Thermal error prediction method and system based on WFGN

Abstract

The invention discloses a thermal error prediction method and system based on WFGN, and the method comprises the steps: S1, obtaining temperature sequence data and part error data, and converting the data into graph structure data; s2, constructing a data set by using the graph structure data, and dividing the data set into a training set, a verification set and a test set; s3, constructing a multi-domain fusion graph neural network which comprises a Fourier transform-based convolutional network used for capturing global features, a wavelet transform-based convolutional network used for capturing local features and a full-connection network, and performing connection through a feature fusion layer; s4, training the multi-domain fusion graph neural network; s5, predicting a corresponding error result according to the temperature sequence data detected during part machining; a deep learning technology is utilized, a Fourier transform convolutional network, a wavelet transform convolutional network and a full-connection network are fused, thermal errors generated at different machine tool machining temperatures are learned and automatically predicted, global frequency features are extracted through Fourier transform, local multi-scale change features are captured through wavelet transform, and the local multi-scale change features are obtained. And a high-precision prediction result is output through full-connection network integration, so that the precision and efficiency of thermal error prediction are effectively improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical control machining data processing, and particularly relates to a thermal error prediction method and system based on WFGN. BACKGROUND

[0002] In the field of modern highly automated numerical control machine tool machining, thermal error has become a key factor restricting the improvement of machining precision. The generation of thermal error is mainly caused by the continuous change of internal and external heat of the machine tool during long-time operation. These heat changes may be caused by the motor operation of the machine tool itself, the frictional heat generated in the cutting process, and the fluctuation of the external environment temperature. The accumulation and transmission of these heat cause slight size and shape changes of various parts of the machine tool, such as the bed, guide rail and tool, which in turn adversely affect the size and shape precision of the machined parts.

[0003] Traditional thermal error compensation methods usually rely on a large amount of field experimental data accumulation and empirical formula derivation. This method faces many challenges in practical application. First, there is a lack of prediction accuracy. Due to the limitations of experimental data, the approximation of empirical formula and the need for a long time to collect and analyze data, it is difficult to achieve rapid response in actual machining process, which affects the machining efficiency and product quality. Therefore, seeking a more accurate and efficient thermal error prediction method has become a problem to be solved in the field of modern numerical control machine tool machining. SUMMARY

[0004] The purpose of the present application is to provide a thermal error prediction method and system based on WFGN to solve the problems raised in the background.

[0005] To achieve the above purpose, the present application provides the following technical scheme:

[0006] A thermal error prediction method based on WFGN, comprising:

[0007] Step S1: Obtain the temperature sequence data of the target point and the error data generated during the machining of the workpiece, and preprocess the collected data to convert the data into graph structure data;

[0008] Step S2: Construct a data set using the graph structure data, and divide the data set into a training set, a validation set and a test set according to a preset proportion;

[0009] Step S3: constructing a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network comprises a Fourier transform-based convolution network for capturing global features, a wavelet transform-based convolution network for capturing local features, and a fully connected network, and the Fourier transform-based convolution network, the wavelet transform-based convolution network, and the fully connected network are connected through a feature fusion layer;

[0010] Step S4: training the multi-domain fusion graph neural network using the training set and the validation set respectively to obtain a trained multi-domain fusion graph neural network; and testing the trained multi-domain fusion graph neural network using a test set;

[0011] Step S5: after the multi-domain fusion graph neural network is tested, predicting a corresponding error result according to temperature sequence data detected during part processing, and adjusting part processing parameters according to the prediction result to reduce errors.

[0012] Further technical solutions, the Fourier transform-based convolution network comprises a Fourier convolution layer, a residual block layer, a max-pooling layer, and an inverse Fourier convolution layer, the wavelet transform-based convolution network comprises four wavelet decomposition layers and a reconstruction layer, the fully connected network is a multi-layer perceptron, and the fully connected network comprises three fully connected layers and an output layer.

[0013] Further technical solutions, the Fourier convolution layer obtains a corresponding Laplace feature matrix according to an adjacency matrix of graph structure data, calculates a Fourier transform result according to the feature matrix and input temperature sequence data, and compresses input data from (32, 256, 128) to (32, 64), the residual block layer is used for retaining data features, a convolution kernel size of the residual block layer is 3×3×3, the inverse Fourier convolution layer restores data dimension to 128 dimensions, and a use function of the Fourier layer is represented as:

[0014]

[0015] wherein is a Hadamard product, and is a convolution filter, is a feature matrix of a Laplace matrix, is temperature sequence data.

[0016] Further technical solutions, a wavelet kernel size of the wavelet transform layer is 5×5, the reconstruction layer is used for implementing inverse wavelet transform, and a use function of the wavelet transform layer is represented as:

[0017]

[0018] wherein is a corresponding scale parameter a target wavelet kernel function, is a corresponding node number, is an eigenvalue of a Laplacian matrix of a graph signal.

[0019] Further technical solutions, for step S1: comprising

[0020] Step S11: providing 16 temperature sensors, of which 7 temperature sensors are distributed along the central axis of the electric spindle, another 7 temperature sensors are distributed in the front bearing water inlet and outlet, the motor water inlet and outlet, the cooling jacket front, middle and rear positions, and the remaining 2 temperature sensors measure the temperature of the workbench and the surrounding environment;

[0021] Step S12: statistics the special expansion error data of the central axis of the electric spindle;

[0022] Step S13: the time interval between the two temperature data measured by the temperature sensor is 1 minute, and the normalized temperature data and error data after sampling are normalized.

[0023] Further technical solutions, for said respectively using the training set and the validation set to train the multi-domain fusion graph neural network, comprising using mean square error as a loss function and RMSProp as an optimizer for optimization training in the multi-domain fusion graph neural network training process, the loss function is expressed as:

[0024]

[0025] where n is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point; then use the back propagation algorithm to update the model parameters.

[0026] Further technical solutions, the multi-domain fusion graph neural network uses a look-ahead correction unit function as the activation function of the Fourier convolution layer, the inverse Fourier convolution layer, the four wavelet decomposition layers, the reconstruction layer and the full connection layer.

[0027] Further technical solutions, the comparison evaluation standard of the output data of the multi-domain fusion graph neural network and the actual data includes the mean absolute error and the root mean square error, the mean absolute error is the average of the absolute value of the difference between the predicted value and the actual value, the smaller the better the deviation of the multi-domain fusion graph neural network, the root mean square error is the square root of the average of the square of the difference between the predicted value and the actual value, the smaller the better the deviation of the multi-domain fusion graph neural network, the expression of the mean absolute error is:

[0028]

[0029] where MAE is the mean absolute error, and m is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point;

[0030] The expression of the root mean square error is:

[0031]

[0032] where RMAE is the root mean square error, and m is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point.

[0033] Further, the degree of explanation of the actual value total variation of the multi-domain fusion graph neural network is R2, the value of R2 is between 0 and 1, the closer the value of R2 is to 1, the better the fitting degree of the multi-domain fusion graph neural network to the data, and the expression of R2 is:

[0034]

[0035] where m is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point.

[0036] A thermal error prediction system based on WFGN, comprising:

[0037] A data acquisition module acquires temperature sequence data of a target point and error data generated during machining of a part, pre-processes the collected data, and converts the data into graph structure data;

[0038] A data processing module constructs a data set using the graph structure data, and divides the data set into a training set, a validation set, and a test set according to a preset proportion;

[0039] A model construction module constructs a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network includes a Fourier transform-based convolutional network for capturing global features, a wavelet transform-based convolutional network for capturing local features, and a fully connected network, and the Fourier transform-based convolutional network, the wavelet transform-based convolutional network, and the fully connected network are connected through a feature fusion layer;

[0040] A model training module trains the multi-domain fusion graph neural network using the training set and the validation set, respectively, to obtain a trained multi-domain fusion graph neural network, and then tests the trained multi-domain fusion graph neural network using the test set;

[0041] The model uses a module, and the multi-domain fusion graph neural network predicts corresponding error results according to temperature sequence data detected during part processing after testing, and adjusts part processing parameters according to the prediction results to reduce errors.

[0042] The present application has the following advantages:

[0043] The present application uses deep learning technology to learn and automatically predict thermal errors generated under different machine tool processing temperatures by fusing a Fourier transform convolution network, a wavelet transform convolution network and a fully connected network through input temperature sequence data and error data, optimizes part processing technology, reduces the workload of manual selection of processing technology, extracts global frequency features through Fourier transform, captures local multi-scale change features through wavelet transform, and integrates and outputs high-precision prediction results through a fully connected network, effectively improving the accuracy and efficiency of the multi-domain fusion graph neural network model for thermal error prediction.

[0044] Other features and advantages of the present application will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 : The step diagram of the thermal error prediction method based on WFGN of the present application.

[0046] Figure 2 : The flowchart of the thermal error prediction method based on WFGN of the present application.

[0047] Figure 3 : The structure diagram of the graph convolution-based neural network model of the present application.

[0048] Figure 4 : The score result graph predicted in the manufacturing process of the test set of the present application. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0050] Please refer to Figures 1-4 ;

[0051] It is known that the traditional thermal error compensation method relies on a large amount of experimental data and empirical formula, and in actual application, due to the limited coverage of experimental data, it is difficult to represent all processing scenes, and the empirical formula is too simplified to accurately describe the nonlinear and dynamic thermal error characteristics, resulting in low prediction accuracy; due to the long time consumption of data collection and analysis, it is difficult to quickly generate a compensation formula, and it lacks dynamic adjustment capability, so it is difficult to track the thermal error change in real time during processing, resulting in insufficient real-time performance;

[0052] Further, the problems encountered in the use of the existing thermal error compensation method cannot be eliminated, even if the data is processed and extracted through deep learning, and the prediction error is learned through a deep learning algorithm, the accuracy is low and the real-time performance is poor, because deep learning lacks explicit modeling of the physical characteristics of the thermal error, and the demand for a large amount of high-quality training data is high, while the thermal error data is often insufficient due to experimental cost and complexity of working conditions, resulting in low prediction accuracy, model overfitting or poor generalization ability; in addition, the deep learning model has large computational complexity and parameter quantity, and the training and inference time is long, which is difficult to meet the real-time requirement of the processing scene.

[0053] Therefore, the present application discloses a thermal error prediction method based on WFGN, which aims to accurately and efficiently automatically learn and predict thermal errors from design and manufacturing data; specifically, as Figures 1-2 , comprising:

[0054] Step S1: obtaining temperature sequence data of a target point and error data generated during processing of a part, preprocessing the collected data, and converting the data into graph structure data;

[0055] Step S2: constructing a data set using the graph structure data, specifically putting the collected data into a unified CSV file to form a data set, and then dividing the data set into a training set, a validation set and a test set according to a predetermined proportion; in this embodiment, the data set is divided into a training set, a validation set and a test set in a ratio of 7:2:1;

[0056] Step S3: constructing a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network includes a Fourier transform-based convolution network for capturing global features, a wavelet transform-based convolution network for capturing local features, and a fully connected network, the Fourier transform-based convolution network, the wavelet transform-based convolution network and the fully connected network are connected through a feature fusion layer;

[0057] Step S4: training the multi-domain fusion graph neural network using the training set and the validation set respectively to obtain a trained multi-domain fusion graph neural network; and testing the trained multi-domain fusion graph neural network using the test set to check the training effect of the multi-domain fusion graph neural network model;

[0058] Step S5: After the multi-domain fusion graph neural network is tested, the corresponding error result is predicted according to the temperature sequence data detected during part processing, and the part processing parameters are adjusted according to the prediction result to reduce the error.

[0059] More specifically, by using deep learning technology, by fusing Fourier transform convolution network, wavelet transform convolution network and full connection network, learning through input temperature sequence data and error data, automatically predicting thermal error generated under different machine tool processing temperatures, optimizing part processing technology, reducing the workload of manual selection of processing technology, extracting global frequency features by Fourier transform, capturing local multi-scale change features by wavelet transform, and integrating high-precision prediction results through full connection network, effectively improving the accuracy and efficiency of the multi-domain fusion graph neural network model for thermal error prediction; compared with the traditional method, the multi-domain fusion graph neural network model significantly reduces the time-consuming of data collection and processing, realizes stronger real-time thermal error compensation, reduces processing error, improves part processing quality and production efficiency, and is especially suitable for high-precision numerical control machine tool processing scene.

[0060] Further, for step S1: comprising

[0061] Step S11: 16 temperature sensors are provided, of which 7 temperature sensors are distributed along the central axis of the motorized spindle, more specifically, 1 temperature sensor is inside the front shaft, 1 temperature sensor is in the front bearing shell, 2 temperature sensors are on the side of the front bearing shell, 1 temperature sensor is on the flange surface of the front bearing shell, 1 temperature sensor is inside the rear bearing, and 1 temperature sensor is outside the rear bearing; the other 7 temperature sensors are distributed in the front bearing water inlet and outlet, motor water inlet and outlet, cooling jacket front, middle and rear positions, and the remaining 2 temperature sensors measure the temperature of the workbench and the surrounding environment.

[0062] Step S12: The thermal error data is obtained by measuring the thermal error data of the motorized spindle center axis, and the target variable represented by the error data is measured by a professional tool.

[0063] Step S13: The time interval between the two temperature data measured by the temperature sensor is 1 minute, and the normalized temperature data and error data after sampling are normalized.

[0064] Further, in the embodiment of the present application, the convolution network based on Fourier transform includes Fourier convolution layer, residual block layer, maximum pooling layer and inverse Fourier convolution layer, the convolution network based on wavelet transform includes four wavelet decomposition layers and reconstruction layers, the full connection network is a multi-layer perception machine, and the full connection network includes three full connection layers and an output layer.

[0065] More specifically, in the multi-domain fusion graph neural network model structure, the Fourier layer obtains information from the adjacency matrix in the input graph structure data to perform Fourier transformation, obtains the corresponding Laplacian matrix through the adjacency matrix, then calculates the eigenmatrix of the Laplacian matrix, and finally uses the eigenmatrix and the input temperature sequence data to calculate the Fourier transform result to compress the input data from (32, 256, 128) to (32, 64); in addition, there is a residual block layer for retaining data features, the input and output channel numbers of the residual block layer are the channel numbers of the data input, the residual block layer performs a three-dimensional convolution inside, the convolution kernel is set to 3x3x3 size, and the padding is set to 1, and at the same time, in order to ensure that the data dimensions can be reconstructed to (32, 64). Then input the data into the 4-fold wavelet decomposition layer, the wavelet kernel used by the wavelet decomposition layer is 5x5 size, and the wavelet transform and inverse wavelet transform are realized through the decomposition and reconstruction of the 4-fold wavelet decomposition layer, and then sufficient local features are extracted, and then the data dimension is restored to 128-dimensional space through inverse Fourier transform, finally, the features are inferred through three fully connected layers, including Fc1(128:64), Fc2(64:16), Fc3(16:1), and finally the prediction result is output by the output layer.

[0066] In this embodiment, the multi-domain fusion graph neural network uses a look-ahead correction unit function as the activation function of the Fourier convolution layer, the inverse Fourier convolution layer, the four wavelet decomposition layers, the reconstruction layer and the fully connected layer, and then uses mean square error (MSE) as the loss function to train the model and uses RMSProp as the optimizer to optimize the parameters.

[0067] More specifically, in this embodiment, the activation function used in the multi-domain fusion graph neural network model is a Tanh function represented as:

[0068]

[0069] In the formula, e represents the base of natural logarithm, x represents the input variable, and tanh(x) represents the activation function.

[0070] The Fourier layer of the multi-domain fusion graph neural network model uses a function represented as:

[0071]

[0072] wherein is the Hadamard product, and is a convolution filter, is the eigenmatrix of the Laplacian matrix, is the temperature sequence data.

[0073] The wavelet layer of the multi-domain fusion graph neural network model uses a function represented as:

[0074]

[0075] wherein is the corresponding scale parameter is the target wavelet kernel function, is the corresponding number of nodes, is the eigenvalue of the Laplacian matrix of the graph signal.

[0076] The multi-domain fusion graph neural network model uses mean squared error (MSE) as a loss function to train the model, which is expressed as:

[0077]

[0078] where n is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point.

[0079] In order to better understand the construction of the multi-domain fusion graph neural network model, as shown in Figure 2 In this embodiment, the main flow of the algorithm of the multi-domain fusion graph neural network model is described,

[0080] As shown in Figure 3 The multi-domain fusion graph neural network model uses a convolutional network based on Fourier transform to extract global features and spatial features, and a convolutional network based on wavelet transform to extract local features. At the same time, a residual block layer is added in the Fourier layer to preserve data information. After feature extraction, a series of fully connected layers are used to gradually reduce the dimension, and finally the prediction result is obtained. The multi-domain fusion graph neural network model improves the training stability through mechanisms such as residual connection and batch normalization, and combines local and global features, which is suitable for processing spatial data and sequence data prediction tasks.

[0081] The specific process is as follows:

[0082] A1: Input: training data set train_loader, validation data set validate_loader, test data set test_loader. Total number n, number of correct predictions correct, learning rate α, training iteration number epochs, batch size batch.

[0083] Model initialization, iteration number t = 1, 2... T:

[0084] A2: Iterative training process:

[0085] a. For each epoch = 1, 2,..., epochs:

[0086] i. Batch the training data set train_loader and perform batch training:

[0087] Iterate through each batch and input the model for training;

[0088] Calculate the loss function of the model output:

[0089]

[0090] where n is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point;

[0091] Update the model parameters using the backpropagation algorithm:

[0092]

[0093] ii. Evaluate the model performance on the validation set:

[0094] Evaluate the performance of the current epoch of the model using the validation data set valid_loader

[0095]

[0096] where correct represents the number of correct predictions, total represents the total number of samples in the validation set, and Accuracy represents the accuracy indicator;

[0097] Further, in order to improve the computational efficiency and practicality of the multi-domain fusion graph neural network model, residual connections are introduced in this embodiment to accelerate the convergence speed in the training process, ensure the stability of the multi-domain fusion graph neural network model in the network structure, and avoid the problem of gradient vanishing.

[0098] In this embodiment, the comparison evaluation criteria of the output data of the multi-domain fusion graph neural network and the actual data include the mean absolute error and the root mean square error. The mean absolute error is the average of the absolute values of the differences between the predicted values and the actual values. The smaller the mean absolute error, the better the deviation of the multi-domain fusion graph neural network. The expression of the mean absolute error is:

[0099]

[0100] where MAE is the mean absolute error, n is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point;

[0101] The root mean square error is the square root of the average of the square of the difference between the predicted value and the actual value, and the smaller it represents the better the bias of the multi-domain fusion graph neural network, and the expression of the root mean square error is:

[0102]

[0103] In the formula, RMAE is the root mean square error, m is the number of data points, is the actual value of the i-th data point, is the predicted value of the i-th data point.

[0104] In addition, in the present embodiment, the mean absolute percentage error (MAPE) can also be used as a multi-domain fusion graph neural network model comparison and measurement standard, the mean absolute percentage error is the average of the absolute value of the difference between the predicted value and the actual value and the ratio of the actual value, and the smaller it is, the better, and it is usually expressed in percentage, and the expression is

[0105]

[0106] In the formula, MAPE is the root mean square error, m is the number of data points, is the actual value of the i-th data point, is the predicted value of the i-th data point.

[0107] Further, the multi-domain fusion graph neural network has an explanation degree of total variation of the actual value R 2, the value of R 2 is between 0 and 1, and the closer the value of R 2 is to 1, the better the fitting degree of the multi-domain fusion graph neural network to the data, and the expression of R 2 is:

[0108]

[0109] In the formula, m is the number of data points, is the actual value of the i-th data point, is the predicted value of the i-th data point.

[0110] In the present embodiment, in the training stage of the multi-domain fusion graph neural network, the root mean square propagation method (RMSProp) is used as the optimizer to determine the optimal weight, and the use of RMSProp has a fast convergence speed and is suitable for complex model training of high-dimensional data, and in the main process of the algorithm, a total of 1000 epochs are used, the batch size is set to 32, and the learning rate is set to 10 -4 ; finally, the trained model is used to test more than 800 test sets that have never been seen, and the experimental results are as shown in Figure 4

[0111] The application also discloses a WFGN-based thermal error prediction system, which comprises:

[0112] ​The data acquisition module acquires temperature sequence data of the target point and error data generated during machining of the part, pre-processes the collected data, and converts the data into graph structure data;

[0113] The data processing module constructs a data set using the graph structure data, and divides the data set into a training set, a validation set and a test set according to a preset ratio;

[0114] The model construction module constructs a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network includes a Fourier transform-based convolution network for capturing global features, a wavelet transform-based convolution network for capturing local features, and a fully connected network, and the Fourier transform-based convolution network, the wavelet transform-based convolution network and the fully connected network are connected through a feature fusion layer;

[0115] The model training module trains the multi-domain fusion graph neural network using the training set and the validation set, respectively, to obtain a trained multi-domain fusion graph neural network, and then tests the trained multi-domain fusion graph neural network using the test set;

[0116] The model using module, after the multi-domain fusion graph neural network is tested, predicts the corresponding error result according to the temperature sequence data detected during machining of the part, and adjusts the part machining parameters according to the prediction result to reduce the error.

[0117] It is apparent to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, but can be implemented in other concrete forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be considered in all respects as illustrative and not restrictive, and the scope of the present application is defined by the appended claims rather than the above description, and it is intended to encompass all changes falling within the meaning and range of equivalents of the elements of the claims. Any reference signs in the claims should not be considered as limiting the claims involved.

[0118] Furthermore, it should be understood that, although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description manner of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be properly combined to form other embodiments that those skilled in the art can understand.

Claims

1. A WFGN-based thermal error prediction method, characterized in that, The method comprises the following steps: Step S1: Obtain the temperature sequence data of the target point and the error data generated during the machining of the part, preprocess the collected data, and convert the data into graph structure data; Step S2: Construct a data set using the graph structure data, and divide the data set into a training set, a validation set, and a test set according to a predetermined proportion; Step S3: Construct a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network comprises a Fourier transform-based convolution network for capturing global features, a wavelet transform-based convolution network for capturing local features, and a fully connected network, and the Fourier transform-based convolution network, the wavelet transform-based convolution network, and the fully connected network are connected through a feature fusion layer; Step S4: Train the multi-domain fusion graph neural network using the training set and the validation set respectively to obtain a trained multi-domain fusion graph neural network; and test the trained multi-domain fusion graph neural network using the test set; Step S5: After the multi-domain fusion graph neural network is tested, predict the corresponding error result according to the temperature sequence data detected during the machining of the part, and adjust the machining parameters of the part to reduce the error according to the prediction result.

2. The WFGN-based thermal error prediction method of claim 1, wherein, The Fourier transform-based convolution network comprises a Fourier convolution layer, a residual block layer, a max-pooling layer, and an inverse Fourier convolution layer, the wavelet transform-based convolution network comprises four wavelet decomposition layers and a reconstruction layer, and the fully connected network is a multi-layer perceptron, which comprises three fully connected layers and an output layer.

3. The WFGN-based thermal error prediction method of claim 2, wherein, The Fourier convolution layer obtains a corresponding Laplacian feature matrix according to the adjacency matrix of the graph structure data, calculates the Fourier transform result of the input data from (32, 256, 128) to (32, 64) according to the feature matrix and the input temperature sequence data, the residual block layer is used to retain data features, the size of the convolution kernel of the residual block layer is 3x3x3, and the inverse Fourier convolution layer restores the data dimension to 128 dimensions; the function used by the Fourier layer is represented as: wherein is a Hadamard product while is a convolution filter, is an eigenmatrix of a Laplacian matrix, is temperature sequence data.

4. The WFGN-based thermal error prediction method of claim 3, wherein, The size of the wavelet kernel of the wavelet transform layer is 5x5, and the reconstruction layer is used to implement inverse wavelet transform; the function used by the wavelet transform layer is represented as: wherein is a target wavelet kernel function of a corresponding scale parameter , is a corresponding number of nodes, is an eigenvalue of a Laplacian matrix of the graph signal.

5. The WFGN-based thermal error prediction method of claim 1, wherein, For step S1: It comprises Step S11: Provide 16 temperature sensors, of which 7 temperature sensors are distributed along the central axis of the electric spindle, and the other 7 temperature sensors are distributed at the front bearing water inlet and outlet, the motor water inlet and outlet, the front, middle, and rear positions of the cooling jacket, and the remaining 2 temperature sensors measure the temperature of the workbench and the surrounding environment; Step S12: Count the special expansion error data of the central axis of the electric spindle; Step S13: The time interval between the two temperature data measured by the temperature sensor is 1 minute, and the normalized temperature data and error data after sampling are normalized.

6. The WFGN-based thermal error prediction method of claim 1, wherein, For training the multi-domain fusion graph neural network using the training set and the validation set respectively, during the training process of the multi-domain fusion graph neural network, the mean square error is used as the loss function and the RMSProp is used as the optimizer for optimization training, and the loss function is represented as: where n is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point; the model parameters are then updated using a backpropagation algorithm.

7. The WFGN-based thermal error prediction method of claim 1, wherein, The multi-domain fusion graph neural network uses a look-ahead correction unit function as an activation function of a Fourier convolution layer, an inverse Fourier convolution layer, four wavelet decomposition layers, a reconstruction layer, and a full connection layer.

8. The WFGN-based thermal error prediction method of claim 1, wherein, The comparison evaluation standard of output data of the multi-domain fusion graph neural network and actual data includes a mean absolute error and a root mean square error, the mean absolute error is an average of absolute values of differences between predicted values and actual values, and the smaller the mean absolute error is, the better the deviation of the multi-domain fusion graph neural network is, the root mean square error is a square root of an average of squares of differences between predicted values and actual values, and the smaller the root mean square error is, the better the deviation of the multi-domain fusion graph neural network is, and an expression of the mean absolute error is: where MAE is the mean absolute error, m is the number of data points, is the true value of the ith data point, is the predicted value of the ith data point; An expression of the root mean square error is: where RMAE is the root mean square error, m is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point.

9. The WFGN-based thermal error prediction method of claim 1, wherein, An explanation degree of the multi-domain fusion graph neural network to total variation of actual values is R 2, the R 2 value is between 0 and 1, the closer the R 2 value is to 1, the better the fitting degree of the multi-domain fusion graph neural network to data is, and an expression of the R 2 is: where m is the number of data points, is the true value of the i-th data point, is the predicted value of the i-th data point.

10. A WFGN-based thermal error prediction system, characterized by, The above claim 1 and: A data acquisition module acquires temperature sequence data of a target point and error data generated when a part is processed, pre-processes collected data, and converts the data into graph structure data; A data processing module constructs a data set by using the graph structure data, and divides the data set into a training set, a validation set, and a test set according to a preset proportion; A model construction module constructs a multi-domain fusion graph neural network, wherein the multi-domain fusion graph neural network includes a Fourier transform-based convolution network for capturing global features, a wavelet transform-based convolution network for capturing local features, and a full connection network, the Fourier transform-based convolution network, the wavelet transform-based convolution network, and the full connection network are connected through a feature fusion layer; A model training module trains the multi-domain fusion graph neural network by using the training set and the validation set, respectively, to obtain a trained multi-domain fusion graph neural network, and then tests the trained multi-domain fusion graph neural network by using the test set; A model use module predicts corresponding error results according to detected temperature sequence data when a part is processed after the multi-domain fusion graph neural network is tested, and adjusts part processing parameters according to the predicted results to reduce errors.

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