A method for intelligent modeling of arbitrary toughening phases in aerospace exotic pieces

Abstract

The application discloses a kind of astronaut special-shaped member arbitrary toughening phase intelligent modeling method, belong to the intersection technical field of computer graphics of calculation simulation;The application is first input to obtain point cloud data set with the face node coordinates in complex special-shaped member, decomposition obtains mid-plane centroid and three partial vectors, project point cloud to local plane and calculate its range and center;Scale curve and rotate translation to the local plane center, after 3D plane mapping, nearest neighbor algorithm projection mapping to point cloud, equal arc length sampling obtains multiple control points;Based on control point file generates multiple fiber objects, by calculating the shortest distance of model node and fiber axis and cross section level set value, identify fiber unit, boundary unit and matrix unit;Boundary unit is again segmented and re-identified unit, after all fiber object determination is completed in cycle, traverse fiber unit and calculate its axial tangent vector, complete modeling;The application can quickly realize the digitization modeling of high-end complex toughening component.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary fields of computational simulation technology and computer graphics, specifically a method for intelligent modeling of arbitrary toughening phases in aerospace irregular-shaped parts. Background Technology

[0002] Composite materials, with their superior properties such as high strength, high stiffness, lightweight, chemical corrosion resistance, wear resistance, and high-temperature creep resistance, have been widely used in core components of high-end critical equipment in aerospace, aviation, nuclear power, and braking systems. Among them, ceramic matrix composites have attracted much attention due to their outstanding advantages of being lightweight, high-strength, high-rigidity, high-temperature resistant, and corrosion-resistant. Systems represented by SiC / SiC and C / SiC are currently the most widely used types of ceramic matrix composites. However, China still lags behind international leading levels in areas such as multi-field, multi-scale design theory and optimization technology for composite materials, dynamic theory, data-driven simulation methods, and strength and life simulation evaluation systems.

[0003] Complex irregular-shaped components, as core load-bearing parts in aerospace, high-end equipment manufacturing, and new energy equipment, possess irregular geometric contours and variable curvature structural features that can precisely adapt to spatial constraints and mechanical load-bearing requirements under extreme working conditions. The spatial distribution and geometric characteristics of toughening phases (such as fiber-based reinforcements) are key factors determining the critical mechanical properties of complex irregular-shaped components, such as impact resistance and crack resistance. Therefore, accurate modeling of toughening phases has become a core prerequisite for the digital design, performance simulation, and engineering application of complex irregular-shaped components.

[0004] For woven composite materials, the diversity of weaving methods leads to extremely complex internal structures. To obtain the material's mechanical properties, traditional methods typically involve constructing a 3D model using geometric modeling software such as SolidWorks and UG during the simulation preprocessing stage, followed by mesh generation using tools like HyperMesh. This process requires tedious data format conversion and makes it difficult to quickly build mesh models in batches. Therefore, how to rapidly achieve geometric modeling and mesh generation for composite materials with arbitrary weaving methods has become a current research challenge.

[0005] Based on this, a method for intelligent modeling of toughening phases that adapts to complex irregular structures and multiple weaving methods, and combines automation and high precision, is established, which can provide technical support for the efficient digital R&D of high-end complex toughened components. Summary of the Invention

[0006] This invention discloses an intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped components. This method combines digital twin technology, computational simulation technology, and computer graphics theory to solve related problems in modeling toughening phases of complex irregular-shaped components, and can quickly realize the digital modeling of high-end complex toughened components.

[0007] The technical solution provided by this invention to solve the above-mentioned technical problems is: a smart modeling method for arbitrary toughening phases of aerospace irregular-shaped parts, comprising the following steps: S1. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset, and decompose it using the PCA algorithm to obtain the mid-surface centroid and three component vectors; S2. Project the point cloud onto a local plane and calculate its range and center. Scale the curve and rotate and translate it to the center of the local plane. S3. Map the curve back to the 3D plane. Use the nearest neighbor projection algorithm to map the curve to the point cloud. Obtain 20 control points by sampling with equal arc length. S4. Generate multiple fiber objects based on the control point file. Identify fiber elements, boundary elements, and matrix elements by calculating the shortest distance between the model nodes and the fiber axis and the horizontal set function value of the cross-section objects. S5. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axis tangent vectors, and the modeling is finally completed. A further technical solution is that the specific implementation method of step S1 includes: S11. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset; S12, PCA algorithm principle; Principal Component Analysis (PCA) is the most commonly used linear dimensionality reduction method. Its goal is to map high-dimensional data into a low-dimensional space through some linear projection, and to maximize the information content (variance) of the data in the projected dimension, thereby using fewer data dimensions while retaining more of the characteristics of the original data points.

[0008] The fundamental purpose of the PCA algorithm is to transform data from the original feature space (high-dimensional space) to a new feature space (low-dimensional space), which is composed of a linear combination of the original features. Each dimension of this new feature space is called a principal component.

[0009] Definition of principal components: Principal components are a new set of uncorrelated variables in a dataset, which are linear combinations of the original features. Each principal component captures the direction of the maximum variance in the data.

[0010] Interpretation of variance: The variance of data reflects the breadth of its distribution. The goal of PCA is to find a set of principal components such that the first principal component captures the largest variance in the data, the second principal component captures the second largest variance, and so on. S13, Data Standardization; Before using the PCA algorithm, data standardization is usually required. This is because the PCA algorithm is sensitive to data scale, especially when the data contains features with different units or magnitudes. Standardization ensures that each feature contributes equally to the PCA result.

[0011] The standardization process involves subtracting the mean from each feature and dividing by its standard deviation, resulting in a dataset with a mean of 0 and a standard deviation of 1. The formula is as follows: ; in, x It is the raw data. m It is the mean. s It is the standard deviation; S14. Calculate the covariance matrix; For a standardized dataset, the next step in the PCA algorithm is to compute the covariance matrix. The covariance matrix describes the correlation between features. For a dataset containing m features, the covariance matrix is ​​m×m in size, and each element represents the covariance between two features.

[0012] The formula for the covariance matrix is: ; Where X is the standardized data matrix and n is the number of samples.

[0013] For a three-dimensional dataset {x,y,z}, the covariance matrix has the following form: ; in, ; ; ; ; ; ; ; ; .

[0014] S15. Calculate the eigenvalues ​​and eigenvectors; The PCA algorithm uses Singular Value Decomposition (SVD) to compute the eigenvalues ​​and eigenvectors of the covariance matrix. The SVD decomposition form is as follows: ; Among them, matrix U and VΣ is an orthogonal matrix, representing the left and right singular vectors respectively; Σ represents a diagonal matrix containing singular values.

[0015] The eigenvectors of the covariance matrix correspond to the principal component directions in the dataset, and the eigenvalues ​​represent the data variance explained by each principal component.

[0016] Eigenvectors: Each eigenvector represents a new coordinate axis (i.e., the direction of the principal component), equivalent to the right singular vector in SVD. V .

[0017] Eigenvalues: Each eigenvalue represents the variance of the data along the direction of the corresponding eigenvector. The larger the eigenvalue, the stronger the explanatory power of the principal component for the data. A further technical solution is that the specific implementation method of step S2 includes: S21. Project the point cloud onto a local plane and calculate its extent and center. Based on the theory of 3D point cloud projection, the 3D point cloud set {P} is projected onto a 2D local coordinate system (u,v) spanned by the component vectors e1 and e2 obtained by PCA algorithm. The purpose of the projection is to define and manipulate curves in the 2D plane. The projection formula is: ; in, The center of mass of the point cloud.

[0018] By traversing the UV coordinates of all projection points, the coordinate range of the projection area within the local plane is calculated, and then the centerUV of the projection area is determined. S22, Generation curve; Taking the butterfly curve as an example, based on parametric curve theory, using parameters... t Define the polar equation of the butterfly curve, and the corresponding polar radius expression is: ; Then, using the formula to convert polar coordinates to rectangular coordinates: ; The coordinates of the butterfly curve in a two-dimensional plane can be obtained; S23. Perform an affine transformation; Based on the theory of affine transformations (scaling, rotation, translation), the above butterfly curve is operated on sequentially: first, the scaling operation is performed ( S After normalizing the curve, scale it according to the scaling factor of the fitted mid-surface size; then perform a rotation operation. R The curve's orientation is adjusted using a rotation matrix; finally, a translation operation is performed. TThe curve center is moved to the mid-plane projection center centerUV obtained in step S21; finally, a butterfly curve matching the local plane center is obtained. Rotation matrix: ; The formula for calculating affine transformation is: ; A further technical solution is that the specific implementation method of step S3 includes: S31. Map the curve back to the 3D plane; Specifically, based on the basis transformation (inverse mapping) theory in manifold projection, and utilizing the properties of orthogonal bases, the curve coordinates (u,v) in the two-dimensional local coordinate system are restored to points in three-dimensional space; the restoration formula is: ; in, Let e1 be the centroid of the point cloud, and e2 be the component vectors obtained by PCA algorithm decomposition. This operation can realize the "lifting" mapping of two-dimensional curves to three-dimensional local planes.

[0019] S32. Use the K-nearest neighbor algorithm to map the curve to the point cloud; The principle of the K-nearest neighbor algorithm is as follows; The K-Nearest Neighbor (KNN) algorithm is an instance-based, nonparametric supervised learning algorithm widely used in classification and regression problems. It is suitable for situations with small sample spaces, low data dimensionality, and low feature space dimensionality, and has advantages such as simplicity, ease of implementation, and no training required.

[0020] The basic principle of the KNN algorithm is to calculate the distance between the sample to be classified or predicted and other samples in the training set, select the K closest neighbors of the sample to be predicted, and make a prediction based on the labels or values ​​of these neighbors. In classification tasks, KNN uses majority voting to determine the category of the sample to be classified.

[0021] The core assumption of the KNN algorithm is that similar sample points have similar labels. The KNN algorithm relies on similarity metrics between samples for classification or regression. Unlike traditional algorithms, it does not explicitly build the model during training; instead, it directly stores the training data in memory. When a new sample needs to be predicted, the KNN algorithm finds the K nearest neighbors from the stored training samples based on a distance metric, and then makes a prediction based on the labels or values ​​of these neighbors.

[0022] In the KNN algorithm, the most common distance metric is Euclidean distance. Euclidean distance is the "straight-line" distance between sample points, that is, the straight-line distance between two points in space. Suppose there are two samples... and They are in d The formula for calculating the Euclidean distance in the 3D feature space is: ; Among them, X ik and X jk They are the first k The values ​​of each feature, d It is the dimension of the feature space. This distance calculates the distance between two sample points. d Distance in the dimensional feature space.

[0023] The KNN algorithm first calculates the distance between the sample to be classified and every sample in the training set. It then selects the K nearest neighbors, performs a majority vote based on the class of these K neighbors, and finally selects the class of the nearest neighbor. The category that appears most frequently is taken as the category of the sample to be classified. Assume the K neighbor categories of the sample to be classified are... ,in It is the first i Given the categories of the neighbors, the KNN algorithm classifies them as follows: `mode` represents the majority voting operation, selecting the category that appears most frequently as the predicted category. If multiple categories appear with the same frequency, the category of the nearest neighbor is usually chosen to break the tie.

[0024] Nearest neighbor search finds K nearest neighbors or all nearest neighbors within a specified distance of the query data point based on a specified distance metric.

[0025] knnsearch is a MATLAB function used to perform K-nearest neighbor search. It can find the nearest neighbor of every point in one dataset to every point in another dataset.

[0026] In MATLAB, the basic syntax of the knnsearch function is IDX=knnsearch(X,Y), where X is a matrix containing data points and Y is a matrix containing query points. The function returns IDX, a column vector containing the indices of the nearest neighbors of each point in Y in X.

[0027] Based on the nearest neighbor search theory, the KNN algorithm is used to find the point in the discrete point cloud that has the closest Euclidean distance to the 3D curve point obtained in step S31. This operation can project the ideal geometry onto the discrete manifold, ensuring that the mapped curve point corresponds to the actual surface node of the irregular part, avoiding the control point from being suspended in the fitting plane, and ensuring the solid fit of the subsequent modeling. S33, 20 control points were obtained by sampling with equal arc length; Arc length parameterization theory based on curve resampling: due to parameter t Corresponding arc length ds Since the value is not constant, uniform sampling is performed based on the cumulative arc length. The steps are as follows: (1) Calculate the distance between adjacent points using the following formula: ; (2) Calculate the cumulative arc length using the formula: ; (3) In the cumulative arc length S Perform equal-interval interpolation on the domain to determine the corresponding sampling point index; Simultaneously, spatial filtering is introduced. By setting a minimum distance threshold, the Euclidean distance between any two output control points is ensured to be greater than the threshold, thus avoiding numerical noise that causes the points to be too dense. Finally, 20 control points are evenly distributed. A further technical solution is that the specific implementation method of step S4 includes: S41. Generate multiple fiber objects based on the control point file; To construct composite preform models of complex irregular components such as turbine guide vanes and probes with arbitrary weaving patterns, this invention employs a parametric modeling method for the toughening phase of composite materials based on the level set method and non-uniform rational B-spline curves. Variables describing the toughening phase are introduced, including fiber cross-sectional shape parameters, fiber distribution parameters in the matrix, and discrete size parameters of the fiber mesh.

[0028] B-spline curves are used to describe the fiber positions in arbitrary weaving patterns, and the shortest distance between nodes and the B-spline curves is calculated using a grid method combined with gradient descent. The separation of fibers and matrix in complex irregular-shaped composite preforms is achieved through the level set method, simultaneously completing the finite element mesh discretization of the model, providing a geometric model basis for the mechanical property analysis of the toughening phase in complex irregular-shaped parts.

[0029] Non-uniform rational B-spline (NURB) curves, often simply referred to as NURBS curves, are parametric curves formed by interpolation or fitting multiple rational polynomials based on a set of control points. Their analytical expression... C(t) It can be defined as: ; in, As control points, express k The th B-spline curve i The number of basis functions is 1. It is easy to see that the order of the basis functions is 1. k +1, and this basis function is uniquely determined by a non-decreasing node sequence t containing m elements: ; According to the definition of B-spline curves, their basis functions need to be solved recursively. This recursive calculation process is usually called the DeBoor-Cox cyclic recursive formula, and its specific form can be expressed as: ; From the above formula, it can be seen that when k When = 0, the basis function form of the first-order B-spline curve can be expressed as: .

[0030] In the process of generating composite fibers, the start and end points of the fibers are usually specified based on the boundary positions. To ensure that the generated fiber axis curve meets the constraint requirement of passing through the start and end control points, the Clamped-B spline from the B-spline is selected. k The core characteristic of the node sequence of a Clamped-B spline curve is: the preceding... k+1 All nodes have the same value, and finally... k+1 Each node has the same value (this node constraint method is the definition of "Clamped"), and this node sequence can be represented as: ; In summary, B-spline curves with arbitrary spatial distributions can be generated by setting control points, and these curves can be directly used as the axis of composite fiber. S42. Calculate the shortest distance between the model node and the fiber axis; To determine whether a cell crosses the fiber-matrix interface layer, it is necessary to calculate any point in space. P a ( a , b , c The shortest distance to the fiber curve d The shortest distance d It can be regarded as a point on the fiber curve P b ( x , y , z The function is expressed as: .

[0031] This invention combines a gradient method with a lattice descent method. Due to the points on the fiber axis... P b ( x , y , z The parameter t[0,1) can be used to represent this, and thus... P a ( a , b , c)arrive P b ( x , y , z The distance is transformed into information about t The function is then used to find the minimum value (i.e., the shortest distance) of the function through gradient descent.

[0032] The process of combining gradient method with grid descent method is as follows: Figure 2 As shown, using the above algorithm, the shortest distance from any point in space to the fiber axis can be calculated, and the parameters of the feature point on the fiber axis corresponding to the shortest distance can also be obtained. t and spatial coordinates.

[0033] S43. Calculate the level set function value through the section object to identify fiber elements, boundary elements and matrix elements; After calculating the distances from all nodes in space to the fiber axis, the generalized fiber cross-sectional shape can be constructed using the following formula: ; in, x c , y c , z c These represent the spatial coordinates of a feature point on the fiber axis; parameters l Used to control the shape of the fiber cross-section, for example when l When the value is 2, a circular cross section can be generated.

[0034] The following section employs the level set method to determine the spatial distribution characteristics of fibers and the matrix, thereby achieving accurate separation between the two. For a cubic model discretized by tetrahedral elements, if it contains one or more fibers, the spatial position of the fiber surface can be accurately characterized by the level set function corresponding to the fiber.

[0035] The Level Set Method (LSM) is a numerical technique suitable for interface tracing and shape modeling. In three-dimensional space, this method sets the fiber surface (curved surface) into a linear shape. x The zero level set of the auxiliary function Ф of the three-dimensional level set is represented as: ; To accurately characterize the spatial shape and extent Ω of the fiber, a three-dimensional level set function is introduced. F R ( x , y , zThe zero level set corresponds to the fiber-matrix interface Γ. In three-dimensional space, the distance from any point to the fiber boundary can be expressed by the following formula: ; Specifically, the symbolic definition of the level set function is as follows: when Ф<0, the corresponding point is located inside the fiber region; when Ф>0, the corresponding point is located outside the fiber region. .

[0036] The level set function of all nodes in the space is calculated based on the above method. F R ( x , y , z If the level set function values ​​of each node in the tetrahedral mesh element of the model have both values ​​greater than 0 and values ​​less than 0, then the element is determined to be a fiber-matrix intersecting element. After completing the determination calculation for all elements, for all intersecting elements, the bisection method is used to solve for the intersection positions between their interiors and the fiber boundaries, and new nodes are generated at these positions; then, according to the element connection order, the original intersecting elements are divided into new elements. A further technical solution is that the specific implementation method of step S5 includes: S51. Calculate the axial tangent vector of the fiber element; To define the cross-sectional shape of a fiber, its spatial location must first be determined. This is achieved through a parametric expression of the fiber's centerline. C(t) Regarding parameters t Taking the first derivative yields the expression for the tangent vector along the fiber axis, and thus the tangent vector at any point along the axis. The expression is as follows: ; ; in, N i,j-1 ( t )and N i+1,j-1 ( t All of these can be obtained from the DeBoor-Cox iterative formula in step S41, and then the tangent vector is... T ( v 1 ,v 2 ,v 3) Perform normalization. The normalization expression is as follows: ; in, u 1. u 2 and u 3 represent the normalized tangent vector components; Select points on the fiber axis P b ( x , y , z ) yOz The plane serves as the defining plane for the fiber cross-section. Fiber cross-section shapes encompass ellipses, rectangles, and irregular shapes. To verify the universality of the proposed modeling method, this paper selects two typical cross-sections—ellipses and rectangles—for definition and explanation: For an elliptical cross section, its semi-major axis is defined as... a The semi-minor axis is b Its geometric shape is characterized by parametric equations, the specific expressions of which are as follows: ; in, x ( i ), y ( i )and z ( i () represents the coordinates of a point on the elliptical cross section. i A local coordinate system for the tangent vector between a point on the elliptical cross section and a point on the fiber axis. y The angle between the ′ axis, For the local coordinate system of the tangent vector y Similarly, the three components after axis normalization are... For the local coordinate system of the tangent vector z The three components after axis normalization.

[0037] For a rectangular cross-section, its length is defined as... a Width is b In Cartesian coordinates, the four vertices of this cross section V 1. V 2. V 3. V The specific expression for the coordinates of 4 is as follows: ; Then, parameters are introduced using the piecewise function shown in the following formula. t Interpolation is performed on each side of the rectangle to define the cross-sectional shape; then, coordinate transformation is used to obtain the final coordinates of each point within the rectangular cross-section. The geometric shapes of the two typical cross-sections, ellipse and rectangle, are as follows: Figure 3 As shown; ; in, V 12i , V 23i , V 34i , V 14iThese are the coordinates of points on the four sides of the rectangle.

[0038] Based on the above equations, the horizontal set function value from the spatial point to the fiber interface is calculated, and then the spatial positional relationship between any point in the cross-sectional plane and the elliptical cross section and the rectangular cross section is determined. S52. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axis tangent vectors, and the modeling is finally completed. Based on the aforementioned intelligent modeling algorithm for toughening phases in complex irregular-shaped parts, a geometric model of a precast ceramic matrix composite component with a complex woven structure was successfully constructed. The visualization results are shown below. Figure 4 As shown.

[0039] The beneficial effects of this invention are as follows: Based on the numerical analysis and visualization characteristics of MATLAB, this invention combines the cross-platform graphical interface support of the Qt framework with the 3D rendering capabilities of the VTK visualization toolkit. This invention integrates point cloud processing, PCA decomposition, parametric curve generation, manifold projection, and adaptive element segmentation technologies, achieving integrated intelligent execution of toughening phase modeling for complex irregular-shaped parts. It eliminates the need for cross-platform operation relying on traditional geometric modeling software such as SolidWorks and UG, and mesh generation tools such as HyperMesh, effectively avoiding geometric errors caused by cross-software format compatibility and automating the modeling process. This invention employs VTK's ray casting algorithm and Qt's multi-threading mechanism to achieve dynamic rendering of the model. Through an intelligent digital modeling process, this invention enables the control of process parameters such as the cross-sectional shape of the toughening phase, the weaving trajectory form, and the spatial distribution density, eliminating the repetitive operations of traditional manual geometric modeling. It can quickly complete model reconstruction for different weaving methods and different toughening phase distribution schemes, greatly facilitating subsequent performance simulation and structural optimization of complex irregular-shaped parts, and significantly improving design efficiency and model scalability. Attached Figure Description

[0040] Figure 1 This is a flowchart of an intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to the present invention; Figure 2 This is a flowchart of the gradient method combined with the grid descent algorithm of the present invention. Figure 3 This is a schematic diagram defining the cross-sectional shape of the toughening phase fiber according to the present invention; Figure 4 This is a schematic diagram of the geometric model of a ceramic matrix composite preform with a complex woven structure according to the present invention. Detailed Implementation

[0041] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] like Figure 1 As shown, this invention provides an intelligent modeling method for arbitrary toughening phases in aerospace irregular-shaped components, comprising the following steps: S1. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset, and decompose it using the PCA algorithm to obtain the mid-surface centroid and three component vectors; Specifically, it includes the following steps: S11. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset; S12, PCA algorithm principle; Principal Component Analysis (PCA) is the most commonly used linear dimensionality reduction method. Its goal is to map high-dimensional data into a low-dimensional space through some linear projection, and to maximize the information content (variance) of the data in the projected dimension, thereby using fewer data dimensions while retaining more of the characteristics of the original data points.

[0043] The fundamental purpose of the PCA algorithm is to transform data from the original feature space (high-dimensional space) to a new feature space (low-dimensional space), which is composed of a linear combination of the original features. Each dimension of this new feature space is called a principal component.

[0044] Definition of principal components: Principal components are a new set of uncorrelated variables in a dataset, which are linear combinations of the original features. Each principal component captures the direction of the maximum variance in the data.

[0045] Interpretation of variance: The variance of data reflects the breadth of its distribution. The goal of PCA is to find a set of principal components such that the first principal component captures the largest variance in the data, the second principal component captures the second largest variance, and so on. S13, Data Standardization; Before using the PCA algorithm, data standardization is usually required. This is because the PCA algorithm is sensitive to data scale, especially when the data contains features with different units or magnitudes. Standardization ensures that each feature contributes equally to the PCA result.

[0046] The standardization process involves subtracting the mean from each feature and dividing by its standard deviation, resulting in a dataset with a mean of 0 and a standard deviation of 1. The formula is as follows: ; in, xIt is the raw data. m It is the mean. s It is the standard deviation; S14. Calculate the covariance matrix; For a standardized dataset, the next step in the PCA algorithm is to compute the covariance matrix. The covariance matrix describes the correlation between features. For a dataset containing m features, the covariance matrix is ​​m×m in size, and each element represents the covariance between two features.

[0047] The formula for the covariance matrix is: ; Where X is the standardized data matrix and n is the number of samples.

[0048] For a three-dimensional dataset {x,y,z}, the covariance matrix has the following form: ; in, ; ; ; ; ; ; ; ; .

[0049] S15. Calculate the eigenvalues ​​and eigenvectors; The PCA algorithm uses Singular Value Decomposition (SVD) to compute the eigenvalues ​​and eigenvectors of the covariance matrix. The SVD decomposition form is as follows: ; Among them, matrix U and V Σ is an orthogonal matrix, representing the left and right singular vectors respectively; Σ represents a diagonal matrix containing singular values.

[0050] The eigenvectors of the covariance matrix correspond to the principal component directions in the dataset, and the eigenvalues ​​represent the data variance explained by each principal component.

[0051] Eigenvectors: Each eigenvector represents a new coordinate axis (i.e., the direction of the principal component), equivalent to the right singular vector in SVD. V .

[0052] Eigenvalues: Each eigenvalue represents the variance of the data along the direction of the corresponding eigenvector. The larger the eigenvalue, the stronger the explanatory power of the principal component for the data. S2. Project the point cloud onto a local plane and calculate its range and center. Scale the curve and rotate and translate it to the center of the local plane. Specifically, it includes the following steps: S21. Project the point cloud onto a local plane and calculate its extent and center. Based on the theory of 3D point cloud projection, the 3D point cloud set {P} is projected onto a 2D local coordinate system (u,v) spanned by the component vectors e1 and e2 obtained by PCA algorithm. The purpose of the projection is to define and manipulate curves in the 2D plane. The projection formula is: ; in, The center of mass of the point cloud.

[0053] By traversing the UV coordinates of all projection points, the coordinate range of the projection area within the local plane is calculated, and then the centerUV of the projection area is determined. S22, Generation curve; Taking the butterfly curve as an example, based on parametric curve theory, using parameters... t Define the polar equation of the butterfly curve, and the corresponding polar radius expression is: ; Then, using the formula to convert polar coordinates to rectangular coordinates: ; The coordinates of the butterfly curve in a two-dimensional plane can be obtained; S23. Perform an affine transformation; Based on the theory of affine transformations (scaling, rotation, translation), the above butterfly curve is operated on sequentially: first, the scaling operation is performed ( S After normalizing the curve, scale it according to the scaling factor of the fitted mid-surface size; then perform a rotation operation. R The curve's orientation is adjusted using a rotation matrix; finally, a translation operation is performed. T The curve center is moved to the mid-plane projection center centerUV obtained in step S21; finally, a butterfly curve matching the local plane center is obtained. Rotation matrix: ; The formula for calculating affine transformation is: ; S3. Map the curve back to the 3D plane. Use the nearest neighbor projection algorithm to map the curve to the point cloud. Obtain 20 control points by sampling with equal arc length. Specifically, the steps include the following: Specifically, based on the basis transformation (inverse mapping) theory in manifold projection, and utilizing the properties of orthogonal bases, the curve coordinates (u,v) in the two-dimensional local coordinate system are restored to points in three-dimensional space; the restoration formula is: ; in, Let e1 be the centroid of the point cloud, and e2 be the component vectors obtained by PCA algorithm decomposition. This operation can realize the "lifting" mapping of two-dimensional curves to three-dimensional local planes.

[0054] S32. Use the K-nearest neighbor algorithm to map the curve to the point cloud; The principle of the K-nearest neighbor algorithm is as follows; The K-Nearest Neighbor (KNN) algorithm is an instance-based, nonparametric supervised learning algorithm widely used in classification and regression problems. It is suitable for situations with small sample spaces, low data dimensionality, and low feature space dimensionality, and has advantages such as simplicity, ease of implementation, and no training required.

[0055] The basic principle of the KNN algorithm is to calculate the distance between the sample to be classified or predicted and other samples in the training set, select the K closest neighbors of the sample to be predicted, and make a prediction based on the labels or values ​​of these neighbors. In classification tasks, KNN uses majority voting to determine the category of the sample to be classified.

[0056] The core assumption of the KNN algorithm is that similar sample points have similar labels. The KNN algorithm relies on similarity metrics between samples for classification or regression. Unlike traditional algorithms, it does not explicitly build the model during training; instead, it directly stores the training data in memory. When a new sample needs to be predicted, the KNN algorithm finds the K nearest neighbors from the stored training samples based on a distance metric, and then makes a prediction based on the labels or values ​​of these neighbors.

[0057] In the KNN algorithm, the most common distance metric is Euclidean distance. Euclidean distance is the "straight-line" distance between sample points, that is, the straight-line distance between two points in space. Suppose there are two samples... and They are in d The formula for calculating the Euclidean distance in the 3D feature space is: ; Among them, X ik and X jk They are the first k The values ​​of each feature, d It is the dimension of the feature space. This distance calculates the distance between two sample points. dDistance in the dimensional feature space.

[0058] The KNN algorithm first calculates the distance between the sample to be classified and every sample in the training set. It then selects the K nearest neighbors, performs a majority vote based on the class of these K neighbors, and finally selects the class of the nearest neighbor. The category that appears most frequently is taken as the category of the sample to be classified. Assume the K neighbor categories of the sample to be classified are... ,in It is the first i Given the categories of the neighbors, the KNN algorithm classifies them as follows: `mode` represents the majority voting operation, selecting the category that appears most frequently as the predicted category. If multiple categories appear with the same frequency, the category of the nearest neighbor is usually chosen to break the tie.

[0059] Nearest neighbor search finds K nearest neighbors or all nearest neighbors within a specified distance of the query data point based on a specified distance metric.

[0060] knnsearch is a MATLAB function used to perform K-nearest neighbor search. It can find the nearest neighbor of every point in one dataset to every point in another dataset.

[0061] In MATLAB, the basic syntax of the knnsearch function is IDX=knnsearch(X,Y), where X is a matrix containing data points and Y is a matrix containing query points. The function returns IDX, a column vector containing the indices of the nearest neighbors of each point in Y in X.

[0062] Based on the nearest neighbor search theory, the KNN algorithm is used to find the point in the discrete point cloud that has the closest Euclidean distance to the 3D curve point obtained in step S31. This operation can project the ideal geometry onto the discrete manifold, ensuring that the mapped curve point corresponds to the actual surface node of the irregular part, avoiding the control point from being suspended in the fitting plane, and ensuring the solid fit of the subsequent modeling. S33, 20 control points were obtained by sampling with equal arc length; Arc length parameterization theory based on curve resampling: due to parameter t Corresponding arc length ds Since the value is not constant, uniform sampling is performed based on the cumulative arc length. The steps are as follows: (1) Calculate the distance between adjacent points using the following formula: ; (2) Calculate the cumulative arc length using the formula: ; (3) In the cumulative arc length S Perform equal-interval interpolation on the domain to determine the corresponding sampling point index; Simultaneously, spatial filtering is introduced. By setting a minimum distance threshold, the Euclidean distance between any two output control points is ensured to be greater than the threshold, thus avoiding numerical noise that causes the points to be too dense. Finally, 20 control points are evenly distributed. A further technical solution is that the specific implementation method of step S4 includes: S4. Generate multiple fiber objects based on the control point file. Identify fiber elements, boundary elements, and matrix elements by calculating the shortest distance between model nodes and fiber axes and the horizontal set function values ​​of cross-sectional objects. Specifically, the following steps are included: S41. Generate multiple fiber objects based on the control point file; To construct composite preform models of complex irregular components such as turbine guide vanes and probes with arbitrary weaving patterns, this invention employs a parametric modeling method for the toughening phase of composite materials based on the level set method and non-uniform rational B-spline curves. Variables describing the toughening phase are introduced, including fiber cross-sectional shape parameters, fiber distribution parameters in the matrix, and discrete size parameters of the fiber mesh.

[0063] B-spline curves are used to describe the fiber positions in arbitrary weaving patterns, and the shortest distance between nodes and the B-spline curves is calculated using a grid method combined with gradient descent. The separation of fibers and matrix in complex irregular-shaped composite preforms is achieved through the level set method, simultaneously completing the finite element mesh discretization of the model, providing a geometric model basis for the mechanical property analysis of the toughening phase in complex irregular-shaped parts.

[0064] Non-uniform rational B-spline (NURB) curves, often simply referred to as NURBS curves, are parametric curves formed by interpolation or fitting multiple rational polynomials based on a set of control points. Their analytical expression... C(t) It can be defined as: ; in, As control points, express k The th B-spline curve i The number of basis functions is 1. It is easy to see that the order of the basis functions is 1. k +1, and this basis function is uniquely determined by a non-decreasing node sequence t containing m elements: .

[0065] According to the definition of B-spline curves, their basis functions need to be solved recursively. This recursive calculation process is usually called the DeBoor-Cox cyclic recursive formula, and its specific form can be expressed as: ; From the above formula, it can be seen that when k When = 0, the basis function form of the first-order B-spline curve can be expressed as: .

[0066] In the process of generating composite fibers, the start and end points of the fibers are usually specified based on the boundary positions. To ensure that the generated fiber axis curve meets the constraint requirement of passing through the start and end control points, the Clamped-B spline from the B-spline is selected. k The core characteristic of the node sequence of a Clamped-B spline curve is: the preceding... k+1 All nodes have the same value, and finally... k+1 Each node has the same value (this node constraint method is the definition of "Clamped"), and this node sequence can be represented as: .

[0067] In summary, B-spline curves with arbitrary spatial distributions can be generated by setting control points, and these curves can be directly used as the axis of composite fiber. S42. Calculate the shortest distance between the model node and the fiber axis; To determine whether a cell crosses the fiber-matrix interface layer, it is necessary to calculate any point in space. P a ( a , b , c The shortest distance to the fiber curve d The shortest distance d It can be regarded as a point on the fiber curve P b ( x , y , z The function is expressed as: .

[0068] This invention combines a gradient method with a lattice descent method. Due to the points on the fiber axis... P b ( x , y , z The parameter t[0,1) can be used to represent this, and thus... P a ( a , b , c )arrive P b ( x , y , zThe distance is transformed into information about t The function is then used to find the minimum value (i.e., the shortest distance) of the function through gradient descent.

[0069] The flowchart of the gradient method combined with the grid descent method is shown in the figure. With the help of the above algorithm, the shortest distance from any point in space to the fiber axis can be obtained, and the parameters of the feature points on the fiber axis corresponding to the shortest distance can be obtained. t and spatial coordinates.

[0070] S43. Calculate the level set function value through the section object to identify fiber elements, boundary elements and matrix elements; After calculating the distances from all nodes in space to the fiber axis, the generalized fiber cross-sectional shape can be constructed using the following formula: ; in, x c , y c , z c These represent the spatial coordinates of a feature point on the fiber axis; parameters l Used to control the shape of the fiber cross-section, for example when l When the value is 2, a circular cross section can be generated.

[0071] The following section employs the level set method to determine the spatial distribution characteristics of fibers and the matrix, thereby achieving accurate separation between the two. For a cubic model discretized by tetrahedral elements, if it contains one or more fibers, the spatial position of the fiber surface can be accurately characterized by the level set function corresponding to the fiber.

[0072] The Level Set Method (LSM) is a numerical technique suitable for interface tracing and shape modeling. In three-dimensional space, this method sets the fiber surface (curved surface) into a linear shape. x The zero level set of the auxiliary function Ф of the three-dimensional level set is represented as: ; To accurately characterize the spatial shape and extent Ω of the fiber, a three-dimensional level set function is introduced. F R ( x , y , z The zero level set corresponds to the fiber-matrix interface Γ. In three-dimensional space, the distance from any point to the fiber boundary can be expressed by the following formula: .

[0073] Specifically, the symbolic definition of the level set function is as follows: when Ф<0, the corresponding point is located inside the fiber region; when Ф>0, the corresponding point is located outside the fiber region. .

[0074] The level set function of all nodes in the space is calculated based on the above method. F R ( x , y , z If the level set function values ​​of each node in the tetrahedral mesh element of the model have both values ​​greater than 0 and values ​​less than 0, then the element is determined to be a fiber-matrix intersecting element. After completing the determination calculation for all elements, for all intersecting elements, the bisection method is used to solve for the intersection positions between their interiors and the fiber boundaries, and new nodes are generated at these positions; then, according to the element connection order, the original intersecting elements are divided into new elements. S5. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axis tangent vectors, and the modeling is finally completed. Specifically, the following steps are included: S51. Calculate the axial tangent vector of the fiber element; To define the cross-sectional shape of a fiber, its spatial location must first be determined. This is achieved through a parametric expression of the fiber's centerline. C(t) Regarding parameters t Taking the first derivative yields the expression for the tangent vector along the fiber axis, and thus the tangent vector at any point along the axis. The expression is as follows: ; ; in, N i,j-1 ( t )and N i+1,j-1 ( t All of these can be obtained from the DeBoor-Cox iterative formula in step S41, and then the tangent vector is... T ( v 1 ,v 2 ,v 3) Perform normalization. The normalization expression is as follows: .

[0075] in, u 1. u 2 and u 3 represent the normalized tangent vector components; Select points on the fiber axis Pb ( x , y , z ) yOz The plane serves as the defining plane for the fiber cross-section. Fiber cross-section shapes encompass ellipses, rectangles, and irregular shapes. To verify the universality of the proposed modeling method, this paper selects two typical cross-sections—ellipses and rectangles—for definition and explanation: For an elliptical cross section, its semi-major axis is defined as... a The semi-minor axis is b Its geometric shape is characterized by parametric equations, the specific expressions of which are as follows: ; in, x ( i ), y ( i )and z ( i () represents the coordinates of a point on the elliptical cross section. i A local coordinate system for the tangent vector between a point on the elliptical cross section and a point on the fiber axis. y The angle between the ′ axis, For the local coordinate system of the tangent vector y Similarly, the three components after axis normalization are... For the local coordinate system of the tangent vector z The three components after axis normalization.

[0076] For a rectangular cross-section, its length is defined as... a Width is b In Cartesian coordinates, the four vertices of this cross section V 1. V 2. V 3. V The specific expression for the coordinates of 4 is as follows: ; Then, parameters are introduced using the piecewise function shown in the following formula. t Interpolation is performed on each side of the rectangle to define the cross-sectional shape; then, coordinate transformation is used to obtain the final coordinates of each point within the rectangular cross-section. The geometric shapes of the two typical cross-sections, ellipse and rectangle, are as follows: Figure 3 As shown; ; in, V 12i , V 23i , V 34i , V 14i These are the coordinates of points on the four sides of the rectangle.

[0077] Based on the above equations, the horizontal set function value from the spatial point to the fiber interface is calculated, and then the spatial positional relationship between any point in the cross-sectional plane and the elliptical cross section and the rectangular cross section is determined. S52. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axis tangent vectors, and the modeling is finally completed. Based on the aforementioned intelligent modeling algorithm for toughening phases in complex irregular-shaped parts, a geometric model of a precast ceramic matrix composite component with a complex woven structure was successfully constructed. The visualization results are shown below. Figure 4 As shown.

[0078] This invention combines computational simulation technology and computer graphics theory to solve problems related to modeling toughening phases in complex irregular components. It can quickly realize the digital modeling of high-end complex toughened components and provide technical support for the efficient digital R&D of high-end complex toughened components.

[0079] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for intelligent modeling of arbitrary toughening phases in aerospace irregular-shaped components, characterized in that, Includes the following steps: S1. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset, and decompose it using the PCA algorithm to obtain the mid-surface centroid and three component vectors; S2. Project the point cloud onto a local plane and calculate its range and center. Scale the curve and rotate and translate it to the center of the local plane. S3. Map the curve back to the 3D plane. Use the nearest neighbor projection algorithm to map the curve to the point cloud. Obtain 20 control points by sampling with equal arc length. S4. Generate multiple fiber objects based on the control point file. Identify fiber elements, boundary elements, and matrix elements by calculating the shortest distance between the model nodes and the fiber axis and the horizontal set function value of the cross-section objects. S5. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axial tangent vectors, and the modeling is finally completed.

2. The intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to claim 1, characterized in that, The specific implementation method of step S1 includes: S1. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset, and decompose it using the PCA algorithm to obtain the mid-surface centroid and three component vectors; Specifically, it includes the following steps: S11. Input the coordinates of the mid-surface nodes to obtain the point cloud dataset; S12. The PCA algorithm is used to transform the data from the original feature space to a new feature space. The new feature space is composed of a linear combination of the original features. Each dimension of this new feature space is called a principal component. Principal components: Principal components are a new set of uncorrelated variables in a dataset that are linear combinations of the original features; each principal component captures the direction of the maximum variance in the data. The PCA algorithm is used to find a set of principal components, such that the first principal component captures the largest variance in the data, the second principal component captures the second largest variance, and so on. S13, Data Standardization: Subtract the mean from each feature and divide by its standard deviation to obtain a dataset with a mean of 0 and a standard deviation of 1, as shown in the following formula: ； in, x It is the raw data. μ It is the mean. σ It is the standard deviation; S14. Calculate the covariance matrix: The covariance matrix is ​​calculated from the standardized dataset. For a dataset containing m features, the size of the covariance matrix is ​​m×m, and each element represents the covariance between two features. The formula for the covariance matrix is: ； Where X is the standardized data matrix and n is the number of samples; For a three-dimensional dataset {x,y,z}, the covariance matrix has the following form: ； in, ； ； ； ； ； ； ； ； ； S15. Calculate eigenvalues ​​and eigenvectors: The PCA algorithm uses Singular Value Decomposition (SVD) to calculate the eigenvalues ​​and eigenvectors of the covariance matrix; the decomposition form of SVD is as follows: ； Among them, matrix U and V Σ is an orthogonal matrix, representing the left and right singular vectors respectively; Σ represents a diagonal matrix containing singular values; The eigenvectors of the covariance matrix correspond to the principal component directions in the dataset, and the eigenvalues ​​represent the data variance explained by each principal component. Eigenvectors: Each eigenvector represents a new coordinate axis, i.e., the direction of the principal component, equivalent to the right singular vector in SVD. V； Eigenvalues: Each eigenvalue represents the variance of the data along the direction of the corresponding eigenvector.

3. The intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to claim 1, characterized in that, The specific implementation method of step S2 includes: S21. Project the point cloud onto a local plane and calculate its extent and center: Project the 3D point cloud set {P} onto the 2D local coordinate system (u,v) spanned by the component vectors e1 and e2 obtained by PCA algorithm. The projection formula is: ； in, The center of mass of the cloud surface; By traversing the UV coordinates of all projection points, the coordinate range of the projection area within the local plane is calculated, and then the centerUV of the projection area is determined. S22, Generation Curve: With parameters t Define the polar equation of the butterfly curve, and the corresponding polar radius expression is: ； Then, using the formula to convert polar coordinates to rectangular coordinates: ； Obtain the coordinates of the butterfly curve in a two-dimensional plane; S23. Perform affine transformation: Perform the following operations on the butterfly curve: First, perform the scaling operation. S After normalizing the curve, scale it according to the scaling factor of the fitted mid-surface size; then perform the rotation operation. R The curve's orientation is adjusted using a rotation matrix; finally, a translation operation is performed. T Move the curve center to the mid-plane projection center centerUV obtained in step S21; finally, obtain the butterfly curve that matches the local plane center. Rotation matrix: ; The formula for calculating affine transformation is: 。 4. The intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to claim 1, characterized in that, The specific implementation method of step S3 includes: S31. Map the curve back to the 3D plane; Based on the basis transformation theory in manifold projection, and utilizing the properties of orthogonal bases, the curvilinear coordinates (u,v) in the two-dimensional local coordinate system are restored to points in three-dimensional space; the restoration formula is: ； in, e1 and e2 are the centroids of the point cloud, and e1 and e2 are the component vectors obtained by PCA algorithm decomposition, realizing the "lifting" mapping of the two-dimensional curve to the three-dimensional local plane; S32. Use the K-nearest neighbor algorithm to map the curve to the point cloud; Suppose there are two samples, and They are in d The formula for calculating the Euclidean distance in the 3D feature space is: ； in, and They are the first k The values ​​of each feature, d It is the dimension of the feature space; this distance is used to calculate the distance between two sample points. d Distance in 3D feature space; Select the K nearest samples to the sample to be classified, and then perform a majority vote based on the categories of these K neighbors to ultimately select the sample. The category that appears most frequently is taken as the category of the sample to be classified; assuming the K neighbor categories of the sample to be classified are... ,in It is the first i The KNN algorithm classifies the categories of its neighbors as follows: mode represents the majority voting operation, selecting the category that appears most frequently as the predicted category; if multiple categories appear the same number of times, the category of the nearest neighbor is selected to break the tie. Nearest neighbor search finds K nearest neighbors or all nearest neighbors within a specified distance of a queried data point based on a specified distance metric. Find the point in the discrete point cloud that has the closest Euclidean distance to the three-dimensional curve point obtained in step S31; S33, 20 control points were obtained by sampling with equal arc length; Uniform sampling based on cumulative arc length is performed as follows: (1) Calculate the distance between adjacent points using the following formula: ； (2) Calculate the cumulative arc length using the formula: ； (3) In the cumulative arc length S Perform equal-interval interpolation on the domain to determine the corresponding sampling point index; Simultaneously, spatial filtering is introduced. By setting a minimum distance threshold, the Euclidean distance between any two output control points is ensured to be greater than the threshold, ultimately resulting in 20 evenly distributed control points.

5. The intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to claim 1, characterized in that, The specific implementation method of step S4 includes: S41. Generate multiple fiber objects based on the control point file: Variables describing the toughening phase are introduced, including fiber cross-sectional shape parameters, fiber distribution parameters in the matrix, and discrete size parameters of the fiber mesh; B-spline curves are used to describe the fiber positions of arbitrary weaving methods. The shortest distance between the nodes and the B-spline curves is calculated. The separation of fibers and matrix in complex irregular composite prefabricated parts is realized through the level set method, and the finite element mesh discretization of the model is completed simultaneously. The parameterized curve formed by interpolating or fitting multiple rational polynomials using NURBS curves has an analytical expression. C(t) Defined as: ； in, As control points, express k The first B-spline curve i The number of basis functions is 1. It is easy to see that the order of the basis functions is 1. k +1, and this basis function is uniquely determined by a non-decreasing node sequence t containing m elements: ； The solution is obtained using a recursive method. The specific form of the recursive calculation process is as follows: ； From the above formula, it can be seen that when k When = 0, the basis function form of the first-order B-spline curve can be expressed as: ； In the process of fiber generation in composite materials, the start and end points of the fiber are specified based on the boundary position. Clamped-B splines from the B-splines are selected. k The core characteristic of the node sequence of a Clamped-B spline curve is: the preceding... k+1 All nodes have the same value, and finally... k+1 All nodes have the same value, and based on this node sequence, it can be represented as: ； In summary, B-spline curves with arbitrary spatial distributions are generated by setting control points, and these curves are used as the axis of the composite fiber. S42. Calculate the shortest distance between the model node and the fiber axis: To determine whether a cell crosses the fiber-matrix interface layer, it is necessary to calculate any point in space. P a ( a , b , c The shortest distance to the fiber curve d The shortest distance d It can be regarded as a point on the fiber curve P b ( x , y , z The function is expressed as: ； Points on the fiber axis P b ( x , y , z Using the parameter t[0,1) to represent, P a ( a , b , c )arrive P b ( x , y , z The distance is transformed into information about t The function is then used to find its minimum value using gradient descent. The solution yields the shortest distance from any point in space to the fiber axis, and simultaneously obtains the parameters of the feature point on the fiber axis corresponding to this shortest distance. t and spatial coordinates; S43. Calculate the level set function value using the section object to identify fiber elements, boundary elements, and matrix elements: After calculating the distances from all nodes in space to the fiber axis, the generalized fiber cross-sectional shape is constructed using the following formula: ； in, x c , y c , z c These represent the spatial coordinates of a feature point on the fiber axis; where the parameters are... λ Used to control the shape of the fiber cross-section, for example when λ When the value is 2, a circular cross-section is generated; For a cube model discretized by tetrahedral elements, if it contains one or more fibers, the spatial position of the fiber surface is accurately characterized by the level set function corresponding to the fiber. Fiber surface, i.e., curved surface ξ The zero level set is represented as the auxiliary function Ф of the three-dimensional level set, i.e.: ； Introducing a three-dimensional level set function for accurately characterizing the spatial shape and extent Ω of fibers. F R ( x , y , z The zero level set corresponds to the fiber-matrix interface Γ; in three-dimensional space, the distance from any point to the fiber boundary is expressed by the following formula: ； The symbolic definition of the level set function is as follows: when Ф<0, the corresponding point is located inside the fiber region; when Ф>0, the corresponding point is located outside the fiber region. ； The level set function of all nodes in the space is calculated based on the above method. F R ( x , y , z If the level set function values ​​of each node in the tetrahedral mesh element of the model have both values ​​greater than 0 and values ​​less than 0, then the element is determined to be a fiber-matrix intersecting element. After completing the determination calculation for all elements, the bisection method is used to solve the intersection position between the element and the fiber boundary for all intersecting elements, and a new node is generated at the position. Then, according to the element connection order, the original intersecting element is divided into new elements.

6. The intelligent modeling method for arbitrary toughening phases of aerospace irregular-shaped parts according to claim 1, characterized in that, The specific implementation method of step S5 includes: S51. Calculate the axial tangent vector of the fiber element: By using the parameterized expression of the fiber axis C(t) Regarding parameters t Taking the first derivative, we obtain the expression for the tangent vector along the fiber axis, and then obtain the tangent vector at any point along the axis, as shown in the following expression: ； ； in, N i,j-1 ( t )and N i+1,j-1 ( t The result is obtained from step S41, and then the tangent vector is... T ( v 1 ,v 2 ,v 3) Perform normalization. The normalization expression is as follows: ； in, u 1. u 2 and u 3 represent the normalized tangent vector components; Select points on the fiber axis P b ( x , y , z ) yOz The plane, as the defining plane of the fiber cross-section, encompasses elliptical, rectangular, and irregular shapes. For an elliptical cross section, its semi-major axis is defined as... a The semi-minor axis is b Its geometric shape is characterized by parametric equations, the specific expressions of which are as follows: ； in, x ( θ ), y ( θ )and z ( θ () represents the coordinates of a point on the elliptical cross section. θ A local coordinate system for the tangent vector between a point on the elliptical cross section and a point on the fiber axis. y The angle between the ′ axis, For the local coordinate system of the tangent vector y Similarly, the three components after axis normalization are... For the local coordinate system of the tangent vector z The three components after axis normalization; For a rectangular cross-section, its length is defined as... a Width is b In Cartesian coordinates, the four vertices of this cross section V 1. V 2. V 3. V The specific expression for the coordinates of 4 is as follows: ； Then, parameters are introduced through a piecewise function. t Interpolation is performed on each side of the rectangle to define the cross-sectional shape; then, coordinate transformation is used to obtain the final coordinates of each point within the rectangular cross-section. ； in, V 12i , V 23i , V 34i , V 14i These are the coordinates of points on the four sides of the rectangle; Based on the above equations, the horizontal set function value from the spatial point to the fiber interface is calculated, and then the spatial positional relationship between any point in the cross-sectional plane and the elliptical cross section and the rectangular cross section is determined. S52. The boundary elements are further subdivided and re-identified using the proportional method. After the determination of all fiber objects is completed in a loop, the fiber elements are traversed to calculate their axis tangent vectors, and the modeling is finally completed.

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