Fuel rod fretting wear analysis method and device

Abstract

The invention provides a fuel rod fretting wear analysis method and device, and the method comprises the steps: processing the distribution type and characteristic value of engineering parameters through Box-Mueller transformation, obtaining random parameters, carrying out the Monte Carlo sampling, and constructing a high-dimensional probability space; according to a parallel strategy, calculating free vibration displacement of any point on the fuel rod under n samples in the high-dimensional probability space along with time; obtaining a free vibration speed corresponding to the free vibration displacement based on a difference method; correcting the displacement information and the speed information through a post-processing function; the abrasion power is calculated, and the abrasion volume and the abrasion depth of the fuel rod are calculated through the Achade abrasion law; and finally generating a visual result and outputting the visual result. And the transformation efficiency is improved by optimizing a discretization strategy and parallel computing. And solving a nonlinear vibration equation of the fuel rod by using a difference method, and accurately capturing a nonlinear effect. And a free vibration solving and simulation processing method is adopted, so that the problems of numerical explosion and iteration non-convergence under high rigidity are avoided.

Description

Technical Field

[0001] The present invention relates to the fields of nuclear engineering and nuclear technology, and in particular to a method and device for analyzing fretting wear of fuel rods. Background Art

[0002] Fuel rod wear refers to the gradual wear or damage of the fuel rod surface within a nuclear reactor due to various external forces and environmental factors. Existing fuel rod fretting wear analysis techniques primarily combine nonlinear vibration models with wear models, analyzing the fretting wear behavior of fuel rods in high-temperature, high-pressure, and hydrochemical environments through numerical simulation and experimental verification. Monte Carlo methods are often used to treat multiple factors as random variables. Modal analysis is then used to calculate the nonlinear vibration response of the fuel rods within the support structure and predict the cladding wear depth and probability distribution.

[0003] However, the existing technology has the following problems: first, there is a lack of domestic software platforms, which restricts independent research and development and application; second, the Laplace transform has low computational efficiency, which affects the simulation speed; third, it may cause numerical explosion under high stiffness conditions, affecting the convergence of the solution; fourth, the modal analysis method is based on linear assumptions, which makes it difficult to accurately handle nonlinear contact and complex boundary conditions, resulting in deviations between the results and the actual situation.

[0004] Therefore, it is urgent to propose a domestic tool chain to improve computing stability and support rapid evaluation and optimization design in engineering scenarios. Summary of the Invention

[0005] In view of this, an embodiment of the present invention provides a fuel rod fretting wear analysis method and apparatus to solve the problems of instability and low accuracy in fuel rod fretting wear analysis.

[0006] To achieve the above objectives, the embodiments of the present invention provide the following technical solutions:

[0007] A first aspect of the present invention discloses a method for analyzing fretting wear of a fuel rod, the method comprising:

[0008] The distribution type and eigenvalue of the obtained engineering parameters are processed by Box-Muller transformation to obtain random parameters;

[0009] Performing n Monte Carlo sampling on the random parameters to obtain a high-dimensional probability space;

[0010] Calculating each of the n samples in the high-dimensional probability space with the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages according to a parallel strategy to obtain the free vibration displacement of any point on the fuel rod over time under each sample;

[0011] For each of the free vibration displacements, performing a central difference calculation based on the free vibration displacement to obtain a free vibration velocity corresponding to the free vibration displacement;

[0012] Performing correction processing according to the free vibration velocity and preset gap information through a post-processing function to obtain corrected displacement information and velocity information;

[0013] Calculating the abrasion power through the displacement information, and calculating the abrasion volume and abrasion depth of the fuel rod through Archard's wear law in combination with a preset wear time and a preset wear coefficient;

[0014] A visualization result is generated and outputted according to the displacement information, the speed information, the abrasion power, the abrasion volume, and the abrasion depth.

[0015] Preferably, performing Monte Carlo sampling on the random parameters n times to obtain a high-dimensional probability space includes:

[0016] Performing n Monte Carlo sampling on each of the random parameters, performing multi-dimensional sampling each time, to obtain n high-dimensional probability space samples consisting of multiple dimensions;

[0017] The space spanned by n high-dimensional probability space samples composed of multiple dimensions is marked as a high-dimensional probability space.

[0018] Preferably, the step of calculating each of the n samples in the high-dimensional probability space with the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages according to a parallel strategy to obtain the free vibration displacement of any point on the fuel rod over time under each sample includes:

[0019] Allocate a thread to each of the n samples in the high-dimensional probability space according to a parallel strategy;

[0020] In the thread, the number of x-axis nodes, the total simulation time and the number of frequency stages are obtained, and the grid is discretized to obtain a position-time plane discrete network;

[0021] The right-hand side force of the equation corresponding to the position-time plane discrete network is obtained by a fast Laplace transform algorithm, and a two-point boundary value problem is constructed;

[0022] Solve the two-point boundary value problem by using the second-order central difference method and the one-sided second-order central difference method to obtain the position-time displacement corresponding to the sample;

[0023] Using a fast inverse Laplace transform algorithm in combination with the displacement, the free vibration displacement of any point on the fuel rod under the sample over time is calculated;

[0024] After all threads are executed, the free vibration displacement of any point on the fuel rod under each sample over time is obtained.

[0025] Preferably, the correction processing is performed according to the free vibration velocity and the preset gap information by a post-processing function to obtain the corrected displacement information and velocity information, including:

[0026] Traversing n time steps, if the free vibration displacement is greater than the right gap function in the preset gap information, then using a post-processing function to calculate the corrected displacement information according to the right gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring;

[0027] If the free vibration displacement is less than the left gap function in the preset gap information, then calculating the corrected displacement information according to the left gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring through a post-processing function;

[0028] Calculate the force of the fuel rod at each position and at each time according to the displacement information;

[0029] Corrected velocity information is calculated based on the force and the free vibration velocity.

[0030] Preferably, the calculating of the abrasion power by the displacement information and the calculating of the abrasion volume and abrasion depth of the fuel rod by Archard's wear law in combination with a preset wear time and a preset wear coefficient include:

[0031] Calculating impact power and Y-normal friction power based on the force and the velocity information;

[0032] Calculating the sum of the impact power and the Y-normal friction power to obtain the abrasive power;

[0033] The abrasion volume of the fuel rod is calculated by using Archard's wear law, combined with the preset wear time and the preset wear coefficient;

[0034] The abrasion depth is calculated based on the abrasion volume.

[0035] A second aspect of the present invention discloses a fuel rod fretting wear analysis device, comprising:

[0036] A data interaction module is used to perform Box-Muller transformation on the distribution type and characteristic value of the acquired engineering parameters to obtain random parameters; the data interaction module is also used to perform Monte Carlo sampling on the random parameters n times to obtain a high-dimensional probability space;

[0037] a numerical calculation core module for calculating, according to a parallel strategy, each of the n samples in the high-dimensional probability space and the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages, to obtain the free vibration displacement of any point on the fuel rod over time under each sample;

[0038] a simulation processing module configured to perform a central difference calculation based on each free vibration displacement to obtain a free vibration velocity corresponding to the free vibration displacement; the simulation processing module is further configured to perform correction processing based on the free vibration velocity and preset gap information using a post-processing function to obtain corrected displacement information and velocity information; the simulation processing module is further configured to calculate the abrasion power based on the displacement information, and calculate the abrasion volume and abrasion depth of the fuel rod using Archard's wear law in combination with a preset wear time and a preset wear coefficient;

[0039] The output data visualization module is used to generate and output visualization results based on the displacement information, the speed information, the abrasion power, the abrasion volume and the abrasion depth.

[0040] Preferably, the data interaction module includes:

[0041] A Monte Carlo sampling submodule, configured to perform n Monte Carlo sampling on each of the random parameters, wherein each Monte Carlo sampling performs multi-dimensional sampling to obtain n high-dimensional probability space samples consisting of multiple dimensions;

[0042] The labeling submodule is used to label the space spanned by n high-dimensional probability space samples composed of multiple dimensions as a high-dimensional probability space.

[0043] Preferably, the numerical calculation core module includes:

[0044] an allocation submodule, configured to allocate a thread to each of the n samples in the high-dimensional probability space according to a parallel strategy;

[0045] A grid discretization submodule is used to obtain the number of x-axis nodes, the total simulation time and the number of frequency stages in the thread, and perform grid discretization to obtain a position-time plane discrete network;

[0046] A construction submodule is used to obtain the right-hand side force of the equation corresponding to the position-time plane discrete network by a fast Laplace transform algorithm, and construct a two-point boundary value problem;

[0047] A solving submodule, configured to solve the two-point boundary value problem by using a second-order central difference method and a unilateral second-order central difference method to obtain a position-time displacement corresponding to the sample;

[0048] A first calculation submodule is configured to calculate the free vibration displacement of any point on the fuel rod under the sample over time by using a fast inverse Laplace transform algorithm in combination with the displacement;

[0049] The statistical submodule is used to obtain the free vibration displacement of any point on the fuel rod under each sample over time after all threads are executed.

[0050] Preferably, the simulation processing module includes:

[0051] A second calculation submodule is configured to traverse n time steps, and if the free vibration displacement is greater than the right-side gap function in the preset gap information, calculate corrected displacement information according to the right-side gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring through a post-processing function;

[0052] a post-processing function calculation submodule, configured to calculate corrected displacement information using a post-processing function according to the left gap function, a standard deviation of a preset exciting force, and a preset spring stiffness if the free vibration displacement is less than the left gap function in the preset gap information;

[0053] a third calculation submodule, configured to calculate the force of the fuel rod at each position and at each time according to the displacement information;

[0054] The velocity calculation submodule is configured to calculate corrected velocity information according to the force and the free vibration velocity.

[0055] Preferably, the simulation processing module includes:

[0056] a friction power calculation submodule, configured to calculate the impact power and the Y-normal friction power according to the force and the velocity information;

[0057] an abrasion power calculation submodule, configured to calculate the sum of the impact power and the Y-normal friction power to obtain the abrasion power;

[0058] An abrasion volume calculation submodule is used to calculate the abrasion volume of the fuel rod by using Archard's wear law, combined with a preset wear time and a preset wear coefficient;

[0059] The abrasion depth calculation submodule is used to calculate the abrasion depth based on the abrasion volume.

[0060] Based on the above-mentioned embodiment of the present invention, a method and device for analyzing the micro-wear of fuel rods are provided. The distribution type and eigenvalues ​​of engineering parameters are processed through the Box-Muller transform to obtain random parameters and perform Monte Carlo sampling to construct a high-dimensional probability space. According to a parallel strategy, the free vibration displacement of any point on the fuel rod over time under n samples in the high-dimensional probability space is calculated. The free vibration velocity corresponding to the free vibration displacement is obtained based on the difference method. The displacement information and velocity information are corrected through a post-processing function. The abrasion power is calculated, and the abrasion volume and abrasion depth of the fuel rod are calculated using Archard's wear law. Finally, a visual result is generated and output. The transformation efficiency is improved by optimizing the discretization strategy and parallel computing. The nonlinear vibration equation of the fuel rod is solved using the difference method to accurately capture the nonlinear effect. The free vibration solution and simulation processing method are adopted to avoid the numerical explosion and iterative non-convergence problems under high stiffness. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0062] Figure 1 A flowchart of a fuel rod fretting wear analysis method provided by an embodiment of the present invention;

[0063] Figure 2 A schematic diagram of a fuel rod fretting wear analysis method provided by an embodiment of the present invention;

[0064] Figure 3 This is a structural block diagram of a fuel rod fretting wear analysis device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0066] In this application, the terms "comprises," "comprising," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0067] As can be seen from the background technology, the problems existing in the existing technology include: lack of domestic software platform, low efficiency of Laplace transform, numerical explosion under high stiffness, and modal analysis cannot handle nonlinearity and complex boundaries.

[0068] Therefore, an embodiment of the present invention provides a method and device for analyzing micro-wear of fuel rods. The method processes the distribution type and eigenvalues ​​of engineering parameters through Box-Muller transformation, obtains random parameters, performs Monte Carlo sampling, and constructs a high-dimensional probability space. According to a parallel strategy, the free vibration displacement of any point on the fuel rod under n samples in the high-dimensional probability space over time is calculated. The free vibration velocity corresponding to the free vibration displacement is obtained based on the difference method. The displacement information and velocity information are corrected through a post-processing function. The abrasion power is calculated, and the abrasion volume and abrasion depth of the fuel rod are calculated through Archard's wear law. Finally, a visualization result is generated and output. The transformation efficiency is improved by optimizing the discretization strategy and parallel computing. The nonlinear vibration equation of the fuel rod is solved by the difference method to accurately capture the nonlinear effect. The free vibration solution and simulation processing method are adopted to avoid the numerical explosion and iterative non-convergence problems under high stiffness.

[0069] See also Figure 1 , which shows a flow chart of a fuel rod fretting wear analysis method provided by an embodiment of the present invention. The method includes:

[0070] Step S101: performing Box-Muller transformation on the distribution type and eigenvalue of the acquired engineering parameters to obtain random parameters.

[0071] In the specific implementation of step S101, Figure 2 As shown, the "data interaction module" obtains the distribution type and characteristic value of the engineering parameters, processes them through Box-Muller transformation (i.e., Box-Muller transformation), and obtains random parameters (e.g., M random parameters).

[0072] It should be noted that the Box-Muller transform is a method for generating a normally distributed (Gaussian distributed) random variable from a uniformly distributed random variable. It generates two independent normally distributed random variables from two independent uniformly distributed random variables.

[0073] See also Figure 2 As shown in the figure, during the application process, users can select the specific distribution type of engineering parameters and input parameters through the "parameter input visualization module" provided by the visualization interface, or users can manually input the distribution type and characteristic values ​​of engineering parameters based on engineering experience, expert knowledge, and test data.

[0074] Step S102: performing n Monte Carlo sampling on the random parameters to obtain a high-dimensional probability space.

[0075] In the specific implementation of step S102, combined with Figure 2 As shown in the details of the "Data Interaction Module" in the "Technical Explanation" section, Monte Carlo (MC) sampling is performed on each random parameter n times. Each Monte Carlo sampling is multi-dimensional sampling to obtain n high-dimensional probability space samples composed of multiple dimensions; the space spanned by n high-dimensional probability space samples composed of multiple dimensions is marked as high-dimensional probability space.

[0076] For example, MC sampling is performed on 6 random parameters quantified by uncertainty. Multi-dimensional sampling is performed each time MC sampling to obtain 6 high-dimensional probability space samples composed of multiple dimensions. The space spanned by these high-dimensional probability space samples is recorded as high-dimensional probability space.

[0077] Step S103: Calculate each of the n samples in the high-dimensional probability space with the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages according to the parallel strategy to obtain the free vibration displacement of any point on the fuel rod over time under each sample.

[0078] In the specific implementation of step S103, the parallel strategy is automatically selected by the Matlab parallel pool strategy. According to the parallel strategy, n (n here can be different from the n in step S102) samples are independently extracted from the high-dimensional probability space, each sample is calculated separately, and the calculation process of all samples is executed in parallel. The specific calculation process is as follows Figure 2 As shown in the "Equation Solving Module" in the "Technical Detailed Explanation" section, it includes processes A1 to A6.

[0079] It should be noted that Matlab (Matrix Laboratory) is a high-level programming language and interactive environment, mainly used for numerical calculations, data analysis, algorithm development, and visualization.

[0080] Process A1: Allocate a thread to each of n samples in the high-dimensional probability space according to the parallel strategy.

[0081] Combine Figure 2As shown, each sample is input into the "Numerical Computing Core" for calculation. The "Numerical Computing Core" includes the Laplace transform module, the ODE solver module (i.e., the module for solving ordinary differential equations (ODEs)), the inverse Laplace transform module, and the simulation processing module.

[0082] Specific, combined Figure 2 As shown, the "Numerical Calculation Core" belongs to the "Monte Carlo Simulation Core" module, and the "Monte Carlo Simulation Core" module also includes the "Parameter Distribution Simulation and Statistical Analysis Module".

[0083] Process A2: In the thread, obtain the number of x-axis nodes, the total simulation time, and the number of frequency stages, and perform grid discretization to obtain a position-time plane discrete network.

[0084] It can be understood that the parameters such as the number of x-axis nodes, the total simulation time and the number of frequency stages N can be input by the user.

[0085] It should be noted that the position-time plane discrete network can be expressed as an xs plane discrete network, where x represents the coordinate along the length of the fuel rod in meters, t represents time in seconds, and s represents the integral of time t.

[0086] In practical applications, the damped continuous system Euler Bernoulli beam model is used for modeling, and the nonlinear vibration equation is shown in formula (1):

[0087] (1)

[0088] In formula (1), x represents the coordinate along the length of the fuel rod, and the unit is m.

[0089] t represents time, unit is s.

[0090] Indicates the lateral offset at the x position at time t, in meters.

[0091] E represents the Young's modulus of the material, in Pa.

[0092] I represents the moment of inertia of the area, in m 4 .

[0093] c is the viscous damping coefficient, which represents the damping distributed along the length of the system, and its unit is N·s / m.

[0094] Indicates linear density in kg / m.

[0095] Represents the grid constraint force vector, which is the composite of the normal force and the friction force, in N.

[0096] Represents the external excitation force vector, unit N.

[0097] represents the second-order partial derivative operator with respect to x. represents the first-order and second-order partial derivative operators with respect to t.

[0098] It can be understood that the force on the right side is as shown in formula (2):

[0099] (2)

[0100] In formula (2), f represents the resultant force vector, which is the sum of the grid constraint force vector and the external excitation force vector ( ), unit N.

[0101] It should be noted that the grid constraint force can be modeled as the vector sum of the normal force and the friction force, as shown in formula (3):

[0102] (3)

[0103] In formula (3), It represents the normal force of the grid on the fuel rod, in N.

[0104] Represents friction.

[0105] It should be noted that the normal force is modeled as (as shown in formula (4)):

[0106] (4)

[0107] In formula (4), Represents the contact stiffness coefficient, which indicates the stiffness of the grid spring or bump, in N / m.

[0108] It represents the sign function, which takes +1 or -1 to distinguish the pushing or separation direction of the normal displacement.

[0109] It represents the reserved gap, i.e. the distance between the fuel rod and the grid when they are not in contact initially, in meters.

[0110] Indicates that at position x s The normal displacement at is in m.

[0111] x s Represents the position of the grid contact point in the coordinate system along the rod length, in meters.

[0112] Represents the contact damping coefficient, unit: N·s / m.

[0113] It can be understood that the friction force is modeled as (as shown in formula (5)):

[0114] (5)

[0115] In formula (5), It represents the tangential (friction) force component of the grid on the fuel rod, in N. represents the coefficient of friction, which defines the ratio of the tangential friction force to the normal force. Represents the normal impact force.

[0116] It should be noted that the initial value conditions and boundary conditions are as follows (as shown in formulas (6) to (11)):

[0117] (6)

[0118] (7)

[0119] (8)

[0120] (9)

[0121] (10)

[0122] (11)

[0123] In formulas (6) to (11), x represents the coordinate along the length of the fuel rod, in meters.

[0124] t represents time, unit is s.

[0125] In formula (9) and formula (11), l represents the total length of the fuel rod, and the boundary conditions are = , unit: m.

[0126] In formula (7) to the following formula (16), represents the first-order, second-order, and fourth-order partial derivative operators with respect to x. represents the first-order and second-order partial derivative operators with respect to t.

[0127] Process A3: Obtain the right-hand side force of the equation corresponding to the discrete network in the position-time plane through the fast Laplace transform algorithm and construct a two-point boundary value problem.

[0128] In the specific implementation process A3, for the nonlinear vibration equation shown in the above formula (1), the fast Laplace transform algorithm (i.e., Laplace transform) is used on both sides. Combined with the initial value conditions shown in formulas (6) and (7), and the boundary conditions shown in formulas (8) to (11), the nonlinear vibration partial differential equation shown in the original formula (1) can be transformed into the following equation (as shown in formula (12)):

[0129] (12)

[0130] In formula (12), the displacement Perform Laplace transform to get Force on the right end Perform Laplace transform to get .

[0131] express Function obtained by Laplace transform in the t direction, s-domain displacement.

[0132] represents f s +f e The resultant force after Laplace transformation.

[0133] s represents the complex frequency domain variable in Laplace transform, unit s -1 .

[0134] E represents the Young's modulus of the material, in Pa.

[0135] I represents the moment of inertia of the area, in m 4 .

[0136] c is the viscous damping coefficient, which represents the damping distributed along the length of the system, and its unit is N·s / m.

[0137] Indicates linear density in kg / m.

[0138] Similarly, the initial boundary conditions are also Laplace transformed, and the results are as follows (as shown in formulas (13) to (16)):

[0139] (13)

[0140] (14)

[0141] (15)

[0142] (16)

[0143] In formula (14) and formula (16), l represents the total length of the fuel rod, and the boundary conditions are = , unit is m. s represents the complex frequency domain variable in Laplace transform, unit is s -1 .

[0144] Based on this, the original boundary value nonlinear vibration equation problem is transformed into a fixed Two-point boundary value problem.

[0145] Process A4: Solve the two-point boundary value problem using the second-order central difference method and the one-sided second-order central difference method to obtain the position-time displacement corresponding to the sample.

[0146] In the specific implementation process A4, for the above two-point boundary value problem, the second-order central difference format is used to discretize the fourth-order derivative term, where the central difference format is a five-point central difference, as shown in formula (17).

[0147] (17)

[0148] Formula (17) is a common five-point second-order central difference format derived using Taylor expansion.

[0149] In formula (17) to the following formula (19), h x Represents the spatial discrete step length, that is, the distance between adjacent grid points, in meters.

[0150] x j represents the position of the j-th spatial node in the length direction, .

[0151] Represents node x j Laplace domain shift at is an abbreviation of = .

[0152] j represents the grid node index, and its value range in the five-point format is ; In the boundary second-order derivative expression, it corresponds to the node number near each endpoint.

[0153] Indicates the total number of grid points in space, with nodes numbered from 1 to n.

[0154] They represent the discretized derivatives of the fourth-order central difference and second-order difference operators of x, respectively.

[0155] For the second-order derivative terms in the boundary conditions, a one-sided second-order central difference is used, as shown in formulas (18) and (19).

[0156] (18)

[0157] (19)

[0158] It is also derived using Taylor expansion and uses a differential format that uses a one-sided four-point approximation to approximate the second-order derivative.

[0159] Process A5: Using the fast inverse Laplace transform algorithm combined with the displacement, the free vibration displacement of any point on the fuel rod under the sample over time is calculated.

[0160] It is important to note that since the Laplace transform is numerically implemented on the computer, fast Laplace transform and inverse transform must be considered. The two-point boundary value problem to be solved is fixed s.

[0161] First determine the inverse Laplace transform required The nodes and the corresponding differences required to solve the two-point boundary value problem Nodes, for each of these nodes use numerical methods to find The Laplace transform of , further use the difference method to solve the two-point boundary value problem at each node, and get the , using the fast inverse Laplace algorithm to obtain Numerical solution on the required interval.

[0162] When implementing process A5, let the maximum time length used in the simulation process be , unit s; according to the fast inverse Laplace algorithm, take , the time interval is ,but:

[0163] (20)

[0164] In formula (20), t max Indicates the actual simulation end time, which is the same as tt, so t max =tt.

[0165] Indicates the time window length used for the inverse Laplace transform, in seconds.

[0166] Indicates the time step (time interval) of inverse Laplace sampling, in seconds.

[0167] N1 represents the number of sampling points of each time series during inverse transformation.

[0168] The total number of truncated terms in the Laplace series is still recorded as , then the series folding multiples .

[0169] It should be noted that the series folding multiples Used for frequency domain overlap sampling.

[0170] (twenty one)

[0171] in, (twenty two)

[0172] In formula (21) and formula (22), represents the normalized response of the vibration displacement.

[0173] Represents the exponential function.

[0174] N is the number of nodes of the fast Laplace transform.

[0175] j represents the time sampling index, j=0, 1,…, N1-1.

[0176] k represents the frequency domain sampling index, k=0, 1,…, N1-1.

[0177] Indicates the basic step size of the original time domain. N indicates the total number of original time samples.

[0178] represents the kth spectral coefficient, which is obtained by sampling D(s) at equal intervals in the complex plane and taking the real part and accumulating it. Where D(s) represents the displacement D in the frequency domain.

[0179] Represents the operation of taking the real part of a complex number.

[0180] It should be noted that represents the kth, nth fold s domain sampling point. As shown in formula (23), record:

[0181] (twenty three)

[0182] In formula (23), i represents an imaginary unit, satisfying i 2 =-1. Indicates a set integration node. Represents the transform coefficient.

[0183] Assume that the difference method is used Node discrete Axis, the spatial step length is recorded as h , the spatial nodes are recorded as , from the above formula, we can see that we need to clarify , so consider exist The numerical Laplace transform at is defined by:

[0184]

[0185] (twenty four)

[0186] Use the complex trapezoidal formula to approximate the infinite interval integral, and the upper limit of the integral is , the step length is , the number of integration steps have:

[0187] (25)

[0188] In formula (24) and formula (25), It represents the upper limit time point of numerical integration, and is also the end point of truncated infinite interval, in units of s. Indicates the time step of the complex trapezoidal formula integration, unit is s.

[0189] m represents the time index of the integral summation, m=1, 2, ..., N2-1, corresponding to time t= .

[0190] Indicates that the node At time t= The original function value when .

[0191] Can be abbreviated as .

[0192] After solving the two-point boundary value problem by the difference method, we can The fast inverse Laplace algorithm is used to obtain That is, the displacement d at a certain position x at a certain time t, that is, the numerical solution d on xt is obtained.

[0193] Process A6: After all threads are executed, the free vibration displacement of any point on the fuel rod under each sample over time is obtained.

[0194] Combine Figure 2As shown, after obtaining the free vibration displacement of any point on the fuel rod under each sample over time, the automatic vibration displacement is input into the "Simulation Processing Module" to calculate the displacement information, velocity information, abrasion power, abrasion volume, and abrasion depth of the fuel rod. The specific process is described in the following steps.

[0195] Step S104: For each free vibration displacement, perform a center difference calculation based on the free vibration displacement to obtain a free vibration velocity corresponding to the free vibration displacement.

[0196] In the specific implementation of step S104, Figure 2 The content shown in "Get Free Vibration" is to get each free vibration displacement; Figure 2 The "Center Differential Displacement" and "Get Velocity Information" in the figure are used to calculate the center difference based on the free vibration displacement to obtain the free vibration velocity corresponding to the free vibration displacement.

[0197] It is understandable that the free vibration displacement It is a discretized matrix, and the right direction is defined as the positive direction.

[0198] Therefore, the central difference calculation is performed to obtain the free vibration velocity As shown in formula (26):

[0199] (26)

[0200] Step S105: performing correction processing according to the free vibration velocity and the preset gap information through a post-processing function to obtain corrected displacement information and velocity information.

[0201] It should be noted that if or , it is clear that the fuel rods collided.

[0202] It is understandable that represents the gap function on the right side, represents the gap function on the left, and Used to define the contact threshold between the fuel rods and the grid on both sides.

[0203] In the specific implementation of step S105 , a post-processing function (Post_processing function) is used to adjust the free vibration velocity and the preset gap information, thereby obtaining the corrected displacement information and velocity information, as shown in processes B1 to B4 .

[0204] Process B1: Traverse n time steps. If the free vibration displacement is greater than the right-side gap function in the preset gap information, the corrected displacement information is calculated through the post-processing function based on the right-side gap function, the standard deviation of the preset excitation force, and the stiffness of the preset spring.

[0205] In the specific implementation process B1, if the free vibration displacement is greater than the right gap function in the preset gap information, that is, , it is clear that the fuel rod hit the spring.

[0206] The corrected displacement information is then calculated using the post-processing function based on the right-side gap function, the standard deviation of the preset excitation force, and the stiffness of the preset spring. This is shown in Formulas (27) to (29):

[0207] (27)

[0208] (28)

[0209] (29)

[0210] In formulas (27) to (29), N represents the total time step (from t0 to t N N steps in total).

[0211] t0, t N Represent the start and end time of the time series respectively.

[0212] t k , t k+1 They represent the time points corresponding to the k-th step and the (k+1)-th step respectively.

[0213] Indicates the standard deviation of the exciting force, unit is N.

[0214] Indicates the grid spring stiffness coefficient in N / m.

[0215] Indicates the time t after contact k Corrected displacement, unit: m.

[0216] Process B2: If the free vibration displacement is less than the left gap function in the preset gap information, the corrected displacement information is calculated by the post-processing function according to the left gap function, the standard deviation of the preset exciting force and the stiffness of the preset spring.

[0217] In the specific implementation process B2, if the free vibration displacement is less than the left gap function in the preset gap information, that is, , it is clear that the fuel rod hit the rigid convex.

[0218] The corrected displacement information is obtained by calculating the left gap function, the standard deviation of the preset excitation force, and the stiffness of the preset spring through the post-processing function. This is shown in formulas (30) and (31):

[0219] (30)

[0220] (31)

[0221] In formula (30) and formula (31), is the standard deviation of the exciting force, and are the stiffness of the spring and the convex body respectively.

[0222] Process B3: Calculate the force on the fuel rod at each position and time based on the displacement information.

[0223] It should be noted that for the new Do the same difference to get the new velocity , as shown in formula (32).

[0224] (32)

[0225] pass Calculate the force at each position and time , as shown in formula (33).

[0226] = (33)

[0227] In formula (33), and Indicates the stiffness and spacing in the positive and negative directions. Specifically, Indicates the maximum allowable gap (or contact threshold) for the spring action, which is related to the positive and negative directions. and Corresponding, used for calculation in .

[0228] Process B4: Calculate the corrected velocity information based on the force and free vibration velocity.

[0229] It can be understood that repeating the above steps twice will obtain the corrected displacement information of the y-normal direction. , Corrected impact force information , Corrected and processed speed and the corrected displacement information in the z-normal direction , Corrected impact force information , Corrected and processed speed .

[0230] if , then To decelerate, there are:

[0231] (34)

[0232] Similarly, as shown in formula (35):

[0233] (35)

[0234] In formula (34) and formula (35), represents the friction coefficient in the z-direction (dimensionless), which is used to calculate the velocity attenuation and friction power after the collision. represents the friction coefficient in the y-normal direction (dimensionless).

[0235] Step S106: Calculate the abrasion power through the displacement information, and calculate the abrasion volume and abrasion depth of the fuel rod through Archard's wear law in combination with the preset wear time and the preset wear coefficient.

[0236] In the specific implementation of step S106, the impact power, Y-normal friction power, and Z-normal friction power are calculated based on the force and velocity information calculated in steps B3 and B4. Next, the sum of the impact power and the Y-normal friction power is calculated to obtain the abrasion power. The abrasion volume of the fuel rod is then calculated using Archard's wear law, combined with the preset wear time and wear coefficient. Finally, the abrasion depth is calculated based on the abrasion volume.

[0237] Specifically, normal (impact) power The calculation formula is as follows (as shown in formula (36)):

[0238] (36)

[0239] In formula (36), Indicates the velocity after the collision, in m / s. Represents the normal impact force after the collision.

[0240] Represents a strict step function, used for forward filtering when calculating impact power and friction power. When x>0, ; When x<0, .

[0241] It should be noted that Represents the friction power, including both Y and Z directions, that is, The vector sum of .

[0242] The calculation formula of the Y-normal friction power is shown in (37):

[0243] (37)

[0244] The Z-normal friction power is the same, as shown in formula (38):

[0245] (38)

[0246] In formula (37) and formula (38), the strict step function .

[0247] The calculation formula of abrasive power is shown in (39):

[0248] (39)

[0249] The process of obtaining the abrasion volume through Archard's law is shown in formula (40):

[0250] (40)

[0251] In formula (40), is the wear coefficient, unit , which represents the proportionality coefficient between wear volume and wear work. It represents the arithmetic mean of power P at all locations and times. The meaning here is different from T1 and T2 in the above inverse Laplace transform. Here it represents the total time (s) of the entire wear process.

[0252] Abrasion depth The answer can be obtained by solving the following nonlinear equation, as shown in formula (41):

[0253] (41)

[0254] In formula (41), Indicates the depth of abrasion The residual function of Used to solve the actual wear depth.

[0255] r represents the original radius of the fuel rod, in meters.

[0256] d represents the wear depth, in m, which is the thickness of the material removed from the circumference.

[0257] h represents the length of the wear volume calculated along the axial direction, in meters.

[0258] It represents the total wear volume calculated by Archard's law or power integration, in m 3 .

[0259] Represents the arc cosine function, which is used to calculate the central angle of the circle corresponding to the cut-off part.

[0260] It is a square root expression, corresponding to half the chord length when the cutting height on the circular section is d.

[0261] Step S107: Generate and output visualization results based on the displacement information, velocity information, abrasion power, abrasion volume, and abrasion depth.

[0262] As can be understood, displacement information records the displacement of the fuel rod at different locations or times, reflecting its spatial variation. Velocity information describes the rate of displacement change, indirectly reflecting the dynamic behavior of the fuel rod during operation or erosion. Abrasion power information, as an indicator of energy consumption, reflects the rate of energy consumption due to wear of the nuclear fuel rod cladding. The abrasion power can be used to calculate the abrasion volume, and further, through mathematical relationships, the abrasion depth can be derived.

[0263] In the specific implementation of step S107 , a variety of visualization results can be generated according to the displacement information, speed information, abrasion power, abrasion volume, and abrasion depth, and then output and displayed through an interactive interface.

[0264] Specifically, various visualization results include but are not limited to:

[0265] 1. Line graphs of displacement and velocity versus time. These two types of graphs show the dynamic behavior of the fuel rods at different time points.

[0266] Displacement map: shows the position changes of fuel rods during operation, revealing their motion trajectory and spatial evolution.

[0267] Velocity diagram: shows the speed of change in fuel rod displacement, reflecting the acceleration or deceleration of the motion state.

[0268] These two figures can be used to determine whether the fuel rod has abnormal dynamic response under abrasion, such as mutation or oscillation, which is of great reference value for subsequent abrasion depth calculation and cumulative distribution analysis.

[0269] 2. FFT spectrum of displacement data. The spectrum obtained by performing a fast Fourier transform (FFT) on the fuel rod displacement data converts the signal in the time domain into the frequency domain, thereby revealing possible periodic vibration or resonance phenomena.

[0270] Frequency distribution: The amplitude of different frequency components reflects the distribution of energy and helps to identify potential mechanical vibration characteristics and periodic impact characteristics during the abrasion process.

[0271] This spectrum diagram provides a basic basis for the subsequent analysis of the probability of impact events using the cumulative distribution function (CDF) function.

[0272] 3. Frequency histogram of impact force during the abrasion process. The histogram counts the number of occurrences or frequencies of impact forces of different magnitudes experienced by the fuel rod during the abrasion process.

[0273] Frequency distribution: intuitively shows the frequency of occurrence at different impact force levels.

[0274] Cumulative probability distribution basis: Combined with the cumulative distribution function (CDF), the cumulative probability of an impact force event or a larger impact force event occurring under a given impact force threshold can be analyzed, thereby evaluating the safety of the system and the risks under extreme working conditions.

[0275] This histogram not only shows the discrete distribution of impact force, but can also be combined with CDF to form a complete description of the statistical characteristics and cumulative probability of the impact event.

[0276] 4. Fuel rod grid abrasion depth map. Based on the previous calculation results, a fuel rod grid abrasion depth map is provided to compare the abrasion depths of different fuel rod grids, providing a basis for subsequent analysis and optimization.

[0277] It can be understood that through these charts and analyses, the dynamic behavior of fuel rods during the erosion process and its potential risks can be more comprehensively evaluated, providing data support for system safety assessment and optimization.

[0278] In this embodiment of the present invention, a highly efficient numerical Laplace transform and inverse transform software module has been developed. By optimizing discretization strategies and parallel computing, the computational efficiency of the transform is significantly improved. This module directly solves the nonlinear vibration equations of the fuel rods using the difference method, accurately capturing nonlinear effects such as gaps, friction, and collisions between the fuel rods and the spacer grid.

[0279] Secondly, a free vibration solution combined with simulation processing effectively avoids numerical explosion and iterative non-convergence issues that can occur under high stiffness conditions. This approach not only accurately describes the random coupling effects of multiple parameters, but also successfully builds a domestic software platform that supports rapid parameter input, graphical display of results, and quantitative analysis of the uncertainty of the overall wear state.

[0280] Corresponding to the fuel rod fretting wear analysis method provided in the above embodiment of the present invention, see Figure 3, shows a structural block diagram of a fuel rod fretting wear analysis device provided by an embodiment of the present invention.

[0281] The device includes: a data interaction module 301 , a numerical calculation core module 302 , a simulation processing module 303 and an output data visualization module 304 .

[0282] The data interaction module 301 is used to perform Box-Muller transformation on the distribution type and eigenvalue of the acquired engineering parameters to obtain random parameters. The data interaction module is also used to perform Monte Carlo sampling on the random parameters n times to obtain a high-dimensional probability space.

[0283] The numerical calculation core module 302 is used to calculate each sample in the n samples of the high-dimensional probability space with the obtained number of x-axis nodes, the total simulation time and the number of frequency stages according to the parallel strategy, and obtain the free vibration displacement of any point on the fuel rod under each sample over time.

[0284] The simulation processing module 303 is used to perform a central difference calculation based on the free vibration displacement for each free vibration displacement to obtain the free vibration velocity corresponding to the free vibration displacement; the simulation processing module is also used to perform correction processing based on the free vibration velocity and preset gap information through a post-processing function to obtain corrected displacement information and velocity information; the simulation processing module is also used to calculate the abrasion power based on the displacement information, and calculate the abrasion volume and abrasion depth of the fuel rod based on Archard's wear law, combined with the preset wear time and preset wear coefficient.

[0285] The output data visualization module 304 is used to generate and output visualization results based on the displacement information, velocity information, abrasion power, abrasion volume, and abrasion depth.

[0286] In an embodiment of the present invention, a set of efficient numerical Laplace transform and inverse transform software modules has been developed, which improves the transformation efficiency by optimizing discretization strategies and parallel computing. The nonlinear vibration equations of the fuel rods are solved using the difference method, accurately capturing nonlinear effects such as gaps, friction, and collisions. The free vibration solution and simulation processing method is adopted to avoid numerical explosion and iterative non-convergence problems under high stiffness. The embodiment of the present application supports fast parameter input, graphical result display, and quantification of the uncertainty of the wear state.

[0287] Combine Figure 3 The content shown, data interaction module 301, includes: Monte Carlo sampling submodule and labeling submodule.

[0288] The Monte Carlo sampling submodule is used to perform n Monte Carlo sampling on each random parameter. Each Monte Carlo sampling performs multi-dimensional sampling to obtain n high-dimensional probability space samples composed of multiple dimensions.

[0289] The labeling submodule is used to label the space spanned by n high-dimensional probability space samples composed of multiple dimensions as a high-dimensional probability space.

[0290] Combine Figure 3 The content shown, the numerical calculation core module 302, includes: an allocation submodule, a grid discretization submodule, a construction submodule, a solution submodule, a first calculation submodule and a statistics submodule.

[0291] The allocation submodule is used to allocate a thread to each of n samples in the high-dimensional probability space according to a parallel strategy.

[0292] The grid discretization submodule is used to obtain the number of x-axis nodes, the total simulation time and the number of frequency stages in the thread, and perform grid discretization to obtain a position-time plane discrete network.

[0293] A submodule is constructed to obtain the right-hand side force of the equation corresponding to the discrete network in the position-time plane through the fast Laplace transform algorithm, and to construct a two-point boundary value problem.

[0294] The solving submodule is used to solve the two-point boundary value problem through the second-order central difference method and the one-sided second-order central difference method to obtain the position-time displacement corresponding to the sample.

[0295] The first calculation submodule is used to calculate the free vibration displacement of any point on the fuel rod under the sample over time by using the fast inverse Laplace transform algorithm combined with the displacement.

[0296] The statistical submodule is used to obtain the free vibration displacement of any point on the fuel rod under each sample over time after all threads are executed.

[0297] Combine Figure 3 The content shown, the simulation processing module 303, includes: a second calculation submodule, a post-processing function calculation submodule, a third calculation submodule and a speed calculation submodule.

[0298] The second calculation submodule is used to traverse n time steps. If the free vibration displacement is greater than the right gap function in the preset gap information, the corrected displacement information is calculated through the post-processing function according to the right gap function, the standard deviation of the preset exciting force and the stiffness of the preset spring.

[0299] The post-processing function calculation submodule is used to calculate the corrected displacement information based on the left gap function, the standard deviation of the preset exciting force and the stiffness of the preset spring through the post-processing function if the free vibration displacement is less than the left gap function in the preset gap information.

[0300] The third calculation submodule is used to calculate the force of the fuel rod at each position and at each time according to the displacement information.

[0301] The velocity calculation submodule is used to calculate the corrected velocity information based on the force and free vibration velocity.

[0302] Combine Figure 3 The content shown, the simulation processing module, includes: a friction power calculation submodule, an abrasion power calculation submodule, an abrasion volume calculation submodule and an abrasion depth calculation submodule.

[0303] The friction power calculation submodule is used to calculate the impact power and Y-normal friction power based on the force and velocity information.

[0304] The abrasion power calculation submodule is used to calculate the sum of the impact power and the Y-normal friction power to obtain the abrasion power.

[0305] The abrasion volume calculation submodule is used to calculate the abrasion volume of the fuel rod by using Archard's wear law, combined with a preset wear time and a preset wear coefficient.

[0306] The abrasion depth calculation submodule is used to calculate the abrasion depth based on the abrasion volume.

[0307] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple. For relevant parts, refer to the partial description of the method embodiment. The system and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without expending creative work.

[0308] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0309] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing fretting wear of fuel rods, characterized in that: The method comprises: The distribution type and eigenvalue of the obtained engineering parameters are processed by Box-Muller transformation to obtain random parameters; Performing n Monte Carlo sampling on the random parameters to obtain a high-dimensional probability space; Calculating each of the n samples in the high-dimensional probability space with the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages according to a parallel strategy to obtain the free vibration displacement of any point on the fuel rod over time under each sample; For each of the free vibration displacements, performing a central difference calculation based on the free vibration displacement to obtain a free vibration velocity corresponding to the free vibration displacement; Performing correction processing according to the free vibration velocity and preset gap information through a post-processing function to obtain corrected displacement information and velocity information; Calculating the abrasion power through the displacement information, and calculating the abrasion volume and abrasion depth of the fuel rod through Archard's wear law in combination with a preset wear time and a preset wear coefficient; A visualization result is generated and outputted according to the displacement information, the speed information, the abrasion power, the abrasion volume, and the abrasion depth.

2. The method according to claim 1, characterized in that The performing of n Monte Carlo sampling on the random parameters to obtain a high-dimensional probability space includes: Performing n Monte Carlo sampling on each of the random parameters, performing multi-dimensional sampling each time, to obtain n high-dimensional probability space samples consisting of multiple dimensions; The space spanned by n high-dimensional probability space samples composed of multiple dimensions is marked as a high-dimensional probability space.

3. The method according to claim 1, characterized in that The method of calculating each of the n samples in the high-dimensional probability space and the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages according to the parallel strategy to obtain the free vibration displacement of any point on the fuel rod over time under each sample includes: Allocate a thread to each of the n samples in the high-dimensional probability space according to a parallel strategy; In the thread, the number of x-axis nodes, the total simulation time and the number of frequency stages are obtained, and the grid is discretized to obtain a position-time plane discrete network; The right-hand side force of the equation corresponding to the position-time plane discrete network is obtained by a fast Laplace transform algorithm, and a two-point boundary value problem is constructed; Solve the two-point boundary value problem by using the second-order central difference method and the one-sided second-order central difference method to obtain the position-time displacement corresponding to the sample; Using a fast inverse Laplace transform algorithm in combination with the displacement, the free vibration displacement of any point on the fuel rod under the sample over time is calculated; After all threads are executed, the free vibration displacement of any point on the fuel rod under each sample over time is obtained.

4. The method according to claim 1, wherein The post-processing function performs correction processing according to the free vibration velocity and the preset gap information to obtain corrected displacement information and velocity information, including: Traversing n time steps, if the free vibration displacement is greater than the right gap function in the preset gap information, then using a post-processing function to calculate the corrected displacement information according to the right gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring; If the free vibration displacement is less than the left gap function in the preset gap information, then calculating the corrected displacement information according to the left gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring through a post-processing function; Calculate the force of the fuel rod at each position and at each time according to the displacement information; Corrected velocity information is calculated based on the force and the free vibration velocity.

5. The method according to claim 4, characterized in that Calculating the abrasion power by using the displacement information, and calculating the abrasion volume and abrasion depth of the fuel rod by using Archard's wear law in combination with a preset wear time and a preset wear coefficient, includes: Calculating impact power and Y-normal friction power based on the force and the velocity information; Calculating the sum of the impact power and the Y-normal friction power to obtain the abrasive power; The abrasion volume of the fuel rod is calculated by using Archard's wear law, combined with the preset wear time and the preset wear coefficient; The abrasion depth is calculated based on the abrasion volume.

6. A fuel rod fretting wear analysis device, characterized in that: The device comprises: A data interaction module is used to perform Box-Muller transformation on the distribution type and characteristic value of the acquired engineering parameters to obtain random parameters; the data interaction module is also used to perform Monte Carlo sampling on the random parameters n times to obtain a high-dimensional probability space; a numerical calculation core module for calculating, according to a parallel strategy, each of the n samples in the high-dimensional probability space and the obtained number of x-axis nodes, the total simulation time, and the number of frequency stages, to obtain the free vibration displacement of any point on the fuel rod over time under each sample; a simulation processing module configured to perform a central difference calculation based on each free vibration displacement to obtain a free vibration velocity corresponding to the free vibration displacement; the simulation processing module is further configured to perform correction processing based on the free vibration velocity and preset gap information using a post-processing function to obtain corrected displacement information and velocity information; the simulation processing module is further configured to calculate the abrasion power based on the displacement information, and calculate the abrasion volume and abrasion depth of the fuel rod using Archard's wear law in combination with a preset wear time and a preset wear coefficient; The output data visualization module is used to generate and output visualization results based on the displacement information, the speed information, the abrasion power, the abrasion volume and the abrasion depth.

7. The device according to claim 6, characterized in that The data interaction module includes: A Monte Carlo sampling submodule, configured to perform n Monte Carlo sampling on each of the random parameters, wherein each Monte Carlo sampling performs multi-dimensional sampling to obtain n high-dimensional probability space samples consisting of multiple dimensions; The labeling submodule is used to label the space spanned by n high-dimensional probability space samples composed of multiple dimensions as a high-dimensional probability space.

8. The device according to claim 6, characterized in that The numerical calculation core module includes: an allocation submodule, configured to allocate a thread to each of the n samples in the high-dimensional probability space according to a parallel strategy; A grid discretization submodule is used to obtain the number of x-axis nodes, the total simulation time and the number of frequency stages in the thread, and perform grid discretization to obtain a position-time plane discrete network; A construction submodule is used to obtain the right-hand side force of the equation corresponding to the position-time plane discrete network by a fast Laplace transform algorithm, and construct a two-point boundary value problem; A solving submodule, configured to solve the two-point boundary value problem by using a second-order central difference method and a unilateral second-order central difference method to obtain a position-time displacement corresponding to the sample; A first calculation submodule is configured to calculate the free vibration displacement of any point on the fuel rod under the sample over time by using a fast inverse Laplace transform algorithm in combination with the displacement; The statistical submodule is used to obtain the free vibration displacement of any point on the fuel rod under each sample over time after all threads are executed.

9. The device according to claim 6, characterized in that The simulation processing module includes: A second calculation submodule is configured to traverse n time steps, and if the free vibration displacement is greater than the right-side gap function in the preset gap information, calculate corrected displacement information according to the right-side gap function, the standard deviation of the preset exciting force, and the stiffness of the preset spring through a post-processing function; a post-processing function calculation submodule, configured to calculate corrected displacement information using a post-processing function according to the left gap function, a standard deviation of a preset exciting force, and a preset spring stiffness if the free vibration displacement is less than the left gap function in the preset gap information; a third calculation submodule, configured to calculate the force of the fuel rod at each position and at each time according to the displacement information; The velocity calculation submodule is configured to calculate corrected velocity information according to the force and the free vibration velocity.

10. The device according to claim 9, characterized in that The simulation processing module includes: a friction power calculation submodule, configured to calculate the impact power and the Y-normal friction power according to the force and the velocity information; an abrasion power calculation submodule, configured to calculate the sum of the impact power and the Y-normal friction power to obtain the abrasion power; An abrasion volume calculation submodule is used to calculate the abrasion volume of the fuel rod by using Archard's wear law, combined with a preset wear time and a preset wear coefficient; The abrasion depth calculation submodule is used to calculate the abrasion depth based on the abrasion volume.

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