Gaussian regression model tool wear monitoring method based on hybrid drive

Abstract

The invention belongs to the technical field of tool wear state monitoring, and provides a Gaussian regression model tool wear monitoring method based on hybrid drive, which comprises the following steps of: acquiring three-axis cutting force, axial bending moment and three-axis vibration signals in a milling process; extracting a multi-domain feature representing the degradation state of the tool, performing feature fitness analysis, and screening out a health index having the highest correlation with a tool wear curve; gaussian weighted moving average filtering is carried out on the health indexes; establishing a display physical mapping model between the health indexes and the tool wear data; utilizing the feature information and a prior physical model to constrain a mean value function of a Gaussian regression process; and a grid search algorithm is used to optimize model parameters, and precise prediction of tool wear is realized. The technical problem that it is difficult to monitor the tool wear condition in real time is solved, and the stability and reliability of the prediction process are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of tool wear state monitoring, and specifically relates to a tool wear monitoring method based on a Gaussian regression model driven by physical information hybrid, which is applied to the field of tool wear state monitoring under variable working conditions. Background Art

[0002] Cutting tools, as the terminal components that directly contact the workpiece, play a crucial role in the machining process. Especially during high-speed, high-precision machining, tool wear directly impacts the workpiece's surface quality. To meet high-quality requirements, conservative tool life estimates are often adopted. Current statistics indicate that tool life only reaches 50% to 80% of the recommended lifespan, while tool failures result in 20% of machine downtime. This wasted tooling increases economic costs and reduces machining efficiency. Therefore, the development and application of online tool wear monitoring systems has become a key area of ​​focus for the development of intelligent machining systems.

[0003] In tool wear monitoring, there are direct methods based on wear measurement and indirect methods based on machine learning. The direct method generally uses optical microscopes, scanning electron microscopes and other equipment to observe and measure the tool surface, and evaluates the degree of tool wear by measuring indicators such as the size, shape and surface roughness of the tool edge. The advantage of the direct method is that it can provide more accurate tool wear information, but it requires downtime detection and is difficult to achieve real-time monitoring. Indirect methods can be divided into physical models and data-driven models. Traditional physical models mainly use processing parameters as variables, which leads to the separation of tool wear prediction from actual working conditions and the inability to provide prediction results related to the dynamics of the cutting process. The data-driven model's requirement for a large amount of high-quality labeled data and physical knowledge limits its high-precision prediction capabilities.

[0004] In summary, in order to overcome the above shortcomings, the inventors proposed a tool wear monitoring method based on a Gaussian regression model driven by physical information hybrid. Summary of the Invention

[0005] Aiming at the problem of how to effectively handle tool wear status monitoring under variable working conditions, the present invention provides a tool wear monitoring method based on a hybrid-driven Gaussian regression model, which greatly improves the stability and reliability of the prediction process.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: A method for tool wear monitoring based on a hybrid-driven Gaussian regression model comprises the following steps: Collect three-axis cutting force, axial bending moment and three-axis vibration signals during milling; Extract multi-domain features that characterize tool degradation status, perform feature fitness analysis, and select the health indicator with the highest correlation with tool wear curve; Perform Gaussian weighted moving average filtering on health indicators; Establish a physical mapping model between health indicators and tool wear data; Utilize feature information and prior physical models to constrain the mean function of the Gaussian regression process; A grid search algorithm is used to optimize model parameters and achieve accurate prediction of tool wear.

[0007] As a further solution of the present invention: the multi-domain features characterizing the tool degradation state are extracted, and feature fitness analysis is performed to screen out the health indicators with the highest correlation with the tool wear curve, specifically: Different features are extracted from the time domain and frequency domain, including mean, maximum, minimum, peak-to-peak value, root mean square, standard deviation, variance, crest factor, skewness factor, kurtosis factor, margin factor, pulse factor, shape factor, center of gravity frequency, frequency root mean square, frequency variance, frequency band energy and relative power spectrum entropy. The Pearson correlation coefficient between each signal feature and the actual tool wear curve was calculated, and the feature with the highest score was selected as the health factor, representing the tool wear process.

[0008] As a further solution of the present invention: the Gaussian weighted moving average filtering of the health indicators is specifically as follows: A Gaussian weighted moving average filter is used to smooth the health factor to reduce the adverse effects of noise on wear prediction (reduce the volatility and uncertainty of the signal to make it conform to the progressive physical law of tool wear).

[0009] As a further solution of the present invention: by changing the standard deviation and window size of the Gaussian weighted moving average filter, the smoothness of the health factor and the number of sensitive signals of the cutting signal can be changed.

[0010] As a further solution of the present invention: the establishment of a display physical mapping model between health indicators and tool wear data is specifically as follows: There is an obvious linear proportional relationship between the smoothed health factor and the tool wear process, and a linear tool wear physical model can be established.

[0011] As a further solution of the present invention: the characteristics of the Gaussian process are determined by the mean function and the covariance function, which affect the prediction performance of the Gaussian process regression model.

[0012] As a further solution of the present invention: the use of feature information and a priori physical model to constrain the mean function of the Gaussian regression process is specifically: The established tool wear physical model is embedded in the mean function of the Gaussian regression process to incorporate physical prior information and improve the interpretability of the model.

[0013] As a further solution of the present invention: the grid search algorithm is used to optimize the model parameters and achieve accurate prediction of tool wear, specifically: The prediction function of the model can be achieved by using the grid search algorithm to determine the hyperparameters in the covariance function of the Gaussian regression process.

[0014] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This application proposes a health factor construction strategy based on feature fitness analysis and Gaussian weighted moving average filtering to address the changes in the spatial and temporal distribution of signal characteristics in milling processing. This strategy can eliminate interference and redundancy in the measurement signal, make it conform to the progressive physical law of tool wear, and improve monitoring efficiency.

[0015] 2. This application develops a new explicit physical model of tool wear, which can establish a dynamic mapping with tool wear data from the perspective of cutting force, and can provide key physical information guidance for the hybrid prediction model.

[0016] 3. The hybrid drive method developed in this application predicts tool wear under variable working conditions by combining data mining with physical models.

[0017] 4. This application can effectively reduce tool waste and achieve accurate tool wear detection. The above method can effectively address tool wear status monitoring under variable operating conditions, significantly improving the stability and reliability of the prediction process. This has been verified in composite material processing on models such as the LZ100 and LZ101. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a method for tool wear monitoring based on a Gaussian regression model driven by hybrid physical information in this application; Figure 2 Gaussian weight maps with different (standard deviation) values ​​were used for this application; Figure 3 This is a comparison chart of the health factor before and after smoothing for this application; Figure 4 This is a functional relationship diagram of the health factor and tool wear curve for this application; Figure 5 A fitness score plot of the Gaussian regression process hyperparameters determined by the grid search algorithm for this application; Figure 6 This is the tool wear monitoring result diagram for this application; Figure 7This is the tool wear measurement result diagram under different working conditions of this application; Figure 8 This is the prediction result diagram of the target dataset using the PIGPR prediction model in this application; Figure 9 This is the prediction result diagram of the target dataset using the GPR prediction model in this application; Figure 10 This is the prediction result diagram of the target dataset using the SBiLSTM prediction model in this application; Figure 11 This application uses the attention-based Transformer model (AT-Transformer) prediction model to predict the target dataset. Figure 12 This is the prediction result diagram of the target dataset using the GRU prediction model in this application; Figure 13 Performance comparison of five tool wear prediction models for this application (PIGPR, GPR, SBiLSTM, AT-Transformer, and GRU), with mean and standard deviation plots of the prediction indicators for nine tools; Figure 14 This is a comparison chart of the predicted confidence interval mean and standard deviation of GPR and PIGPR for this application. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0020] In the drawings, the same or similar reference numerals throughout the drawings represent the same or similar elements or elements having the same or similar functions. The described embodiments are only some of the embodiments of the present invention, but not all of the embodiments.

[0021] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0022] The following is combined with Figure 1-14 The embodiments of the present invention are described in detail.

[0023] Example 1 See also Figure 1The tool wear monitoring method based on the Gaussian regression model driven by physical information hybrid includes: collecting three-axis cutting force, axial bending moment and three-axis vibration signals during milling; extracting multi-domain features that characterize the tool degradation state, and performing feature fitness analysis to screen out the health indicators with the highest correlation with the tool wear curve; performing Gaussian weighted moving average filtering on the health indicators; establishing a display physical mapping model between health indicators and tool wear data; using feature information and prior physical models to constrain the mean function of the Gaussian regression process; using a grid search algorithm to optimize model parameters and achieve accurate prediction of tool wear.

[0024] First, the multi-domain features that characterize the degradation state of the tool are extracted from the collected signals, and feature fitness analysis is performed to screen out the health indicators with the highest correlation with the tool wear curve. Different features are extracted from the time domain and frequency domain, including eighteen features such as mean, maximum, minimum, peak-to-peak value, root mean square, standard deviation, variance, peak factor, skewness factor, kurtosis factor, margin factor, pulse factor, waveform factor, center of gravity frequency, frequency root mean square, frequency variance, frequency band energy and relative power spectrum entropy; the Pearson correlation coefficient of each signal feature and the actual tool wear curve is calculated, and the feature with the highest score is selected as the health factor to represent the tool wear process. In this example, the variance of the cutting force in the Z direction is selected as the health factor. The Pearson correlation coefficient is defined as:

[0025] in, is the calculated eigenvalue, It is the tool wear value collected by the tool wear observation platform. is the feature mean, is the collected mean value of tool wear.

[0026] Gaussian weighted moving average filtering is performed on the health factor. A Gaussian weighted moving average filter is used to smooth the health factor to reduce the adverse effects of noise on wear prediction.

[0027] The Gaussian weighted moving average method uses a Gaussian kernel function to assign different weights to each data point based on the width of the Gaussian bell curve. Taking into account different window sizes, the adjustment of the Gaussian weight can be expressed as the formula:

[0028] in, The Gaussian weight coefficient associated with each data point, is the measurement point number, is the middle point measurement number in the moving average window, is the window size, is the standard deviation of the Gaussian distribution.

[0029] The standard deviation and window size in the Gaussian weighted moving average method affect the distribution of weights. Figure 2 To use different (standard deviation) values ​​of Gaussian weights, indicating that the lower The value corresponds to the higher contribution of the midpoint. In this application, the smoothing effect and detail information are weighed comprehensively, and the standard deviation is used. and window .

[0030] like Figure 3 As shown in Figure 3, the filtered health factor is smoother, which reduces the influence of random disturbances caused by different cutting parameters and tool wear conditions and is more in line with the physical law of progressive tool wear.

[0031] like Figure 4 The figure shows the relationship between tool health factor and wear data. It can be seen that there is an obvious linear relationship between the health factor and the tool wear data. From the regression analysis of the data points, the determination coefficient of the tool wear curve regression fitting is The value is 0.9942. This shows that the linear curve fits the data points very well. Therefore, the health factor extracted from the multi-domain features during the cutting process can be reliably used for online tool wear monitoring. Based on this finding, a universal tool wear physical model between the health factor and the wear data was established and used as the prior mean function of the Gaussian regression model to constrain the prediction process. In this way, prior information or domain knowledge can be easily incorporated, which is also beneficial to the interpretability of the model. The mathematical expression of the universal tool wear physical model between the health factor and the wear data is:

[0032] in, Indicates the actual wear width of the tool, For health factors screened by feature fitness analysis, and is the fitting coefficient, t is a time variable that needs to be inferred from the training data. In this example, the physical model is: .

[0033]

[0034] In the standard Gaussian regression procedure, the hyperparameter is unknown, among which, is the mean of the output corresponding to the value to be predicted, Output the posterior variance of the predicted value, is the characteristic scale parameter related to input and output, is the signal standard deviation, is the standard deviation of the noise. Unknown parameters and It can be precisely given by the physical model, so only the hyperparameters in the covariance function need to be determined , the model prediction function can be realized.

[0035] In this example, the grid search algorithm is used to determine the optimal hyperparameters of the model, and the fitness is the MAE (mean absolute error) indicator of the prediction results. The standard deviation of the signal and noise ranges are: , characteristic scale parameter The value range is [0.1,1.5]. The grid search algorithm results are as follows Figure 5 As shown, the best hyperparameters are determined to be 、 、 .

[0036] The Gaussian process regression result is the tool wear monitoring result, such as Figure 6 As shown in the figure, the actual wear amount is basically within the 95% confidence interval of the predicted value, and the predicted value of the model is highly consistent with the actual value.

[0037] Example 2 First, during milling experiments, a signal acquisition system was used to measure triaxial cutting force, axial bending moment, and triaxial vibration signals online at sampling frequencies of 2.5 kHz and 10.24 kHz, respectively. Multi-domain features characterizing tool degradation were then extracted from these seven measured signals. Feature fitness analysis was performed to identify the health index with the highest correlation with the tool wear curve. The health index was then filtered using a Gaussian weighted moving average filter to further reduce signal volatility and uncertainty, thereby aligning it with the asymptotic physical laws of tool wear. Next, an explicit physical mapping model between the health index and tool wear data was established, and its regression performance was compared with that of the classic Taylor formula and a tool wear model with adjustable coefficients. Feature information and a priori physical models were then used to constrain the mean function of a Gaussian regression process (GPR), combining data mining and physical models to provide key physical domain knowledge for prediction guidance in the hybrid model. A grid search algorithm was then used to optimize the model parameters, ultimately achieving accurate tool wear predictions with a 95% confidence interval for enhanced reliability.

[0038] 1.1 Experimental design and experimental setup description Tool wear experiments were conducted on a VMC-855 five-axis vertical machining center. To minimize the impact of cutting fluid on the monitoring signals, all experiments were conducted in a dry state. The workpiece was a ceramic-matrix composite material with dimensions of 160 mm × 26 mm × 100 mm, and each cutting stroke was 160 mm. The experiments were performed using a two-flute polycrystalline diamond (PCD) tool with a diameter of 16 mm, a corner radius of 0.4, and a helix angle of 11°. The milling cutter shank was EHA162-100L, and the insert was APKT113504.

[0039] During the cutting process, the force acquisition system and acceleration acquisition system are used to collect the three-axis cutting force signal of the tool. F x 、 F y 、 F z and Z-axis bending moment M z , and the three-axis vibration signal of the machine tool spindle a x 、 a y 、 a z The force acquisition system consists of a wireless rotational dynamometer (Kistler-9170B2511), a wireless transmission module, and display software, with a sampling frequency of 2.5 kHz. The acceleration acquisition system consists of a triaxial piezoelectric accelerometer (PCB 356A15), an NI cDAQ-9171 acquisition card, and display software. The accelerometer is mounted on the machine tool spindle via a magnetic base, with a sampling frequency of 10.24 kHz.

[0040] In actual cutting, tool wear degradation is influenced by the complex coupling of multiple operating conditions, including cutting parameters, tool type, and material properties. This example focuses on the impact of varying cutting parameter combinations on tool wear evolution. To validate the proposed method, three cutting parameters—cutting width (R1:3, R2:5, R3:7 mm), spindle speed (S1:1600, S2:2000, S3:2400 r / min), and feed rate (F1:1600, F2:1280, F3:1920 mm / min)—were considered design variables. A three-factor, three-level Taguchi L9 orthogonal experiment was designed, as shown in Table 1. Furthermore, the cutting depth for all parameter combinations was fixed at 0.2 mm, ensuring that the cutting depth was less than the tool tip radius R0.4 mm to minimize tool chipping.

[0041] Table 1 Test parameter settings

[0042] GFRP part milling experiments were conducted using nine identical cutting tools, each using the nine parameter combinations listed in Table 1. A total of nine sets of cutting signal and wear data were obtained, with each tool's data considered as a separate dataset, T1 to T9. Tool wear values ​​were collected using a tool wear observation platform consisting of a 3-DOF coordinate controller, an industrial camera, a bi-telecentric lens, and a light source. The industrial camera model was an MV-HS2000GM2 with a resolution of 20 megapixels, and the bi-telecentric lens model was BT-F064. A vertical annular light source with adjustable brightness was used. To minimize measurement error, wear images of two inserts were collected after each cutting experiment without removing the inserts, and the corresponding wear values ​​were measured. According to the ISO 8688 standard for measuring tool wear, the average wear value of the two inserts, VB, was used as the label for the experimental dataset. For tool T1, during the initial wear phase, a uniform wear zone formed along the contact area between the cutting tool and the workpiece, with minor damage observed. As the cutting process progressed, the uniform wear zone gradually expanded in size, and the depth of the wear edge deepened. At the end of the machining process (80th cut), the tool is in a severe wear stage.

[0043] Based on the above method, the wear curves under 9 working conditions are as follows Figure 7 As shown in Figure 2, it can be seen that different milling parameters lead to different trends in tool wear values, and some even have significant differences. Figure 7 (d) and Figure 7 (e) shows a clear wear mutation trend at different cutting moments. Therefore, it is extremely challenging to accurately model these data using only physical models established under ideal experimental conditions or purely data-driven models.

[0044] 1.2 Multi-domain feature extraction and health factor construction In order to fully reflect the changing laws of the dynamic characteristics of the cutting system, the changes of the signal in the time domain and frequency domain are described by calculating the amplitude, time distribution index and the statistical characteristics of the spectrum concentration. Table 2 lists the description and formula of each feature. Among them, represents the original processed signal, . is the number of sampling points. represents the spectrum, , is the number of spectral points in the signal. Indicates the Frequency amplitude of each spectrum point. Time domain characteristics It reflects the amplitude and energy in the time domain. Reflects the overall distribution of the signal, frequency domain characteristics It reflects the changes in the dominant frequency band. Characterizes the concentration of the spectrum, It reflects the energy in the frequency domain.

[0045] Table 2 List of extracted features.

[0046] A good feature should show a trend consistent with the wear propagation, so the purpose of feature fitness analysis is to find a feature that best represents the tool wear process. In other words, as tool wear progresses in the degradation process, the ideal prediction feature should show a trend that continuously increases in proportion to tool wear. The Pearson correlation coefficient (PCC) is a mathematical standard that measures the degree of correlation between two variables. It is used as a fitness value to measure the correlation between a feature and the prediction target. The Pearson correlation coefficient is defined as:

[0047] in, is the calculated eigenvalue, It is the tool wear value collected by the tool wear observation platform.

[0048] The value of the Pearson correlation coefficient ranges from -1 to 1. The closer its absolute value is to 1, the better the correlation between the feature and the wear process.

[0049] In addition, a Gaussian weighted moving average (GSWMA) filter is used to smooth the noisy HI to reduce its adverse effects on wear prediction. Unlike the simple moving average method, the GSWMA uses a Gaussian kernel function, assigning different weights to each data point based on the width of the Gaussian bell curve. The adjustment of the Gaussian weights to account for different window sizes can be expressed using a formula.

[0050]

[0051] in, The Gaussian weight coefficient associated with each data point, is the measurement point number, is the middle point measurement number in the moving average window, is the window size, is the standard deviation of the Gaussian distribution.

[0052] From the above formula, it can be concluded that the standard deviation and window size in GSWMA affect the distribution of weights. Generally speaking, larger weights usually correspond to higher smoothing degrees. On the contrary, smaller weights may correspond to more subtle changes and better retain sensitive information in the cutting signal. Therefore, smaller windows and standard deviations can be selected to retain more detailed information. In this embodiment, the smoothing effect and detailed information are comprehensively weighed, and the standard deviation is used. and window .

[0053] 1.3 Performance evaluation of the proposed tool wear physical model There is an obvious linear relationship between the health factor and the tool wear data. From the regression analysis of the data points, the determination coefficient of the regression fitting of the wear curve of the 9 tools is The average value of the values ​​is 0.9913. This shows that the linear curve fits the data points very well. Therefore, the health factor extracted from the multi-domain features during the cutting process can be reliably used for online tool wear monitoring. In summary, there is an obvious linear proportional relationship between the health factor and the tool wear process during CMC milling (through The value can be directly verified).

[0054] Based on this discovery, a universal tool wear physics model linking health factors and wear data was established and used as a prior mean function in the GPR model to constrain the prediction process. This facilitates the incorporation of prior information or domain knowledge and improves model interpretability. The mathematical expression of the universal tool wear physics model linking health factors and wear data is:

[0055] in, Indicates the actual wear width of the tool, For health factors screened by feature fitness analysis, and To fit the coefficients, they need to be inferred from the training data.

[0056] Detailed fitting coefficients and determination coefficients of the physical models of the 9 cutting tools The values ​​are shown in Table 3. In order to show the stability of the regression results, the mean (Mean) and standard deviation (SD) of the coefficient of determination of the 9 groups of test data were calculated and displayed in the last two rows.

[0057] Table 3 Fitting coefficients of the proposed tool wear physical model and value

[0058] In order to quantitatively evaluate the performance of the three tool wear physical models, Tables 4 and 5 give the fitting coefficients and determination coefficients of the classic Taylor formula and the universal wear model. By comparing Tables 3 to 5, it can be concluded that the determination coefficient of the tool wear model proposed in this embodiment under 9 cutting parameter combinations The average value is 0.9913 and the standard deviation is only 0.0046. The average coefficient of determination of the classic Taylor formula and the universal wear model The values ​​are 0.9849 and 0.9782, and the standard deviations are 0.0094 and 0.0153, respectively. Therefore, among the three tool wear physical models, the method proposed by us obtains the largest coefficient of determination. value, and its standard deviation is also the smallest, which means that our proposed method provides more accurate and stable tool wear modeling results than other methods and can describe the tool wear process with higher accuracy.

[0059] Table 4 Fitting coefficients of the classic Taylor formula wear model and value

[0060] Table 5 Fitting coefficients of universal wear model and value

[0061] 1.4 Grid Search to Determine the Optimal Parameters of the PIGPR Model In the standard GPR model, the hyperparameters In this embodiment, since an accurate tool wear physical model is established as the mean function, the unknown parameters in the mean function are and It can be precisely given by the physical model, which greatly improves the interpretability of the model. Therefore, only the hyperparameters in the covariance function need to be determined. , the model prediction function can be realized.

[0062] This example uses a grid search algorithm to determine the optimal hyperparameters of the model, and the fitness is the MAE (mean absolute error) indicator of the prediction results. The standard deviation of the signal and noise ranges are: , characteristic scale parameter l The value range is [0.1, 1.5], the search times are 3375 times, and the time taken is 2.9566 seconds. The best hyperparameters are 、 、 .

[0063] 1.5 Evaluation of the Prediction Performance of the Proposed PIGPR Model To demonstrate the superior performance of the proposed model, five methods were compared using datasets T1 to T9: the PIGPR model proposed in this example, the Gaussian Regression model (GPR), the Stacked Bi-directional Long Short-Term Memory (SBiLSTM), the Attention-based Transformer model (AT-Transformer), and the Gated Recurrent Unit (GRU). Testing was performed using leave-one-out cross-validation, with eight datasets used for training and the remaining dataset used as the test set. It is worth noting that the test set data was not used for training in any experiment. The basic parameters of the comparison models are set as follows: For the Stacked Bi-directional Long Short-Term Memory (SBiLSTM), dropout was applied during training to reduce overfitting, with a dropout rate of 0.2. To keep computational complexity low, the number of hidden layers in the first BiLSTM network was 64, and the number of hidden units in the second layer was half that of the first layer. Hyperparameters in the AT-Transformer model play a crucial role in model performance, including batch size, dropout rate, learning rate, and the number of heads in the multi-head self-attention mechanism (H). A grid search strategy was used to determine the optimal parameters: batch size = 256, epochs = 70, dropout rate = 0.3, H = 3, and learning rate = 0.001. As a variant of LSTM, the gated recurrent unit (GRU) optimizes the logical structure to improve computational efficiency while maintaining tool wear identification accuracy. A GRU with two hidden layers containing 128 neurons was used to predict tool wear.

[0064] The prediction results of five tool wear prediction models (PIGPR, GPR, SBiLSTM, AT-Transformer and GRU) are shown in Figure 2. Figures 8 to 12 As shown in Figure 2. The bold blue line in each sub-figure represents the actual tool flank wear value measured in the experiment, and the prediction error represents the absolute value of the difference between the predicted value and the measured tool wear. It can be seen that the pure data-driven model has obvious fluctuations throughout the prediction process. Figure 9As shown in Figure 1, the GPR model can only predict the overall trend of tool wear, and there are large prediction errors in both the early and late stages of tool wear. As for the SBiLSTM model, its stacked two-layer BiLSTM has a strong sequence modeling capability when processing time series data. And because of its bidirectional loop structure, it can better capture the temporal relationships and patterns in the sequence, thus obtaining better prediction results than the GPR model. However, there are multiple mutations in the entire prediction process, and the results are unstable, such as Figure 10 (c) Figure 10 (g) and Figure 10 (h). Figure 11 As shown in Figure 2, the AT-Transformer model achieves better prediction results than the GPR model and the SBiLSTM model. This may be because the introduction of the attention mechanism allows the model to dynamically allocate attention when processing input, allowing the model to focus on key information in the input, which helps to improve the generalization ability of the AT-Transformer model. However, it still fails to accurately identify the wear mutation trend, as shown in Figure 2. Figure 11 (e) is shown in the T5 working condition. Figure 12 As shown in , the GRU model has a large error in the early stage of wear and tear, which will improve as the prediction progresses, but the error will increase again in the later stage of wear and tear. In contrast, the proposed PIGPR model, such as Figure 8 As shown in Figure 2, good results and consistency are achieved on different test data sets. And because of the embedded physical knowledge, the wear mutation point can be identified and the dynamic degradation trajectory can be accurately tracked, as shown in Figure 2. Figure 8 (e) T5 working condition. In order to quantitatively compare the performance of the five tool wear prediction models, four evaluation indicators were studied, namely:

[0065]

[0066]

[0067]

[0068] in, is the measured true tool wear value, The tool wear prediction model at the test point The predicted value of yes The corresponding eigenvector. MAE is the mean absolute error, RMSE is the root mean square error, MAPE is the mean absolute percentage error, and PCC is the Pearson correlation coefficient. It is worth noting that smaller MAE, RMSE, and MAPE and larger PCC mean better prediction accuracy of the tool wear prediction model.

[0069] The detailed performance comparison of the five tool wear prediction models under the four evaluation indicators is shown in Table 6, and the best prediction results are bolded. Figure 13 This figure more intuitively demonstrates the average and standard deviation of the performance metrics of the five tool wear prediction models across nine test datasets. In each subplot, the numbers above the bars represent the values ​​of the evaluation metrics. It can be seen that among the five tool wear prediction models, the PIGPR model has the smallest MAE / RMSE / MAPE values ​​and the largest PCC value, at 4.603, 5.500, 0.034, and 0.997, respectively. This significantly outperforms the prediction results of the GPR, SBiLSTM, AT-Transformer, and GRU models. The next best prediction results are from the AT-Transformer and GRU, followed by the GPR and SBiLSTM.

[0070] Based on the results of different models, the reason why the comparison model produces significant prediction errors is that data-driven models usually rely on a large amount of training data to fully map the relationship between input features and outputs. Although any complex functional relationship can be fitted in theory, the physical process of tool wear is not taken into account and there is a lack of physical constraints, which makes it difficult for the model to achieve a good training level in practice. Moreover, the uneven distribution of model training data also has a significant impact on the prediction parameters of the model. On the contrary, the tool wear physics model provides prior knowledge for the proposed model. This knowledge can be used to guide the establishment and optimization of PIGPR, thereby reducing the difficulty of the model searching for the optimal solution. Secondly, the additional input of physical information also constrains the learning process of the model, making it robust in reasoning under changing working conditions and the presence of noise, making the model prediction more accurate and reliable. However, the data model has different degrees of prediction mutations due to factors such as environmental noise, which reduces the accuracy of the model prediction. Therefore, from Figures 8 to 12 Judging from the prediction results, the predictions of the proposed PIGPR model are more consistent with the actual values, and its prediction performance is significantly better than that of the GPR, SBiLSTM, AT-Transformer and GRU models.

[0071] Table 6 Performance comparison results of the compared methods Table6 Performance comparison results of the five compared methods

[0072] In addition, the confidence interval of the prediction results can also be provided by the GPR model. In this embodiment, in addition to the prediction accuracy, the 95% confidence interval of the GPR model prediction results is also quantitatively analyzed. In order to quantitatively analyze the reliability and stability of the 95% confidence interval, this embodiment studies two evaluation indicators for the confidence interval, namely:

[0073]

[0074] in, At the test point The width of the 95% confidence interval. and are the mean width and variance of the 95% confidence interval of the test data, respectively. The smaller the value of , the more accurately the tool wear width can be monitored. reflects the smoothness of the confidence interval, The smaller the value, the more reliable and stable the tool wear monitoring process is.

[0075] Comparison of confidence interval evaluation indicators of PIGPR and GPR Figure 14 As shown in Figure 2, it can be seen that compared with the original purely data-driven GPR model, the 95% confidence interval of the PIGPR model is and The results were 46.44% and 60.80% lower, respectively. Therefore, integrating a more accurate physical model into the GPR model significantly improved the reliability and stability of its monitoring process. This directly demonstrates that the integration of cutting physics knowledge produces significant benefits.

[0076] To address the limitations of purely data-driven and physical models in tool wear prediction, this example proposes a data-model-linked prediction method guided by physical information. Its advantage lies in its comprehensive consideration of the physical laws of tool wear, enabling the purely data-driven model to achieve more accurate wear prediction results under the guidance of the physical model while reducing prediction uncertainty. The effectiveness of the proposed method was verified through multi-condition milling tests and compared with advanced wear prediction models in existing literature. The main conclusions are as follows: 1. A new explicit physical model of tool wear was developed based on the linear relationship between tool flank wear data and the established health factor. Experimental results show that the coefficient of determination of the explicit physical model of tool wear is The regression performance is not less than 0.98, and it is significantly better than the traditional Taylor tool life model and the universal wear model.

[0077] 2. A dual-physics-data driven modeling strategy for tool wear prediction was proposed, improving the prediction accuracy of the Gaussian regression process. By embedding the established tool wear physics model into the mean function of the Gaussian regression process, data mining and physical principles were effectively combined, improving the model's interpretability. Experimental results demonstrate that incorporating physical prior knowledge has a significant positive impact on prediction performance compared to the traditional GPR model using a constant mean function. The mean width and variance of the 95% confidence interval of the prediction results were reduced by 46.44% and 60.80%, respectively, demonstrating that the integration of cutting physics knowledge yields significant benefits, significantly improving the smoothness, reliability, and versatility of the prediction process.

[0078] 3. The physics-based and data fusion-based training strategy fully exploits the wear state and operating condition information in the observed signals, improving the model's prediction accuracy and generalization under different machining conditions. The effectiveness of the developed model was verified through nine sets of high-speed cutting experiments under different machining conditions. Experimental results show that the PIGPR model achieves an average prediction accuracy of 0.997, with MAE, RMSE, and MAPE values ​​of 4.603 μm, 5.500 μm, and 0.034, respectively. The fluctuation of wear estimates is also confined to a narrow range. The prediction performance significantly outperforms currently popular models such as SBiLSTM, AT-Transformer, and GRU.

[0079] So far, the purpose of the present invention has been achieved.

[0080] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for tool wear monitoring based on a hybrid-driven Gaussian regression model, characterized in that: The following steps are involved: Collect three-axis cutting force, axial bending moment and three-axis vibration signals during milling; Extract multi-domain features that characterize tool degradation status, perform feature fitness analysis, and select the health indicator with the highest correlation with tool wear curve; Perform Gaussian weighted moving average filtering on health indicators; Establish a physical mapping model between health indicators and tool wear data; Utilize feature information and prior physical models to constrain the mean function of the Gaussian regression process; A grid search algorithm is used to optimize model parameters and achieve accurate prediction of tool wear.

2. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 1, characterized in that: The multi-domain features characterizing the tool degradation state are extracted, and feature fitness analysis is performed to screen out the health indicators with the highest correlation with the tool wear curve, specifically: Different features are extracted from the time domain and frequency domain, including mean, maximum, minimum, peak-to-peak value, root mean square, standard deviation, variance, crest factor, skewness factor, kurtosis factor, margin factor, pulse factor, shape factor, center of gravity frequency, frequency root mean square, frequency variance, frequency band energy and relative power spectrum entropy. The Pearson correlation coefficient between each signal feature and the actual tool wear curve was calculated, and the feature with the highest score was selected as the health factor, representing the tool wear process.

3. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 1, characterized in that: The Gaussian weighted moving average filtering of the health indicators is specifically as follows: The health factor is smoothed using a Gaussian weighted moving average filter to reduce the adverse effects of noise on wear prediction.

4. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 3 is characterized in that: By changing the standard deviation and window size of the Gaussian weighted moving average filter, the smoothing degree of the health factor and the amount of sensitive signals in the cutting signal can be changed.

5. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 1, characterized in that: The physical mapping model between the health index and the tool wear data is established as follows: There is an obvious linear proportional relationship between the smoothed health factor and the tool wear process, and a linear tool wear physical model can be established.

6. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 1, characterized in that: The characteristics of the Gaussian process are determined by the mean function and covariance function, which affect the prediction performance of the Gaussian process regression model.

7. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 6, characterized in that: The method of using feature information and a priori physical model to constrain the mean function of the Gaussian regression process is as follows: The established tool wear physical model is embedded in the mean function of the Gaussian regression process to incorporate physical prior information and improve the interpretability of the model.

8. The method for tool wear monitoring based on hybrid-driven Gaussian regression model according to claim 1, characterized in that: The grid search algorithm is used to optimize the model parameters and achieve accurate prediction of tool wear, specifically: The prediction function of the model can be achieved by using the grid search algorithm to determine the hyperparameters in the covariance function of the Gaussian regression process.

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