Adaptive sampling method for CAE (Computer Aided Engineering) agent model of numerical control machine tool for network topology reconstruction

Abstract

The invention discloses a network topology reconstruction-based adaptive sampling method for a CAE (Computer Aided Engineering) agent model of a numerical control machine tool, and relates to the research field of sampling methods for agent models in multi-dimensional complex scenes such as the numerical control machine tool. S12, a sample point preprocessing and validity checking stage; s2, a network topology construction stage; s23, a network topology validity verification and weight normalization stage; s3, a topology reconstruction stage; and S4, a dynamic optimization stage. According to the network topology reconstruction-based adaptive sampling method for the CAE agent model of the numerically-controlled machine tool, a sampling process is converted into a dynamic network reconstruction process, power-law distribution, small-world effect and scale invariance characteristics in a complex network theory are fused, system key information is captured by using a network topology structure, and global search capability of a simulated annealing algorithm is combined, so that the network topology reconstruction-based adaptive sampling method for the CAE agent model of the numerically-controlled machine tool is realized. The adaptive optimization distribution of sampling points is realized, the coverage rate and representativeness of samples to different working condition characteristics are improved, and high-quality training data are provided for a numerical control machine tool CAE agent model.

Description

Technical Field

[0001] This invention relates to the field of research on proxy model sampling methods for multi-dimensional complex scenarios such as CNC machine tools, specifically an adaptive sampling method for CNC machine tool CAE proxy models based on network topology reconstruction. Background Technology

[0002] As a typical complex mechatronic system, CNC machine tools require the integration of multiple dimensions of variables, such as temperature, cutting load, spindle speed, tool type, and specimen material, in their CAE surrogate model construction. The strong coupling between these variables constitutes a typical high-dimensional sampling scenario. The prediction accuracy and generalization performance of the surrogate model directly depend on the quality of the initial sampling points. High-quality sampling needs to comprehensively cover the characteristics of different working conditions to ensure that the neural network can learn the complete dynamic characteristics of the system.

[0003] Existing sampling methods have significant limitations: random sampling easily leads to uneven point distribution, failing to effectively cover key regions in high-dimensional space and resulting in the loss of important operational information; uniform grid sampling is affected by the curse of dimensionality, with the number of sampling points increasing exponentially with the dimension, leading to a surge in computational costs and making it difficult to apply to practical engineering. Latin hypercube sampling, due to the limitation of hierarchical orthogonal arrangement, may not be able to fully explore the boundary regions of high-dimensional space. Especially in highly nonlinear problems, the presence of multiple extrema and saddle points leads to large differences in local information of the sampled data, creating blank information regions and seriously affecting the prediction accuracy of the surrogate model.

[0004] All of the above methods ignore the inherent structural characteristics of the system and fail to consider the concentration of key information brought about by the coupling relationship of variables. The sampling points are difficult to capture the dynamic essence of the system and the working condition transformation mechanism, which ultimately leads to the weak generalization ability of the CAE proxy model and its inability to adapt to the prediction needs of complex processing scenarios.

[0005] The power-law distribution, small-world effect, and scale invariance revealed by complex network theory offer new insights for solving this problem: the power-law distribution indicates that key system information is concentrated in a few pivot nodes; the small-world effect can reduce the number of sampling points while ensuring coverage; and scale invariance supports sampling consistency across different operating scales. Therefore, this invention proposes an adaptive sampling method for CNC machine tool CAE proxy models based on network topology reconstruction that can perceive system structural characteristics. By dynamically adjusting the sampling distribution, it overcomes the limitations of traditional methods and provides high-quality data support for CNC machine tool CAE proxy models. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive sampling method for CNC machine tool CAE proxy models in network topology reconstruction, to solve the technical problems of low sampling quality and insufficient generalization of existing CNC machine tool CAE proxy model sampling methods in the background art. Specifically, these problems include: uneven distribution of sampling points leading to missing coverage of key areas; failure to consider variable coupling relationships, resulting in poor sample representativeness; difficulty in balancing sampling efficiency and computational cost; and easy getting trapped in local optima in high-dimensional space, failing to capture the global features of the system.

[0007] To achieve the above objectives, the present invention provides the following technical solution: an adaptive sampling method for a CNC machine tool CAE proxy model of network topology reconstruction, comprising the following steps: S1. Initial uniform sampling stage: Define the input variables and value range of the CNC machine tool CAE proxy model, construct a high-dimensional sampling space Ω, and use Latin hypercube sampling to generate the initial sample point set X0; S12, Sample point preprocessing and validity verification stage: Preprocess and verify the validity of the initial sample point set X0 to eliminate outliers and dimensional interference, and provide a reliable data foundation for network topology construction; S2. Network topology construction stage: Calculate the Euclidean distance between sample points in X0, and construct a weighted undirected graph G=(V,E) with sample points as nodes and Euclidean distance as edge weights. S23. Network topology validity verification and weight normalization stage: Connectivity verification and edge weight normalization are performed on the weighted undirected graph G to ensure the accuracy and comparability of node centrality calculation. S3. Topology Reconstruction Stage: Calculate the betweenness centrality and compact centrality of nodes, evaluate the importance of nodes by combining the information entropy of the sample point set, apply Gaussian perturbation to non-critical nodes (the perturbation amplitude is negatively correlated with the importance of nodes), and generate a temporary sample point set X1. S34. Temporary Sample Point Set Feasibility Screening and Boundary Constraint Stage: Perform boundary verification and feasibility screening on the temporary sample point set X1, remove invalid sample points and supplement compliant candidate points to ensure the validity of inputs in the dynamic optimization stage. S4. Dynamic Optimization Stage: An improved simulated annealing algorithm is adopted, with "maximizing minimum distance + information entropy constraint" as the objective function, to iteratively optimize X1 and output the optimal sample point set X. * .

[0008] In this embodiment, the input variables in S1 include spindle speed, cutting load, feed rate, ambient temperature, tool type, and specimen material. Discrete variables are converted into continuous dimensions through one-hot encoding to determine the sampling space and parameters: based on the variables such as temperature, cutting load, spindle speed, tool type, and specimen material involved in the CNC machine tool CAE proxy model, the value range of each variable is determined, a high-dimensional sampling space Ω is constructed, and the expected number of samples n is set. Perform sampling operation: The Latin hypercube sampling method is adopted to generate an initial sample point set X0 in the sampling space Ω, ensuring that the initial sample points are evenly distributed in all dimensions, laying the foundation for subsequent sampling optimization and avoiding sample distribution imbalance in the initial stage.

[0009] In this embodiment, the specific operations of step S12, sample point preprocessing and validity verification, are as follows: ①Outlier removal: using The criteria identify outliers in each dimension of the initial sample point set X0 (i.e., sample points that exceed the mean ± 3 standard deviations). Outliers are corrected using the "nearest sample mean replacement method". If the proportion of outliers exceeds 5%, the Latin hypercube sampling of S1 is re-executed. ② Dimensional Normalization: For input variables with different dimensions (such as spindle speed in r / min and cutting load in kN), min-max normalization is used to map the sample values ​​of each dimension to the [0,1] interval. The formula is as follows: , in, For the original value of a certain dimension of the sample points, These are the minimum and maximum values ​​for that dimension, respectively. The value is the normalized value; ③ Validity Verification: Verify whether the normalized sample point set completely covers the core value range of each variable (e.g., spindle speed of 500-6000 r / min corresponds to 0-1 after normalization). If there is insufficient dimensional coverage, supplement the sampling until the coverage is ≥95%, and finally output the preprocessed valid sample point set. , which serves as the input to S2.

[0010] In this embodiment, the specific operations of S2, the network topology construction stage, are as follows: Calculate the distance between sample points: For any two sample points in the initial sample point set X0 Calculate the Euclidean distance between them using the following formula: , .

[0011] Constructing a weighted undirected graph: Based on the Euclidean distance between any two points in the initial sample point set X0, construct a weighted undirected graph G=(V,E), where the node set V corresponds to the sample point set X0, and the edge set E contains the weights. Define as a node and The Euclidean distance between the sample points is used as a weight to reflect the relative distance between them, providing a data foundation for subsequent topological analysis.

[0012] In this embodiment, the specific operations of step S23, network topology validity verification and weight normalization, are as follows: ①Topological connectivity verification: Traverse all nodes of the weighted undirected graph G and check whether there are isolated nodes (i.e., nodes without any edge connections). If there are isolated nodes, calculate the Euclidean distance between the node and the nearest node, add an edge with a weight equal to that distance, and ensure that G is a connected graph. ②Edge weight normalization: normalize the weights of edge set E. The Euclidean distance is normalized to the [0,1] interval to eliminate the influence of differences in absolute distance values ​​on centrality calculation. The formula is as follows: ; , .

[0013] ③ Topology rationality check: Calculate the average clustering coefficient and average path length of G. If the average clustering coefficient is <0.1 or the average path length is >5 times the dimension, the topology is determined to be unreasonable. Return to S2 to recalculate the Euclidean distance (the distance calculation method can be adjusted to Mahalanobis distance). Otherwise, output the normalized weighted undirected graph G'=(V,E') as the input of S3.

[0014] In this embodiment, the specific operations of the topology reconstruction stage S3 are as follows: ① Calculate the node centrality index: Calculate the betweenness centrality of each node. With tight centrality , , in, Represents a node Betweenness centrality; and They are any two distinct nodes in the network, and and None of them equal ; From node To the node The total number of shortest paths; From node To the node And passing through nodes The number of shortest paths; , in, Represents a node The close centrality; In addition to the network Any node other than; It is a node arrive The shortest path length.

[0015] Betweenness centrality reflects the importance of a node as a bridge in a network, while compact centrality measures how close a node is to all other nodes. By combining these two centrality indicators, sampling points that play a key role in the network topology can be identified and their positions can be adjusted accordingly.

[0016] ② Calculate the sample point set The information entropy H is assigned information entropy weights based on the distribution characteristics of each dimension. ③ Combine betweenness centrality, compact centrality, and information entropy weights to evaluate node importance. Based on the node importance evaluation results, apply Gaussian perturbations to non-critical nodes (i.e., nodes with relatively low importance) to generate candidate points. The perturbation amplitude is negatively correlated with node importance; that is, the higher the importance of a node, the smaller the perturbation amplitude is applied to avoid disrupting the global structure of the network. Nodes with lower importance can accept larger perturbations to promote their movement to better positions. This operation forms a temporary sample point set. Preliminary optimization of sample point distribution.

[0017] In this embodiment, the steps of S34, the feasibility screening and boundary constraint stage of temporary sample point set, are as follows: ① Boundary check: Traverse the temporary sample point set For all sample points, verify whether the values ​​of each dimension of each sample point are within the range of variable values ​​set by S1 (i.e., whether they belong to the high-dimensional sampling space Ω). If any dimension of a sample point exceeds the range, it is marked as an invalid point. ② Invalid point replacement: Invalid points are replaced by the "nearest valid point Gaussian fine-tuning method" - select the 3 valid points that are closest to the invalid point in Euclidean distance, calculate their mean, apply a small Gaussian perturbation (perturbation amplitude ≤ 0.05) on the basis of the mean to generate new sample points, and ensure that the new sample points fall within Ω; ③ Feasibility verification: Calculate the replacement The dimensional coverage (the percentage of each dimension's value range covered) is calculated. If the coverage is less than 90%, supplementary sampling is performed on the uncovered intervals (5%-10% of the total number of samples). The final output is a compliant temporary sample point set. , as the input of S4.

[0018] In this embodiment, the specific operations of S4, the dynamic optimization stage, are as follows: ① Define the objective function: Form a temporary sample point set from the temporary sample point set. To optimize the algorithm, an improved simulated annealing algorithm was designed as the outer framework. This algorithm controls whether to accept candidate solutions after perturbation. Based on the principle of "maximizing minimum distance," it ensures that the sampling points are as dispersed as possible. The optimization objective is to maximize the minimum distance between sampling points. The core idea of ​​the algorithm is to gradually adjust the position of the sampling points by introducing random perturbation and a probability acceptance mechanism. The objective function aims to maximize the distance between sampling points while ensuring a uniform distribution of sampling points. The objective function is designed as follows: , in, It is a set of sampling points; Sampling points and The Euclidean distance between them; It is a balancing parameter used to control information entropy. The weight.

[0019] The iterative process generates a new set of sampling points by adding random perturbations to the current set of sampling points, and selects the set that maximizes the objective function value as the next generation of sampling point set. The iterative process is as follows: , It is the next generation of sampling point set; It is the current set of sampling points; The mean of the appendages is 0, and the variance is... Random perturbations that follow a normal distribution; It is the current temperature, which controls the amplitude of random disturbances; It is the temperature decay factor, usually set to 0.95, used for dynamically adjusting the temperature.

[0020] ② Improved simulated annealing algorithm optimization: Initialization parameters: Initial temperature =1.0, temperature decay factor α=0.95, number of iterations k, global optimization is achieved through the probability acceptance criterion; Generate candidate solutions: for temporary sample point sets Add a random perturbation (following a normal distribution with mean 0 and variance σ²) to obtain the candidate sample point set X' = X1 + Δ, where Δ is the random perturbation; Acceptance criterion: Calculate the difference in objective function between the candidate solution and the current solution, Δf = f(X') - f(X). 1） If Δf>0, the candidate solution is accepted; if Δf≤0, the candidate solution is accepted with probability P=exp(Δf / T). Temperature decay: After each iteration, the temperature is updated according to T=α×T to reduce the perturbation amplitude; Convergence Output: Iterate until the temperature is below the threshold or the maximum number of iterations is reached, then output the optimal sample point set X. * .

[0021] The initial temperature is set to 1.0. After each iteration, the temperature is gradually decreased by an exponential decay factor of 0.95. In each iteration, the algorithm generates candidate solutions and decides whether to accept a new solution based on a set acceptance criterion. According to the probabilistic acceptance criterion of the simulated annealing algorithm, even if the objective function value of a candidate solution is worse than the current solution, it still has a probability of being accepted. This helps the algorithm escape local optima. The specific method of dynamic temperature adjustment is: based on the temperature decay factor... Dynamically adjust temperature As the iterations proceed, the temperature gradually decreases, and the amplitude of the random perturbation gradually decreases. In the early stage of the iteration, the perturbation amplitude is 0.1-0.5, and in the later stage of the iteration, it is 0.01-0.05. The algorithm gradually converges to the optimal solution.

[0022] Compared with the prior art, the beneficial effects of the present invention are: This adaptive sampling method for CNC machine tool CAE surrogate models, based on network topology reconstruction, transforms the sampling process into a dynamic network reconstruction process. By integrating the power-law distribution, small-world effect, and scale invariance properties from complex network theory, it captures key system information using network topology and combines the global search capability of simulated annealing algorithm to achieve adaptive optimization distribution of sampling points. This improves the coverage and representativeness of samples for different working conditions, providing high-quality training data for CNC machine tool CAE surrogate models.

[0023] 1. Transforming high-dimensional sampling into dynamic network reconstruction: Breaking through the traditional "static coordinate sampling" mindset, this paper defines for the first time the sampling process of constructing a CAE proxy model for CNC machine tools as a dynamic reconstruction process of a weighted undirected graph. Sampling points are not only spatial coordinates, but also network nodes with "importance assessment" and "self-adjustment capabilities". By capturing the internal structure of the system through network topology features (betweenness centrality and tight centrality), and by using the power-law distribution characteristics of complex networks to locate high-information-value areas, this paper solves the problems of traditional sampling neglecting variable coupling relationships and insufficient capture of key information, and realizes intelligent adaptation of sampling to follow the system structure.

[0024] 2. Multi-factor fusion mechanism for node importance assessment: A node importance assessment model combining betweenness centrality, tight centrality, and information entropy is designed to achieve a sampling balance between "global coverage" and "local accuracy," resolving the contradiction between "uniformity and representativeness" in traditional sampling. Multi-factor node importance assessment and "minimum distance maximization" optimization ensure uniform sample distribution and reflect variable coupling relationships, improving the prediction accuracy of the surrogate model by more than 25%.

[0025] 3. Adaptive control strategy for perturbation amplitude: To address the problem that high-dimensional space sampling is prone to destroying the global structure or getting trapped in local optima, a "node importance-perturbation amplitude negative correlation" mechanism is designed: small-amplitude Gaussian perturbation is applied to hub nodes with high importance (to avoid destroying key information of the system), and large-amplitude perturbation is applied to redundant nodes with low importance (to promote migration to information sparse regions). This strategy preserves the stability of the global sampling structure and enhances the local exploration capability, balancing the efficiency of sampling "development" (optimizing existing regions) and "exploration" (expanding new regions).

[0026] 4. Improved simulated annealing objective function and convergence mechanism: In the early stage of iteration, a large perturbation is applied to help the algorithm escape local optima and explore more potential high-quality regions. In the later stage of iteration, a small perturbation is applied to only the sample points for local fine-tuning, which promotes accurate convergence of the algorithm. The composite mechanism retains the "static constraint" of node importance on the perturbation (avoiding damage to key nodes) and achieves "dynamic adaptation" of the perturbation through temperature (matching the algorithm's convergence requirements), ultimately generating a high-quality sample point set.

[0027] 5. Relying on the small-world effect of complex networks, redundant sampling points are reduced while ensuring coverage. Compared with uniform grid sampling, the number of samples is reduced by more than 40%, and the computational efficiency is significantly improved. At the same time, it has generalization and adaptability capabilities, and scale invariance supports sampling consistency across working conditions. It can adapt to the construction of CAE proxy models for different specifications of CNC machine tools and different processing conditions, and has strong versatility. Attached Figure Description

[0028] Figure 1 This is a step diagram of the adaptive sampling method for CNC machine tool CAE proxy model network topology reconstruction according to the present invention; Figure 2 This is a schematic diagram of the simulated annealing optimization algorithm of the present invention; Figure 3 This is a schematic diagram of the initial uniform sampling stage of the present invention; Figure 4 This is a schematic diagram of the sample point preprocessing and validity verification stages of the present invention; Figure 5 This is a schematic diagram of the network topology construction stage of the present invention; Figure 6This is a schematic diagram of the network topology validity verification and weight normalization stage of the present invention; Figure 7 This is a schematic diagram of the topology reconstruction stage of the present invention; Figure 8 This is a schematic diagram of the feasibility screening and boundary constraint stage of the temporary sample point set in this invention; Figure 9 This is a schematic diagram of the dynamic optimization stage of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0030] This invention provides an adaptive sampling method for CNC machine tool CAE proxy models in network topology reconstruction. Its core involves: an initial uniform sampling stage: defining the input variables and their value ranges of the CNC machine tool CAE proxy model, constructing a high-dimensional sampling space Ω, and generating an initial sample point set X0 using Latin hypercube sampling; a sample point preprocessing and validity verification stage: preprocessing and validating the initial sample point set X0 to eliminate outliers and dimensional interference, providing a reliable data foundation for network topology construction; a network topology construction stage: calculating the Euclidean distance between sample points in X0, using sample points as nodes and Euclidean distances as edge weights to construct a weighted undirected graph G=(V,E); a network topology validity verification and weight normalization stage: verifying the connectivity of the weighted undirected graph G and normalizing the edge weights to ensure the accuracy and comparability of node centrality calculations; and a topology reconstruction stage: calculating the betweenness centrality and compact centrality of nodes, evaluating node importance based on the information entropy of the sample point set, applying Gaussian perturbations to non-critical nodes (the perturbation amplitude is negatively correlated with node importance), and generating a temporary sample point set X. 1； Temporary sample point set feasibility screening and boundary constraint stage: Boundary verification and feasibility screening are performed on the temporary sample point set X1, invalid sample points are removed and compliant candidate points are added to ensure the validity of the input in the dynamic optimization stage; Dynamic optimization stage: An improved simulated annealing algorithm is used, with "maximizing minimum distance + information entropy constraint" as the objective function, to iteratively optimize X1 and output the optimal sample point set X. *The sampling process is transformed into a dynamic network reconstruction process. By integrating the power-law distribution, small-world effect, and scale invariance properties from complex network theory, and utilizing the network topology to capture key system information, combined with the global search capability of the simulated annealing algorithm, adaptive optimization distribution of sampling points is achieved. This improves the coverage and representativeness of samples for different working conditions, providing high-quality training data for CNC machine tool CAE proxy models.

[0031] Example 1: To better understand the above technical solution, the following will provide a detailed description of the technical solution in conjunction with the accompanying drawings and specific implementation methods. (Refer to...) Figure 1 and Figure 2 As shown, Figure 1 This is a schematic diagram of the adaptive sampling method for CNC machine tool CAE proxy model in network topology reconstruction. Figure 2 This is a flowchart of the simulated annealing optimization algorithm. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction includes the following steps: In step S1, the initial uniform sampling stage: the input variables and their value ranges of the CNC machine tool CAE proxy model are defined, a high-dimensional sampling space Ω is constructed, and the initial sample point set X0 is generated by Latin hypercube sampling.

[0032] refer to Figure 3 As shown in the figure, this is a schematic diagram of the initial uniform sampling stage. In specific implementation, the input variables in S1 include spindle speed, cutting load, feed rate, ambient temperature, tool type, and specimen material. Discrete variables are converted into continuous dimensions through one-hot encoding to determine the sampling space and parameters: Based on the variables such as temperature, cutting load, spindle speed, tool type, and specimen material involved in the CNC machine tool CAE proxy model, the value range of each variable is clarified, a high-dimensional sampling space Ω is constructed, and the expected sampling number n is set; Sampling operation is performed: The Latin hypercube sampling method is used to generate an initial sample point set X0 in the sampling space Ω to ensure that the initial sample points are uniformly distributed in all dimensions, laying the foundation for subsequent sampling optimization and avoiding sample distribution imbalance in the initial stage.

[0033] It should be noted that in step S1, the core of the initial uniform sampling stage is to build a high-dimensional sampling framework that fits the actual machining scenario, providing accurate and comprehensive basic data for subsequent topology reconstruction. When defining the input variables, in addition to defining the value range of continuous variables such as spindle speed (500-6000 r / min) and cutting load (0.5-5 kN), for the two discrete variables, tool type (1-4 codes) and workpiece material (1-3 codes), one-hot encoding is used for dimensional expansion: tool type is converted into 4 binary dimensions (e.g., code 1 corresponds to [1,0,0,0]), and workpiece material is converted into 3 binary dimensions (e.g., code 1 corresponds to [1,0,0]), ultimately expanding the original 6 basic variables into a 9-dimensional continuous space, ensuring that the features of discrete variables can be fully captured by the sampling process; When performing Latin hypercube sampling, each dimension of the 9-dimensional sampling space is first divided into 200 equally probable intervals (matching the expected sampling number n=200). Then, a sample point is randomly selected from different intervals in each dimension to ensure that the 200 sample points do not have overlapping interval coverage in the 9 dimensions. This achieves uniform distribution in each dimension and covers the coupling relationship of different working conditions through cross-dimensional random combination. It effectively avoids the problem of local density and incomplete global coverage that is prone to occur in traditional uniform sampling in high-dimensional space, and provides initial data support with balanced distribution and comprehensive working conditions for subsequent network topology construction.

[0034] In step S12, the sample point preprocessing and validity verification stage is performed: the initial sample point set X0 is preprocessed and its validity is verified to eliminate outliers and dimensional interference, providing a reliable data foundation for network topology construction.

[0035] refer to Figure 4 As shown in the figure, this is a schematic diagram of the sample point preprocessing and validity verification stages. In practice, the specific operations of the sample point preprocessing and validity verification steps are as follows: ①Outlier removal: using The criteria identify outliers in each dimension of the initial sample point set X0 (i.e., sample points that exceed the mean ± 3 standard deviations). Outliers are corrected using the "nearest sample mean replacement method". If the proportion of outliers exceeds 5%, the Latin hypercube sampling of S1 is re-executed. ② Dimensional Normalization: For input variables with different dimensions (such as spindle speed in r / min and cutting load in kN), min-max normalization is used to map the sample values ​​of each dimension to the [0,1] interval. The formula is as follows: , in, For the original value of a certain dimension of the sample points, These are the minimum and maximum values ​​for that dimension, respectively. The value is the normalized value; ③ Validity Verification: Verify whether the normalized sample point set completely covers the core value range of each variable (e.g., spindle speed of 500-6000 r / min corresponds to 0-1 after normalization). If there is insufficient dimensional coverage, supplement the sampling until the coverage is ≥95%, and finally output the preprocessed valid sample point set. , which serves as the input to S2.

[0036] It should be noted that in the outlier removal process, the "nearest neighbor mean replacement method" specifically calculates the mean of the five nearest valid sample points to the outlier in the 9-dimensional space and replaces the outlier with this mean. This avoids the sample size reduction caused by direct deletion and maximizes the fit with local data distribution characteristics. Furthermore, when determining the proportion of outliers, statistics are calculated on a single dimension basis (e.g., number of outliers in the spindle speed dimension / total number of samples in that dimension). If the proportion of outliers in any dimension exceeds 5%, resampling is triggered to ensure the reliability of data in each dimension and prevent local dimensional anomalies from affecting the overall topology construction.

[0037] During dimensional normalization, for binary dimensions after one-hot encoding (such as the four dimensions of tool type conversion), the original values ​​are only 0 or 1. After normalization, the original values ​​remain unchanged, requiring no additional mapping calculations. However, continuous dimensions such as spindle speed and cutting load are strictly executed according to the formula to ensure that all dimension data are on the same order of magnitude. In the validity verification stage, the "interval segmented verification" method is adopted, dividing the core value interval of each variable into 10 segments on average. If there are no sample points in a certain segment, it is determined that the coverage is insufficient. During supplementary sampling, new sample points are generated first in the blank segment until all segments are covered by samples, ultimately meeting the requirement of coverage ≥95%.

[0038] In step S2, the network topology construction stage: calculate the Euclidean distance between sample points in X0, and construct a weighted undirected graph G=(V,E) with sample points as nodes and Euclidean distance as edge weights.

[0039] refer to Figure 5 As shown in the diagram, this is a schematic diagram of the network topology construction phase. In practice, the specific operations of the network topology construction phase are as follows: Calculate the distance between sample points: For any two sample points in the initial sample point set X0 Calculate the Euclidean distance between them using the following formula: , .

[0040] Constructing a weighted undirected graph: Based on the Euclidean distance between any two points in the initial sample point set X0, construct a weighted undirected graph G=(V,E), where the node set V corresponds to the sample point set X0, and the edge set E contains the weights. Define as a node and The Euclidean distance between the sample points is used as a weight to reflect the relative distance between them, providing a data foundation for subsequent topological analysis.

[0041] It should be noted that when calculating the Euclidean distance between sample points, the calculation is based on the preprocessed 9-dimensional data. Each sample point participates in the calculation as a 9-dimensional vector. (The formula is incomplete in the original text.) , Corresponding to sample points To improve computational efficiency, the normalized value in the k-th dimension (k=1 to 9, including the original continuous dimension and the one-hot encoded dimension) is processed by matrix operations to batch process the pairwise distances of 200 sample points. By constructing a 200×9 sample matrix, a 200×200 distance matrix is ​​generated in batch using vector operation formulas, and the Euclidean distance results of all sample point pairs are directly output, avoiding redundant operations of calculating each pair one by one.

[0042] When constructing the weighted undirected graph, the node set V contains 200 sample points, with each node corresponding to a complete set of 9-dimensional working condition data; the edge set E is constructed using a "fully connected" approach, meaning that there is an edge between any two nodes, and the weight of each edge is specified. We directly use the corresponding Euclidean distance values. At the same time, for ease of subsequent topology analysis, we perform symmetry processing on the distance matrix (ensuring...). = The weighted undirected graph is then processed by removing the distance values ​​of the nodes themselves (setting the diagonal elements to 0). This process preserves the spatial relationships between the sample points and quantifies the strength of these relationships through weights, providing accurate topological data support for node centrality assessment.

[0043] In step S23, the network topology validity verification and weight normalization stage: the connectivity of the weighted undirected graph G is verified and the edge weights are normalized to ensure the accuracy and comparability of the node centrality calculation.

[0044] refer to Figure 6 As shown in the diagram, this is a schematic diagram of the network topology validity verification and weight normalization stage. In specific implementation, the specific operations of the network topology validity verification and weight normalization steps are as follows: ①Topological connectivity verification: Traverse all nodes of the weighted undirected graph G and check whether there are isolated nodes (i.e., nodes without any edge connections). If there are isolated nodes, calculate the Euclidean distance between the node and the nearest node, add an edge with a weight equal to that distance, and ensure that G is a connected graph. ②Edge weight normalization: normalize the weights of edge set E. The Euclidean distance is normalized to the [0,1] interval to eliminate the influence of differences in absolute distance values ​​on centrality calculation. The formula is as follows: , , .

[0045] ③ Topology rationality check: Calculate the average clustering coefficient and average path length of G. If the average clustering coefficient is <0.1 or the average path length is >5 times the dimension, the topology is determined to be unreasonable. Return to S2 to recalculate the Euclidean distance (the distance calculation method can be adjusted to Mahalanobis distance). Otherwise, output the normalized weighted undirected graph G'=(V,E') as the input of S3.

[0046] It should be noted that in the topology connectivity verification, for a fully connected graph with 200 nodes, isolated nodes are identified by traversing the row vectors of the distance matrix. If all edge weights of a node are 0 (no effective connection except for itself), it is determined to be an isolated node. In this case, the minimum Euclidean distance between the node and all other nodes is located through the distance matrix, and connecting edges are added with this minimum value as the weight. This ensures the connectivity of the graph without destroying the real spatial relationship between sample points. When verifying the rationality of the topology, a 5x dimension is calculated as 45 in a 9-dimensional sampling space. If the average clustering coefficient is lower than 0.1, it indicates that the relationship between nodes is too sparse and cannot effectively capture the coupling relationship of the working conditions. If the average path length exceeds 45, it indicates that the information transmission efficiency between nodes is too low, and it is necessary to switch to Mahalanobis distance for recalculation (Mahalanobis distance can eliminate the interference of correlation between variables) to ensure that the topology structure can reflect the inherent characteristics of the system. When normalizing edge weights, first extract all off-diagonal elements (i.e., effective edge weights) from the 200×200 distance matrix, and then filter out the maximum value (max). ), and then through the formula The weights of each edge are mapped one by one. For the distance component contributed by the one-hot encoding dimension, the calculation logic is consistent with that of the continuous dimensions during the normalization process to ensure that the influence of all dimensions on the weights is balanced. After normalization, the smaller the edge weight, the higher the similarity of the working conditions between sample points, and the larger the edge weight, the more significant the difference in working conditions. This provides a unified quantitative basis for subsequent node centrality calculation and avoids evaluation bias caused by differences in the original distance units.

[0047] In step 3, the topology reconstruction stage: calculate the betweenness centrality and tight centrality of the nodes, evaluate the importance of the nodes by combining the information entropy of the sample point set, apply Gaussian perturbation to non-critical nodes (the perturbation amplitude is negatively correlated with the importance of the nodes), and generate a temporary sample point set X1.

[0048] refer to Figure 7 As shown in the diagram, this is a schematic diagram of the topology reconfiguration phase. In practice, the specific operations of the topology reconfiguration phase are as follows: ① Calculate the node centrality index: Calculate the betweenness centrality of each node. With tight centrality , , in, Represents a node Betweenness centrality; and They are any two distinct nodes in the network, and and None of them equal ; From node To the node The total number of shortest paths; From node To the node And passing through nodes The number of shortest paths; , in, Represents a node The close centrality; In addition to the network Any node other than; It is a node arrive The shortest path length.

[0049] Betweenness centrality reflects the importance of a node as a bridge in a network, while compact centrality measures how close a node is to all other nodes. By combining these two centrality indicators, sampling points that play a key role in the network topology can be identified and their positions can be adjusted accordingly.

[0050] ② Calculate the sample point set The information entropy H is assigned information entropy weights based on the distribution characteristics of each dimension. ③ Combine betweenness centrality, compact centrality, and information entropy weights to evaluate node importance. Based on the node importance evaluation results, apply Gaussian perturbations to non-critical nodes (i.e., nodes with relatively low importance) to generate candidate points. The perturbation amplitude is negatively correlated with node importance; that is, the higher the importance of a node, the smaller the perturbation amplitude is applied to avoid disrupting the global structure of the network. Nodes with lower importance can accept larger perturbations to promote their movement to better positions. This operation forms a temporary sample point set. Preliminary optimization of sample point distribution.

[0051] It should be noted that when calculating the node centrality index, based on the normalized weighted undirected graph G', the shortest path algorithm is used to solve for the shortest path between any two nodes. Since the edge weights have been normalized, the path length is directly calculated by accumulating the edge weights. In the betweenness centrality calculation, the percentage of the number of nodes passing through the target node in the shortest path of all node pairs is counted. The higher the percentage, the stronger the "bridging role" of the node in the work condition association. The compact centrality is calculated by taking the reciprocal of the mean of the shortest path lengths from the target node to the other 199 nodes. The smaller the mean and the larger the reciprocal, the stronger the node's coverage of the global work conditions. Both indices are standardized using [0,1] to ensure the rationality of subsequent weight fusion.

[0052] Information entropy calculation is based on a 9-dimensional sample space. First, the frequency distribution of sample values ​​in each dimension is statistically analyzed, and then the information entropy H of each dimension is calculated using the information entropy formula. K The more uniform the dimensional distribution, the better. The larger the value, the richer the operational information contained in that dimension. Weights are then assigned according to the proportion of information entropy in each dimension (e.g., for a certain dimension H). K (If the node accounts for 20% of the total entropy, its weight is 0.2). This weighted sum is then applied to the standardized betweenness centrality and compact centrality in a 3:3:4 ratio to obtain the overall importance score of the node. During Gaussian perturbation, the nodes are divided into three levels based on their scores: the top 30% of nodes are subjected to a small perturbation of 0.01-0.03, the middle 40% are subjected to a medium perturbation of 0.03-0.05, and the bottom 30% of non-critical nodes are subjected to a large perturbation of 0.05-0.08. This ensures that the perturbation does not destroy critical operating condition information while optimizing the distribution of redundant nodes.

[0053] In step S34, the temporary sample point set feasibility screening and boundary constraint stage: boundary verification and feasibility screening are performed on the temporary sample point set X1, invalid sample points are eliminated and compliant candidate points are added to ensure the validity of the input in the dynamic optimization stage.

[0054] refer to Figure 8 As shown in the figure, this is a schematic diagram of the feasibility screening and boundary constraint stage of the temporary sample point set. In specific implementation, the steps of the feasibility screening and boundary constraint stage of the temporary sample point set are as follows: ① Boundary check: Traverse the temporary sample point set For all sample points, verify whether the values ​​of each dimension of each sample point are within the range of variable values ​​set by S1 (i.e., whether they belong to the high-dimensional sampling space Ω). If any dimension of a sample point exceeds the range, it is marked as an invalid point. ② Invalid point replacement: Invalid points are replaced by the "nearest valid point Gaussian fine-tuning method" - select the 3 valid points that are closest to the invalid point in Euclidean distance, calculate their mean, apply a small Gaussian perturbation (perturbation amplitude ≤ 0.05) on the basis of the mean to generate new sample points, and ensure that the new sample points fall within Ω; ③ Feasibility verification: Calculate the replacement The dimensional coverage (the percentage of each dimension's value range covered) is calculated. If the coverage is less than 90%, supplementary sampling is performed on the uncovered intervals (5%-10% of the total number of samples). The final output is a compliant temporary sample point set. , as the input of S4.

[0055] It should be noted that the boundary verification process requires separate verification of the original variable dimensions and the one-hot encoded dimensions: the original continuous variables (spindle speed, cutting load, etc.) need to be verified to see if the normalized values ​​correspond to the physical value range set by S1 (e.g., a normalized spindle speed value of 0 corresponds to 500 r / min, 1 corresponds to 6000 r / min, and values ​​exceeding [0,1] are considered invalid); the one-hot encoded dimensions need to be verified to see if the values ​​are only 0 or 1, and if only one of the encoded dimensions corresponding to the same discrete variable is 1 (e.g., the tool type encoded dimension needs to satisfy that only one dimension is 1, and the rest are 0). Violations are marked as invalid points. When replacing invalid points, the three nearest valid points need to be selected based on the Euclidean distance in 9-dimensional space. The Gaussian perturbation applied after calculating the mean needs to be processed separately for each dimension—the perturbation for the continuous variable dimensions is performed in the normalized space, while no perturbation is applied to the one-hot encoded dimensions (to avoid disrupting the encoding logic of discrete variables). After generating new sample points, it is necessary to verify again whether they meet the boundary requirements to ensure that 100% fall within the sampling space Ω.

[0056] In the feasibility verification, dimensional coverage is calculated separately for each original variable dimension (one-hot encoded dimensions are excluded to avoid duplicate statistics). The value range of each original variable is divided into 10 equidistant sub-intervals according to S1 setting. Coverage = number of sub-intervals with sample points / 10 × 100%. If the coverage of an original variable is less than 90% (i.e., fewer than 9 sub-intervals have samples), supplementary sampling is performed in the blank sub-intervals. The number of supplementary samples is calculated as 5%-10% of the total number of samples (200) (i.e., 10-20). The Latin hypercube sampling logic is used during supplementary sampling to ensure that the new sample points uniformly fill the blank areas, resulting in the final output set of compliant sample points. A sample size of 200 is required to eliminate invalid points, fill blank areas, and preserve the working condition correlation of the original samples through small perturbations, thus providing high-quality input for subsequent dynamic optimization.

[0057] In step S4, an improved simulated annealing algorithm is used, with "maximizing minimum distance + information entropy constraint" as the objective function, to iteratively optimize X1 and output the optimal sample point set X.* .

[0058] refer to Figure 9 As shown in the diagram, this is a schematic diagram of the dynamic optimization stage. In practice, the specific operations of the dynamic optimization stage are as follows: ① Define the objective function: Form a temporary sample point set from the temporary sample point set. To optimize the algorithm, an improved simulated annealing algorithm was designed as the outer framework. This algorithm controls whether to accept candidate solutions after perturbation. Based on the principle of "maximizing minimum distance," it ensures that the sampling points are as dispersed as possible. The optimization objective is to maximize the minimum distance between sampling points. The core idea of ​​the algorithm is to gradually adjust the position of the sampling points by introducing random perturbation and a probability acceptance mechanism. The objective function aims to maximize the distance between sampling points while ensuring a uniform distribution of sampling points. The objective function is designed as follows: , in, It is a set of sampling points; Sampling points and The Euclidean distance between them; It is a balancing parameter used to control information entropy. The weight.

[0059] The iterative process generates a new set of sampling points by adding random perturbations to the current set of sampling points, and selects the set that maximizes the objective function value as the next generation of sampling point set. The iterative process is as follows: , It is the next generation of sampling point set; It is the current set of sampling points; The mean of the appendages is 0, and the variance is... Random perturbations that follow a normal distribution; It is the current temperature, which controls the amplitude of random disturbances; It is the temperature decay factor, usually set to 0.95, used for dynamically adjusting the temperature.

[0060] ② Improved simulated annealing algorithm optimization: Initialization parameters: Initial temperature =1.0, temperature decay factor α=0.95, number of iterations k, global optimization is achieved through the probability acceptance criterion; Generate candidate solutions: for temporary sample point sets Add a random perturbation (following a normal distribution with mean 0 and variance σ²) to obtain the candidate sample point set X' = X1 + Δ, where Δ is the random perturbation; Acceptance criterion: Calculate the difference in objective function between the candidate solution and the current solution, Δf = f(X') - f(X). 1） If Δf>0, the candidate solution is accepted; if Δf≤0, the candidate solution is accepted with probability P=exp(Δf / T). Temperature decay: After each iteration, the temperature is updated according to T=α×T to reduce the perturbation amplitude; Convergence Output: Iterate until the temperature is below the threshold or the maximum number of iterations is reached, then output the optimal sample point set X. * .

[0061] The initial temperature is set to 1.0. After each iteration, the temperature is gradually decreased by an exponential decay factor of 0.95. In each iteration, the algorithm generates candidate solutions and decides whether to accept a new solution based on a set acceptance criterion. According to the probabilistic acceptance criterion of the simulated annealing algorithm, even if the objective function value of a candidate solution is worse than the current solution, it still has a probability of being accepted. This helps the algorithm escape local optima. The specific method of dynamic temperature adjustment is: based on the temperature decay factor... Dynamically adjust temperature As the iterations proceed, the temperature gradually decreases, and the amplitude of the random perturbation gradually decreases. In the early stage of the iteration, the perturbation amplitude is 0.1-0.5, and in the later stage of the iteration, it is 0.01-0.05. The algorithm gradually converges to the optimal solution.

[0062] It should be noted that the objective function parameters and iteration logic are as follows: the balancing parameter λ in the objective function is set to 0.3 (verified through engineering practice, this value can balance sample dispersion and information richness), and the information entropy H is based on a temporary sample point set. The 9-dimensional data calculation follows the same logic as the information entropy calculation in S3, and is used to constrain the operational condition coverage integrity of the sample set. During the iteration process, the variance σ² of the random disturbance Δ is positively correlated with the current temperature T, and the initial temperature... When T = 1.0, σ² = 0.02. As the temperature decays, σ² decreases synchronously with the ratio of T (e.g., when T = 0.5, σ² = 0.01), ensuring that the perturbation amplitude matches the temperature dynamics. At the same time, the one-hot encoding dimension is processed separately during the iteration process—perturbation is only added to the continuous variable dimension, while the one-hot encoding dimension remains unchanged, avoiding the destruction of the working condition characteristics of discrete variables. The algorithm parameters and candidate solution generation details also include: during parameter initialization, the number of iterations k is set to 500 (for a sample size of 200 points, this number can balance optimization efficiency and search effect), and the temperature threshold is set to 0.001 (the algorithm converges when T < 0.001). When generating candidate solutions, random perturbations strictly follow the "dimensional independence" principle: for the normalized values ​​of continuous variables such as spindle speed and cutting load, Δ is randomly added according to a normal distribution; for one-hot encoded dimensions, the encoding validity is only checked after perturbation (ensuring that only one encoded dimension corresponding to the same discrete variable is 1), and if it fails, the perturbation of that dimension is regenerated. In addition, after the candidate solutions are generated, a simple boundary check must be performed first to remove sample points that obviously exceed the Ω range, reducing the redundancy of subsequent acceptance criterion calculations; The acceptance criterion and convergence determination optimization also include: In the acceptance criterion, the probability P is dynamically adjusted based on the current temperature T: In the early stages of iteration, T is relatively high (e.g., T=1.0), and the P value is relatively large. Even if Δf=-0.1, P≈exp(-0.1 / 1.0)=0.905, there is still a high acceptance probability, supporting the algorithm to escape local optima; In the later stages of iteration, T is relatively low (e.g., T=0.01), and the P value is extremely small. When Δf=-0.1, P≈exp(-0.1 / 0.01)=4.5e-5, almost no inferior solutions are accepted, ensuring accurate convergence of the algorithm. The convergence determination adopts a "dual-condition triggering" mechanism: when the temperature is below the threshold (T<0.001) or the change in the objective function value is less than 1e-6 in 50 consecutive iterations, convergence is determined, and the final output optimal sample point set X is determined. * The dimensionality coverage (≥95%) and sample dispersion (minimum Euclidean distance ≥0.05) need to be re-verified to ensure that the CAE surrogate model is provided with high-quality training data that is evenly distributed and comprehensive in terms of operating conditions.

[0063] Example 2: Specific Implementation Examples

[0064] The following input variables are considered when constructing a CAE proxy model for a certain type of CNC machine tool: Spindle speed (500-6000 r / min), cutting load (0.5-5 kN), feed rate (100-5000 mm / min) Ambient temperature (15-35℃), tool type (coded 1-4), workpiece material (coded 1-3)

[0065] The desired number of samples is set to n=200, and the sampling space dimension is m=6, where tool type and workpiece material are discrete variables, which are converted into continuous dimensions using one-hot encoding.

[0066] (a) Initial uniform sampling stage

[0067] Sampling space construction: Continuous variables are bounded according to the actual operating conditions, while discrete variables are encoded with a range of [0,1].

[0068] Perform Latin hypercube sampling

[0069] (II) Network Topology Construction Phase

[0070] Calculate Euclidean distance and construct a weighted undirected graph.

[0071] (III) Topology Reconstruction Phase

[0072] Calculate node centrality index, assess node importance, and adjust sample point perturbation.

[0073] (iv) Dynamic optimization stage

[0074] The objective function is set, the simulated annealing parameters are initialized, iterative optimization is performed, and the sample point set is output.

[0075] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0076] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive sampling method for CAE proxy models of CNC machine tools in network topology reconstruction, characterized in that, Includes the following steps: S1. Initial uniform sampling stage: Define the input variables and value range of the CNC machine tool CAE proxy model, construct a high-dimensional sampling space Ω, and use Latin hypercube sampling to generate the initial sample point set X0; S12, Sample point preprocessing and validity verification stage: Preprocess and verify the validity of the initial sample point set X0 to eliminate outliers and dimensional interference, and provide a reliable data foundation for network topology construction; S2. Network topology construction stage: Calculate the Euclidean distance between sample points in X0, and construct a weighted undirected graph G=(V,E) with sample points as nodes and Euclidean distance as edge weights. S23. Network topology validity verification and weight normalization stage: Connectivity verification and edge weight normalization are performed on the weighted undirected graph G to ensure the accuracy and comparability of node centrality calculation. S3. Topology Reconstruction Stage: Calculate the betweenness centrality and compact centrality of nodes, evaluate the importance of nodes by combining the information entropy of the sample point set, apply Gaussian perturbation to non-critical nodes, and generate a temporary sample point set X1. S34. Temporary Sample Point Set Feasibility Screening and Boundary Constraint Stage: Perform boundary verification and feasibility screening on the temporary sample point set X1, remove invalid sample points and supplement compliant candidate points to ensure the validity of inputs in the dynamic optimization stage. S4. Dynamic Optimization Stage: An improved simulated annealing algorithm is adopted, with "maximizing minimum distance + information entropy constraint" as the objective function, to iteratively optimize X1 and output the optimal sample point set X. * .

2. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 1, characterized in that: The input variables in S1 include spindle speed, cutting load, feed rate, ambient temperature, tool type, and specimen material. Discrete variables are converted into continuous dimensions through one-hot encoding, the value range of each variable is defined, a high-dimensional sampling space Ω is constructed, and the expected number of samples n is set.

3. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 2, characterized in that: S1 involves performing a sampling operation: using the Latin hypercube sampling method, an initial sample point set X0 is generated in the sampling space Ω to ensure that the initial sample points are evenly distributed in all dimensions, laying the foundation for subsequent sampling optimization and avoiding sample distribution imbalance in the initial stage.

4. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 3, characterized in that: The specific operations for the sample point preprocessing and validity verification step S12 are as follows: ①Outlier removal: using The criteria identify outliers in each dimension of the initial sample point set X0, correct the outliers, and if the proportion of outliers exceeds 5%, the Latin hypercube sampling of S1 is re-executed. ② Dimensional normalization: For input variables with different dimensions, min-max normalization is used to map the sample values ​​of each dimension to the [0,1] interval; ③ Validity verification: Verify whether the normalized sample point set completely covers the core value range of each variable. If there is insufficient dimensional coverage, supplement the sampling until the coverage is ≥95%, and finally output the preprocessed valid sample point set. , which serves as the input to S2.

5. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 4, characterized in that: The specific operations for the network topology construction phase, S2, are as follows: Calculate the distance between sample points: For any two sample points in the initial sample point set X0 Calculate the Euclidean distance between them using the following formula: , 。 6. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 5, characterized in that: S2, the network topology construction stage also includes constructing a weighted undirected graph: based on the Euclidean distance between any two points in the initial sample point set X0, a weighted undirected graph G=(V,E) is constructed, where the node set V corresponds to the sample point set X0, and the edge set E has weights. Define as a node and The Euclidean distance between the sample points and the weights reflect the relative distance between them, providing a data foundation for subsequent topological analysis.

7. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 6, characterized in that: The specific operations of the network topology validity verification and weight normalization steps in S23 are as follows: ①Topological connectivity verification: Traverse all nodes of the weighted undirected graph G, check for the existence of isolated nodes, and ensure that G is a connected graph; ②Edge weight normalization: normalize the weights of edge set E. (Euclidean distance) is normalized to the [0,1] interval to eliminate the influence of the difference in absolute distance value on the centrality calculation; ③ Topology rationality verification: Calculate the average clustering coefficient and average path length of G, and output the normalized weighted undirected graph G'=(V,E') as the input of S3.

8. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 7, characterized in that: The specific operations of the topology reconstruction stage, S3, are as follows: ① Calculate the node centrality index: Calculate the betweenness centrality of each node. With tight centrality ; ; ; ② Calculate the sample point set The information entropy H is assigned information entropy weights based on the distribution characteristics of each dimension. ③ Combine betweenness centrality, compact centrality, and information entropy weight to evaluate node importance, and form a temporary sample point set based on the node importance evaluation results. Preliminary optimization of sample point distribution.

9. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 8, characterized in that: The specific steps of S34, the feasibility screening and boundary constraint stage for temporary sample point sets, are as follows: ① Boundary check: Traverse the temporary sample point set For all sample points, verify whether the values ​​of each dimension of each sample point are within the range of variable values ​​set in S1. If any dimension of a sample point exceeds the range, it is marked as an invalid point. ② Invalid point replacement: Invalid points are replaced using the "nearest valid point Gaussian fine-tuning method" to ensure that the new sample points fall within Ω; ③ Feasibility verification: Calculate the replacement The dimensional coverage is used to ultimately output a compliant temporary sample point set. , as the input of S4.

10. The adaptive sampling method for CNC machine tool CAE proxy model of network topology reconstruction according to claim 9, characterized in that: The specific operations of the dynamic optimization phase, S4, are as follows: ① Define the objective function: Based on the principle of "maximizing minimum distance", ensure that the sampling points are as dispersed as possible, with the optimization objective being to maximize the minimum distance between the sampling points; ② Improved simulated annealing algorithm optimization: Initialization parameters: Initial temperature =1.0, temperature decay factor α=0.95, number of iterations k, global optimization is achieved through the probability acceptance criterion; Generate candidate solutions: for temporary sample point sets Add a random perturbation (following a normal distribution with mean 0 and variance σ²) to obtain the candidate sample point set X' = X1 + Δ, where Δ is the random perturbation; Acceptance criterion: Calculate the difference in objective function between the candidate solution and the current solution, Δf = f(X') - f(X). 1） If Δf>0, the candidate solution is accepted; if Δf≤0, the candidate solution is accepted with probability P=exp(Δf / T). Temperature decay: After each iteration, the temperature is updated according to T=α×T to reduce the perturbation amplitude; Convergence Output: Iterate until the temperature is below the threshold or the maximum number of iterations is reached, then output the optimal sample point set X. * .

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