A fast inference method for neutron flux distribution changes in nuclear reactor core

Abstract

A method for rapid inference of changes in the core neutron flux distribution of a nuclear reactor, in the offline training stage, a full-order solver is used to solve the transient neutron transport equation to obtain spatial distribution data of neutron flux and delayed precursor nuclear density over time, and a reduced-order basis and a reduced-order coefficient data set of the training data set are obtained by proper orthogonal decomposition, and a reduced-order model is obtained by least squares fitting in the reduced-order coefficient data set; in the online prediction stage, after solving the reduced-order model according to the parameters of the predicted working condition, the reduced-order basis is applied to the solved reduced-order coefficients to reconstruct a physical field including core neutron flux, delayed precursor nuclear density distribution, etc. that changes with time. The present invention constructs a rapid prediction model using data from a high-fidelity full-order model, and describes the changes in high-resolution core neutron flux over time in neutronics simulation in a precise and efficient manner, which plays an important role in conducting reactor safety analysis, reactor data assimilation, and solving inverse problems.

Description

Technical Field

[0001] The present invention relates to a technology in the field of nuclear reactor control, in particular to a method for rapidly inferring changes in neutron flux distribution in a nuclear reactor core. Background Art

[0002] The neutron flux distribution in the core of a pressurized water reactor is one of the most important physical quantities in a nuclear reactor, and plays an important role in the safety analysis and state prediction of the reactor. Aiming at the demand for high-fidelity and fast calculation of core neutron flux in the fields of safety analysis and core prediction in existing nuclear reactors, the present invention proposes a fast inference method suitable for neutronics models. Summary of the invention

[0003] In view of the shortcomings of the prior art that the operating parameters in the reactor change with time and that the reduced-order model needs to be generalized to different parameter scenarios with the help of interpolation methods, the present invention proposes a method for rapid inference of changes in the neutron flux distribution in the core of a nuclear reactor. The rapid prediction model is constructed using data from a high-fidelity full-order model, and the changes in the core neutron flux with time with high resolution are described precisely and efficiently in neutronic simulations, which plays an important role in conducting reactor safety analysis, reactor data assimilation, and solving inverse problems.

[0004] The present invention is achieved through the following technical solutions:

[0005] The invention relates to a method for rapidly inferring the change of neutron flux distribution in a nuclear reactor core. In an offline training stage, a transient neutron transport equation is solved by a full-order solver to obtain spatial distribution data of neutron flux and delayed precursor nuclear density changing with time. A reduced-order basis and a reduced-order coefficient data set of a training data set are obtained by proper orthogonal decomposition. A reduced-order model is obtained in the reduced-order coefficient data set by least square fitting. In an online prediction stage, after solving the reduced-order model according to the parameters of the prediction working condition, the reduced-order basis is applied to the solved reduced-order coefficients to reconstruct a physical field including the core neutron flux, the delayed precursor nuclear density distribution and the like changing with time.

[0006] The proper orthogonal decomposition is adopted but not limited to the method described 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).

[0007] https: / / doi.org / 10.1016 / j.ymssp.2019.01.018) is implemented by the technology described in .

[0008] The present invention relates to a system for implementing the above method, comprising: 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; the online prediction and reconstruction unit solves the equation according to the reduced-order model matrix obtained by fitting to obtain the predicted reduced-order coefficients, and then reconstructs the full-order data using the reduced-order coefficients.

[0009] Technical Effects

[0010] The present invention is based on the intrinsic orthogonal decomposition and reduced-order model matrix fitting method, uses the data of the high-fidelity full-order model, obtains the matrix in the reduced-order model through parameter affine decomposition and least squares fitting, and thus obtains the reduced-order model. Compared with the prior art, the present invention solves the reduced-order model with a dimension much lower than that of the full-order model, and quickly obtains the changes of key physical quantities such as the core neutron flux and the delayed precursor nuclear density distribution over time when the operating parameters that change over time are given, while reducing the calculation time and maintaining a low prediction error, which plays an important role in the safety analysis and state prediction of the reactor core. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the present invention;

[0012] Figure 2 A top view of the component arrangement of Example C5G7-TD3-4;

[0013] Figure 3 It 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

[0014] like Figure 1 As shown, this embodiment involves a method for rapid inference of changes in the 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 spatial distribution data of neutron flux and delayed precursor nuclear density changing with time, and the reduced-order basis and reduced-order data set of the training data set are obtained by intrinsic orthogonal decomposition; the reduced-order matrix in the reduced-order model is obtained by least squares fitting in the reduced-order coefficient data set; in the online prediction stage, after solving the reduced-order model according to the parameters of the predicted operating conditions, the reduced-order basis is applied to the solved reduced-order coefficients to reconstruct a physical field including the core neutron flux and the delayed precursor nuclear density distribution.

[0015] The training data set is obtained in the following way: by using any full-order model solver of the transient neutron transport equation, under the condition of given geometric, material and operating parameter changes, the data of neutron flux and precursor nuclear density in the core changing with time is solved.

[0016] The intrinsic orthogonal decomposition specifically includes:

[0017] 1) The n obtained by the full-order model solver t Time point The length is n-th order vector Store as snapshot matrix Among them: φ includes the neutron standard flux of each energy group and the density of each group of delayed precursor nuclei, and n is the product of the number of energy groups, the number of delayed groups and the spatial degree of freedom.

[0018] 2) The snapshot matrix is ​​subjected to intrinsic orthogonal decomposition, specifically: singular value decomposition is used to obtain in: is the orthogonal basis matrix unitary matrix of the subspace; is a diagonal matrix containing singular values. Usually, the diagonal singular values ​​are arranged in descending order; is also a unitary matrix. If we only keep the matrix An orthogonal basis of the first r << n columns will result in a truncated basis in the subspace.

[0019] The retention parameter r satisfies: Among them: τ is a number less than 1, usually selected as 0.9999; λ is the diagonal element of Λ, that is, the singular value. This inequality describes the proportion of the retained orthogonal basis in the total information. The matrix The first r columns of are denoted as U.

[0020] 3) Applying the reduced-order basis matrix U to the full-order solution vector will obtain a snapshot of the reduced-order coefficients, specifically:

[0021] The reduced-order model is specifically: Where: t is time; is the reduction coefficient; and is 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 changes with time in the following form: 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.

[0022] The reduced-order matrix of the reduced-order model is obtained by least squares fitting, which specifically includes: 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 directly solved as follows, specifically: The reduced-order equation matrix and Solve the elements of each row in turn.

[0023] The reconstruction specifically includes: given the parameters of the predicted working condition With a given core initial state 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 And given the initial state φ0 of the core, the core state is predicted in time series.

[0024] Through specific practical experiments, typical small pressurized water reactor problems are simulated, such as Figure 2 As shown, the simulation parameters use the parameters 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. Only the training set data is used to train the reduced-order model. In the online stage, the reduced-order model obtained by training is used to predict the change of physical quantities over time in the 0-1s interval, and compared with the results of the full-order model. Figure 3 As shown, the prediction results of the reduced-order model trained by this method and the relative error data of the full-order model are shown.

[0025] Compared with the existing technology, this method reduces the computation time while maintaining a low prediction error. In the above simulation results, the solution time of the full-order transport model is 36 core seconds / time step; the solution time of the reduced-order model is 3.3×10-5 kernel seconds / time step, the reconstruction time of full-order physical quantities is 6.4×10 -3 The total computation time is reduced by three orders of magnitude. Figure 3 As shown, compared with the spatial distribution of neutron flux and delayed precursor 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 is improved (i.e., the effect obtained by using new technology in the above link) in that the dimension of the reduced-order model constructed by the method is much lower than that of the full-order model, so fast solution and prediction are achieved.

[0026] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for rapidly inferring changes in neutron flux distribution in a nuclear reactor core, characterized in that: In the offline training stage, the transient neutron transport equation is solved by a full-order solver to obtain the spatial distribution data of the neutron flux and the delayed precursor nuclear density varying with time. The reduced-order basis and reduced-order coefficient data set of the training data set are obtained by proper orthogonal decomposition, and the reduced-order model is obtained by least squares fitting in the reduced-order coefficient data set. In the online prediction stage, after solving the reduced-order model according to the parameters of the predicted operating conditions, the reduced-order basis is applied to the solved reduced-order coefficients to reconstruct the physical field including the core neutron flux and the delayed precursor nuclear density distribution. The intrinsic orthogonal decomposition specifically includes: 1) The n obtained by the full-order model solver t Time point The length is n-th order vector Store as snapshot matrix Among them: Φ includes the neutron standard flux of each energy group and the density of each group of delayed precursor nuclei, n is the product of the number of energy groups and the number of delayed groups and the spatial degree of freedom; 2) The snapshot matrix is ​​subjected to intrinsic orthogonal decomposition, specifically: singular value decomposition is used to obtain in: is the orthogonal basis matrix unitary matrix of the subspace; is a diagonal matrix containing singular values, and the diagonal singular values ​​are arranged in order from large to small; is also a unitary matrix; retain the matrix The orthogonal basis of the first r columns obtains the truncated basis in the subspace, the matrix The first r columns of are recorded as the reduced-order basis matrix U, where: r is the retained parameter, r<<n; 3) Applying the reduced-order basis matrix U to the full-order solution vector will obtain a snapshot of the reduced-order coefficients, specifically: The retention parameters r satisfy: in: τ is a number less than 1, λ i are the diagonal elements of Λ, that is, the singular values; The reduced-order model is specifically: Where: μ(t) is the core operating parameter that changes with time, and t is time; is the reduction coefficient; and is a reduced-order matrix; The reduced-order matrix of the reduced-order model is obtained by least squares fitting, which specifically includes: 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; n t is the number of time steps, and the time derivative of the reduced-order coefficient vector is approximated by difference, specifically: Each least squares problem is directly solved as follows, specifically: The reduced-order equation matrix and Solve the elements of each row in turn.

2. The method for rapidly inferring changes in neutron flux distribution in a nuclear reactor core according to claim 1, characterized in that: The training data set is obtained in the following way: by using any full-order model solver of the transient neutron transport equation, under the condition of given geometric, material and operating parameter changes, the data of neutron flux and precursor nuclear density in the core changing with time are solved.

3. The method for rapidly inferring changes in neutron flux distribution in a nuclear reactor core according to claim 1, characterized in that: The reconstruction specifically includes: Given the parameters of the predicted operating conditions With a given core initial state 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 unit matrix; Δt is the discrete time step; The initial conditions are 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: Parameters to achieve a given new core prediction condition And given the initial state φ0 of the core, the core state is predicted in time series.

4. A rapid inference system for changes in neutron flux distribution in a nuclear reactor core implementing the method described in any one of claims 1 to 3, characterized in that: include: 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 based on 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 squares fitting based on the reduced-order coefficient data set to obtain a matrix in the reduced-order model; the online prediction and reconstruction unit solves the equation based on the reduced-order model matrix obtained by fitting to obtain the predicted reduced-order coefficients, and then reconstructs the full-order data using the reduced-order coefficients.

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