Fundamental wave extraction improved source multiplication online measurement method, system and equipment based on digital twin data driving technology

Abstract

The invention discloses a fundamental wave extraction improved source multiplication online measurement method, system and equipment based on a digital twin data driving technology, and relates to the technical field of subcritical reactivity measurement. The method comprises the following steps: establishing a digital twinning mapping harmonic expansion model, taking an actually measured detector counting rate as data drive, iteratively correcting a harmonic expansion coefficient in the digital twinning mapping harmonic expansion model, obtaining corrected fundamental wave neutron information, and then applying an improved source multiplication method to obtain absolute reactivity. Therefore, the reactivity on-line measurement of the subcritical degree is realized. According to the method, digital twinning and data driving technologies are combined, the counting rate of the detector is actually measured to serve as data driving, the harmonic expansion coefficient in the digital twinning harmonic expansion model is iteratively corrected, fundamental neutron information can be extracted more accurately, then the reactive online measurement precision of the wide subcriticality can be improved, and the measurement accuracy of the wide subcriticality is improved. And the reactivity accurate online measurement of the wide-range subcritical degree is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of subcritical reactivity measurement, and in particular to a fundamental wave extraction improved source multiplication online measurement method, system and equipment based on digital twin data driven technology. Background Art

[0002] The essential problem of the control rod calibration and shutdown depth measurement of marine reactors in subcritical state is to cover a wide range of subcritical reactivity measurement. Taking into account the comparative factors such as the arrangement of external neutron sources in marine reactors, the subcritical span from shutdown to criticality, and the off-line measurement methods, the source multiplication method (NSM) and the improved source multiplication method (MSM) in the subcritical reactivity measurement method provide technical feasibility for the wide range of subcritical online measurement of marine reactors.

[0003] The traditional source multiplication method (NSM) is based on the subcritical multiplication theory of the point reactor model, assuming that the neutron fluence rate distribution is defined as the fundamental mode of the neutron diffusion equation and remains unchanged at any subcriticality. However, in actual measurements, the spatial distribution of the steady-state neutron fluence rate of the subcritical system does not follow the fundamental mode, and the deviation from the fundamental mode increases with the increase of subcriticality, which results in the NSM method only giving a reliable k when the reactor is very close to criticality. eff (Effective multiplication coefficient of neutrons in a nuclear reactor), which can generally only be used for k eff Estimation of changing trends.

[0004] In order to make the NSM method applicable to slightly deeper subcriticality measurements, the academic community proposed an improved source multiplication method (MSM). Compared with the NSM method, the MSM is based on the actual steady-state neutron injection rate of the externally driven subcritical system and uses the detector correction factor f D , external neutron source correction factor f S Implicitly associate the detected count rate M with the predicted k eff (usually calculated) to force a correlation in the expectation that M will pass through f D 、f S Correction to get k eff The MSM method improves the accuracy of the NSM method for slightly deeper subcriticality, but this correction method does not reveal the physical essence that the steady-state neutron fluence rate of the subcritical system is the superposition of the fundamental wave and the higher-order harmonics: that is, the steady-state neutron fluence rate of the externally driven subcritical system is formed by the direct contribution of the external neutron source, the superposition of the fundamental wave and the higher-order harmonic neutron fluence rate contribution of the subcritical multiplication process, and the contribution of the higher-order harmonics increases with the deepening of the subcriticality, making the steady-state neutron fluence rate deviate significantly from the fundamental wave distribution. This results in the need for MSM to calculate a personalized f for each scheme (different core schemes, different neutron sources, different detector positions) D 、f S, its universality is not strong. Practical applications show that at deeper subcriticality, the k given by MSM eff The error of the measurement results still cannot meet engineering requirements, and it is difficult to use it to accurately measure the subcritical reactivity of a wide range of marine reactors covering deep and shallow subcriticality. Summary of the invention

[0005] One of the purposes of the present invention is to provide a new method for online measurement of improved source multiplication based on fundamental wave extraction method combined with digital twin and data-driven technology, so as to provide an efficient and reliable means for accurate online measurement of wide range subcritical reactivity of marine reactors.

[0006] In order to achieve the above object, the present invention adopts the following technical solution: a fundamental wave extraction improved source multiplication online measurement method based on digital twin data driven technology, comprising the following steps:

[0007] A digital twin mapping harmonic expansion model is established, and the measured detector count rate is used as data drive to iteratively correct the harmonic expansion coefficients in the digital twin mapping harmonic expansion model to obtain the corrected fundamental neutron information. Then the improved source multiplication method is applied to obtain the absolute reactivity, thereby realizing online measurement of subcritical reactivity.

[0008] Furthermore, the established digital twin mapping harmonic expansion model is

[0009]

[0010] Among them, φ s,c Mapping the neutron flux of the harmonic expansion model for the digital twin, A i,c is the harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

[0011] Furthermore, the measured detector count rate is used as data drive to iteratively correct the harmonic expansion coefficient in the harmonic expansion model of the digital twin mapping, and the specific steps of obtaining the corrected fundamental neutron information include:

[0012] By using the measured detector count rate as data drive, the detector count rate corresponding to the digital twin mapping harmonic expansion model is corrected, and then the harmonic expansion coefficient is corrected to obtain the corrected fundamental neutron information;

[0013] The detector count rate R corresponding to the harmonic expansion model of the digital twin mapping c for

[0014] R c =φ s,c Σ d

[0015] Among them, φ s,cMapping the neutron flux of the harmonic expansion model for the digital twin, Σ d is the nuclear reaction macroscopic cross section of the neutron detector;

[0016] The measured detector count rate R m for

[0017] R m =φ s,m Σ d

[0018] Among them, φ s,m is the actual measured neutron flux, Σ d is the nuclear reaction macroscopic cross section of the neutron detector;

[0019] Corrected digital twin mapping neutron flux φ of the harmonic expansion model s ' ,c for

[0020]

[0021] Among them, A' i,c is the corrected harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

[0022] Furthermore, the method further comprises the following steps: extracting the fundamental mode component from the measured neutron count rate:

[0023]

[0024] Among them, M 1,ex is the extracted fundamental mode component, M ex is the measured neutron counting rate, C1 M (r d ) is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector.

[0025] Furthermore, when the improved source multiplication method is used to obtain the absolute reactivity, the absolute reactivity of the subcritical system is calculated according to the following formula:

[0026]

[0027] in, and is the correction factor, Q l is the neutron count multiplication, and the subscript ref is the reference subcritical state, that is, is the absolute reactivity of the reference subcritical state.

[0028] Furthermore, the correction factor for

[0029]

[0030] in, is the characteristic function, s is the external neutron source, and the subscript ref is the reference subcritical state, that is, is the characteristic function of the reference subcritical state.

[0031] Furthermore, the correction factor for

[0032]

[0033] in, is the fundamental neutron injection rate of the subcritical system, r d is the neutron detector position, Σ d is the nuclear reaction macroscopic cross section of the neutron detector, and the subscript ref is the reference subcritical state, that is, is the fundamental neutron fluence rate of the reference subcritical state.

[0034] Furthermore, the correction factor for

[0035]

[0036] in, is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector, and the subscript ref is the reference subcritical state, that is, is the extraction coefficient of the reference subcritical state.

[0037] Another object of the present invention is to provide an online measurement system for fundamental wave extraction and improved source multiplication based on digital twin data-driven technology, which comprises:

[0038] A digital twin model building unit, used to build a digital twin mapping harmonic expansion model;

[0039] A data driving unit, used for using the measured detector count rate as data driving;

[0040] A correction unit, used for iteratively correcting the harmonic expansion coefficients in the harmonic expansion model of the digital twin mapping to obtain the corrected fundamental neutron information;

[0041] Computational unit for obtaining absolute reactivity using the modified source multiplication method.

[0042] The system may further include a fundamental wave extraction unit for extracting fundamental wave mode components from the measured neutron count rate.

[0043] In addition, the present invention also provides a fundamental wave extraction improved source multiplication online measurement device based on digital twin data driving technology, which includes:

[0044] Memory for storing computer programs;

[0045] A processor is used to implement the steps of the above-mentioned fundamental wave extraction and improved source multiplication online measurement method based on digital twin data-driven technology when executing the computer program.

[0046] The present invention is a new method for improved source multiplication based on the fundamental wave extraction method, which combines digital twin and data-driven technology. The experimentally measured detector count rate is used as data drive, and the harmonic expansion coefficient in the digital twin harmonic expansion model is iteratively corrected to make it consistent with the fundamental wave neutron information of the real typical experimental device. The fundamental wave neutron information can be extracted more accurately, thereby improving the online measurement accuracy of the reactivity with a wide subcriticality, and realizing accurate online measurement of the reactivity with a wide range of subcriticality. It can provide an efficient and reliable means for accurate online measurement of the wide range of subcritical reactivity of marine reactors. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Flowchart for iterative modification of the harmonic expansion model for digital twin data-driven technology. DETAILED DESCRIPTION

[0048] In order to facilitate those skilled in the art to better understand the improvements of the present invention relative to the prior art, the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0049] Reactivity reflects the neutron multiplication characteristics when neutrons in the reactor are distributed according to the fundamental wave characteristics. To achieve accurate measurement, the traditional wide-range subcritical reactivity online measurement methods: source multiplication method (NSM) and improved source multiplication method (MSM) need to accurately extract the fundamental wave information from the steady-state neutron injection rate of the superposition of the fundamental wave and high-order harmonics, and develop a new improved source multiplication method based on fundamental wave extraction.

[0050] In the eigenvalue problem of the neutron balance equation, harmonics and conjugate harmonics are in a biorthogonal relationship, which provides complete mathematical characteristics for the extraction of fundamental information. The new improved source multiplication method based on fundamental extraction needs to consider factors including fundamental mode extraction, neutron value perturbation, and spatial effect correction; at the same time, due to the difference between the physical model and the actual device in the harmonic calculation process, numerical calculation uncertainty factors such as nuclear data will also affect the accuracy of fundamental extraction. Therefore, it is necessary to establish an accurate and reliable physical model that can reflect the real state of the subcritical reactor.

[0051] Digital twin is a technology that realizes the mapping of physical system to digital model of information space. Digital twin technology based on data drive feeds back the actual data output by the detector to the high-order harmonic reconstruction calculation results of steady-state neutron injection rate, and corrects the theoretical calculation results through data assimilation technology, which can effectively avoid the uncertainty introduced by theoretical modeling and numerical calculation processes, and can effectively improve the calculation accuracy, so that the results of fundamental wave extraction can more truly reflect the neutron characteristics of the actual object. Therefore, combining digital twin and data drive, accurately extracting fundamental wave information from the steady-state neutron injection rate superimposed by fundamental wave and high-order harmonics, and establishing a new improved source multiplication method based on fundamental wave extraction can provide an efficient and reliable means for accurate online measurement of wide-range subcritical reactivity of marine reactors.

[0052] Based on the above conception, the present invention provides a new method for online measurement of subcritical reactor reactivity over a wide range (i.e., a new method for online measurement of fundamental wave extraction and improved source multiplication based on digital twin data-driven technology), which can realize high-efficiency and accurate calibration of shipboard reactor control rods and online determination of shutdown depth of deep subcritical reactors, and has important theoretical value and engineering significance for reactor physics and experimental technology.

[0053] The details are as follows:

[0054] High-order harmonics and conjugate harmonics have biorthogonal characteristics, and the neutron injection rate for any working condition can be expanded into the following expression:

[0055]

[0056] Among them A n is the expansion coefficient, which is related to the proliferation characteristics and exogenous characteristics of the deep subcritical system driven by a steady-state exogenous source, and can be obtained by harmonic and conjugate harmonic calculations. For the calculation method of high-order harmonics, it can be calculated using the deterministic method or the Monte Carlo method.

[0057] From formula (1), we can see that the neutron injection rate is expanded into the following form:

[0058]

[0059] Among them, φ i,λ represents the neutron fluence rate of the i-th group of λ eigenvalues.

[0060] In order to distinguish the neutron flux rate of the digital twin mapping model from that of the experimental measurement, the neutron flux of the digital twin mapping model is defined as: s,c , the experimentally measured real neutron flux is: φ s,realThe digital twin mapping model and the real neutron flux measured in the experiment are driven by the detector count rate, thereby realizing the iterative correction between the neutron injection rate of the digital twin mapping model and the real neutron flux measured in the experiment. The detector count rate R corresponding to the digital twin mapping model is c and the detector count rate R obtained by experimental measurement m The definition is as follows:

[0061] R c =φ s,c Σ d (3)

[0062] R m =φ s,m Σ d (4)

[0063] Among them, φ s,m is the experimentally measured neutron flux, Σ d is the macroscopic cross section of nuclear reactions in the neutron detector.

[0064] By R m (experimental measurement value) as data driver, and then to R c Make corrections, that is, correct the harmonic expansion coefficient A i,c , the corrected harmonic expansion coefficient can be defined as A' i,c , so the corrected calculated value is:

[0065]

[0066] Among them, φ s ' ,c Mapping model neutron flux for the revised digital twin.

[0067] At this time, the fundamental neutron information obtained by equation (5) can be considered to be almost consistent with the fundamental neutron information obtained in the experiment, and then the improved source multiplication method is applied to obtain the absolute reactivity. The absolute reactivity obtained at this time can truly express the subcriticality of the actual core. That is, by establishing a digital twin mapping harmonic expansion model, using the measured detector count rate as data drive, the digital twin harmonic model and the typical experimental device are iteratively corrected The harmonic expansion coefficient makes the corrected fundamental neutron information can truly reflect the subcriticality of the typical experimental device. The relevant interactive process is as follows Figure 1 shown.

[0068] To realize the above overall process, how to extract fundamental information from complex detector information is a key issue. Therefore, the steady-state neutron diffusion equation of the subcritical system with an external neutron source can be described as:

[0069] Lφ s (r)=Fφ s(r)+s(r) (6)

[0070] Where L is the neutron disappearance operator, F is the neutron production operator, and s(r) is the external neutron source. Subcritical systems can also be analyzed using the neutron diffusion equation of the eigenvalue problem:

[0071]

[0072] Among them, k i is the i-th eigenvalue, φ i c is the corresponding characteristic function. It is known that the maximum characteristic value of the above formula is "neutron multiplication factor (k eff )”, the corresponding characteristic function is the fundamental mode. For the eigenvalue problem of formula (6), its conjugate equation is defined as follows:

[0073]

[0074] in and is the conjugate operator of L and F; is the same as the ith eigenvalue k i The associated i-th adjoint eigenfunction. and The orthogonal relationship is as follows:

[0075]

[0076] in Defined as:

[0077]

[0078] The superscript "T" indicates the transpose of a matrix or vector, and the integration is performed over the entire region of the neutron multiplication system. The characteristic function φ of equations (7) and (8) is known. i c and As a complete set, the neutron fluence rate distribution φ for the fixed source problem s It can be expanded into formula (1) using characteristic function. i is the expansion coefficient. i The neutron generation operator F can be combined from the left side of equation (1) to both sides of equation (1), and the inner product defined by equation (11) can be applied to obtain the following result:

[0079]

[0080] Therefore, the neutron fluence rate distribution φ s The characteristic function φ can be used i c Expand, such as:

[0081]

[0082] In order to s Extract the fundamental mode from the g-th group and introduce the subgroup coefficient C s 1,g (r), as follows:

[0083]

[0084] in, is the fundamental neutron fluence rate of the gth group of the subcritical system, is the g-th group neutron fluence rate of the subcritical system with an external neutron source.

[0085] in and is the g-group flux distribution normalized by the total number of fission neutrons, such as:

[0086]

[0087] The neutron count rate M(r d ) and the fundamental mode component (M1) contained in M ​​can be expressed as:

[0088] M(r d )=Σ d φ s (r d ) (16)

[0089]

[0090] where r d is the position of the neutron detector. Symbol Σ d and C1 s represents a row vector with G elements and is defined as a diagonal matrix with G diagonal elements:

[0091] Σ d =[ε1Σ d,1 ,…,ε G Σ d,G ] (18)

[0092]

[0093] Among them, Σ d,g is the macroscopic cross section of the neutron detection nuclear reaction of the g-th group neutrons, ε g is the detector efficiency of the nuclear detection process caused by the g-th group of neutrons, is the neutron group coefficient of the Gth group.

[0094] The extraction coefficients for extracting the fundamental mode components from the measured data are defined as:

[0095]

[0096] And the coefficient C1 M (r d ) can be calculated in advance based on the numerical analysis of equations (7) and (8). Then the neutron counting rate (M) obtained from the actual measurement is ex ) contains the fundamental mode component (M 1,ex ) can be extracted as:

[0097]

[0098] In summary, combined with the digital twin data-driven technology, the experimental detector count rate is used as the data driver to iteratively correct the A in the digital twin harmonic expansion model. i,c , which makes it consistent with the fundamental neutron information of a real typical experimental device. The improved source multiplication method based on the fundamental wave extraction method proposed in the present invention can realize more accurate extraction of fundamental wave neutron information.

[0099] In order to measure the reactivity of the subcritical system, d A reference subcritical state is designated at , and a neutron detector is placed. It is assumed that the intensity of the external neutron source remains constant in any subcritical state. Problems with variable intensity can also be handled with some minor modifications to the following procedure. The fundamental mode component M contained in the measurement data 1,ref Related to subcriticality, as follows:

[0100]

[0101] The subscript "ref" is called the reference subcritical state. The neutron count multiplication Q in the first subcritical state l Can be defined as

[0102]

[0103] For neutron count multiplication Q l , the following three correction factors are introduced:

[0104]

[0105] Where s is the external neutron source, is the fundamental neutron fluence rate of the subcritical system, Σ d is the macroscopic cross section of nuclear reactions in the neutron detector.

[0106] Using these correction factors, the reactivity of the subcritical system can be obtained for:

[0107]

[0108] The change in reactivity disturbs the neutron important field and the neutron flux distribution, causing the intensity of the fundamental mode contained in the neutron source to change. Changes in fundamental mode The distribution of has also changed. From equations (24), (25) and (26), we can see that Related to the extraction of the fundamental mode, Corrected the effects caused by neutron important field perturbations, Corrected spatial effects caused by fundamental mode perturbations.

[0109] In the traditional MSM method, instead of using three correction factors and Instead, we use two factors f s and f ε To correct the subcriticality. These two factors can be expressed by the three correction coefficients mentioned above as follows:

[0110]

[0111]

[0112] From the above expression, it can be found that in the traditional MSM method, f defined as the “detector efficiency” ε is decomposed into two correction factors for fundamental mode extraction and spatial correction. These correction factors vary in a very complex way, depending on the reactivity addition method, the geometry of the neutron multiplication system, the location of the neutron detectors, and the distribution of the external neutron source. Therefore, f, which is a combination of the two factors, ε The changes will become more complicated. From this perspective, compared with the traditional method, the new method proposed in the present invention can evaluate the effect of each correction separately and in detail, and through these analyses, give a clear physical explanation of the correction process. In addition, the present invention combines digital twin data-driven technology and uses the experimental detector count rate as data drive to achieve more accurate extraction of fundamental neutron information, thereby improving the online measurement accuracy of wide subcritical reactivity.

[0113] The above embodiments are preferred implementation schemes of the present invention. In addition, the present invention may also be implemented in other ways. Any obvious replacement without departing from the concept of the present technical solution is within the protection scope of the present invention.

Claims

1. The fundamental wave extraction and improved source multiplication online measurement method based on digital twin data-driven technology is characterized by: The following steps are involved: A digital twin mapping harmonic expansion model is established, and the measured detector count rate is used as data drive to iteratively correct the harmonic expansion coefficients in the digital twin mapping harmonic expansion model to obtain the corrected fundamental neutron information. Then the improved source multiplication method is applied to obtain the absolute reactivity, thereby realizing online measurement of subcritical reactivity.

2. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: The established digital twin mapping harmonic expansion model is Among them, φ s,c Mapping the neutron flux of the harmonic expansion model for the digital twin, A i,c is the harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

3. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: Using the measured detector count rate as data drive, the harmonic expansion coefficients in the digital twin mapping harmonic expansion model are iteratively corrected to obtain the corrected fundamental neutron information. The specific steps include: By using the measured detector count rate as data drive, the detector count rate corresponding to the digital twin mapping harmonic expansion model is corrected, and then the harmonic expansion coefficient is corrected to obtain the corrected fundamental neutron information; The detector count rate R corresponding to the harmonic expansion model of the digital twin mapping c for R c =φ s,c S d Among them, φ s,c Mapping the neutron flux of the harmonic expansion model for the digital twin, Σ d is the nuclear reaction macroscopic cross section of the neutron detector; The measured detector count rate R m for R m =φ s,m S d Among them, φ s,m is the actual measured neutron flux, Σ d is the nuclear reaction macroscopic cross section of the neutron detector; Corrected digital twin mapping neutron flux φ of the harmonic expansion model s ' ,c for Among them, A' i,c is the corrected harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

4. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: The following steps are also included: Extract the fundamental mode component from the measured neutron count rate: Among them, M 1,ex is the extracted fundamental mode component, M ex is the measured neutron counting rate, C1 M (r d ) is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector.

5. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: When the improved source multiplication method is used to obtain absolute reactivity, the absolute reactivity is calculated according to the following formula: in, and is the correction factor, Q l is the neutron count multiplication, and the subscript ref is the reference subcritical state.

6. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 5 is characterized in that: The correction factor for in, is the characteristic function, s is the external neutron source, and the subscript ref is the reference subcritical state.

7. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 5 is characterized in that: The correction factor for in, is the fundamental neutron injection rate of the subcritical system, r d is the neutron detector position, Σ d is the nuclear reaction macroscopic cross section of the neutron detector, and the subscript ref is the reference subcritical state.

8. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 5 is characterized in that: The correction factor for in, is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector, and the subscript ref is the reference subcritical state.

9. Fundamental wave extraction based on digital twin data-driven technology to improve source multiplication online measurement system, characterized by: include: A digital twin model building unit, used to build a digital twin mapping harmonic expansion model; A data driving unit, used for using the measured detector count rate as data driving; A correction unit, used for iteratively correcting the harmonic expansion coefficients in the harmonic expansion model of the digital twin mapping to obtain the corrected fundamental neutron information; Computational unit for obtaining absolute reactivity using the modified source multiplication method.

10. Fundamental wave extraction based on digital twin data-driven technology to improve source multiplication online measurement equipment, characterized in that: include: Memory for storing computer programs; A processor is used to implement the steps of the fundamental wave extraction improved source multiplication online measurement method based on digital twin data driven technology as described in any one of claims 1 to 8 when executing the computer program.

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