is obtained, namely (Y, F).

[0054] (7) Determine the reactor operating parameter domain. Assume that the nuclear reactor input parameters that affect the distribution of the physical field F are μ = (μ1, μ2, ..., μ p ) T , which can be reactor power level, control rod position, burnup level, boron concentration, coolant inlet temperature, etc. Its operating parameter domain is expressed as In one embodiment, each dimension (μ i ,i=1,2,…,p) determine a local interval, for example [μ i -Δμ i ,μ i +Δμ i ], where Δμ i It can be called μ i The domain formed by the offset values ​​of all p dimensions of the state parameter μ is called the parameter domain of the state parameter μ.

[0055] (8) In the operating parameter domain The heap parameters are randomly sampled according to the sampling parameters μ sample Based on the core physics calculation software (such as CORCA-3D), the core physics calculation is performed to obtain the corresponding physical fields (such as power distribution P(r), fast group flux distribution φ1(r) and hot group flux distribution φ2(r)), forming the N sample A collection of physical fields F of samples.

[0056] (9) Based on the detector vibration range 2δ determined by (4) and the physical field sample generated by (8), the specific positions within the vibration range of the M detectors are jointly randomly sampled. For a given physical field F, a detector random position sample Y can be obtained.

[0057] (10) Generate samples: According to the operations of (8) and (9), a large number of samples corresponding to the detector and the physical field can be obtained.

[0058] (11) Training: Using deep convolutional neural network (CNN), Perform training to obtain the mapping relationship from Y to F, that is The CNN training network proposed in this invention has specific training parameters that need to be determined based on the sample It is confirmed that the adopted method is consistent with the commonly used CNN training method.

[0059] (12) During training, the observation field Y is measurable, specifically the thermal mass flux in the core; the physical field F can be the thermal mass flux, the fast mass flux, or the power distribution. Different CNN networks can be trained based on different pairings. See Figure 3 .

[0060] (13) Physical field reconstruction: After obtaining the trained neural network For the core detector configuration at any time, relevant measurement values ​​are obtained. According to the preparations (1) to (5), step (6) is repeated. The current observation field Y can be obtained based on the detector observation value y. After inputting the trained network, the reconstructed physical field distribution F can be obtained.

[0061] Example:

[0062] Taking the 2D IAEA benchmark example certified by the International Atomic Energy Agency as an example, the physical field reconstruction process and effect provided by the present invention are demonstrated, with reference to the aforementioned steps (1) to (13).

[0063] First, the core geometry is regularized and supplemented into a rectangular shape.

[0064] Determine the detector location distribution. In this verification, a detector is installed at the center of each component.

[0065] The flux and power distribution of the core are obtained by calculating the two-group neutron diffusion equations based on core physics calculation software (such as CORCA-3D).

[0066] In order to obtain a large number of training samples, the present invention randomly samples the given parameters of the 2D IAEA benchmark example within the range of plus or minus 10%, performs core physics calculations, and obtains N sample A collection of physical fields F of samples.

[0067] The detector is sampled with observation values ​​in the vibration areas of 1cm, 3cm, and 5cm to construct the observation field Y corresponding to the physical field F.

[0068] Based on the convolutional neural network training, the model is obtained

[0069] Get the model After that, the discrete representation F of the corresponding physical field distribution f can be reconstructed according to any given observation value y.

[0070] Figure 5 Shows the 2D IAEA fast group flux distribution, Figure 6 Shown is the reconstructed 2D IAEA fast group flux distribution, with detector activity within 1 cm. Figure 7 shows the 2D IAEA heat cluster flux distribution, Figure 8 Shown is the reconstructed 2D IAEA thermal cluster flux distribution, with detector activity at 1 cm. Figure 9 shows the 2D IAEA power distribution, Figure 10 Shown is the reconstructed 2D IAEA power distribution with detector activity within 1 cm.

[0071] It can be found that the present invention can reconstruct the core physical field distribution with very high accuracy when the detector moves. After a large number of verifications, it was found that the present invention can reconstruct the physical field within 5 cm of the detector movement position, and the mean square error is within 5%, which meets the engineering accuracy requirements.

Claims

1. A method for reconstructing core power distribution by processing detector movement, characterized in that: The steps are as follows: S1. Regularize the core geometry and expand it into a two-dimensional or three-dimensional rectangle Ω. The grid points are grouped into n x ×n y The total number of grid points is N, N = n x ×n y , the discrete representation of the physical field f(r) is S2. Determine the distribution of core detector positions: Assume that there are M detectors in the core, with positions r s =(r1, r2, ..., r M ) T , for a given physical field f, at each detector location r i The observed value y i (f), the total observation vector is y(f) = (y1(f), y2(f), ..., y M (f)) T , the superscript "T" indicates transposition; S3. Determine the disturbance interval δ of the core detector at the nominal position, that is, the detector can be i For any activity in a square area with a length and width of 2δ as the center, the signal detected by the detector is the signal of the physical field at the current position of the square area; S4. Divide the effective range of detector position: Calculate the relationship between all grid points in the two-dimensional or three-dimensional rectangular Ω area and each detector position. k , calculated with r s The distance between the points in the i If point r is closest, k Classify into group i and obtain a segmentation g1, g2, ..., g in Ω M , regarded as detector r s Segmentation, each region g i Included in r i The i-th detector at ; S5. Construct an observation field consistent with the structure of the physical field F For each point Y(r k ), if r k In the split g i In the detector y i (f) The value of, that is, Y contains the detection values ​​and detector position information of M detectors; S6. Based on S1-S5, a set of representations of the detector and the physical field in the same network structure is obtained, i.e., (Y, F); S7. Determine the reactor operating parameter domain And in the running parameter domain Random sampling heap parameters in the formation of N sample The physical field F set of samples; S8. Based on the detector vibration interval 2δ determined in S3, perform joint random sampling on specific positions within the vibration interval of the M detectors, and obtain a detector random position sample Y for a given physical field F; S9. According to S7 and S8, obtain samples of detectors and physical fields under the same network structure S10. Using deep convolutional neural network CNN, Train to obtain the mapping relationship from Y to F, that is, the neural network model S11. Physical field reconstruction: After getting the trained neural network For the core detector configuration at any time, obtain the measurement value, repeat S5 according to the preparations of S1.-S4., and obtain the current observation field Y according to the detector's observation value y, and input it into the trained neural network model Obtain the reconstructed physical field distribution F.

2. The method for reconstructing core power distribution by processing detector movement according to claim 1, characterized in that: The step S7 determines the reactor operating parameter domain And in the running parameter domain Random sampling heap parameters in the formation of N sample The physical field F set of samples includes: S7.1 Assume that the nuclear reactor state parameters μ = (μ1, μ2, ..., μ p ) T , μ i The operating parameters of the nuclear reactor are reactor power level, control rod position, burnup level, boron concentration and coolant inlet temperature. S7.2 is the state parameter μ for each dimension (μ i , i=1,2,…,p) determine a local interval [μ i -Δμ i , μ i +Δμ i ], where Δμ i μ i The domain formed by the offset values ​​of all p dimensions of the state parameter μ is called the operating parameter domain of the state parameter μ. S7.3 in the operating parameter field The heap parameters are randomly sampled according to the sampling parameters μ sample , perform core physics calculations and obtain the corresponding physical field F, including power distribution P(r), fast group flux distribution φ1(r) and hot group flux distribution φ2(r), forming N sample A collection of physical fields F of samples.

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