Comprehensive thermal positioning error modeling method based on data driving and sparse serialization

Abstract

The invention relates to the technical field of machine tool thermal error modeling, and particularly discloses a comprehensive thermal positioning error modeling method based on data driving and sparse serialization, and the method comprises the steps: collecting historical temperature data and historical comprehensive thermal positioning error data of a plurality of temperature measurement points in a full-closed-loop multi-shaft transmission system of a machine tool; decomposing the historical comprehensive thermal positioning error data of each temperature measurement point into historical thermal drift data and historical thermal slope data; respectively establishing a GGT thermal drift prediction model and a thermal slope prediction model according to the training data set; performing effect verification on the GGT thermal drift prediction model and the thermal slope prediction model according to the verification data set; and combining the GGT thermal drift prediction model passing the verification and the thermal slope prediction model passing the verification into a comprehensive thermal positioning error model, and evaluating the comprehensive thermal positioning error model according to the verification data set. According to the method, the comprehensive thermal positioning error can be accurately predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of machine tool thermal error modeling, and more specifically, to a comprehensive thermal positioning error modeling method based on data drive and sparse serialization. Background Art

[0002] With the wide application of full-closed-loop multi-axis drive systems in the fields of high-precision equipment and precision control, the accuracy and reliability of the transmission system have become the focus of attention. In this context, the present invention conducts a comprehensive analysis and modeling of the comprehensive thermal positioning error of the full-closed-loop multi-axis drive system, focusing on two aspects: thermal drift and thermal positioning error. Under the combined influence of the full-closed-loop transmission system with different drive modes and the heating of the spindle, the complex interaction between thermal drift and thermal positioning error becomes a difficult point in the study.

[0003] High-precision machine tools often use cooling systems and optical grating position feedback to mitigate the thermal positioning errors generated by the transmission system in this area. However, the spindle of a precision machine tool can significantly affect the stability of the thermal positioning errors in a multi-axis system, and research on this issue has not been fully explored. The complexity of the comprehensive thermal positioning error is mainly due to the fact that the locking of the spindle also generates heat, causing the thermal deformation of the spindle to interweave and interfere with the thermal positioning errors of the transmission system, resulting in severe thermal drift in the multi-axis transmission system.

[0004] Therefore, the variation of comprehensive thermal positioning error in the fully closed-loop controlled multi-axis transmission system is very complex. This paper firstly conducts in-depth research on comprehensive thermal positioning error, innovatively divides it into thermal drift problem and thermal positioning error problem, and conducts data characteristic analysis and modeling prediction research respectively. Summary of the invention

[0005] In response to the above-mentioned technical problems existing in the microscope autofocus based on natural images, the present invention provides a comprehensive thermal positioning error modeling method based on data-driven and sparse serialization, which can achieve accurate prediction of the comprehensive thermal positioning error.

[0006] As a first aspect of the present invention, a comprehensive thermal positioning error modeling method based on data-driven and sparse serialization is provided, comprising the following steps:

[0007] Step S1: collecting historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measuring points in a fully closed-loop multi-axis transmission system of a machine tool, wherein the historical temperature data and historical comprehensive thermal positioning error data of each temperature measuring point are used as a data set, and the multiple data sets are divided into a training data set and a verification data set;

[0008] Step S2: decomposing the historical comprehensive thermal positioning error data of each temperature measurement point into historical thermal drift data and historical thermal slope data;

[0009] Step S3: establishing a GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the training data set, and establishing a thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler;

[0010] Step S4: verifying the effect of the GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the verification data set; and verifying the effect of the thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the verification data set;

[0011] Step S5: Combining the verified GGT thermal drift prediction model and the verified thermal slope prediction model into a comprehensive thermal positioning error model, and evaluating the comprehensive thermal positioning error model based on the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set.

[0012] Furthermore, the step S1 further includes:

[0013] Incrementally process the collected multiple historical temperature data to obtain incremental historical temperature data;

[0014] A sparse serialization operation is performed on the incremental historical temperature data to obtain sparse serialized historical temperature data.

[0015] Furthermore, the step of performing a sparse serialization operation on the incremental historical temperature data to obtain sparse serialized historical temperature data further includes:

[0016] Determine the sampling quantity and sampling step of historical temperature data;

[0017] Determine the initial sampling point position of the historical temperature data according to the timestamp of the historical comprehensive thermal positioning error data;

[0018] Obtain the locations of all sampling points of historical temperature data according to the sampling step length and the sampling quantity;

[0019] Among them, if the sampling point position is empty, it means that before time zero, the historical temperature data will be completely filled with zero; finally, sparse serialized historical temperature data and its corresponding historical comprehensive thermal positioning error data are obtained.

[0020] Furthermore, the GGT thermal drift prediction model comprises a GCN module, a Bi-GRU module, an encoder module, a first linear layer, a ReLu activation layer, a second linear layer and an output layer, and the GGT thermal drift prediction model is established according to the historical temperature data and the historical thermal drift data in the training data set, and further comprises:

[0021] Step S311: construct a GCN module, the core formula of the GCN module is as follows:

[0022] Z=ReLU(AXW)

[0023] Among them, Z is the output, ReLU is a nonlinear activation function, A is the deformation adjacency matrix, X is the input historical temperature data, and W is the weight matrix;

[0024] Step S312: construct a Bi-GRU module, the core formula of the Bi-GRU module is as follows:

[0025]

[0026] Among them, X t is the historical temperature data currently input; Z t , R t , H t and Respectively represent the current update gate, the current reset gate, the current candidate hidden state and the current hidden state; H t—1 represents the previous candidate hidden state; W, U and b are all weight matrices; φ h and σ g represent the hyperbolic tangent and Sigmod function respectively; ⊙ is the Hadamard product;

[0027] Step S313: Integrate the feature information output by the GCN module and the feature information output by the Bi-GRU module, and then perform regression prediction on the integrated feature information through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer in sequence, and finally output the thermal drift prediction result through the output layer, wherein the formula of the multi-head attention mechanism in the encoder module is as follows:

[0028]

[0029] Where Q is the query; K is the key; V is the value; softmax() is the normalized exponential function, d k is the vector dimension.

[0030] Furthermore, it also includes:

[0031] The input historical temperature data is passed through the GCN module and the Bi-GRU module respectively to learn the spatial information features and the temporal information features; the GCN module and the Bi-GRU module output a one-dimensional feature vector respectively, and the two one-dimensional feature vectors are concatenated and integrated to obtain a new one-dimensional encoding feature vector;

[0032] The new one-dimensional encoded feature vector is sequentially passed through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer for regression prediction, and finally the thermal drift prediction result is output through the output layer;

[0033] The encoder module includes a multi-head attention mechanism, a first residual connection layer and a normalization layer, a feedforward neural network layer, and a second residual connection layer and a normalization layer.

[0034] Furthermore, the thermal slope prediction model is established according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler, and further includes:

[0035] Step S321: using a random forest model to perform regression prediction on the thermal slope;

[0036] Step S322: using the Bayesian inference method to optimize the hyperparameters of the random forest model to obtain a trained random forest model;

[0037] Step S323: Establish a physical model based on the thermal expansion coefficient of the grating ruler. The core formula of the physical model is:

[0038]

[0039] Among them, y ex Represents historical thermal slope data in μm / L; is the average temperature around the grating ruler; α is the thermal expansion coefficient of the grating ruler, expressed in 12μm / ℃ / m; L is the stroke length of the moving axis, in meters.

[0040] Furthermore, the random forest model is a machine learning model including multiple decision trees, historical temperature data is input into a single decision tree to obtain a thermal slope prediction value, and the thermal slope prediction values ​​of multiple decision trees are weighted and superimposed to form a random forest model to obtain better prediction ability and model robustness;

[0041] Among them, the random forest model contains multiple hyperparameters. The multiple hyperparameters of the random forest model are optimized by Bayesian optimization to obtain the optimal hyperparameters, thereby obtaining a trained random forest model; the historical temperature data is input into the trained random forest model to obtain the final thermal slope prediction result.

[0042] Further, the evaluating the comprehensive thermal positioning error model according to the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set also includes:

[0043] The evaluation indicators of the comprehensive thermal positioning error model include root mean square error RMSE, mean absolute error MAE, correction determination coefficient R 2 Adj And total absolute error TAE, where the formulas for each evaluation indicator are as follows:

[0044]

[0045] in,

[0046]

[0047] Among them, y i is the observed value; is the observed value y i The average value of is the predicted value; n is the number of samples; p is the number of features; R 2 is the coefficient of determination.

[0048] Furthermore, the acquisition of historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool also includes:

[0049] The historical temperature data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool are collected through the FBG temperature sensor;

[0050] The historical comprehensive thermal positioning error data of multiple temperature measuring points in the full-closed-loop multi-axis transmission system of the machine tool is collected by a laser interferometer; among them, the comprehensive thermal positioning error data of the full-closed-loop multi-axis transmission system of the machine tool with different drive modes is measured at different movement speeds, among which the Z-axis drive mode is a ball screw, the X-axis drive mode is a linear motor, and the full-closed-loop mode is a high-precision grating ruler.

[0051] Furthermore, the acquisition frequency of the historical temperature data is 1 Hz; each acquisition of complete historical comprehensive thermal positioning error data takes 1 minute, the interval time is 10 minutes, and a single experiment is 180 minutes.

[0052] The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization provided by the present invention has the following beneficial effects:

[0053] (1) A novel sparse time series method is proposed for effective thermal error analysis and to sparsely serialize the data without losing temporal information.

[0054] (2) Thermal drift has a significant impact on the comprehensive thermal positioning error. In view of the spatiotemporal characteristics of temperature data, this paper proposes a GGT deep learning model to effectively predict thermal drift changes. Experimental results show that in the proposed model, it is effective to replace Transformer data encoding with GRU and GCN modules;

[0055] (3) The grating scale suppresses and simplifies the thermal positioning error. The Thermal_ex model directly based on the thermal expansion coefficient can simply and effectively predict the thermal positioning error, while the Bayes-RF model further improves the prediction accuracy of the thermal positioning error;

[0056] (4) The proposed GGT thermal drift model and Bayes-RF thermal positioning error model significantly improve the prediction accuracy of the comprehensive thermal positioning error. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present invention, but do not constitute a limitation of the present invention.

[0058] Figure 1 A flow chart of the comprehensive thermal positioning error modeling method based on data-driven and sparse serialization provided by the present invention.

[0059] Figure 2 A framework diagram of the comprehensive thermal positioning error modeling method based on data-driven and sparse serialization provided by the present invention.

[0060] Figure 3 A schematic diagram of the sparse serialization operation provided by the present invention.

[0061] FIG. 4( a ) is a graph showing the trend of historical temperature data and historical comprehensive thermal positioning error data over time provided by the present invention.

[0062] FIG4( b ) is a trend diagram of historical comprehensive thermal positioning error data versus position provided by the present invention.

[0063] Figure 5 This is the overall structure diagram of the GGT thermal drift prediction model provided by the present invention.

[0064] Figure 6 A random forest model diagram based on Bayesian optimization provided by the present invention.

[0065] Figure 7 A schematic diagram showing a comparison of prediction effects of the thermal drift prediction model provided by the present invention.

[0066] Figure 8 A schematic diagram showing a comparison of prediction effects of the thermal slope prediction model provided by the present invention.

[0067] Fig. 9 This is a diagram showing the prediction effect of the comprehensive thermal positioning error model provided by the present invention. DETAILED DESCRIPTION

[0068] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation method, structure, characteristics and effects of a comprehensive thermal positioning error modeling method based on data-driven and sparse serialization proposed by the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0069] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so as to describe the embodiments of the present invention described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0070] In order to solve the complex and changing thermal drift problem, the present invention regards the thermal drift problem as a multivariate time series problem. A GGT thermal drift prediction model based on graph convolutional network (GCN), bidirectional gated recurrent unit (Bi-GRU) and Transformer architecture is established. The GGT thermal drift prediction model as a whole utilizes the spatiotemporal characteristics of thermal error data, uses GCN and Bi-GRU for feature extraction, and finally forms the final deep learning thermal drift model based on Transformer fusion features. The basic principle of using the Transformer architecture for feature fusion lies in its powerful feature learning ability and ability to capture global information.

[0071] For the problem of thermal positioning error, the present invention proposes an accurate Bayesian optimized random forest (Bayes-RF) model for the prediction of thermal slope of the heat-affected part based on error separation, and also proposes a concise and effective physical model based on grating thermal expansion.

[0072] The invention proves that the introduced thermal error modeling method is effective through experimental data and modeling prediction, and provides valuable insights for mitigating thermal effects in multi-axis drive systems. Through the invention, it is expected to contribute to improving the performance and stability of fully closed-loop multi-axis systems and provide useful guidance for research and application in related fields.

[0073] In this embodiment, a comprehensive thermal positioning error modeling method based on data-driven and sparse serialization is provided. Figure 1 Please also refer to Figure 2 The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization includes the following steps:

[0074] Step S1: collecting historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measuring points in a fully closed-loop multi-axis transmission system of a machine tool, wherein the historical temperature data and historical comprehensive thermal positioning error data of each temperature measuring point are used as a data set, and the multiple data sets are divided into a training data set and a verification data set;

[0075] Preferably, the step S1 further includes:

[0076] Incrementally process the collected multiple historical temperature data to obtain incremental historical temperature data;

[0077] Performing a sparse serialization operation on the incremental historical temperature data to obtain sparse serialized historical temperature data, thereby reducing the amount of data serialization without losing time information;

[0078] Due to the time lag and seriality of thermal errors, it is necessary to serialize the temperature data that changes over time. Considering the density of the original temperature data, the serialized data for a certain period of time becomes bloated and huge, but the time information it contains is relatively limited. In order to solve this problem, a strategy of fixed step size and fixed amount sampling is adopted to perform sparse sampling of temperature data in the context of multivariate time series. The present invention is called sparse multivariate time serialization, or sparse serialization for short.

[0079] Specifically, Figure 3 As shown, the step of performing a sparse serialization operation on the incremental historical temperature data to obtain sparse serialized historical temperature data further includes:

[0080] Determine the sampling quantity and sampling step of historical temperature data;

[0081] Determine the initial sampling point position of the historical temperature data according to the timestamp of the historical comprehensive thermal positioning error data; wherein, x tIt represents the value of each temperature point (T1-Tn) at time t, Mark represents the axis mark. Timestep represents the sampling step, and Steps represents the number of samples;

[0082] Obtain the locations of all sampling points of historical temperature data according to the sampling step length and the sampling quantity;

[0083] If the sampling point position is empty, it means that before time zero, the historical temperature data will be completely filled with zeros; finally, the sparse serialized historical temperature data X t and its corresponding historical comprehensive thermal positioning error data y t Through sparse multivariate time series operations, not only the amount of input data is reduced, but also the structured data is ensured to contain long-term temporal information.

[0084] This designed data processing step not only effectively reduces the storage and computational burden, but also retains key information about the long-term temporal evolution. This provides a more efficient and informative data foundation for the subsequent thermal error model construction.

[0085] Preferably, the acquisition of historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool also includes:

[0086] The historical temperature data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool are collected through the FBG temperature sensor;

[0087] The XM60 multi-beam laser interferometer is used to collect historical comprehensive thermal positioning error data of multiple temperature measuring points in the machine tool's fully closed-loop multi-axis transmission system. Among them, the comprehensive thermal positioning error data of the machine tool's fully closed-loop multi-axis transmission system with different drive modes is measured at different movement speeds, where the Z-axis drive mode is a ball screw, the X-axis drive mode is a linear motor, and the full-closed-loop mode is a high-precision grating ruler.

[0088] Specifically, the FBG temperature sensor is a distributed series structure, which does not interfere with the movement of the machine tool, and the collection frequency of the historical temperature data is 1 Hz; the laser interferometer collects positioning error data in multiple measurement mode (only the first measurement corrects the zero point), and it takes about 1 minute to collect complete historical comprehensive thermal positioning error data each time, with an interval of about 10 minutes, and a single experiment takes about 180 minutes.

[0089] It should be noted that monitoring the overall temperature of the machine while it is running is a challenging task, mainly because the wiring of the traditional temperature sensor installation method will interfere with the movement of the machine. In order to meet this challenge, the present invention adopts an FBG temperature sensor data acquisition system based on a distributed series structure. The distributed design of the fiber grating temperature system ensures that the multi-axis system operates undisturbed during reciprocating spatial motion. The FBG temperature sensor system has a resolution of 0.1°C, and the sampling frequency of the demodulator is 1Hz, which can provide high-precision and high-resolution temperature data. These temperature measurement points mainly include the spindle system, moving axis, bed and grating scale. The specific distribution of the sensors is shown in Table 1, where multiple sensors are continuously spaced near the grating scale to ensure comprehensive monitoring of temperature changes at different positions of different components of the transmission system.

[0090] Table 1 Distribution of temperature measurement points

[0091]

[0092] This distributed temperature measurement method not only minimizes the interference with the machine tool movement, but also provides high temporal and spatial resolution for capturing long-term temperature changes in key areas of the system. This provides reliable data support for the subsequent comprehensive analysis of thermal errors, data structuring and modeling prediction of the present invention.

[0093] When studying the thermal errors of a transmission system, the main goal is to collect data on the positioning error as it changes with temperature when the spindle is in a locked state. Traditional measurement methods usually involve zero point calibration or re-measuring the instrument after each measurement. However, the disadvantage of this operation is that it is difficult to observe the zero point drift phenomenon caused by temperature changes, which is called thermal drift in this paper. Ignoring the thermal drift phenomenon will lead to a huge deviation in the analysis of the machine tool's spatial errors.

[0094] To overcome this limitation, the present invention adopts a novel thermal positioning error measurement mode. Specifically, during the measurement process, the spindle is first locked, and then continuous measurement is performed using Renishaw's measurement software "CARTO" in multiple measurement mode. This mode means that in subsequent measurements, the first measurement is used as a reference, and no zero point calibration is required. This enables the acquired data to show the dynamic evolution of thermal drift and positioning error with temperature changes.

[0095] Since both the X-axis and the Y-axis are driven by linear motors, in order to improve the clarity and simplicity of the research objectives, this chapter focuses specifically on the thermal drift and thermal positioning errors of the X-axis and the Z-axis. The specific experimental configuration is shown in Table 2, which shows the experiments of the Z-axis and the X-axis in different motion states.

[0096] Table 2 Experimental settings

[0097]

[0098] Step S2: decomposing the historical comprehensive thermal positioning error data of each temperature measurement point into historical thermal drift data and historical thermal slope data;

[0099] It should be noted that, based on the data characteristics, the comprehensive thermal positioning error problem of the transmission system is decomposed into two components: thermal drift and thermal positioning error. The offset of the origin of the error measurement curve is called thermal drift, and the slope change is the change of thermal positioning error, which can also be called thermal slope. Thermal error modeling and prediction are performed separately.

[0100] The focus of the present invention is the comprehensive study of "thermal drift and thermal positioning error". In order to intuitively illustrate the research problem, a set of comprehensive error data of the Z axis is given as an example in Figure 4. It can be seen in Figure 4 (a) that each vertical line segment represents a measurement of the thermal positioning error, in which the round-trip average value is considered, and the width of the vertical line segment reflects the dynamic change of the thermal positioning error. At the same time, representative temperature data of multiple spindle and Z-axis grating scale temperature measurement points are selected to comprehensively observe the impact of temperature changes on positioning errors. In Figure 4 (b), the evolution of thermal drift is illustrated by plotting the change graph of the error zero point, and the change in the error slope represents the thermal slope caused by the thermal positioning error. This visual representation helps to understand the performance of thermal drift and thermal positioning errors in experimental data, laying the foundation for subsequent analysis.

[0101] Through in-depth exploration of this set of comprehensive thermal positioning error data, the aim is to reveal the correlation between thermal drift and thermal positioning error, thereby gaining a deeper understanding of the behavior of thermal positioning error in multi-axis drive systems. Discussion of this issue will help develop more effective comprehensive thermal positioning error modeling and compensation strategies.

[0102] Step S3: establishing a GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the training data set, and establishing a thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler;

[0103] Preferably, given the extensive and complex data sets associated with thermal drift, in order to address this complex modeling challenge, the present invention proposes a GGT thermal drift prediction model, such as Figure 5As shown, the GGT thermal drift prediction model includes a GCN (graph convolutional network) module, a Bi-GRU (bidirectional gated recurrent unit) module, an encoder module, a first linear layer, a ReLu activation layer, a second linear layer and an output layer. The tasks of the GCN module and the Bi-GRU module are to capture the characteristics of the spatial and temporal dimensions of the input data, replace the encoding process of the Transformer, and finally use the Transformer encoder structure for regression prediction. The GGT thermal drift prediction model is established based on the historical temperature data and historical thermal drift data in the training data set, and also includes:

[0104] Step S311: construct a GCN module, the core formula of the GCN module is as follows:

[0105] Z=ReLU(AXW)

[0106] Among them, Z is the output, ReLU is a nonlinear activation function, A is the deformation adjacency matrix, which contains the spatial information of the input data; X is the input historical temperature data, and W is a parameterized and learnable weight matrix;

[0107] Step S312: The present invention uses a Bi-GRU module to perform feature learning of time series information on the data and construct a Bi-GRU module. The core formula of the Bi-GRU module is as follows:

[0108]

[0109] Among them, X t is the historical temperature data currently input; Z t , R t , H t and Respectively represent the current update gate, the current reset gate, the current candidate hidden state and the current hidden state; H t—1 represents the previous candidate hidden state; W, U and b are all weight matrices; φ h and σ g represent the hyperbolic tangent and Sigmod function respectively; ⊙ is the Hadamard product;

[0110] Step S313: Integrate the feature information output by the GCN module and the feature information output by the Bi-GRU module, and then perform regression prediction on the integrated feature information through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer in sequence, and finally output the thermal drift prediction result through the output layer, wherein the formula of the multi-head attention mechanism in the encoder module is as follows:

[0111]

[0112] Where Q is the query; K is the key; V is the value; softmax() is the normalized exponential function, d k is the vector dimension.

[0113] Specifically, it also includes:

[0114] In order to effectively integrate the information learned by the GCN module and the Bi-GRU module, the Transformer encoding module is used to perform further regression prediction on the thermal error. Figure 5 In the method, first, the input historical temperature data is passed through the GCN module and the Bi-GRU module respectively to learn the spatial information features and the temporal information features; the GCN module and the Bi-GRU module output a one-dimensional feature vector respectively, and the two one-dimensional feature vectors are concatenated and integrated to obtain a new one-dimensional encoding feature vector;

[0115] The new one-dimensional encoded feature vector is sequentially passed through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer for regression prediction, and finally the thermal drift prediction result is output through the output layer;

[0116] The encoder module includes a multi-head attention mechanism, a first residual connection layer and a normalization layer, a feedforward neural network layer, and a second residual connection layer and a normalization layer. Through this innovative deep learning framework, it aims to fully explore and integrate the spatial and temporal information embedded in the temperature data, thereby enhancing the prediction performance of the thermal error model for thermal drift changes.

[0117] For the thermal positioning problem, we first find out that the core part of the thermal influence is the thermal slope. We then establish an accurate Bayesian optimized random forest (Bayes-RF) model for the thermal slope and a physical model based on grating thermal expansion.

[0118] The trend of thermal slope is relatively simple, so machine learning is used for modeling. The temperature changes of sensors near the grating are highly consistent, and the data show obvious multicollinearity. In order to predict the thermal slope, a random forest model is used. The reason for choosing this model is that the decision tree model is not sensitive to multicollinearity, and the random forest model contains multiple decision tree models, which enhances the robustness of the prediction model.

[0119] The hyperparameters of the random forest model can significantly affect the prediction performance. Therefore, the present invention uses Bayesian optimization to search for the optimal hyperparameters of the random forest model. The core idea of ​​Bayesian optimization includes constructing the posterior probability distribution of the objective function, combining prior information with observed data, continuously updating the estimate of the objective function, and selecting the next candidate point in the search space for evaluation.

[0120] Preferably, if Figure 6As shown, the thermal slope prediction model is established according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler, and further includes:

[0121] Step S321: using a random forest model to perform regression prediction on the thermal slope;

[0122] Step S322: using the Bayesian inference method to optimize the hyperparameters of the random forest model to obtain a trained random forest model;

[0123] Step S323: A physical model is established based on the thermal expansion coefficient of the grating ruler. The thermal positioning error of the X-axis and Z-axis closed-loop motion control systems is constrained by the grating ruler. The thermal expansion coefficient of the grating ruler and the temperature information of its surrounding environment are directly used to achieve accurate calculation of the thermal slope change. The present invention refers to the physical model based on the thermal expansion coefficient of the grating ruler as the "thermal_ex" model. In order to obtain accurate calculation results, it is necessary to select the temperature values ​​of the three temperature sensors around the grating ruler and take the average value. For the Z moving axis, select temperature points T3, T4 and T5; and for the X moving axis, select temperature points T11, T12 and T13. The thermal slope calculation is performed according to the following formula, and the core formula of the physical model is:

[0124]

[0125] Among them, y ex Represents historical thermal slope data in μm / L; is the average temperature around the grating ruler; α is the thermal expansion coefficient of the grating ruler, expressed in 12μm / ℃ / m; L is the stroke length of the moving axis, in meters.

[0126] Specifically, the random forest model is a machine learning model that includes multiple decision trees. Figure 6 In the , historical temperature data are input into a single decision tree to obtain a thermal slope prediction value, and the thermal slope prediction values ​​of multiple decision trees are weighted and superimposed to form a random forest model to obtain better prediction ability and model robustness;

[0127] Among them, the random forest model contains multiple hyperparameters, such as the number of trees n_estimators, the minimum number of samples required to split the tree node min_samples_split, the minimum number of samples that a node must have min_samples_leaf, the feature ratio max_features considered during splitting, and the maximum depth max_depth hyperparameter value of the tree. By optimizing the multiple hyperparameters of the random forest model through Bayesian optimization to obtain the optimal hyperparameters, a trained random forest model can be obtained; the historical temperature data is input into the trained random forest model to obtain the final thermal slope prediction result. Through this modeling method, the purpose is to accurately capture the characteristics of temperature changes near the grating sensor, so as to accurately predict the thermal slope changes. This research framework not only enhances the robustness of the model, but also provides an efficient and reliable method for hyperparameter optimization in the modeling process.

[0128] The present invention selects three sets of data for the X-axis and the Z-axis for model training, with a total of 6 data sets. Due to the limited quantity, the six data sets are copied multiple times to increase the total amount of sample set data, and then randomly shuffled to form the final training data set. A set of remaining data is reserved for the X-axis and the Z-axis to verify the performance of the model. The detailed parameters of the thermal drift model and the thermal slope model are shown in Table 3 and Table 4, respectively.

[0129] Table 3 Key parameters of GGT model

[0130]

[0131] Table 4 Key parameters of the Bayes-RF model

[0132]

[0133] Step S4: verifying the effect of the GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the verification data set; and verifying the effect of the thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the verification data set;

[0134] Step S5: Combining the verified GGT thermal drift prediction model and the verified thermal slope prediction model into a comprehensive thermal positioning error model, and evaluating the comprehensive thermal positioning error model based on the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set.

[0135] Preferably, the thermal drift and thermal slope models are combined to form the comprehensive thermal positioning error model of the present invention. In order to evaluate the effectiveness and robustness of the model in thermal error prediction, it is necessary to use model regression ability evaluation indicators, including root mean square error (RMSE), mean absolute error (MAE), correction determination coefficient (R 2 Adj ) and total absolute error (TAE) indicators. The total absolute error (TAE) indicator intuitively reflects the proportion of error reduction to a certain extent. The verification data used are separate experimental data of different working conditions.

[0136] Among them, the TAE indicator is based on MAE, which makes the evaluation of model prediction accuracy easier to understand. It can express the proportion of error elimination and intuitively express the prediction accuracy. The smaller the RMSE and MAE values, the better the performance. 2 Adj The larger the TAE value, the better. The evaluating the comprehensive thermal positioning error model according to the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set also includes:

[0137] The evaluation indicators of the comprehensive thermal positioning error model include root mean square error RMSE, mean absolute error MAE, correction determination coefficient R 2 Adj And total absolute error TAE, where the formulas for each evaluation indicator are as follows:

[0138]

[0139] in,

[0140]

[0141] Among them, y i is the observed value; is the observed value y i The average value of is the predicted value; n is the number of samples; p is the number of features; R 2 is the coefficient of determination.

[0142] In order to verify the effectiveness of the GGT thermal drift model based on the GCN, GRU and Transformer (encoder structure only) architectures, the present invention established multiple comparative models. The temperature data serialized into a sparse time series was regarded as an image, and a CNN thermal drift model was established. In addition, in order to evaluate the performance of the deep learning model, the present invention developed a multi-layer perceptron (MLP) model and a multivariate regression (MR) model. Since the MR model is sensitive to multicollinearity in the data, a step size of 5 was used. Table 5 lists the comparative analysis of the prediction indicators of all thermal drift models. It should be emphasized that the sample size n is relatively small, while the feature dimension p is high, which may lead to R 2 Adj The prediction performance of the proposed model and some of the compared models is shown in Figure 7 shown.

[0143] Table 5 Comparison of thermal drift model prediction results

[0144]

[0145]

[0146] As can be seen from Table 5, the GGT model proposed in the present invention shows excellent prediction performance and achieves the best results in all parameter indicators. It is particularly worth mentioning the TAE indicator, which exceeds other comparative models and reaches 87.26%. Figure 7 It is further shown that the residuals of the GGT model fluctuate within the range of ±5 μm, indicating its strong predictive ability.

[0147] The present invention establishes the Bayes-RF and Thermal_ex thermal positioning error models. In order to verify the effectiveness of the model, the random forest (RF), decision tree (Dtr), support vector regression (SVR), multilayer perceptron (MLP), multivariate regression (MR) and ridge regression models are used for comparative analysis. It is worth noting that the time step of the MR model is 1. The performance indicators of the thermal slope model are shown in Table 6. The prediction performance of the key thermal slope model is shown in Table 6. Figure 8 shown.

[0148] Table 6 Comparison of thermal slope model prediction results

[0149]

[0150] The change of thermal positioning error shows a simple trend. Both Bayes-RF and Thermal_ex models have excellent prediction performance, with TAE exceeding 80%. Figure 8The Thermal_ex model shows a strong ability to predict thermal slope. This shows that the thermal positioning error in the multi-axis drive system is mainly manifested as the thermal expansion of the grating scale. In other words, no matter what drive method is used, the grating scale can effectively suppress the thermal positioning error. The predicted value of the Thermal_ex model is higher than the original value, indicating that correcting the thermal expansion coefficient of the grating scale can lead to better prediction results.

[0151] The premise of comprehensive thermal positioning error is the separation of overall error, which represents a new exploration of this problem. Due to the lack of relevant research on comprehensive thermal positioning error, this paper does not make an overall effect comparison. The overall prediction performance of comprehensive thermal positioning error is given below, Fig. 9 The prediction results of the comprehensive thermal positioning error of the Z axis are shown.

[0152] This paper studies the comprehensive thermal positioning error of multi-axis transmission systems under different drive modes and closed-loop control for the first time. The heat generated by the transmission system and the spindle is intertwined, which increases the complexity of error variation. By dividing the problem into thermal drift and thermal positioning error, Fig. 9 The effectiveness of the proposed method in error compensation is demonstrated. It is obvious from the figure that the amplitude of thermal drift variation is larger than that of thermal positioning error. Regarding the compensation results, although the residual fluctuation is large, the amplitude of fluctuation is small. This shows that modeling thermal drift variation (essentially the variation of spindle thermal error) is more complicated and poses a greater challenge in compensation. However, within a certain time frame, the impact of thermal positioning error is relatively small, so it is easier to model with more effective compensation. Therefore, it can be concluded that the importance and complexity of spindle thermal error research, as well as the effectiveness of grating scale closed-loop control in constraining thermal positioning error. The present invention affirms the effectiveness and simplicity of the proposed thermal positioning error modeling method.

[0153] This paper analyzes and studies the comprehensive thermal positioning error of a fully closed-loop controlled multi-axis motion system. The comprehensive thermal positioning error problem is decomposed into thermal drift and thermal positioning error. Due to the time lag and timing of thermal effects, the temperature data is structured preprocessed into sparse multivariate time series. Subsequently, effective thermal drift models and thermal positioning error models are established respectively, and the prediction of the comprehensive thermal positioning error is realized. Through the analysis and research of the comprehensive thermal positioning error, the following findings and contributions are obtained:

[0154] 1) This paper discusses the new problem of comprehensive thermal positioning error of ball screw system and linear motor system under the influence of spindle heating, which is controlled by grating ruler in full closed loop. Then the comprehensive thermal positioning error problem is decomposed into thermal drift and thermal positioning problems, and modeling and analysis are performed separately, which reduces the complexity of the research.

[0155] 2) It is proved that the grating ruler effectively suppresses the thermal positioning error in the transmission system under different driving modes and greatly reduces the complexity of modeling.

[0156] 3) The present invention regards the thermal error problem as a time series problem and proposes a method for sparse multivariate time series of temperature data to reduce the amount of data series without losing time information.

[0157] 4) Thermal drift has a significant impact on the comprehensive thermal localization error. In view of the spatiotemporal characteristics of temperature data, this paper proposes a GGT deep learning model to effectively predict thermal drift changes. Experimental results show that in the proposed model, it is effective to replace Transformer data encoding with GRU and GCN modules.

[0158] 5) The Thermal_ex model directly established based on the thermal expansion coefficient can simply and effectively predict the thermal positioning error, while the Bayes-RF model further improves the prediction accuracy of the thermal positioning error.

[0159] This paper first introduces the problem of comprehensive thermal positioning error of a fully closed-loop multi-axis system, and then introduces the experimental setup and data acquisition process in detail, covering the description of the multi-axis transmission system and the precise acquisition of temperature and comprehensive thermal positioning error data. Afterwards, a novel sparse time series method is proposed for temperature field information for effective thermal error analysis, and the data is sparsely serialized without losing time information. This paper deeply studies the research on comprehensive thermal positioning error, innovatively divides it into thermal drift problem and thermal positioning error problem, in which the core manifestation of thermal positioning error is the change of thermal slope, and conducts data characteristic analysis and modeling prediction research respectively. In the analysis and modeling methodology of comprehensive thermal positioning error problem, through in-depth problem analysis, a thermal drift model based on GCN-GRU-Transformer, a random forest thermal slope model based on Bayesian optimization, and a physical thermal slope modeling based on thermal expansion coefficient are proposed. Finally, through the comparison and analysis of model training, evaluation indicators and prediction capabilities, the prediction performance and advantages and disadvantages of various modeling methods are demonstrated, providing readers with a comprehensive perspective for in-depth understanding of the thermal positioning error of a fully closed-loop multi-axis system. Overall, the present invention has achieved key conclusions and effective modeling methods on comprehensive thermal positioning errors in theoretical analysis and empirical research, providing useful guidance for research and applications in related fields.

[0160] In summary, the present invention first introduces the problem of comprehensive thermal positioning error of a fully closed-loop multi-axis system, and then introduces the experimental setup and data collection process in detail, covering the description of the multi-axis transmission system and the precise collection of temperature and comprehensive thermal positioning error data. In the comprehensive thermal positioning error problem analysis and modeling methodology, through in-depth problem analysis, methods such as a thermal drift model based on GCN-GRU-Transformer, a random forest thermal slope model based on Bayesian optimization, and a physical thermal slope modeling based on thermal expansion coefficient are proposed. Finally, through model training, comparison and analysis of evaluation indicators and prediction capabilities, the prediction performance and advantages and disadvantages of various modeling methods are demonstrated, providing readers with a comprehensive perspective for an in-depth understanding of the thermal positioning error of a fully closed-loop multi-axis system.

[0161] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A comprehensive thermal positioning error modeling method based on data-driven and sparse serialization, characterized in that: The steps include: Step S1: collecting historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measuring points in a fully closed-loop multi-axis transmission system of a machine tool, wherein the historical temperature data and historical comprehensive thermal positioning error data of each temperature measuring point are used as a data set, and the multiple data sets are divided into a training data set and a verification data set; Step S2: decomposing the historical comprehensive thermal positioning error data of each temperature measurement point into historical thermal drift data and historical thermal slope data; Step S3: establishing a GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the training data set, and establishing a thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler; Step S4: verifying the effect of the GGT thermal drift prediction model according to the historical temperature data and the historical thermal drift data in the verification data set; and verifying the effect of the thermal slope prediction model according to the historical temperature data and the historical thermal slope data in the verification data set; Step S5: Combining the verified GGT thermal drift prediction model and the verified thermal slope prediction model into a comprehensive thermal positioning error model, and evaluating the comprehensive thermal positioning error model based on the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set.

2. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 1 is characterized in that: The step S1 further includes: Incrementally process the collected multiple historical temperature data to obtain incremental historical temperature data; A sparse serialization operation is performed on the incremental historical temperature data to obtain sparse serialized historical temperature data.

3. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 2 is characterized in that: The step of performing a sparse serialization operation on the incremental historical temperature data to obtain sparse serialized historical temperature data further includes: Determine the sampling quantity and sampling step of historical temperature data; Determine the initial sampling point position of the historical temperature data according to the timestamp of the historical comprehensive thermal positioning error data; Obtain the locations of all sampling points of historical temperature data according to the sampling step length and the sampling quantity; Among them, if the sampling point position is empty, it means that before time zero, the historical temperature data will be completely filled with zero; finally, sparse serialized historical temperature data and its corresponding historical comprehensive thermal positioning error data are obtained.

4. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 1 is characterized in that: The GGT thermal drift prediction model comprises a GCN module, a Bi-GRU module, an encoder module, a first linear layer, a ReLu activation layer, a second linear layer and an output layer. The GGT thermal drift prediction model is established according to the historical temperature data and the historical thermal drift data in the training data set, and further comprises: Step S311: construct a GCN module, the core formula of the GCN module is as follows: Z=ReLU(AXW) Among them, Z is the output, ReLU is a nonlinear activation function, A is the deformation adjacency matrix, X is the input historical temperature data, and W is the weight matrix; Step S312: construct a Bi-GRU module, the core formula of the Bi-GRU module is as follows: Among them, X t is the historical temperature data currently input; Z t , R t , H t and Respectively represent the current update gate, the current reset gate, the current candidate hidden state and the current hidden state; H t—1 represents the previous candidate hidden state; W, U and b are all weight matrices; φ h and σ g represent the hyperbolic tangent and Sigmod function respectively; ⊙ is the Hadamard product; Step S313: Integrate the feature information output by the GCN module and the feature information output by the Bi-GRU module, and then perform regression prediction on the integrated feature information through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer in sequence, and finally output the thermal drift prediction result through the output layer, wherein the formula of the multi-head attention mechanism in the encoder module is as follows: Where Q is the query; K is the key; V is the value; softmax() is the normalized exponential function, d k is the vector dimension.

5. The method for comprehensive thermal positioning error modeling based on data-driven and sparse serialization according to claim 4 is characterized in that: Also includes: The input historical temperature data is passed through the GCN module and the Bi-GRU module respectively to learn the spatial information features and the temporal information features; the GCN module and the Bi-GRU module output a one-dimensional feature vector respectively, and the two one-dimensional feature vectors are concatenated and integrated to obtain a new one-dimensional encoding feature vector; The new one-dimensional encoded feature vector is sequentially passed through the encoder module, the first linear layer, the ReLu activation layer, and the second linear layer for regression prediction, and finally the thermal drift prediction result is output through the output layer; The encoder module includes a multi-head attention mechanism, a first residual connection layer and a normalization layer, a feedforward neural network layer, and a second residual connection layer and a normalization layer.

6. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 1 is characterized in that: The thermal slope prediction model is established according to the historical temperature data and the historical thermal slope data in the training data set, wherein the thermal slope prediction model is a random forest model or a physical model based on thermal expansion of a grating ruler, and further includes: Step S321: using a random forest model to perform regression prediction on the thermal slope; Step S322: using the Bayesian inference method to optimize the hyperparameters of the random forest model to obtain a trained random forest model; Step S323: Establish a physical model based on the thermal expansion coefficient of the grating ruler. The core formula of the physical model is: Among them, y ex Represents historical thermal slope data in μm / L; is the average temperature around the grating ruler; α is the thermal expansion coefficient of the grating ruler, expressed in 12μm / ℃ / m; L is the stroke length of the moving axis, in meters.

7. The method for comprehensive thermal positioning error modeling based on data-driven and sparse serialization according to claim 6 is characterized in that: The random forest model is a machine learning model that includes multiple decision trees. The historical temperature data is input into a single decision tree to obtain a thermal slope prediction value. The thermal slope prediction values ​​of multiple decision trees are weighted and superimposed to form a random forest model to obtain better prediction ability and model robustness. Among them, the random forest model contains multiple hyperparameters. The multiple hyperparameters of the random forest model are optimized by Bayesian optimization to obtain the optimal hyperparameters, thereby obtaining a trained random forest model; the historical temperature data is input into the trained random forest model to obtain the final thermal slope prediction result.

8. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 1 is characterized in that: The evaluating the comprehensive thermal positioning error model according to the historical temperature data and the historical comprehensive thermal positioning error data in the verification data set also includes: The evaluation indicators of the comprehensive thermal positioning error model include root mean square error RMSE, mean absolute error MAE, correction determination coefficient R 2 Adj And total absolute error TAE, where the formulas for each evaluation indicator are as follows: in, Among them, y i is the observed value; is the observed value y i The average value of is the predicted value; n is the number of samples; p is the number of features; R 2 is the coefficient of determination.

9. The comprehensive thermal positioning error modeling method based on data-driven and sparse serialization according to claim 1 is characterized in that: The acquisition of historical temperature data and historical comprehensive thermal positioning error data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool also includes: The historical temperature data of multiple temperature measurement points in the fully closed-loop multi-axis transmission system of the machine tool are collected through the FBG temperature sensor; The historical comprehensive thermal positioning error data of multiple temperature measuring points in the full-closed-loop multi-axis transmission system of the machine tool is collected by a laser interferometer; among them, the comprehensive thermal positioning error data of the full-closed-loop multi-axis transmission system of the machine tool with different drive modes is measured at different movement speeds, among which the Z-axis drive mode is a ball screw, the X-axis drive mode is a linear motor, and the full-closed-loop mode is a high-precision grating ruler.

10. The method for comprehensive thermal positioning error modeling based on data-driven and sparse serialization according to claim 9, characterized in that: The acquisition frequency of the historical temperature data is 1 Hz; each acquisition of complete historical comprehensive thermal positioning error data takes 1 minute, the interval time is 10 minutes, and a single experiment is 180 minutes.

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