Automatic generation method of multi-parameter lognormal random field based on finite element grid

Abstract

The application discloses a kind of multi-parameter lognormal random field automation generation method based on finite element grid, the method first reads finite element grid file, parses the unit topological relation of target analysis area and automatically extracts the geometric center point coordinate of entity unit;Obtain multidimensional uniform distribution sample, and convert into independent initial standard normal random matrix;Respectively construct the cross correlation matrix of each parameter space autocorrelation matrix and parameter;Multi-parameter lognormal random field is generated using nonlinear mapping equation;Finally, the random field data is mapped according to unit number and verified.Outputs.Through the combination of original finite element grid analysis and multiple correlation decoupling calculation, the method can efficiently and accurately generate the random field subject to complex correlation structure, effectively eliminate the error caused by traditional independent grid interpolation mapping, provide a fully automated pre-processing tool for large-scale random finite element simulation and engineering reliability assessment.

Description

Technical Field

[0001] This invention relates to the fields of engineering reliability analysis and stochastic finite element technology, and in particular to a method for the automated generation and batch processing of multi-parameter log-normal random fields based on finite element mesh structures. Background Technology

[0002] In numerical simulation analysis in fields such as geotechnical engineering, hydraulic engineering, and structural mechanics, traditional deterministic finite element analysis often fails to accurately reflect the reliability of structures due to the significant spatial variability of geological materials, such as rocks, soils, and engineering materials. Random field theory, by describing the spatial correlation and variability of material parameters, has become a standard tool for characterizing this spatial variability.

[0003] Existing random field generation methods are often disconnected from finite element meshes. Researchers typically need to use separate mathematical software to generate random fields with regularized meshes, and then apply them to actual finite element models through complex interpolation or mapping techniques. For three-dimensional finite element meshes with complex topological relationships, such as unstructured meshes exported by software like Abaqus, this mapping is not only inefficient but also prone to introducing errors. Furthermore, multiple physical and mechanical parameters of engineering materials, such as elastic modulus, Poisson's ratio, and cohesion, often exhibit cross-correlation. Many existing generation tools can only generate independent random fields with single parameters, making it difficult to efficiently handle the joint generation requirements of multi-parameter coupling, multi-dimensional spatially correlated structures, and non-Gaussian distributions, such as log-normal distributions, thus failing to meet the needs of large-scale stochastic finite element batch simulation analysis. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide an automated method for generating multi-parameter log-normal random fields based on finite element meshes. This method can directly read finite element mesh files, automatically extract target element coordinates, and efficiently and in batches generate multi-parameter random fields with cross-correlation and spatial correlation through Latin hypercube sampling, multi-correlation decoupling, and log-normal mapping.

[0005] To achieve the above objectives, in a first aspect, this application provides an automated method for generating multi-parameter log-normal random fields based on finite element meshes, comprising the following steps:

[0006] S1. Read the finite element mesh file containing node coordinates, element topology, and element set; parse and locate the element set of the target analysis region; calculate the center point coordinates of each target element in the element set. S2. Obtain the statistical characteristic parameters and simulation parameters of the multi-parameter random field, including the mean, coefficient of variation, horizontal correlation distance, vertical correlation distance, cross-correlation matrix between parameters, autocorrelation function type, and number of random field simulations for each parameter; S3. Generate uniformly distributed random samples in a multidimensional space, and then convert the uniformly distributed random samples into mutually independent initial standard normal random matrices; S4. Based on the coordinates of the center point of the target cell and the selected autocorrelation function type, construct the spatial autocorrelation matrix of each parameter; perform Cholesky decomposition on the cross-correlation matrix between parameters and the spatial autocorrelation matrix of each parameter to obtain the lower triangular matrix of cross-correlation and the lower triangular matrix of spatial correlation. Step S5: Multiply the initial standard normal random matrix with the cross-correlation lower triangular matrix and the spatial correlation lower triangular matrix respectively to generate a standard normal random field that has both multi-parameter cross-correlation and spatial autocorrelation; obtain the multi-parameter log-normal random field through log-normal mapping transformation and establish a mapping output file to the cell number.

[0007] In one possible implementation, in S1, the calculation of the center point coordinates of each target element specifically refers to the center point coordinates of an eight-node hexahedral element. The formula for calculation is: ; in, The first element that makes up this eight-node hexahedral unit The coordinates of each node.

[0008] In one possible implementation, in S3, a uniformly distributed random sample is generated in a multidimensional space using the Latin hypercube sampling method, and the uniformly distributed random sample is converted into an independent initial standard normal random matrix by the standard normal quantile function approximation algorithm.

[0009] In one possible implementation, in S4, the spatial autocorrelation matrix is ​​calculated from the correlation coefficient between any two cell center points based on the autocorrelation function. Composition; Let the horizontal distance between the center points of any two units be denoted as . The vertical distance is The horizontal correlation distance of each parameter is The vertical correlation distance is The autocorrelation function type includes any one of the following: Exponential type: ; Gaussian type: ; Second-order autoregressive type: ; Exponential-cosine type: ; Triangle: When ,and hour, ;otherwise .

[0010] In one possible implementation, the specific computational process for generating a standard normal random field with both multi-parameter cross-correlation and spatial autocorrelation in S5 is as follows: Denote the cross-correlation matrix between parameters The Cholesky decomposition matrix is , No. The spatial autocorrelation matrix of each parameter The Cholesky decomposition matrix is ; The initial standard normal random matrix is ​​divided into blocks and reassembled, denoted as . First, the cross-correlation between parameters is injected into independent samples: ; Then, the matrix columns with cross-correlation are extracted, and the first column is... By injecting spatial autocorrelation into each parameter dimension, a correlated standard normal random field is obtained: .

[0011] As described in S5, a multi-parameter log-normal random field is obtained through log-normal mapping transformation. The specific calculation formula is as follows: ; ; ; In the formula, for, for, For the first The final log-normal random field vector with parameters. For the first Given the mean of each parameter, The standard deviation is, and , is the coefficient of variation.

[0012] Secondly, this application also provides an automated generation device for multi-parameter log-normal random fields based on finite element meshes, used to implement the method, comprising: Mesh analysis and center point calculation module: used to read finite element mesh files, extract element topology relationships and node coordinates, and calculate the center point coordinates of the target region elements; Normal sample generation module: used to generate independent uniformly distributed samples based on the set Latin hypercube sampling, and convert them into independent standard normal random matrices through quantile function approximation algorithm; The correlation matrix decomposition module is used to construct the spatial autocorrelation matrix based on the cell center coordinates and the specified autocorrelation function model, and to perform Cholesky decomposition on the multi-parameter cross-correlation matrix and the spatial autocorrelation matrix respectively. The correlation injection and mapping module is used to multiply the independent standard normal random matrix with the lower triangular matrix after Cholesky decomposition to achieve multiple correlation injection, and perform log-normal mapping. Finally, it outputs random field parameter files with cell number mapping in batches.

[0013] Thirdly, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: when the processor executes the program, it implements the aforementioned automated generation method for multi-parameter log-normal random fields based on finite element meshes.

[0014] Fourthly, this application also provides a non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, enables the automated generation method of a multi-parameter log-normal random field based on a finite element mesh.

[0015] Compared with the prior art, the above-conceptual technical solution conceived in this application has the following beneficial effects: 1. This invention directly extracts element topology and node coordinates from native finite element mesh files (such as Abaqus input file format) to construct random fields, eliminating the mapping error between independent meshes and finite element meshes in traditional methods, and realizing seamless connection and full automation of random finite element preprocessing.

[0016] 2. By combining the decoupled calculations of Latin hypercube sampling (LHS), multi-parameter cross-correlation, and spatial autocorrelation, and applying the robust Acklam approximation method for inverse normal transformation, this method can generate large-scale log-normal random fields with complex correlation structures with high efficiency and high accuracy, which greatly improves the efficiency of large-scale Monte Carlo stochastic finite element simulation. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the overall process of an automated method for generating multi-parameter log-normal random fields based on finite element meshes, provided in an embodiment of the present invention.

[0019] Figure 2 This is a geometric extraction diagram illustrating the analysis of the finite element mesh (eight-node hexahedral element) and the calculation of the center point of the target element, provided in an embodiment of the present invention.

[0020] Figure 3 The computational flow diagram for Latin hypercube sampling, correlation matrix decomposition, and multiple correlation injection provided in the embodiments of the present invention is shown.

[0021] Figure 4 The present invention provides a module structure block diagram of an automated generation device for multi-parameter log-normal random fields based on finite element meshes.

[0022] Figure 5 This is a schematic diagram of the hardware structure of an electronic device for executing the above-described automated random field generation method, provided in an embodiment of the present invention.

[0023] Figure 6 This is a comparative schematic diagram of the spatial distribution cloud maps of multi-parameter log-normal random fields generated under different spatial autocorrelation function models provided in the embodiments of the present invention; wherein, sub-figure a is the simulation result of the corresponding exponential type and b is the simulation result of the Gaussian type.

[0024] In the picture: Central calculation module 41, normal sample generation module 42, correlation matrix decomposition module 43, correlation injection and mapping module 44, visualization and statistical verification module 45; Processor 510, communication interface 520, memory 530, communication bus 540. Detailed Implementation

[0025] To more clearly illustrate the purpose, technical solution, and beneficial effects of this application, a further detailed description of this application is provided below in conjunction with illustrations and specific embodiments. It should be specifically noted that the specific embodiments described below are only for illustrating the technical content of this application and do not constitute a limitation on the scope of protection of this application.

[0026] Example 1: This implementation provides an automated workflow, primarily for directly assigning random field properties to solid elements with complex topologies (such as C3D8P elements) in a three-dimensional finite element model. See also... Figure 1 The entire execution process includes the following steps: Step 1: Analysis and geometric extraction of the finite element model mesh.

[0027] Read the node definitions exported from the finite element model ( Node) and unit definition ( The data text (Element) is used to extract the spatial coordinate dictionary of the grid nodes and the dictionary of the nodes of the elements. By matching the specified element set name (such as the surrounding rock set), the numbers of all target elements are obtained.

[0028] Obtain the statistical characteristic parameters and simulation parameters of a multi-parameter random field; the statistical characteristic parameters and simulation parameters include: the mean, coefficient of variation, horizontal correlation distance, vertical correlation distance, cross-correlation matrix between parameters, autocorrelation function type, and number of random field simulations.

[0029] See Figure 2 For an eight-node hexahedral element (C3D8P), what are the coordinates of its center point? It contains the coordinates of 8 nodes The arithmetic mean is determined by traversing the 8 nodes corresponding to each unit. The spatial centroid position is calculated as the discretization node of the random field. Geometric center The calculation is as follows: ; This step effectively avoids the positional deviation that occurs when random fields generated directly from regular grids are subsequently mapped to unstructured finite element grids.

[0030] Step 2: Generate the initial independent standard normal random sequence.

[0031] See Figure 3 To improve the convergence accuracy of Monte Carlo simulations with small samples, the system uses Latin hypercube sampling (LHS) to obtain uniformly distributed random sequences for multidimensional independent random variables within a set total sample size space. Subsequently, to avoid the computational bottleneck caused by the table lookup method, this method uses Acklam's piecewise rational approximation to approximate the inverse cumulative distribution function (Inverse CDF) of the standard normal distribution, combined with Halley's iterative method for residual correction, to efficiently transform uniformly distributed samples into independent standard normal random sequences. .

[0032] Step 3: Construction and numerical decomposition of the composite correlation matrix.

[0033] In multi-parameter random fields (such as simultaneously simulating elastic modulus and Poisson's ratio), different physical parameters often exhibit cross-correlation. Let the covariance (or correlation coefficient) matrix between the parameters be... The lower triangular matrix was extracted using Cholesky decomposition. ,satisfy .

[0034] The spatial autocorrelation matrix is ​​calculated from the correlation coefficient between any two cell center points using the autocorrelation function. Composition; Let the horizontal distance between the center points of any two units be denoted as . The vertical distance is The horizontal correlation distance of each parameter is The vertical correlation distance is The autocorrelation function type includes any of the following: Exponential type: ; Gaussian type: ; Second-order autoregressive type: ; Exponential-cosine type: ; Triangle: When ,and hour, ;otherwise .

[0035] In this embodiment, for any two unit center points in three-dimensional space and Its horizontal absolute distance Vertical absolute distance Based on the engineering geological characteristics, an exponential autocorrelation function is selected to establish... Spatial autocorrelation matrix of dimension : ; After the matrix is ​​constructed Then, we consider the diagonal pivot normalization and similarly use Cholesky decomposition to obtain the lower triangular matrix in space. In this process, to prevent matrix ill-conditioned (non-positive definite) problems caused by excessively close grid spacing, the system will automatically inject a minimum dithering factor into the diagonal to ensure the numerical stability of the decomposition.

[0036] Step 4: Correlation injection and log-normal nonlinear mapping.

[0037] The independent normal matrix obtained in the second step After reorganizing and partitioning, first with Multiplying the correlation coupling of the execution parameter dimensions yields a standard normal basis matrix with cross-correlation features. : ; Subsequently, the spatial association structure corresponding to each engineering parameter was determined. Each element is multiplied by the corresponding random matrix column to ensure that the data in each unit has a continuous spatial dimension, thus obtaining the relevant standard normal random field. : ; Since geotechnical parameters (such as permeability coefficient and elastic modulus) cannot be negative, this method ultimately uses a rigorous log-normal mapping equation for nonlinear transformation: ; ; ; At this point, a complete log-normal random field sample containing multi-parameter cross-relationships and specified autocorrelation function characteristics can be obtained. .

[0038] Finally, the system outputs a row index mapping file (such as .csv format) based on the model element number, and writes the calculation results according to the element row number, so that the finite element solver (such as Abaqus) can perform batch reading and automated simulation calculation in the INP file, forming a closed loop.

[0039] Example 2: Figure 4 This invention illustrates a schematic diagram of an automated multi-parameter log-normal random field generation device based on a finite element mesh, comprising: Mesh Analysis and Center Calculation Module 41: Provides a file reading and parsing interface for directly importing external native finite element mesh files, automatically parsing element topology relationships and extracting node spatial coordinates, and calculating and outputting the coordinates of the geometric center point of each solid element within the target analysis area.

[0040] Normal sample generation module 42: Built-in Latin hypercube sampling algorithm and standard normal quantile function approximation algorithm, used to automatically generate mutually independent initial standard normal random matrices according to the number of random field simulations and parameter dimensions set by the user.

[0041] Correlation matrix decomposition module 43: It has built-in multiple spatial autocorrelation function models (i.e., the exponential type, Gaussian type, etc. formulas described in claim 3), calls the center coordinates output by module 41 to construct the spatial autocorrelation matrix, and automatically performs Cholesky decomposition on the multi-parameter cross-correlation matrix and the spatial autocorrelation matrix to output the corresponding lower triangular matrix.

[0042] Correlation Injection and Mapping Module 44: It has a built-in matrix coupling algorithm and nonlinear transformation algorithm (i.e., the formula described in claim 5), which multiplies the random matrix of module 42 with the lower triangular matrix of module 43 to inject multiple correlations, then performs log-normal mapping, and automatically outputs the final random field parameter mapping file according to the unit number.

[0043] Visualization and Statistical Validation Module 45: Supports remapping the discrete random field data output by Module 44 back to the finite element mesh, automatically generating and comparing spatial distribution contour maps under different autocorrelation functions, such as... Figure 6 As shown, the mean and coefficient of variation of the generated samples were simultaneously post-processed and statistically verified to provide a reliable basis for subsequent Monte Carlo stochastic finite element simulations.

[0044] Figure 5 A schematic diagram of the physical structure of an electronic device is provided. The device includes a processor 510, a communication interface 520, a memory 530, and a communication bus 540. The processor 510, communication interface 520, and memory 530 are interconnected via the communication bus 540. The memory 530 stores a computer program, which, when invoked by the processor 510, can be used to execute the aforementioned automated generation method of multi-parameter random fields based on finite element meshes.

[0045] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0046] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An automated method for generating multi-parameter log-normal random fields based on finite element meshes, characterized in that, Includes the following steps: S1. Read the finite element mesh file containing node coordinates, element topology, and element set; parse and locate the element set of the target analysis region; calculate the center point coordinates of each target element in the element set. S2. Obtain the statistical characteristic parameters and simulation parameters of the multi-parameter random field; S3. Generate uniformly distributed random samples in a multidimensional space, and then convert the uniformly distributed random samples into mutually independent initial standard normal random matrices; S4. Based on the coordinates of the center point of the target cell and the selected autocorrelation function type, construct the spatial autocorrelation matrix of each parameter; perform Cholesky decomposition on the cross-correlation matrix between parameters and the spatial autocorrelation matrix of each parameter to obtain the lower triangular matrix of cross-correlation and the lower triangular matrix of spatial correlation. Step S5: Multiply the initial standard normal random matrix with the cross-correlation lower triangular matrix and the spatial correlation lower triangular matrix respectively to generate a standard normal random field that has both multi-parameter cross-correlation and spatial autocorrelation; obtain the multi-parameter log-normal random field through log-normal mapping transformation and establish a mapping output file to the cell number.

2. The method according to claim 1, characterized in that, In S1, the calculation of the center point coordinates of each target element specifically refers to the calculation of the center point coordinates of an eight-node hexahedral element. The formula for calculation is: ； in, The first element that makes up this eight-node hexahedral unit The coordinates of each node.

3. The method according to claim 1, characterized in that, In S2, the statistical characteristic parameters and simulation parameters include: the mean, coefficient of variation, horizontal correlation distance, vertical correlation distance, cross-correlation matrix between parameters, autocorrelation function type, and number of random field simulations.

4. The method according to claim 1, characterized in that, In S3, the Latin hypercube sampling method is used to generate uniformly distributed random samples in multidimensional space, and the uniformly distributed random samples are transformed into mutually independent initial standard normal random matrices through the standard normal quantile function approximation algorithm.

5. The method according to claim 1, characterized in that, In S4, the spatial autocorrelation matrix is ​​calculated from the correlation coefficient between any two cell center points based on the autocorrelation function. Composition; Let the horizontal distance between the center points of any two units be denoted as . The vertical distance is The horizontal correlation distance of each parameter is The vertical correlation distance is The autocorrelation function type includes any one of the following: Exponential type: ; Gaussian type: ; Second-order autoregressive type: ; Exponential-cosine type: ; Triangle: When ,and hour, ;otherwise .

6. The method according to claim 1, characterized in that, In S5, the specific calculation process for generating a standard normal random field that simultaneously possesses multi-parameter cross-correlation and spatial autocorrelation is as follows: Denote the cross-correlation matrix between parameters The Cholesky decomposition matrix is , No. The spatial autocorrelation matrix of each parameter The Cholesky decomposition matrix is ; The initial standard normal random matrix is ​​divided into blocks and reassembled, denoted as . First, the cross-correlation between parameters is injected into independent samples: ; Then, the matrix columns with cross-correlation are extracted, and the first column is... By injecting spatial autocorrelation into each parameter dimension, a correlated standard normal random field is obtained: .

7. The method according to claim 6, characterized in that, As described in S5, a multi-parameter log-normal random field is obtained through log-normal mapping transformation. The specific calculation formula is as follows: ； ； ； In the formula, For the log-space standard deviation, The mean of the logarithmic space, For the first The final log-normal random field vector with parameters. For the first Given the mean of each parameter, The standard deviation is, and , is the coefficient of variation.

8. An automated device for generating multi-parameter log-normal random fields based on finite element meshes, used to implement the method described in any one of claims 1 to 7, characterized in that, include: Mesh analysis and center point calculation module: used to read finite element mesh files, extract element topology relationships and node coordinates, and calculate the center point coordinates of the target region elements; Normal sample generation module: used to generate independent uniformly distributed samples based on the set Latin hypercube sampling, and convert them into independent standard normal random matrices through quantile function approximation algorithm; The correlation matrix decomposition module is used to construct the spatial autocorrelation matrix based on the cell center coordinates and the specified autocorrelation function model, and to perform Cholesky decomposition on the multi-parameter cross-correlation matrix and the spatial autocorrelation matrix respectively. The correlation injection and mapping module is used to multiply the independent standard normal random matrix with the lower triangular matrix after Cholesky decomposition to achieve multiple correlation injection, and perform log-normal mapping. Finally, it outputs random field parameter files with cell number mapping in batches.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the automated generation method for multi-parameter log-normal random fields based on finite element meshes as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium storing a computer program, characterized in that, When the program is executed by the processor, it can realize the automated generation method of multi-parameter log-normal random fields based on finite element mesh as described in any one of claims 1 to 7.

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