Rapid inference method for neutron flux distribution change of reactor core of nuclear reactor

Abstract

A rapid inference method for a neutron flux distribution change of a reactor core of a nuclear reactor. In an offline training stage, a transient neutron transport equation is solved by means of a full-order solver, so as to obtain spatial distribution data of neutron flux and a delayed neutron precursor density changing over time, a reduced-order basis and a reduced-order coefficient data set of a training data set are obtained by means of proper orthogonal decomposition, and a reduced-order model is obtained by means of least squares fitting into the reduced-order coefficient data set; and in an online prediction stage, after the reduced-order model is solved on the basis of parameters of a predicted working state, the reduced-order basis is applied to a solved reduced-order coefficient, so as to reconstruct a physical field, which includes a neutron flux distribution of a reactor core, a delayed neutron precursor density distribution, etc. changing over time. In the present invention, data of a high-fidelity full-order model is used to construct a rapid prediction model, and a high-resolution change in the neutron flux of a reactor core over time is finely and efficiently described in a neutronics simulation, which plays an important role in reactor safety analysis, reactor data assimilation and inverse problem solving.

Description

Fast inference method for changes in neutron flux distribution in nuclear reactor core TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear reactor control, and particularly relates to a fast inference method for changes in neutron flux distribution in nuclear reactor core. BACKGROUND

[0002] The neutron flux distribution in a pressurized water reactor core is one of the most important physical quantities in a nuclear reactor, and plays an important role in safety analysis and state prediction of the reactor. The present application aims to meet the demand for high-fidelity and fast calculation of the core neutron flux in the field of safety analysis and core prediction of the existing nuclear reactor, and proposes a fast inference method suitable for neutron models. SUMMARY

[0003] The present application aims to solve the problem that the prior art cannot be directly applied to the scene where the working condition parameters of the reactor change over time, and needs to use an interpolation method to extend the reduced-order model to different parameter scenes. A fast inference method for changes in neutron flux distribution in nuclear reactor core is proposed, which uses the data of a high-fidelity full-order model to construct a fast prediction model, finely and efficiently describes the high-resolution changes in core neutron flux over time in neutron simulation, and plays an important role in carrying out safety analysis of the reactor, data assimilation of the reactor, and solution of inverse problems.

[0004] The present application is implemented by the following technical solutions:

[0005] The present application relates to a fast inference method for changes in neutron flux distribution in nuclear reactor core. In the offline training stage, a full-order solver is used to solve the transient neutron transport equation to obtain the spatial distribution data of the neutron flux and the time-varying delayed precursor density. The reduced-order basis and the reduced-order coefficient data set of the training data set are obtained by eigenvalue orthogonal decomposition, and the reduced-order model is obtained by least square fitting in the reduced-order coefficient data set. In the online prediction stage, the reduced-order model is solved according to the parameters of the predicted working condition, and the reduced-order basis is applied to the reduced-order coefficient obtained by solving to reconstruct the physical field including the time-varying distribution of the core neutron flux and the delayed precursor density.

[0006] The proper orthogonal decomposition is implemented by, but not limited to, the technology described in Lu, K. et al. in Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. Mechanical Systems and Signal Processing, 123, 264-297. https: / / doi.org / 10.1016 / j.ymssp.2019.01.018.

[0007] The present application relates to a system for implementing the above method, comprising a data order reduction unit, an order reduction model fitting unit and an online prediction and reconstruction unit, wherein: the data order reduction unit performs proper orthogonal decomposition on the calculation result data of the provided full order model to obtain an order reduction basis and an order reduction coefficient data set; the order reduction model fitting unit performs least squares fitting on the order reduction coefficient data set to obtain a matrix in the order reduction model; and the online prediction and reconstruction unit solves the equation according to the fitted order reduction model matrix to obtain predicted order reduction coefficients, and then reconstructs the full order data using the order reduction coefficients. Technical effects

[0008] The present application is based on the proper orthogonal decomposition and order reduction model matrix fitting method, uses the data of the high-fidelity full order model, obtains the matrix in the order reduction model through parameter affine decomposition and least squares fitting, and thus obtains the order reduction model. Compared with the prior art, the present application solves the order reduction model with a dimension much lower than the full order model, quickly obtains the changes of key physical quantities such as the neutron flux and the delayed precursor nuclear density distribution in the core with time under the condition that the time-varying working condition parameters are given, reduces the calculation time while maintaining a low prediction error, and plays an important role in the safety analysis and state prediction of the reactor core. BRIEF DESCRIPTION OF DRAWINGS

[0009] Fig. 1 is a flowchart of the present application;

[0010] Fig. 2 is a top view of the arrangement of the C5G7-TD3-4 problem assembly in the embodiment;

[0011] Fig. 3 is a schematic diagram of the maximum relative error of the predicted physical quantities (neutron flux and delayed precursor nuclear density) in the embodiment. DETAILED DESCRIPTION

[0012] As shown in Figure 1, for the embodiment related to a method for rapidly inferring the change of neutron flux distribution in a nuclear reactor core, in the offline training stage, the transient neutron transport equation is solved by a full-order solver to obtain the spatial distribution data of neutron flux and delayed precursor density changing with time, and the reduced basis and reduced data set of the training data set are obtained by eigenvalue orthogonal decomposition; in the reduced coefficient data set, the reduced matrix in the reduced model is obtained by least square fitting; in the online prediction stage, after the reduced model is solved according to the parameters of the predicted working condition, the reduced basis is applied to the reduced coefficient obtained by solving to reconstruct the physical field containing the distribution of neutron flux and delayed precursor density in the core.

[0013] The training data set is obtained by the following method: by using an arbitrary transient neutron transport equation full-order model solver, the data of neutron flux and precursor density changing with time in the core is solved under the condition of given geometry, material and working condition parameter change.

[0014] The eigenvalue orthogonal decomposition specifically includes:

[0015] 1) n t time points The length of the n solution vector is stored as a snapshot matrix Wherein: φ contains the neutron flux of each energy group and the density of each group of delayed precursors, and n is the product of the number of energy groups, the number of delayed groups and the spatial degree of freedom.

[0016] 2) The snapshot matrix is subjected to eigenvalue orthogonal decomposition, specifically: singular value decomposition is used to obtain Wherein: is an orthogonal basis matrix unitary matrix of the subspace; is a diagonal matrix containing singular values, and generally, the singular values on the diagonal are arranged in descending order; is also a unitary matrix. If only the first r columns of the matrix are retained as the orthogonal basis, the truncated basis in the subspace will be obtained.

[0017] The retention parameter r satisfies: Wherein: τ is a number less than 1, and is usually selected as 0.9999; λ is the diagonal element of Λ, that is, the singular value. The inequality describes the proportion of the retained orthogonal basis in the total information, and the first r columns of the matrix are recorded as U.

[0018] 3) The reduced basis matrix U is applied to the full-order solution vector to obtain the reduced coefficient snapshot, specifically:

[0019] The reduced model specifically includes: Where: t is time; is the reduction coefficient; and For a reduced-order matrix, the equation is obtained in the following way: In the transient process of neutronics, the macroscopic cross section Σ of neutrons often has the following form of time variation, specifically: Σ(t) = Σ (0) +μ(t)Σ (1) , where μ(t) is the core operating parameters that change with time, such as control rod position, coolant density, etc.

[0020] The reduced-order matrix of the reduced-order model is obtained by least squares fitting, specifically including: fitting by least squares method and Specifically: Among them: ||||2 and |||| F are the 2-norm of the vector and the Frobenius norm of the matrix respectively; The time derivative of the reduced-order coefficient vector is approximated by difference, specifically: Each least squares problem is solved directly as follows, specifically: The reduced-order equation matrix and Solve the elements of each row in turn.

[0021] The reconstruction specifically includes: given the parameters of the predicted working condition Given the initial state of the core φ0, the core state is predicted in time series by solving the reduced-order equation obtained, specifically: Where: j = 1,...,n t , n t is the number of time steps; is the identity matrix; Δt is the discrete time step; the initial condition is given by the reduced-order relation Apply the reduced-order basis matrix to the reduced-order coefficients obtained We can get the neutron flux and the delayed precursor density at t j The spatial distribution of time is as follows: That is, the parameters of the given new core prediction conditions are realized Given the initial state φ0 of the core, the core state is predicted in time series.

[0022] After specific experiments, a typical small pressurized water reactor problem is simulated, as shown in FIG. 2, and the simulation parameters are provided in the international benchmark problem C5G7-TD3-4. In the offline stage, the solution time step of the full-order model is selected as 0.02s, the calculation time period is 0-1s, the first 0.5s is used as the training set, and the last 0.5s is used as the test set, and only the training set data is used to train the reduced-order model. In the online stage, the reduced-order model trained is used to predict the change of physical quantities with time in the interval of 0-1s, and the results are compared with those of the full-order model. As shown in FIG. 3, the relative error data of the prediction results of the reduced-order model trained by the method and the full-order model are shown.

[0023] Compared with the prior art, the method reduces the calculation time while maintaining a low prediction error. In the simulation results described above, the solution time of the full-order transport model is 36 core seconds / time step; the solution time of the reduced-order model is 3.3x10 -5 core seconds / time step, and the reconstruction time of the full-order physical quantity is 6.4x10 -3 core seconds / time step, and the total calculation time is reduced by three orders of magnitude. As shown in FIG. 3, compared with the spatial distribution of the neutron flux and the delayed precursor nuclear density calculated by the full-order transport model, the maximum error of the reduced-order prediction model is less than 1%. The performance index of the device / method (i.e. the effect of using the new technology in the above-mentioned link) is that the dimension of the reduced-order model constructed by the method is much lower than that of the full-order model, so that fast solution and prediction are realized.

[0024] The above specific embodiments can be adjusted by those skilled in the art in different ways without departing from the principles and purposes of the present application, the protection scope of the present application is subject to the claims and is not limited by the above specific embodiments, and each implementation scheme within the scope is subject to the constraints of the present application.

Claims

1. A method for rapid inference of changes in the neutron flux distribution in a nuclear reactor core, characterized in that, The transient neutron transport equation is solved by a full-order solver in an offline training stage to obtain spatial distribution data of neutron flux and delayed precursor density changing with time, intrinsic orthogonal decomposition is used to obtain a reduced-order basis and a reduced-order coefficient data set of the training data set, and a reduced-order model is obtained by least square fitting in the reduced-order coefficient data set; in an online prediction stage, the reduced-order model is solved according to parameters of a predicted working condition, and the reduced-order basis is applied to the reduced-order coefficient obtained by solving to reconstruct a physical field including neutron flux and delayed precursor density distribution in a reactor core.

2. The method of claim 1, wherein the method is characterized by, The training data set is obtained by using an arbitrary transient neutron transport equation full-order model solver to solve neutron flux and precursor density changing with time in a given geometry, material and working condition parameter change.

3. The method of claim 1, wherein the method is characterized by: The intrinsic orthogonal decomposition specifically includes: 1) n t time points length n solution vector Storing as a snapshot matrix Wherein φ includes neutron specific flux of each energy group and delayed precursor density of each group, and n is the product of the number of energy groups, the number of delayed groups and spatial degrees of freedom; 2) Eigen-orthogonal decomposition is applied to the snapshot matrix, specifically: singular value decomposition is used to obtain wherein: an orthogonal basis matrix of a subspace is a unitary matrix; for a diagonal matrix containing singular values, the singular values on the diagonal are arranged in order from largest to smallest; Also unitary matrices; preserving matrices The orthogonal basis in the first r < < n columns obtains a truncated basis in a subspace; 3) Apply the reduced basis matrix U to the full-order solution vector to obtain the reduced-order coefficient snapshot, specifically:

4. The method of claim 3, wherein the method is characterized by: The retention parameter r satisfies: where: τ is a number less than 1, λ is a diagonal element of Λ, i.e., a singular value, and the first r columns of the matrix are denoted by U.

5. The method of claim 1, wherein the method is characterized by: The reduced order model, in particular, wherein: t is time; is a reduced order coefficient; and is a reduced order matrix.

6. The method of claim 1 or 5, wherein the method is characterized by, The reduced order matrix of the reduced order model is obtained by least square fitting, and specifically comprises: fitting by least square method With Specifically: Wherein: || ||2 and || || F Respectively, the 2-norm of the vector and the Frobenius norm of the matrix; The time derivative of the reduced order coefficient vector is approximated by difference, and specifically comprises: Each least square problem is directly solved as follows, and specifically comprises: The reduced order equation matrix And The elements of each row are solved in turn.

7. The method of claim 1, wherein the method is characterized by: The reconstruction specifically includes: In a given predicted operating condition and given the initial state of the core φ0, the core state is predicted in time by solving the resulting reduced equation, in particular: where: j = 1,..., n t , n t is the number of time steps; Is a unit matrix, and Δt is a discrete time step; The initial conditions are given by the reduced order relationship applying the reduced basis matrix to the reduced coefficients The neutron flux and the density of the delayed precursor nuclei at the time t0can be obtained, i.e. j The neutron flux and the density of the delayed precursor nuclei at the time t0can be obtained, i.e. Implementing parameters for a given new core predicted operating condition And the time sequence of the core state is predicted under the condition of a given core initial state φ0.

8. A system for rapid inference of changes in the neutron flux distribution in the core of a nuclear reactor implementing the method of any of claims 1-7, characterized in that, It includes: A data reduction unit, a reduced-order model fitting unit and an online prediction and reconstruction unit, wherein the data reduction unit performs intrinsic orthogonal decomposition according to the calculation result data of the provided full-order model to obtain a reduced-order basis and a reduced-order coefficient data set; the reduced-order model fitting unit performs least square fitting according to the reduced-order coefficient data set to obtain a matrix in the reduced-order model; and the online prediction and reconstruction unit solves the equation according to the fitted reduced-order model matrix to obtain predicted reduced-order coefficients, and then reconstructs the full-order data by using the reduced-order coefficients.

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