Reactor core power distribution on-line monitoring sensitivity coefficient calculation method and system

Abstract

The invention discloses a reactor core power distribution on-line monitoring sensitivity coefficient calculation method and a reactor core power distribution on-line monitoring sensitivity coefficient calculation system. Deriving a sensitivity coefficient analytical calculation formula based on a harmonic expansion method and a least square method as a power distribution reconstruction method by using an analytical method; for a spline function fitting method, due to the use of a regularization coefficient, an analytic calculation formula of a sensitivity coefficient cannot be derived, so that only a direct numerical perturbation method is adopted to solve the sensitivity coefficient; in addition, if the detector measurement signal irrelevant hypothesis is not established, a direct numerical perturbation method needs to be adopted to calculate the sensitivity coefficient no matter what reconstruction method is adopted. Compared with a traditional method, the method has the advantages of being high in sensitivity coefficient calculation speed and high in calculation precision.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear reactor engineering, and in particular to a method and system for calculating a sensitivity coefficient of online monitoring of reactor core power distribution. Background Art

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

[0003] The core power distribution online monitoring system combines theoretical calculation results with detector measurement signals. Therefore, the online monitoring calculation includes not only the uncertainty introduced by solving the neutron diffusion equation, such as the uncertainty introduced by nuclear data, core geometry, core material and other parameters, but also the uncertainty introduced by the self-powered neutron detector measurement signal. The uncertainty introduced by the self-powered neutron detector measurement signal is unique to the core power distribution online monitoring process, so it is necessary to conduct uncertainty analysis of the core monitoring results based on the uncertainty introduced by the neutron detector measurement signal.

[0004] There are two main types of sensitivity and uncertainty analysis methods based on input parameters. One is the deterministic analysis method, which first calculates the sensitivity coefficient. Commonly used methods include direct numerical perturbation and perturbation theory, and then calculates the uncertainty of the output parameter based on the input parameter uncertainty, covariance matrix and sensitivity coefficient. The other is the probabilistic analysis method, which first samples the input parameter uncertainty and covariance matrix to generate the sample space of the input parameter, and then repeats the neutronics-related calculations to obtain the output result corresponding to each different sample in the sample space, that is, the response. Finally, the response is statistically calculated to obtain its mathematical expectation and variance, and then the uncertainty of the response is obtained. Summary of the invention

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

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

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] In the 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 detector measurement signals do not affect each other is established, an analytical method is used to derive an analytical calculation formula for the sensitivity coefficient based on the harmonic expansion method and the least squares method as a power distribution reconstruction method; for the spline function fitting method and the case where the assumption that the detector measurement signals are independent is not established, a direct numerical perturbation method is used to solve the sensitivity coefficient.

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

[0010] For the harmonic expansion method, consider the expansion coefficient a n The detector signal measurement value I(r d ) It is expressed as:

[0011]

[0012] The core power distribution reconstruction value P(r) is calculated according to the harmonic expansion method and is expressed as:

[0013]

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

[0015] Considering the sensitivity coefficient of the expansion coefficient based on the core power distribution reconstruction value It is expressed as:

[0016]

[0017] in:

[0018]

[0019] The sensitivity coefficient of the expansion factor is considered based on the reconstruction value of the core power distribution Simplified to:

[0020]

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

[0022] The core power distribution reconstruction value is proportional to the detector signal measurement value I(rd ) The calculation is:

[0023]

[0024] As a preferred solution of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution of the present invention, the calculation of 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 ends by dI(r d ) can be obtained:

[0029]

[0030] Assuming that the measurement values ​​of detectors at different positions do not affect each other, we have:

[0031]

[0032] Then for position r d The detector at has the 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 core power distribution reconstruction value to the detector signal measurement value can also be calculated.

[0039] As a preferred solution of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution of the present invention, the calculation of 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 Assume that the detector measurement values ​​at different positions do not affect each other, take the derivative of the above formula and divide both ends by dI(r d ), and applying the least squares principle again, the analytical form of the sensitivity coefficient in the least squares method can be calculated, expressed as:

[0043]

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

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

[0046] By numerically perturbing the input parameters one by one, calculating the changes in the output parameters, and calculating the sensitivity coefficient by replacing the derivative with the difference quotient, the definition of the sensitivity coefficient is:

[0047]

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

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

[0050] The number of online reconstruction calculations using the direct numerical perturbation method is (2M+1). When the sensitivity coefficient is known, the uncertainty is calculated according to the "sandwich" principle:

[0051]

[0052] Where σ(P(r)) represents the absolute uncertainty of the power distribution reconstruction value, σ(P(r)) / P(r) represents the relative uncertainty of the power distribution reconstruction value, and Represents the power distribution reconstruction value pair r i and r j The relative sensitivity coefficient matrix of the detector signal measurement value at i ) and I(r j ) represents the detector signal measurement value at any detector position, represents the relative covariance matrix.

[0053] In a second aspect, the present invention provides a reactor core power distribution online monitoring sensitivity coefficient calculation system, comprising:

[0054] An analytical method calculation unit, used for deriving a sensitivity coefficient analytical calculation formula based on a harmonic expansion method and a least square method as a power distribution reconstruction method by using an analytical method if the assumption that the detector measurement signals do not affect each other holds true;

[0055] The direct numerical perturbation method calculation unit is used to solve the sensitivity coefficient by using the direct numerical perturbation method when the spline function fitting method and the detector measurement signal irrelevant assumption are not established.

[0056] In a third aspect, 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. When the computer-executable instructions are executed by the processor, the steps of the method are implemented.

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

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows: based on the assumption that the detector measurement signals do not affect each other, the present invention uses an analytical method to derive an analytical calculation formula for the sensitivity coefficient based on the harmonic expansion method and the least square method as a power distribution reconstruction method based on the definition of the sensitivity coefficient; while for the spline function fitting method, due to the use of the regularization coefficient, it is impossible to derive an analytical calculation formula for the sensitivity coefficient, so only the direct numerical perturbation method can be used to solve the sensitivity coefficient; in addition, if the assumption that the detector measurement signals are independent does not hold, no matter which reconstruction method is used, the direct numerical perturbation method must be used to calculate the sensitivity coefficient. Compared with the traditional method, it has the advantages of fast sensitivity coefficient calculation speed and high calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

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

[0063] Figure 2 A sensitivity and uncertainty analysis calculation flow chart of a method for calculating a sensitivity coefficient of online monitoring of reactor core power distribution according to an embodiment of the present invention;

[0064] Figure 3 A schematic diagram of the sensitivity coefficient and relative deviation of the radial power distribution to the "D14" channel detector signal measurement value based on the harmonic expansion method of the reactor core power distribution online monitoring sensitivity coefficient calculation method according to an embodiment of the present invention;

[0065] Figure 4 A schematic diagram of the sensitivity coefficient of the radial power distribution to the "D14" channel detector signal measurement value based on the spline function fitting method of the reactor core power distribution online monitoring sensitivity coefficient calculation method according to one embodiment of the present invention;

[0066] Figure 5 It is a schematic diagram of the sensitivity coefficient of radial power distribution to the "D14" channel detector signal measurement value based on the least squares method of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution described in one embodiment of the present invention. DETAILED DESCRIPTION

[0067] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0068] Example 1

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

[0070] S100: If the assumption that the detector measurement signals do not affect each other is established, an analytical method is used to derive an analytical calculation formula for the sensitivity coefficient based on the harmonic expansion method and the least square method as a power distribution reconstruction method;

[0071] In the embodiments of the present application, Figure 2 As shown in the figure, the calculation method of the sensitivity coefficient in the sensitivity and uncertainty analysis of the online monitoring results of the core power distribution of the pressurized water reactor is given. For the harmonic expansion method, the expansion coefficient a is considered. n The detector signal measurement value I(r d ) It is expressed as:

[0072]

[0073] The core power distribution reconstruction value P(r) is calculated according to the harmonic expansion method and is expressed as:

[0074]

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

[0076] Sensitivity coefficient of expansion factor based on core power distribution reconstruction value It is expressed as:

[0077]

[0078] in:

[0079]

[0080] The sensitivity coefficient of the expansion factor is considered based on the reconstruction value of the core power distribution Simplified to:

[0081]

[0082] Furthermore, the core power distribution reconstruction value is proportional to the detector signal measurement value I(r d ) The calculation is:

[0083]

[0084] It should be noted that due to the use of the least squares principle when solving the expansion coefficients in the harmonic expansion method, the variables in the above formula is unknown and its expression cannot be derived explicitly. The present invention again applies the least squares principle to calculate the unknown quantity. For the convenience of description, the present invention will Named "Expansion coefficient of sensitivity coefficient";

[0085] Furthermore, for 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 ends by dI(r d ) can be obtained:

[0089]

[0090] Assuming that the measurement values ​​of detectors at different positions do not affect each other, we have:

[0091]

[0092] Then for position r d The detector at has the 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, the analytical method can also be applied in the least squares method, and its sensitivity coefficient is expressed as:

[0100]

[0101] For calculation Assume that the detector measurement values ​​at different positions do not affect each other, take the derivative of the above formula and divide both ends by dI(r d ), and applying the least squares principle again, the analytical form of the sensitivity coefficient in the least squares method can be calculated, expressed as:

[0102]

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

[0104] It should be noted that a corresponding solution is required for each detector signal measurement value. The calculation time of the 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 derivation of the analytical method is based on the assumption that the detector signal measurement values ​​do not affect each other. If the detector measurement signals affect each other, this method cannot be used. In addition, for the spline function fitting method, due to the selection of the fitting function and the addition of the regularization coefficient, it is impossible to use the analytical method to derive the calculation formula of the sensitivity coefficient, so this method cannot be used either.

[0106] S200: When the spline function fitting method and the assumption that the detector measurement signal is independent do not hold true, the sensitivity coefficient is solved by the direct numerical perturbation method;

[0107] In the embodiments of the present application, Figure 2 As shown, by numerically perturbing the input parameters one by one, calculating the changes in the output parameters, and calculating the sensitivity coefficient by replacing the derivative with the difference quotient, according to the definition of the sensitivity coefficient:

[0108]

[0109] in, represents the power reconstruction value P(r) at the core r versus r d The detector signal measurement value I(r d ) sensitivity coefficient, I0(r d ),I + (r d ) and I -(r d ) represents r under no disturbance, positive disturbance and negative disturbance d The detector signal measurement value at P0(r),P + (r) and P - (r) represents the power reconstruction value at r under no disturbance, positive disturbance and negative disturbance conditions;

[0110] Furthermore, the number of online reconstruction calculations using the direct numerical perturbation method is (2M+1) times. When the sensitivity coefficient is known, the uncertainty is calculated according to the "sandwich" principle:

[0111]

[0112] Where σ(P(r)) represents the absolute uncertainty of the power distribution reconstruction value, σ(P(r)) / P(r) represents the relative uncertainty of the power distribution reconstruction value, and Represents the power distribution reconstruction value pair r i and r j The relative sensitivity coefficient matrix of the detector signal measurement value at i ) and I(r j ) represents the detector signal measurement value at any detector position, represents the relative covariance matrix.

[0113] Therefore, it can be seen from the above that the present invention is based on the assumption that the detector measurement signals do not affect each other, starting from the definition of the sensitivity coefficient, and using analytical methods to derive the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least square method as the power distribution reconstruction method; and for the spline function fitting method, due to the use of the regularization coefficient, it is impossible to derive the analytical calculation formula of the sensitivity coefficient, so only the direct numerical perturbation method can be used to solve the sensitivity coefficient; in addition, if the assumption that the detector measurement signal is independent does not hold, no matter which reconstruction method is used, the direct numerical perturbation method must be used to calculate the sensitivity coefficient. Compared with the traditional method, it has the advantages of fast sensitivity coefficient calculation speed and high calculation accuracy.

[0114] The above is a schematic scheme of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution in this embodiment. It should be noted that the technical scheme of the system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution and the technical scheme of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution mentioned above belong to the same concept. For details not described in detail in the technical scheme of the system for calculating the sensitivity coefficient of online monitoring of reactor core power distribution in this embodiment, please refer to the description of the technical scheme of the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution mentioned above.

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

[0116] An analytical method calculation unit, used for deriving a sensitivity coefficient analytical calculation formula based on a harmonic expansion method and a least square method as a power distribution reconstruction method by using an analytical method if the assumption that the detector measurement signals do not affect each other holds true;

[0117] The direct numerical perturbation method calculation unit is used to solve the sensitivity coefficient by using the direct numerical perturbation method when the spline function fitting method and the detector measurement signal irrelevant assumption are not established.

[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 embodiment.

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

[0122] The storage medium proposed in this embodiment and the method proposed in the above embodiment belong to the same inventive concept. The technical details not fully described in this embodiment can be referred to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

[0123] Through the above description of the implementation methods, the technicians in the relevant field can clearly understand that the present invention can be implemented by means of software and necessary general hardware, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ReadOnly, Memory, ROM), random access memory (RandomAccess Memory, RAM), flash memory (FLASH), hard disk or optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform the methods of various embodiments of the present invention.

[0124] Example 2

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

[0126] In the embodiment of the present application, there are two methods for calculating the sensitivity coefficient: an analytical method and a direct numerical perturbation method. The analytical method includes a harmonic expansion method and a least squares method.

[0127] Verification of sensitivity coefficient: 0.01MWD(tu) for BEAVRS benchmark -1 The core state is calculated based on the harmonic expansion method using analytical methods and direct numerical perturbation methods, such as Figure 3 The figure shows the sensitivity coefficient comparison of the core radial power distribution calculated by analytical method to the measured value of the detector signal in the "D14" channel. The calculation result of the direct numerical perturbation method is used as the reference solution. The relative deviation is also listed in Figure 3 The expansion order is 30.

[0128] It can be seen that the two sensitivity coefficient calculation methods are in good agreement. In fact, the sensitivity coefficient verification calculation is not only performed in the "D14" channel, but also in other channels. Figure 3 The deviations are shown in 10 -3 ~10 -5 Therefore, it is not listed repeatedly. It can be seen that the program developed by the present invention has a high accuracy in calculating the sensitivity coefficient. It is worth noting that Figure 3 The maximum sensitivity coefficient is 0.2568 in the "C14" channel, which means that a +1% disturbance in the detector signal measurement value in the "D14" channel will cause a +0.2568% change in the power reconstruction value of the "C14" component. The most "sensitive" component is not the "D14" channel itself, but the "C14" component. Mathematically, the core power distribution reconstruction value is proportional to the detector signal measurement value I(r d ) can be seen from the sensitivity coefficient expression that the size of the sensitivity coefficient is determined by the harmonics of the neutron diffusion equation, the power distribution reconstruction value and the expansion coefficient of the sensitivity coefficient. d The detector equation group at shows that the size of the expansion coefficient of the sensitivity coefficient is determined by the harmonics, the number of detectors and the expansion order. The combined effect of these more complex influencing factors makes it impossible to directly point out the location where the maximum value of the sensitivity coefficient occurs. If the expansion order is equal to the number of detectors, the maximum value of the sensitivity coefficient must occur in the component where the disturbed detector is located; in reality, the expansion order is less than the number of detectors, so each component has the potential to become the location of the maximum value of the sensitivity coefficient, but the component where the disturbed detector is located and its surrounding components are more likely to become the most sensitive components. Figure 3 In the example of , the power reconstruction value in the "C14" channel is smaller than that in the "D14" channel, which results in the relative change value of the power reconstruction value in the "C14" channel being greater than that in the "D14" channel. Another phenomenon worth noting is that Figure 3 A negative sensitivity coefficient appears in the graph, indicating that a +1% change in the signal measurement value of the detector of the "D14" channel will cause a negative change in the radial power reconstruction value. Since the harmonics of the neutron diffusion equation are distributed in a positive and negative petal-like manner, the detector signal measurement value I(r d )’s sensitivity coefficient expression is normal in both positive and negative values.

[0129] in addition, Figure 3 The change trend of the sensitivity coefficient is that it is positive near the disturbed detector, then negative, and then positive again. This is because the online monitoring of the core power distribution can be regarded as a type of fitting, and the disturbance of the input parameters will cause the relative change of the output parameters at different positions to be positive or negative. In the above example of the present invention, the disturbance of the signal measurement value of the "D14" channel detector most directly and mainly affects the monitoring results of the components close to this channel, and then this influence is transmitted to a farther position in the form of an amplitude attenuation. Therefore, there is Figure 3 The phenomenon that the medium sensitivity coefficient appears alternately positive, negative and positive.

[0130] The sensitivity coefficient of the core radial power distribution to the detector signal measurement value in the "D14" channel calculated based on the spline function fitting method combined with the direct numerical perturbation method is as follows: Figure 4 As shown. The regularization coefficient is 80.0. Obviously, the change trend of the sensitivity coefficient is similar to and slightly different from the change trend of the sensitivity coefficient calculated based on the harmonic expansion method. The sensitivity coefficient calculated based on the spline function fitting method also presents positive-negative-positive alternating fluctuation transmission and the amplitude continues to decay, but its main impact on the "D14" component and its surrounding components has little impact on farther 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 value in the "D14" channel is shown as follows Figure 5 As shown. The weight coefficient is 1.0. The alternating positive and negative wave transfer shapes are also observed, and similar to the spline function fitting method, the sensitivity coefficient of the components far from the "D14" channel is almost zero. This is because in the latter two online reconstruction methods, the detector signal measurement values ​​are used more explicitly and directly. From the calculation formula, it can be clearly observed that the online reconstruction calculation of the core power distribution is actually a fit and adjustment between the solution of the neutron diffusion equation and the detector signal measurement values, while in the harmonic expansion method, this fit cannot be directly observed.

[0131] Therefore, it can be seen from the above that the present invention is based on the assumption that the detector measurement signals do not affect each other, starting from the definition of the sensitivity coefficient, and using analytical methods to derive the analytical calculation formula of the sensitivity coefficient based on the harmonic expansion method and the least square method as the power distribution reconstruction method; and for the spline function fitting method, due to the use of the regularization coefficient, it is impossible to derive the analytical calculation formula of the sensitivity coefficient, so only the direct numerical perturbation method can be used to solve the sensitivity coefficient; in addition, if the assumption that the detector measurement signal is independent does not hold, no matter which reconstruction method is used, the direct numerical perturbation method must be used to calculate the sensitivity coefficient. Compared with the traditional method, it 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 rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in 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 affect each other holds true, an analytical calculation formula for the sensitivity coefficient based on the harmonic expansion method and the least square method as a power distribution reconstruction method is derived using an analytical method; For the spline function fitting method and the case where the assumption of irrelevant detector measurement signals is not valid, the direct numerical perturbation method is used to solve the sensitivity coefficient.

2. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 1, characterized in that: The calculation of the analytical method includes: For the harmonic expansion method, consider the expansion coefficient a n The detector signal measurement value I(r d ) It is expressed as: The core power distribution reconstruction value P(r) is calculated according to the harmonic expansion method and is expressed as: Among them, N order represents the expansion order, G represents the number of energy groups, κ∑ f,g (r) represents the fission heat release of the g energy group at position r, Φ n,g (r) represents the n-order neutron flux density of the g energy group at position r; The sensitivity coefficient S of the expansion coefficient is considered based on the core power distribution reconstruction value p(r) ,a n It is expressed as: in: The sensitivity coefficient of the expansion factor is considered based on the reconstruction value of the core power distribution Simplified to:

3. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 2, characterized in that: The calculation of the analytical method also includes: The core power distribution reconstruction value is proportional to the detector signal measurement value I(r d ) The calculation is:

4. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 3, characterized in that: The calculation of the analytical method also includes: For the detector signal: 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; Differentiate the above equation and divide both ends by dI(r d ) can be obtained: Assuming that the measurement values ​​of detectors at different positions do not affect each other, we have: Then for position r d The detector at has the equation: 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.

5. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 4, characterized in that: The calculation of the analytical method also includes: The analytical method can also be applied in the least squares method, and its sensitivity coefficient is expressed as: For calculation Assume that the detector measurement values ​​at different positions do not affect each other, take the derivative of the above formula and divide both ends by dI(r d ), and applying the least squares principle again, the analytical form of the sensitivity coefficient in the least squares method can be calculated, which is expressed as: Where M represents the number of detectors, k represents the eigenvalue, F represents the fission operator, ω represents the weight coefficient, Φ represents the neutron flux density, and I represents the detector signal measurement value.

6. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 1, characterized in that: The calculation of the direct numerical perturbation method includes: By numerically perturbing the input parameters one by one, calculating the changes in the output parameters, and calculating the sensitivity coefficient by replacing the derivative with the difference quotient, the definition of the sensitivity coefficient is: in, represents the power reconstruction value P(r) at the core r versus r d The detector signal measurement value I(r d ) sensitivity coefficient, I0(r d ),I + (r d ) and I - (r d ) represents r under no disturbance, positive disturbance and negative disturbance d The detector signal measurement value at P0(r),P + (r) and P - (r) represents the power reconstruction value at r under no disturbance, positive disturbance and negative disturbance.

7. The method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to claim 6, characterized in that: The calculation of the direct numerical perturbation method also includes: The number of online reconstruction calculations using the direct numerical perturbation method is (2M+1). When the sensitivity coefficient is known, the uncertainty is calculated according to the "sandwich" principle: Where σ(P(r)) represents the absolute uncertainty of the power distribution reconstruction value, σ(P(r)) / P(r) represents the relative uncertainty of the power distribution reconstruction value, and Represents the power distribution reconstruction value pair r i and r j The relative sensitivity coefficient matrix of the detector signal measurement value at i ) and I(r j ) represents the detector signal measurement value at any detector position, represents the relative covariance matrix.

8. A system using the method for calculating the sensitivity coefficient of online monitoring of reactor core power distribution according to any one of claims 1 to 7, characterized in that: include: An analytical method calculation unit, used for deriving a sensitivity coefficient analytical calculation formula based on a harmonic expansion method and a least square method as a power distribution reconstruction method by using an analytical method if the assumption that the detector measurement signals do not affect each other holds true; The direct numerical perturbation method calculation unit is used to solve the sensitivity coefficient by using the direct numerical perturbation method when the spline function fitting method and the detector measurement signal irrelevant assumption are not established.

9. 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. When the computer executable instructions are executed by the processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having computer program instructions stored thereon, wherein the computer-executable instructions, when executed by a processor, implement the steps of the method according to any one of claims 1 to 7.

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