Main shaft system thermal error compensation method fused with non-contact measuring points

By integrating non-contact measurement points, a spatiotemporal feature fusion model is constructed using one-dimensional and two-dimensional temperature data. This solves the problem of incomplete data acquisition in the spindle thermal error prediction model, achieves high-precision thermal error compensation, and improves the machining accuracy of CNC machine tools.

CN121900293APending Publication Date: 2026-04-21JILIN UNIVERSITY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
JILIN UNIVERSITY
Filing Date
2026-01-20
Publication Date
2026-04-21

AI Technical Summary

Technical Problem

In the existing technology, the spindle thermal error prediction model relies on direct-measurement temperature sensors, which cannot collect temperature information of rotating spindle components in real time. This results in incomplete data acquisition, insufficient model prediction accuracy, and an inability to meet the requirements of high-precision machining.

Method used

A non-contact measurement method is adopted, combining one-dimensional temperature measurement data and two-dimensional temperature field image data. By constructing a two-dimensional infrared image feature extraction network and a one-dimensional temperature rise time series feature extraction network, feature fusion is performed to build a multi-source data spatiotemporal feature fusion thermal error prediction model, which realizes real-time prediction and compensation of thermal errors of the spindle system.

Benefits of technology

The accuracy of the thermal error prediction model has been improved, enabling real-time and accurate compensation for thermal errors in the spindle system and enhancing the machining accuracy of CNC machine tools.

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Abstract

The invention is applicable to the technical field of thermal error control, and provides a spindle system thermal error compensation method fusing non-contact measuring points, which comprises the following steps: acquiring one-dimensional temperature measuring point data near a machine tool spindle box, a stand column and a machine tool body, two-dimensional temperature field image data at the front end of a machine tool spindle and thermal errors of the machine tool spindle; processing the one-dimensional temperature measuring point data and the two-dimensional temperature field image data; constructing a two-dimensional infrared image feature extraction network, and extracting two-dimensional temperature field spatial features; constructing a one-dimensional temperature rise time sequence feature extraction network, and extracting time sequence and spatial features of one-dimensional temperature measurement points; carrying out feature fusion on the one-dimensional temperature rise time sequence feature extraction network and the two-dimensional infrared image feature extraction network, constructing an MSD-STFFM, and obtaining a thermal error prediction result; and based on the thermal error prediction result, setting the required error compensation value as the thermal error prediction result in the negative direction to realize real-time prediction compensation. The thermal error prediction precision is improved, and high-precision machining of the numerical control machine tool is achieved.
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Description

Technical Field

[0001] This invention belongs to the field of thermal error control technology, and particularly relates to a thermal error compensation method for a spindle system that integrates non-contact measuring points. Background Technology

[0002] High-end CNC machine tools, as a key cornerstone of the manufacturing industry's transformation towards precision, modernization, and intelligence, play an irreplaceable supporting role in the high-quality development of the real economy. Precision, as a core technical indicator of high-end CNC machine tools, directly determines the quality and market share of machine tool products and is crucial for enterprises to build core competitiveness. In recent years, with the continuous improvement of machine tool design, component manufacturing, and assembly processes, the proportion of traditional machining errors such as geometric errors and servo errors has gradually decreased. However, thermal errors caused by the thermal deformation of various components have become increasingly prominent, becoming the primary factor restricting the improvement of machining accuracy. Extensive engineering practice and experimental research show that thermal errors account for 40% to 70% of the total machining errors of CNC machine tools, and this proportion is even more significant in precision machine tools. The spindle, as a core component of CNC machine tools, is one of the main heat sources, and its thermal deformation directly determines the metal removal rate and the machining accuracy of the workpiece. Therefore, accurate thermal error control of the spindle is key to improving the precision of CNC machine tools.

[0003] Thermal error control strategies are mainly divided into two categories: error prevention and error compensation. Thermal error prevention relies on optimizing mechanical structure design and adding auxiliary temperature control devices. However, with the increasing demands for machining accuracy, the research and development and manufacturing costs of this method have significantly increased. Furthermore, it has poor adaptability to existing machine tools already in production, making large-scale application difficult. In contrast, thermal error compensation actively applies a "compensation amount" opposite to the original error direction to offset thermal errors. Compared to prevention, compensation offers advantages such as ease of operation and flexible adjustment, and it does not require large-scale modifications to the machine tool itself, making it easier to implement on existing equipment. Therefore, it has been widely used in industrial production.

[0004] The key prerequisite for accurately implementing thermal error compensation is the construction of a high-precision thermal error prediction model. Currently, most commonly used models in engineering are data-driven: to accurately identify "thermal sensitive points" that significantly affect thermal errors, a certain number of temperature sensors need to be placed on the machine tool. Finally, algorithms such as multiple linear regression and neural networks are used to achieve quantitative prediction of thermal errors. However, for the thermal error prediction process of machine tool spindle systems, the thermal error prediction models currently commonly used are based on temperature data collected by direct-measurement temperature sensors (such as PT-100). These models can only collect data from non-moving parts of the machine tool, such as the vicinity of the spindle drive motor, bearings, and environmental boundaries. It is difficult to collect the temperature of rotating spindle components in real time. This results in the loss of a considerable amount of information from key locations during the construction of the thermal error prediction model, making it difficult to build an accurate thermal error prediction model for the spindle system.

[0005] Therefore, the core problem of existing technologies lies in the limitations of constructing spindle thermal error prediction models, with the following specific drawbacks:

[0006] Incomplete data acquisition of thermally sensitive points: Existing models rely on direct-measurement temperature sensors (such as PT-100) to collect temperature data, but these sensors can only be deployed in non-moving parts (such as near the drive motor, near the bearing, and at the environmental boundary), and cannot collect temperature information of rotating spindle components in real time, resulting in the loss of thermal feature data at key locations in the model;

[0007] Insufficient model prediction accuracy: Existing methods generally rely on extracting time-series features from one-dimensional temperature measurement point data to predict thermal errors, ignoring the spatial correlation between temperature measurement point data. In addition, due to the lack of temperature data at key locations (rotating spindle), existing models cannot fully capture the thermal deformation law of the spindle system, ultimately leading to reduced accuracy in thermal error prediction and failing to meet the requirements of high-precision machining. Summary of the Invention

[0008] The purpose of this invention is to provide a method for thermal error compensation of a spindle system that integrates non-contact measuring points, in order to solve the problems mentioned in the background art.

[0009] The present invention is implemented as follows: a method for thermal error compensation of a spindle system integrating non-contact measuring points includes the following steps:

[0010] Step 1: Obtain one-dimensional temperature measurement point data near the machine tool spindle box, column, and bed; two-dimensional temperature field image data at the front end of the machine tool spindle; and thermal error of the machine tool spindle.

[0011] Step 2: Perform unified processing on the one-dimensional temperature measurement point data and the two-dimensional temperature field image data;

[0012] Step 3: Construct a two-dimensional infrared image feature extraction network to extract two-dimensional temperature field spatial features from two-dimensional temperature field image data;

[0013] Step 4: Construct a one-dimensional temperature rise time series feature extraction network to extract the time series and spatial features of one-dimensional temperature measurement points from the one-dimensional temperature measurement point data;

[0014] Step 5: Perform feature fusion between the one-dimensional temperature rise time series feature extraction network and the two-dimensional infrared image feature extraction network to construct the spatiotemporal feature fusion thermal error prediction model MSD-STFFM based on multi-source data and obtain the thermal error prediction results.

[0015] Step 6: Based on the thermal error prediction results, set the required error compensation value to the negative thermal error prediction results to achieve real-time prediction and compensation of thermal errors in the machine tool spindle system.

[0016] The present invention provides a method for thermal error compensation of a spindle system that integrates non-contact measuring points. During the data acquisition stage, it simultaneously acquires one-dimensional and two-dimensional temperature data, which makes up for the limitations of traditional methods that rely only on direct temperature measuring point data. By integrating thermal image data of the spindle front end rotation process, it provides more comprehensive temperature field information and lays the foundation for subsequent thermal error modeling.

[0017] In the feature extraction stage, a spatiotemporal feature fusion network and a residual convolutional network are used to process one-dimensional and two-dimensional data respectively. The spatiotemporal feature fusion network can effectively capture the temporal features of each temperature measurement point data and the spatial relationship between different temperature measurement points, while the ResNet-18 network can effectively extract the spatial features of the two-dimensional temperature field by deepening the network layers through the residual structure; thus comprehensively describing the temperature distribution state of the machine tool.

[0018] The feature fusion stage fuses and outputs the spatiotemporal features of one-dimensional temperature measurement points, fully extracts the temporal and spatial features of each temperature measurement point, and combines the one-dimensional feature output with the spatial features of the two-dimensional temperature image to perform thermal error prediction. This achieves effective fusion of multi-source heterogeneous data and effectively improves the prediction accuracy of the thermal error prediction model.

[0019] At the same time, building a standardized thermal error compensation system, integrating hardware and software equipment, and unifying installation and deployment locations will help promote its application. Attached Figure Description

[0020] Figure 1 A schematic diagram of a spindle system thermal error compensation method integrating non-contact measuring points provided in an embodiment of the present invention;

[0021] Figure 2 A schematic diagram of a two-dimensional infrared image feature extraction network based on ResNet-18 provided in an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram of a one-dimensional temperature measurement point spatiotemporal feature extraction network based on spatiotemporal feature fusion provided in an embodiment of the present invention;

[0023] Figure 4 A schematic diagram of a thermal error compensation system provided in an embodiment of the present invention;

[0024] Figure 5 This is one-dimensional temperature measurement point data provided in an embodiment of the present invention;

[0025] Figure 6 Two-dimensional temperature field image data provided in the embodiments of the present invention;

[0026] Figure 7 The measured error results of the thermal elongation of the machine tool Z-axis provided in the embodiments of the present invention;

[0027] Figure 8 A schematic diagram of the model training process loss provided in an embodiment of the present invention;

[0028] Figure 9 This is a comparison result of the predicted and measured values ​​of thermal error provided in the embodiments of the present invention;

[0029] Figure 10 The comparison results of thermal error values ​​before and after compensation are provided in the embodiments of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0031] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0032] Example 1, such as Figure 1 As shown, a method for thermal error compensation of a spindle system integrating non-contact measuring points includes the following steps:

[0033] Step 1: Construct a temperature measurement module. Use temperature sensors such as PT-100 to collect one-dimensional temperature measurement point data near the machine tool spindle box, column, and bed. Use an infrared thermal imager to collect two-dimensional temperature field image data at the front end of the machine tool spindle. Use displacement sensors such as eddy current sensors to collect the thermal error of the machine tool spindle.

[0034] Step 2: Construct a data processing module to perform unified processing on one-dimensional temperature measurement point data and two-dimensional temperature field image data. Specifically, this includes initial value processing, filtering and noise reduction, data augmentation and data partitioning for two-dimensional temperature field image data, and standardization processing, time series processing and data partitioning for one-dimensional temperature measurement point data.

[0035] Step 3: Construct a two-dimensional infrared image feature extraction network to extract two-dimensional temperature field spatial features from two-dimensional temperature field image data;

[0036] Step 4: Construct a one-dimensional temperature rise time series feature extraction network to extract the time series and spatial features of one-dimensional temperature measurement points from the one-dimensional temperature measurement point data;

[0037] Step 5: Construct a thermal error prediction module, fuse the one-dimensional temperature rise time series feature extraction network with the two-dimensional infrared image feature extraction network, construct a spatiotemporal feature fusion thermal error prediction model based on multi-source data MSD-STFFM, and output the thermal error prediction results;

[0038] Step 6: Construct a thermal error compensation module. Based on the thermal error prediction results, set the required error compensation value to the negative thermal error prediction results. Input the compensation value to the CNC panel through the communication interface reserved by the CNC machine tool system. This communication interface can be wired communication, such as serial communication, Ethernet, etc., or wireless communication, such as Wi-Fi, Bluetooth, etc.

[0039] Step 7: Construct a thermal error compensation system, connect the communication between various devices, and determine their installation and deployment locations to achieve the standardized application of the thermal error compensation method for the spindle system.

[0040] In step 3, the two-dimensional infrared image feature extraction network uses a ResNet-18 residual network for feature extraction, such as... Figure 2 As shown, this network extracts image features through several convolutional and pooling layers. The residual structure ensures the feature extraction performance of the deep network. Finally, the features are flattened and output through a fully connected (FC) layer, with the output feature dimension being [dimensionality missing]. , where B represents the number of input samples (i.e. the number of thermal image samples processed simultaneously), and 512 is the fixed output dimension of the last fully connected layer of ResNet-18 (meaning that each thermal image sample is compressed into a 512-dimensional abstract feature vector).

[0041] In step 4, the one-dimensional temperature rise time series feature extraction network is constructed by stacking two layers of spatiotemporal feature fusion network model with the same number of units. The structure of the spatiotemporal feature fusion network model is as follows: Figure 3 As shown, the spatiotemporal feature fusion network model takes the temperature sequence input feature x as its starting point, and its feature vector dimension is... Where 1 represents the number of channels, S represents the number of temperature sensors, and T represents the time step;

[0042] Based on the input feature x, first use Do it on the sensor-time grid Spatial convolution upscales the temperature channels at each measurement point to obtain features. ,in, Represents the number of hidden layers;

[0043] The module then proceeds to the spatiotemporal feature extraction module, which consists of parallel graph convolutional neural networks (GCN) and causal convolutional neural networks (TCN):

[0044] In the first spatiotemporal feature module, the spatial branch reshapes the up-dimensional input x into... Extracting data by performing graph convolution on the sensor image. Layer-by-layer normalization is performed during the training of the GCN network based on the learnable adjacency matrix. Training yields an effective graph structure, from which the adjacency matrix can be learned. The training process involves random initialization, forward propagation, and backpropagation of the loss function, and outputs the trained matrix. ;

[0045] The time branch reshapes the input x obtained from the dimensionality upscaling into a time series for each sensor. Using dilated causal convolution to capture multi-scale temporal dependencies And perform layer normalization;

[0046] Take the spatial and temporal features of the output of the last layer GCN and TCN network The element-wise weights are obtained through two sets of "linear → layer normalization → sigmoid" gated mappings, and then weighted summed to form a spatiotemporal fusion representation. Then, pooling (max pooling) is performed along the sensor dimension. This yields spatiotemporal fusion features for one-dimensional temperature information.

[0047] In step 5, for the two-dimensional temperature field image data, fully connected vectors are extracted based on the ResNet-18 model. By using linear mapping and normalization (to eliminate differences in the distribution of different features), Aligning to the same semantic dimension as the spatiotemporal features yields... Where H is a custom feature dimension (consistent with the dimension output by the spatiotemporal feature network, used for subsequent concatenation);

[0048] Meanwhile, for one-dimensional temperature measurement data, a spatiotemporal feature fusion network is used to output the data. Where B also represents the number of samples (corresponding one-to-one with the thermal image samples), and H is the number of samples... Aligned feature dimensions (ensuring consistency between the two types of features in the semantic space);

[0049] Next, in terms of feature dimensions, and The vectors are concatenated to form a fused vector. Where 2H is the dimension after stitching (that is, the fused features of each sample are composed of "temperature spatiotemporal features (H-dimensional) + thermal image features (H-dimensional)");

[0050] Finally, the fused vector z is processed by LayerNorm (which normalizes the fused features to accelerate training convergence) and two layers of feedforward network (non-linear activation function ReLU, which introduces the non-linear expressive power of the model; containing Dropout layer, which randomly discards some neurons to prevent overfitting), and outputs the thermal error prediction value y.

[0051] During the training phase, the MSE loss function (mean squared error loss, which calculates the mean squared difference between the predicted value y and the true thermal error value) is constructed, and the model parameters are optimized through backpropagation to make the predicted value as close as possible to the true value.

[0052] In step 7, as Figure 4 As shown, the thermal error compensation system mainly consists of four parts: a temperature measurement module, a data processing module, a thermal error prediction module, and a thermal error compensation module. The temperature measurement module, as the data input, places temperature sensors near the bearings, motor, spindle box, column, and surrounding environment of the machine tool spindle. A thermal imager is positioned on the side / front of the spindle front end (depending on the actual machining process) to acquire temperature images in real time. The data processing module is developed using PyCharm programming software on a PC, with Python as the programming language. The thermal error prediction module is also developed using PyCharm, with PyTorch as the deep learning framework. The thermal error compensation module establishes communication between the PC and the CNC system via wired / wireless connections, inputting the predicted compensation values ​​of the thermal error model into the CNC system in real time for thermal error compensation.

[0053] The process of applying the above method in practice includes the following steps:

[0054] Step 1: Based on the temperature acquisition module, collect temperature data, infrared images of the temperature field, and machine tool thermal errors; arrange several PT-100 temperature sensors near the column, bed, spindle box, motor, and bearings; design an experimental speed spectrum and run the machine tool accordingly, collecting a set of one-dimensional temperature data every minute. The one-dimensional temperature measurement point data based on the PT-100 is as follows: Figure 5As shown, an infrared camera acquires two-dimensional temperature field infrared images of the machine tool spindle front end, monitors the target temperature distribution in real time, and saves a set of two-dimensional temperature field infrared images every 30 seconds. The thermal image data acquired by the infrared thermal imager is as follows: Figure 6 As shown, the axial Z-direction thermal error of the machine tool is collected by an eddy current displacement sensor. The thermal error measurement results are as follows. Figure 7 As shown;

[0055] Step 2: Based on the data processing module, the one-dimensional temperature measurement point data is standardized, and the time series length is set to 30 minutes with a step size of 1 minute. This means that the thermal error value for the next minute is predicted by collecting 30 minutes of data. The two-dimensional temperature field infrared image is preprocessed by first filtering out non-target areas to extract the input image, and then performing grayscale processing on the input image. The input image is subtracted from the initial image to avoid the influence of the initial ambient temperature and obtain dynamic image features reflecting the temperature field changes. Noise is reduced by filtering algorithms such as Gaussian filtering, and data enhancement is performed by adjusting rotation, translation, brightness, and sharpness to enrich the features of the dataset.

[0056] Step 3: Based on the thermal error prediction module, extract spatiotemporal fusion features from the time-series data of one-dimensional temperature direct measurement points, and output the spatiotemporal fusion features. The temperature distribution features of non-directly measured points in the two-dimensional temperature image are fully extracted, and the spatial temperature distribution features are output. The one-dimensional and two-dimensional temperature output features are then fused to obtain a fused feature vector. Finally, the MSE loss function is constructed for training the network model, and a hot error prediction model is built. The loss during the model training process decreases as follows: Figure 8 As shown;

[0057] Step 4: Predict thermal error compensation values ​​based on the trained model, such as... Figure 9 As shown, this is a comparison between the predicted and measured thermal error results in the Z-axis direction. Based on the output of the aforementioned thermal error prediction model, the required error compensation value is set to the negative direction of the predicted thermal error. The compensation value is then input to the CNC panel via the communication interface provided by the CNC machine tool system to determine the thermal error step size. Figure 10 As shown, the thermal error values ​​of the machine tool spindle system after compensation are displayed. It can be seen that the machining accuracy is significantly improved compared to before compensation.

[0058] In summary, this invention overcomes the bottleneck of rotating spindle temperature data acquisition and achieves high-precision thermal error compensation through a technical approach of "multi-source temperature data fusion + dual feature extraction network + dedicated prediction model." Specifically, this can be summarized into three core steps:

[0059] Multi-source temperature data fusion: By combining a non-contact infrared thermal imager (which acquires two-dimensional temperature field images of the front end of the rotating spindle) with a contact temperature sensor (which acquires one-dimensional time-series temperature of non-moving parts), the shortcomings of traditional models that rely solely on one-dimensional data are overcome, and a multi-source thermal feature dataset of the spindle system consisting of "two-dimensional spatial temperature distribution + one-dimensional spatiotemporal features" is constructed.

[0060] Multi-source feature extraction network collaboration: For two-dimensional infrared images, a ResNet-18 residual network is used to extract the spatial distribution features of the principal axis temperature field (such as temperature gradient and hotspot locations); for one-dimensional time-series data, a stacked spatiotemporal feature fusion network (GCN+TCN parallel structure) is used to extract the temporal variation law of temperature (temporal features of each temperature measurement point) and spatial correlation features (temperature conduction relationship between sensors); the two types of features are combined through "linear mapping + dimension alignment + splicing fusion" to form a more comprehensive thermal feature representation;

[0061] The integrated thermal error compensation system based on the MSD-STFFM model: Construct an MSD-STFFM spindle thermal error prediction model and achieve high-precision prediction through MSE loss function training; At the same time, develop a complete thermal error compensation system including "temperature measurement → data processing → model prediction → compensation execution", and achieve real-time compensation through machine tool communication interface (wired / wireless), forming a closed loop from data acquisition to error cancellation.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for thermal error compensation of a spindle system integrating non-contact measuring points, characterized in that, Includes the following steps: Step 1: Obtain one-dimensional temperature measurement point data near the machine tool spindle box, column, and bed; two-dimensional temperature field image data of the front end of the machine tool spindle; and thermal error of the machine tool spindle. Step 2: Perform unified processing on the one-dimensional temperature measurement point data and the two-dimensional temperature field image data; Step 3: Construct a two-dimensional infrared image feature extraction network to extract two-dimensional temperature field spatial features from two-dimensional temperature field image data; Step 4: Construct a one-dimensional temperature rise time series feature extraction network to extract the time series and spatial features of one-dimensional temperature measurement points from the one-dimensional temperature measurement point data; Step 5: Perform feature fusion between the one-dimensional temperature rise time series feature extraction network and the two-dimensional infrared image feature extraction network to construct the spatiotemporal feature fusion thermal error prediction model MSD-STFFM based on multi-source data, and obtain the thermal error prediction results; Step 6: Based on the thermal error prediction results, set the required error compensation value to the negative thermal error prediction results to achieve real-time prediction and compensation of thermal errors in the machine tool spindle system.

2. The spindle system thermal error compensation method with integrated non-contact measuring points according to claim 1, characterized in that, The steps of acquiring one-dimensional temperature measurement point data near the machine tool spindle box, column, and bed, two-dimensional temperature field image data at the front end of the machine tool spindle, and thermal error of the machine tool spindle are as follows: one-dimensional temperature measurement point data is collected using a PT-100 temperature sensor, two-dimensional temperature field image data is collected using an infrared thermal image camera, and thermal error is measured synchronously using an eddy current displacement sensor.

3. The spindle system thermal error compensation method with integrated non-contact measuring points according to claim 1, characterized in that, The steps for uniformly processing one-dimensional temperature measurement point data and two-dimensional temperature field image data specifically include: Standardize, time-series process, and partition one-dimensional temperature measurement data. Initial value processing, filtering and noise reduction, data augmentation, and data partitioning are performed on the two-dimensional temperature field image data.

4. The spindle system thermal error compensation method with integrated non-contact measuring points according to claim 1, characterized in that, The step of constructing a two-dimensional infrared image feature extraction network to extract two-dimensional temperature field spatial features from two-dimensional temperature field image data specifically includes: Based on the ResNet-18 residual network, image features are extracted through several convolutional and pooling layers, and the features are flattened and output through a fully connected (FC) layer. The output feature dimension is [missing value]. , where B represents the number of input samples, and 512 represents the fixed output dimension of the last fully connected layer of ResNet-18.

5. The spindle system thermal error compensation method with integrated non-contact measuring points according to claim 4, characterized in that, The step of constructing a one-dimensional temperature rise time-series feature extraction network to extract the temporal and spatial features of one-dimensional temperature measurement points from one-dimensional temperature measurement point data specifically includes: A one-dimensional temperature rise time-series feature extraction network is constructed by using a stacked two-layer spatiotemporal feature fusion network model with the same number of units. The spatiotemporal feature fusion network model takes the temperature sequence input feature x as its starting point, and its feature vector dimension is... Where 1 represents the number of channels, S represents the number of temperature sensors, and T represents the time step; Based on the input feature x, the following is adopted: Do it on the sensor-time grid Spatial convolution upscales the temperature channels at each measurement point to obtain features. ,in, Represents the number of hidden layers; Based on the Graph Convolutional Neural Network (GCN), the spatial branch reshapes the input features x obtained from the dimensionality upscaling into... Extracting data by performing graph convolution on the sensor image. Layer-by-layer normalization is performed during the training of the GCN network based on the learnable adjacency matrix. The training yields an effective graph structure, and the trained matrix is ​​output. ; Based on the causal convolutional neural network TCN, the time branch reshapes the input features x obtained from the dimensionality upscaling into time series for each sensor. Using dilated causal convolution to capture multi-scale temporal dependencies And perform layer normalization; Take the spatial and temporal features of the output of the last layer GCN and TCN network and The element-wise weights are obtained through two sets of gating mappings and then weighted summed to form a spatiotemporal fusion representation. Where H is the feature dimension, pooled along the sensor dimension. This yields spatiotemporal fusion features for one-dimensional temperature information.

6. The spindle system thermal error compensation method with integrated non-contact measuring points according to claim 5, characterized in that, The step of fusing features from a one-dimensional temperature rise time-series feature extraction network and a two-dimensional infrared image feature extraction network to construct a spatiotemporal feature fusion thermal error prediction model MSD-STFFM based on multi-source data and obtaining thermal error prediction results specifically includes: For two-dimensional temperature field image data, fully connected vectors are extracted based on the ResNet-18 model. Through linear mapping and normalization, Aligning to the same semantic dimension as the spatiotemporal features yields... , where H is a custom feature dimension, consistent with the dimension output by the spatiotemporal feature network; For one-dimensional temperature measurement data, the output is obtained through a spatiotemporal feature fusion network. Where B represents the number of samples, corresponding one-to-one with the thermal image samples, and H is the number of samples... Alignment feature dimensions; In terms of feature dimension and The vectors are concatenated to form a fused vector. Where 2H is the dimension after splicing; The fused vector z passes through LayerNorm and two layers of feedforward network to output the thermal error prediction value y.

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