A data-driven condensation method and system

Abstract

The present invention relates to the field of nuclear reactor engineering technology, and discloses a data-driven polycondensation method and system, comprising the following specific steps: S1: establishing a model of a rod bundle assembly of a pressurized water reactor; applying node loads to the model, and performing static calculations to obtain node displacements; saving the node displacements in a snapshot matrix; assuming X1=A·X2, performing DMD decomposition on the matrix A to obtain DMD modes, and selecting the first m-order DMD modes according to frequency sorting to obtain a conversion matrix T; obtaining and solving full-order vibration equations and reduced-order vibration equations; comparing the obtained reduced-order frequency, vibration mode and displacement with the obtained full-order frequency, vibration mode and displacement, and if the preset accuracy threshold is met, it is proved that m is reasonably selected and polycondensation is completed; if the accuracy threshold is not met, m is increased. The present invention solves the problem that the prior art wastes computing resources and is not accurate and reliable enough, and has the characteristics of being able to improve the computing efficiency of solving the flow-induced vibration characteristics of fuel assemblies.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor engineering technology, and more specifically, to a data-driven polycondensation method and system. Background Art

[0002] The high complexity of the core structure of large pressurized water reactors, combined with its millions of structural degrees of freedom, greatly increases the difficulty of solving flow-induced vibration problems. The flow-induced vibration of fuel assemblies may not only cause micro-wear between fuel rods and grids, thereby causing fuel rod leakage, but may also change the assembly channels, thereby affecting the stability of neutron flux. Given the high computational cost of traditional flow-induced vibration analysis, it is particularly important to develop an effective reduced-order model that can maintain the accuracy and reliability of the analysis while reducing computing resources. The reduced-order model can provide key technical support for the design and operation of pressurized water reactors, ensuring their safe and efficient operation.

[0003] The prior art provides a digital reactor simulation analysis method for flow-induced vibration of a core structure of a large pressurized water reactor, the method comprising the following steps: S1: taking the flow fields in the reactor pressure vessel lower head, the core and the fuel assembly as objects, respectively, to perform data-driven in-core flow field flow characteristics and fluid force analysis simulation; S2: according to the results of the analysis and simulation output of step S1, a structural dynamics model of finite element discrete equations for element-level fuel rods, assembly-level fuel assemblies and full-core fuel assemblies under fluid excitation is established, and a control equation solution strategy for multi-nonlinear factors and multi-space-time scale coupling of the core structure is analyzed; S3: solving the mechanical behavior of the core structure according to the control equation, and performing sensitivity analysis and uncertainty quantification on the data of the solved input-output samples, and completing the analysis of the multi-space-time scale flow-induced vibration behavior law of the core structure.

[0004] However, the existing technology has the problems of wasting computing resources and being inaccurate and unreliable. Therefore, how to invent a data-driven condensation method and system is a technical problem that urgently needs to be solved in this technical field. Summary of the invention

[0005] In order to solve the problems of waste of computing resources and lack of accuracy and reliability in the prior art, the present invention provides a data-driven condensation method and system, which has the characteristics of improving the computing efficiency of solving the flow-induced vibration characteristics of fuel assemblies.

[0006] In order to achieve the above-mentioned purpose of the present invention, the technical scheme adopted is as follows:

[0007] A data-driven polycondensation method comprises the following specific steps:

[0008] S1: Establish a model of the rod bundle assembly of a pressurized water reactor; apply node loads to the model and perform static calculations to obtain node displacements; save the node displacements in the snapshot matrix X1 = [x1, x2, x3, …, x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector;

[0009] S2: Assume X1 = A · X2, perform DMD decomposition on matrix A to obtain DMD mode And select the first m-order DMD modes according to frequency sorting Get the conversion matrix

[0010] S3: Let the matrix U = T·Z, and get the full-order vibration equation: Where q is the full-order matrix, U is the full-order vibration displacement, Z is the reduced-order vibration displacement, U(t) is the full-order displacement vector, M q is the full-order mass matrix, C q is the full-order damping matrix, K q is the full-order stiffness matrix, F q (t) is the full-order external force vector; the reduced-order vibration equation is obtained Where m1 is the reduced-order matrix, Z(t) is the reduced-order displacement vector, and M m1 is the reduced-order mass matrix, C m1 is the reduced-order damping matrix, K m1 is the reduced-order stiffness matrix, F m1 (t) is the reduced-order external force vector, and the full-order vibration equation and the reduced-order vibration equation are solved;

[0011] S4: Compare the reduced-order frequency, mode shape and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, mode shape and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, increase m and return to step S2.

[0012] Preferably, in step S1, the rod cluster assembly model is specifically a rod cluster model of a 5×5 rod cluster assembly with mixing vanes.

[0013] Furthermore, in step S1, the node load is specifically F i =sin(k·θ), where k is a non-zero positive integer and θ is the phase.

[0014] Furthermore, in step S2, assuming that X1=A·X2, the matrix A is decomposed by DMD to obtain the DMD mode The specific steps are:

[0015] a) Let X1 = A·X2;

[0016] b) Let A ≈ WKW T , where W is the left singular value matrix and K is the right singular value matrix;

[0017] c) Let G1=WΣV T , where Σ is a non-negative real diagonal matrix and V is a unitary matrix;

[0018] d) Substituting c) and b) into a) yields: F = W T X2VΣ -1 ;

[0019] e) in is the DMD mode, α is the modal amplitude, μ is the eigenvalue, N is the reconstruction time, and K is the spatial dimension.

[0020] Furthermore, in the step S4, the preset accuracy threshold includes the difference between the full-order frequency and the reduced-order frequency and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement; the threshold of the difference between the full-order frequency and the reduced-order frequency is 0.01, and the threshold of the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is 0.96.

[0021] Furthermore, in step S4, if the difference between the full-order frequency and the reduced-order frequency is less than 0.01, and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is greater than 0.96, it is judged that the preset accuracy threshold is met, otherwise it is judged that the accuracy threshold is not met.

[0022] Furthermore, in step S3, q is greater than m1.

[0023] Furthermore, in step S3, U is directly obtained according to the full-order model.

[0024] Furthermore, in step S3, the full-order vibration equation and the reduced-order vibration equation are solved by using the Runge-Kutta method.

[0025] A data-driven condensation system, comprising a model building module, a DMD decomposition module, a full-order vibration and reduced-order vibration calculation module, and a condensation module;

[0026] The model building module is used to build a model of the rod bundle assembly of the pressurized water reactor, apply node loads, perform static calculations, and obtain node displacements; the node displacements are saved in the snapshot matrix X1 = [x1, x2, x3, ..., x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector;

[0027] The DMD decomposition module is used to assume that X1 = A·X2, and perform DMD decomposition on the matrix A to obtain the DMD mode And select the first m-order DMD modes according to frequency sorting Get the conversion matrix

[0028] The full-order vibration and reduced-order vibration calculation module is used to substitute the matrix U=T·Z into the full-order vibration equation: Where q is the full-order matrix, U is the full-order vibration displacement, Z is the reduced-order vibration displacement, U(t) is the full-order displacement vector, M q is the full-order mass matrix, C q is the full-order damping matrix, K q is the full-order stiffness matrix, F q (t) is the full-order external force vector, and the reduced-order vibration equation is obtained Where m1 is the reduced-order matrix, Z(t) is the reduced-order displacement vector, and M m1 is the reduced-order mass matrix, C m1 is the reduced-order damping matrix, K m1 is the reduced-order stiffness matrix, F m1 (t) is the reduced-order external force vector, and the full-order vibration equation and the reduced-order vibration equation are solved;

[0029] The condensation module is used to compare the reduced-order frequency, vibration mode and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, vibration mode and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, m is increased.

[0030] The beneficial effects of the present invention are as follows:

[0031] In order to solve the problems of waste of computing resources and lack of accuracy and reliability in the prior art, the present invention first establishes a model of a rod bundle assembly of a pressurized water reactor and establishes a snapshot matrix; DMD decomposition is performed on the snapshot matrix to obtain a conversion matrix, and a full-order vibration equation and a reduced-order vibration equation are obtained based on the conversion matrix, the full-order vibration equation and the reduced-order vibration equation are solved, and the solution results are compared to complete the condensation; thereby, the present invention improves the computational efficiency of solving the flow-induced vibration characteristics of the fuel assembly, provides key technical support for the design and operation of the pressurized water reactor, and solves the problems of waste of computing resources and lack of accuracy and reliability in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic flow chart of a data-driven polycondensation method of the present invention.

[0033] Figure 2 It is a schematic diagram of a 5×5 rod bundle structure based on a data-driven polycondensation method of the present invention.

[0034] Figure 3 It is a schematic diagram of modeling of a data-driven polycondensation method of the present invention. DETAILED DESCRIPTION

[0035] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1

[0037] like Figure 1 As shown, a data-driven polycondensation method includes the following specific steps:

[0038] S1: Establish a model of the rod bundle assembly of a pressurized water reactor; apply node loads to the model and perform static calculations to obtain node displacements; save the node displacements in the snapshot matrix X1 = [x1, x2, x3, …, x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector;

[0039] S2: Assume X1 = A · X2, perform DMD decomposition on matrix A to obtain DMD mode And select the first m-order DMD modes according to frequency sorting Get the conversion matrix

[0040] S3: Let the matrix U = T·Z, and get the full-order vibration equation: Where q is the full-order matrix, U is the full-order vibration displacement, Z is the reduced-order vibration displacement, U(t) is the full-order displacement vector, M q is the full-order mass matrix, C q is the full-order damping matrix, K q is the full-order stiffness matrix, F q (t) is the full-order external force vector; the reduced-order vibration equation is obtained Where m1 is the reduced-order matrix, Z(t) is the reduced-order displacement vector, and M m1 is the reduced-order mass matrix, C m1 is the reduced-order damping matrix, K m1 is the reduced-order stiffness matrix, F m1 (t) is the reduced-order external force vector, and the full-order vibration equation and the reduced-order vibration equation are solved;

[0041] S4: Compare the reduced-order frequency, mode shape and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, mode shape and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, increase m and return to step S2.

[0042] In this embodiment, if the accuracy threshold is not met, m is increased to m+1 order.

[0043] Example 2

[0044] In a specific embodiment, Figure 2 As shown, in step S1, the rod cluster assembly model is specifically a rod cluster assembly model with mixing vanes of a 5×5 rod cluster assembly. The length of the rod cluster assembly is 400 mm.

[0045] In this embodiment, Figure 3 As shown in FIG. 1 , a model of a rod bundle assembly of a pressurized water reactor is established; node loads are applied to the model, and static calculations are performed to obtain node displacements; the node displacements are saved in a snapshot matrix X1 = [x1, x2, x3, …, x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector;

[0046] In a specific embodiment, in step S1, the node load is specifically F i =sin(k·θ), where k is a non-zero positive integer and θ is the phase.

[0047] In a specific embodiment, in step S2, assuming that X1=A·X2, the matrix A is decomposed by DMD to obtain the DMD mode The specific steps are:

[0048] a) Let X1 = A·X2;

[0049] b) Let A ≈ WKW T , where W is the left singular value matrix and K is the right singular value matrix;

[0050] c) Let G1=WΣV T , where Σ is a non-negative real diagonal matrix and V is a unitary matrix;

[0051] d) Substituting c) and b) into a) yields: F = W T X2VΣ -1 ;

[0052] e) in is the DMD mode, α is the modal amplitude, μ is the eigenvalue, N is the reconstruction time, and K is the spatial dimension.

[0053] In a specific embodiment, in the step S4, the preset accuracy threshold includes the difference between the full-order frequency and the reduced-order frequency and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement; the threshold of the difference between the full-order frequency and the reduced-order frequency is 0.01, and the threshold of the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is 0.96.

[0054] In a specific embodiment, in step S4, if the difference between the full-order frequency and the reduced-order frequency is less than 0.01, and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is greater than 0.96, it is judged that the preset accuracy threshold is met, otherwise it is judged that the accuracy threshold is not met.

[0055] In a specific embodiment, in step S3, q is greater than m1.

[0056] In a specific embodiment, in step S3, U is directly obtained according to the full-order model.

[0057] In a specific embodiment, in step S3, the full-order vibration equation and the reduced-order vibration equation are solved by using the Runge-Kutta method.

[0058] In this embodiment, the present invention proposes a data-driven condensation method, which aims to improve the computational efficiency of solving the flow-induced vibration characteristics of fuel assemblies and provide key technical support for the design and operation of pressurized water reactors.

[0059] Example 3

[0060] A data-driven condensation system, comprising a model building module, a DMD decomposition module, a full-order vibration and reduced-order vibration calculation module, and a condensation module;

[0061] The model building module is used to build a model of the rod bundle assembly of the pressurized water reactor, apply node loads, perform static calculations, and obtain node displacements; the node displacements are saved in the snapshot matrix X1 = [x1, x2, x3, ..., x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector;

[0062] The DMD decomposition module is used to assume that X1 = A·X2, and perform DMD decomposition on the matrix A to obtain the DMD mode And select the first m-order DMD modes according to frequency sorting Get the conversion matrix

[0063] The full-order vibration and reduced-order vibration calculation module is used to substitute the matrix U=T·Z into the full-order vibration equation: Where q is the full-order matrix, U is the full-order vibration displacement, Z is the reduced-order vibration displacement, U(t) is the full-order displacement vector, M q is the full-order mass matrix, C q is the full-order damping matrix, K q is the full-order stiffness matrix, F q (t) is the full-order external force vector, and the reduced-order vibration equation is obtained Where m1 is the reduced-order matrix, Z(t) is the reduced-order displacement vector, and M m1 is the reduced-order mass matrix, C m1 is the reduced-order damping matrix, K m1 is the reduced-order stiffness matrix, F m1 (t) is the reduced-order external force vector, and the full-order vibration equation and the reduced-order vibration equation are solved;

[0064] The condensation module is used to compare the reduced-order frequency, vibration mode and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, vibration mode and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, m is increased.

[0065] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A data-driven polycondensation method, characterized in that: The specific steps include: S1: Establish a model of the rod bundle assembly of a pressurized water reactor; apply node loads to the model and perform static calculations to obtain node displacements; save the node displacements in the snapshot matrix X1=[x1,x2,x3,…,x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector; S2: Let X1 = A · X2, perform DMD decomposition on the matrix A to obtain DMD modes φ1, φ2, φ3, …, φ s-1 , and select the first m-order DMD modes φ1, φ2, φ3, …, φ according to the frequency sorting m , and obtain the transformation matrix T=[φ1, φ2, φ3,…, φ m ]; S3: Assume matrix U = T·Z, and get the full-order vibration equation: , where q is the full-order matrix, U is the full-order vibration displacement, and Z is the reduced-order vibration displacement. is the full-order displacement vector, is the full-order mass matrix, is the full-order damping matrix, is the full-order stiffness matrix, is the full-order external force vector; the reduced-order vibration equation is obtained , where m1 is the reduced-order matrix, is the reduced-order displacement vector, is the reduced-order mass matrix, is the reduced-order damping matrix, is the reduced-order stiffness matrix, Solve the full-order vibration equation and the reduced-order vibration equation for the reduced-order external force vector; S4: Compare the reduced-order frequency, mode shape and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, mode shape and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, increase m and return to step S2.

2. The data-driven polycondensation method according to claim 1, characterized in that: In the step S1, the rod cluster assembly model is specifically a rod cluster model of a 5×5 rod cluster assembly with mixing vanes.

3. The data-driven polycondensation method according to claim 1, characterized in that: In step S1, the node load is specifically F i = sin(k·θ), where k is a non-zero positive integer and θ is the phase.

4. The data-driven polycondensation method according to claim 1, characterized in that: In the step S4, the preset accuracy threshold includes the difference between the full-order frequency and the reduced-order frequency and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement; the threshold of the difference between the full-order frequency and the reduced-order frequency is 0.01, and the threshold of the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is 0.

96.

5. The data-driven polycondensation method according to claim 4, characterized in that: In step S4, if the difference between the full-order frequency and the reduced-order frequency is less than 0.01, and the correlation coefficient between the full-order vibration mode and displacement and the reduced-order vibration mode and displacement is greater than 0.96, it is judged that the preset accuracy threshold is met, otherwise it is judged that the accuracy threshold is not met.

6. The data-driven polycondensation method according to claim 1, characterized in that: In step S3, q is greater than m1.

7. The data-driven polycondensation method according to claim 1, characterized in that: In step S3, U is directly obtained according to the full-order model.

8. The data-driven polycondensation method according to claim 1, characterized in that: In step S3, the full-order vibration equation and the reduced-order vibration equation are solved by using the Runge-Kutta method.

9. A data-driven polycondensation system, characterized in that: It includes model building module, DMD decomposition module, full-order vibration and reduced-order vibration calculation module, and condensation module; The model building module is used to build a model of the rod bundle assembly of the pressurized water reactor, apply node loads, perform static calculations, and obtain node displacements; the node displacements are saved in the snapshot matrix X1=[x1,x2,x3,…,x s-1 ] and X2=[x1,x2,x3,…,x s ], where s is the snapshot number and x is the node displacement vector; The DMD decomposition module is used to assume that X1=A·X2, and perform DMD decomposition on the matrix A to obtain DMD modes φ1, φ2, φ3, …, φ s-1 , and select the first m-order DMD modes φ1, φ2, φ3, …, φ according to the frequency sorting m , and obtain the transformation matrix T=[φ1, φ2, φ3,…, φ m ]; The full-order vibration and reduced-order vibration calculation module is used to substitute the matrix U=T·Z into the full-order vibration equation: , where q is the full-order matrix, U is the full-order vibration displacement, and Z is the reduced-order vibration displacement. is the full-order displacement vector, is the full-order mass matrix, is the full-order damping matrix, is the full-order stiffness matrix, As the full-order external force vector, the reduced-order vibration equation is obtained , where m1 is the reduced-order matrix, is the reduced-order displacement vector, is the reduced-order mass matrix, is the reduced-order damping matrix, is the reduced-order stiffness matrix, Solve the full-order vibration equation and the reduced-order vibration equation for the reduced-order external force vector; The condensation module is used to compare the reduced-order frequency, vibration mode and displacement obtained by solving the reduced-order vibration equation with the full-order frequency, vibration mode and displacement obtained by solving the full-order vibration equation. If the preset accuracy threshold is met, it proves that the selection of m is reasonable and the condensation is completed; if the accuracy threshold is not met, m is increased.

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