Displacement field prediction method and device fusing multi-scale features and relative distance coding

Abstract

The application provides a displacement field prediction method and device fusing multi-scale features and relative distance coding, relates to the field of engineering structure mechanics analysis and machine learning agent model, and the method comprises the following steps: extracting node macroscopic boundary constraint features, local surface curvature features and relative distance coding features, and constructing a multi-scale space feature matrix; adopting a weighted boundary farthest point sampling strategy to adaptively select key control points; after dimension reduction through principal component analysis, inputting key control point displacement information, and using a LightGBM model to realize high-precision and rapid prediction of the whole field displacement of the structure. The application does not depend on neighborhood displacement prior information, eliminates absolute coordinate translation sensitivity, reduces the calculation time by hundreds of times while ensuring the prediction accuracy, and is suitable for real-time digital twinning and multi-working condition rapid evaluation of engineering structures.

Description

Technical Field

[0001] This application relates to the field of engineering structural mechanics analysis and machine learning surrogate models, and in particular to a displacement field prediction method and device that integrates multi-scale features and relative distance encoding. Background Technology

[0002] Structural mechanics performance analysis is an indispensable core component of mechanical engineering design and optimization. Finite element analysis (FEM), a classic numerical tool for studying the deformation behavior of mechanical structures, discretizes continuous structures into a finite number of mesh nodes and elements, enabling accurate prediction of the displacement response and stress distribution of complex engineering structures under different load conditions. It has been widely applied in engineering fields such as aerospace structural design, automotive body stiffness verification, bridge load-bearing capacity assessment, and performance verification of precision mechanical equipment. However, for complex three-dimensional mechanical structures containing high-density meshes and a large number of nodes, the traditional FEM solution process relies on discrete iteration of high-order partial differential equations and large-scale stiffness matrix inversion operations, resulting in extremely high computational resource consumption and long solution cycles. When faced with tasks such as parametric design variable scanning, multi-condition combined evaluation, and real-time feedback optimization, the computational efficiency bottleneck of the traditional FEM method becomes particularly prominent, making it difficult to meet the practical engineering needs of rapid multi-condition evaluation, real-time digital twin monitoring, and rapid structural topology optimization.

[0003] To reduce computational costs and improve engineering analysis efficiency, data-driven machine learning surrogate models have gained widespread attention in recent years as an efficient alternative to finite element simulation. Existing research has constructed nonlinear mapping relationships between structural parameters and mechanical responses based on models such as deep neural networks, support vector machines, random forests, gradient boosting trees, and graph neural networks. For example, Zhao Hang et al. proposed a data-learning-based method for predicting the static performance of structures. Using a cantilever beam as the research object, they established a finite element simulation model to obtain displacement field data, constructed a boundary condition-displacement field surrogate model, and verified the feasibility of the surrogate model in displacement field prediction. Yan Yuehui et al. utilized surrogate model technology based on multidimensional order reduction and deep learning to achieve rapid reconstruction of the cabin's force-thermal coupling response field within 0.6 seconds, with single-condition response reconstruction time significantly lower than traditional numerical calculation methods. However, existing surrogate model research still has significant shortcomings in predicting the overall displacement field of complex mechanical structures: In terms of spatial feature representation, most methods only focus on the macroscopic mapping between global geometric parameters and target response, making it difficult to effectively capture the spatial topological relationships and local geometric complexity between nodes within the structure; some methods use the three-dimensional coordinates of nodes as spatial location features, but absolute coordinates are translationally sensitive and scale-dependent, limiting their generalization ability when structural geometric parameters change; other methods use the average displacement of neighboring nodes as auxiliary features, leading to data leakage problems and limiting the model's true generalization ability. Regarding control point sampling strategies, existing random sampling, uniform grid sampling, or traditional farthest point sampling methods either fail to guarantee the coverage probability of key areas or cannot adapt to differences in structural stiffness distribution, making it difficult to focus sampling points on boundary constraint areas and high stress concentration areas, affecting the prediction accuracy of key areas. Summary of the Invention

[0004] The purpose of this invention is to address the technical problems of existing mechanical structure displacement field prediction methods, such as low computational efficiency, insufficient spatial topology and local geometric feature representation, and the inability of control point sampling strategies to adaptively focus on key high-deformation regions, which limit prediction accuracy and generalization ability. This invention provides a displacement field prediction method that integrates multi-scale features and relative distance coding.

[0005] The above-mentioned objective of this application is achieved through the following technical solution: S1: Obtain the set of all mesh nodes of the mechanical structure to be predicted and their three-dimensional spatial coordinates, and construct multi-scale spatial features; the multi-scale spatial features include: macroscopic boundary constraint features, local surface curvature features and relative distance encoding features; S2: Identify the set of boundary nodes of the mechanical structure to be predicted by using a preset boundary distance threshold. Based on the local surface curvature features, construct normalized curvature weights and introduce boundary enhancement coefficients to the boundary nodes to form a comprehensive sampling weight. In each iteration, calculate the minimum Euclidean distance from the unsampled node to the sampled set, multiply the minimum Euclidean distance by the comprehensive sampling weight, and select the node with the largest weighted distance to add to the control point set. Continue until the preset number of control points is reached; S3: Based on multi-scale spatial features, construct a multi-scale feature matrix and perform Z-Score standardization; use principal component analysis to reduce the dimensionality of the multi-scale feature matrix according to the cumulative variance contribution rate threshold to obtain low-dimensional spatial features, and splice them with the external load parameters of the working condition and the displacement information of key control points to establish a gradient boosting decision tree surrogate model based on LightGBM, and output the displacement prediction values ​​of all nodes in the structure.

[0006] Optionally, step S1 includes: Based on the axis-aligned bounding box, the geometric boundaries of the mechanical structure to be predicted along the three coordinate axes are determined, the shortest Euclidean distance from each mesh node in the mechanical structure to the six boundary surfaces of the bounding box is calculated, and the macroscopic boundary constraint features are constructed by combining the normalized spatial coordinates. The K-nearest neighbor algorithm is used to search the local neighborhood point set of each node, construct the covariance matrix and perform singular value decomposition to extract local surface curvature features; The cKDTree spatial index is used to retrieve the nearest control point and local neighborhood node of each node, and the relative position vector and Euclidean distance are calculated to construct the relative distance encoding feature; The multi-scale spatial feature extraction relies solely on the geometric priors and load conditions of the mechanical structure to be predicted, without involving any displacement information.

[0007] Optionally, step S1 may further include: The construction of the macroscopic boundary constraint features includes: Let the set of all grid nodes be ,in The total number of grid nodes is given by the following formula: (The formula is missing from the original text) The structure is determined based on the axis-aligned bounding box. Geometric boundaries of the three coordinate axes , and For any node The shortest Euclidean distance from it to the six boundary faces of the bounding box The calculation formula is:

[0008] Globally normalize the absolute 3D coordinates of the nodes to obtain normalized spatial coordinate features:

[0009]

[0010]

[0011] Normalized spatial coordinate features and shortest Euclidean distance This refers to the macroscopic boundary constraint characteristic; The extraction of the local surface curvature features includes: For any node The K-nearest neighbor algorithm is used to search for the nearest neighbor in three-dimensional space. Each set of neighboring nodes constitutes a local neighborhood node set. ,in The value of is 30 to 50; calculate the coordinates of the geometric center of the neighborhood. :

[0012] Based on the spatial offset vectors of each node in the neighborhood relative to the geometric center, construct covariance matrix :

[0013] in Indicates transpose; For covariance matrix Perform singular value decomposition to obtain three non-negative eigenvalues. These parameters reflect the spatial dispersion of the neighborhood point cloud along three principal directions; surface curvature indices are used. Characterizing local geometric complexity:

[0014] Curvature index The range of values ​​is That is, the local surface curvature characteristics; The construction of the relative distance encoded features includes: The control point set is established using the cKDTree algorithm. A hierarchical spatial binary tree index structure; for any grid node Use cKDTree to retrieve its nearest neighbor control points Calculate the three-dimensional relative position vector between the two. Euclidean distance :

[0015]

[0016] in, Number of control points; Further node search using cKDTree In three-dimensional space Find the nearest neighbor nodes and calculate the distance from the node to each neighbor node. Relative position vector:

[0017] in, For RDE neighborhood parameters, relative position vector That is, relative distance encoding features.

[0018] Optionally, step S2 includes: Set boundary distance judgment threshold For each node When its distance to the shortest boundary of the bounding box When this happens, the node is determined to be a boundary node and added to the boundary node set. ; Based on the local surface curvature characteristics of each node Construct normalized curvature weights:

[0019] in, This is the weighting adjustment coefficient. and These represent the maximum and minimum values ​​of curvature for all nodes globally; For the set of boundary nodes For nodes, an additional boundary enhancement coefficient is introduced. Differentiated comprehensive sampling weights are formed: when hour, ,in The typical value is 1.5; when hour, ; Initialize the set of sampled control points Empty, from the set of boundary nodes The node with the highest curvature value is selected as the seed control point and added to the set. In each subsequent iteration, for all unsampled nodes Calculate its distance to the current set of sampled control points. Minimum Euclidean spatial distance between all control points:

[0020] in, Represents the set of currently sampled control points Any control point in the system; Introducing the comprehensive sampling weight Calculate the weighted distance and select the node that maximizes it as the next control point:

[0021] Will join in Repeat in a loop until The number of control points in the system has reached the preset target value. .

[0022] Optionally, step S3 includes: The training set feature matrix and the test set feature matrix are obtained by partitioning the multi-scale feature matrix. Calculate the mean for each dimension of the feature matrix of the training set. with standard deviation Perform Z-Score normalization transformation:

[0023] To unify all features to a standard distribution with zero mean and unit variance; Principal component analysis was performed on the standardized training set feature matrix, and a cumulative variance contribution rate threshold was set. :

[0024] Before keeping One principal component; Obtain the external load parameters of the working condition; Obtain displacement information of key control points; The low-dimensional spatial features after dimensionality reduction by principal component analysis are combined with the external load parameters of the working condition and the displacement information of key control points to form the final input feature vector, and a gradient boosting decision tree surrogate model based on LightGBM is established. The hyperparameters of the LightGBM model are configured as follows: number of leaf nodes. Learning rate Maximum number of iterations The objective function is L2 regression loss.

[0025] Optionally, step S3 may also include: The prediction accuracy of the gradient boosting decision tree surrogate model is evaluated using the coefficient of determination. Root mean square error and average relative error As an indicator.

[0026] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a displacement field prediction method that integrates multi-scale features and relative distance encoding.

[0027] A computer-readable storage medium storing instructions that, when executed, perform a displacement field prediction method that integrates multi-scale features and relative distance encoding.

[0028] The beneficial effects of the technical solution provided in this application are: Multi-scale spatial feature fusion mechanism. Breaking through the limitations of traditional surrogate models that rely solely on global parameters or absolute coordinates, this mechanism constructs a three-tiered feature system of macro-micro-meso-scale by using AABB boundary distance to characterize the macro-constraint environment, curvature to represent local geometric complexity, and RDE relative position encoding to describe the meso-scale spatial topology. Furthermore, it does not rely on neighborhood displacement information throughout the entire process, thus fundamentally preventing data leakage.

[0029] Weighted Boundary-FPS adaptive sampling strategy. Based on the traditional FPS spatial uniform coverage, it innovatively introduces curvature deformation weight and boundary enhancement coefficient, so that control points automatically gather in high curvature change region and boundary constraint region, overcoming the defect of pure geometric sampling that ignores mechanical sensitivity.

[0030] A highly efficient surrogate model prediction framework. It compresses 126-dimensional features into 18-dimensional principal components using PCA, and combines this with the strong nonlinear fitting capability of LightGBM to achieve second-level prediction of full-field displacement. Attached Figure Description

[0031] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart illustrating the overall process of predicting the displacement field of a mechanical structure in a specific embodiment of this application. Figure 2 This is a flowchart of finite element simulation and data extraction in a specific embodiment of this application; Figure 3 This is a schematic diagram illustrating the principle of local surface curvature extraction in a specific embodiment of this application; Figure 4 This is a schematic diagram of the construction of relative distance encoding features in a specific embodiment of this application; Figure 5 This is a topological spatial distribution and sampling cloud map of the Weighted Boundary-FPS control points in a specific embodiment of this application; Figure 6 This is a quantitative analysis chart of the prediction accuracy of the LightGBM proxy model in a specific embodiment of this application; Figure 7 These are three-dimensional visualization comparison diagrams of the displacement field in specific embodiments of this application; Figure 8 This is a heatmap of the number of control points and the orthogonal experimental determination coefficient and root mean square error of the RDE neighborhood parameters in a specific embodiment of this application; Figure 9 This is a schematic diagram of the electronic device structure in the embodiments of this application. Detailed Implementation

[0032] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0033] The embodiments of this application provide a displacement field prediction method that integrates multi-scale features and relative distance encoding.

[0034] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a displacement field prediction method that integrates multi-scale features and relative distance coding, as described in an embodiment of this application. S1: Obtain the set of all mesh nodes of the mechanical structure to be predicted and their three-dimensional spatial coordinates, and construct multi-scale spatial features; the multi-scale spatial features include: macroscopic boundary constraint features, local surface curvature features and relative distance encoding features; As one embodiment, the mechanical structure includes a frame support, a load-bearing beam structure, a space truss, a precision equipment housing, and a 3D printer frame.

[0035] S2: Identify the set of boundary nodes of the mechanical structure to be predicted by using a preset boundary distance threshold. Based on the local surface curvature features, construct normalized curvature weights and introduce boundary enhancement coefficients to the boundary nodes to form a comprehensive sampling weight. In each iteration, calculate the minimum Euclidean distance from the unsampled node to the sampled set, multiply the minimum Euclidean distance by the comprehensive sampling weight, and select the node with the largest weighted distance to add to the control point set. Continue until the preset number of control points is reached; S3: Based on multi-scale spatial features, construct a multi-scale feature matrix and perform Z-Score standardization; use principal component analysis to reduce the dimensionality of the multi-scale feature matrix according to the cumulative variance contribution rate threshold to obtain low-dimensional spatial features, and splice them with the external load parameters of the working condition and the displacement information of key control points to establish a gradient boosting decision tree surrogate model based on LightGBM, and output the displacement prediction values ​​of all nodes in the structure.

[0036] This application, by adopting the aforementioned technical solution, systematically extracts macroscopic AABB bounding box boundary constraint features, local surface curvature features, and RDE relative distance topological encoding. Combined with a Weighted Boundary-FPS control point adaptive sampling strategy and a highly efficient surrogate model based on PCA-LightGBM, it achieves extremely rapid and high-precision prediction of all-field node displacements without relying on prior information about the displacements of the point to be predicted and its neighborhood. It utilizes only structural geometric priors, load conditions, and key control point displacement information. This provides a complete technical solution for real-time digital twins of engineering structures, rapid design iteration under multiple load conditions, and online assessment of structural health status. The Chinese name for the LightGBM model is Lightweight Gradient Boosting Machine.

[0037] Step S1 includes: Based on the axis-aligned bounding box, the geometric boundaries of the mechanical structure to be predicted along the three coordinate axes are determined, the shortest Euclidean distance from each mesh node in the mechanical structure to the six boundary surfaces of the bounding box is calculated, and the macroscopic boundary constraint features are constructed by combining the normalized spatial coordinates. The K-nearest neighbor algorithm is used to search the local neighborhood point set of each node, construct the covariance matrix and perform singular value decomposition to extract local surface curvature features; The cKDTree spatial index is used to retrieve the nearest control point and local neighborhood node of each node, and the relative position vector and Euclidean distance are calculated to construct the relative distance encoding feature; The multi-scale spatial feature extraction relies solely on the geometric priors and load conditions of the mechanical structure to be predicted, without involving any displacement information.

[0038] As one example, multi-scale spatial feature extraction includes macroscopic boundary constraint feature construction (calculating the shortest distance and normalized coordinates from nodes to the six boundary surfaces based on AABB bounding boxes), local surface curvature feature extraction (calculating surface curvature values ​​based on KNN neighborhood retrieval and covariance matrix SVD decomposition), and relative distance encoding (RDE) feature engineering (calculating the relative position vectors and Euclidean distances from nodes to nearest neighbor control points and local neighbor nodes based on control point cKDTree spatial index). Figure 1 This is the overall flowchart of the module. Figure 3 This is a schematic diagram illustrating the principle of local surface curvature extraction in this module. Figure 4 This is a schematic diagram of RDE feature construction in this module.

[0039] Step S1 also includes: The construction of the macroscopic boundary constraint features includes: Let the set of all grid nodes be ,in The total number of grid nodes is given by the following formula: (The formula is missing from the original text) The structure is determined based on the axis-aligned bounding box. Geometric boundaries of the three coordinate axes , and For any node The shortest Euclidean distance from it to the six boundary faces of the bounding box The calculation formula is:

[0040] As one example, the macroscopic boundary constraint characteristics reflect the relative spatial position of the nodes in the overall structure and the degree to which they are constrained by the boundary. Nodes closer to the boundary usually have greater stiffness and smaller displacement response, while nodes far from the boundary constraint area are more likely to undergo significant deformation under load.

[0041] Globally normalize the absolute 3D coordinates of the nodes to obtain normalized spatial coordinate features:

[0042]

[0043]

[0044] Normalized spatial coordinate features and shortest Euclidean distance This refers to the macroscopic boundary constraint characteristic; As one embodiment, the normalized spatial coordinate feature maps all node coordinates to Within the standard unit cube space, the interference of absolute size differences between different structures on model training is eliminated.

[0045] The extraction of the local surface curvature features includes: For any node The K-nearest neighbor algorithm is used to search for the nearest neighbor in three-dimensional space. Each set of neighboring nodes constitutes a local neighborhood node set. ,in The value of is 30 to 50; calculate the coordinates of the geometric center of the neighborhood. :

[0046] Based on the spatial offset vectors of each node in the neighborhood relative to the geometric center, construct covariance matrix :

[0047] in Indicates transpose; For covariance matrix Perform singular value decomposition to obtain three non-negative eigenvalues. These parameters reflect the spatial dispersion of the neighborhood point cloud along three principal directions; surface curvature indices are used. Characterizing local geometric complexity:

[0048] Curvature index The range of values ​​is That is, the local surface curvature characteristics; As one example, curvature index The range of values ​​is When the node is located in a flat surface region, the normal dispersion is minimal. The curvature value approaches zero; when the node is located in a transition zone, corner, chamfer, or region of abrupt geometric change, Increasing the curvature value significantly improves its ability to effectively characterize local geometric complexity, such as... Figure 3 As shown.

[0049] The construction of the relative distance encoded features includes: The control point set is established using the cKDTree algorithm. A hierarchical spatial binary tree index structure; for any grid node Use cKDTree to retrieve its nearest neighbor control points Calculate the three-dimensional relative position vector between the two. Euclidean distance :

[0050]

[0051] in, Number of control points; Further node search using cKDTree In three-dimensional space Find the nearest neighbor nodes and calculate the distance from the node to each neighbor node. Relative position vector:

[0052] in, For RDE neighborhood parameters, relative position vector That is, relative distance encoding features.

[0053] As one embodiment, a Weighted Boundary-FPS sampling strategy is used to select from all N nodes. A set of key control points (typically ranging from 128 to 512) constitutes the control point set. To improve the spatial query efficiency of large-scale grid nodes, the cKDTree algorithm is used to establish the control point set. The hierarchical spatial binary tree index structure reduces the computational complexity of traditional brute-force search from... Down to For any grid node Use cKDTree to retrieve its nearest neighbor control points Calculate the three-dimensional relative position vector between the two. Euclidean distance The relative position vector from the node to its nearest neighbor control point It encodes the relative spatial orientation information of nodes within the global structure, and This encodes the spatial distance information from the node to the key reference point. Furthermore, nodes are further searched using cKDTree (C-language KD-Tree). In the three-dimensional space, find the K nearest neighbor nodes (K is the RDE neighborhood parameter, typically 16 or 32), and calculate the distance from the node to each neighbor node. The relative position vector; RDE features encode spatial relationships using relative position vectors rather than absolute coordinates, naturally eliminating the translation sensitivity of absolute coordinates. Furthermore, it relies solely on geometric priors (control point coordinates, neighbor node coordinates) without involving any displacement information, fundamentally eliminating the possibility of data leakage. Simultaneously, it integrates the spatial relationship encoding of two levels: nearest neighbor control points (global scale) and K neighbor nodes (local scale), such as... Figure 4 As shown.

[0054] As one example, the spatial sampling distribution of control points determines the quality of the RDE features in representing the overall displacement field of the structure.

[0055] Step S2 includes: Set boundary distance judgment threshold For each node When its distance to the shortest boundary of the bounding box When this happens, the node is determined to be a boundary node and added to the boundary node set. ; Based on the local surface curvature characteristics of each node Construct normalized curvature weights:

[0056] in, This is the weighting adjustment coefficient. and These represent the maximum and minimum values ​​of curvature for all nodes globally; For the set of boundary nodes For nodes, an additional boundary enhancement coefficient is introduced. Differentiated comprehensive sampling weights are formed: when hour, ,in The typical value is 1.5; when hour, ; Initialize the set of sampled control points Empty, from the set of boundary nodes The node with the highest curvature value is selected as the seed control point and added to the set. In each subsequent iteration, for all unsampled nodes Calculate its distance to the current set of sampled control points. Minimum Euclidean spatial distance between all control points:

[0057] in, Represents the set of currently sampled control points Any control point in the system; Introducing the comprehensive sampling weight Calculate the weighted distance and select the node that maximizes it as the next control point:

[0058] Will join in Repeat in a loop until The number of control points in the system has reached the preset target value. .

[0059] As one embodiment, boundary node identification and determination is performed. A boundary distance determination threshold is set. (Typically, the value is 1% to 3% of the shortest side length of the bounding box). For each node Utilizing its macroscopic bounding box shortest boundary distance ,when When this happens, the node is determined to be a boundary node and added to the boundary node set. Boundary nodes are typically located near fixed supports, contact surfaces, or constrained regions of the structure, and changes in the displacement field in these regions have a global impact on the overall structural response.

[0060] Deformation sensitivity comprehensive weighting is constructed based on the local surface curvature of each node. Construct normalized curvature weights; The coefficients serve to maintain a baseline for the sampling probability of all nodes, preventing the sampling weights of nodes in low curvature regions from degenerating to zero. This applies to sets of boundary nodes. For nodes, an additional boundary enhancement coefficient is introduced. (Typical value is 1.5), forming a differentiated comprehensive sampling weight: when hour: ;when hour: .

[0061] Weighted farthest point iterative extraction. Initialize the set of sampled control points. Empty, from the set of boundary nodes The node with the highest curvature value is selected as the seed control point and added. In each subsequent iteration, for all unsampled nodes... First calculate its distance to the current sampled set. The minimum Euclidean spatial distance between all control points.

[0062] Then introduce the constructed comprehensive sampling weights Calculate the weighted distance and select the node that maximizes it as the next control point; join in This completes one iteration. Repeat the loop until... The number of control points in the system has reached the preset target value. The WB-FPS (Weighted Boundary-Farthest Point Sampling) strategy prioritizes sampling nodes that are both far from existing sampling points and have high mechanical sensitivity in each iteration. The resulting set of control points, while ensuring uniform global spatial coverage, naturally exhibits an ideal distribution pattern: clustering along boundary constraint regions, dense distribution in regions of high curvature geometric abrupt changes, and reasonable dispersion within the structure. Figure 5 As shown.

[0063] Step S3 includes: The training set feature matrix and the test set feature matrix are obtained by partitioning the multi-scale feature matrix. Calculate the mean for each dimension of the feature matrix of the training set. with standard deviation Perform Z-Score normalization transformation:

[0064] To unify all features to a standard distribution with zero mean and unit variance; Principal component analysis was performed on the standardized training set feature matrix, and a cumulative variance contribution rate threshold was set. :

[0065] Before keeping One principal component; Obtain the external load parameters of the working condition; Obtain displacement information of key control points; The low-dimensional spatial features after dimensionality reduction by principal component analysis are combined with the external load parameters of the working condition and the displacement information of key control points to form the final input feature vector, and a gradient boosting decision tree surrogate model based on LightGBM is established. The hyperparameters of the LightGBM model are configured as follows: number of leaf nodes. Learning rate Maximum number of iterations The objective function is L2 regression loss.

[0066] As one example, after multi-scale feature stitching, the original feature vector constructed by each node can reach 126 dimensions, including various heterogeneous features such as macroscopic boundary distance, normalized coordinates, local surface curvature, RDE relative position vectors and distances, neighborhood relative vectors, and working loads. Due to significant differences in dimensions and linear correlations among different features, the following standardization and dimensionality reduction processing is required: First, calculate the mean for each dimension of the feature matrix in the training set. with standard deviation Z-Score standardization is performed to unify all features to a standard distribution with zero mean and unit variance. Test set samples are strictly transformed using the statistical parameters of the training set to prevent leakage of test information into the training process.

[0067] Secondly, Principal Component Analysis (PCA) is performed on the standardized feature matrix. This involves solving the orthogonal eigenvalue decomposition of the covariance matrix and extracting principal components by sorting the eigenvalues ​​from largest to smallest. A cumulative variance contribution rate threshold is set. The first m principal components are retained. In one embodiment, the original 126-dimensional features, after PCA dimensionality reduction, retain 18 principal components (cumulative variance contribution rate of 95.23%), achieving a dimensionality compression rate of approximately 86%, significantly reducing the time and space complexity of subsequent model training.

[0068] Third, the low-dimensional spatial features obtained from PCA dimensionality reduction are concatenated with the external load parameters and control point displacement information to form the final model input feature vector, establishing a gradient boosting decision tree surrogate model based on LightGBM (Light Gradient Boosting Machine). The LightGBM model employs a histogram-based decision tree splitting algorithm and a leaf-wise growth strategy, with its core hyperparameter configuration being: the number of leaf nodes. Learning rate Maximum number of iterations The objective function is L2 regression loss. After training, the model can directly receive structural geometric features and load conditions under any new working condition, and output the displacement prediction values ​​of all nodes in the entire field within seconds, achieving a computational speedup of hundreds of times compared to traditional finite element methods.

[0069] Step S3 also includes: The prediction accuracy of the gradient boosting decision tree surrogate model is evaluated using the coefficient of determination. Root mean square error and average relative error As an indicator.

[0070] As one example, in an embodiment of a 3D printer frame, the model achieved a coefficient of determination. Root mean square error Average relative error Extremely high prediction accuracy. For example... Figure 6 As shown, the scatter plots of predicted and actual values ​​are closely clustered in... Near the ideal reference line, the error distribution is approximately symmetrical around zero, and the residuals are randomly scattered around zero without any systematic overestimation or underestimation trend. Figure 7 As shown, the spatial distribution pattern of the displacement field predicted by the model is highly consistent with the finite element simulation results, and the absolute error distribution cloud map shows that the prediction error in most areas is at an extremely low level. Figure 8 As shown, the number of control points A two-factor orthogonal experimental design with the RDE neighborhood parameter K was used to determine the optimal parameter combination ( ).

[0071] This invention also relates to a displacement field prediction system that integrates multi-scale features and relative distance encoding. The system includes the following functional modules: a data preprocessing module configured to receive structural node mesh data and load case data files exported from finite element simulation software, and automatically perform data parsing, missing value detection and processing, numerical format standardization, and global AABB bounding box parameter calculation. Simultaneously, the data preprocessing module is responsible for dividing the dataset according to a preset ratio (e.g., 80% training set and 20% test set), and adopts a strategy of forcibly including extreme load cases in the training set—forcibly including the load cases corresponding to the maximum and minimum loads in the load parameter space into the training set, to ensure that the model can fully learn the structural deformation laws within the complete load variation range.

[0072] The multi-scale feature extraction module is configured to call three feature extraction sub-modules in parallel: a macroscopic boundary constraint feature construction sub-module, which calculates the shortest distance and normalized 3D coordinates from each node to the six boundary surfaces based on AABB bounding box parameters; a local surface curvature feature extraction sub-module, which calculates the SurfaceVariation curvature value based on KNN neighborhood retrieval and SVD decomposition of the covariance matrix; and an RDE feature engineering sub-module, which calculates the relative position vector and Euclidean distance from a node to its nearest neighbor control point, as well as the relative position vector encoding from a node to its K local neighbor nodes, based on the cKDTree spatial index of control points. The outputs of the three sub-modules are concatenated and fused to form a unified high-dimensional multi-scale feature matrix.

[0073] Control point adaptive sampling module: configured to execute the complete WeightedBoundary-FPS algorithm flow—first, scan all nodes based on a preset boundary distance threshold to identify the boundary node set, then construct a deformation sensitivity comprehensive sampling weight vector based on curvature features and boundary attributes, and finally generate a specified number of key control point sets and their corresponding cKDTree spatial index structures through a weighted farthest point iterative extraction algorithm for use by the RDE feature engineering submodule.

[0074] The surrogate model training and prediction module: During the training phase, Z-Score standardized parameter learning (calculating the mean and standard deviation of each dimension of the training set features), PCA projection matrix learning (SVD decomposition and principal component selection based on the covariance matrix of the training set), and LightGBM model parameter optimization (iterative decision tree training based on the gradient boosting framework) are executed sequentially. During the inference and prediction phase, the standardized parameters, PCA projection matrix, and LightGBM model file saved in the training phase are loaded sequentially. The new input structural features and load conditions are processed in a pipeline of standardization → dimensionality reduction → model inference, and the displacement prediction values ​​of all nodes in the structure are output.

[0075] The system achieves fully automated end-to-end integration from input of raw finite element simulation data to output of full-field displacement prediction results. It can complete the entire training and online inference process on conventional computing hardware, meeting the practical needs of rapid multi-condition evaluation, parameter sensitivity analysis, and real-time digital twin mechanical state updates in industrial scenarios.

[0076] In one embodiment, Figure 1 This is the overall flowchart. Figure 2 This is a flowchart of finite element simulation and data extraction. Figure 3 This is a schematic diagram illustrating the principle of local surface curvature extraction. Figure 4 A schematic diagram of constructing Relative Distance Encoding (RDE) features. Figure 5 The topological spatial distribution and sampling cloud map of Weighted Boundary-FPS control points. Figure 6 Quantitative analysis of prediction accuracy for the LightGBM surrogate model (including) Figure 6 (a) Scatter plot comparing test set predicted values ​​with finite element simulation results; Figure 6 (b) Histogram of prediction error distribution; Figure 6 (c) Scatter plot of residual analysis in the middle. Figure 7 Comparison of three-dimensional visualizations of displacement fields (including) Figure 7 (a) Model prediction of displacement field contour plot; Figure 7 (b) Finite element simulation displacement field contour plot; Figure 7 (c) Absolute error distribution cloud map in the middle. Figure 8 The coefficient of determination for the orthogonal experiment of the number of control points and the RDE neighborhood parameters. Heatmap of root mean square error (RMSE).

[0077] This application also discloses an electronic device. (See reference...) Figure 9 , Figure 9 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.

[0078] The communication bus 502 is used to enable communication between these components.

[0079] The user interface 503 may include a display screen, and optionally, the user interface 503 may also include a standard wired interface or a wireless interface.

[0080] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0081] This application also discloses a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute the above-described displacement field prediction method that integrates multi-scale features and relative distance encoding.

[0082] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.

[0083] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A displacement field prediction method integrating multi-scale features and relative distance encoding, characterized in that, The method includes the following steps: S1: Obtain the set of all mesh nodes of the mechanical structure to be predicted and their three-dimensional spatial coordinates, and construct multi-scale spatial features; Multi-scale spatial features include: macroscopic boundary constraint features, local surface curvature features, and relative distance encoding features; S2: Identify the set of boundary nodes of the mechanical structure to be predicted by using a preset boundary distance threshold. Based on the local surface curvature features, construct normalized curvature weights and introduce boundary enhancement coefficients to the boundary nodes to form a comprehensive sampling weight. In each iteration, calculate the minimum Euclidean distance from the unsampled node to the sampled set, multiply the minimum Euclidean distance by the comprehensive sampling weight, and select the node with the largest weighted distance to add to the control point set. Continue until the preset number of control points is reached; S3: Based on multi-scale spatial features, construct a multi-scale feature matrix and perform Z-Score standardization; use principal component analysis to reduce the dimensionality of the multi-scale feature matrix according to the cumulative variance contribution rate threshold to obtain low-dimensional spatial features, and splice them with the external load parameters of the working condition and the displacement information of key control points to establish a gradient boosting decision tree surrogate model based on LightGBM, and output the displacement prediction values ​​of all nodes in the structure.

2. The displacement field prediction method integrating multi-scale features and relative distance encoding according to claim 1, characterized in that, Step S1 includes: Based on the axis-aligned bounding box, the geometric boundaries of the mechanical structure to be predicted along the three coordinate axes are determined, the shortest Euclidean distance from each mesh node in the mechanical structure to the six boundary surfaces of the bounding box is calculated, and the macroscopic boundary constraint features are constructed by combining the normalized spatial coordinates. The K-nearest neighbor algorithm is used to search the local neighborhood point set of each node, construct the covariance matrix and perform singular value decomposition to extract local surface curvature features; The cKDTree spatial index is used to retrieve the nearest control point and local neighborhood node of each node, and the relative position vector and Euclidean distance are calculated to construct the relative distance encoding feature; The multi-scale spatial feature extraction relies solely on the geometric priors and load conditions of the mechanical structure to be predicted, without involving any displacement information.

3. The displacement field prediction method integrating multi-scale features and relative distance encoding according to claim 2, characterized in that, Step S1 also includes: The construction of the macroscopic boundary constraint features includes: Let the set of all grid nodes be ,in The total number of grid nodes is given by the following formula: (The formula is missing from the original text) The structure is determined based on the axis-aligned bounding box. Geometric boundaries of the three coordinate axes , and For any node The shortest Euclidean distance from it to the six boundary faces of the bounding box The calculation formula is: Globally normalize the absolute 3D coordinates of the nodes to obtain normalized spatial coordinate features: Normalized spatial coordinate features and shortest Euclidean distance This refers to the macroscopic boundary constraint characteristic; The extraction of the local surface curvature features includes: For any node The K-nearest neighbor algorithm is used to search for the nearest neighbor in three-dimensional space. Each set of neighboring nodes constitutes a local neighborhood node set. ; Calculate the coordinates of the geometric center of the neighborhood : Based on the spatial offset vectors of each node in the neighborhood relative to the geometric center, construct covariance matrix : in Indicates transpose; For covariance matrix Perform singular value decomposition to obtain three non-negative eigenvalues. These parameters reflect the spatial dispersion of the neighborhood point cloud along three principal directions; surface curvature indices are used. Characterizing local geometric complexity: Curvature index The range of values ​​is That is, the local surface curvature characteristics; The construction of the relative distance encoded features includes: The control point set is established using the cKDTree algorithm. A hierarchical spatial binary tree index structure; for any grid node Use cKDTree to retrieve its nearest neighbor control points Calculate the three-dimensional relative position vector between the two. Euclidean distance : in, Number of control points; Further node search using cKDTree In three-dimensional space Find the nearest neighbor nodes and calculate the distance from the node to each neighbor node. Relative position vector: in, For RDE neighborhood parameters, relative position vector That is, relative distance encoding features.

4. The displacement field prediction method integrating multi-scale features and relative distance encoding according to claim 1, characterized in that, Step S2 includes: Set boundary distance judgment threshold For each node When its distance to the shortest boundary of the bounding box When this happens, the node is determined to be a boundary node and added to the boundary node set. ; Based on the local surface curvature characteristics of each node Construct normalized curvature weights: in, This is the weighting adjustment coefficient. and These represent the maximum and minimum values ​​of curvature for all nodes globally; For the set of boundary nodes For nodes, an additional boundary enhancement coefficient is introduced. Differentiated comprehensive sampling weights are formed: when hour, ,in The typical value is 1.5; when hour, ; Initialize the set of sampled control points Empty, from the set of boundary nodes The node with the highest curvature value is selected as the seed control point and added to the set. In each subsequent iteration, for all unsampled nodes Calculate its distance to the current set of sampled control points. Minimum Euclidean spatial distance between all control points: in, Represents the set of currently sampled control points Any control point in the system; Introducing the comprehensive sampling weight Calculate the weighted distance and select the node that maximizes it as the next control point: Will join in Repeat in a loop until The number of control points in the system has reached the preset target value. .

5. The displacement field prediction method integrating multi-scale features and relative distance encoding according to claim 1, characterized in that, Step S3 includes: The training set feature matrix and the test set feature matrix are obtained by partitioning the multi-scale feature matrix. Calculate the mean for each dimension of the feature matrix of the training set. with standard deviation Perform Z-Score normalization transformation: To unify all features to a standard distribution with zero mean and unit variance; Principal component analysis was performed on the standardized training set feature matrix, and a cumulative variance contribution rate threshold was set. : Before keeping One principal component; Obtain the external load parameters of the working condition; Obtain displacement information of key control points; The low-dimensional spatial features after dimensionality reduction by principal component analysis are combined with the external load parameters of the working condition and the displacement information of key control points to form the final input feature vector, and a gradient boosting decision tree surrogate model based on LightGBM is established. The hyperparameters of the LightGBM model are configured as follows: number of leaf nodes. Learning rate Maximum number of iterations The objective function is L2 regression loss.

6. The displacement field prediction method integrating multi-scale features and relative distance encoding according to claim 5, characterized in that, Step S3 also includes: The prediction accuracy of the gradient boosting decision tree surrogate model is evaluated using the coefficient of determination. Root mean square error and average relative error As an indicator.

7. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform the displacement field prediction method that integrates multi-scale features and relative distance coding as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the displacement field prediction method as described in any one of claims 1-6, which integrates multi-scale features and relative distance coding.

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