A cylindrical shell composite geometric defect simulation method based on pca joint random field
By using PCA combined with random field methods, the problems of modeling singleness and adaptability of composite defects in cylindrical shell structures are solved, realizing efficient and accurate simulation and full-dimensional verification of composite defects, which is applicable to the analysis of cylindrical shell structures of different sizes and working conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-27
- Publication Date
- 2026-06-26
AI Technical Summary
Existing methods for simulating geometric defects in cylindrical shell structures suffer from problems such as simplistic defect modeling, poor manifold adaptability, low computational efficiency, lack of coupling mechanism characterization, and incomplete verification systems, making it difficult to accurately describe the spatial correlation and coupling effects of composite defects.
A PCA-based joint random field approach is adopted. By generating a discrete point cloud uniformly distributed on the surface of a cylindrical shell, calculating the geodesic distance, constructing a joint correlation matrix, using PCA dimensionality reduction technology to screen principal components, constructing a radius and thickness defect field, reshaping it into a grid form, and finally constructing a composite geometric defect model.
It achieves accurate coupled modeling and efficient generation of composite defects, reduces computational complexity, is applicable to the simulation of cylindrical shell structures of different sizes and working conditions, and provides a full-dimensional verification method to ensure the accuracy and reliability of the modeling results.
Smart Images
Figure CN122287186A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of cylindrical shell structure defect simulation and finite element analysis technology, and in particular to a method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields. Background Technology
[0002] The structural performance of a cylindrical shell is closely related to its geometric integrity. Geometric defects, as unavoidable problems in manufacturing and operation, have a significant impact on its mechanical behavior. In particular, the buckling capacity of a thin-walled cylindrical shell under axial compression is extremely sensitive to initial geometric defects. The buckling load measured in experiments is often much lower than the theoretical prediction. The core cause of this difference is the existence of geometric defects such as local radius deviation and uneven thickness.
[0003] Currently, the industry mainly uses three types of methods to characterize the geometric defects of cylindrical shells: The first type is based on actual measurements, which directly obtains defect data through technologies such as laser scanning and digital image correlation. Although it can reflect the real defect morphology, the testing process is time-consuming and labor-intensive, and it can only obtain specific defect patterns of a single structure, making it difficult to extend to large-scale simulation scenarios; The second type is based on the buckling mode hypothesis, which simplifies defects into single or combined buckling characteristic mode forms. This method ignores the random nature of defects and does not conform to the random distribution law of defects in the actual manufacturing process; The third type is based on random field theory, which constructs random fields to describe the spatial distribution and correlation of defects, and has become the most valuable defect modeling approach for engineering applications.
[0004] However, existing random field-based defect simulation methods still face many key technical bottlenecks, which limit their application in cylindrical shell structures: most studies focus only on simulating single defects of radius or thickness, ignoring the coupling effect of two types of defects in actual manufacturing. For example, during processing, concave regions of radius are often accompanied by local wall thickness reduction. This coupling relationship can significantly change the stress concentration characteristics of the structure, but existing methods lack a systematic characterization of this type of coupling mechanism, resulting in a large deviation between the modeling results and engineering reality. Traditional random field generation methods (such as Karhunen-Loève (KL) expansion and spectral representation) are mostly based on Euclidean distance to construct spatial correlation, while the intrinsic correlation between discrete points on the surface of a cylindrical shell, as a typical two-dimensional manifold structure, should be described by geodesic distance. Existing methods directly apply planar random field generation logic to curved structures, failing to capture the geometric characteristics of manifolds and resulting in low accuracy in modeling the spatial correlation of defects. The number of random variables in existing random field methods (such as point discretization) is directly related to the number of discrete points in the structure. For large-size, high-discrete-density cylindrical shell models, the scale of random variables grows exponentially, significantly increasing the complexity of subsequent stochastic analysis and reliability calculations, making them unsuitable for large-scale simulations and optimization designs. A few random field generation techniques developed for curved structures (such as dimensionality reduction methods based on isometric mapping) are only applicable to manifolds without inherent closed-loop structures and cannot be adapted to closed curved surfaces like cylindrical shells, limiting their application scope. Existing research focuses primarily on verifying the statistical characteristics of single defects, lacking comprehensive verification of the spatial correlation, coupling effects, and relationship with structural mechanical responses of composite defects, making it difficult to guarantee the reliability and engineering applicability of modeling methods.
[0005] Therefore, there is an urgent need to propose a theoretically rigorous, adaptable, and efficient method for modeling composite geometric defects, so as to achieve accurate coupled characterization and efficient generation of composite defects of cylindrical shell radius and thickness, and provide reliable structural model support for subsequent mechanical performance analysis and failure mechanism research. Summary of the Invention
[0006] This invention aims to at least solve one of the technical problems existing in related technologies. To this end, this invention provides a method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields, which solves the problems of single defect modeling, poor manifold adaptability, low computational efficiency, lack of coupling mechanism representation, and imperfect verification system in existing methods, and achieves accurate coupled modeling, efficient generation, and full-dimensional verification of composite defects.
[0007] This invention provides a method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields, comprising: S1: Determine the cylindrical shell's reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria; S2: Based on the cylindrical shell's reference parameters, defect parameters, and discretization parameters, and using the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, a uniformly distributed discrete point cloud is generated on the surface of the cylindrical shell, forming uniformly distributed discrete points. S3: Calculate the geodesic distances between discrete points and construct a spatial distance matrix based on the geodesic distances between discrete points; S4: Construct a joint correlation matrix by combining the exponential correlation function with the spatial distance matrix; S5: Calculate the cumulative contribution rate based on the joint correlation matrix and PCA reconstruction criteria, select principal components based on the cumulative contribution rate, and construct the defect field based on the principal components; S6: Construct a defect mesh based on the defect field, and construct a composite geometric defect model of the cylindrical shell based on the defect mesh and the reference geometric parameters of the cylindrical shell.
[0008] Furthermore, step S3 includes: S31: Calculate the axial distance between two discrete points based on their coordinates; S32: Calculate the shortest circumferential arc length between two discrete points based on their coordinates; S33: Calculate the geodesic distance between two discrete points based on the axial distance between the two discrete points and the shortest circumferential arc length between the two discrete points; S34: Calculate the geodesic distances between all discrete points to form a spatial distance matrix.
[0009] Furthermore, step S4 includes: S41: Construct the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects using the exponential correlation function and the spatial distance matrix; S42: Construct a cross-correlation matrix based on the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects; S43: Concatenate the autocorrelation matrix of the radius defect and the autocorrelation matrix of the thickness defect with the cross-correlation matrix to obtain the joint correlation matrix.
[0010] Furthermore, the joint correlation matrix satisfies symmetric positive definiteness.
[0011] Furthermore, step S5 includes: S51: Perform singular value decomposition on the joint correlation matrix to obtain the eigenvalue matrix and eigenvector matrix; S52: Arrange the eigenvalues of the eigenvalue matrix in descending order, select the eigenvalues whose cumulative contribution rate is greater than the PCA reconstruction criterion, obtain the number of principal components, and reduce the dimensionality of the eigenvalue matrix and eigenvector matrix according to the number of principal components to obtain the dimensionality-reduced eigenvector matrix and eigenvalue matrix. S53: Construct a standard Gaussian random vector based on the number of principal components, and construct a standard Gaussian random field based on the standard Gaussian random vector, the dimension-reduced eigenvector matrix, and the dimension-reduced eigenvalue matrix. S54: Decompose the standard Gaussian random field into a radius standard random field and a thickness standard random field; S55: The radius standard random field is combined with the radius defect standard deviation to generate the radius defect field, and the thickness standard random field is combined with the thickness defect standard deviation to generate the thickness defect field. The defect field includes the radius defect field and the thickness defect field.
[0012] Furthermore, the calculation expression for a standard Gaussian random field is as follows: in, For a standard Gaussian random field, The eigenvector matrix after dimensionality reduction. The eigenvalue matrix after dimensionality reduction. It is a standard Gaussian random vector.
[0013] Furthermore, step S6 includes: S61: Reshape the radius defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the radius defect mesh; S62: Reshape the thickness defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the thickness defect mesh; S63: Add the radius defect mesh to the reference radius of the cylindrical shell to obtain the actual radius mesh containing the defect; S64: Add the thickness defect mesh to the reference thickness of the cylindrical shell to obtain the actual thickness mesh containing the defect; S65: A cylindrical shell composite geometric defect model consisting of a mesh containing the actual radius of the defect and a mesh containing the actual thickness of the defect.
[0014] This invention also provides a simulation system for composite geometric defects in cylindrical shells based on PCA joint random fields, used to execute the aforementioned simulation method for composite geometric defects in cylindrical shells based on PCA joint random fields, comprising: The parameter determination module determines the cylindrical shell reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria. The discrete module generates a uniformly distributed discrete point cloud on the surface of the cylindrical shell based on the reference parameters, defect parameters, and discretization parameters of the cylindrical shell, and on the basis of the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, thus forming uniformly distributed discrete points. A spatial distance matrix construction module calculates the geodesic distances between discrete points and constructs a spatial distance matrix based on the geodesic distances between discrete points. A joint correlation matrix construction module, wherein the joint correlation matrix is constructed by combining an exponential correlation function with a spatial distance matrix; A defect field construction module, which calculates the cumulative contribution rate based on the joint correlation matrix and the PCA reconstruction criterion, selects principal components based on the cumulative contribution rate, and constructs a defect field based on the principal components; The defect model construction module constructs a radius defect mesh and a thickness defect mesh based on the defect field, and constructs a composite geometric defect model of the cylindrical shell based on the radius defect mesh, the thickness defect mesh and the reference geometric parameters of the cylindrical shell.
[0015] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-described method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields.
[0016] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields.
[0017] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: This invention constructs a coupled modeling method based on joint Gaussian random fields. It accurately characterizes the intrinsic correlation between radius and thickness defects through cross-correlation coefficients, and the modeling results highly match actual engineering conditions, overcoming the limitations of traditional methods in modeling single defects. By using geodesic distance instead of Euclidean distance, it perfectly adapts to the curved manifold characteristics of cylindrical shells, accurately capturing the spatial correlation of defects and solving the problem of insufficient adaptability of traditional methods to curved structures, filling the technical gap in defect modeling of closed manifold structures. Dimensionality reduction through PCA significantly reduces the number of random variables, greatly reducing computational complexity while ensuring modeling accuracy, avoiding the computational bottleneck caused by too many random variables in traditional random field methods, and providing an efficient solution for large-scale simulation and optimization design. Based on geometric theory and probability statistics principles, it does not rely on specific software or computing platforms and is applicable to cylindrical shell structures of different sizes and types. Furthermore, defect parameters (standard deviation, correlation length, cross-correlation coefficient) can be flexibly adjusted to adapt to different manufacturing processes and engineering scenarios. A comprehensive verification method covering dimensionality reduction effects, statistical characteristics, spatial correlation, and coupling effects is established to fully guarantee the accuracy and reliability of the modeling results, providing a solid foundation for subsequent mechanical performance analysis and failure mechanism research.
[0018] This invention solves the problems of single defect modeling, poor manifold adaptability, low computational efficiency, lack of coupling mechanism characterization, and imperfect verification system in existing methods. It achieves accurate coupled modeling, efficient generation, and full-dimensional verification of composite defects, and can significantly reduce computational complexity while ensuring modeling accuracy. It is applicable to defect simulation and mechanical performance analysis of cylindrical shell structures of different sizes and under different working conditions.
[0019] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0020] 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 some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0021] Figure 1 This is a flowchart illustrating a method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields, provided by the present invention.
[0022] Figure 2 This is a schematic diagram of the feature value distribution and dimensionality reduction in an embodiment of the present invention.
[0023] Figure 3 This is a schematic diagram of a radius defect random field according to an embodiment of the present invention.
[0024] Figure 4 This is a schematic diagram of a random field for thickness defects according to an embodiment of the present invention.
[0025] Figure 5 This is an embodiment of the present invention. Comparison chart of probability density functions (PDF).
[0026] Figure 6 This is an embodiment of the present invention. Comparison chart of probability density functions (PDF).
[0027] Figure 7 This is an embodiment of the present invention. Comparison chart of autocorrelation functions.
[0028] Figure 8 This is an embodiment of the present invention. Comparison chart of autocorrelation functions.
[0029] Figure 9 This is a comparison chart of the radius-thickness cross-correlation function of embodiments of the present invention.
[0030] Figure 10 This is a schematic diagram of the structure of a cylindrical shell composite geometric defect simulation system based on PCA joint random field provided by the present invention.
[0031] Figure 11 This is a block diagram of the electronic device provided by the present invention.
[0032] Figure label: 101. Parameter Determination Module; 102. Discretization Module; 103. Spatial Distance Matrix Construction Module; 104. Joint Correlation Matrix Construction Module; 105. Defect Field Construction Module; 106. Defect Model Construction Module. Detailed Implementation
[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but cannot be used to limit the scope of this invention.
[0034] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0035] The following is combined Figures 1 to 11 This invention describes a method for simulating complex geometric defects in cylindrical shells based on PCA joint random fields.
[0036] like Figure 1 As shown, a method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields includes: S1: Determine the cylindrical shell's reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria; S11: Determine the baseline parameters; The datum parameters include the geometric datum parameters and material parameters of the cylindrical shell. The geometric datum parameters of the cylindrical shell include the datum radius of the cylindrical shell. ,high Reference thickness Material parameters include elastic modulus. Poisson's ratio ; S12: Determine defect parameters; Defect parameters include radius defect parameters, thickness defect parameters, and cross-defect cross-correlation coefficients; Radius defect parameters include the standard deviation of radius defects. (Percentage relative to the baseline radius), radius-related length ; Thickness defect parameters include the standard deviation of thickness defects. (Percentage relative to reference thickness), thickness-related length ; Cross-defect cross-correlation coefficient , , Indicates that the defect is independent. Indicates defect coupling; S13: Discretization parameter settings; Discretization parameters include the number of discrete points in the circumferential direction. , number of discrete points along the axis ; Total number of discrete points , Discrete density needs to satisfy a balance between geometric representation accuracy and computational efficiency; S14: Restructuring Criteria Setting: Using cumulative contribution rate As a reconstruction criterion for PCA dimensionality reduction, it ensures that key information of the original defect field can still be retained after dimensionality reduction.
[0037] In some specific embodiments of the present invention r =105.0mm, L =210.0mm, =0.120mm, E =105000MPa , , , , , , , , , .
[0038] S2: Based on the cylindrical shell's reference parameters, defect parameters, and discretization parameters, and using the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, a uniformly distributed discrete point cloud is generated on the surface of the cylindrical shell, forming uniformly distributed discrete points. Cylindrical coordinate system is shaped like a circle angle , axial coordinates , The surface of the cylindrical shell is divided into a regular discrete point array by meshing; Calculate the Cartesian coordinates of each discrete point. The specific calculation formula is as follows: , , ; The coordinates of all discrete points are organized into vector form to provide basic data for subsequent distance calculations.
[0039] In some specific embodiments of the present invention, 5984 uniformly distributed discrete points are generated based on the transformation between cylindrical coordinates and Cartesian coordinates. Among them, the circumferential angle... From 0 to Divide the area into 68 evenly spaced nodes, with axial coordinates Divide the area into 88 nodes evenly from 0 to 210.0 mm. The Cartesian coordinates of each discrete point are obtained using the formula... , , The result was calculated and then rearranged into a vector form.
[0040] S3: Calculate the geodesic distances between discrete points and construct a spatial distance matrix based on the geodesic distances between discrete points; S31: Calculate the axial distance between two discrete points based on their coordinates; Define any two discrete points and , For the first discrete points, For the first A discrete point; The expression for calculating the axial distance between two discrete points is: in, The axial distance between discrete points. For the first The axial coordinates of a discrete point For the first The axial coordinates of a discrete point; S32: Calculate the shortest circular arc length between two discrete points based on their coordinates. The calculation expression is: in, Let be the shortest arc length of the circle between discrete points. To find the minimum value function, For the first The inscribed angle at discrete points For the first The circular angle at discrete points; S33: Calculate the geodesic distance between two discrete points based on the axial distance between the two discrete points and the shortest circumferential arc length between the two discrete points; For the curved manifold characteristics of a cylindrical shell, the expression for calculating the geodesic distance between two discrete points is: in, This represents the geodesic distance between two discrete points.
[0041] S34: Calculate the geodesic distances between all discrete points to form a spatial distance matrix.
[0042] Calculate the geodesic distances between all discrete points to form 3D spatial distance matrix This provides a spatial correlation basis for the subsequent construction of the correlation matrix.
[0043] In some specific embodiments of the present invention, the distance between all discrete points is calculated according to the geodesic distance formula, forming... A 3D spatial distance matrix. Represented by discrete points. and For example, For the first discrete point, For the second discrete point, its geodesic distance is calculated as follows: in, The distance between the first discrete point and the second discrete point is the geodesic distance.
[0044] S4: Construct a joint correlation matrix by combining the exponential correlation function with the spatial distance matrix; S41: The autocorrelation matrices for radius defects and thickness defects are constructed using the exponential correlation function and the spatial distance matrix. The calculation expressions are as follows: , in, The autocorrelation matrix of the radius defect. The thickness defect autocorrelation matrix is... It is a spatial distance matrix. For radius-related length, The length is related to the thickness. and All are 3D symmetric matrix The elements in the equation characterize the spatial correlation strength of the radius defect between corresponding discrete points. The elements in the equation characterize the spatial correlation strength of thickness defects between corresponding discrete points.
[0045] S42: Construct a cross-correlation matrix based on the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects; To accurately characterize the coupling effect of radius-thickness defects, a cross-correlation matrix is constructed, and its calculation expression is as follows: in, This is the cross-correlation matrix with dimension 1. , This refers to the cross-correlation coefficient across defects; The elements in the model characterize the cross-correlation strength between radius defects and thickness defects at corresponding discrete points.
[0046] S43: Concatenate the autocorrelation matrix of the radius defect and the autocorrelation matrix of the thickness defect with the cross-correlation matrix to obtain the joint correlation matrix.
[0047] Ensuring the joint correlation matrix satisfies the symmetric positive definite property provides a mathematical foundation for random field generation. The calculation expression is as follows: in, For the joint correlation matrix, This is the transpose of the matrix. and This is used to ensure the symmetry of the joint correlation matrix.
[0048] S5: Calculate the cumulative contribution rate based on the joint correlation matrix and PCA reconstruction criteria, select principal components based on the cumulative contribution rate, and construct the defect field based on the principal components; S51: Perform singular value decomposition on the joint correlation matrix to obtain the eigenvalue matrix and eigenvector matrix; For the joint correlation matrix Perform singular value decomposition (SVD) to obtain the eigenvalue matrix. and eigenvector matrix Arrange the feature values in descending order and adjust the column order of the feature vector accordingly; S52: Arrange the eigenvalues of the eigenvalue matrix in descending order, select the eigenvalues whose cumulative contribution rate is greater than the PCA reconstruction criterion, obtain the number of principal components, and reduce the dimensionality of the eigenvalue matrix and eigenvector matrix according to the number of principal components to obtain the dimensionality-reduced eigenvector matrix and eigenvalue matrix. Based on the set cumulative contribution rate Select eigenvalues whose cumulative contribution rate exceeds 95%; filter out the top eigenvalues that meet the cumulative contribution rate requirement. The principal components form the dimensionality-reduced eigenvector matrix. and eigenvalue matrix This achieves compression of the dimension of random variables; S53: Construct a standard Gaussian random vector based on the number of principal components, and construct a standard Gaussian random field based on the standard Gaussian random vector, the dimension-reduced eigenvector matrix, and the dimension-reduced eigenvalue matrix. generate 3D standard Gaussian random vector ,satisfy Generate a standard Gaussian random field : S54: Decompose the standard Gaussian random field into a radius standard random field and a thickness standard random field; Standard Gaussian random field Decomposed into radius standard random fields according to dimensionality (First n dimensions) and thickness standard random fields (Later n dimensions); S55: The radius standard random field is combined with the standard deviation of the radius defect to generate the radius defect field, and the thickness standard random field is combined with the standard deviation of the thickness defect to generate the thickness defect field. The calculation expression is as follows: , in, For the radius defect field, This represents the defect mean. The standard deviation of radius defects, For thickness defect field, This represents the standard deviation of thickness defects.
[0049] The defect field includes the radius defect field and the thickness defect field.
[0050] S6: Construct a defect mesh based on the defect field, and construct a composite geometric defect model of the cylindrical shell based on the defect mesh and the reference geometric parameters of the cylindrical shell.
[0051] S61: Reshape the radius defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the radius defect mesh; S62: Reshape the thickness defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the thickness defect mesh; S63: Add the radius defect mesh to the reference radius of the cylindrical shell to obtain the actual radius mesh containing the defect. The calculation expression is: in, For the actual radius mesh containing defects, Let be the reference radius of the cylindrical shell. The actual radius mesh contains defects; S64: Add the thickness defect mesh to the reference thickness of the cylindrical shell to obtain the actual thickness mesh containing the defect. The calculation expression is: in, For actual thickness mesh containing defects, This is the reference thickness of the cylindrical shell. The actual thickness mesh contains defects; S65: A cylindrical shell composite geometric defect model consisting of a mesh containing the actual radius of the defect and a mesh containing the actual thickness of the defect.
[0052] Example: S1: Determine the cylindrical shell's reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria; Reference geometric parameter: Reference radius of the cylindrical shell r =105.0mm, height L =210.0mm, reference thickness =0.120mm; Material parameters: Elastic modulus E =105000MPa, Poisson's ratio ; Defect parameters: Standard deviation of radius defects Relevant length Standard deviation of thickness defects Relevant length Cross-correlation coefficient ; Discretization parameter: Number of discrete points in the circumferential direction Number of discrete points along the axis Total number of discrete points ; Reconstruction Criteria: PCA Dimensionality Reduction Reconstruction Criteria .
[0053] S2: Based on the cylindrical shell's reference parameters, defect parameters, and discretization parameters, and using the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, a uniformly distributed discrete point cloud is generated on the surface of the cylindrical shell, forming uniformly distributed discrete points. Based on the transformation between cylindrical and Cartesian coordinate systems, 5984 uniformly distributed discrete points are generated. Among them, the circumferential angle... From 0 to Divide the area into 68 evenly spaced nodes, with axial coordinates Divide the area into 88 nodes evenly from 0 to 210.0 mm. The Cartesian coordinates of each discrete point are obtained using the formula... , , The results were calculated and organized into vector form for later use.
[0054] S3: Calculate the geodesic distances between discrete points and construct a spatial distance matrix based on the geodesic distances between discrete points; Based on the geodesic distance formula, calculate the distance between all discrete points to form... 3D distance matrix With discrete points and For example, For the first discrete point, For the second discrete point, its geodesic distance is calculated as follows: S4: Construct a joint correlation matrix by combining the exponential correlation function with the spatial distance matrix; S41: Construct the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects using the exponential correlation function and the spatial distance matrix; Based on the exponential correlation function, calculate the autocorrelation matrix of the radius defect respectively. Autocorrelation matrix of thickness defects , This indicates that the spatial correlation of radius defects is extremely weak at this distance; S42: Construct a cross-correlation matrix based on the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects; Based on the cross-correlation coefficient Calculate the cross-correlation matrix To quantify the radius-thickness defect coupling effect.
[0055] S43: Concatenate the autocorrelation matrix of the radius defect and the autocorrelation matrix of the thickness defect with the cross-correlation matrix to obtain the joint correlation matrix.
[0056] Will , , and Assemble according to the set pattern to form... Joint correlation matrix It has been verified that the matrix satisfies symmetric positive definiteness.
[0057] S5: Calculate the cumulative contribution rate based on the joint correlation matrix and PCA reconstruction criteria, select principal components based on the cumulative contribution rate, and construct the defect field based on the principal components; S51: Perform singular value decomposition on the joint correlation matrix to obtain the eigenvalue matrix and eigenvector matrix; For the joint correlation matrix Perform singular value decomposition to obtain eigenvalues. and eigenvectors , After being sorted in descending order of eigenvalues, the cumulative contribution rate of the first 1568 eigenvalues reached 95.1%. Therefore, the number of principal components is determined. =1568; see attached Figure 2 As shown, the eigenvalue distribution curve clearly presents the decay law of the principal components. The original dimension of the joint field is 11968, and the dimension after dimensionality reduction is 1568, which meets the critical requirement of 95% cumulative contribution rate. The retention rate is 13.1%, which verifies the rationality of dimensionality reduction.
[0058] S53: Construct a standard Gaussian random vector based on the number of principal components, and construct a standard Gaussian random field based on the standard Gaussian random vector, the dimension-reduced eigenvector matrix, and the dimension-reduced eigenvalue matrix. according to Generate 1568-dimensional standard Gaussian random vectors Standard Gaussian random fields are generated through matrix operations. .
[0059] S54: Decompose the standard Gaussian random field into a radius standard random field and a thickness standard random field; After splitting the standard Gaussian random field, the radius standard random field is obtained. (5984-dimensional) and thickness standard random field (5984 dimensions).
[0060] S55: The radius standard random field is combined with the radius defect standard deviation to generate the radius defect field, and the thickness standard random field is combined with the thickness defect standard deviation to generate the thickness defect field. Radius defect field Thickness defect field According to statistical analysis, obey distributed, obey distributed.
[0061] S6: Construct a defect mesh based on the defect field, and construct a composite geometric defect model of the cylindrical shell based on the defect mesh and the reference geometric parameters of the cylindrical shell.
[0062] Will and The meshes were reshaped into 88×68 two-dimensional grids, and the actual radius of the mesh containing defects was calculated. Actual thickness mesh containing defects This forms a complete geometric model of the cylindrical shell radius-thickness composite defect, which can be directly imported into finite element software such as ABAQUS for subsequent buckling analysis.
[0063] As attached Figure 3 As shown in the visualization of the radius defect random field, concave and convex defects are evenly distributed without any unreasonable abrupt changes; as attached... Figure 4 As shown in the random field visualization of thickness defects, the spatial distribution of thinning defects and thickening defects conforms to the manufacturing process rules.
[0064] Dimensionality reduction effect verification: Eigenvalue distribution analysis shows that the cumulative contribution rate of the first 1568 principal components is 95.1%, which meets the reconstruction criterion requirements, indicating that the dimensionality reduction is effective; Figure 2 As shown, the cumulative contribution rate curve is in When the value was 1568, it reached 95.1%, which verified the accuracy of principal component screening and ensured that more than 95% of the original information was retained after dimensionality reduction. Statistical characteristic verification: PDF comparison results show that... and The fitting errors between the simulated distribution and the target Gaussian distribution were 2.3% and 1.9%, respectively, both ≤3%; Figure 5 As shown, the bar chart in the radius defect PDF comparison graph closely matches the target curve; as... Figure 6 As shown, the bar chart in the thickness defect PDF comparison image fits well with the target curve, which quantitatively verifies the consistency of statistical characteristics. Spatial correlation verification: Autocorrelation function analysis shows that the measured correlation length of the radius defect is 10.7 mm, and the measured correlation length of the thickness defect is 15.4 mm, with deviations from the set values of 2.7% and 3.8%, respectively, both ≤5%. Figure 7 As shown, the simulated dot of the autocorrelation function of the radius defect follows the same trend as the target exponential curve; as Figure 8 As shown, the simulated dots of the autocorrelation function of the thickness defect fit the target curve, verifying the accuracy of the spatial correlation modeling. Coupling effect verification: The measured cross-correlation coefficient was 0.34, which is consistent with the set value. The deviation is 6.2%, which is less than 7%; Figure 9 As shown, the simulated dots of the cross-correlation function fit the target curve well, which intuitively verifies the accuracy of the coupling effect modeling.
[0065] Geometric morphology verification: Defect visualization results show that the concave and convex distribution of radius defects and the thickening and thinning distribution of thickness defects all conform to actual engineering laws, with no unreasonable abrupt changes or abnormal distributions, ensuring that the defect morphology conforms to actual engineering laws. For example... Figure 3 and Figure 4As shown, the defect morphology is consistent with the defect patterns that naturally form during the manufacturing process.
[0066] like Figure 10 As shown, a simulation system for complex geometric defects in cylindrical shells based on PCA joint random fields is used to execute the aforementioned simulation method for complex geometric defects in cylindrical shells based on PCA joint random fields, including: The parameter determination module 101 determines the cylindrical shell reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria; The discrete module 102 generates a uniformly distributed discrete point cloud on the surface of the cylindrical shell based on the reference parameters, defect parameters, and discretization parameters of the cylindrical shell and the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, thus forming uniformly distributed discrete points. The spatial distance matrix construction module 103 calculates the geodesic distances between discrete points and constructs a spatial distance matrix based on the geodesic distances between discrete points. The joint correlation matrix construction module 104 uses an exponential correlation function combined with a spatial distance matrix to construct a joint correlation matrix; The defect field construction module 105 calculates the cumulative contribution rate based on the joint correlation matrix and the PCA reconstruction criterion, selects principal components based on the cumulative contribution rate, and constructs the defect field based on the principal components. The defect model construction module 106 constructs a radius defect mesh and a thickness defect mesh based on the defect field, and constructs a composite geometric defect model of the cylindrical shell based on the radius defect mesh, the thickness defect mesh and the reference geometric parameters of the cylindrical shell.
[0067] This invention constructs a coupled modeling method based on joint Gaussian random fields. It accurately characterizes the intrinsic correlation between radius and thickness defects through cross-correlation coefficients, and the modeling results highly match actual engineering conditions, overcoming the limitations of traditional methods in modeling single defects. By using geodesic distance instead of Euclidean distance, it perfectly adapts to the curved manifold characteristics of cylindrical shells, accurately capturing the spatial correlation of defects and solving the problem of insufficient adaptability of traditional methods to curved structures, filling the technical gap in modeling defects in closed manifold structures. Furthermore, by using PCA dimensionality reduction, the number of random variables is significantly reduced, greatly decreasing computational complexity while maintaining modeling accuracy, avoiding the limitations of traditional methods. The computational bottleneck caused by the large number of random variables in the random field method provides an efficient solution for large-scale simulation and optimization design. The method is built on geometric theory and probability and statistics principles, does not depend on specific software or computing platforms, and is applicable to cylindrical shell structures of different sizes and types. Moreover, the defect parameters (standard deviation, correlation length, cross-correlation coefficient) can be flexibly adjusted to adapt to different manufacturing processes and engineering scenarios. A full-dimensional verification method covering dimensionality reduction effect, statistical characteristics, spatial correlation and coupling effect is established to fully ensure the accuracy and reliability of the modeling results, and provide a solid foundation for subsequent mechanical performance analysis and failure mechanism research.
[0068] Figure 11 An example is a block diagram of an electronic device, such as... Figure 11 As shown, the electronic device may include a processor 201, a communication interface 203, a memory 204, and a communication bus 202. The processor 201, communication interface 203, and memory 204 communicate with each other via the communication bus 202. The processor 201 can call logical instructions from the memory 204 to execute a simulation method for composite geometric defects in cylindrical shells based on PCA joint random fields.
[0069] Furthermore, the logical instructions in the aforementioned memory 204 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0070] On the other hand, the present invention also provides a computer program product, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to execute a method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields provided by the above methods.
[0071] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields provided by the above methods.
[0072] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.
[0073] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.
[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for simulating complex geometric defects in cylindrical shells based on PCA joint random fields, characterized in that, include: S1: Determine the cylindrical shell's reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria; S2: Based on the cylindrical shell's reference parameters, defect parameters, and discretization parameters, and using the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, a uniformly distributed discrete point cloud is generated on the surface of the cylindrical shell, forming uniformly distributed discrete points. S3: Calculate the geodesic distances between discrete points and construct a spatial distance matrix based on the geodesic distances between discrete points; S4: Construct a joint correlation matrix by combining the exponential correlation function with the spatial distance matrix; S5: Calculate the cumulative contribution rate based on the joint correlation matrix and PCA reconstruction criteria, select principal components based on the cumulative contribution rate, and construct the defect field based on the principal components; S6: Construct a defect mesh based on the defect field, and construct a composite geometric defect model of the cylindrical shell based on the defect mesh and the reference geometric parameters of the cylindrical shell.
2. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 1, characterized in that, Step S3 includes: S31: Calculate the axial distance between two discrete points based on their coordinates; S32: Calculate the shortest circumferential arc length between two discrete points based on their coordinates; S33: Calculate the geodesic distance between two discrete points based on the axial distance between the two discrete points and the shortest circumferential arc length between the two discrete points; S34: Calculate the geodesic distances between all discrete points to form a spatial distance matrix.
3. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 1, characterized in that, Step S4 includes: S41: Construct the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects using the exponential correlation function and the spatial distance matrix; S42: Construct a cross-correlation matrix based on the autocorrelation matrix of radius defects and the autocorrelation matrix of thickness defects; S43: Concatenate the autocorrelation matrix of the radius defect and the autocorrelation matrix of the thickness defect with the cross-correlation matrix to obtain the joint correlation matrix.
4. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 1, characterized in that, The joint correlation matrix satisfies symmetric positive definiteness.
5. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 1, characterized in that, The S5 steps include: S51: Perform singular value decomposition on the joint correlation matrix to obtain the eigenvalue matrix and eigenvector matrix; S52: Arrange the eigenvalues of the eigenvalue matrix in descending order, select the eigenvalues whose cumulative contribution rate is greater than the PCA reconstruction criterion, obtain the number of principal components, and reduce the dimensionality of the eigenvalue matrix and eigenvector matrix according to the number of principal components to obtain the dimensionality-reduced eigenvector matrix and eigenvalue matrix. S53: Construct a standard Gaussian random vector based on the number of principal components, and construct a standard Gaussian random field based on the standard Gaussian random vector, the dimension-reduced eigenvector matrix, and the dimension-reduced eigenvalue matrix. S54: Decompose the standard Gaussian random field into a radius standard random field and a thickness standard random field; S55: The radius standard random field is combined with the radius defect standard deviation to generate the radius defect field, and the thickness standard random field is combined with the thickness defect standard deviation to generate the thickness defect field. The defect field includes the radius defect field and the thickness defect field.
6. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 5, characterized in that, The calculation expression for a standard Gaussian random field is: in, For a standard Gaussian random field, The eigenvector matrix after dimensionality reduction. The eigenvalue matrix after dimensionality reduction. It is a standard Gaussian random vector.
7. The method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields according to claim 5, characterized in that, Step S6 includes: S61: Reshape the radius defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the radius defect mesh; S62: Reshape the thickness defect field into a two-dimensional mesh form that matches the discrete mesh of the cylindrical shell to obtain the thickness defect mesh; S63: Add the radius defect mesh to the reference radius of the cylindrical shell to obtain the actual radius mesh containing the defect; S64: Add the thickness defect mesh to the reference thickness of the cylindrical shell to obtain the actual thickness mesh containing the defect; S65: A cylindrical shell composite geometric defect model consisting of a mesh containing the actual radius of the defect and a mesh containing the actual thickness of the defect.
8. A simulation system for composite geometric defects in cylindrical shells based on PCA joint random fields, characterized in that, To perform a method for simulating composite geometric defects in cylindrical shells based on PCA joint random fields as described in any one of claims 1 to 7, comprising: The parameter determination module determines the cylindrical shell reference parameters, defect parameters, discretization parameters, and PCA reconstruction criteria. The discrete module generates a uniformly distributed discrete point cloud on the surface of the cylindrical shell based on the reference parameters, defect parameters, and discretization parameters of the cylindrical shell, and on the basis of the transformation relationship between the cylindrical coordinate system and the Cartesian coordinate system, thus forming uniformly distributed discrete points. A spatial distance matrix construction module calculates the geodesic distances between discrete points and constructs a spatial distance matrix based on the geodesic distances between discrete points. A joint correlation matrix construction module, wherein the joint correlation matrix is constructed by combining an exponential correlation function with a spatial distance matrix; A defect field construction module, which calculates the cumulative contribution rate based on the joint correlation matrix and the PCA reconstruction criterion, selects principal components based on the cumulative contribution rate, and constructs a defect field based on the principal components; The defect model construction module constructs a radius defect mesh and a thickness defect mesh based on the defect field, and constructs a composite geometric defect model of the cylindrical shell based on the radius defect mesh, the thickness defect mesh and the reference geometric parameters of the cylindrical shell.
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 computer program, it implements the steps of the method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields as described in any one of claims 1 to 7.
10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for simulating composite geometric defects of cylindrical shells based on PCA joint random fields as described in any one of claims 1 to 7.