Improved principal component regression machine tool thermal error modeling method based on density clustering

Abstract

The invention relates to the technical field of precision control of numerical control machine tools, and discloses an improved principal component regression machine tool thermal error modeling method based on density clustering, which comprises the following steps of: performing dimension reduction processing on original temperature data through principal component analysis to obtain a plurality of principal components; establishing a plurality of principal component regression models based on the principal components, wherein each model corresponds to a different principal component number; performing clustering analysis on prediction results of the plurality of principal component regression models by using a density clustering algorithm, and identifying and eliminating abnormal prediction values; and performing comprehensive processing on the prediction result after the abnormal value is removed to obtain a final thermal error prediction model. The principal component regression model prediction results corresponding to different principal component numbers are screened and optimized by combining a density clustering algorithm, abnormal prediction values are effectively eliminated, and reliable prediction results are integrated, so that a thermal error prediction model with higher precision is constructed.

Description

Technical Field

[0001] The present invention relates to the technical field of precision control of numerically controlled machine tools, and in particular to an improved principal component regression machine tool thermal error modeling method based on density clustering. Background Art

[0002] In the modern machining industry, as part precision requirements continue to increase, the impact of machine tool thermal errors on machining quality is becoming increasingly significant. As a key technology for improving the thermal accuracy of CNC machine tools, machine tool thermal error modeling has attracted considerable attention. Currently, machine tool thermal error modeling methods are primarily categorized into two types: mechanism-driven models and data-driven models.

[0003] Mechanism-driven models rely on research into frictional heat generation during machine tool operation, as well as heat exchange with functional components and the environment, to establish thermal error models based on heat transfer mechanisms and elastic deformation theory. However, this approach requires a deep understanding of the complex thermal physics within the machine tool, placing extremely high demands on the machine tool's structure and thermal characteristics. Furthermore, the modeling process is cumbersome, making it difficult to adapt to machine tools of varying models and operating conditions.

[0004] Data-driven models, on the other hand, do not require detailed investigation of the deformation mechanisms of functional components. Instead, they directly establish a regression model between temperature and machine tool thermal deformation based on thermal characterization experiments. Common data-driven modeling methods include multivariate linear regression, support vector machines, and neural networks. Principal component regression and partial least squares regression, due to their high accuracy and robustness, have been widely used in machine tool thermal error modeling.

[0005] Principal component regression uses principal component analysis to reduce the dimensionality of raw temperature data, extract the main component variables, and construct a regression model. However, in practical applications, the predictive performance of principal component regression is easily affected by the selection of the number of principal components. Existing studies usually determine the number of principal components based on the cumulative variance contribution rate, such as selecting principal components with a cumulative variance contribution rate greater than 85%, 90%, or 95%. However, this modeling approach with a fixed number of principal components has obvious flaws. Under different operating conditions and data characteristics, the optimal number of principal components may vary greatly. A fixed number of principal components is difficult to adapt to complex and changing actual situations, resulting in unstable model prediction accuracy and even severe distortion.

[0006] In summary, existing principal component regression modeling methods are unable to meet the requirements for high-precision and robust modeling of thermal errors in CNC machine tools due to the fixed number of principal components and inappropriate selection. Therefore, an improved modeling method is urgently needed that can overcome the limitation of the fixed number of principal components, effectively filter principal components, and eliminate abnormal prediction results to improve the accuracy and stability of machine tool thermal error modeling. Summary of the Invention

[0007] In view of the deficiencies of the prior art, the present invention provides an improved principal component regression machine tool thermal error modeling method based on density clustering, which solves the problems raised in the above background technology.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions: an improved principal component regression machine tool thermal error modeling method based on density clustering, comprising the following steps:

[0009] The original temperature data is processed by principal component analysis to reduce the dimension and obtain multiple principal components;

[0010] Establishing multiple principal component regression models based on the principal components, each model corresponding to a different number of principal components;

[0011] Performing cluster analysis on the prediction results of the multiple principal component regression models using a density clustering algorithm to identify and eliminate abnormal prediction values;

[0012] The prediction results after removing outliers are comprehensively processed to obtain the final thermal error prediction model.

[0013] Preferably, the principal component analysis step specifically includes:

[0014] Collect temperature data and thermal error data of key measurement points of machine tools as raw data;

[0015] Perform standardization preprocessing on the original temperature data;

[0016] Calculate the covariance matrix of the preprocessed data and solve the eigenvalues ​​and eigenvectors of the covariance matrix;

[0017] The first k principal components are selected in sequence according to the eigenvalue sorting, and regression modeling is performed with the thermal error data, k = 1, 2, 3..., to obtain the corresponding principal component regression model.

[0018] Preferably, the density clustering algorithm is the DBSCAN algorithm, and its parameter setting strategy is:

[0019] The minimum number of samples minPts takes a fixed value [X];

[0020] The neighborhood radius ε is the standard deviation of all model predictions.

[0021] Preferably, the comprehensive processing step is to take the arithmetic mean of the prediction results after removing the outliers, and use this as the final thermal error prediction value.

[0022] The machine tool thermal error compensation system based on the modeling method includes the following modules:

[0023] Data acquisition module, used to collect temperature data and thermal error data of key measurement points of machine tools;

[0024] Data processing module, used for preprocessing and principal component analysis of the collected data;

[0025] A model building module is used to build multiple principal component regression models based on principal components;

[0026] Cluster analysis module, used to perform density cluster analysis on the prediction results of multiple principal component regression models;

[0027] Model optimization module, used to eliminate abnormal prediction values ​​and comprehensively process them to obtain the final thermal error prediction model;

[0028] Compensation execution module, used to perform error compensation on the machine tool processing according to the final thermal error prediction model

[0029] Preferably, the data acquisition module includes a plurality of temperature sensors and displacement sensors, the temperature sensors are distributed at key positions of the machine tool, and the displacement sensors are used to measure thermal deformation of the machine tool.

[0030] Preferably, the compensation execution module includes a numerical control system and a servo drive system, the numerical control system outputs compensation instructions according to the thermal error prediction model, and the servo drive system adjusts the position of the motion axis of the machine tool according to the compensation instructions.

[0031] Preferably, a monitoring and display module is also included for displaying information such as the thermal error status of the machine tool, model prediction results, and compensation effects in real time to assist operators in monitoring and managing the thermal error compensation process of the machine tool.

[0032] The present invention provides an improved principal component regression method for machine tool thermal error modeling based on density clustering. It has the following beneficial effects:

[0033] 1. This invention uses a density clustering algorithm to screen and optimize the prediction results of the principal component regression model corresponding to different numbers of principal components, effectively eliminating abnormal prediction values ​​and integrating reliable prediction results, thereby constructing a more accurate thermal error prediction model. Compared with the traditional modeling method with a fixed number of principal components, experiments show that this method significantly reduces the mean root mean square error (RMS) in multiple prediction tasks, achieving high-precision and stable prediction of machine tool thermal errors, significantly improving the machining accuracy of CNC machine tools, and having important significance for the production of high-precision parts. It is expected to reduce the post-processing part correction process and improve production efficiency.

[0034] 2. This invention breaks through the limitation of fixed number of principal components in traditional principal component regression modeling. It does not limit the number of components in the principal component model, establishes principal component models under all component numbers and performs cluster analysis and screening, which can adapt to the thermal error modeling requirements under different working conditions and data characteristics. The density clustering algorithm can effectively identify noise data and valid data in the prediction results of different models, so that the final model is not affected by individual abnormal principal component models, thereby enhancing the stability and generalization ability of the model in the face of complex and changeable machine tool processing environments, ensuring that good prediction performance can be maintained under variable working conditions such as different experimental batches and different speeds, reducing the risk of model failure due to changes in working conditions, and expanding the scope of application of machine tool thermal error modeling methods.

[0035] 3. In terms of density clustering parameter setting, the present invention adopts the strategy of taking the standard deviation of the prediction results as the neighborhood radius and taking the fixed empirical value as the minimum sample number, which reduces the sensitivity to the selection of clustering parameters, simplifies the modeling process, and avoids the problem of affecting the clustering effect and model performance due to improper parameter selection, making the modeling method more practical and operational, and easy to promote and apply in actual industrial production environments. It does not require excessive manual debugging and complex parameter optimization processes, and lowers the threshold for technical application. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a general flow chart of the method of the present invention;

[0037] Figure 2 Flowchart of the machine tool thermal error compensation system based on the modeling method of the present invention;

[0038] Figure 3 This is a data point classification diagram of the points under DBSCAN clustering in an embodiment of the present invention;

[0039] Figure 4 PCR-DBSCAN thermal error modeling flow chart in an embodiment of the present invention;

[0040] Figure 5 Measured thermal error diagrams of five experiments of the embodiment of the present invention;

[0041] Figure 6 is a cumulative variance contribution rate graph in principal component analysis in an embodiment of the present invention;

[0042] Figure 7 Graphs showing prediction results of various models at t=60 min in an embodiment of the present invention;

[0043] Figure 8 Graphs showing thermal error model prediction performance at various moments in an embodiment of the present invention;

[0044] Figure 9This is a principal component thermal error model prediction residual graph in an embodiment of the present invention;

[0045] Figure 10 1 is a performance comparison diagram of different principal component regression models in machine tool thermal error prediction in an embodiment of the present invention;

[0046] Figure 11 Graph showing the performance of thermal error model prediction under different numbers of principal components in an embodiment of the present invention; DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] Please see the attached Figure 1 -Attached Figure 11 The embodiment of the present invention provides an improved principal component regression machine tool thermal error modeling method based on density clustering, comprising the following steps:

[0049] The original temperature data is processed by principal component analysis to reduce the dimension and obtain multiple principal components;

[0050] Based on the principal components, multiple principal component regression models are established, and each model corresponds to a different number of principal components;

[0051] The prediction results of multiple principal component regression models are clustered using a density clustering algorithm to identify and eliminate abnormal prediction values. The density clustering algorithm is the DBSCAN algorithm, and its parameter setting strategy is as follows:

[0052] The minimum number of samples minPts takes a fixed value [X];

[0053] The neighborhood radius ε is the standard deviation of all model predictions.

[0054] The prediction results after removing outliers are comprehensively processed to obtain the final thermal error prediction model.

[0055] The comprehensive processing step is to take the arithmetic mean of the prediction results after removing outliers, and use it as the final thermal error prediction value.

[0056] Specifically, principal component analysis (PCA) is a statistical method that transforms raw temperature data into a set of uncorrelated variables (principal components) through an orthogonal transformation, thereby reducing the data dimension and extracting key information. Based on the principal components, multiple principal component regression models are established, each corresponding to a different number of principal components, to model and analyze thermal errors from different dimensions. A density clustering algorithm (DBSCAN) is used to cluster the prediction results of these models, identifying and removing outliers. The minimum number of samples, minPts, is a fixed value [X], and the neighborhood radius, ε, is the standard deviation of all model predictions, adaptively reflecting the degree of dispersion of the predictions. Finally, the prediction results after removing outliers are comprehensively processed, namely, the arithmetic mean is taken to obtain the final thermal error prediction model. This model combines the advantages of multiple principal component regression models and has higher prediction accuracy and stability.

[0057] The principal component analysis steps include:

[0058] Collect temperature data of key measurement points of machine tools as raw data;

[0059] Specifically, we collect temperature data from key measurement points on the machine tool as raw data. During machine operation, temperature variations at different locations can affect machining accuracy. This data is collected to comprehensively capture temperature variations during machining, providing foundational data for subsequent thermal error modeling.

[0060] Perform standardization preprocessing on the original temperature data;

[0061] Specifically, the raw temperature data is preprocessed for standardization: Because data from different temperature measurement points may have different dimensions and orders of magnitude, directly using this raw data for analysis can lead to large errors. Standardization preprocessing converts the temperature data from different measurement points to the same scale, eliminating the effects of dimensions and orders of magnitude, thereby improving the accuracy and reliability of subsequent principal component analysis.

[0062] Calculate the covariance matrix of the preprocessed data and solve the eigenvalues ​​and eigenvectors of the covariance matrix;

[0063] Specifically, the covariance matrix of the preprocessed data is calculated, and the eigenvalues ​​and eigenvectors of the covariance matrix are solved: the covariance matrix reflects the correlation between different temperature measurement points. By calculating the eigenvalues ​​and eigenvectors of the covariance matrix, it is possible to determine in which directions the temperature changes have the greatest impact on the thermal error, providing a basis for extracting the principal components.

[0064] The machine tool thermal error compensation system based on the modeling method includes the following modules:

[0065] The data acquisition module is used to collect temperature data and thermal error data of key measurement points of the machine tool; the data acquisition module includes multiple temperature sensors and displacement sensors. The temperature sensors are distributed at key parts of the machine tool, and the displacement sensors are used to measure the thermal deformation of the machine tool.

[0066] Data processing module, used for preprocessing and principal component analysis of the collected data;

[0067] A model building module is used to build multiple principal component regression models based on principal components;

[0068] Cluster analysis module, used to perform density cluster analysis on the prediction results of multiple principal component regression models;

[0069] Model optimization module, used to eliminate abnormal prediction values ​​and comprehensively process them to obtain the final thermal error prediction model;

[0070] The compensation execution module is used to compensate for errors during the machine tool processing process based on the final thermal error prediction model. The compensation execution module includes a numerical control system and a servo drive system. The numerical control system outputs compensation instructions based on the thermal error prediction model, and the servo drive system adjusts the position of the machine tool's motion axis based on the compensation instructions.

[0071] It also includes a monitoring and display module for displaying information such as the thermal error status of the machine tool, model prediction results, and compensation effects in real time to assist operators in monitoring and managing the thermal error compensation process of the machine tool.

[0072] In the thermal error modeling based on principal component regression, it is necessary to reduce the dimension of the original temperature data through principal component analysis to obtain relatively independent principal component variables, and then establish a regression model of thermal error and principal component variables. Since the input variables of the thermal error model in this paper are the temperatures of each key measurement point of the machine tool, and their values ​​are in the same order of magnitude, there is no need for regularization processing, and the calculation can be performed directly according to the formula, where X and Y are the original temperature data and thermal error data, X * 、Y * are the processed temperature data and thermal error data.

[0073]

[0074] Secondly, the variable X is calculated based on the eigenvalue decomposition * The eigenvalue λ and eigenvector L of the covariance matrix of , and calculate the variance contribution rate α corresponding to the kth component k , as follows, λ k is the eigenvalue sorted from large to small, and m is the total number of components.

[0075]

[0076] The cumulative variance contribution rate G(k) of the first k components is calculated as follows.

[0077]

[0078] At the same time, the principal component vector Z can be obtained from X * The product of the corresponding eigenvector L is expressed as follows.

[0079] Z=X * ·L

[0080] Select the first p principal components with sufficiently high cumulative variance contribution rate G(k) to construct a new independent variable Z p , establish the independent variable Z p With the dependent variable Y * The regression equation is as follows, where β is the coefficient and can be calculated as follows.

[0081] Y * =Z p β

[0082]

[0083] The performance of thermal error models established with different numbers of principal components varies significantly. The number of principal components can be determined based on the cumulative variance contribution rate, but this method still has room for optimization in terms of prediction accuracy. To this end, this paper proposes a DBSCAN method based on density clustering to optimize the existing principal component regression modeling method. As a typical density clustering algorithm, the core parameters of the algorithm include the neighborhood radius ε and the minimum number of samples minPts. The data points are divided into the following three categories by density accessibility, such as Figure 3 As shown:

[0084] Core point: The ε neighborhood contains at least minPts sample points;

[0085] Boundary point: a non-core point but located within the ε neighborhood of a core point;

[0086] Noise points: neither core points nor boundary points.

[0087] The DBSCAN clustering process classifies and filters the model's prediction results in the order of "core points → boundary points → noise points," where noise points correspond to outlier predictions, boundary points represent transitional predictions, and core points represent a set of reliable predictions. The clustering effect of the DBSCAN algorithm is primarily influenced by two key parameters: the neighborhood radius ε and the minimum number of samples, minPts. ε determines the search range of the sample neighborhood and directly affects the connectivity judgment of the cluster. When the value of ε is too large, clusters of different densities may be incorrectly merged; conversely, if ε is too small, sample points that should belong to the same cluster may be incorrectly split into multiple small clusters or noise points. The minPts parameter defines the criteria for determining core points. A value that is too small reduces the ability to identify noise points, while a value that is too large may ignore valid low-density clusters in the data.

[0088] Since there are currently no reports on the application of DBSCAN clustering for thermal error prediction or similar scenario screening, in order to maintain the robustness of the method, this study appropriately simplifies the application of DBSCAN: it is only used to identify significant outliers (noise points) in the prediction results of multiple thermal error models, without accurately classifying core points and boundary points, thereby reducing dependence on the sensitivity of clustering parameters.

[0089] Based on the above considerations, this study adopts the following parameter setting strategy: the minimum sample number minPts takes the empirical value of 3, which is the lowest threshold commonly used in density clustering; the neighborhood radius ε takes the standard deviation of all model prediction results to adaptively reflect the degree of discreteness of the prediction value.

[0090] Compared with the conventional principal component regression modeling method, the improved PCR-DBSCAN method proposed in this paper does not limit the number of principal components, retains all principal component models and prediction results, removes noise points from the DBSCAN clustering results, retains the core points and boundary points, and takes the mean as the final thermal error prediction value. The process is as follows: Figure 4 shown.

[0091] The specific applications are as follows:

[0092] A thermal characteristic experiment was carried out on a CNC machining center of a certain brand in Chongqing. The PT100 temperature sensor was used to measure the temperature of 24 key points such as the spindle box and the motor. The eddy current displacement sensor was used to measure the thermal error of the spindle. Figure 3 ,The temperature measurement number and layout description are shown in Table 1.

[0093]

[0094] Table 1

[0095] A total of five batches of experiments were conducted, denoted as P1 to P5. In the P1 experiment, the spindle speed was set to 1650rpm, in the P2 experiment, the speed was set to 2500rpm, in the P3 experiment, the speed was set to 3500rpm, and in the P4 and P5 experiments, the speed was set to 0-5000rpm. This paper focuses on the spindle axial thermal elongation error. The error values ​​measured in the five experiments are as follows: Figure 3 As shown in Figure 2, the thermal error variation trend in the constant speed experiments of P1 to P3 is simpler than that in the variable speed experiments of P4 and P5. In terms of thermal error values, the thermal error value of experiment P4 is the largest, reaching -91.5μm. The test results are shown in Figure 2. Figure 5 shown.

[0096] In data-driven thermal error modeling, data quality will significantly affect the performance of the model, so when selecting the modeling group data, it is necessary to cover as many working conditions as possible. Figure 7 As shown. Experiments P1 and P4 are used as the modeling group, and experiment P3 is used as the prediction group. Principal component analysis is used to reduce the dimension of the original temperature variable. The cumulative variance contribution rate G(k) corresponding to the first k components is as follows: Figure 5 It is generally believed that the greater the variance contribution rate, the less information is lost in the principal component. Figure 5 In the model, when using 1 and 2 components, the cumulative variance contribution is 88.46% and 96.66% respectively. When using the first 10 components, the cumulative variance contribution rate G(k) is very close to 100%. Then, as the number of principal components increases, the cumulative variance contribution rate tends to be stable.

[0097] In order to compare the effect of the number of principal components on the performance of the thermal error model, the corresponding thermal error models were established when the number of principal components was 1, 2, 3, up to 24, and recorded as PCR-O1 to O24. The thermal error prediction was performed at t = 60 minutes. At the same time, the density clustering method DBSCAN proposed in this paper was used to cluster and filter the predicted values ​​of the thermal error models PCR-O1 to O24. After removing noise points and taking the mean, the prediction results of the PCR-DBSCAN model 1 are as follows: Figure 8 shown.

[0098] The results show that among the 24 thermal error model predictions, the order of similarity to the measured results is: PCR-O7 > O23 > O21 > O24 > O13 > O22, etc., with the highest prediction accuracy achieved when the number of principal components is 7. After DBSCAN density clustering, the predictions of the PCR-O7, PCR-O8, and PCR-O9 models were removed as noise points. The remaining points were divided into two clusters based on clustering, and the PCR-DBSCAN prediction results were averaged to obtain the predicted results. The predicted results are relatively close to the measured thermal error values ​​(dashed lines in the figure), demonstrating the effectiveness of the DBSCAN method.

[0099] It's important to note that in this case, despite the PCR-O7 model's predictions showing optimal accuracy, they were still identified as noise points during the DBSCAN clustering process. This was because the predicted values ​​were significantly isolated in feature space and lacked the local density distribution required for effective clustering. These outlier observations, which fail to meet the core point criteria within their neighborhood, are automatically filtered out according to the algorithm's principles.

[0100] At the same time, the thermal errors at 120min, 180min, and 240min are predicted, and the results are as follows: Figure 8 (ac) is shown. The number of components corresponding to the cumulative variance contribution rate G(k)>95% is selected to establish the thermal error model PCR-G(k), which is PCR-O2 in this case. Figure 8 The PCR-G(k) thermal error model shown in (bc) has good prediction performance, while the performance in Figure (a) is average.

[0101] In addition, by comparing the model prediction values ​​at the four moments with the actual measured values, it can be seen that the model prediction accuracy tends to be better as the number of principal components increases. However, when the number reaches a certain value, the prediction accuracy decreases. Figure 8 In (ac), the thermal error model can achieve the best global prediction performance when the number of principal components is 7, 23, and 21, respectively, indicating that the optimal number of components is not fixed at different prediction times.

[0102] On the other hand, the thermal error model PCR-G(k) that uses the cumulative variance contribution rate G(k)>95% to determine the number of components, the thermal error model PCR-ALL that uses all 24 components, and the improved principal component thermal error model PCR-DBSCAN proposed in this paper were established respectively. The thermal error of the experiment P3 accumulated for 4 hours was predicted, and the comparison with the measured value and the prediction residual were as follows: Figure 8 、 9 As shown in the figure, it can be seen intuitively that the improved principal component model PCR-DBSCAN performs better than the typical principal component thermal error model PCR-G(k); and its performance is better than PCR-ALL in the time range of 0-120 minutes, and is comparable to the performance of the PCR-ALL model in the time range of 120-240 minutes. Overall, the PCR-DBSCAN modeling method performs better than the typical principal component modeling method.

[0103] Furthermore, the maximum residual δmax, root mean square error (RMSE) and mean absolute error (MAE) of the thermal error model prediction results of each model prediction performance parameter are calculated as shown in Table 2 and Figure 10The PCR-DBSCAN model predicts a maximum residual error of δmax of 4.3 μm and a root mean square error (RMSE) of 2.7 μm, which is better than the typical principal component models PCR-G(k) and PCR-ALL, and even slightly better than the prediction performance of the principal component model PCR-BEST with the optimal number of components.

[0104]

[0105] Table 2

[0106] In the thermal error prediction task described above, the modeling groups were constant speed experiment P1 and variable speed experiment batch P4, and the prediction group was constant speed experiment batch P3. The proposed improved principal component modeling method, PCR-DBSCAN, achieved better prediction performance than typical methods. To further validate the superiority of the proposed method, multiple cross-group predictions were performed on more experimental batches, as shown in Table 3.

[0107] To validate the performance of the proposed method, various thermal error models were established using typical methods commonly used in the field of machine tool thermal error modeling, including fuzzy clustering combined with multiple linear regression (FCM-MLR), support vector machine (SVM), and convolutional long short-term memory neural network (CNN-LSTM). The FCM-MLR and SVM modeling methods require the selection of temperature-sensitive points. The number of temperature-sensitive points is typically 2 to 4, which is the number of clusters. The SVM modeling method uses grid search combined with cross-validation to quickly determine model parameters based on the selection of temperature-sensitive points. The CNN-LSTM modeling method reduces the dimensionality of the raw temperature data during the convolution process, eliminating the need for temperature-sensitive point selection. Parameters such as the convolution kernel and the number of LSTM layers are set empirically or by default. Hyperparameters such as the number of hidden units (hiddenUnits) and the number of samples per training run (batchSize) are determined using grid search combined with cross-validation. On the other hand, 24 principal component thermal error models were established according to the number of components, and the best model PCR-BEST was selected from all thermal error models, and the corresponding optimal number of components was marked.

[0108] Based on the above method, corresponding prediction tasks were executed, denoted as #1 to #10. The variable speed experiments P4 and P5 cover a relatively wide range of operating conditions, and the modeling groups all include experimental data from batches P4 or P5. The RMSE metrics for the 10 prediction results and the measured results are shown in Table 3.

[0109] There are significant differences in the performance of different modeling methods in the 10 prediction tasks. From the perspective of the best prediction performance indicators, the SVM model performs best in prediction #1, the FCM-MLR-4 model performs best in prediction #2, and the PCR-DBSCAN model performs best in predictions #3, #4, #6, #8, and #9.

[0110] The PCR-DBSCAN method proposed in this paper has poor prediction performance only in #7, with an RMSE value of 27.9 μm. The possible reason is that the experiment P4 is a variable speed experiment, and the thermal error curve changes more complexly, such as Figure 4 As shown. In comparison, the performance of the other methods in prediction #7 was relatively average. Overall, the PCR-DBSCAN method achieved high prediction accuracy, with an average RMSE of 7.3 μm across 10 predictions. This method outperformed the listed FCM-MLR, SVM, and CNN-LSTM methods. Compared to conventional principal component models such as PCR-G(k) and PCR-ALL, its prediction accuracy increased by 50.0% and 47.9%, respectively.

[0111]

[0112]

[0113] Table 3

[0114] On the other hand, the optimal number of principal components generally varies across different prediction tasks. Even when using the same modeling data, such as when using P3 and P4 in #1 and #4 to predict the thermal errors of P1 and P2, respectively, the optimal number of principal components is 8 and 23, respectively. Therefore, while the optimal PCR-BEST model achieves exceptional performance, with an RMSE as low as 2.5 μm in #7, far outperforming other modeling methods, there is currently no method for determining the optimal number of principal components.

[0115] Taking the spindle thermal error modeling of a three-axis CNC machining center as an example, this paper reveals the limitations of existing methods for determining the number of principal components based on cumulative variance contribution rates in principal component thermal error modeling. The paper also compares the prediction performance of the proposed PCR-DBSCAN modeling method with that of conventional principal component modeling methods. The PCR-DBSCAN modeling method is essentially a reprocessing of the prediction results of a conventional principal component regression model. It uses density clustering to eliminate outliers in the prediction results of each principal component model. While optimal performance cannot be guaranteed in each of the 10 prediction tasks shown in Table 3, it achieves superior prediction performance compared to conventional principal component modeling methods in the vast majority of cases.

[0116] The PCR-DBSCAN method is an improved principal component modeling method for thermal errors, retaining the high robustness of the principal component regression model. However, as shown in Table 3, which compares the performance of various model types, principal component regression remains a superior thermal error modeling method. However, the difficulty lies in determining the optimal number of principal components. If a method can be developed to determine the optimal number of components, the principal component model may achieve predictive performance far superior to other models. However, there is currently no mature theory to support the optimal number of components in principal component thermal error modeling, which greatly limits the performance of principal component models and is an important direction worthy of research.

[0117] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. An improved principal component regression machine tool thermal error modeling method based on density clustering, characterized by: The following steps are involved: The original temperature data is processed by principal component analysis to reduce the dimension and obtain multiple principal components; Establishing multiple principal component regression models based on the principal components, each model corresponding to a different number of principal components; Performing cluster analysis on the prediction results of the multiple principal component regression models using a density clustering algorithm to identify and eliminate abnormal prediction values; The prediction results after removing outliers are comprehensively processed to obtain the final thermal error prediction model.

2. The improved principal component regression machine tool thermal error modeling method based on density clustering according to claim 1 is characterized in that: The principal component regression modeling step specifically includes: Collect temperature data of key measurement points of machine tools and thermal error data of machine tools as raw data; Perform standardization preprocessing on the original temperature data; Calculate the covariance matrix of the preprocessed data and solve the eigenvalues ​​and eigenvectors of the covariance matrix; The first k principal components are selected in sequence according to the eigenvalue sorting, and regression modeling is performed with the thermal error data, k = 1, 2, 3..., to obtain the corresponding principal component regression model.

3. The improved principal component regression machine tool thermal error modeling method based on density clustering according to claim 1 is characterized in that: The density clustering algorithm is the DBSCAN algorithm, and its parameter setting strategy is: The minimum number of samples minPts takes a fixed value [X]; The neighborhood radius ε is the standard deviation of all model predictions.

4. The improved principal component regression machine tool thermal error modeling method based on density clustering according to claim 1 is characterized in that: The comprehensive processing step is to take the arithmetic mean of the prediction results after removing the outliers, and use this as the final thermal error prediction value.

5. A machine tool thermal error compensation system based on a modeling method, according to the improved principal component regression machine tool thermal error modeling method based on density clustering according to any one of claims 1 to 4, characterized in that: Includes the following modules: Data acquisition module, used to collect temperature data and thermal error data of key measurement points of machine tools; Data processing module, used for preprocessing and principal component analysis of the collected data; A model building module is used to build multiple principal component regression models based on principal components; Cluster analysis module, used to perform density cluster analysis on the prediction results of multiple principal component regression models; Model optimization module, used to eliminate abnormal prediction values ​​and comprehensively process them to obtain the final thermal error prediction model; The compensation execution module is used to perform error compensation on the machine tool processing process according to the final thermal error prediction model.

6. The machine tool thermal error compensation system based on the modeling method according to claim 5, characterized in that: The data acquisition module includes a plurality of temperature sensors and displacement sensors. The temperature sensors are distributed at key positions of the machine tool, and the displacement sensors are used to measure the thermal deformation of the machine tool.

7. The machine tool thermal error compensation system based on the modeling method according to claim 5, characterized in that: The compensation execution module includes a numerical control system and a servo drive system. The numerical control system outputs compensation instructions according to the thermal error prediction model, and the servo drive system adjusts the position of the motion axis of the machine tool according to the compensation instructions.

8. The machine tool thermal error compensation system based on the modeling method according to claim 5, characterized in that: It also includes a monitoring and display module for displaying information such as the thermal error status of the machine tool, model prediction results, and compensation effects in real time to assist operators in monitoring and managing the thermal error compensation process of the machine tool.

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