A method for predicting normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning

Abstract

This invention discloses a method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning, comprising the following steps: establishing a UVAIDC normal cutting force theoretical model based on indentation fracture theory and obtaining N sets of parameters; obtaining a first training set based on the N sets of samples; substituting the first training set into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training; fixing the parameters of the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model; substituting the training set corresponding to the target domain data into the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training; substituting the target domain samples for prediction to obtain the predicted normal cutting force value of the target domain samples. This invention reduces the dependence of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model on the amount of training data and improves the generalization ability of the model in small sample scenarios.

Description

Technical Field

[0001] This invention belongs to the field of machine learning and industrial processing technology, specifically relating to a method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning. Background Technology

[0002] Ultrasonic-assisted internal diameter cutting (UVAIDC) is an important advanced machining technology for cutting small and medium-sized wafers, enabling the fabrication of wafers with high surface quality and finding wide applications in semiconductors, precision manufacturing, and other fields. Normal cutting force is a key indicator in the UVAIDC process, directly affecting the wafer's geometric accuracy, surface quality, and machining process stability, and is crucial for ensuring machining quality and optimizing material removal patterns. Therefore, in-depth research into the prediction technology of normal cutting force in ultrasonic-assisted internal diameter cutting is of significant practical importance, providing technical assurance for the machining quality of hard and brittle materials.

[0003] With the development of artificial intelligence, deep learning has demonstrated unique advantages by exploring the complex nonlinear relationship between machining parameters and normal cutting forces, with models such as backpropagation regression (BP) and convolutional neural networks (CNN) achieving significant results. However, these models generally suffer from strong data dependence: when the number of samples is insufficient or the distribution is uneven, the model struggles to learn the true characteristics of the data, and the prediction accuracy cannot be guaranteed. Studies have shown that increasing the training samples for cutting force prediction models from 20 to 100 can reduce the error rate by 50%, but obtaining a large number of high-quality experimental samples in actual industrial scenarios is extremely costly. To address the problem of insufficient sample size, existing methods mainly fall into two categories: one is to select models that are well-suited to small samples, and the other is to expand the sample capacity. The former limits the range of models that can be selected, making it difficult to meet the needs of complex machining scenarios; the latter, conventional data augmentation methods, are prone to model overfitting. Furthermore, single learning algorithms have low prediction accuracy and poor extrapolation on small sample data, making it difficult to meet the high-precision prediction requirements of industry.

[0004] Transfer learning, as an emerging machine learning algorithm, provides a new approach to solving the problem of few-shot learning. It can use source domain data that is similar to the target domain to pre-train the model in the source domain and then transfer it to the target domain for further training, reducing the number of samples required for training in the target domain. However, the application of transfer learning in the field of predicting the normal cutting force of ultrasonic-assisted internal diameter cutting is still immature and a systematic and effective technical solution has not yet been formed. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning includes the following steps:

[0008] Step 1: Establish a theoretical model of the UVAIDC normal cutting force based on the indentation fracture theory. The theoretical model of the UVAIDC normal cutting force is as follows:

[0009]

[0010] In the formula, It is a constant. , , K IC v and E are, respectively, the feed rate of the workpiece to be cut, the workpiece radius, the Vickers hardness, the fracture toughness, the Poisson's ratio, and the elastic modulus of the workpiece. , , , , ,φ, And t represents, in order, the saw blade thickness, saw blade inner diameter, abrasive particle size, abrasive concentration, abrasive density, abrasive cone half-angle, penetration depth, and sawing time of the inner circular saw blade; A u Ω represents the ultrasonic amplitude applied to the inner circular saw blade; Ω represents the spindle speed of the ultrasonic-assisted inner diameter cutting machine. Normal cutting force;

[0011] set up , K IC v, E, , φ is a fixed value, a p The intermediate variables for solving the UVAIDC normal cutting force theoretical model are t and t, respectively, which are time variables that vary with the machining process. Neither of these variables participates in the input setting of process parameters; they are only used for the mechanical derivation of the theoretical model. Different values ​​are set for the workpiece diameter, feed rate, spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive particle size within the working layer of the internal saw blade. A full factorial experimental design method is used to combine these values, resulting in N sets of parameter combinations. Each set of parameters includes: workpiece diameter, feed rate, spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive particle size. The N sets of parameter combinations are then substituted into the UVAIDC normal cutting force theoretical model for calculation, yielding the theoretical value of the normal cutting force for each parameter combination.

[0012] Step 2: Take each parameter combination in the N sets of parameters ("workpiece diameter, feed rate, spindle speed, ultrasonic amplitude, saw blade thickness, saw blade inner diameter, and abrasive particle size") as a sample. Take the theoretical value of the normal cutting force corresponding to the parameter combination as the actual value of the sample. Obtain the first training set based on the N sets of samples. Substitute the first training set into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training to obtain the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model. The ultrasonic-assisted internal diameter cutting normal cutting force prediction model includes: a multi-layer BP neural network model. The input of the multi-layer BP neural network model is a sample. Each sample includes: the workpiece diameter, the feed rate of the workpiece, the spindle speed of the ultrasonic-assisted internal diameter cutting machine, the ultrasonic amplitude applied to the internal circular saw blade, the saw blade thickness, the saw blade inner diameter, and the abrasive particle size in the working layer of the internal circular saw blade. The output of the multi-layer BP neural network model is the predicted value of the normal cutting force of the workpiece.

[0013] Step 3: Fix the parameters of the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model, substitute the training set corresponding to the target domain data into the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training, and obtain the ultrasonic-assisted internal diameter cutting normal cutting force prediction model based on transfer learning.

[0014] Step 4: Substitute the target domain samples into the ultrasonic-assisted internal diameter cutting normal force prediction model based on transfer learning to obtain the predicted value of the normal cutting force of the target domain samples.

[0015] In the above technical solution, the multilayer BP neural network model includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer connected in sequence. The input layer receives samples and passes them to the first hidden layer. After receiving the samples, the first hidden layer outputs primary features. The second hidden layer receives the primary features output by the first hidden layer and outputs intermediate features. The third hidden layer receives the intermediate features output by the second hidden layer and outputs global features. The output layer outputs the predicted value of the normal cutting force based on the global features. The activation functions of the first hidden layer, the second hidden layer, and the third hidden layer are all ReLU activation functions.

[0016] In the above technical solution, the number of neurons in the first hidden layer is 10, the number of neurons in the second hidden layer is 8, and the number of neurons in the third hidden layer is 6.

[0017] The above technical solution also includes: a loss function, which is the root mean square error loss function.

[0018] The beneficial effects of this invention are as follows:

[0019] 1. This invention trains a predictive model for the normal cutting force of ultrasonic-assisted internal diameter cutting based on the workpiece diameter and feed rate, the spindle speed of the ultrasonic-assisted internal diameter cutting machine, the ultrasonic amplitude applied to the internal saw blade, the saw blade thickness, the saw blade inner diameter, and the abrasive particle size in the working layer of the internal saw blade. This model can capture the mapping relationship between machining parameters and normal cutting force, thereby predicting the normal cutting force and providing reliable data support for optimizing the machining process of the workpiece. Furthermore, this invention generates a large amount of sample data based on the UVAIDC normal cutting force theoretical model, solving the problem of high cost and small quantity of experimental samples in actual ultrasonic-assisted internal diameter cutting scenarios. This reduces the dependence of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model of this invention on the amount of training data and improves the generalization ability of the model in small sample scenarios.

[0020] 2. This invention proposes a method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning. This method achieves knowledge transfer and can accurately predict the normal cutting force using only a small amount of experimental data from ultrasonic-assisted internal diameter cutting of single-crystal silicon. Compared to ultrasonic-assisted internal diameter cutting normal cutting force prediction models that do not use transfer learning, this method significantly reduces prediction error (RMS percentage error reduced by 4.42%) and improves prediction accuracy (normal cutting force prediction accuracy increased by 4.42%). Furthermore, by leveraging a cross-data type knowledge transfer mechanism, the transfer learning-based ultrasonic-assisted internal diameter cutting normal cutting force prediction model can flexibly adapt to various ultrasonic-assisted internal diameter cutting production scenarios for hard and brittle materials, exhibiting good versatility and scalability. Attached Figure Description

[0021] Figure 1 This is a flowchart of the ultrasonic-assisted internal diameter cutting normal force prediction method based on transfer learning according to the present invention.

[0022] Figure 2 (a) is a schematic diagram comparing the predicted and true values ​​of the normal cutting force in Embodiment 7, Comparative Example 1, and Comparative Example 2 of the present invention. Figure 2 (b) is a schematic diagram comparing the absolute percentage error of the normal cutting force in Embodiment 7, Comparative Example 1, and Comparative Example 2 of the present invention;

[0023] Figure 3 (a) is the regression fitting plot of Comparative Example 2 of this invention. Figure 3 (b) is the regression fitting plot of Comparative Example 1 of this invention. Figure 3 (c) is the regression fitting graph of Embodiment 7 of the present invention. Detailed Implementation

[0024] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0025] Example 1

[0026] An ultrasonic-assisted internal diameter cutting normal cutting force prediction model includes: a multi-layer BP neural network model. The input of the multi-layer BP neural network model is samples, each sample including: the workpiece diameter, the feed rate of the workpiece, the spindle speed of the ultrasonic-assisted internal diameter cutting machine (i.e., the rotation speed of the internal circular saw blade), the ultrasonic amplitude applied to the internal circular saw blade, the saw blade thickness, the saw blade inner diameter (i.e., the diameter of the hollow circular hole in the middle of the internal circular saw blade), and the abrasive particle size in the working layer of the internal circular saw blade; the output of the multi-layer BP neural network model is the predicted value of the normal cutting force of the workpiece.

[0027] The multilayer backpropagation (BP) neural network model comprises an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer connected in sequence. The input layer receives samples and passes them to the first hidden layer, which outputs primary features. The first hidden layer has 10 neurons. The second hidden layer receives the primary features from the first hidden layer and outputs intermediate features. The second hidden layer has 8 neurons. The third hidden layer receives the intermediate features from the second hidden layer and outputs global features. The third hidden layer has 6 neurons. The output layer outputs the predicted normal cutting force based on the global features (the output layer has no activation function). The activation functions for the first, second, and third hidden layers are all ReLU activation functions, which enhance the nonlinear expressive power of each hidden layer.

[0028] Example 2

[0029] An ultrasonic-assisted internal diameter cutting normal cutting force prediction model, based on Example 1, further includes: a loss function L. In this example, the root mean square error loss function (RMSE) is selected, and the loss function L is as follows:

[0030]

[0031] in, This represents the actual (true) value of the normal cutting force for the i-th sample. Let represent the predicted normal cutting force value of the i-th sample, and n represent the number of samples, i=1,2,…,n.

[0032] Example 3

[0033] Based on Example 2, to address the issues of high sample acquisition costs and insufficient sample size in actual cutting scenarios, a UVAIDC normal cutting force theoretical model was established based on indentation fracture theory. This model was used to construct a large amount of sample data to train the ultrasonic-assisted internal diameter cutting normal cutting force prediction model. The UVAIDC normal cutting force theoretical model is as follows:

[0034]

[0035] In the formula, It is a constant. , , K IC v and E are, respectively, the feed rate of the workpiece to be cut, the workpiece radius of the workpiece to be cut, the Vickers hardness of the workpiece to be cut, the fracture toughness of the workpiece to be cut, the Poisson's ratio of the workpiece to be cut, and the elastic modulus of the workpiece to be cut. , , , , ,φ, And t represents, in order, the saw blade thickness, saw blade inner diameter, abrasive particle size, abrasive concentration, abrasive density, abrasive cone half-angle (i.e., the angle between the cone axis and the generatrix when the abrasive particle is idealized as a cone), penetration depth, and sawing time; A u Ω represents the ultrasonic amplitude applied to the inner circular saw blade; Ω represents the spindle speed of the ultrasonic-assisted inner diameter cutting machine. This is the normal cutting force.

[0036] In this embodiment, within the UVAIDC normal cutting force theoretical model:

[0037] = 8.960×10 -4 ;

[0038] =247.8480;

[0039] =1.10×10 4 MPa

[0040] ,

[0041] v=0.28,

[0042] E=1.30×10 5 MPa

[0043] =100,

[0044] ,

[0045] φ = 0.9553 rad.

[0046] set up , K IC v, E, , φ is a fixed value, a p The intermediate variable for solving the UVAIDC normal cutting force theoretical model is t, which is a time variable that varies with the machining process. The two (a p (and t) are not involved in the input setting of process parameters, but are only used for the derivation of the normal cutting force in the UVAIDC normal cutting force theoretical model. For seven variables—workpiece diameter, workpiece feed rate, spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive grain size—different values ​​were set as shown in Table 1. A full factorial experimental design method was used to combine these values, resulting in 5400 parameter combinations (source domain data). Each parameter combination includes: workpiece diameter, workpiece feed rate, ultrasonic spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive grain size.

[0047] Table 1

[0048]

[0049] Substitute the above 5400 sets of parameters into the UVAIDC normal cutting force theoretical model for calculation to obtain the theoretical value of the normal cutting force corresponding to each set of parameters.

[0050] Example 4

[0051] Based on Example 3, the ultrasonic-assisted internal diameter cutting normal cutting force prediction model is trained. The training method for the ultrasonic-assisted internal diameter cutting normal cutting force prediction model includes the following steps:

[0052] Each parameter combination in the 5400 parameter combinations, including "workpiece diameter, feed rate, spindle speed, ultrasonic amplitude, saw blade thickness, saw blade inner diameter, and abrasive grain size," is taken as a sample. The theoretical value of the normal cutting force corresponding to this parameter combination is taken as the actual value (true value) of the sample, resulting in 5400 samples. 60% of the 5400 samples are used to form the first training set (3240 sets), 25% of the 5400 samples are used to form the first validation set (1350 sets), and the remaining 15% of the 5400 samples are used to form the first test set (810 sets). The first training set is then substituted into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model in Example 2 for training, resulting in the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model. The training employs an early stopping strategy. After each training round, the performance of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model is tested using the first validation set. Training terminates when the loss function L of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model does not decrease for ten consecutive rounds on the first validation set, resulting in the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model. If early stopping is not triggered, training terminates naturally after 300 rounds.

[0053] Example 5

[0054] A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting includes: substituting the first test set from Example 4 into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model trained in Example 4 to obtain the predicted normal cutting force value for each sample in the first test set. The prediction results are then evaluated, and the calculated root mean square percentage error (MAPE) is 10.64%, and the prediction accuracy is 89.36%.

[0055] Example 6

[0056] like Figure 1 As shown, the ultrasonic-assisted internal diameter cutting normal force prediction method based on transfer learning includes the following steps:

[0057] The experimental data of ultrasonic-assisted inner diameter cutting of monocrystalline silicon was defined as the target domain data (a standard monocrystalline silicon wafer with a diameter of 100 mm was selected for the cutting experiment, and the ultrasonic amplitude was constant in this cutting experiment). The "workpiece diameter, feed rate, spindle speed, ultrasonic amplitude, saw blade thickness, saw blade inner diameter and abrasive size" in the target domain data were taken as a sample. The normal cutting force in the target domain data was taken as the actual value (true value) of the sample. A total of 40 samples were obtained. 30 samples were used as the second training set and the remaining 10 samples were used as the second test set.

[0058] The ultrasonic-assisted internal diameter cutting normal cutting force prediction model (i.e., the model trained in Example 4) is fixed. Figure 1The parameters of the first, second, and third hidden layers in the BPneural network prediction model are used to train the ultrasonic-assisted internal diameter cutting normal cutting force prediction model by substituting the second training set into the trained model. This yields an ultrasonic-assisted internal diameter cutting normal cutting force prediction model based on transfer learning.

[0059] The maximum number of training epochs was set to 200. The connection weights of the output layer of the trained ultrasonic-assisted internal diameter cutting normal force prediction model were adjusted by minimizing the loss function L. Five-fold cross-validation was used, with 10% of the second training set allocated as a temporary validation set for each epoch. An early stopping strategy was employed, where training stopped when the loss value of the temporary validation set did not decrease for 10 consecutive epochs. This resulted in the ultrasonic-assisted internal diameter cutting normal force prediction model based on transfer learning.

[0060] Example 7

[0061] A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting includes: substituting the samples (target domain samples) in the second test set of Example 6 into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model based on transfer learning in Example 6 to obtain the predicted value of the normal cutting force of the samples in the second test set.

[0062] Comparative Example 1

[0063] A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting includes: substituting samples from the second test set in Example 6 into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model trained in Example 4 to obtain the predicted value of the normal cutting force.

[0064] Comparative Example 2

[0065] A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting includes: substituting the samples in the second test set in Example 6 into the UVAIDC normal cutting force theoretical model (theoretical model) of Example 4 to obtain the predicted value of the normal cutting force.

[0066] The root mean square percentage error (MAPE), prediction accuracy, and coefficient of determination are used to measure the accuracy of predictions. Three evaluation metrics were used to assess the prediction results in Example 7, Comparative Example 1, and Comparative Example 2, as shown in Table 2:

[0067] Table 2

[0068]

[0069] As shown in Table 2, the results of Comparative Example 1 indicate that, compared with the UVAIDC normal cutting force theoretical model, the MAPE of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model is reduced by 3.4%, the prediction accuracy is improved by 3.4%, and the model's generalization ability is effectively improved. Further comparison between Example 7 and Comparative Example 1 shows that Example 7 has the lowest MAPE value, the highest prediction accuracy, and the best R². This indicates that by training the ultrasonic-assisted internal diameter cutting normal cutting force prediction model with actual experimental data and then optimizing it through transfer learning, the model has good universality and can achieve high-precision prediction of normal cutting force even under conditions of a small number of samples.

[0070] Combination Figure 2 and Figure 3 Further verification shows that the ultrasonic-assisted internal diameter cutting normal force prediction model based on transfer learning in this invention performs excellently. For example... Figure 2 As shown, the predicted normal cutting force of this model basically coincides with the true normal cutting force, and compared with comparative examples 1 and 2, the overall absolute percentage error (APE) is the smallest; at the same time, combined with Figure 3 It can be seen that the normal cutting force data points of the ultrasonic-assisted internal diameter cutting normal cutting force prediction model based on transfer learning of the present invention are more closely distributed near the ideal fitting line, and the 95% confidence interval is narrower (the data point dispersion is low). This indicates that the model of the present invention has good prediction consistency and low uncertainty, and has high normal cutting force prediction accuracy and generalization ability.

[0071] The present invention has been described above by way of example. It should be noted that any simple modifications, alterations or other equivalent substitutions that can be made by those skilled in the art without creative effort without departing from the core of the present invention fall within the protection scope of the present invention.

Claims

1. A method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting based on transfer learning, characterized in that, Includes the following steps: Step 1: Establish a theoretical model of the UVAIDC normal cutting force based on the indentation fracture theory. The theoretical model of the UVAIDC normal cutting force is as follows: In the formula, It is a constant. , , K IC v and E are, respectively, the feed rate of the workpiece to be cut, the workpiece radius, the Vickers hardness, the fracture toughness, the Poisson's ratio, and the elastic modulus of the workpiece. , , , , ,φ, And t represents, in order, the saw blade thickness, saw blade inner diameter, abrasive particle size, abrasive concentration, abrasive density, abrasive cone half-angle, sawing depth, and sawing time of the internal circular saw blade; A u Ω represents the ultrasonic amplitude applied to the inner circular saw blade; Ω represents the spindle speed of the ultrasonic-assisted inner diameter cutting machine. Normal cutting force; set up , K IC v, E, , φ is a fixed value, a p As an intermediate variable in the internal solution of the UVAIDC normal cutting force theoretical model, t represents the time variable that varies with the machining process. Different values ​​are set for the workpiece diameter, feed rate, spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive particle size within the working layer of the internal saw blade. A full factorial experimental design method is used to combine these values, resulting in N sets of parameter combinations. Each parameter combination includes: workpiece diameter, feed rate, spindle speed of the ultrasonic-assisted internal diameter cutting machine, ultrasonic amplitude applied to the internal saw blade, saw blade thickness, saw blade inner diameter, and abrasive particle size. The N sets of parameter combinations are then substituted into the UVAIDC normal cutting force theoretical model for calculation, yielding the theoretical value of the normal cutting force for each parameter combination. Step 2: Take each parameter combination in the N sets of parameters ("workpiece diameter, feed rate, spindle speed, ultrasonic amplitude, saw blade thickness, saw blade inner diameter, and abrasive particle size") as a sample. Take the theoretical value of the normal cutting force corresponding to the parameter combination as the actual value of the sample. Obtain the first training set based on the N sets of samples. Substitute the first training set into the ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training to obtain the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model. The ultrasonic-assisted internal diameter cutting normal cutting force prediction model includes: a multi-layer BP neural network model. The input of the multi-layer BP neural network model is a sample. Each sample includes: the workpiece diameter, the feed rate of the workpiece, the spindle speed of the ultrasonic-assisted internal diameter cutting machine, the ultrasonic amplitude applied to the internal circular saw blade, the saw blade thickness, the saw blade inner diameter, and the abrasive particle size in the working layer of the internal circular saw blade. The output of the multi-layer BP neural network model is the predicted value of the normal cutting force of the workpiece. Step 3: Fix the parameters of the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model, substitute the training set corresponding to the target domain data into the trained ultrasonic-assisted internal diameter cutting normal cutting force prediction model for training, and obtain the ultrasonic-assisted internal diameter cutting normal cutting force prediction model based on transfer learning. Step 4: Substitute the target domain samples into the ultrasonic-assisted internal diameter cutting normal force prediction model based on transfer learning to obtain the predicted value of the normal cutting force of the target domain samples.

2. The method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting according to claim 1, characterized in that, The multilayer BP neural network model includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer connected in sequence. The input layer receives samples and passes them to the first hidden layer. The first hidden layer outputs primary features after receiving the samples. The second hidden layer receives the primary features output by the first hidden layer and outputs intermediate features. The third hidden layer receives the intermediate features output by the second hidden layer and outputs global features. The output layer outputs the predicted value of the normal cutting force based on the global features. The activation functions of the first hidden layer, the second hidden layer, and the third hidden layer are all ReLU activation functions.

3. The method for predicting the normal cutting force in ultrasonic-assisted internal diameter cutting according to claim 1 or 2, characterized in that, Also includes: The loss function is the root mean square error loss function.

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