Abnormal vibration control rod positioning method, system and medium based on neutron noise signal

Abstract

The present invention discloses a method, system and medium for locating abnormal vibration control rods based on neutron noise signals; and relates to the technical field of control rod monitoring. The present invention evaluates whether there is abnormal vibration in the control rod based on neutron noise signal data measured by a self-powered neutron detector, and determines the cause of the abnormal vibration; then uses the neutron transport equation to calculate the transfer function between the control rod and the neutron detector, and determines the position of the control rod where the abnormal vibration occurs through a minimization algorithm theory. This solves the problem of being unable to monitor abnormal vibration of the control rod in the reactor, avoids abnormal vibration of the control rod, and effectively ensures the safety and reliability of the reactor control rod.

Description

Technical Field

[0001] The present invention relates to the technical field of control rod monitoring, and in particular to a method, system and medium for positioning abnormal vibration control rods based on neutron noise signals. Background Art

[0002] Control rods are a crucial component of nuclear power plant internals, controlling reactor power and core reactivity. They are essential safety features for ensuring the safe shutdown of the reactor in the event of an accident. Their reliable function is crucial for the safe operation of nuclear power plants and the stable operation of nuclear submarines. In recent years, a number of control rod drive failures have occurred in various reactor types both domestically and internationally, including rod jamming, component wear, pitting, and abnormal rod drop. These failures pose significant safety risks to the normal operation of the reactors. In 1985, abnormal vibration of the number 4 control rod was discovered in the Paks-2 pressurized water reactor in Hungary.

[0003] Because the control rods are located inside the reactor, surrounded by high radioactivity and limited space, it is not possible to deploy vibration detectors to monitor their vibration. Self-powered detectors, a crucial tool for measuring core power and thermal-hydraulic parameters, are sensitive not only to thermal-hydraulic phenomena (standing acoustic waves, coolant boiling, and temperature fluctuations transported at the coolant velocity from the reactor inlet) but also to mechanical vibrations (vibration of the pressure vessel, core basket, and control rods), effectively detecting abnormal control rod vibrations. Summary of the Invention

[0004] The technical problem to be solved by the present invention is that control rods are located in the reactor core, where the surrounding radioactivity is high and the space is small, making it impossible to arrange vibration detectors in the reactor to detect the vibration state of the control rods. The present invention aims to provide a method, system and medium for locating abnormally vibrating control rods based on neutron noise signals. By arranging multiple self-powered neutron detectors in the reactor to monitor neutron noise signal data, and judging whether the control rods have abnormal vibration based on the neutron noise signal data, the transfer function between the control rods and the self-powered neutron detectors is constructed in combination with the neutron transport equation, and the position of the abnormally vibrating control rods is determined by minimization algorithm theory. This solves the problem of being unable to monitor abnormal vibration of control rods in the reactor, avoids abnormal vibration of the control rods, and effectively ensures the safety and reliability of the reactor control rods.

[0005] The present invention is achieved through the following technical solutions:

[0006] This solution provides a method for locating abnormal vibration control rods based on neutron noise signals, including:

[0007] Multiple self-powered neutron detectors are deployed in the reactor to collect neutron noise signal data measured by the self-powered neutron detectors;

[0008] Preprocessing the neutron noise signal data;

[0009] Determine whether the control rod has abnormal vibration based on the pre-processed neutron noise signal data;

[0010] The transfer function between the control rod and the self-powered neutron detector is constructed based on the neutron transport equation;

[0011] The position of abnormally vibrating control rod is determined based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector.

[0012] The working principle of this scheme is that the control rods are located in the reactor core, where the surrounding radioactivity is high and the space is limited, making it impossible to arrange vibration detectors inside the reactor to detect the vibration state of the control rods. The purpose of the present invention is to provide a method, system and medium for locating abnormal vibration control rods based on neutron noise signals. By deploying multiple self-powered neutron detectors in the reactor to monitor neutron noise signal data, and judging whether the control rods are vibrating abnormally based on the neutron noise signal data, the transfer function between the control rods and the self-powered neutron detectors is constructed in combination with the neutron transport equation, and the position of the abnormal vibration control rods is determined by minimization algorithm theory. This solves the problem of being unable to monitor abnormal vibration of control rods inside the reactor, avoids abnormal vibration of the control rods, and effectively ensures the safety and reliability of the reactor control rods.

[0013] A further optimized solution is that the multiple self-powered neutron detectors are arranged in the reactor, including the following method:

[0014] The first control rod assembly and the second control rod assembly are determined according to condition a; condition a: there is no control rod assembly around the first control rod assembly or the first control rod assembly is the second control rod assembly;

[0015] A plurality of self-powered neutron detectors are arranged at a central position of the first control rod assembly and at equal depth intervals along the control rod insertion direction.

[0016] A further optimization solution is that the neutron noise signal data includes neutron current signal noise data.

[0017] The specific neutron noise signal data δφ(r,t) is:

[0018] δφ(r,t)=cδi(r,t)=c[i(r,t)-E(i(r,t))]

[0019] Where δi(r,t) represents the neutron current signal noise data; E(·) represents the time-scale mean of the signal; i(r,t) represents the neutron current signal; r represents the position of the core; t represents time; and c represents the linear conversion coefficient of the self-powered neutron detector, which is obtained based on the characteristics of the self-powered detector that collects the neutron noise signal.

[0020] A further optimization scheme is that the neutron noise signal data is preprocessed, including the following method:

[0021] separating an AC signal and a DC signal from the neutron noise signal data, and amplifying the AC signal;

[0022] sampling the DC signal and the amplified AC signal respectively, and filtering the amplified AC signal to obtain a first AC signal;

[0023] The first AC signal is divided by the DC signal.

[0024] A further optimized solution is that the method of determining whether the control rod has abnormal vibration based on the pre-processed neutron noise signal data includes:

[0025] Obtain neutron noise signals from different self-powered detectors deployed at the same depth;

[0026] Calculate the cross-correlation function between self-powered detectors at the same depth based on neutron noise signals;

[0027] Determine whether the control rod has abnormal vibration based on the cross-correlation function:

[0028] Obtain the natural frequency of each control rod;

[0029] At the natural frequency of the control rod, a cross-correlation threshold is preset, and when the cross-correlation function is greater than the cross-correlation threshold, it is determined that an abnormality exists in the control rod.

[0030] A further optimization scheme is that the cross-correlation function between self-powered detectors at the same depth is calculated based on the neutron noise signal, including the following method:

[0031] The cross-correlation function R(r,ω) between the self-powered detector x and the self-powered detector y at depth z is:

[0032]

[0033] Where S xx (r,ω) represents the power spectrum density of the self-powered detector x at depth z; S yy (r,ω) represents the power spectrum density of the self-powered detector y at depth S; S xy(r, ω) represents the cross-power spectral density of the self-powered detector x and the self-powered detector y at depth z; r represents the position of the self-powered neutron detector, and ω represents the circular frequency of the neutron noise signal.

[0034] A further optimization scheme is to construct a transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation; including the following method:

[0035] Based on neutron transport theory, the neutron noise equation caused by the fluctuation of the absorption cross section is:

[0036]

[0037] Where L is an operator defined on the Hilbert space, S(r,ω) is the disturbance source caused by the control rod vibration, and D is the neutron diffusion coefficient; δφ(r,ω) represents the acquired neutron noise signal; r represents the position of the self-powered neutron detector, and ω represents the circular frequency of the neutron noise signal;

[0038] Based on Green's function theory, the Green's function solution G(r, r′, ω) of the neutron noise equation is the transfer function between the control rod vibration and the neutron flux at the neutron detector:

[0039] δφ(r,ω)=∫G(r,r′,ω)S(r′,ω)dr′

[0040] Where r′ represents the position of the control rod; S(r′,ω) represents the disturbance source caused by the control rod vibration;

[0041] A further optimization scheme is to determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector, including the following method:

[0042] Acquire basic evaluation data, including: self-power spectrum density of self-powered detectors i, j, and k at depth S; cross-power spectrum density between self-powered detectors i, j, and k; and transfer functions of different abnormal vibration control rods to self-powered detectors i, j, and k; i≠j≠k;

[0043] Calculate the evaluation function Δ(r) based on the evaluation basic data:

[0044]

[0045] Where G ij (r p ) represents the transfer function between the self-powered detector i and the self-powered detector j; G jk (r p) represents the transfer function between the self-powered detector i and the self-powered detector k; Indicates G ij (r p ) inverse operator; Indicates G jk (r p ) inverse operator; Indicates G ij (r p )’s adjoint operator; Indicates G jk (r p )'s adjoint operator; S ij represents the neutron noise spectrum matrix of self-powered detector i and self-powered detector j; S jk represents the neutron noise spectrum matrix of self-powered detector j and self-powered detector k; r p represents the position of the control rod p; r p ={x p ,y p};

[0046] in,

[0047]

[0048] Where, represents the self-power spectrum density of the self-powered detector i; represents the self-power spectrum density of the self-powered detector j; represents the cross power spectrum density of self-powered detector j and self-powered detector i; represents the cross power spectrum density of self-powered detector i and self-powered detector j; φ0(r p ) represents r p Neutron flux level at the position; G(r i ,r p ,ω) represents the Green function solution of the neutron noise equation of the self-powered detector i; G(r j ,r p ,ω) represents the Green function solution of the neutron noise equation of the self-powered detector j.

[0049] The r with the minimum evaluation function p As abnormal vibration control rod position.

[0050] This solution also provides an abnormal vibration control rod positioning system based on neutron noise signals, which is used to implement the above-mentioned abnormal vibration control rod positioning method based on neutron noise signals. The system includes:

[0051] An acquisition module is used to deploy multiple self-powered neutron detectors in the reactor and collect neutron noise signal data measured by each of the self-powered neutron detectors;

[0052] A preprocessing module, used for preprocessing the neutron noise signal data;

[0053] a judgment module, configured to judge whether the control rod has abnormal vibration based on the preprocessed neutron noise signal data;

[0054] A construction module for constructing a transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation;

[0055] The positioning module is used to determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector.

[0056] The present solution also provides a computer-readable medium having a computer program stored thereon. The computer program is executed by a processor to implement the above-mentioned abnormal vibration control rod positioning method based on neutron noise signals.

[0057] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0058] The present invention provides a method, system, and medium for locating abnormal vibration control rods based on neutron noise signals. The method evaluates whether the control rods have abnormal vibrations based on neutron noise signal data measured by a self-powered neutron detector and determines the cause of the abnormal vibrations. The method then uses a neutron transport equation to calculate the transfer function between the control rods and the neutron detector, and determines the position of the control rods experiencing abnormal vibrations through a minimization algorithm. The method solves the problem of being unable to monitor abnormal vibrations of control rods within a reactor, prevents abnormal vibrations of the control rods, and effectively ensures the safety and reliability of the reactor control rods. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the examples. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be considered as limiting the scope. A person of ordinary skill in the art can also derive other relevant drawings based on these drawings without inventive effort. In the drawings:

[0060] Figure 1 The figure is a flow chart of the abnormal vibration control rod positioning method based on neutron noise signals;

[0061] Figure 2 This is a structural diagram of the abnormal vibration control rod positioning system based on neutron noise signals;

[0062] Figure 3This is a flow chart of the abnormal vibration control rod positioning method of Example 4. DETAILED DESCRIPTION

[0063] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0064] Since the control rods are located inside the reactor, the surrounding radioactivity is high, and the space is small, it is impossible to arrange vibration detectors inside the reactor to detect the vibration state of the control rods. In view of this, the present invention provides the following embodiments to solve the above technical problems:

[0065] Example 1

[0066] This embodiment provides a method for locating abnormal vibration control rods based on neutron noise signals, such as Figure 1 Shown, including:

[0067] Step 1: deploying multiple self-powered neutron detectors in the reactor and collecting neutron noise signal data measured by each powered neutron detector;

[0068] The method of deploying multiple self-powered neutron detectors in a reactor includes:

[0069] The first control rod assembly and the second control rod assembly are determined according to condition a; condition a: there is no control rod assembly around the first control rod assembly or the first control rod assembly is the second control rod assembly;

[0070] At the center of the first control rod assembly, multiple self-powered neutron detectors are arranged at equal depths along the control rod insertion direction; preferably, at least seven self-powered neutron detectors are arranged; the control rod assembly is specifically configured to include control rods, stainless steel rods, and fuel rods, and the seven self-powered neutron detectors are evenly installed at different depths in the instrument tube grid element; control rod assemblies surrounding the first control rod assembly where the self-powered neutron detectors are arranged do not need to be equipped with self-powered neutron detectors, and therefore the second control rod assemblies are distributed around the first control rod assembly.

[0071] The neutron noise signal data includes neutron current signal noise data.

[0072] The specific neutron noise signal data δφ(r,t) is:

[0073] δφ(r,t)=cδi(r,t)=c[i(r,t)-E(i(r,t))]

[0074] Where δi(r,t) represents the neutron current signal noise data; E(·) represents the time-scale mean of the signal; i(r,t) represents the neutron current signal; r represents the position of the core; t represents time; and c represents the linear conversion coefficient of the self-powered neutron detector, which is obtained based on the characteristics of the self-powered detector that collects the neutron noise signal.

[0075] Step 2: preprocessing the neutron noise signal data; specifically including the following method:

[0076] separating an AC signal and a DC signal from the neutron noise signal data, and amplifying the AC signal;

[0077] sampling the DC signal and the amplified AC signal respectively, and filtering the amplified AC signal to obtain a first AC signal;

[0078] The first AC signal is divided by the DC signal.

[0079] Step 3: Determine whether the control rod has abnormal vibration based on the pre-processed neutron noise signal data; specifically, the method includes:

[0080] S31, obtaining neutron noise signals of different self-powered detectors deployed at the same depth;

[0081] S32, calculating the cross-correlation function between self-powered detectors at the same depth based on the neutron noise signal;

[0082] The cross-correlation function R(r,ω) between the self-powered detector x and the self-powered detector y at depth z is:

[0083]

[0084] Where S xx (r,ω) represents the power spectrum density of the self-powered detector x at depth z; S yy (r,ω) represents the power spectrum density of the self-powered detector y at depth S; S xy (r, ω) represents the cross-power spectral density of the self-powered detector x and the self-powered detector y at depth z; r represents the position of the self-powered neutron detector, and ω represents the circular frequency of the neutron noise signal.

[0085] S33, judging whether the control rod has abnormal vibration based on the cross-correlation function:

[0086] Obtain the natural frequency of each control rod; in this embodiment, it is 1.1 Hz;

[0087] At the natural frequency of the control rod, a cross-correlation threshold is preset to 0.9. When the cross-correlation function is greater than the cross-correlation threshold, it is determined that an abnormality exists in the control rod;

[0088] The cross-correlation spectrum of the two detectors at the same height is obtained, and the frequency corresponding to the threshold is exceeded. If the frequency is the natural frequency of the control rod, it is determined that the abnormal vibration of the control rod is caused by the loosening of its own fasteners.

[0089] If the frequency is not the natural frequency of the control rods, the cause of the abnormal vibration can be determined by comparing it with the frequencies of power equipment such as the main pumps, turbulent excitation, acoustic standing waves caused by the interaction between the tube bundle and the coolant, and the vibration of the core basket. By analyzing the frequency range of the abnormal cross-correlation function corresponding to the frequency, combined with the cross-power spectrum density amplitude, phase, and auto-power spectrum density, the cause of the abnormal vibration can be determined. For example, if the value near 16Hz is too large, it can be roughly assumed that the abnormal forced vibration of the control rods is caused by acoustic standing waves excited by the main pumps. At this time, the cause of the abnormality can be further determined by investigating the operation of the main pumps or the fluid design of the reactor's primary circuit.

[0090] Step 4: Construct a transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation; the specific method includes:

[0091] S41, based on neutron transport theory, the neutron noise equation caused by the fluctuation of the absorption cross section is:

[0092]

[0093] Where L is the operator defined on the Hilbert space, S(r,ω) is the disturbance source caused by the control rod vibration, D is the neutron diffusion coefficient, and δφ(r,ω) is the neutron noise signal acquired.

[0094] S42, based on Green's function theory, the Green's function solution G(r, r', ω) of the neutron noise equation is the transfer function between the control rod vibration and the neutron flux at the neutron detector:

[0095] δφ(r,ω)=∫G(r,r′,ω)S(r′,ω)dr′

[0096] Where r′ represents the position of the control rod; S(r′,ω) represents the disturbance source caused by the control rod vibration;

[0097] Step 5: Determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector; specifically, the method includes:

[0098] Acquiring basic evaluation data, the basic evaluation data including: the self-power spectrum density of each of the three self-powered detectors at the depth S, the cross-power spectrum density between each of the three self-powered detectors, and the transfer functions from different abnormal vibration control rods to the three self-powered detectors;

[0099] Calculate the evaluation function Δ(r) based on the evaluation basic data:

[0100]

[0101] Where G ij (r p ) represents the transfer function between the self-powered detector i and the self-powered detector j; G jk (r p ) represents the transfer function between the self-powered detector i and the self-powered detector k; Indicates G ij (r p ) inverse operator; Indicates G jk (r p ) inverse operator; Indicates G ij (r p )'s adjoint operator; Indicates G jk (r p )'s adjoint operator; S ij represents the neutron noise spectrum matrix of self-powered detector i and self-powered detector j; S jk represents the neutron noise spectrum matrix of self-powered detector j and self-powered detector k; r p represents the position of the control rod p;

[0102] in,

[0103]

[0104] Where, represents the self-power spectrum density of the self-powered detector i; represents the self-power spectrum density of the self-powered detector j; represents the cross power spectrum density of self-powered detector j and self-powered detector i; represents the cross power spectrum density of self-powered detector i and self-powered detector j; φ0(r p ) represents r p Neutron flux level at the position; G(r i ,r p ,ω) represents the Green function solution of the neutron noise equation of the self-powered detector i; G(r j ,r p ,ω) represents the Green function solution of the neutron noise equation of the self-powered detector j.

[0105] The r with the minimum evaluation function p As abnormal vibration control rod position.

[0106] This embodiment evaluates whether abnormal vibration of control rods occurs based on neutron noise signal data measured by an in-core self-powered neutron detector and determines the cause of the abnormal vibration. It uses the neutron transport equation to calculate the transfer function between the control rods and the neutron detector, and determines the position of the control rods where abnormal vibration occurs through a minimization algorithm. The overall logic is clear, easy to implement and promote, and solves the problem of being unable to monitor abnormal vibration of control rods in the reactor, avoiding abnormal vibration of the control rods and effectively ensuring the safety and reliability of the reactor control rods.

[0107] Example 2

[0108] This embodiment provides an abnormal vibration control rod positioning system based on neutron noise signals, which is used to implement the abnormal vibration control rod positioning method based on neutron noise signals in embodiment 1, such as Figure 2 As shown, the system includes:

[0109] An acquisition module is used to deploy multiple self-powered neutron detectors in the reactor and collect neutron noise signal data measured by each of the self-powered neutron detectors;

[0110] The acquisition module includes a self-powered neutron detector;

[0111] A preprocessing module is used to preprocess the neutron noise signal data; the preprocessing module includes an amplifier circuit, a filter circuit and a DC isolation circuit, etc. The DC isolation circuit separates the AC signal and the DC signal of the neutron noise signal data, the amplifier circuit is used to amplify the AC signal, and the filter circuit is used to filter the amplified AC signal.

[0112] a judgment module, configured to judge whether the control rod has abnormal vibration based on the preprocessed neutron noise signal data;

[0113] A construction module for constructing a transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation;

[0114] The positioning module is used to determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector.

[0115] Example 3

[0116] This embodiment provides a computer-readable medium having a computer program stored thereon. The computer program is executed by a processor to implement the abnormal vibration control rod positioning method based on neutron noise signals as in Embodiment 1. Specifically, the following steps are performed:

[0117] Step 1: Collect neutron noise signal data measured by each energized neutron detector;

[0118] Step 2: preprocessing the neutron noise signal data;

[0119] Step 3: Determine whether there is abnormal vibration of the control rod based on the pre-processed neutron noise signal data;

[0120] Step 4: Construct the transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation;

[0121] Step 5: Determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector.

[0122] Example 4

[0123] In this embodiment, the neutron noise signal of the self-powered detector is used to analyze the abnormal vibration of the control rod. First, the neutron noise signal data measured by the self-powered neutron detector in the reactor is obtained; whether the control rod has abnormal vibration and the cause of the abnormal vibration is determined; the transfer function between the control rod and the self-powered neutron detector is calculated using the neutron transport equation; and the position of the control rod where the abnormal vibration occurs is determined by the minimization algorithm theory. In this embodiment, a rhodium self-powered neutron detector is used. The specific process is as follows: Figure 3 As shown:

[0124] First, the neutron current data measured by the in-pile rhodium self-powered neutron detector is obtained and the signal is DC-blocked, filtered, and amplified. Then, the rhodium self-powered neutron detector conversion coefficient H(ω) is calculated based on the rhodium self-powered neutron detector's response to neutron flux:

[0125]

[0126] Where λ1 and λ2 represent the elements and elements The decay constants are 0.016s -1 and 0.0027s -1 ; N(ω) represents the neutron flux density at the rhodium self-powered neutron detector; I(ω) represents the output current of the rhodium self-powered neutron detector; a1 and a2 represent the element and elements c represents the instantaneous response component of the rhodium self-powered neutron detector current, which is less than 1. The value of ω is in the fuel vibration range (4π, 120π). In this range, the first-order and second-order terms of the transfer function are much smaller than the constant term. The fluctuation component of the neutron current signal and the neutron noise signal data are approximately linearly related, that is:

[0127]

[0128] δφ(r,t)=cδi(r,t)=c(i(r,t)-E(i(r,t)))

[0129] Determine whether abnormal control rod vibration exists and identify the cause. Neutron noise signals are caused by abnormal self-excited vibration of the control rods, as well as abnormal forced vibrations caused by factors such as the main pump, turbulent flow excitation, acoustic standing waves caused by the interaction between the tube bundle and the coolant, and core basket vibration. These forced vibration signals are transmitted to various detection components through the system transfer function, causing fluctuations in the measured signal. Using the cyclic cross-correlation function between these signals, random signals in the core (cross-correlation between random signals is zero) are filtered out, highlighting the characteristic signals caused by abnormal forced control rod vibration. The cause of the abnormal vibration is determined by analyzing the frequency range corresponding to the abnormal cross-correlation function and combining the cross-power spectral density amplitude, phase, and auto-power spectral density. For example, a frequency peak around 9 Hz corresponds to abnormal forced control rod vibration caused by core basket vibration.

[0130] The transfer function between the control rod and the neutron detector is calculated using the neutron transport equation. If the single-group neutron approximation is used, the neutron noise equation caused by the fluctuation of the absorption cross section is:

[0131]

[0132] In the formula is the vector differential operator, B(ω) is the geometric curvature of the reactor, S(r,ω) is the disturbance source caused by the control rod vibration, and D is the neutron diffusion coefficient.

[0133] According to Green's function theory, the Green's function solution G(r, r′, ω) of the neutron noise equation is the transfer function between the control rod vibration and the neutron flux at the neutron detector.

[0134] δφ(r,ω)=∫G(r,r′,ω)S(r′,ω)dr′

[0135] Use the Fourier transform method to solve the Green's function of the differential equation:

[0136]

[0137] Where, δ(rr p ) is the Dirac function, the position of the detector is r, and the position of the control rod is r p ={x p ,y p}, ε (t) is the two-dimensional displacement near the equilibrium position, and its Fourier transform result is ε(ω)={ε x (ω),ε y (ω)}.

[0138] Finally, the position of the control rod where abnormal vibration occurs is determined by minimization algorithm theory; under ideal conditions, the neutron noise spectrum amplitude δφ(r,ω) of a single sensor is equal to the ratio of its transfer function amplitude.

[0139] δφ(r,ω)=γ{ε x (ω)G x (r,r p ,ω)+ε y (ω)G y (r,r p ,ω)}

[0140] Where:

[0141]

[0142] In engineering applications, considering a certain error, at the location where abnormal vibration of the control rod occurs, the square of the difference between the above two equations is the smallest. In order to reduce the influence of random signals on the desired results, the Wiener-Khinchin theorem is used to consider the use of the detector signal's autopower spectrum APSD δφ (r i ,ω) and cross power spectrum CPSD δφ (r i ,r j ,ω) and the auto-power spectrum and cross-power spectrum S of the vibration components xx (ω), S yy (ω) and S xy (ω) Replace the spectrum value to eliminate the unknown variable S xx (ω), S yy (ω), S xy The influence of (ω) and γ is obtained, and the relationship between the auto-power spectrum and cross-power spectrum of the neutron noise signal of the rhodium self-powered neutron detector and the transfer function is obtained. The neutron noise signals of the rhodium self-powered neutron detector at three different positions {r1, r2, r3} are taken together.

[0143]

[0144] CPSD δφ (r1, r2, ω) = γ 2 {G 1x G 2x S xx +G 1y G 2y S yy +(G 1x G 2y +G 2x G 1y )S xy}

[0145] CPSDδφ (r2, r3, ω) = γ 2 {G 2x G 3x S xx +G 2y G 3y S yy +(G 2x G 3y +G 3x G 2y )S xy}

[0146] CPSD δφ (r1, r3, ω) = γ 2 {G 1x G 3x S xx +G 1y G 3y S yy +(G 1x G 3y +G 3x G 1y )S xy}

[0147] Where:

[0148] G ix ≡G x (r i ,r p ,ω);i=1,2,3

[0149] G iy ≡G y (r i ,r p ,ω);i=1,2,3

[0150] Solve the above equations simultaneously to eliminate the unknown variable S xx (ω), S yy (ω), S xy The influence of (ω) and γ.

[0151]

[0152] Among them S ij is the neutron noise spectrum matrix of Rh self-powered neutron detector i and Rh self-powered neutron detector j;

[0153]

[0154] G ij is the transfer function matrix between Rh self-powered neutron detector i and Rh self-powered neutron detector j;

[0155]

[0156] In order to obtain the minimum estimate, while considering the signal interference of the sensors in the project, four rhodium self-powered neutron detectors are polled to obtain the optimal evaluation function, namely:

[0157]

[0158] Make the evaluation function take the minimum r p The value is the position of the control rod where abnormal vibration occurs.

[0159] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for locating abnormal vibration control rods based on neutron noise signals, characterized in that: include: Multiple self-powered neutron detectors are deployed in the reactor to collect neutron noise signal data measured by the self-powered neutron detectors; Preprocessing the neutron noise signal data; the preprocessing includes the following methods: separating an AC signal and a DC signal from the neutron noise signal data, and amplifying the AC signal; sampling the DC signal and the amplified AC signal respectively, and filtering the amplified AC signal to obtain a first AC signal; dividing the first AC signal by the DC signal; Determine whether the control rod has abnormal vibration based on the pre-processed neutron noise signal data; The transfer function between the control rod and the self-powered neutron detector is constructed based on the neutron transport equation; Determining the position of an abnormally vibrating control rod based on a minimization algorithm theory and a transfer function between the control rod and the self-powered neutron detector; specifically, the method includes: obtaining basic evaluation data, the basic evaluation data including: the auto-power spectrum density of self-powered detector i, self-powered detector j, and self-powered detector k at a depth S; the cross-power spectrum density between self-powered detector i, self-powered detector j, and self-powered detector k; and the transfer function from different abnormally vibrating control rods to self-powered detector i, self-powered detector j, and self-powered detector k; i≠j≠k; Calculate the evaluation function Δ(r) based on the evaluation basic data: Where G ij (r p ) represents the transfer function between the self-powered detector i and the self-powered detector j; G jk (r p ) represents the transfer function between the self-powered detector i and the self-powered detector k; Indicates G ij (r p ) inverse operator; Indicates G jk (r p ) inverse operator; Indicates G ij (r p )’s adjoint operator; Indicates G jk (r p )'s adjoint operator; S ij represents the neutron noise spectrum matrix of self-powered detector i and self-powered detector j; S jk represents the neutron noise spectrum matrix of self-powered detector j and self-powered detector k; r p represents the position of the control rod p; The r with the minimum evaluation function p As the position of the control rod for abnormal vibration.

2. The abnormal vibration control rod positioning method based on neutron noise signal according to claim 1 is characterized in that: The method of deploying multiple self-powered neutron detectors in a reactor includes: The first control rod assembly and the second control rod assembly are determined according to condition a; condition a: there is no control rod assembly around the first control rod assembly or the first control rod assembly is the second control rod assembly; A plurality of self-powered neutron detectors are arranged at a central position of the first control rod assembly and at equal depth intervals along the control rod insertion direction.

3. The abnormal vibration control rod positioning method based on neutron noise signal according to claim 1 is characterized in that: The neutron noise signal data includes neutron current signal noise data; The neutron noise signal data δφ(r,t) is: δφ(r,t)=cδi(r,t)=c[i(r,t)-E(i(r,t))] where δi(r,t) represents the neutron current signal noise data; E(·) represents the time-scale mean of the signal; i(r,t) represents the neutron current signal; r represents the position of the core; t represents time; and c represents the linear conversion coefficient of the self-powered neutron detector.

4. The abnormal vibration control rod positioning method based on neutron noise signal according to claim 2, characterized in that: The method of judging whether the control rod has abnormal vibration based on the preprocessed neutron noise signal data includes: Obtain neutron noise signals from different self-powered detectors deployed at the same depth; Calculate the cross-correlation function between self-powered detectors at the same depth based on neutron noise signals; Determine whether the control rod has abnormal vibration based on the cross-correlation function: Obtain the natural frequency of each control rod; At the natural frequency of the control rod, a cross-correlation threshold is preset, and when the cross-correlation function is greater than the cross-correlation threshold, it is determined that an abnormality exists in the control rod.

5. The abnormal vibration control rod positioning method based on neutron noise signal according to claim 4 is characterized in that: The method of calculating the cross-correlation function between self-powered detectors at the same depth based on the neutron noise signal includes: The cross-correlation function R(r,ω) between the self-powered detector x and the self-powered detector y at depth z is: Where S xx (r,ω) represents the power spectrum density of the self-powered detector x at depth z; S yy (r,ω) represents the power spectrum density of the self-powered detector y at depth S; S xy (r, ω) represents the cross-power spectral density of the self-powered detector x and the self-powered detector y at depth z; r represents the position of the self-powered neutron detector, and ω represents the circular frequency of the neutron noise signal.

6. The abnormal vibration control rod positioning method based on neutron noise signal according to claim 1 is characterized in that: The method of constructing a transfer function between a control rod and a self-powered neutron detector based on a neutron transport equation includes: Based on neutron transport theory, the neutron noise equation caused by the fluctuation of the absorption cross section is: Where L is an operator defined on the Hilbert space, S(r,ω) is the disturbance source caused by the control rod vibration, D is the neutron diffusion coefficient, δφ(r,ω) represents the neutron noise signal, r represents the position of the self-powered neutron detector, and ω represents the circular frequency of the neutron noise signal. Based on Green's function theory, the Green's function solution G(r, r′, ω) of the neutron noise equation is the transfer function between the control rod vibration and the neutron flux at the neutron detector: δφ(r,ω)=∫G(r,r′,ω)S(r′,ω)dr′ Where r′ represents the position of the control rod; S(r′,ω) represents the disturbance source caused by the control rod vibration.

7. Abnormal vibration control rod positioning system based on neutron noise signal, characterized in that: The system is used to implement the abnormal vibration control rod positioning method based on neutron noise signals as described in any one of claims 1 to 6, comprising: An acquisition module is used to deploy multiple self-powered neutron detectors in the reactor and collect neutron noise signal data measured by each of the self-powered neutron detectors; A preprocessing module, used for preprocessing the neutron noise signal data; a judgment module, configured to judge whether the control rod has abnormal vibration based on the preprocessed neutron noise signal data; A construction module for constructing a transfer function between the control rod and the self-powered neutron detector based on the neutron transport equation; The positioning module is used to determine the position of the abnormally vibrating control rod based on the minimization algorithm theory and the transfer function between the control rod and the self-powered neutron detector.

8. A computer-readable medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement the abnormal vibration control rod positioning method based on neutron noise signals as described in any one of claims 1 to 6.

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