A method for predicting material removal power in drill-reactor hybrid processing based on SR-TELM

Abstract

This invention provides a method for predicting material removal power in drilling-expansion hybrid machining based on SR-TELM, relating to the field of CNC machine tool power prediction technology. It delves into the physical mechanism between machining parameters and material removal power in drilling-expansion hybrid machining by using a symbolic regression algorithm. By embedding the mechanism model into the hidden layer neurons of TELM, it organically combines the advantages of symbolic regression in analyzing physical mechanisms with the powerful nonlinear approximation capability of TELM. This effectively improves power prediction accuracy under limited data conditions while ensuring the physical interpretability of the model, providing a new solution for modeling material removal power in drilling-expansion hybrid machining of machine tools.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool power prediction technology, and in particular to a method for predicting the power of material removal in drilling-reaming hybrid machining based on SR-TELM. Background Technology

[0002] With increasing global focus on sustainable development, reducing energy consumption and carbon emissions has become a common challenge across industries. In the manufacturing sector, energy consumption and carbon emissions are particularly prominent issues.

[0003] CNC machine tools, known as "industrial mother machines," are widely used in the manufacturing industry. However, CNC machine tools generally suffer from low energy efficiency and high energy intensity in discrete manufacturing processes. Therefore, conducting research on the energy consumption characteristics analysis and prediction of CNC machine tools is of great significance and has important scientific value for energy conservation and emission reduction in the manufacturing industry.

[0004] Traditional CNC 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 formulas, or on the mechanism analysis and computer simulation of complex machine tool systems, which limits their application scope.

[0005] In the field of CNC machine tool energy consumption prediction, traditional mechanistic models struggle to fully reflect the impact of multiple factors on energy loss. With the rapid development of artificial intelligence algorithms, cloud computing architectures, big data analytics, and advanced sensor technologies, data-driven black-box modeling methods have achieved breakthroughs in industrial system modeling. These methods, by deeply exploring the nonlinear correlation characteristics between multidimensional data, construct high-precision prediction models with strong generalization capabilities. In the field of intelligent manufacturing, data-driven machine tool system energy consumption modeling research has become a focus of attention in both academia and industry. However, purely data-driven models face challenges such as dependence on large amounts of data and insufficient physical interpretability. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method for predicting material removal power in drill-reamer hybrid processing based on SR-TELM, comprising:

[0007] S1. Collect drilling-reaming hybrid machining parameters and material removal power data of CNC machine tools, and construct training and testing sets.

[0008] S2. The physical mechanism between material removal power and machining parameters in the drilling-reaming hybrid machining process of CNC machine tools is analyzed by symbolic regression algorithm, and a drilling-reaming hybrid machining mechanism model is generated. The drilling-reaming hybrid machining mechanism model consists of a drilling mechanism model and a reaming mechanism model.

[0009] S3. Embed the drilling-reaming hybrid machining mechanism model into a multilayer extreme learning machine to construct an SR-TELM hybrid machining power prediction model, and train the SR-TELM hybrid machining power prediction model using experimental data.

[0010] S4. Use the trained SR-TELM hybrid machining power prediction model to predict the material removal power of drilling and the material removal power of reaming.

[0011] Optionally, step S2 includes:

[0012] The correlation between drilling-reaming hybrid processing parameters and between these parameters and material removal power is calculated using the following formulas:

[0013] .

[0014] .

[0015] in, For the parent data sequence, For sub-data sequences, Let be the grey relational coefficient of the j-th variable in the two sequences, and δ be a user-defined parameter. , The degree of correlation between two sequences.

[0016] The drilling-reaming hybrid processing parameters with a correlation degree greater than a preset correlation threshold were selected as input variables for the PySR algorithm for modeling, resulting in the following expression for the material removal power of the drilling-reaming hybrid processing:

[0017] .

[0018] in, , 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.

[0019] Optionally, step S3 includes:

[0020] A data-driven model based on a two-hidden-layer extreme learning machine is constructed. The data-driven model includes an input layer, a hidden layer, and an output layer.

[0021] By embedding the drilling-reaming hybrid machining mechanism model into the physical neurons of the hidden layer, the SR-TELM hybrid machining power prediction model is obtained.

[0022] The parameters of the SR-TELM hybrid processing power prediction model are initialized as follows: the input layer weights and biases are initialized, the number of hidden layers is initialized to 2, the number of neurons in the first hidden layer is initialized to n1, and the number of neurons in the second hidden layer is initialized to n2. The first hidden layer includes 1 physical neuron and n1-1 ordinary neurons. The regularization term is also initialized. Among them, the physical neurons under drilling conditions are Under the condition of pore expansion, the physical neuron is .

[0023] The training set is input into the SR-TELM hybrid processing power prediction model for parameter optimization. The weights and biases of the input layer are randomly initialized, and the number of neurons in the two hidden layers and the regularization term are searched in the search space.

[0024] The root mean square error (RMSE) was used to evaluate the hyperparameters of the SR-TELM hybrid processing power prediction model. The hyperparameter space was searched using a grid search cross-validation method, and the performance of each set of hyperparameter configurations was evaluated to obtain the optimized hyperparameters.

[0025] The optimized hyperparameters are updated and a new set of hyperparameters is extracted from the search space. The hyperparameters of the SR-TELM hybrid processing power prediction model are evaluated again by the root mean square error (RMSE), and the optimal hyperparameter configuration is retained by the grid search cross-validation method.

[0026] The optimal hyperparameter configuration is updated into the SR-TELM hybrid processing power prediction model. The test set is then input into the trained SR-TELM hybrid processing power prediction model to determine whether the test results meet the target.

[0027] By adopting the above technical solution, the present invention has at least the following beneficial effects:

[0028] (1) This invention proposes a material removal model based on symbolic regression for drilling-expansion hybrid processing. Through the symbolic regression algorithm, the physical laws between processing parameters and power in drilling-expansion hybrid processing material removal are explored in depth.

[0029] (2) This invention proposes a mechanism-data hybrid driving framework based on dual hidden layer extreme learning machine (TELM). This framework 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.

[0030] (3) This invention provides a solution for predicting the material removal power of drilling-expansion hybrid processing, which improves the predictive ability of the data-driven model by using a high-precision mechanism model mined by symbolic regression. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic flowchart of a method for predicting material removal power in a drill-expansion hybrid process based on SR-TELM, provided as an embodiment of this disclosure.

[0033] Figure 2 This is a schematic diagram illustrating the principle of the symbolic regression algorithm.

[0034] Figure 3 The diagram shows the structure of TELM and its corresponding ELM. (a) is a schematic diagram of the ELM output weights relative to the initial weights of the second hidden layer of TELM. (b) is a schematic diagram of the relationship between the first hidden layer and the second hidden layer of TELM. (c) is a schematic diagram of the structure of TELM and its output.

[0035] Figure 4 The diagram shows the structure of the SR-TELM hybrid processing power prediction model.

[0036] Figure 5 This is a structural diagram of the experimental system.

[0037] Figure 6 The GRA values ​​are between drilling-reaming hybrid processing parameters and between drilling-reaming hybrid processing parameters and material removal power. (a) is the GRA value between drilling material removal power and processing parameters, and (b) is the GRA value between reaming material removal power and processing parameters.

[0038] Figure 7 The complexity and error of the power expression are removed for drilling-reaming hybrid processing materials. (a) The complexity and error of the power expression are removed for drilling materials. (b) The complexity and error of the power expression are removed for reaming materials.

[0039] Figure 8 The results show the prediction effect of material removal power in the drilling-reaming hybrid machining power prediction model of SR-TELM. (a) shows the prediction effect of material removal power in drilling, and (b) shows the prediction effect of material removal power in reaming.

[0040] Figure 9 The following are the framework diagrams of the other three models in the ablation experiment: (a) Framework diagram of the dual hidden layer extreme learning machine TELM, (b) Structure diagram of SR-TELM F2, and (c) Structure diagram of SR-ELM.

[0041] Figure 10 This is a framework diagram of the SR-SVR and SR-RF models.

[0042] Figure 11 A comparison chart of the borehole material removal power prediction performance indicators for SVM, RF, SR-SVM, and SR-RF models.

[0043] Figure 12 A comparison chart of power prediction performance indicators for porous materials in SVM, RF, SR-SVM, and SR-RF models.

[0044] Figure 13 A comparison chart of the borehole material removal power prediction performance indicators for the SR-TELM, SR-SVM, and SR-RF models.

[0045] Figure 14 A comparison chart of power prediction performance indicators for porous materials in SR-TELM, SR-SVM, and SR-RF models. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Currently, symbolic regression algorithms have demonstrated significant application value in multiple fields such as mathematics, mechanics, and medicine. Symbolic regression algorithms can extract physical information from data, providing a new approach for mechanism analysis. Although significant progress has been made in machine tool processing energy consumption modeling research, existing studies mainly employ mechanistic models or data-driven models. Some scholars have also conducted relevant research on the application of mechanistic-data hybrid driving methods in machine tool energy consumption modeling.

[0048] Most studies on machine tool material removal power modeling are based on empirical or semi-empirical formulas, and their accuracy is affected by the formulas themselves. Although data-driven methods such as neural networks perform well in general prediction tasks, their inherent "black box" nature leads to insufficient physical interpretability of the models.

[0049] To address the problem of power modeling for material removal in drilling-reaming hybrid machining, this invention proposes a hybrid modeling method combining symbolic regression (SR) and two-hidden-layer extreme learning machine (TELM). This method leverages the advantages of symbolic regression (SR) in analyzing physical mechanisms and the powerful nonlinear approximation capability of TELM, effectively improving power prediction accuracy under limited data conditions while ensuring the physical interpretability of the model. This provides a new solution for power modeling of material removal in drilling-reaming hybrid machining of machine tools.

[0050] like Figure 1 As shown, this disclosure provides a method for predicting material removal power in drill-reamer hybrid processing based on SR-TELM, including:

[0051] S1, Data Acquisition.

[0052] Collect drilling-reaming hybrid machining parameters and material removal power data of CNC machine tools, and construct training and testing sets.

[0053] S2. Modeling of drilling-reaming hybrid processing mechanism based on symbolic regression algorithm.

[0054] (1) Correlation analysis between drilling-reaming hybrid processing parameters and material removal power.

[0055] Grey Relation Analysis (GRA) is a method for evaluating the degree of correlation between variables. It primarily involves preprocessing the data sequences of various processing parameters and material removal power in a drill-reamering hybrid machining process. Then, it reflects the degree of correlation between these parameters and between the parameters and the material removal power. The specific calculation formula is as follows:

[0056] .

[0057] .

[0058] in, For the parent data sequence, For sub-data sequences, Let be the grey relational coefficient of the j-th variable in the two sequences, and δ be a user-defined parameter. It is usually set to 0.5. The degree of correlation between two sequences.

[0059] (2) Symbolic regression algorithm.

[0060] Symbolic Regression (SR) is an evolutionary algorithm that searches the data space and the mathematical symbol space to uncover the patterns between independent and dependent variables, thereby obtaining a highly accurate and interpretable mathematical expression. CNC machine tools, due to their complex mechanical transmission systems, electrical systems, and hydraulic systems, are difficult to analyze mechanistically. Therefore, symbolic regression can be used to uncover the physical patterns between machining parameters and power during CNC machine tool processing. The mathematical expression y output by the PySR algorithm is shown below:

[0061] .

[0062] Where F is the symbol set, including: unary operators such as "+", "-", "*", " / ", "^", etc.; binary operators such as "sin", "cos", "exp", "ln", etc.; and user-defined operators such as "inv(x) = 1 / x". The dataset of drilling-reaming hybrid processing parameters is used as the input variable for the PySR algorithm.

[0063] Compared to traditional evolutionary algorithms, the PySR algorithm dynamically regularizes the mutation process by introducing simulated annealing, and innovatively embeds a genetic algorithm into an iterative evolution-simplification-optimization framework. This dual optimization strategy not only significantly improves the search efficiency of mathematical expressions but also effectively enhances the physical interpretability of the resulting mathematical model. The loss function of the PySR algorithm considers both prediction loss and expression complexity, and its expression is shown below:

[0064] .

[0065] Where l(E) is the loss function; l pred (E) represents the prediction loss; C(E) represents the complexity of expression E; frequency[C(E)] is used to measure the frequency of occurrence and recent occurrence frequency of expressions with complexity C(E) in the population.

[0066] The principle of the PySR algorithm is as follows: Figure 2 As shown, an initial population (mathematical expressions) is first generated. Each population is a combination of data features and mathematical operators. Then, these expressions are evaluated based on the fitness of these models in predicting the power of CNC machine tools. The new generation of individuals with the best pre-fitness is selected for further evolution (operator crossover and mutation). The evolutionary process is repeated until a high-precision interpretable mathematical expression is found.

[0067] The drilling-reaming hybrid processing parameters with a correlation greater than 0.5 are selected as the input variables X for the PySR algorithm for modeling. The output expression for the material removal power of the drilling-reaming hybrid processing is as follows:

[0068] .

[0069] 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.

[0070] S3. Modeling based on the mechanism-data hybrid driven framework (SR-TELM).

[0071] (1) Data-driven modeling method based on dual hidden layer extreme learning machine (TELM).

[0072] The training parameters for ELM are obtained through operations on the generalized inverse matrix. Assuming the training set consists of N samples, ELM can be described as follows:

[0073] .

[0074] .

[0075] .

[0076] Where x represents the input, w i b i , These are the weights, biases, and output weights of the hidden layer nodes, respectively. This is the final output of ELM, where 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. Let represent the activation function, where (i=1,2,…L).

[0077] use The objective function is to minimize the squared difference between the sample label T and the sample label T. The solution that minimizes this objective function is the optimal solution. The objective function is as follows:

[0078] .

[0079] in, It is the output matrix of the hidden layer. It is the target matrix of the training data.

[0080] The optimal solution can be obtained by solving for:

[0081] .

[0082] in, Let H be the Moore–Penrose generalized inverse matrix of matrix H.

[0083] To improve generalization performance, a regularization term is added as follows:

[0084] .

[0085] TELM network structure as follows Figure 3 As shown, the activation function is first given. and training set .

[0086] Randomly initialize the weights of the first hidden layer and bias And calculate the output matrix of the first hidden layer. :

[0087] .

[0088] Randomly initialize the weights of the second hidden layer and bias And calculate the output matrix of the second hidden layer. :

[0089] .

[0090] The connection weights between the second hidden layer and the output layer are calculated as follows:

[0091] .

[0092] in, For matrix The Moore–Penrose generalized inverse matrix.

[0093] To improve generalization performance, a regularization term is added. As shown below:

[0094] .

[0095] The final output of the two hidden-layer extreme learning machine is:

[0096] .

[0097] TELM maps the original input sequence to a new feature space, thus representing more refined features. Due to its powerful non-linear mapping capability, compared with ELM, TELM learns more complex functions. During training, it only needs to calculate the connection weights from the hidden layer to the output layer. This not only greatly improves learning efficiency but also ensures that the model converges to the global optimum while maintaining excellent generalization ability.

[0098] (2) Grid search cross-validation method.

[0099] 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 grid search and cross-validation techniques to effectively improve model performance. GS-CV systematically explores a predefined hyperparameter space and uses cross-validation to evaluate the performance of each set of hyperparameter configurations. This process evaluates multiple hyperparameter combinations and assigns a performance score to each combination, ensuring that the most suitable set of hyperparameters is selected to maximize the model's predictive accuracy on unknown data.

[0100] In GS-CV, cross-validation (CV) plays a crucial role in evaluating a model's generalization ability, i.e., its performance on new data. A common cross-validation method is K-fold cross-validation, where K is 3 (3-fold cross-validation). Specifically, the dataset is divided into three parts, the model is trained on two of these parts, and tested on the remaining parts. 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 training-test split.

[0101] In the design of artificial neural network architectures, the determination of the number of neurons in the hidden layer follows an empirically validated principle: the optimal number of neurons is usually 1 to 3 times the dimension of the input features. Too many neurons may lead to overfitting through overparameterization, while too few neurons may lead to underfitting because they cannot capture high-order feature interactions.

[0102] (3) Construction and training of SR-TELM hybrid processing power prediction model.

[0103] A data-driven model based on a multi-layer extreme learning machine is constructed. The data-driven model includes an input layer, a hidden layer (including ordinary neurons and physical neurons), and an output layer.

[0104] Embedding the drill-reamerization hybrid processing mechanism model into the physical neurons of the hidden layer, such as Figure 4 As shown, the SR-TELM hybrid processing power prediction model is obtained.

[0105] Ordinary neurons are neural network neurons, and their calculation method is as follows:

[0106] .

[0107] The physical neuron incorporates physical formulas into its neuron topology, and the calculation method is as follows:

[0108] or .

[0109] in, This represents the physical neurons in the first hidden layer. This represents a normal neuron in the first hidden layer. This is the expression for the borehole material removal power obtained from the SR algorithm. This is the expression for the material removal power obtained from the SR algorithm. and These are the initial weights and biases for the first hidden layer.

[0110] The parameters of the SR-TELM hybrid processing power prediction model are initialized as follows: the input layer weights and biases are initialized, the number of hidden layers is initialized to 2, the number of neurons in the first hidden layer is initialized to n1, and the number of neurons in the second hidden layer is initialized to n2. The first hidden layer includes 1 physical neuron and n1-1 ordinary neurons. The regularization term is also initialized. Among them, the physical neurons under drilling conditions are Under the condition of pore expansion, the physical neuron is .

[0111] The training set is input into the SR-TELM hybrid processing power prediction model for parameter optimization. The weights and biases of the input layer are randomly initialized, and the number of neurons in the two hidden layers and the regularization term are searched in the search space.

[0112] The root mean square error (RMSE) was used to evaluate the hyperparameters of the SR-TELM hybrid processing power prediction model. The hyperparameter space was searched using a grid search cross-validation method, and the performance of each set of hyperparameter configurations was evaluated to obtain the optimized hyperparameters.

[0113] The optimized hyperparameters are updated and a new set of hyperparameters is extracted from the search space. The hyperparameters of the SR-TELM hybrid processing power prediction model are evaluated again by the root mean square error (RMSE), and the optimal hyperparameter configuration is retained by the grid search cross-validation method.

[0114] The optimal hyperparameter configuration is updated into the SR-TELM hybrid processing power prediction model. The test set is then input into the trained SR-TELM hybrid processing power prediction model to determine whether the test results meet the target.

[0115] S4. Use the trained SR-TELM hybrid machining power prediction model to predict the material removal power of drilling and the material removal power of reaming.

[0116] The following specific examples are provided in conjunction with the above embodiments. It should be understood that the following specific examples are only illustrative of the specific implementation of the above embodiments and are not intended to limit the technical solutions of the above embodiments.

[0117] (1) Experimental system.

[0118] A VMC650L CNC machining center and a high-speed steel M35 straight shank twist drill were selected for experimental research. The main technical specifications of the machining center and the tool are shown in Tables 1 and 2. The drilling-reaming hybrid machining condition was wet cutting, and a common water-based emulsion was used as the cutting fluid. The CNC machining center was connected to a power-energy consumption data acquisition system, such as... Figure 5 As shown, the system includes a Siemens SINUMERIK 828D CNC system, a YOKOGAWA WT333E power analyzer, and WTViewerFreePlus software.

[0119] Table 1 Main Technical Specifications of VMC650L CNC Machining Center

[0120]

[0121] Table 2 Detailed Parameters of High-Speed ​​Steel M35 Straight Shank Twist Drill

[0122]

[0123] (2) Material removal experiment in the drilling-reaming hybrid process.

[0124] 1. Material removal experiment during drilling process.

[0125] Applying Taguchi orthogonal array L 32 (4) 9 Design a three-factor, four-level CNC drilling experiment, selecting tool diameter d0, feed rate f, spindle speed n, and drilling depth a. p As experimental factors, the values ​​of each factor were determined based on the characteristics of the workpiece material and the cutting performance of the CNC machine tool and cutting tool, as shown in Table 3. To increase the accuracy of the experiment and reduce errors, the average value method of multiple experiments in statistics was used. The experimental results are shown in Table 4, where the tool diameter d0, feed rate f, spindle speed n, and drilling depth a are... p The feed rate v is determined by selecting values ​​from an orthogonal array. f The conversion relationship between feed rate f and spindle speed n is as follows:

[0126] .

[0127] Table 3 Experimental settings for borehole material removal parameters

[0128]

[0129] Table 4 Partial Drilling Material Removal Power Data

[0130]

[0131] 2. Material Removal Experiment during Rehole Machining

[0132] Select the feed rate f, spindle speed n, bottom hole diameter d0, and rehole 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 rehole diameter in these 4 experimental factors need to satisfy d0 < d1. The experimental design and experimental results of the rehole material removal are shown in Table 6

[0133] Table 5 Experimental Settings of Rehole Material Removal Parameters

[0134]

[0135] Table 6 Partial Rehole Material Removal Power Data

[0136]

[0137] (3)Modeling of the Drilling-Expanding Hybrid Machining Mechanism Based on the Symbolic Regression Algorithm

[0138] 1. Correlation between Drilling-Expanding Hybrid Machining Parameters and Material Removal Power

[0139] 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-expanding hybrid machining 、 , and the machining parameters 、 and 、 all have GRA values greater than 0.6, indicating that the selected variables are suitable for representing 、 .

[0140] 2. Drilling-Expanding Hybrid Machining Mechanism Model

[0141] 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 of the material removal power for the drilling-expanding hybrid machining is obtained, as shown in Table 8. Three indicators, namely 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:

[0142] .

[0143] .

[0144] .

[0145] in, Representing the The predicted output value for each sample. Representing 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.

[0146] Table 7 PySR Algorithm Parameter Settings

[0147]

[0148] 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.

[0149] Table 8. Drill-reamer hybrid machining mechanism model

[0150]

[0151] (4) Prediction of material removal power in drilling-expansion hybrid processing based on SR-TELM.

[0152] 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.

[0153] Table 9 Model Parameter Selection

[0154]

[0155] 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). 2Typically, 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.

[0156] MAE, RMSE, and R-values ​​of ELM, TELM, and SR-TELM models trained using drill-reamer hybrid material removal experimental data. 2 The analysis results are shown in Table 10. In this case, 70% of the drill-reamerized hybrid material removal experimental data were selected as the training set input. The training set used for all three models was the same to reduce the impact of dataset randomness. The smaller the MAE and RMSE, the better the model's regression performance, while R... 2 Conversely, according to the data in Table 10, the hybrid-driven model constructed in this invention outperforms the data-driven model in all metrics.

[0157] Table 10 Predicted Material Removal Power Performance of Drill-Ampere Hybrid Processing

[0158]

[0159] As can be seen from Table 10:

[0160] (1) The SR-TELM model shows significant advantages in predicting material removal power in drilling and reaming. In drilling tasks, the MAE of SR-TELM is reduced by 55.8% and the RMSE is reduced by 56.0% compared with TELM, and the R² is increased to 0.985. In reaming tasks, the MAE and RMSE are reduced by 43.2% and 46.5% respectively compared with TELM, and the R² reaches 0.975.

[0161] (2) The SR-TELM model has higher performance in all aspects than the TELM model, indicating that embedding the mechanism model into the neurons helps TELM learn more physical information, thereby improving the prediction accuracy of TELM.

[0162] (3) TELM performs better than ELM, with a 7.8% decrease in MAE of drilling material removal power, demonstrating the ability of the dual-hidden-layer enhancement model to learn nonlinear information.

[0163] (5) Comparative analysis.

[0164] 1. Ablation experiment.

[0165] To verify the contribution of each core component in the SR-TELM model, a set of ablation experiments were designed.

[0166] Control group 1: such as Figure 9 In section (a), symbolic regression (SR) is removed, and only the TELM data-driven module is retained, denoted as TELM.

[0167] Control group 2: such as Figure 9 In section (b), the physical formula is changed from neuron embedding to input layer concatenation, denoted as SR-TELM-F2. This compares the hybrid driving methods that embed the physical formula into the network input. The processing parameters are then... , The value of the mechanism formula is , The inputs are merged into the TELM model.

[0168] 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.

[0169] 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.

[0170] Table 11 Comparison of Material Removal Model Indicators in Drill-Ampere Hybrid Processing

[0171]

[0172] Table 12. Changes in other model indicators relative to the SR-TELM model

[0173]

[0174] Table 12 shows the variation of 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:

[0175] (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.

[0176] (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.

[0177] (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.

[0178] 2. Comparison of SVM, RF, SR-TELM, SR-SVM and SR-RF models.

[0179] To further analyze the predictive performance of the SR-TELM model, a drilling-reaming hybrid power prediction model based on Support Vector Machine (SVM) and Random Forest (RF) was established. The model was trained and tested using both pure data-driven and mechanism-data hybrid methods. Predictive results were obtained, and accuracy was analyzed. Since SVM and RF lack hidden layers and neurons, an alternative data-mechanism hybrid model was adopted. This mechanism-data hybrid model inputs both the mechanistic model and the original machine learning input into the machine learning model, incorporating prior physical knowledge to improve the predictive ability of the machine learning model.

[0180] SR-SVR model and SR-RF model, such as Figure 10 Under the condition of drilling material removal, the influencing factors are: The mechanism formula value is The input to the SR-SVM model is about to be... Input into the SVR model. Under the condition of pore-expanding material removal, the influencing factors are: The mechanism formula value is The input to the SR-SVM model is about to be... Input into the SVM model.

[0181] Performance metrics for SVM, RF, SR-TELM, SR-SVM, and SR-RF models, for example... Figure 11 , Figure 12 , Figure 13 , Figure 14 As shown, it can be seen that:

[0182] (1) By comparing the performance metrics before and after the hybrid driving, it is shown that the mechanism model mined by PySR and the hybrid driving of machine learning can enhance the predictive ability of machine learning.

[0183] (2) The SR-SVM model for drilling-reaming hybrid machining has higher MAE, RMSE, and R-values ​​than the SVM model. 2 On average, the MAE, RMSE, and R-values ​​of the SR-RF model were improved by 23%, 21%, and 5.53%, respectively. 2 On average, they increased by 53%, 50%, and 32%.

[0184] (3) The SVM and RF models are more accurate in predicting the removal power of borehole materials than in predicting the removal power of drilling materials, and the performance index of borehole material removal power prediction decreases more after adding the mechanism. This indicates that increasing the amount of dataset can improve the prediction accuracy of the mechanism hybrid model to some extent.

[0185] (4) Among the three mechanisms in the mixed prediction, the SR-TELM model has the highest accuracy. This indicates that the mixed mechanism and TELM model is more likely to learn the nonlinear relationship in the material removal power of the drill-expansion hybrid process.

[0186] The present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for predicting material removal power in drilling-reaming hybrid machining based on SR-TELM, characterized in that, The application relates to a method for predicting material removal power of a drilling and reaming mixed machining process of a numerical control machine tool. S1, collecting drilling and reaming mixed machining parameters and material removal power data of the 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 and reaming mixed machining process of the numerical control machine tool through a symbolic regression algorithm, and generating a drilling and reaming mixed machining mechanism model, wherein the drilling and reaming mixed machining mechanism model is a drilling mechanism model and a reaming mechanism model; S3, embedding the drilling and reaming 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 reaming material removal power; The step S2 comprises: calculating the correlation degrees between the drilling and reaming 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 and reaming mixed machining parameters with the correlation degrees greater than a preset correlation threshold as input variables of the PySR algorithm for modeling, and obtaining a drilling and reaming mixed machining material removal power expression as follows: ； wherein, is a material drilling power, is a material reaming power, , are, respectively, an input variable for the material drilling power and an input variable for the material reaming power, , are, respectively, a symbol set for the material drilling power and a symbol set for the material reaming power; The step S3 comprises: constructing a data-driven model based on a double-hidden-layer extreme learning machine, wherein the data-driven model comprises an input layer, a hidden layer and an output layer; embedding the drilling and reaming mixed machining mechanism model into 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 weights and biases of the input layer, searching the number of neurons 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 a root mean square error (RMSE), searching the hyperparameter space by using a grid search cross-validation method, and evaluating the performance of each group of hyperparameter configurations to obtain optimized hyperparameters; updating the optimized hyperparameters, taking new hyperparameters from the search space, and again evaluating the hyperparameters of the SR-TELM mixed machining power prediction model by using the root mean square error (RMSE), and reserving 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 a target.

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