SR-TELM-based drilling-expanding mixed processing material removal power prediction method

Abstract

The invention provides a drilling-expanding mixed machining material removal power prediction method based on SR-TELM, relates to the technical field of numerical control machine tool power prediction, and deeply excavates a physical mechanism between machining parameters and material removal power in drilling-expanding mixed machining material removal through a symbolic regression algorithm. By embedding a mechanism model into hidden layer neurons of the TELM, the advantage of analyzing a physical mechanism by a symbolic regression algorithm and the strong nonlinear approximation capability of the TELM are organically fused, the power prediction precision is effectively improved under a limited data condition, the physical interpretability of the model is ensured, and the power prediction efficiency is improved. And a new solution is provided for machine tool drilling-expanding mixed machining material removal power modeling.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical control machine tool power prediction, and in particular to a drilling-expanding mixed machining material removal power prediction method based on SR-TELM. BACKGROUND

[0002] With the increasing global concern for sustainable development, reducing energy consumption and carbon emissions has become a common challenge faced by various industries. In the manufacturing industry, energy consumption and carbon emissions are particularly prominent.

[0003] Numerical control machine tools, as "industrial mother machines", are widely used in manufacturing, but there are problems of low energy efficiency and high energy intensity in the discrete manufacturing process of numerical control machine tools. Therefore, it is of great significance to carry out energy consumption characteristic analysis and prediction research of numerical control machine tools, and it has important scientific value for energy saving and emission reduction in manufacturing.

[0004] Traditional numerical control machine tool energy consumption models are mainly based on theoretical or semi-empirical formulas. The accuracy of these theoretical models depends on the completeness and accuracy of the empirical formula, or on the mechanism analysis and computer simulation of the complex system of the machine tool, which limits its application range.

[0005] In the field of numerical control machine tool energy consumption prediction, traditional mechanism models are difficult to fully reflect the influence of multi-factor energy loss. With the rapid development of artificial intelligence algorithms, cloud computing architecture, big data analysis and advanced sensor technology, data-driven black box modeling methods have made breakthroughs in the field of industrial system modeling. This kind of method can deeply excavate the nonlinear correlation characteristics between multi-dimensional data, and build a high-precision prediction model with strong generalization ability. In the field of intelligent manufacturing, data-driven machine tool system energy consumption modeling research has become the focus of academia and industry. However, pure data-driven models rely on a large amount of data and lack physical interpretability. SUMMARY

[0006] In view of the problems existing in the prior art, the present application provides a drilling-expanding mixed machining material removal power prediction method based on SR-TELM, comprising: S1, collecting drilling-expanding mixed machining parameters and material removal power data of the numerical control machine tool, and constructing a training set and a test set.

[0007] S2, analyzing the physical mechanism between the material removal power and the machining parameters in the drilling-expanding mixed machining process of the numerical control machine tool by a symbolic regression algorithm, to generate a drilling-expanding mixed machining mechanism model, wherein the drilling-expanding mixed machining mechanism model is a drilling mechanism model and a reaming mechanism model.

[0008] S3, embedding the drilling-expanding mixed processing mechanism model into a multi-layer extreme learning machine to construct an SR-TELM mixed processing power prediction model, and training the SR-TELM mixed processing power prediction model by using experimental data.

[0009] S4, using the trained SR-TELM mixed processing power prediction model to predict drilling material removal power and expanding material removal power.

[0010] Optionally, the step S2 comprises: Correlation degrees between drilling-expanding mixed processing parameters and between drilling-expanding mixed processing parameters and material removal power are calculated, and the specific calculation formula is as follows: .

[0011] .

[0012] wherein, is a parent data sequence, is a child data sequence, is a grey correlation coefficient of the jth variable in the two sequences, and δ is a self-defined parameter, , is the correlation degree between the two sequences.

[0013] Drilling-expanding mixed processing parameters with correlation degrees greater than a preset correlation threshold are selected as input variables of the PySR algorithm for modeling, and a drilling-expanding mixed processing material removal power expression is obtained as follows: .

[0014] wherein, , are input variables of drilling material removal power and input variables of expanding material removal power respectively, , are a symbol set of drilling material removal power and a symbol set of expanding material removal power respectively.

[0015] Optionally, the step S3 comprises: A data-driven model based on a double-hidden layer extreme learning machine is constructed, and the data-driven model comprises an input layer, a hidden layer and an output layer.

[0016] The drilling-expanding mixed processing mechanism model is embedded into physical neurons of the hidden layer to obtain an SR-TELM mixed processing power prediction model.

[0017] Initialize parameters of the SR-TELM hybrid machining power prediction model: initialize weights and biases of the input layer, initialize the number of hidden layers as 2, initialize the number of neurons n1 of the first hidden layer, initialize the number of neurons n2 of the second hidden layer, the first hidden layer includes 1 physical neuron and n1-1 ordinary neurons, and initialize a regularization term , the physical neuron under the drilling condition is , and the physical neuron under the reaming condition is .

[0018] Input the training set into the SR-TELM hybrid machining power prediction model for parameter optimization, randomly initialize weights and biases of the input layer, search the number of neurons of the two hidden layers and the regularization term in the search space.

[0019] Evaluate the hyperparameters of the SR-TELM hybrid machining power prediction model by using the root mean square error RMSE, search the hyperparameter space by the grid search cross-validation method, evaluate the performance of each set of hyperparameter configurations, and obtain the optimized hyperparameters.

[0020] Update the optimized hyperparameters and take new round of hyperparameters from the search space, evaluate the hyperparameters of the SR-TELM hybrid machining power prediction model by the root mean square error RMSE again, and retain the best hyperparameter configuration by the grid search cross-validation method.

[0021] Update the best hyperparameter configuration to the SR-TELM hybrid machining power prediction model, input the test set into the trained SR-TELM hybrid machining power prediction model, and judge whether the test result reaches the target.

[0022] After adopting the above technical solution, the present application has at least the following beneficial effects: (1) The present application proposes a drilling-reaming hybrid machining material removal model based on symbolic regression, which deeply mines the physical law between the machining parameters and the power in the drilling-reaming hybrid machining material removal through the symbolic regression algorithm.

[0023] (2) The present application proposes a mechanism-data hybrid driving framework based on a double-hidden layer extreme learning machine (TELM), which organically integrates the technical advantages of symbolic regression and multi-layer extreme learning machine by embedding the mechanism model into the hidden layer neurons of TELM.

[0024] (3) The present application provides a drilling-reaming hybrid machining material removal power prediction solution, which improves the prediction ability of the data-driven model through the high-precision mechanism model mined by symbolic regression. DETAILED DESCRIPTION

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0026] Figure 1 A flowchart of a SR-TELM-based drilling-expanding mixed machining material removal power prediction method provided by the embodiments of the present disclosure.

[0027] Figure 2 A schematic diagram of the principle of the symbolic regression algorithm.

[0028] Figure 3 A TELM and a corresponding ELM structure diagram, (a) is a schematic diagram of the initialization weight of the output weight of the ELM relative to the second hidden layer of the TELM, (b) is a schematic diagram of the relationship between the first hidden layer and the second hidden layer of the TELM, and (c) is a schematic diagram of the TELM structure and its output.

[0029] Figure 4 A structure diagram of the SR-TELM mixed machining power prediction model.

[0030] Figure 5 A structure diagram of the experimental system.

[0031] Figure 6 GRA values between drilling-expanding mixed machining parameters and between drilling-expanding mixed machining parameters and material removal power, (a) is a GRA value between drilling material removal power and machining parameters, and (b) is a GRA value between reaming material removal power and machining parameters.

[0032] Figure 7 Drilling-expanding mixed machining material removal power expression complexity and error, (a) is drilling material removal power expression complexity and error, and (b) is reaming material removal power expression complexity and error.

[0033] Figure 8 Drilling-expanding mixed machining material removal power prediction effect of the SR-TELM mixed machining power prediction model, (a) is drilling material removal power prediction effect, and (b) is reaming material removal power prediction effect.

[0034] Figure 9 Framework structure diagrams of other three models in the ablation experiment, (a) is a TELM framework structure diagram of double hidden layers, (b) is a structure diagram of SR-TELM F2, and (c) is a structure diagram of SR-ELM.

[0035] Figure 10 A block diagram of the framework of the SR-SVR model and the SR-RF model.

[0036] Figure 11 A comparison chart of the performance indicators of the SVM, RF, SR-SVM, and SR-RF models in predicting the material removal power in drilling.

[0037] Figure 12 A comparison chart of the performance indicators of the SVM, RF, SR-SVM, and SR-RF models in predicting the material removal power in reaming.

[0038] Figure 13 A comparison chart of the performance indicators of the SR-TELM, SR-SVM, and SR-RF models in predicting the material removal power in drilling.

[0039] Figure 14 A comparison chart of the performance indicators of the SR-TELM, SR-SVM, and SR-RF models in predicting the material removal power in reaming. DETAILED DESCRIPTION

[0040] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0041] At present, symbolic regression algorithms have shown significant application value in many fields such as mathematics, mechanics, and medicine. Symbolic regression algorithms can mine physical information in data and provide a new way for mechanism analysis. Although significant progress has been made in the modeling of machine tool machining energy consumption, existing research mainly adopts mechanism models or data-driven models, and some scholars have also carried out related research on the application of mechanism-data hybrid driving methods in machine tool energy consumption modeling.

[0042] Most of the research on machine tool material removal power modeling is based on empirical formulas or semi-empirical formulas, and the accuracy is affected by the formulas themselves. Although data-driven methods such as neural networks perform well in universal prediction tasks, their inherent “black box” characteristics lead to insufficient physical interpretability of the model.

[0043] To solve the problem of material removal power modeling of drilling-expanding mixed machining, the present application provides a hybrid modeling method combining symbolic regression (SR) and double hidden layer extreme learning machine (TELM), which can exert the advantages of symbolic regression (SR) in analyzing physical mechanism and the powerful nonlinear approximation ability of TELM, effectively improve the power prediction accuracy under limited data conditions, and ensure the physical interpretability of the model, providing a new solution for material removal power modeling of drilling-expanding mixed machining of machine tools.

[0044] As shown in Figure 1 The present application provides a SR-TELM-based drilling-expanding mixed machining material removal power prediction method, which comprises the following steps: S1, data acquisition.

[0045] The drilling-expanding mixed machining parameters and material removal power data of the numerical control machine tool are collected, and the training set and test set are constructed.

[0046] S2, drilling-expanding mixed machining mechanism modeling based on symbolic regression algorithm.

[0047] (1) Analysis of the correlation between drilling-expanding mixed machining parameters and material removal power.

[0048] Grey Relation Analysis (GRA) is an evaluation method for studying the correlation between variables. It mainly preprocesses each machining parameter and material removal power data sequence of drilling-expanding mixed machining, and then calculates the correlation between drilling-expanding mixed machining parameters and material removal power to reflect their correlation, the specific calculation formula is as follows: .

[0049] .

[0050] wherein, is the mother data sequence, is the child data sequence, is the grey correlation coefficient of the jth variable in the two sequences, and δ is a self-defined parameter, , commonly set to 0.5, is the correlation between the two sequences.

[0051] (2) Symbolic regression algorithm.

[0052] Symbolic Regression (SR) is an evolutionary algorithm that searches the data space and mathematical symbol space to mine the relationship between independent variables and dependent variables, and thus obtain a mathematical expression with high precision and strong interpretability. Due to the complex mechanical transmission system, power system, hydraulic system, etc., it is difficult to analyze the mechanism of CNC machine tools, so the symbolic regression algorithm can be used to mine the physical law between the machining parameters and power in the machining process of CNC machine tools. The mathematical expression y output by the PySR algorithm is as follows: .

[0053] Among them, F is a symbol set, including: unary operators such as “+”, “-”, “*”, “ / ”, “^”, etc.; binary operators “sin”, “cos”, “exp”, “ln”, etc.; custom operators such as “inv(x) = 1 / x”; is the drilling-expanding mixed machining parameter data set, which is used as the input variable of the PySR algorithm.

[0054] Compared with traditional evolutionary algorithms, the PySR algorithm dynamically regularizes the mutation process by introducing a simulated annealing mechanism, and innovatively embeds a genetic algorithm into an evolutionary-simplification-optimization iterative loop framework. This dual optimization strategy not only significantly improves the search efficiency of mathematical expressions, but also effectively improves the physical interpretability of the obtained mathematical model. The loss function of the PySR algorithm considers both the prediction loss and the expression complexity, and the loss function expression is as follows: .

[0055] Among them, l(E) is the loss function; l pred (E) is the prediction loss; C(E) represents the complexity of the expression E; frequency[C(E)] is used to measure the frequency of the expression with complexity C(E) in the population and the recent frequency.

[0056] The principle of the PySR algorithm is shown in Figure 2 , which first generates an initial population of mathematical expressions, each of which is a combination of data features and mathematical operators. Then, the fitness of these models in predicting the power of CNC machine tools is evaluated, and the best individuals in the new generation are selected for further evolution (operator crossover and mutation). The evolution process is repeated until a high-precision and interpretable mathematical expression is found.

[0057] The drilling-expanding mixed machining parameters with a correlation greater than 0.5 are selected as the input variables X of the PySR algorithm for modeling, and the output drilling-expanding mixed machining material removal power expression is as follows: .

[0058] wherein, is the material drilling power, is the material reaming power, , are the input variable of the drilling material removal power and the input variable of the reaming material removal power, respectively, , are the symbol set of the drilling material removal power and the symbol set of the reaming material removal power, respectively.

[0059] S3, modeling based on a mechanism-data hybrid driving framework (SR-TELM).

[0060] (1) a data-driven modeling method based on a dual-hidden-layer extreme learning machine (TELM).

[0061] ELM training parameters are obtained by the operation of the generalized inverse matrix. Assuming that the training set consists of N samples, the ELM can be described as follows: .

[0062] .

[0063] .

[0064] wherein x represents the input, w i , b i , are the weight, bias and output weight on the hidden layer node, respectively, is the final output of the ELM, L represents the number of nodes in the hidden layer, H represents the output of the hidden layer, and H represents the output of the hidden layer, represents an activation function, wherein (i=1, 2, …L).

[0065] The least square difference between and the sample label T is minimized as the objective function, so that the solution that minimizes the objective function is the optimal solution, and the objective function is as follows: .

[0066] wherein, is the output matrix of the hidden layer, is the target matrix of the training data.

[0067] The optimal solution is obtained as follows: .

[0068] wherein, is the Moore-Penrose generalized inverse matrix of the matrix H.

[0069] To improve the generalization performance, a regularization term is added as follows: .

[0070] The structure of TELM is shown in Fig. 1. First, the activation function Figure 3 and training set are given.

[0071] The weights and biases of the first hidden layer are randomly initialized, and the output matrix of the first hidden layer is calculated as follows: .

[0072] The weights and biases of the second hidden layer are randomly initialized, and the output matrix of the second hidden layer is calculated as follows: .

[0073] The connection weights between the second hidden layer and the output layer are calculated as follows: .

[0074] where is the Moore-Penrose generalized inverse matrix of matrix .

[0075] To improve the generalization performance, a regularization term is added as follows: .

[0076] The output of the final dual-hidden-layer extreme learning machine is: .

[0077] TELM maps the original input sequence to a new feature space, representing more refined features. Due to its powerful nonlinear mapping ability, TELM learns more complex functions compared to ELM. During the training process, only the connection weights from the hidden layer to the output layer need to be calculated, which not only greatly improves the learning efficiency but also ensures the model converges to the global optimal solution while maintaining excellent generalization ability.

[0078] (2) Grid search cross-validation method.

[0079] ​Grid Search Cross-Validation (GS-CV) is a widely used hyperparameter optimization method that aims to determine the optimal combination of hyperparameters through exhaustive search. This method combines both Grid Search and Cross-Validation techniques, effectively improving the performance of the model. GS-CV systematically explores the predefined hyperparameter space and evaluates the performance of each set of hyperparameters using cross-validation. This process assesses multiple combinations of hyperparameters and assigns a performance score to each combination, ensuring the selection of the most suitable set of hyperparameters to maximize the predictive accuracy of the model on unseen data.

[0080] During the GS-CV process, Cross-Validation (CV) plays a crucial role in evaluating the model's generalization ability, i.e., its performance on new data. Common cross-validation methods include K-fold cross-validation, where K is 3, i.e., 3-fold cross-validation. Specifically, the dataset is divided into three parts, and the model is trained on two of them and tested on the remaining part. This process is repeated three times, each time using a different part as the test set. The final result is the average of the three validations, providing a more reliable performance estimate than a single train-test split.

[0081] In artificial neural network architecture design, the determination of the number of hidden layer neurons follows an empirical validation principle: the optimal number of neurons is usually 1 to 3 times the dimension of the input features. Too many neurons can cause overfitting through excessive parameterization, while too few neurons may lead to underfitting due to the inability to capture high-order feature interactions.

[0082] (3) SR-TELM hybrid processing power prediction model construction and training.

[0083] A data-driven model based on multi-layer extreme learning machine is constructed, which includes an input layer, a hidden layer (including ordinary neurons and physical neurons), and an output layer.

[0084] The drilling-expansion hybrid processing mechanism model is embedded in the physical neurons of the hidden layer, as shown in Figure 4 , to obtain the SR-TELM hybrid processing power prediction model.

[0085] The ordinary neuron is a neural network neuron, and the calculation method is as follows: .

[0086] The physical neuron is a neural network neuron that integrates physical formulas into the neuron topology structure, and the calculation method is as follows: or .

[0087] wherein, represents a physical neuron of the first hidden layer, represents a common neuron of the first hidden layer, is a drilling material removal power expression derived from the SR algorithm, is a reaming material removal power expression derived from the SR algorithm, and are initial weights and biases of the first hidden layer.

[0088] Initializing parameters of the SR-TELM hybrid machining power prediction model: initializing weights and biases of the input layer, initializing the number of hidden layers as 2, initializing the number of neurons n1 of the first hidden layer, initializing the number of neurons n2 of the second hidden layer, the first hidden layer including 1 physical neuron and n1-1 common neurons, and initializing the regularization term wherein, the physical neuron under the drilling condition is , and the physical neuron under the reaming condition is .

[0089] Inputting the training set into the SR-TELM hybrid machining power prediction model for parameter optimization, and searching the number of neurons of the two hidden layers and the regularization term in the search space while randomly initializing weights and biases of the input layer.

[0090] Evaluating hyperparameters of the SR-TELM hybrid machining power prediction model by using the root mean square error RMSE, searching the hyperparameter space by the grid search cross-validation method, and evaluating the performance of each set of hyperparameter configurations to obtain optimized hyperparameters.

[0091] Updating the optimized hyperparameters and taking new round of hyperparameters from the search space, again evaluating the hyperparameters of the SR-TELM hybrid machining power prediction model by the root mean square error RMSE, and retaining the best hyperparameter configuration by the grid search cross-validation method.

[0092] Updating the best hyperparameter configuration to the SR-TELM hybrid machining power prediction model, inputting the test set into the trained SR-TELM hybrid machining power prediction model, and judging whether the test result reaches the target.

[0093] S4, using the trained SR-TELM hybrid machining power prediction model to predict drilling material removal power and reaming material removal power.

[0094] The following specific examples are proposed in combination with the above embodiments. It can be understood that the following specific examples only exemplarily illustrate the specific implementation of the above embodiments, and do not limit the technical solutions of the above embodiments.

[0095] (1) Experimental system.

[0096] The CNC machining center VMC650L and high-speed steel M35 straight shank twist drill were selected for experimental research. The main technical specification parameters of the machining center and tool are shown in Tables 1 and 2. The drill-reaming mixed machining condition is wet cutting, and the cutting fluid is selected as ordinary water-based emulsion. The CNC machining center is connected to the power-energy consumption data acquisition system, as shown in Figure 5 , which includes the Siemens SINUMERIK828D numerical control system, YOKOGAWA WT333E power analyzer, and WTViewerFreePlus software.

[0097] Table 1 Main technical specification parameters of CNC machining center VMC650L

[0098] Table 2 Detailed parameters of high-speed steel M35 straight shank twist drill

[0099] (2) Drill-reaming mixed machining process material removal experiment.

[0100] 1. Drilling process material removal experiment.

[0101] The Taguchi orthogonal table L 32 (4 9 ) was applied to design a three-factor, four-level numerical control drilling experiment. The tool diameter d0, feed rate f, spindle speed n, and drilling depth a p were selected as experimental factors. The values of each factor were determined according to the characteristics of the workpiece material, the cutting performance of the numerical control machine tool and the tool, as shown in Table 3. In order to increase the accuracy of the experiment and reduce errors, the multiple experiment mean value method in statistics was used. The experimental results are shown in Table 4, in which the tool diameter d0, feed rate f, spindle speed n, and drilling depth a p were valued according to the orthogonal table. The conversion relationship between the feed speed v f , feed rate f, and spindle speed n is: .

[0102] Table 3 Drilling material removal parameter experiment setting

[0103] Table 4 Partial drilling material removal power data

[0104] 2. Reaming process material removal experiment.

[0105] Select the feed rate f, spindle speed n, bottom hole diameter d0, and reaming diameter d1 as experimental factors. Each factor is valued according to the workpiece material characteristics, as well as the cutting performance of the CNC machine tool and the cutting tool, as shown in Table 5. The bottom hole diameter and reaming diameter in these 4 experimental factors need to satisfy d0 < d1. The experimental design and experimental results of the reaming material removal are shown in Table 6.

[0106] Table 5 Experimental settings for reaming material removal parameters

[0107] Table 6 Partial reaming material removal power data

[0108] (3) Modeling of the drilling-reaming hybrid machining mechanism based on the symbolic regression algorithm.

[0109] 1. Correlation between drilling-reaming hybrid machining parameters and material removal power.

[0110] The GRA method is used to test the correlation between the input variables and the material removal power. The results are as Figure 6 shown. The numbers in each panel represent the GRA values between paired variables. The material removal power of the drilling-reaming hybrid machining , , and the machining parameters , and , all have GRA values greater than 0.6, indicating that the selected variables are suitable for representing , .

[0111] 2. Drilling-reaming hybrid machining mechanism model.

[0112] Using the PySR algorithm combined with experimental data, with the ratio of the training set to the test set being 7:3 and the parameter settings shown in Table 7, the expression for the material removal power of the drilling-reaming hybrid machining is obtained, as shown in Table 8. Three indicators, the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R 2 ), are used to evaluate the prediction ability of the model. The formulas are as follows: .

[0113] .

[0114] .

[0115] Among them, represents the predicted output value of the rd sample, and represents the The actual output value of each sample. Represents the number of data samples in the dataset. This represents the average of all actual output values.

[0116] Table 7 PySR Algorithm Parameter Settings

[0117] Figure 7 This indicates that the model training error fluctuates with changes in formula complexity. Figure 7 The complexity of (a) is 11 operations. Figure 7 The model with a complexity of 15 in (b) exhibits similar prediction accuracy and generalization performance. Considering that the subsequent drill-reamerized hybrid machining material removal power model will be used in extreme learning (ML-ELM), and based on the practicality and simplicity of the machine tool machining power model, the model chosen is... Figure 7 The expression with a complexity of 11 in (a) is the borehole material removal power model. Figure 7 The expression at (b) with a complexity of 15 is the power model for removing porous materials.

[0118] Table 8. Drill-reamer hybrid machining mechanism model

[0119] (4) Prediction of material removal power in drilling-expansion hybrid processing based on SR-TELM.

[0120] The hyperparameters were selected through grid search and tri-fold cross-validation. The set of hyperparameters selected for each model of material drilling and material reaming, as well as the final selected training hyperparameters, are shown in Table 9.

[0121] Table 9 Model Parameter Selection

[0122] Three different performance quantification metrics are introduced to evaluate the performance of the proposed SR-TELM model, mainly including root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 Typically, MAE measures the deviation between the predicted and actual values ​​of an SR-TELM model, while RMSE indicates the reliability of the prediction model. The standard deviation of the difference between the actual and predicted values ​​further clarifies the prediction accuracy. The predictive performance of the SR-TELM model is as follows: Figure 8 As shown, the predicted values ​​of the SR-TELM model are arranged around the line y=x, indicating that the prediction results are good. Furthermore, the performance indicators of the training set and the test set are close, indicating that the model has good generalization ability.

[0123] MAE, RMSE and R of the ELM model, TELM model and SR-TELM model trained using the drilling-reaming mixed material removal experimental data 2 The analysis results are shown in Table 10. In this case, 70% of the drilling-reaming mixed material removal experimental data is selected as the training set input. The training sets used by the three models are the same to reduce the influence of data set randomness. The smaller the MAE and RMSE, the better the regression performance of the model, while the R 2 is the opposite. According to the data in Table 10, the mixed driving model constructed by the application is superior to the data-driven model in various indicators.

[0124] Table 10 Drilling-reaming mixed material removal power prediction performance

[0125] As can be seen from Table 10: (1) The SR-TELM model shows significant advantages in drilling and reaming material removal power prediction. In the drilling task, the MAE of SR-TELM is reduced by 55.8% compared with TELM, the RMSE is reduced by 56.0%, and the R² is increased to 0.985; in the reaming task, the MAE and RMSE are reduced by 43.2% and 46.5% respectively compared with TELM, and the R² reaches 0.975.

[0126] (2) The SR-TELM model is higher than the TELM model in various indicators, indicating that embedding the mechanism model into the neuron is beneficial to TELM to learn more physical information, thereby improving the prediction accuracy of TELM.

[0127] (3) TELM is better than ELM in performance, with a 7.8% decrease in MAE of drilling material removal power, proving the ability of the double hidden layer enhanced model to learn nonlinear information.

[0128] (5) Comparative analysis.

[0129] 1. Ablation experiment.

[0130] In order to verify the contribution of each core component in the SR-TELM model, a set of ablation experiments are designed.

[0131] Control group 1: as in (a) of the Figure 9 , remove the symbolic regression (SR) and only keep the TELM data-driven module, denoted as TELM.

[0132] Control group 2: as in (b) of the Figure 9 , change the embedding of physical formula from neuron to input layer splicing, denoted as SR-TELM-F2, that is, the mechanism mixed driving mode of embedding the physical formula into the network input is compared. That is, the processing parameters , The value of the mechanism formula is , The inputs are merged into the TELM model.

[0133] Control group 3: such as Figure 9 In (c), the double-hidden-layer TELM is replaced with a single-hidden-layer ELM, denoted as SR-ELM.

[0134] All experiments used the same dataset (drilling and reaming data were evaluated independently). To ensure the validity of the comparison, all hyperparameters were set as follows: number of neurons in the first hidden layer: 8, number of neurons in the second hidden layer: 9, activation function: sig, and performance metrics were the average of 10 independent experiments, as shown in Table 11.

[0135] Table 11 Comparison of Material Removal Model Indicators in Drill-Ampere Hybrid Processing

[0136] Table 12. Changes in other model indicators relative to the SR-TELM model

[0137] Table 12 shows the changes in the performance indices of the TELM, SR-ELM, SR-TELM-F2, and SR-TELM models, based on the performance indices of the SR-TELM model. It can be seen that: (1) By comparing the TELM and SR-TELM models, it is shown that removing SR leads to a 126.27% increase in borehole MAE and a 75.93% increase in reaming MAE. This indicates that the physical relationship mining by symbolic regression significantly improves the model accuracy and makes up for the lack of mechanism understanding by pure data-driven approaches.

[0138] (2) By comparing the SR-TELM-F2 and SR-TELM models, it is shown that the MAE of the model with mechanism as input (SR-TELM-F2) is 55.65% higher than that of the model with hole drilling and hole enlargement, which is 27.19% higher than that of the model with hole enlargement. This shows that the physical formula can be integrated into the topology of the neuron to more effectively couple the mechanism and data features and avoid dilution of the input layer information.

[0139] (3) By comparing the SR-ELM and SR-TELM models, it is shown that the RMSE of single-hidden-layer ELM increases by 97.09% in drilling and 57.13% in reaming, indicating that double-hidden-layer mapping improves the nonlinear expression capability and is more suitable for learning the complex power relationship in drilling-reaming hybrid processing.

[0140] 2. Comparison of SVM, RF, SR-TELM, SR-SVM and SR-RF models.

[0141] To further analyze the prediction effect of SR-TELM model, the drilling-reaming mixed machining power prediction models based on support vector machine (SVM) and random forests (RF) are established, and the models are trained and tested by using pure data-driven and mechanism-data hybrid-driven methods, the results are predicted and the accuracy is analyzed. Because SVM and RF do not have hidden layers and neurons, another form of data-mechanism hybrid-driven model is adopted. This form of mechanism-data driven model inputs the mechanism model and the original input of machine learning into the machine learning model to add physical prior knowledge to improve the prediction ability of the machine learning model.

[0142] The SR-SVR model and the SR-RF model are as shown in Figure 10 Under the drilling material removal condition, the influencing factors are The mechanism formula value is The SR-SVM model input will be input into the SVR model. Under the reaming material removal condition, the influencing factors are The mechanism formula value is The SR-SVM model input will be input into the SVM model.

[0143] The performance index comparison of SVM, RF, SR-TELM, SR-SVM and SR-RF models is as shown in Figure 11 , Figure 12 , Figure 13 , Figure 14 It can be seen that: (1) By comparing the performance indexes before and after the hybrid driving, it is shown that the mechanism model mined by PySR and the machine learning hybrid driving can enhance the prediction ability of machine learning.

[0144] (2) The MAE, RMSE and R 2 of the SR-SVM model of drilling-reaming mixed machining are increased by 23%, 21% and 5.53% on average compared with those of the SVM model. The MAE, RMSE and R 2 of the SR-RF model are increased by 53%, 50% and 32% on average compared with those of the RF model.

[0145] (3) The SVM and RF models have higher accuracy in reaming material removal power prediction than in drilling material removal power prediction, and the performance index of reaming material removal power prediction decreases more after adding the mechanism. It is shown that increasing the number of data sets can improve the prediction accuracy of the mechanism hybrid model to a certain extent.

[0146] (4) In the mixed prediction of the three mechanisms, the SR-TELM model has the highest accuracy. It shows that the mechanism and TELM mixed model are easier to learn the nonlinear relationship in the drilling-expanding mixed processing material removal power.

[0147] The technical scheme of the present application has been described in combination with the preferred embodiments shown in the drawings, but it is easy for those skilled in the art to understand that the protection scope of the present application is obviously not limited to these specific embodiments. Those skilled in the art can make equivalent changes or replacements to the related technical features without departing from the principles of the present application, and the technical schemes after the changes or replacements will fall within the protection scope of the present application.

Claims

1. A method for predicting material removal power in drilling-reaming hybrid machining based on SR-TELM, characterized in that, The method comprises the following steps: S1, collecting drilling-expanding mixed machining parameters and material removal power data of a numerical control machine tool, and constructing a training set and a test set; S2, analyzing the physical mechanism between the material removal power and the machining parameters in the drilling-expanding mixed machining process of the numerical control machine tool through a symbolic regression algorithm, and generating a drilling-expanding mixed machining mechanism model, wherein the drilling-expanding mixed machining mechanism model is a drilling mechanism model and a hole expanding mechanism model; S3, embedding the drilling-expanding mixed machining mechanism model into a multi-layer extreme learning machine to construct an SR-TELM mixed machining power prediction model, and training the SR-TELM mixed machining power prediction model by using experimental data; S4, using the trained SR-TELM mixed machining power prediction model to predict the drilling material removal power and the hole expanding material removal power.

2. The SR-TELM based drill-ream hybrid machining material removal power prediction method of claim 1, wherein, The step S2 comprises: calculating the correlation degrees between the drilling-expanding mixed machining parameters and between the drilling-expanding mixed machining parameters and the material removal power, and the specific calculation formula is as follows: ； ； wherein, is the mother data sequence, is the daughter data sequence, is the grey correlation coefficient of the jth variable in the two sequences, and δ is a self-defined parameter, , is the correlation degree between the two sequences; selecting the drilling-expanding mixed machining parameters with the correlation degrees greater than a preset correlation threshold as the input variables of the PySR algorithm for modeling, and obtaining the drilling-expanding mixed machining material removal power expression as follows: ； in, Drilling power for materials, For the material hole expansion power, , These are the input variables for drilling material removal power and reaming material removal power, respectively. , These are the symbol sets for the material removal power of drilling and the material removal power of reaming, respectively.

3. The SR-TELM based drill-ream hybrid machining material removal power prediction method of claim 2, wherein, The step S3 comprises: constructing a data-driven model based on a double-hidden layer extreme learning machine, the data-driven model comprising an input layer, a hidden layer, and an output layer; embedding the drilling-expanding mixed machining mechanism model into the physical neurons of the hidden layer to obtain the SR-TELM mixed machining power prediction model; Initialize parameters of the SR-TELM hybrid processing power prediction model: initialize weights and biases of the input layer, initialize the number of the hidden layer as 2, initialize the number of neurons n1 of the first hidden layer, initialize the number of neurons n2 of the second hidden layer, the first hidden layer includes 1 physical neuron and n1-1 ordinary neurons, and initialize the regularization term , wherein the physical neuron under the drilling condition is , and the physical neuron under the reaming condition is ; inputting the training set into the SR-TELM mixed machining power prediction model for parameter optimization, randomly initializing the weights and biases of the input layer, searching the neuron numbers of the two hidden layers and the regularization term in the search space; evaluating the hyperparameters of the SR-TELM mixed machining power prediction model by using the root mean square error (RMSE), searching the hyperparameter space by using the grid search cross-validation method, and evaluating the performance of each group of hyperparameter configurations to obtain the optimized hyperparameters; updating the optimized hyperparameters and taking new round of hyperparameters from the search space, again evaluating the hyperparameters of the SR-TELM mixed machining power prediction model by using the root mean square error (RMSE), and retaining the best hyperparameter configuration by using the grid search cross-validation method; updating the best hyperparameter configuration to the SR-TELM mixed machining power prediction model, inputting the test set into the trained SR-TELM mixed machining power prediction model, and judging whether the test result reaches the target.

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