Single-point calibration method for neutron transmission matrix of out-of-pile detector

Abstract

The invention discloses a single-point calibration method for a neutron transmission matrix of an out-of-pile detector. The neutron transmission matrix of the out-of-pile detector can be determined according to a flux diagram measurement test. Firstly, a power correction factor is obtained according to a power measured value and a calculated value, and a current correction factor is obtained according to a current signal measured value and a calculated value; 2, simulating multiple control rod movements by adopting a reactor core physical analysis program to obtain multiple groups of reactor core power calculated values and corresponding out-of-reactor current signal calculated values; thirdly, obtaining multiple groups of reactor core power predicted values and corresponding out-of-pile current signal predicted values according to the current correction factor and the power correction factor; and 4, based on the multiple groups of power and current data, calculating a neutron transmission matrix and a sensitivity coefficient matrix by adopting a conjugate gradient method. According to the method, the neutron transmission matrix of the out-of-pile detector can be calculated only through one-time flux diagram measurement test, and then the axial power distribution of the reactor can be reduced by using six sections of out-of-pile detector measurement signals of the PRC channel.

Description

Technical Field

[0001] The present invention relates to the technical field of core power reconstruction of commercial pressurized water reactors, and particularly relates to a single-point calibration method for the neutron transport matrix of out-of-core detectors. Background Art

[0002] For safety considerations, during the operation of a reactor, it is necessary to continuously monitor the axial power distribution. This monitoring is generally based on the use of the multi-section out-of-core detector function of the power range channel (PRC) of the out-of-core nuclear detection system (PRN), and is carried out using the LSS system. In this function, the neutron transport matrix characterizes the probability that neutrons are transported out of the core and recorded by the out-of-core detectors, and plays a crucial role in axial power reconstruction. The traditional multi-point calibration method for calculating the neutron transport matrix requires, on the basis of a full-core neutron flux density distribution measurement, another 7 - 8 partial neutron flux density measurements. By using the artificial xenon oscillation phenomenon, the axial neutron flux density distributions of each measurement are made different. At the same time, the currents of each section of the out-of-core detectors in the PRC are also different, and the neutron transport matrix is obtained through mathematical fitting. The above traditional method requires multiple control rod movements to trigger artificial xenon oscillations, increasing the reactor control difficulty, operation risk and affecting the economy. Summary of the Invention

[0003] Aiming at the problem that the multi-point calibration for calculating the neutron transport matrix requires multiple control rod movements and flux map measurements, which affect the safety and economy of the reactor, the present invention proposes a single-point calibration method for the neutron transport matrix of out-of-core detectors, which combines theoretical calculation and numerical simulation. On the basis of a single core flux map measurement experiment, the movement of multiple control rods is simulated using a pressurized water reactor core physics analysis software to obtain multiple sets of core axial power distributions and out-of-core detector current signals, and finally the neutron transport matrix is determined.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A single-point calibration method for the neutron transport matrix of out-of-core detectors, characterized by comprising the following steps:

[0006] Step 1: Conduct a single flux map measurement experiment to obtain the in-core axial six-section core power measurement values and the current signal measurement values of the six-section out-of-core detectors in four PRC channels

[0007] Step 2: Use a pressurized water reactor core physics analysis software to track and simulate the core power history, and numerically simulate the flux map measurement points in Step 1 to obtain the in-core axial six-section core power calculation values and the current signal calculation values of the six-section out-of-core detectors in four PRC channels

[0008] Step 3: Obtain the power correction factor based on the measured values of the core power for each section of the core axially obtained from the flux map measurement test and the calculated values of the core power for each section of the core axially calculated by the software:

[0009]

[0010] In the formula:

[0011] —— represents the power correction factor for the j-th section of the core axially;

[0012] —— represents the measured value of the core power for the j-th section of the core axially;

[0013] —— represents the calculated value of the core power for the j-th section of the core axially;

[0014] Obtain the current signal correction factor based on the measured values of the current signals of the out-of-core detectors for each section of each PRC channel and the calculated values of the current signals of the out-of-core detectors for each section of each PRC channel obtained from the flux map measurement test.

[0015]

[0016] In the formula:

[0017] —— represents the current signal correction factor for the i-th out-of-core detector of the k-th PRC channel;

[0018] —— represents the measured value of the current signal of the i-th out-of-core detector of the k-th PRC channel;

[0019] —— represents the calculated value of the current signal of the i-th out-of-core detector of the k-th PRC channel;

[0020] Step 4: Use the core physics analysis program to simulate the movement of multiple groups of control rods, obtain multiple groups of calculated power values and the corresponding calculated current signal values, and then use the power correction factor and current signal correction factor obtained in Step 3 to obtain multiple groups of predicted power values and the corresponding predicted current signal values;

[0021]

[0022] In the formula:

[0023] —— represents the predicted power value for the j-th section of the core axially in the n-th group of data;

[0024] —— represents the calculated value of the power of the j-th core section in the axial direction of the n-th group of data;

[0025]

[0026] In the formula:

[0027] —— represents the predicted value of the current signal of the i-th out-of-core detector in the k-th PRC channel in the axial direction of the n-th group of data;

[0028] —— represents the calculated value of the current signal of the i-th out-of-core detector in the k-th PRC channel in the axial direction of the n-th group of data;

[0029] Step 5: Derive the mathematical model of the neutron transport matrix through simplified assumptions;

[0030] Using the neutron transport matrix, from a set of current signals I of six out-of-core detectors in the PRC channel at a certain level k , reproduce the axial power distribution of the core, that is:

[0031]

[0032] In the formula:

[0033] V k —— represents the column vector composed of current signals, and its i-th element represents the simulated current signal of the i-th out-of-core detector of the k-th PRC;

[0034] P k —— represents the column vector composed of the axial section power of the core, and its j-th element represents the reconstructed axial power of the j-th core section;

[0035] S k —— represents the sensitivity coefficient matrix of the k-th PRC channel, and its element values are related to the sensitivities of each ionization chamber and its electronic instruments in this channel;

[0036] T k —— represents the neutron transport matrix, and its elements represent the probability that neutrons are transported from the j-th layer of the core to the outside of the core and are recorded by the i-th ionization chamber and its instrument system of the k-th PRC;

[0037] For the convenience of derivation, a mathematical model for establishing the mapping relationship between the current of the ex-core detector and the axial power distribution of the reactor core is established. For the PRC channel containing six sections of detectors, its output is six current signals. To make the equation shown in formula (5) have a unique solution, the axial power of the reactor core must be divided into six sections, and the following assumptions are made: (1) The reactor core is equivalent to a one-dimensional uniform cylinder, and this one-dimensional uniform cylinder is divided into six sections, and the height of each section is exactly the center distance between adjacent detectors; (2) The average power of each section of the axial reactor core is proportional to the average neutron flux of this section; (3) The volume of the detector is ignored, and the effective part of the detector is equivalent to a point at the center of the detector; (4) Each section of the reactor core is equivalent to a surface source point located at the center position of each section of the reactor core; (5) Since the distance between the detector and the reactor core is small, the distance between the detector and the reactor core is ignored.

[0038] Based on the above assumptions, if the neutron beam intensity generated by an equivalent surface source point is φ0, then the neutron beam intensity φ after passing through a distance x in the reactor core is:

[0039]

[0040] In the formula:

[0041] Σ t —— represents the macroscopic total cross-section of the reactor core;

[0042] Based on assumption (1), Σ t is a constant. According to formula (6), the probability that neutrons generated by each surface source point still do not undergo any nuclear reactions with atomic nuclei after traveling a distance x in the reactor core is:

[0043]

[0044] Let H be the distance between adjacent equivalent surface source points of each section of the reactor core. According to assumption (5), the probability that neutrons are transmitted from the j-th layer of the reactor core to the outside of the reactor and are recorded by the i-th ionization chamber and its instrument system of the k-th PRC channel is expressed as:

[0045] P ij =exp(H×Σ t ×|i - j|) Formula (8)

[0046] Let

[0047] x1=exp(-H×Σ t ) Formula (9)

[0048] Then each element T k in the neutron transport matrix T ij in formula (5) can be expressed as:

[0049]

[0050] Finally, assume that the total probability that the neutrons generated in the middle two layers of the core are transmitted outside the core and recorded by all detectors is 1. Then, in formula (5), T k is expressed as:

[0051]

[0052] From the definition of the sensitivity coefficient matrix S k , it can be seen that S k should be a diagonal matrix:

[0053]

[0054] In the formula:

[0055] x2~x7——represent the sensitivity coefficients of each out-of-core detector;

[0056] Omitting the subscript k, the relationship between the neutron flux density in the core and the simulated value of the out-of-core detector current signal is expressed in the following form:

[0057]

[0058] In the formula:

[0059] ——represents the vector composed of the average neutron flux density of the six axial core layers;

[0060] I——represents a quantity recombined by and T, S, and its elements are the simulated values of the out-of-core six-section detector current signals.

[0061] According to assumption (2), the vector composed of the average neutron flux density of the six axial core layers is represented by the relative power density of the core. Then, formula (13) is transformed into:

[0062] I = STP Formula (14)

[0063] In the formula:

[0064] P——represents the vector composed of the average power density P j of the six axial core layers;

[0065] Step 6: Based on the mathematical model established in Step 5, according to the multiple groups of power prediction values and the corresponding current signal prediction values obtained in Step 4, the conjugate gradient method is used to obtain the neutron transport matrix T and the sensitivity coefficient matrix S.

[0066] For a single PRC channel, according to formula (14), the reconstructed current signal can be expressed as:

[0067]

[0068] Wherein:

[0069] —— represents the reconstructed value of the current signal of the i-th out-of-core detector in the k-th PRC channel of the n-th group of data;

[0070] S ii —— represents the element in the i-th row and i-th column of the sensitivity coefficient matrix;

[0071] T ij —— represents the element in the i-th row and j-th column of the neutron transport matrix;

[0072] The reconstructed value of the current signal reconstructed using formula (15) and the predicted value of the current signal obtained in step 4 form an objective function:

[0073]

[0074] Wherein:

[0075] F k —— represents the objective function value of the k-th PRC channel;

[0076] As can be seen from the mathematical model established in step 5, the objective function represented by formula (16) actually has 7 parameters to be fitted, namely the sensitivity coefficients x2 to x7 of each out-of-core detector and the probability x1; only by using the conjugate gradient method to fit the values of the above 7 parameters can the neutron transport matrix be calculated; the specific implementation steps are as follows:

[0077] (1) First, give initial values, let the initial values of x2 to x7 be 1, and the initial value of x1 can be arbitrarily selected;

[0078] (2) Use formula (16) to find the gradient value of F k for each variable;

[0079]

[0080] Wherein:

[0081] —— represents the derivative value of the m-th variable x m ;

[0082] (3) Calculate the gradient value of the objective function;

[0083]

[0084] Wherein:

[0085] S m —— represents the gradient value of the objective function;

[0086] (4) Determine whether the iteration converges;

[0087] (5) If it does not converge, update the parameters according to the following formula (19), and then repeat steps (2) to (4) until the convergence condition is met;

[0088]

[0089] In the formula

[0090] —— represents the value of the m-th variable at the n-th iteration;

[0091] Using the above method, the calculation of x1 to x7 can be completed. Then, according to formula (11) and formula (12), the calculation of the neutron transport matrix T and the sensitivity coefficient matrix S can be completed;

[0092] Using the calculated neutron transport matrix T and sensitivity coefficient matrix S, and then based on the current signals of the six-section out-of-core detectors in the PRC channel, the axial six-section core power of the reactor can be reconstructed.

[0093] Preferably, the pressurized water reactor core physical analysis software described in steps 2 and 3 is the pressurized water reactor core physical analysis software SPARK.

[0094] Compared with the prior art, the present invention has the following advantages:

[0095] The present invention proposes a single-point calibration method for the neutron transport matrix of out-of-core detectors. This method can combine numerical simulation and measured data. Based on the experimental data of single-core neutron flux measurement, it uses numerical simulation of pressurized water reactor core physical analysis software to replace multiple control rod movement tests, obtains multiple sets of core axial power distributions and out-of-core detector current signals, and finally determines the neutron transport matrix. It avoids the problems of traditional multi-point calibration methods for out-of-core detectors, such as relying on multiple control rod movements to cause core condition disturbances, resulting in axial xenon oscillations and long test times, and improves the safety and economy of nuclear power plants. Description of the Drawings

[0096] Figure 1 It is the flow chart of the method of the present invention.

[0097] Figure 2 It is the distribution diagram of the root mean square value of the relative error between the reconstructed power calculated by the single-point calibration method for the neutron transport matrix and the measured value. Detailed Embodiments

[0098] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0099] Based on a flux map measurement experiment conducted in a nuclear power plant, this invention obtains multiple sets of power values and current signal values by numerically simulating the process of repeatedly moving control rods in the reactor, and then calculates the neutron transport matrix using the conjugate gradient method. The specific steps are as Figure 1 shown and include the following steps

[0100] Step 1: Conduct a flux map measurement test to obtain the power measurement values of the six axial sections of the reactor core inside the reactor and the current signal measurement values of the detectors outside the six sections of the four PRC channels

[0101] Step 2: Use the PWR core physics analysis software SPARK to track and simulate the core power history, and numerically simulate the flux map measurement points in Step 1 to obtain the calculated power values of the six axial sections of the reactor core inside the reactor and the calculated current signal values of the detectors outside the six sections of the four PRC channels

[0102] Step 3: According to the power measurement values of each axial section of the reactor core obtained from the flux map measurement test and the calculated power values of each axial section of the reactor core calculated by the PWR core physics analysis software SPARK, obtain the power correction factor:

[0103]

[0104] In the formula:

[0105] —— represents the power correction factor of the jth axial section of the reactor core;

[0106] —— represents the power measurement value of the jth axial section of the reactor core;

[0107] —— represents the calculated power value of the jth axial section of the reactor core calculated by SPARK;

[0108] According to the current signal measurement values of each detector outside the six sections of each PRC channel obtained from the flux map measurement test and the calculated current signal values of each detector outside the six sections of each PRC channel calculated by SPARK, obtain the current signal correction factor.

[0109]

[0110] In the formula:

[0111] —— represents the current signal correction factor of the detector outside the ith section of the kth PRC channel;

[0112] —— represents the measured value of the current signal of the i-th out-of-core detector in the k-th PRC channel;

[0113] —— represents the calculated value of the current signal of the i-th out-of-core detector in the k-th PRC channel calculated by SPARK;

[0114] Step 4: Use the core physics analysis program to simulate the movement of multiple control rods, obtain multiple sets of power calculation values and the corresponding current signal calculation values, and then use the power correction factor and current signal correction factor obtained in Step 3 to obtain multiple sets of power prediction values and the corresponding current signal prediction values;

[0115]

[0116] In the formula:

[0117] —— represents the power prediction value of the j-th axial section of the core in the n-th group of data;

[0118] —— represents the power calculation value of the j-th axial section of the core in the n-th group of data calculated by SPARK;

[0119]

[0120] In the formula:

[0121] —— represents the predicted value of the current signal of the i-th out-of-core detector in the k-th PRC channel in the n-th axial group of data;

[0122] —— represents the calculated value of the current signal of the i-th out-of-core detector in the k-th PRC channel in the n-th axial group of data calculated by SPARK;

[0123] Step 5: Through simplified assumptions, derive the mathematical model of the neutron transport matrix;

[0124] Using the neutron transport matrix, the axial power distribution of the core can be reproduced from a set of current signals I of the six out-of-core detectors in the PRC channel at a certain level, that is: k ,

[0125]

[0126] In the formula:

[0127] V k —— represents the column vector composed of current signals, and its i-th element represents the simulated current signal of the i-th out-of-core detector of the k-th PRC;

[0128] Pk —— A column vector representing the axial power profile of the core, where the j-th element represents the reconstructed axial power of the j-th section of the core;

[0129] S k —— The sensitivity coefficient matrix of the k-th PRC channel, whose element values are related to the sensitivities of each section of the ionization chamber and its electronic instruments in this channel;

[0130] T k —— The neutron transport matrix, where the elements represent the probability that neutrons are transported from the j-th layer of the core to outside the core and are recorded by the i-th section of the ionization chamber and its instrument system of the k-th PRC;

[0131] For the purpose of facilitating the derivation of the mathematical model for establishing the mapping relationship between the current of the out-of-core detector and the axial power distribution of the core; for a PRC channel containing six sections of detectors, its output is six current signals. To make the equation shown in formula (4) have a unique solution, the axial power of the core must be divided into six sections, and the following assumptions are made: (1) The reactor core is equivalent to a one-dimensional uniform cylinder, and this one-dimensional uniform cylinder is divided into six sections, and the height of each section is exactly the center-to-center distance of adjacent detectors; (2) The average power of each axial section of the core is proportional to the average neutron flux of this section; (3) The volume of the detector is ignored, and the effective part of the detector is equivalent to a point at the center of the detector; (4) Each section of the core is equivalent to a surface source point located at the center position of each section of the core; (5) Since the distance between the detector and the core is small, the distance between the detector and the core is ignored.

[0132] Based on the above assumptions, if the neutron beam intensity generated by an equivalent surface source point is φ0, then the neutron beam intensity φ after passing through a distance x in the core is:

[0133]

[0134] In the formula:

[0135] Σ t —— Represents the macroscopic total cross-section of the core;

[0136] Based on assumption (1), Σ t is a constant. According to formula (6), the probability that neutrons generated by each surface source point still do not undergo any nuclear reactions after traveling a distance x in the core is:

[0137]

[0138] Let H be the distance between adjacent equivalent surface source points of each section of the core. According to assumption (5), the probability that neutrons are transported from the j-th layer of the core to outside the core and are recorded by the i-th section of the ionization chamber and its instrument system of the k-th PRC can be expressed as:

[0139] P ij = exp(H × Σ t × |i - j|) Equation (8)

[0140] Let

[0141] x1 = exp(-H × Σ t ) Equation (9)

[0142] Then, each element T k in the neutron transport matrix T ij in Equation (5) can be expressed as:

[0143]

[0144] Finally, assume that the total probability that the neutrons generated in the middle two layers (the 3rd and 4th layers) of the core are transported out of the core and recorded by all detectors is 1. Then, T k in Equation (5) is expressed as:

[0145]

[0146] From the definition of the sensitivity coefficient matrix S k , it can be seen that S k should be a diagonal matrix:

[0147]

[0148] In the formula:

[0149] x2 to x7 - represent the sensitivity coefficients of each out-of-core detector;

[0150] Omitting the subscript k, the relationship between the neutron flux density in the core and the simulated value of the out-of-core detector current signal can be expressed in the following form:

[0151]

[0152] In the formula:

[0153] - represents the vector composed of the average neutron flux density of the six axial core layers;

[0154] I - represents a quantity recombined from and T, S, and its elements are the simulated values of the out-of-core six-section detector current signals.

[0155] According to assumption (2), the vector composed of the average neutron flux density of the six axial core layers is represented by the relative power density of the core. Then, Equation (13) is transformed into:

[0156] I = STP Equation (14)

[0157] In the formula:

[0158] P——represents the average power density P of the six - layer axial core j The vector composed of;

[0159] Step 6: Based on the mathematical model established in Step 5, according to the multiple groups of power prediction values and the corresponding current signal prediction values obtained in Step 4, the neutron transport matrix T and the sensitivity coefficient matrix S can be obtained by using the conjugate gradient method.

[0160] For a single PRC pass, according to formula (14), the reconstructed electrical signal can be expressed as:

[0161]

[0162] In the formula:

[0163] ——represents the reconstructed value of the current signal of the i - th out - of - core detector in the k - th PRC channel in the n - th group of data;

[0164] S ii ——represents the element in the i - th row and the j - th column of the sensitivity coefficient matrix;

[0165] T ij ——represents the element in the i - th row and the j - th column of the neutron transport matrix;

[0166] The reconstructed value of the current signal reconstructed by using formula (15) and the current signal prediction value obtained in Step 4 form an objective function:

[0167]

[0168] In the formula:

[0169] F k ——represents the objective function value of the k - th PRC channel;

[0170] It can be seen from the mathematical model established in Step 5 that there are actually 7 fitting parameters in the objective function represented by formula (16), which are the sensitivity coefficients x2 - x7 of each out - of - core detector and the probability x1; only by using the conjugate gradient method to fit the values of the above 7 parameters can the neutron transport matrix be calculated; the specific implementation steps are as follows:

[0171] (1) First, give the initial values. Let the initial values of x2 - x7 be 1, and the initial value of x1 can be chosen arbitrarily.

[0172] (2) Use formula (16) to find the gradient value of F k for each variable;

[0173]

[0174] In the formula:

[0175] —— represents the derivative value of the m-th variable x m ;

[0176] (3) Calculate the gradient value of the objective function;

[0177]

[0178] In the formula:

[0179] S m —— represents the gradient value of the objective function;

[0180] (4) Determine whether the iteration converges;

[0181] (5) If it does not converge, update the parameters according to the following formula (19), and then repeat steps (2) to (4) until the convergence condition is satisfied;

[0182]

[0183] In the formula

[0184] —— represents the value of the m-th variable at the n-th iteration;

[0185] Using the above method, the calculation of x1 to x7 can be completed. Then, according to formula (11) and formula (12), the calculation of the neutron transport matrix T and the sensitivity coefficient matrix S can be completed;

[0186] Using the calculated neutron transport matrix T and sensitivity coefficient matrix S, and then based on the current signals of the six-section off-core detectors in the PRC channel, the axial six-section core power of the reactor can be reconstructed.

[0187] The method of the present invention is verified by using the measured data of four cycles, namely the 24th cycle of Unit 1 of Daya Bay Nuclear Power Base, the 20th cycle of Unit 1 of Ling Ao, the 13th cycle of Unit 3 of Ling Ao, and the 12th cycle of Unit 4 of Ling Ao. During the operation of these cycles, the neutron transport matrix was calculated by the multi-point calibration method. Therefore, when verifying the present invention, the flux map measurement data in step 1 uses the first measured point in each multi-point calibration. Based on this measured point, the calculation data of each group of power values and current signal values are obtained. And according to these data, the neutron transport matrix T and the sensitivity coefficient matrix S are calculated. Finally, the core power value is reconstructed according to the current signal values obtained from each flux map measurement test in the multi-point calibration.

[0188] The four loops to be verified above altogether contain 28 state point data. For each state point, the power of the TS matrix calculated by the method of the present invention for the current signals of 4 radially arranged detectors needs to be reconstructed and the mean square error is calculated. Therefore, there are altogether 112 reconstructed data. Figure 2 It is the distribution diagram of the root mean square value of the relative error between the reconstructed power of the TS matrix calculated by the single-point calibration proposed by the present invention and the measured value. It can be seen therefrom that the maximum value of the mean square error of the reconstructed power of the TS matrix obtained by single-point calibration is 1.18%. Among them, there are 52 points where the mean square error of the reconstructed power is between 0 and 0.5%, accounting for 46%; there are 57 points where the mean square error of the reconstructed power is between 0.5% and 1%, accounting for 51%. It has a good verification result, indicating that the reconstructed power of the TS matrix obtained by using the method of the present invention has a good effect.

Claims

1. A method for single-point calibration of the neutron transport matrix of an out-of-core detector, characterized in that: It includes the following steps: Step 1: Conduct a flux map measurement test once to obtain the in-core axial six-section core power measurement values and the current signal measurement values of the four PRC channel six-section out-of-core detectors Step 2: Use the pressurized water reactor core physics analysis software to track and simulate the core power history, and perform numerical simulation on the flux map measurement points in Step 1 to obtain the calculated values of the in-core axial six-section core power and the calculated values of the current signals of the six-section out-of-core detectors of the four PRC channels Step 3: Obtain a power correction factor based on the core power measurement values of each section of the core in the axial direction obtained from the flux map measurement test and the core power calculation values of each section of the core in the axial direction calculated by the pressurized water reactor core physics analysis software: Where: —— represents the power correction factor of the j-th axial core segment; —— represents the power measurement value of the j-th axial core segment; —— represents the calculated power value of the j-th axial core segment; Obtain a current signal correction factor based on the measured values of the out-of-core detector current signals of each section of each PRC channel obtained from the flux map measurement test and the calculated values of the out-of-core detector current signals of each section of each PRC channel. Where: —— represents the current signal correction factor of the i-th out-of-core detector in the k-th PRC channel; —— represents the measured value of the current signal of the i-th out-of-core detector in the k-th PRC channel; —— represents the calculated value of the current signal of the i-th off-core detector in the k-th PRC channel; Step 4: Use the pressurized water reactor core physics analysis software to perturb the numerical simulation points in Step 2, simulate the movement of multiple control rods, obtain multiple sets of power calculation values and the corresponding current signal calculation values, and then use the power correction factor and current signal correction factor obtained in Step 3 to obtain multiple sets of power prediction values and the corresponding current signal prediction values; Where: —— represents the predicted value of the power of the j-th core section in the axial direction in the n-th group of data; —— represents the calculated power value of the j-th axial core segment in the n-th group of data; Where: —— represents the predicted value of the current signal of the i-th out-of-core detector in the k-th PRC channel of the n-th axial group of data in the axial direction; —— represents the calculated value of the current signal of the i-th off-core detector in the k-th PRC channel in the n-th axial group of axial data; Step 5: Derive a mathematical model of the neutron transport matrix through simplified assumptions; Using the neutron transport matrix, a set of current signals I of the six out-of-core detectors in the PRC channel at a certain level is used to reproduce the axial power distribution of the reactor core, that is: k , Where: V k —— represents a column vector composed of current signals, and its i-th element represents the analog current signal of the i-th out-of-core detector of the k-th PRC; P k —— A column vector representing the axial power profile of the core, where the j-th element represents the reconstructed axial power of the j-th section of the core; S k —— represents the sensitivity coefficient matrix of the k-th PRC channel, and the element values thereof are related to the sensitivities of the ionization chambers and their electronic instruments of each section of this channel; T k —— represents the neutron transport matrix, and its elements represent the probability that neutrons are transported from the j-th layer of the core to outside the reactor and are recorded by the i-th ionization chamber and its instrument system of the k-th PRC; For the convenience of derivation, establish a mathematical model of the mapping relationship between the out-of-core detector current and the core axial power distribution. For a PRC channel containing six detectors, its output is six current signals. To make the equation shown in formula (5) have a unique solution, the core axial power must be divided into six sections, and the following assumptions are made at the same time: (1) Equivalent the reactor core to a one-dimensional uniform cylinder, and divide this one-dimensional uniform cylinder into six sections, and the height of each section is exactly the center distance between adjacent detectors; (2) The average power of each section of the core in the axial direction is proportional to the average neutron flux of this section; (3) Ignore the volume of the detector and equivalent the effective part of the detector to a point at the center of the detector; (4) Equivalent each section of the core to a surface source point located at the center position of each section of the core; (5) Since the distance between the detector and the core is small, the distance between the detector and the core is ignored; Based on the above assumptions, if the neutron beam intensity generated by an equivalent surface source point is φ0, then the neutron beam intensity φ after passing through a distance x in the core is: Where: Σ t —— represents the macroscopic total cross-section of the core; Based on assumption (1), Σ t is a constant. According to formula (6), the probability that neutrons generated by each surface source point still do not undergo any nuclear reaction with atomic nuclei after traveling a distance x in the reactor core is: Let H be the distance between adjacent equivalent surface source points of each section of the core. According to assumption (5), the probability that neutrons are transmitted from the jth layer of the core to the out-of-core and recorded by the ith ionization chamber and its instrument system of the kth PRC channel is expressed as: P ij = exp(H × Σ t × |i - j|) Formula (8) Let x1 = exp(-H×Σ t ) Equation (9) Then each element \(T_{ k}\) of the neutron transport matrix \(T\) in formula (5) is expressed as: k in \(T_{ ij}\) is expressed as: ij as follows: Finally, assume that the total probability that the neutrons generated in the middle two layers of the core are transmitted outside the core and recorded by all detectors is 1. Then T in formula (5) k is expressed as: From the definition of the sensitivity coefficient matrix S k it can be seen that S k should be a diagonal matrix: Where: x2~x7——represent the sensitivity coefficients of each out-of-core detector; Omit the subscript k, and the relationship between the neutron flux density of the core and the simulated value of the out-of-core detector current signal is expressed in the following form: Where: —— a vector representing the average neutron flux density composition of the six axial core layers; I——represents a quantity recombined by and T, S, and its elements are the analog values of the current signals of the six out-of-core detectors; According to assumption (2), the vector composed of the average neutron flux density of the axial six-layer core is represented by the relative power density of the core, and then Equation (13) is transformed into: I = STP formula (14) Where: P——denotes the average power density P of the axial six-layer core j The vector formed; Step 6: Based on the mathematical model established in Step 5, according to the multiple sets of power prediction values and the corresponding current signal prediction values obtained in Step 4, use the conjugate gradient method to obtain the neutron transport matrix T and the sensitivity coefficient matrix S; For a single PRC channel, according to formula (14), the reconstructed current signal is expressed as: Where: —— represents the reconstructed value of the current signal of the i-th out-of-core detector in the k-th PRC channel of the n-th group of data; S ii —— represents the element in the \(i\)-th row and \(i\)-th column of the sensitivity coefficient matrix; T ij —— represents the element in the \(i\)-th row and \(j\)-th column of the neutron transport matrix; The reconstructed value of the current signal reconstructed using formula (15) and the current signal prediction value obtained in Step 4 form an objective function: Where: F k —— represents the objective function value of the k-th PRC channel; As can be seen from the mathematical model established in Step 5, there are actually 7 parameters to be fitted in the objective function represented by Formula (16), namely the sensitivity coefficients x2 to x7 of each out-of-core detector and the probability x1; only by using the conjugate gradient method to fit the values of the above 7 parameters can the neutron transport matrix be calculated; the specific implementation steps are as follows: (1) First, given the initial values, let the initial values of x2 to x7 be 1, and the initial value of x1 can be arbitrarily selected; (2) Use formula (16) to find F k The gradient values for each variable; Where: —— represents the derivative value of the m-th variable x m ; (3) Calculate the gradient value of the objective function; Where: S m —— represents the gradient value of the objective function; (4) Determine whether the iteration converges; (5) If it does not converge, update the parameters according to the following Formula (19), and then repeat steps (2) to (4) until the convergence condition is satisfied; Where —— represents the value of the m-th variable at the n-th iteration; Using the above method, the calculation of x1 to x7 can be completed, and then according to Formula (11) and Formula (12), the calculation of the neutron transport matrix T and the sensitivity coefficient matrix S can be completed; Using the calculated neutron transport matrix T and sensitivity coefficient matrix S, and then according to the current signals of the six out-of-core detectors in the PRC channel, the axial six-section core power of the reactor can be reconstructed.

2. The single-point calibration method for the neutron transport matrix of the in-core detector according to claim 1, characterized in that: The pressurized water reactor core physics analysis software described in Step 2 and Step 3 uses the pressurized water reactor core physics analysis software SPARK.

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