Spatiotemporal error prediction model based on dynamic distance semantic hypergraph convolution network

Abstract

This invention discloses a spatiotemporal error prediction model based on a dynamic distance-semantic hypergraph convolutional network. It addresses the two types of dependencies in spatial information: distance-based and semantic-based information. By distinguishing between the distance graph and the semantic graph, it comprehensively captures spatial behavior, including both distance-based and semantic-based thermal error information. Furthermore, semantic hypergraph convolution can characterize the dependencies between multiple sensor nodes, capturing high-order spatial behavior by constructing a semantic hypergraph. Dynamic distance graph convolution characterizes the temporal changes in the positions of sensor nodes in the sensor network, capturing dynamic spatial behavior by constructing a dynamic distance graph. Finally, by combining the dynamic distance graph and the semantic hypergraph with a minimum gate unit, dynamic spatiotemporal hypergraph convolution captures the dynamic high-order spatiotemporal behavior of thermal errors, mining the dynamic spatiotemporal features of thermal errors, and effectively improving error prediction accuracy and robustness.

Description

Technical Field

[0001] This invention belongs to the field of mechanical error control technology, specifically a spatiotemporal error prediction model based on a dynamic distance semantic hypergraph convolutional network. Background Technology

[0002] Various errors exist during the machining process, leading to reduced machining accuracy, with thermal error being one of the most significant. To mitigate the impact of thermal error on machining accuracy, existing technologies generally employ two methods: data-driven and simulation-driven. Simulation-driven methods include the finite element method (FEM) and the finite difference method (FD), incorporating thermal contact residence time and convection coefficients into the simulation model to improve modeling accuracy. However, simulation-driven methods still suffer from drawbacks such as time consumption and limited application scope. Data-driven methods are currently a hot topic, with traditional data-driven approaches including robust ridge regression, adaptive regression, principal component regression, and multiple linear regression (MLR). Traditional data-driven methods analyze the correlation between data from different sensors but do not analyze the generation mechanism of thermal error, resulting in lower prediction accuracy. LSTM can effectively capture the temporal behavior of thermal error and has good predictive performance, but it neglects the spatial behavior of thermal error due to the lack of comprehensive analysis of its generation mechanism. LSTM-based thermal error modeling methods only explore the temporal behavior of measurement data, but thermal error has spatiotemporal characteristics. Therefore, the spatial behavior of thermal error should also be considered; otherwise, the error data is not constrained by the sensor network.

[0003] In existing technologies, there is no difference between semantic maps obtained from collected data and distance maps obtained from the distances between sensor points. However, semantic maps and distance maps are both part of spatial behavior and should be considered together. Traditional semantic maps can only mine pairwise spatial dependencies between two nodes, but not higher-order spatial dependencies between multiple nodes. Furthermore, the measurement points and objects in traditional spatiotemporal modeling are fixed, so the generated distance map is static. However, the ball screw nut of a machine tool moves during machining, causing the measurement points to move accordingly, making traditional static distance maps unsuitable. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a spatiotemporal error prediction model based on a dynamic distance semantic hypergraph convolutional network. By constructing a semantic hypergraph to capture high-order spatial behavior, by constructing a dynamic distance graph to capture dynamic spatial behavior, and finally by mining the dynamic spatiotemporal features of thermal errors through dynamic spatiotemporal hypergraph convolution, the accuracy and robustness of error prediction can be effectively improved.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A spatiotemporal error prediction model based on a dynamic distance semantic hypergraph convolutional network is proposed. The model principle is as follows:

[0007]

[0008]

[0009]

[0010] Among them, f t Indicates the forgetting gate; W f and W h The weight matrix is ​​represented by σ; the sigmoid activation function is represented by b. f and b h Represents the bias matrix; and h t These represent the outputs of the candidate memory and the final memory at time t, respectively; h t-1 represents the output at time t-1; Relu represents the Relu activation function; ⊙ represents the element-wise product of two vectors; Let represent dynamic spatiotemporal hypergraph convolution, and:

[0011]

[0012] Among them, Cov H Represents semantic hypergraph convolution; Cov G Represents dynamic distance graph convolution; X t Represents time-series data; Represents the adjacency matrix of a semantic hypergraph; This represents the normalized self-loop adjacency matrix. Represents a self-loop adjacency matrix; A t Represents a time-varying adjacency matrix. represents the elements in the self-loop adjacency matrix; FC(·) represents the connection operation of the fully connected layer.

[0013] Furthermore, the semantic hypergraph convolution is represented as:

[0014]

[0015] Among them, W H The weight parameters represent the semantic hypergraph.

[0016] Furthermore, the semantic hypergraph adjacency matrix is ​​represented as:

[0017]

[0018] Where H represents the correlation matrix; D vLet R represent the vertex degree matrix; W represents the diagonal matrix, and W = R. M×M M represents the number of superedges; and:

[0019]

[0020] D v =∑ e∈ε W(e)H(v,e)

[0021] Where v represents a vertex; ε represents a hyperedge; W(e) represents a diagonal matrix; and H(v,e) represents an incidence matrix.

[0022] Define a hypergraph as G H = (V, E), where V represents the vertex set and E represents the hyperedge set, and each hyperedge ε∈E is assigned a weight W. εε All weights are stored in a diagonal matrix W.

[0023] Furthermore, the dynamic distance graph convolution is represented as:

[0024]

[0025] Among them, W s This represents the weighting coefficients of the dynamic distance map.

[0026] The beneficial effects of this invention are as follows:

[0027] This invention presents a spatiotemporal error prediction model based on a dynamic distance-semantic hypergraph convolutional network. Addressing the issue that existing technologies, which only capture the temporal behavior of thermal errors, are insufficient to achieve high prediction accuracy and robustness, this spatiotemporal error prediction model comprehensively captures spatial behavior, including both distance-based and semantic-based thermal error information, by distinguishing between distance graphs and semantic graphs. Furthermore, while traditional semantic graphs only represent pairwise dependencies between sensor nodes, this invention uses semantic hypergraph convolution to represent dependencies between multiple sensor nodes, capturing higher-order spatial behavior through the construction of a semantic hypergraph. Traditional distance graphs are static, while the ball screw nut of a machine tool moves during machining, meaning the sensor measurement points are mobile. This invention uses dynamic distance graph convolution to represent the temporal changes in the position of sensor nodes in the sensor network, capturing dynamic spatial behavior through the construction of a dynamic distance graph. Finally, by utilizing minimum gating units combined with the dynamic distance graph and semantic hypergraph, the dynamic spatiotemporal hypergraph convolution captures the dynamic higher-order spatiotemporal behavior of thermal errors, mining the dynamic spatiotemporal features of thermal errors, and effectively improving error prediction accuracy and robustness. Attached Figure Description

[0028] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0029] Figure 1 This is a schematic diagram of the structure of a ball screw nut;

[0030] Figure 2 Here is a structural diagram of MGU;

[0031] Figure 3 A comparison of traditional semantic graphs and semantic hypergraphs; (a) traditional semantic graph; (b) semantic hypergraph;

[0032] Figure 4 Here is a structural diagram of the DSTM-HCN model;

[0033] Figure 5 A framework for dynamic spatiotemporal prediction of thermal errors;

[0034] Figure 6 (a) A thermal image of a machine tool; (b) The sensor network structure diagram;

[0035] Figure 7 Physical diagram of sensor arrangement and measurement; (a) temperature sensor; (b) laser interferometer;

[0036] Figure 8 This is the distance between the temperature measurement point and the displacement measurement point.

[0037] Figure 9 This is the dynamic distance adjacency matrix of the measurement points;

[0038] Figure 10 For the sensor dynamic adjacency matrix;

[0039] Figure 11 Temperature and thermal error measured at a feed rate of 1200 mm / min; (a) measured temperature; (b) thermal error;

[0040] Figure 12 Temperature and thermal error measured at a feed rate of 600 mm / min; (a) measured temperature; (b) thermal error. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0042] 1. Dynamic spatiotemporal behavior of ball screw nuts

[0043] For the screw shaft, its length is much greater than its diameter, and axial thermal expansion is unavoidable. The screw shaft within its motion range is discretely divided into M segments, each segment having a length of L, as shown below. Figure 1As shown. The temperature field of the screw shaft is affected by the frictional heat of the screw nut and bearings. Under the influence of the frictional heat of the nut, the heat balance equation can be expressed as:

[0044] Q f (l i ,Δt)-Q d (l i ,Δt)-Q v (l i ,Δt)=ΔQ(l i ,Δt)

[0045] Among them, Q f (l i ,Δt), Q d (l i ,Δt), Q v (l i ,Δt) and ΔQ(l i Δt) represents the heat generated by friction, the heat dissipated by heat conduction, the heat dissipated by convection, and the increase in internal energy, respectively. i is the length of the i-th segment, and Δt is the running time. Where:

[0046] Q f (l i ,Δt)=Q·n

[0047] Where Q is the heat generated by friction between the nut and the i-th segment; n is the number of times friction occurs between the nut and the i-th segment within the time interval Δt.

[0048] The heat flux density of heat conduction is:

[0049]

[0050] Where λ is thermal conductivity; T s This is the temperature of the screw shaft. Therefore, the heat dissipated through heat conduction is:

[0051]

[0052] Among them, T s (l i-1 (t) is the temperature of the (i-1)th segment at time t; T s (l i+1 (t) is the temperature of segment i+1 at time t; T s (l i ,t) is the temperature of the i-th segment at time t; d s It is the equivalent diameter of the screw shaft.

[0053] The heat flux density for convective heat transfer is:

[0054] q v =h×(T)s -T a )

[0055] Where h is the convective heat transfer coefficient; T a This is the air temperature. Therefore, heat dissipation via convection is:

[0056] Q v (l i ,t)=π·[T s (l i ,t)-T a (t)]·hd s L·Δt

[0057] Among them, T a (t) represents the ambient temperature at time t.

[0058] The increase in internal energy over time Δt is:

[0059]

[0060] In the formula, c is the specific heat capacity; ρ is the density; and L is the length of the i-th segment. Thus, the temperature field is obtained as follows:

[0061]

[0062] Then, the thermal error is as follows:

[0063] E(l i ,t)=α·[T s (l i ,t)-T a (t0)]·L

[0064]

[0065] Here, α is the coefficient of thermal expansion. The thermal error of the i-th segment is a function of time and spatial location, proving the spatiotemporal behavior of the thermal error.

[0066] 2. Minimum Gating Unit

[0067] Capturing the spatial behavior of thermal errors can improve prediction accuracy, but it increases the number of computational parameters. To ensure real-time control of thermal errors, the thermal error model should have good convergence speed. To reduce computational parameters, MGU is used to capture temporal behavior. LSTM and GRU are recurrent neural networks; in previous studies, GRU was used to capture temporal behavior because GRU has fewer gate structures than LSTM. Since gate structure is crucial for improving the prediction performance of neural networks, the forget gate is consistently considered the most important gate. To further reduce the number of parameters, MGU merges the reset and update gates in the GRU model into a forget gate, such as... Figure 2As shown. With the same number of hidden neurons, MGU has 2 / 3 the number of parameters of GRU, while its prediction accuracy is comparable to GRU. Therefore, MGU is more suitable than GRU for capturing temporal behavior. The principle of MGU is as follows:

[0068] f t =σ(W f [h t-1 ,x t ]+b f )

[0069]

[0070]

[0071] Among them, f t It is the door to forgetting; W f and W h is the weight matrix; · is the sigmoid activation function; b f and b h It is the bias matrix; and h t These represent the candidate memory and the final memory output, respectively; ⊙ represents the element-wise product of the two vectors. During training, MGU has fewer parameters than GRU. Therefore, MGU is used to capture the temporal behavior of thermal errors.

[0072] 3. Spatiotemporal error prediction model based on dynamic distance semantic hypergraph convolutional network

[0073] Capturing the temporal behavior of thermal errors is insufficient for achieving high prediction accuracy and robustness; capturing their spatial behavior is also necessary. Graph structures are increasingly used to explore the spatial correlations of networks. However, previous spatiotemporal prediction methods have mostly relied on distance modeling of sensor nodes, failing to distinguish between distance graphs and semantic graphs. In fact, spatial information contains two types of dependencies: distance-based and semantic-based. The latter is also known as logic-based dependency. Spatial behavior should be comprehensively captured, including both distance-based and semantic-based thermal error information. Furthermore, traditional semantic graphs only represent pairwise dependencies between sensor nodes, not dependencies between multiple sensor nodes. Hypergraphs can capture complex and high-order dependencies and can be used to overcome the aforementioned problems, such as... Figure 3 As shown. In Figure 3 In (a), edge e1 can only connect two nodes. Figure 3 In (b), edge e2 can connect the three nodes n1, n5, and n7, meaning that the three nodes are closely related.

[0074] Specifically, the equation for GCN is:

[0075]

[0076] in, I is the identity matrix; A is the distance-adjacency matrix; · represents ...; X is the feature sequence; W0 is the weight parameter; · is the activation function.

[0077] Unlike static structures, the positions of sensor nodes in a ball screw system sensor network change over time. Therefore, the distance-adjacency matrix is ​​related to the running time. The above equation can then be updated to:

[0078]

[0079] in, This represents the normalized self-loop adjacency matrix. Represents a self-loop adjacency matrix; I is the identity matrix; A t X is a time-varying adjacency matrix; X is a time-varying feature sequence.

[0080] To comprehensively characterize the spatial behavior of thermal errors, dynamic spatiotemporal hypergraph convolution is defined. The hypergraph is defined as G. H = (V, E), where V is the set of vertices and E is the set of hyperedges. Each hyperedge ε∈E is assigned a weight W. εε All weights are stored in the diagonal matrix W = R M×M In the expression, M is the number of hyperedges.

[0081] The hypergraph is represented by the incidence matrix H, and:

[0082]

[0083] Vertex degree matrix D v Represented as:

[0084] D v =∑ e∈ε W(e)H(v,e)

[0085] Where v represents a vertex; ε represents a hyperedge; W(e) represents a diagonal matrix; and H(v,e) represents an incidence matrix.

[0086] Semantic hypergraph adjacency matrix Represented as:

[0087]

[0088] Where H represents the correlation matrix; D v Let R represent the vertex degree matrix; W represents the diagonal matrix, and W = R. M×M M represents the number of superedges;

[0089] Introducing semantic hypergraphs into the model, semantic hypergraph convolution CovH and dynamic distance graph convolution Cov G Defined as:

[0090]

[0091]

[0092] Among them, W H W represents the weight parameters of the semantic hypergraph. s This represents the weighting coefficients of the dynamic distance map.

[0093] The results of the semantic hypergraph and the dynamic distance graph are connected by a fully connected layer, then the dynamic spatiotemporal hypergraph convolution is:

[0094]

[0095] Among them, Cov H Represents semantic hypergraph convolution; Cov G Represents dynamic distance graph convolution; X t Represents time-series data; Represents the adjacency matrix of a semantic hypergraph; This represents the normalized self-loop adjacency matrix. Represents a self-loop adjacency matrix; A t Represents a time-varying adjacency matrix. represents the elements in the self-loop adjacency matrix; FC(·) represents the connection operation of the fully connected layer.

[0096] To capture the spatiotemporal correlation of sensor networks, this embodiment proposes a spatiotemporal error prediction model based on MGU and HCN (hereinafter referred to as the DSTM-HCN model). The spatiotemporal prediction process of DSTM-HCN is as follows: Figure 4 As shown, the dynamic distance graph adjacency matrix, semantic hypergraph adjacency matrix, and sensor temporal data are used as inputs to the DTSM-HCN model. HCN captures the spatial behavior of the sensor in real time using the dynamic distance graph adjacency matrix and semantic hypergraph adjacency matrix. MGU is used to capture the temporal behavior of thermal error data. Predictive data is then obtained based on the proposed DSTM-HCN model. Specifically, the DSTM-HCN model in this embodiment is expressed as follows:

[0097]

[0098]

[0099]

[0100] Among them, f tIndicates the forgetting gate; W f and W h The weight matrix is ​​represented by σ; the sigmoid activation function is represented by b. f and b h Represents the bias matrix; and h t These represent the outputs of the candidate memory and the final memory at time t, respectively; h t-1 represents the output at time t-1; Relu represents the Relu activation function; ⊙ represents the element-wise product of two vectors; This represents dynamic spatiotemporal hypergraph convolution.

[0101] 4. Modeling Experiment

[0102] Figure 5 A dynamic spatiotemporal prediction framework for thermal errors is presented. The spatiotemporal prediction framework consists of four steps: sensor network construction, dataset construction of dynamic distance graph and semantic hypergraph, parameter construction of DTSM-HCN model, and thermal error prediction.

[0103] 4.1 Sensor Network Construction

[0104] Typically, temperature sensors are placed on the main heat source. However, the placement of temperature sensors relies on expert experience, leading to incomplete thermal information collection. To overcome the shortcomings of expert experience, such as... Figure 6 As shown in (a), thermal imaging is used to guide the placement of measurement points. This differs from the previous reliance on expert experience to arrange temperature sensors. The brighter the image, the higher the temperature of the machine part, and these points are then used as measurement points. That is, temperature sensors should be placed at these measurement points. Note that the brightest part in the lower left corner is the coolant motor, which is not connected to the machine tool. Therefore, there are 8 temperature measurement points and 1 thermal error measurement point. The sensors are then connected to form a sensor network, as shown... Figure 6 As shown in (b), S represents the displacement measurement point and is placed on the sliding seat. The positions of the measurement points are shown in Table 1. The temperature of the measurement point is measured by a temperature sensor, which is a precision magnetic platinum resistance thermometer Pt100, as shown in Table 1. Figure 7 As shown in (a). Thermal error was measured using a Renishaw XL80 laser interferometer, as... Figure 7 As shown in (b), the above eight temperature measurement points can reflect the temperature field distribution of the upper and lower screw shafts. The dependence of thermal errors on the temperatures at these eight points should be investigated. Spatiotemporal prediction can then effectively address this correlation.

[0105] Table 1 Measurement points and nodes

[0106]

[0107] 4.2 Construction of Dynamic Distance Graphs and Semantic Hypergraphs

[0108] Existing technologies do not distinguish between distance maps and semantic maps, resulting in a lack of spatial behavior. To comprehensively explore the spatial behavior of thermal errors, this embodiment establishes dynamic distance maps and semantic hypergraphs respectively. The feed speed of the sliding block is 1200 mm / min, and the length of the screw shaft on both the X and Y axes is 1.8 m. Then, based on the feed speed of the screw shaft and the sliding block, the relative positions of each temperature measurement point and displacement measurement point are established, such as... Figure 8 As shown. Based on the positional changes between measurement points, a dynamic distance adjacency matrix is ​​obtained and expressed as:

[0109]

[0110] Among them, w i,j δ is the edge weight, and it is related to the positions of the i-th and j-th nodes; δ is the control weight for w. i,j The threshold of the distribution; d i,j It is the distance between the i-th node and the j-th node.

[0111] The dynamic distance adjacency matrix is ​​then obtained using the above formula. To illustrate its change process, Figure 9 The image shows a portion of the dynamic adjacency matrix. Figure 9 The x-axis represents the sensor label, and the y-axis represents the dynamic distance adjacency matrix. The dynamic distance adjacency matrix has a dimension of 5×5. It can be seen that the dynamic distance adjacency matrix changes with the distance between sensor nodes. Therefore, it is necessary to construct a dynamic distance adjacency matrix.

[0112] The correlation between measurement points changes over time. Therefore, it is necessary to construct a semantic hypergraph. The historical value of each measurement point is represented as a feature vector. The feature vector is sliced ​​into N segments. Each segment of the feature vector is clustered using a fuzzy clustering method, and the distance is calculated using Euclidean distance. Temperature measurement points closely related to displacement measurement points are obtained. Figure 10 As shown, the correlation matrix H for the i-th period is obtained. The correlation matrix H consists of the correlation matrices of each contact period. This yields the adjacency matrix of the semantic hypergraph, and then the dynamic distance adjacency matrix is ​​used as input to comprehensively capture spatial behavior.

[0113] When the feed rate is 1200 mm / min and the running time is approximately 550 minutes, the measured temperature and thermal error are obtained, such as... Figure 11 As shown. With a feed rate of 600 mm / min and a running time of approximately 550 minutes, the measured temperature and thermal deviation were obtained, as shown... Figure 12As shown, data at a feed rate of 1200 mm / min was used as the training set, and data at a feed rate of 600 mm / min was used as the test set. The amplitude of thermal error fluctuations increased with increasing temperature, as heat is the primary factor contributing to thermal error. Furthermore, temperature and thermal error exhibited the same trend, with the rate of increase gradually decreasing, as the ball screw system was entering thermal equilibrium.

[0114] 4.3 Model Construction

[0115] This embodiment compares the prediction performance to validate the proposed DSTM-HCN model. To highlight the effectiveness of the proposed DTSM-GCN model, comparisons are made using MLR, LSTM, GRU, CNN-LSTM, Temporal Graph Convolutional Network (T-GCN), and Hypergraph Neural Network (HGNN). Due to the different signal levels at the sensor nodes, the measured data values ​​are normalized to train the above models, and then inverse normalization is performed to obtain the prediction results. The PyTorch machine learning library is used for programming; the time step is set to 2, the learning rate to 0.001, the optimizer to Adam, the activation function to swish, and the batch size to 64.

[0116] MLR is a traditional method for predicting thermal errors. It selects temperature measurement points, T = (T1, T5, T6), as inputs using a clustering algorithm. Then, the regression toolbox in MATLAB is used to identify the regression coefficients as b0 = 5.8387, b1 = -0.20167, b2 = 1.6444, and b3 = -0.48548. Therefore, the established MLR model is:

[0117] E=5.8387-0.20167T1+1.6444T5-0.48548T6

[0118] LSTM neural networks are a widely used type of recurrent neural network whose unique input gate, forget gate, and output gate can effectively capture the temporal characteristics of data.

[0119] GRU is a variant of LSTM that has fewer gates than LSTM, resulting in faster convergence. GRU's prediction accuracy is similar to that of LSTM.

[0120] CNN-LSTM is a combination of CNN and LSTM neural networks, where the CNN consists of a fully connected layer, two pooling layers, and two convolutional layers. CNN is used to capture spatial features, while LSTM is used to capture temporal features.

[0121] T-GCN is a combination of GCN and GRU, where GCN is used to capture spatial correlations and GRU is used to capture temporal correlations.

[0122] HGNN uses a unique hypergraph to capture high-order correlations between data points and was originally used for classification tasks. The classifier can be replaced by GRU. The combination of HGNN and GRU achieves spatiotemporal prediction tasks. HGNN is used to capture high-order spatial correlations in the data, while GRU is used to capture temporal correlations.

[0123] 4.4 Thermal Error Prediction

[0124] 4.4.1 Model Comparison Experiment

[0125] Different models exhibit varying predictive performance. The MLR model only captures the trend of thermal errors. The results show that the error model that considers the mechanism of thermal error generation performs better than the model that does not.

[0126] The fitting and prediction results of each model were then evaluated, as shown in Tables 2 and 3. For fitting performance, the RMSE values ​​for MLR, LSTM, GRU, CNN-LSTM, T-GCN, HGNN, and DSTM-HCN were 0.8539, 0.4096, 0.4215, 0.4560, 0.3956, 0.3829, and 0.2789, respectively. For prediction performance, the RMSE values ​​for MLR, LSTM, GRU, CNN-LSTM, T-GCN, HGNN, and DSTM-HCN were 1.1336, 0.5690, 0.6055, 0.6161, 0.5274, 0.5653, and 0.3492, respectively. DSTM-HCN's fitting and prediction performance significantly outperformed other machine learning models. Because thermal errors are spatiotemporal data, and because dynamic distance graphs and semantic hypergraphs are combined with MGU, the dynamic spatiotemporal behavior of thermal errors is fully explored in DSTM-HCN. Compared to DSTM-HCN, T-GCN and HGNN uncover incomplete spatial behavior, resulting in lower fitting accuracy and poorer prediction performance. Since CNNs are not suitable for non-Euclidean data, they cannot capture the spatial behavior of thermal errors. The RMSE of the CNN-LSTM fitting and prediction model is higher than that of T-GCN and HGNN. The prediction and fitting performance of LSTM, GRU, and CNN-LSTM are not significantly different. Notably, CNN-LSTM performs worse than LSTM because CNNs are not well-suited for capturing the dynamic spatial behavior of thermal errors. The traditional data-based method MLR performs the worst because it does not analyze the generation mechanism of thermal errors and cannot capture their spatiotemporal behavior.

[0127] Table 2 Fitting performance of different thermal error models

[0128]

[0129] Table 3 Predictive performance of different thermal error models

[0130]

[0131] 4.4.2 Ablation Experiment

[0132] Ablation experiments demonstrated the effectiveness of MGU, dynamic distance graph, and semantic hypergraph. In this embodiment, DSTM-HCN was designed based on T-GCN, and the ablation experiment results are listed in Table 4. The results show that DSTM-HCN has higher prediction accuracy than Dynamic Spatiotemporal Minimum Graph Convolutional Network (DSTM-GCN) because the dynamic distance graph and semantic hypergraph are comprehensively considered by DSTM-HCN. However, the DSTM-GCN model does not distinguish between the distance graph and the semantic graph, nor does it fully capture spatial behavior. The prediction accuracy of DSTM-GCN is higher than that of Temporal Minimum Graph Convolutional Network (TM-GCN) because the DSTM-GCN model introduces a dynamic distance adjacency matrix, while the TM-GC network uses a static distance adjacency matrix. The prediction accuracy and time consumption of TM-GCN are slightly lower than those of T-GCN. MGU can improve the convergence speed, but it will lead to a slight decrease in prediction accuracy.

[0133] Table 4 Predictive performance of ablation experiments

[0134]

[0135] 4.4.3 Cross-validation

[0136] To demonstrate the robustness of the proposed model, the training and test sets were swapped for experiments. In the cross-validation experiments, measurements at a feed rate of 1200 mm / min were used as the test set, and measurements at a feed rate of 600 mm / min were used as the training set. According to Table 3, the T-GCN model exhibits the best prediction performance among MLR, LSTM, GRU, CNN-LSTM, T-GCN, and HGNN. It was then compared with the proposed DSTM-HCN listed in Table 5. The results show that the proposed DSTM-HCN model has excellent robustness. When the training and test sets were swapped, the prediction accuracy of DSTM-HCN was superior to that of T-GCN.

[0137] Table 5 Predictive performance of cross-validation

[0138]

[0139] 4.4.4 The impact of the number of nodes in a hypergraph

[0140] The number of nodes in the semantic hypergraph significantly impacts the prediction accuracy of the proposed DSTM-HCN model. The MAE, MSE, RMSE, and R² of DSTM-HCN all change with the number of nodes. The DSTM-HCN model achieves the highest prediction accuracy when the hypergraph contains 4 nodes. When the number of nodes is 2, DSTM-HCN degenerates into DSTM-GCN. With 2 nodes, the prediction performance of DSTM-HCN is close to that of DSTM-GCN listed in Table 4.

[0141] 5. Conclusion

[0142] Modeling the generation mechanism of thermal errors reveals their spatiotemporal behavior. Based on this mechanism, this embodiment proposes a novel DTSM-HCN model to capture their dynamic spatiotemporal behavior. The DTSM-HCN model in this embodiment distinguishes between a distance graph and a semantic graph. Based on the motion equations of the ball screw, the dynamic relative positions between measurement points are obtained, and a dynamic distance graph is established. A semantic hypergraph is constructed based on the values ​​of the measurement points and a fuzzy clustering algorithm. A dynamic spatiotemporal hypergraph convolution combining the dynamic distance graph and the semantic hypergraph is defined. Then, the dynamic distance graph and the semantic hypergraph are combined with MGU to comprehensively mine the dynamic spatiotemporal behavior of thermal errors. Prediction results show that, compared with other machine learning models, the DTSM-HCN model proposed in this embodiment has the best prediction performance and robustness. The conclusions are as follows:

[0143] (1) The generation mechanism of thermal error was revealed using the energy conservation equation. The results show that thermal error has spatiotemporal characteristics and needs to be characterized by a spatiotemporal model. The RMSE of the prediction results of T-GCN and HGNN is lower than that of LSTM and GRU, indicating that the spatiotemporal model has higher thermal error prediction accuracy than the time model.

[0144] (2) GCN was applied for the first time to thermal error prediction to capture spatial behavior. Compared with CNN, GCN is better suited to capture the spatial behavior of thermal errors. The RMSE of the prediction results of T-GCN and HGNN is lower than that of CNN-LSTM because CNN is not suitable for representing non-European data.

[0145] (3) For thermal error prediction, the construction of dynamic distance graphs and semantic hypergraphs is of great significance for improving prediction accuracy. The proposed DSTM-HCN model comprehensively explores the spatiotemporal behavior of thermal errors by combining dynamic distance graphs and semantic hypergraphs with MGU. The results show that the RMSE of DSTM-HCN is lower than that of DSTM-GCN, TM-GCN, HGNN, T-GCN and CNN-LSTM, GRU, LSTM and MLR.

[0146] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A spatio-temporal error prediction model based on dynamic distance semantic hypergraph convolution network, characterized in that: The measuring point of the ball screw system is determined based on thermal imaging, and a temperature sensor is arranged at the measuring point, and the principle of the space-time error prediction model is: in, Indicates the Gate of Oblivion; and Represents the weight matrix; This represents the Sigmoid activation function; and Represents the bias matrix; and They represent Outputs from the candidate time memory and the final time memory; express Output at any moment; This represents the ReLU activation function; Represents the element-wise product of two vectors; Let represent dynamic spatiotemporal hypergraph convolution, and: in, This represents a semantic hypergraph convolution, used to capture high-order spatial dependencies between sensor nodes; This represents dynamic distance map convolution, used to capture time-varying positional changes between sensor nodes; Represents time-series data; Represents the adjacency matrix of a semantic hypergraph; This represents the normalized self-loop adjacency matrix. Represents a self-loop adjacency matrix; , ; Represents a time-varying adjacency matrix. , This represents the elements in a self-loop adjacency matrix; This represents the connection operation of the fully connected layer.

2. The spatio-temporal error prediction model based on dynamic distance semantic hypergraph convolution network according to claim 1, characterized in that: The semantic hypergraph convolution is represented as: wherein, denotes a weight parameter of the semantic hypergraph.

3. The spatio-temporal error prediction model based on dynamic distance semantic hypergraph convolution network according to claim 2, characterized in that: The semantic hypergraph adjacency matrix is represented as: in, Represents the correlation matrix; Represents the vertex degree matrix; Denotes a diagonal matrix, and , Indicates the number of superedges; and: wherein, denotes a vertex; denotes a hyperedge; denotes a diagonal matrix; denotes an incidence matrix; Define a hypergraph as , Represents a vertex set. Represents a set of superedges, where each superedge... Assigned weights All weights are stored in a diagonal matrix. middle.

4. The spatiotemporal error prediction model based on a dynamic distance semantic hypergraph convolutional network according to claim 1, characterized in that: The dynamic distance graph convolution is represented as: wherein, denotes a weight coefficient of the dynamic distance map.

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