Milling amplitude prediction method based on multi-fidelity surrogate model

Abstract

The application relates to a kind of milling amplitude prediction methods based on multi-fidelity proxy model. Including: 1) initialization processing parameter space;2) obtain processing parameter value in parameter space, calculate tool amplitude theoretical value by milling mechanism model, and constitute data set I with processing parameter;3) establish low-fidelity proxy model based on BP neural network, input data set I to train low-fidelity proxy model, extract each network layer parameter of low-fidelity proxy model;4) design orthogonal experiment in parameter space, measure milling tool vibration data, calculate tool amplitude experimental value, and constitute data set II with processing parameter;5) establish multi-fidelity proxy model on the basis of low-fidelity proxy model, load each layer parameter of low-fidelity proxy model in step 3) and freeze the network layer, input data set II to train multi-fidelity proxy model. The application fully combines the advantages of neural network model and mechanism model, and can effectively improve the accuracy of milling amplitude prediction.

Description

Technical Field

[0001] This invention belongs to the field of tool amplitude prediction in milling, and specifically relates to a milling amplitude prediction method based on a multi-fidelity surrogate model. Background Technology

[0002] With the continuous advancement of information technology and intelligentization in modern industry, the demand for parameter optimization in milling processes is constantly increasing. Milling amplitude, as an important evaluation standard for milling processes, is crucial for accurately predicting the milling vibrations generated by different milling parameters. Currently, there are three main methods for predicting milling amplitude: empirical models, mechanistic models, and deep learning models. Empirical and deep learning models rely on a large amount of milling experimental data, while mechanistic models, through theoretical modeling, do not rely on milling experimental data, but their prediction accuracy is relatively low. Therefore, this invention proposes a milling amplitude prediction method based on a multi-fidelity surrogate model. Combining the advantages of mechanistic models and deep learning models, and relying on a large amount of theoretical data from mechanistic models and a small amount of milling experimental data, a relatively accurate milling amplitude prediction model is constructed. Summary of the Invention

[0003] The purpose of this invention is to provide a milling amplitude prediction method based on a multi-fidelity surrogate model. This method fully combines the advantages of mechanistic models and neural network models, which can effectively improve the accuracy of milling amplitude prediction. It can be applied to the prediction of CNC machine tool amplitude in milling production, and is of great significance for milling process optimization and machining parameter selection.

[0004] To achieve the above objectives, the technical solution of the present invention is: a milling amplitude prediction method based on a multi-fidelity surrogate model, comprising the following steps: Step 1: Initialize the machining parameter space; Step 2: Obtain the machining parameters in the parameter space, calculate the theoretical value of the tool amplitude through the milling mechanism model, and combine it with the machining parameters to form dataset I; Step 3: Establish a low-fidelity proxy model based on a BP neural network. Train the low-fidelity proxy model by inputting dataset I and extracting the parameters of each network layer of the low-fidelity proxy model. Step 4: Design an orthogonal experiment in the parameter space, measure the vibration data of the milling tool, calculate the experimental value of the tool amplitude, and combine it with the machining parameters to form dataset II; Step 5: Build a multi-fidelity proxy model based on the low-fidelity proxy model, load the parameters of each layer of the low-fidelity proxy model in Step 3 and freeze the network layer, and input dataset II to train the multi-fidelity proxy model.

[0005] In one embodiment of the present invention, the processing parameter values ​​in step 2 are obtained in the processing parameter space by a method of sampling at equal intervals and then randomly sampling, as follows: First, the sampling interval of each processing parameter is initialized; then, equal-interval sampling is performed in the processing parameter space to obtain a list of equal-interval sampled values ​​for each parameter; then, within the list of equal-interval sampled values, the parameter values ​​for each parameter are obtained by random sampling; finally, the parameter values ​​are combined to form the processing parameter group of the mechanism model.

[0006] In one embodiment of the present invention, the establishment and training of the low-fidelity proxy model in step 3 is specifically as follows: First, a low-fidelity proxy model framework based on a backpropagation (BP) neural network is established, consisting of 6 hidden layers and 1 fully connected layer. Neurons utilize linear activation functions and their variants. The first 4 hidden layers use the ELU activation function, and the last 2 use the ReLU activation function. The outputs of the first 4 hidden layers are normalized using the BatchNorm1d function. Then, the weights of each layer are initialized using a normal distribution, and the model loss function is set to mean squared error. The Adamax optimization algorithm is used to train the low-fidelity proxy model, with a learning rate of 0.001. The model is then iteratively trained using dataset I until the loss value stabilizes. Finally, the parameters of each layer of the trained low-fidelity proxy model are extracted and saved as a parameter file.

[0007] In one embodiment of the present invention, the orthogonal experimental parameter values ​​in step 4 are obtained in the machining parameter space by sampling at equal intervals. The amplitude experimental value is the average value of the amplitude of multiple rotational cycles under stable cutting. Specifically: First, the tool vibration data is preprocessed by low-pass filtering, with the low-pass filter cutoff frequency set to twice the tooth frequency. Then, the preprocessed tool vibration data is decomposed into data segments at equal intervals according to the rotation period. Next, the difference between the maximum and minimum values ​​in each data segment is calculated. Finally, the average of all differences is calculated as the experimental value of the tool amplitude.

[0008] In one embodiment of the present invention, the establishment and training of the multi-fidelity proxy model in step 5 is specifically as follows: First, a multi-fidelity proxy model is built based on the low-fidelity proxy model from step 3, consisting of 3 hidden layers and 3 fully connected layers. The first hidden layer uses the ELU activation function and its output is normalized using the BatchNorm1d function, while the last two layers use the ReLU activation function. The first two fully connected layers receive the outputs of the hidden layers from the low-fidelity proxy model, and the last layer receives the output of the multi-fidelity proxy model. Then, the weights of each layer are initialized using a normal distribution, and the model loss function is set to the mean squared error loss function. The Adamax optimization algorithm is used to train the low-fidelity proxy model, with a learning rate of 0.001. Next, the network parameters of the low-fidelity proxy model from step 3 are loaded. Finally, dataset II is input, and the multi-fidelity proxy model is iteratively trained until the loss value stabilizes.

[0009] Compared to existing technologies, this invention has the following advantages: It integrates a mechanistic model, which, while ensuring accuracy, significantly reduces the amount of experimental data required and lowers model construction costs compared to empirical and deep learning models. Furthermore, this invention can construct a multi-fidelity surrogate model using a large amount of theoretical data and a small amount of experimental data, achieving relatively accurate prediction of milling amplitude. This invention can be practically applied in modern industrial production; the multi-fidelity surrogate model established in this solution is tailored to specific milling machines in a factory. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating the construction process of the multi-fidelity proxy model proposed in this invention. Figure 2 This is a structural diagram of the low-fidelity proxy model proposed in this invention; Figure 3 This is a schematic diagram of the displacement sensor installation in an example of the present invention; Figure 4 This is a structural diagram of the multi-fidelity proxy model proposed in this invention; Figure 5 This is a flowchart of the prediction process for the multi-fidelity proxy model proposed in this invention. Figure 6 This is an error graph showing the difference between the experimental results and the predicted results in an example of the present invention. Detailed Implementation

[0011] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0012] This invention provides a milling amplitude prediction method based on a multi-fidelity surrogate model, comprising the following steps: Step 1: Initialize the machining parameter space; Step 2: Obtain the machining parameters in the parameter space, calculate the theoretical value of the tool amplitude through the milling mechanism model, and combine it with the machining parameters to form dataset I; Step 3: Establish a low-fidelity proxy model based on a BP neural network. Train the low-fidelity proxy model by inputting dataset I and extracting the parameters of each network layer of the low-fidelity proxy model. Step 4: Design an orthogonal experiment in the parameter space, measure the vibration data of the milling tool, calculate the experimental value of the tool amplitude, and combine it with the machining parameters to form dataset II; Step 5: Build a multi-fidelity proxy model based on the low-fidelity proxy model, load the parameters of each layer of the low-fidelity proxy model in Step 3 and freeze the network layer, and input dataset II to train the multi-fidelity proxy model.

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to specific embodiments and accompanying drawings, such as... Figure 1 As shown, the present invention provides a milling amplitude prediction method based on a multi-fidelity surrogate model, as detailed below: S1. Initialize the machining parameter space, including four milling machining parameters: depth of cut, width of cut, feed per pass, and spindle speed. The parameter ranges are set to 0~3 (mm), 7.0~9.5 (mm), 0.05~0.20 (mm), and 3500~5000 (r / min), respectively.

[0014] S2. Initialize the sampling intervals of the four milling parameters from step S1 above, setting them to 0.1 (mm), 0.1 (mm), 0.001 (mm), and 100 (r / min), respectively. Perform equal-interval sampling within the machining parameter space to obtain a list of equal-interval sampled values ​​for each parameter. Within this list, obtain parameter values ​​by random sampling and combine these values ​​into machining parameter groups, totaling 1024 groups. Input these machining parameter groups into the milling tool amplitude mechanism model to calculate the corresponding theoretical tool amplitude values, and combine them with the machining parameters to form dataset I.

[0015] S3. Establish a low-fidelity proxy model based on a BP neural network, as shown in the attached diagram. Figure 2 As shown, the low-fidelity proxy model consists of 6 hidden layers and 1 fully connected layer. Neurons utilize linear activation functions and their variants. The first 4 hidden layers use ELU activation, and the last 2 use ReLU activation. The outputs of the first 4 hidden layers are normalized using the BatchNorm1d function. The number of neurons in each hidden layer is 64, 64, 32, 32, 16, and 16, respectively. The weights of each layer are initialized using a normal distribution, and the model loss function is set to mean squared error. The Adamax optimization algorithm is used to train the low-fidelity proxy model, with a learning rate of 0.001. Dataset I is input into the low-fidelity proxy model, and iterative training is performed until the loss value stabilizes. Finally, the parameters of each layer of the trained low-fidelity proxy model are extracted and saved as a parameter file.

[0016] S4. Experimental parameter values ​​are obtained by sampling at equal intervals within the parameter space. A 4-factor, 6-level orthogonal experiment is designed, totaling 36 groups, with sampling intervals of 0.2, 0.5, 0.05, and 1000. Additionally, 5 groups of machining parameters are randomly sampled from the parameter space obtained in step S2 above as the test group for the multi-fidelity surrogate model. Sensors are installed to measure the displacement at the smooth surface of the tool; the specific arrangement is shown in the attached figure. Figure 3 As shown, 1 is the spindle, 2 is the cutting tool, 3 is the displacement sensor, 4 is the workpiece, 5 is the workpiece stage, and 6 is the machine tool housing. The experiment begins by measuring the vibration data of the milling tool. The tool vibration data is preprocessed using a low-pass filter, with the low-pass filter cutoff frequency set to twice the tooth frequency. The preprocessed tool vibration data is then decomposed into data segments at equal intervals according to the tool rotation cycle. The difference between the maximum and minimum values ​​within each data segment is calculated, and the average of all differences is then calculated as the experimental value of the tool amplitude. This average, along with the corresponding machining parameters, forms dataset II.

[0017] S5. Based on the low-fidelity proxy model in step S3, establish a multi-fidelity proxy model, as shown in the appendix. Figure 4 As shown. The multi-fidelity proxy model, based on the low-fidelity proxy model, includes 3 hidden layers and 3 fully connected layers. The first hidden layer uses the ELU activation function and the output is normalized using the BatchNorm1d function, while the last two layers use the linear (ReLU) activation function. The number of neurons in each hidden layer is 16, 8, and 8 respectively. The first two fully connected layers are inputs to the outputs of the hidden layers of the low-fidelity proxy model, and the output of the last layer is used as the output of the multi-fidelity proxy model. The weights of each layer are initialized using a normal distribution, and the model loss function is set to the mean squared error loss function. The Adamax optimization algorithm is used when training the low-fidelity proxy model, and the learning rate is set to 0.001. The network parameters of the low-fidelity proxy model from step S3 are loaded and the network layers are frozen. The 36 sets of training data from dataset II are input into the multi-fidelity proxy model, and iterative training is performed until the loss value stabilizes.

[0018] S6. Input the test data from dataset II into the multi-fidelity proxy model trained in step S5 above for testing, as shown in the attached figure. Figure 5 The diagram shown illustrates the prediction process during testing of the multi-fidelity proxy model. The error in the test results is shown in the attached figure. Figure 6 As shown.

[0019] From the appendix Figure 6It can be seen that the milling amplitude prediction method based on a multi-fidelity surrogate model proposed in this invention exhibits relatively small percentage and absolute average errors between the predicted milling tool amplitude and the actual tool amplitude. This indicates that the proposed method has good prediction accuracy, and the variance of the absolute error is also small, suggesting that the proposed multi-fidelity surrogate prediction model has good stability. In conclusion, the milling amplitude prediction method based on a multi-fidelity surrogate model proposed in this invention is effective in the field of tool amplitude prediction in milling processes.

[0020] This invention proposes a multi-fidelity surrogate model to predict the tool amplitude in milling, and has achieved good results. It can be applied to the prediction of CNC machine tool amplitude in milling production, and is of great significance for the optimization of milling process and the selection of machining parameters. It is innovative and practical.

[0021] It should be noted that the specific implementation of the present invention is not limited to the above examples. Similar solutions proposed in accordance with the principles and ideas of the present invention should all be considered within the scope of protection of the present invention patent.

Claims

1. A method for predicting milling amplitude based on a multi-fidelity surrogate model, characterized in that, Includes the following steps: Step 1: Initialize the machining parameter space; Step 2: Obtain the machining parameters in the parameter space, calculate the theoretical value of the tool amplitude through the milling mechanism model, and combine it with the machining parameters to form dataset I; Step 3: Establish a low-fidelity proxy model based on a BP neural network. Train the low-fidelity proxy model by inputting dataset I and extracting the parameters of each network layer of the low-fidelity proxy model. Step 4: Design an orthogonal experiment in the parameter space, measure the vibration data of the milling tool, calculate the experimental value of the tool amplitude, and combine it with the machining parameters to form dataset II; Step 5: Build a multi-fidelity proxy model based on the low-fidelity proxy model, load the parameters of each layer of the low-fidelity proxy model in Step 3 and freeze the network layer, and input dataset II to train the multi-fidelity proxy model. The processing parameter values ​​in step 2 are obtained in the parameter space by sampling at equal intervals and then randomly sampling. The specific implementation method for obtaining the processing parameter values ​​in the parameter space using the method of sampling at equal intervals and then randomly sampling is as follows: First, the sampling interval of each processing parameter is initialized; then, equal-interval sampling is performed in the parameter space to obtain a list of equal-interval sampled values ​​for each parameter; then, within the list of equal-interval sampled values, the parameter values ​​for each parameter are obtained by random sampling; finally, the parameter values ​​are combined to form the processing parameter group of the mechanism model. The low-fidelity surrogate model in step 3 includes 6 hidden layers and 1 fully connected layer. The neuron activation function is a linear activation function or its variant. The first 4 hidden layers use the ELU activation function, and the last 2 layers use the linear ReLU activation function. The output of the first 4 hidden layers is normalized using the BatchNorm1d function. The training process of the low-fidelity proxy model is as follows: The weights of each layer of the low-fidelity proxy model are initialized using a normal distribution. The loss function of the low-fidelity proxy model is set to the mean squared error loss function. The Adamax optimization algorithm is used when training the low-fidelity proxy model, and the learning rate is set to 0.

001. Then, the dataset I is input, and the low-fidelity proxy model is iteratively trained until the loss value stabilizes. Finally, the parameters of each layer of the trained low-fidelity proxy model are extracted and saved as a parameter file. The machining parameter values ​​of the orthogonal experiment in step 4 are obtained in the parameter space by sampling at equal intervals, and the tool amplitude experimental value is the average value of the amplitude of multiple rotation cycles under stable cutting. The machining parameter values ​​for the orthogonal experiment are obtained in the parameter space by sampling at equal intervals. The specific implementation method for the tool amplitude experimental value being the average value of the amplitude of multiple rotation cycles under stable cutting is as follows: First, the tool vibration data is preprocessed using a low-pass filter with the cutoff frequency set to twice the tooth frequency. Then, the preprocessed tool vibration data is decomposed into data segments at equal intervals according to the rotation period. Next, the difference between the maximum and minimum values ​​in each data segment is calculated. Finally, the average of all differences is calculated as the experimental value of the tool amplitude. The multi-fidelity proxy model in step 5 is built on the basis of the low-fidelity proxy model and includes 3 hidden layers and 3 fully connected layers. The first hidden layer selects the ELU activation function and the output is normalized by the BatchNorm1d function, while the last two layers select the linear ReLU activation function. The first two fully connected layers are the outputs of the hidden layers of the low-fidelity proxy model, and the last layer is the output of the multi-fidelity proxy model.

2. The milling amplitude prediction method based on a multi-fidelity surrogate model according to claim 1, characterized in that, The training process of the multi-fidelity proxy model is as follows: The weights of each layer are initialized using a normal distribution, and the model loss function is set to the mean squared error loss function. When training the multi-fidelity proxy model, the Adamax optimization algorithm is used, and the learning rate is set to 0.

001. Then, the network parameters of the low-fidelity proxy model from step 3 are loaded. Finally, the dataset II is input, and the multi-fidelity proxy model is iteratively trained until the loss value stabilizes.

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