Method and system for calculating sensitivity coefficients of reactor core power distribution on-line monitoring

Abstract

The application discloses a reactor core power distribution online monitoring sensitivity coefficient calculation method and system, comprising: based on the assumption that the detector measurement signals do not affect each other, starting from the definition of the sensitivity coefficient, the analytic calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least square method as the power distribution reconstruction method is derived by using the analytic method; for the spline function fitting method, due to the use of the regularization coefficient, the analytic calculation formula of the sensitivity coefficient cannot be derived, so the direct numerical perturbation method can only be used for the solution of the sensitivity coefficient; in addition, if the assumption that the detector measurement signals are irrelevant is not established, no matter which reconstruction method is used, the direct numerical perturbation method needs to be used for the calculation of the sensitivity coefficient. Compared with the traditional method, the application has the advantages of fast sensitivity coefficient calculation speed and high calculation precision.

Description

Technical Field

[0001] This invention relates to the field of nuclear reactor engineering technology, specifically to a method and system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution. Background Technology

[0002] The results of online monitoring of reactor core power distribution will be used to determine parameters such as power peak factor and fuel burnup. These parameters directly affect the safety margin of the reactor core, and it is necessary to provide the confidence range of the calculated results. Therefore, uncertainty analysis of online monitoring of reactor core power distribution is particularly important.

[0003] The online core power distribution monitoring system combines theoretical calculations with detector measurement signals. Therefore, the online monitoring calculations include not only uncertainties introduced by solving the neutron diffusion equations (such as uncertainties introduced by parameters like nuclear data, core geometry, and core materials), but also uncertainties introduced by the measurement signals from the self-powered neutron detector. The uncertainties introduced by the self-powered neutron detector measurement signals are unique to the online core power distribution monitoring process; therefore, uncertainty analysis of the core monitoring results is required, specifically addressing the uncertainties introduced by the neutron detector measurement signals.

[0004] There are two main types of sensitivity and uncertainty analysis methods based on input parameters. One type is deterministic analysis, which first calculates the sensitivity coefficient, commonly using methods such as direct numerical perturbation and perturbation theory. Then, it calculates the uncertainty of the output parameter based on the input parameter uncertainty, covariance matrix, and sensitivity coefficient. The other type is probabilistic analysis, which first samples the input parameters based on their uncertainty and covariance matrix, generating a sample space. Then, it repeatedly performs neutronics correlation calculations to obtain the output result (response) corresponding to each different sample in the sample space. Finally, it performs statistical calculations on the response to obtain its expected value and variance, thus obtaining the uncertainty of the response. Summary of the Invention

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a method and system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution, which solves the problems of slow calculation speed and low calculation accuracy of traditional calculation methods.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] In a first aspect, the present invention provides a method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution, including: if the assumption that the detector measurement signals do not affect each other is valid, then the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method is derived using analytical methods; if the spline function fitting method and the assumption that the detector measurement signals are independent are not valid, the direct numerical perturbation method is used to solve for the sensitivity coefficient.

[0009] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the calculation of the analytical method includes:

[0010] For the harmonic expansion method, consider the expansion coefficient α. n The detector signal measurement value I(r) d Sensitivity coefficient Represented as:

[0011]

[0012] The reconstructed value P(r) of the core power distribution, calculated using the harmonic expansion method, is expressed as:

[0013]

[0014] Where, N order κ∑ represents the expansion order, G represents the number of energy groups, and κ∑ represents the expansion order. f,g (r) represents the heat release from fission in energy group g at position r, Φ n,g (r) represents the nth-order neutron flux density of the g energy group at position r;

[0015] Sensitivity coefficient considering the unfolding coefficient based on the core power distribution reconstruction value. Represented as:

[0016]

[0017] in:

[0018]

[0019] The sensitivity coefficient considering the expansion coefficient based on the core power distribution reconstruction value. Simplified to:

[0020]

[0021] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the analytical method further includes:

[0022] The reconstructed core power distribution value corresponds to the detector signal measurement value I(r)d Sensitivity coefficient The calculation is as follows:

[0023]

[0024] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the analytical method further includes:

[0025] For the detector signal:

[0026]

[0027] Where I(r) represents the detector signal measurement value at position r, S neutron (r) represents the seed sensitivity of the self-powered detector at position r;

[0028] Differentiate the above equation and divide both sides by dI(r) d We can obtain:

[0029]

[0030] If we assume that the detector measurements at different locations do not affect each other, then we have:

[0031]

[0032] Then for position r d The detector at that location has the following equation:

[0033]

[0034] ...

[0035]

[0036] ...

[0037]

[0038] By applying the least squares principle again, the expansion coefficient of the sensitivity coefficient can be solved, and the sensitivity coefficient of the reconstructed core power distribution value to the detector signal measurement value can also be calculated.

[0039] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the analytical method further includes:

[0040] The analytical method can also be applied in the least squares method, and its sensitivity coefficient is expressed as:

[0041]

[0042] For calculation Assuming that the detector measurements at different locations are independent, differentiate the above equation and divide both sides by dI(r). d Applying the least squares principle again, we can calculate the analytical form of the sensitivity coefficient in the least squares method, which is expressed as:

[0043]

[0044] Where M represents the number of detectors, k represents the eigenvalue, F represents the fission operator, ω represents the weighting coefficient, Φ represents the neutron flux density, and I represents the detector signal measurement.

[0045] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the calculation of the direct numerical perturbation method includes:

[0046] By numerically perturbing each input parameter, the change in the output parameter is calculated. The sensitivity coefficient is then calculated by substituting the derivative with the difference quotient. According to the definition of the sensitivity coefficient, we have:

[0047]

[0048] in, The power reconfiguration value P(r) at core r represents the value of power reconfiguration at core r. d The detector signal measurement value I(r) at the location d The sensitivity coefficient of I0(r) d ),I + (r d ) and I - (r d The ) represents the values ​​of r under no disturbance, positive disturbance, and negative disturbance. d The detector signal measurement values ​​at the location, P0(r), P + (r) and P - (r) represents the power reconstruction value at point r under the conditions of no disturbance, positive disturbance, and negative disturbance.

[0049] As a preferred embodiment of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to the present invention, the calculation of the direct numerical perturbation method further includes:

[0050] The online reconstruction calculations were performed (2M+1) times using the direct numerical perturbation method. Given the sensitivity coefficient, the uncertainty was calculated according to the "sandwich" principle.

[0051]

[0052] Where σ(P(r)) represents the absolute uncertainty of the reconstructed power distribution value, and σ(P(r)) / P(r) represents the relative uncertainty of the reconstructed power distribution value. and Indicates the power distribution reconstruction value with respect to r i and r j The relative sensitivity coefficient matrix of the detector signal measurement at point I(r) i ) and I(r j () represents the detector signal measurement value at any detector location. This represents the relative covariance matrix.

[0053] Secondly, the present invention provides a system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution, comprising:

[0054] The analytical method calculation unit is used to derive the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method if the assumption that the detector measurement signals do not affect each other is true.

[0055] The direct numerical perturbation method calculation unit is used to solve for the sensitivity coefficient by employing the direct numerical perturbation method when the spline function fitting method and the assumption that the detector measurement signal is independent do not hold.

[0056] Thirdly, the present invention provides a computing device, comprising:

[0057] Memory and processor;

[0058] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the method.

[0059] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the method.

[0060] Compared with existing technologies, the advantages of this invention are as follows: Based on the assumption that detector measurement signals do not interfere with each other, this invention derives analytical calculation formulas for the sensitivity coefficient using harmonic expansion and least squares methods as power distribution reconstruction methods, starting from the definition of the sensitivity coefficient. However, for the spline function fitting method, the use of regularization coefficients makes it impossible to derive analytical calculation formulas for the sensitivity coefficient; therefore, only the direct numerical perturbation method can be used to solve for the sensitivity coefficient. Furthermore, if the assumption that detector measurement signals are independent does not hold, the direct numerical perturbation method must be used to calculate the sensitivity coefficient regardless of the reconstruction method employed. Compared with traditional methods, this invention has the advantages of fast sensitivity coefficient calculation speed and high calculation accuracy. Attached Figure Description

[0061] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is an overall flowchart of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to an embodiment of the present invention;

[0063] Figure 2 This is a flowchart illustrating the sensitivity and uncertainty analysis calculation of the online monitoring sensitivity coefficient calculation method for reactor core power distribution according to an embodiment of the present invention.

[0064] Figure 3 This is a schematic diagram showing the sensitivity coefficient and relative deviation of radial power distribution to the measured value of the "D14" channel detector signal, based on the harmonic expansion method, in an embodiment of the sensitivity coefficient calculation method for online monitoring of reactor core power distribution according to an embodiment of the present invention.

[0065] Figure 4 This is a schematic diagram illustrating the sensitivity coefficient of radial power distribution to the measured signal value of the "D14" channel detector, based on the spline function fitting method, in an embodiment of the sensitivity coefficient calculation method for online monitoring of reactor core power distribution according to an embodiment of the present invention.

[0066] Figure 5 This is a schematic diagram illustrating the sensitivity coefficient of radial power distribution to the measured signal value of the "D14" channel detector, based on the least squares method, in an embodiment of the sensitivity coefficient calculation method for online monitoring of reactor core power distribution according to an embodiment of the present invention. Detailed Implementation

[0067] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0068] Example 1

[0069] Reference Figures 1-2 As an embodiment of the present invention, a method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution is provided, specifically including the following steps:

[0070] S100: If the assumption that the detector measurement signals do not affect each other is true, then the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method is derived using analytical methods.

[0071] In the embodiments of this application, such as Figure 2 As shown, the method for calculating the sensitivity coefficient in the sensitivity and uncertainty analysis of online monitoring results of pressurized water reactor core power distribution is presented. For the harmonic expansion method, the expansion coefficient α is considered. n The detector signal measurement value I(r) d Sensitivity coefficient Represented as:

[0072]

[0073] The reconstructed value P(r) of the core power distribution, calculated using the harmonic expansion method, is expressed as:

[0074]

[0075] Where, N order κ∑ represents the expansion order, G represents the number of energy groups, and κ∑ represents the expansion order. f,g (r) represents the heat release from fission in energy group g at position r, Φ n,g (r) represents the nth-order neutron flux density of the g energy group at position r;

[0076] Sensitivity coefficient based on core power distribution reconfiguration value considering the expansion coefficient Represented as:

[0077]

[0078] in:

[0079]

[0080] The sensitivity coefficient considering the expansion coefficient based on the core power distribution reconstruction value. Simplified to:

[0081]

[0082] Furthermore, the reconstructed core power distribution value correlates with the detector signal measurement value I(r) d Sensitivity coefficient The calculation is as follows:

[0083]

[0084] It should be noted that, due to the use of the least squares principle when solving for the expansion coefficients in the harmonic expansion method, the variables in the above formula... Since the unknown quantity is not explicitly derived, this invention again applies the least squares principle to calculate this unknown quantity; for ease of description, this invention will... Named "expansion coefficient of sensitivity coefficient";

[0085] Furthermore, regarding the detector signal:

[0086]

[0087] Where I(r) represents the detector signal measurement value at position r, S neutron (r) represents the seed sensitivity of the self-powered detector at position r;

[0088] Differentiate the above equation and divide both sides by dI(r) d We can obtain:

[0089]

[0090] If we assume that the detector measurements at different locations do not affect each other, then we have:

[0091]

[0092] Then for position r d The detector at that location has the following equation:

[0093]

[0094] ...

[0095]

[0096] ...

[0097]

[0098] By applying the least squares principle again, the expansion coefficient of the sensitivity coefficient can be solved, and the sensitivity coefficient of the core power distribution reconstruction value to the detector signal measurement value can also be calculated.

[0099] Furthermore, analytical methods can also be applied in the least squares approach, and its sensitivity coefficient is expressed as:

[0100]

[0101] For calculation Assuming that the detector measurements at different locations are independent, differentiate the above equation and divide both sides by dI(r). d Applying the least squares principle again, we can calculate the analytical form of the sensitivity coefficient in the least squares method, which is expressed as:

[0102]

[0103] Where M represents the number of detectors, k represents the eigenvalue, F represents the fission operator, ω represents the weighting coefficient, Φ represents the neutron flux density, and I represents the detector signal measurement value.

[0104] It should be noted that a corresponding solution needs to be performed for each detector signal measurement. The calculation time of this equation is the same as the time of a reconstruction calculation. Therefore, the calculation time of solving the sensitivity coefficient using the analytical method is proportional to the number of detectors M.

[0105] The analytical method is based on the assumption that the detector signal measurements do not interfere with each other. If the detector signal measurements interfere with each other, this method cannot be used. Furthermore, for the spline function fitting method, the selection of the fitting function and the addition of the regularization coefficient make it impossible to derive the formula for calculating the sensitivity coefficient analytically; therefore, this method cannot be used either.

[0106] S200: For cases where the spline function fitting method and the assumption that the detector measurement signal is independent do not hold, the direct numerical perturbation method is used to solve for the sensitivity coefficient.

[0107] In the embodiments of this application, such as Figure 2 As shown, by numerically perturbing each input parameter, the change in the output parameter is calculated. The sensitivity coefficient is then calculated by substituting the derivative with the difference quotient. According to the definition of the sensitivity coefficient, we have:

[0108]

[0109] in, The power reconfiguration value P(r) at core r represents the value of power reconfiguration at core r. d The detector signal measurement value I(r) at the location d The sensitivity coefficient of I0(r) d ),I + (r d ) and I -(r d The ) represents the values ​​of r under no disturbance, positive disturbance, and negative disturbance. d The detector signal measurement values ​​at the location, P0(r), P + (r) and P - (r) represents the power reconfiguration value at point r under the conditions of no disturbance, positive disturbance, and negative disturbance;

[0110] Furthermore, the online reconstruction calculation is performed (2M+1) times using the direct numerical perturbation method. Given the sensitivity coefficient, the uncertainty is calculated according to the "sandwich" principle.

[0111]

[0112] Where σ(P(r)) represents the absolute uncertainty of the reconstructed power distribution value, and σ(P(r)) / P(r) represents the relative uncertainty of the reconstructed power distribution value. and Indicates the power distribution reconstruction value with respect to r i and r j The relative sensitivity coefficient matrix of the detector signal measurement at point I(r) i ) and I(r j () represents the detector signal measurement value at any detector location. This represents the relative covariance matrix.

[0113] Therefore, as described above, this invention, based on the assumption that detector measurement signals do not interfere with each other, derives analytical formulas for calculating the sensitivity coefficient using harmonic expansion and least squares methods as power distribution reconstruction methods, starting from the definition of the sensitivity coefficient. However, for the spline function fitting method, the use of regularization coefficients prevents the derivation of analytical formulas for the sensitivity coefficient; therefore, only the direct numerical perturbation method can be used to solve for the sensitivity coefficient. Furthermore, if the assumption that detector measurement signals are independent does not hold, the direct numerical perturbation method must be used to calculate the sensitivity coefficient regardless of the reconstruction method employed. Compared with traditional methods, this invention has the advantages of fast sensitivity coefficient calculation speed and high calculation accuracy.

[0114] The above is a schematic scheme for calculating the sensitivity coefficient of reactor core power distribution online monitoring according to this embodiment. It should be noted that the technical solution of the system for calculating the sensitivity coefficient of reactor core power distribution online monitoring in this embodiment belongs to the same concept as the technical solution of the above-described method for calculating the sensitivity coefficient of reactor core power distribution online monitoring. Details not described in detail in the technical solution of the system for calculating the sensitivity coefficient of reactor core power distribution online monitoring in this embodiment can be found in the description of the technical solution of the above-described method for calculating the sensitivity coefficient of reactor core power distribution online monitoring.

[0115] This embodiment also provides a reactor core power distribution online monitoring sensitivity coefficient calculation system, including:

[0116] The analytical method calculation unit is used to derive the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method if the assumption that the detector measurement signals do not affect each other is true.

[0117] The direct numerical perturbation method calculation unit is used to solve for the sensitivity coefficient by employing the direct numerical perturbation method when the spline function fitting method and the assumption that the detector measurement signal is independent do not hold.

[0118] This embodiment also provides a computing device, including:

[0119] Memory and processor;

[0120] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the method proposed in the above embodiments.

[0121] This embodiment also provides a storage medium on which a computer program is stored, which, when executed by a processor, implements the method proposed in the above embodiments.

[0122] The storage medium proposed in this embodiment belongs to the same inventive concept as the method proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0123] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0124] Example 2

[0125] Reference Figures 3-5Based on the previous embodiment, this embodiment provides an application example of the method and system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution, to verify and illustrate the technical effects adopted in this method.

[0126] In the embodiments of this application, the sensitivity coefficient is calculated using two methods: analytical methods and direct numerical perturbation methods. Analytical methods include harmonic expansion and least squares methods.

[0127] Sensitivity coefficient verification: Based on the BEAVRS benchmark problem of 0.01 MWD(tu) -1 The core condition was assessed, and its sensitivity coefficient was calculated using both analytical and direct numerical perturbation methods based on the harmonic expansion method. Figure 3 The figure shows a comparison of the sensitivity coefficients of the core radial power distribution calculated analytically to the detector signal measurements in channel "D14". The results calculated using the direct numerical perturbation method are used as the reference solution, and the relative deviations are listed below. Figure 3 In the example, the expansion order is 30.

[0128] Therefore, it is evident that the two methods for calculating the sensitivity coefficient agree well. In fact, the verification calculation of the sensitivity coefficient is not limited to the "D14" channel; the verification calculations for other channels also demonstrate similar accuracy. Figure 3 The results are comparable, with deviations all around 10. -3 ~10 -5 Therefore, they are not listed repeatedly. It is evident that the program developed in this invention has high accuracy in calculating the sensitivity coefficient. It is worth noting that... Figure 3 The highest sensitivity coefficient is 0.2568 in channel "C14", meaning that a +1% disturbance in the detector signal measurement in channel "D14" will cause a +0.2568% change in the power reconfiguration value of component "C14". The most "sensitive" component is not channel "D14" itself, but rather component "C14". Mathematically, the core power distribution reconfiguration value affects the detector signal measurement value I(r). d As can be seen from the expression for the sensitivity coefficient, the magnitude of the sensitivity coefficient is jointly determined by the harmonics of the neutron diffusion equation, the reconstructed power distribution value, and the expansion coefficient of the sensitivity coefficient. For position r... d The detector equations at the location show that the magnitude of the expanded coefficient of the sensitivity coefficient is determined by harmonics, the number of detectors, and the expansion order. The combined effect of these complex influencing factors makes it impossible to directly pinpoint the location of the maximum sensitivity coefficient. If the expansion order equals the number of detectors, the maximum sensitivity coefficient must occur in the component containing the disturbed detector; however, in reality, the expansion order is less than the number of detectors, so any component could potentially be the location of the maximum sensitivity coefficient, but the component containing the disturbed detector and its surrounding components are more likely to be the most sensitive component. Figure 3 In the example, the power reconstruction value in channel "C14" is less than that in channel "D14", resulting in a greater relative change in the power reconstruction value in channel "C14" compared to channel "D14". Another noteworthy phenomenon is that... Figure 3 The presence of a negative sensitivity coefficient indicates that a +1% change in the detector signal measurement value of channel "D14" will cause a negative change in the radial power reconstruction value. Since the harmonics in the neutron diffusion equation are distributed in a petal-like pattern of alternating positive and negative values, the detector signal measurement value I(r) is affected by the core power distribution reconstruction value. d The positive and negative values ​​of the sensitivity coefficient expression are both normal.

[0129] in addition, Figure 3 The trend of the sensitivity coefficient is that it is positive near the disturbed detector location, then negative, and then positive again. This is because online monitoring of core power distribution can be considered a type of fitting; disturbances in the input parameters will cause relative changes in the output parameters at different locations, either positive or negative. In the above example of this invention, the disturbance in the signal measurement value of the "D14" channel detector most directly and significantly affects the monitoring results of components near this channel, and this effect is then transmitted to more distant locations in the form of amplitude attenuation. Therefore, a phenomenon occurs... Figure 3 The phenomenon of alternating positive-negative-positive values ​​in the sensitivity coefficient.

[0130] The sensitivity coefficient of the core radial power distribution calculated based on spline function fitting combined with direct numerical perturbation method to the detector signal measurement values ​​in channel "D14" is as follows: Figure 4 As shown. The regularization coefficient is 80.0. It is evident that the trend of this sensitivity coefficient is similar to, but slightly different from, the trend of the sensitivity coefficient calculated based on the harmonic expansion method. The sensitivity coefficient calculated based on the spline function fitting method also exhibits alternating positive-negative-positive fluctuations with continuously decreasing amplitude, but its main influence is minimal on the "D14" component and its surrounding components, with little impact on more distant locations. Correspondingly, the sensitivity coefficient of the core radial power distribution calculated based on the least squares method combined with the direct numerical perturbation method to the detector signal measurement values ​​within the "D14" channel is as follows: Figure 5 As shown. The weighting coefficient is 1.0. The alternating positive and negative wave propagation shape is also observed, and similar to the spline function fitting method, the sensitivity coefficient of components farther from the "D14" channel is almost zero. This is because the latter two online reconstruction methods more directly utilize detector signal measurements. From their calculation formulas, it can be clearly observed that the online reconstruction calculation of the core power distribution is actually a fitting and adjustment between the solution of the neutron diffusion equation and the detector signal measurements. However, in the harmonic expansion method, this fitting cannot be directly observed.

[0131] Therefore, as described above, this invention, based on the assumption that detector measurement signals do not interfere with each other, derives analytical formulas for calculating the sensitivity coefficient using harmonic expansion and least squares methods as power distribution reconstruction methods, starting from the definition of the sensitivity coefficient. However, for the spline function fitting method, the use of regularization coefficients prevents the derivation of analytical formulas for the sensitivity coefficient; therefore, only the direct numerical perturbation method can be used to solve for the sensitivity coefficient. Furthermore, if the assumption that detector measurement signals are independent does not hold, the direct numerical perturbation method must be used to calculate the sensitivity coefficient regardless of the reconstruction method employed. Compared with traditional methods, this invention has the advantages of fast sensitivity coefficient calculation speed and high calculation accuracy.

[0132] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution, characterized in that, include: If the assumption that the detector measurement signals do not interfere with each other holds true, then the analytical calculation formula for the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method is derived using analytical methods. For cases where the spline function fitting method and the assumption that the detector measurement signal is independent do not hold, the direct numerical perturbation method is used to solve for the sensitivity coefficient. The calculations of the analytical method include: For the harmonic expansion method, consider the expansion coefficients. Detector signal measurement value Sensitivity coefficient , is represented as: Calculate the reconstructed core power distribution value using the harmonic expansion method. , is represented as: in, The expansion order is represented by G, and the number of energy groups is represented by G. This represents the heat release from fission in the g energy group at position r. Let r represent the nth-order neutron flux density of the g-energy group at position r; Sensitivity coefficient considering the unfolding coefficient based on the core power distribution reconstruction value. Represented as: in: The sensitivity coefficient considering the expansion coefficient based on the core power distribution reconstruction value. Simplified to: The calculation of the analytical method also includes: The core power distribution reconstruction value is related to the detector signal measurement value. Sensitivity coefficient The calculation is as follows: The calculation of the analytical method also includes: For the detector signal: in, This represents the detector signal measurement value at position r. This indicates the seed sensitivity of the self-powered detector at position r; Differentiate the above expression and divide both sides by We can obtain: If we assume that the detector measurements at different locations do not affect each other, then we have: ， Then for position The detector at that location has the following equation: The least squares principle is applied again to solve for the expansion coefficient of the sensitivity coefficient, and the sensitivity coefficient of the reconstructed core power distribution value to the detector signal measurement value can be obtained by calculation. The calculation of the analytical method also includes: The analytical method is applied in the least squares approach, and its sensitivity coefficient is expressed as: For calculation Assuming that the detector measurements at different locations do not affect each other, differentiate the above equation and divide both sides by . Applying the least squares principle again, the analytical form of the sensitivity coefficient in the least squares method is obtained, expressed as: in, M Indicates the number of detectors. k Represents eigenvalues. F Represents the fission operator. Indicates the weighting coefficient. Represents neutron flux density. I This represents the measured value of the detector signal; The calculations of the direct numerical perturbation method include: By numerically perturbing each input parameter, the change in the output parameter is calculated. The sensitivity coefficient is then calculated by substituting the derivative with the difference quotient. According to the definition of the sensitivity coefficient, we have: in, This represents the power reconfiguration value at core r. right Detector signal measurement at the location The sensitivity coefficient, and This indicates the cases of no disturbance, positive disturbance, and negative disturbance. The detector signal measurement value at that location, and This represents the power reconfiguration value at point r under the conditions of no disturbance, positive disturbance, and negative disturbance; The calculations using the direct numerical perturbation method also include: The online reconstruction calculations were performed (2M+1) times using the direct numerical perturbation method. Given the sensitivity coefficient, the uncertainty was calculated according to the "sandwich" principle. in, This represents the absolute uncertainty of the reconstructed power distribution value. This represents the relative uncertainty of the reconstructed power distribution value. and Indicates the power distribution reconstruction value pair and The relative sensitivity coefficient matrix of the detector signal measurements at the location, and This represents the measured value of the detector signal at any detector location. This represents the relative covariance matrix.

2. A system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution as described in claim 1, characterized in that, include: The analytical method calculation unit is used to derive the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least squares method as the power distribution reconstruction method if the assumption that the detector measurement signals do not affect each other is true. The direct numerical perturbation method calculation unit is used to solve for the sensitivity coefficient by employing the direct numerical perturbation method when the spline function fitting method and the assumption that the detector measurement signal is independent do not hold.

3. An electronic device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the method of claim 1.

4. A computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the steps of the method of claim 1.

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