Method for predicting residual stress of milled surface layer of high-temperature alloy based on multi-source signal

Abstract

The invention belongs to the technical field of precision milling processing, and discloses a high-temperature alloy milling surface layer residual stress prediction method based on a multi-source signal, and the method comprises the steps: obtaining residual stress data of a high-temperature alloy surface in a depth direction; a mathematical model of the high-temperature alloy surface layer residual stress gradient distribution curve is constructed, and the optimal value of model parameters is obtained through fitting; constructing a Gaussian process regression model, and training the Gaussian process regression model by taking the key features of the multi-source signals as input and the optimal value of the model parameters as theoretical output; inputting the key features of any group of multi-source signals into the trained Gaussian process regression model to obtain corresponding model parameters; according to the method, the key features of the multi-source signals are used as input, so that the gradient distribution of the residual stress on the surface layer of the workpiece is accurately predicted, the problem that the gradient distribution of the residual stress on the surface layer of the high-temperature alloy workpiece cannot be predicted in real time is solved, and possibility is provided for online monitoring of the residual stress on the surface layer of the high-temperature alloy workpiece.

Description

Technical Field

[0001] The invention belongs to the technical field of precision milling, and in particular relates to a method for predicting residual stress of a high-temperature alloy milling surface based on multi-source signals. Background Art

[0002] As the new generation of major aerospace equipment develops in the direction of large-scale and integrated structures, the application ratio of high-performance lightweight alloy materials such as titanium alloys and high-temperature alloys has increased significantly in the field of aviation manufacturing. Among them, GH4169G high-temperature alloy has become the core manufacturing material for key components such as thin-walled blades of aircraft engines due to its excellent mechanical properties, high-temperature resistance, oxidation resistance and corrosion resistance. However, during the milling process of this type of material, the processed surface will produce residual stress due to thermal coupling. The size and distribution of residual stress will directly affect the fatigue strength, dimensional accuracy and other key performance indicators of the high-temperature alloy workpiece, thereby threatening the service performance of the equipment. In order to ensure the performance requirements of aerospace devices, it has become an indispensable technical link in the manufacturing process to accurately predict the gradient distribution of residual stress on the surface of high-temperature alloy workpieces while maintaining the integrity of the high-temperature alloy workpieces.

[0003] At present, most prediction methods based on machine learning prediction models are used to characterize the gradient distribution of residual stress on the surface of high-temperature alloy workpieces. However, the prediction methods based on machine learning prediction models cannot reflect the dynamic changes of surface residual stress during the milling process of high-temperature alloy workpieces, and thus cannot predict the gradient distribution of surface residual stress of high-temperature alloy workpieces in real time. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting residual stress on the surface of high-temperature alloy milling based on multi-source signals, which takes the key features extracted from the multi-source signals as input, so as to accurately predict the gradient distribution of residual stress on the surface of high-temperature alloy workpieces, and provide the possibility for online monitoring of residual stress on the surface of high-temperature alloy workpieces.

[0005] The present invention adopts the following technical solutions: A method for predicting residual stress of surface layer of high temperature alloy milling based on multi-source signals comprises the following steps: Obtain residual stress data along the depth direction of the workpiece surface after milling of high-temperature alloy layer by layer; Constructing a mathematical model of the residual stress gradient distribution curve of the surface layer of the high-temperature alloy, inputting the residual stress data into the mathematical model, and fitting to obtain the optimal values ​​of the model parameters of the mathematical model; A Gaussian process regression model is constructed, and the key features of the multi-source signals are used as the input of the Gaussian process regression model. The optimal values ​​of the model parameters are used as the theoretical output of the Gaussian process regression model. The Gaussian process regression model is trained to obtain a trained Gaussian process regression model. The multi-source signals include cutting force signals, cutting vibration signals, cutting noise signals, and cutting temperature signals in the milling process of high-temperature alloys. The key features of any group of multi-source signals are input into the trained Gaussian process regression model to obtain the model parameters corresponding to the key features of any group of multi-source signals.

[0006] Furthermore, the key feature extraction process includes: Extract the time domain features and frequency domain features of multi-source signals respectively; Normalizing the time domain features and the frequency domain features to obtain normalized features; The normalized features are reduced in dimension to obtain the key features.

[0007] Furthermore, the mathematical model is constructed based on the exponentially decaying cosine function, which is expressed as: , In the formula, The depth from the workpiece surface is The residual stress at is the amplitude constant of the mathematical model, is the damping coefficient of the mathematical model, is the damping frequency of the mathematical model, is the phase angle of the mathematical model, and are all constants, among which, , , and are the model parameters to be optimized.

[0008] Furthermore, the residual stress data is input into the mathematical model, and the optimal values ​​of the model parameters of the mathematical model are obtained by fitting, including: Input the residual stress data into the mathematical model and initialize the model parameters; Initialize the firefly algorithm and perform fitting calculations on the model parameters to obtain the correlation coefficient; At the end of the Firefly algorithm N In the iterations, if the change in the correlation coefficient is less than , the fitting is successful and the current model parameters are selected as the optimal values ​​of the model parameters. Otherwise, the model parameters are updated and the fitting calculation is performed again.

[0009] Furthermore, the mean function used by the Gaussian process regression model is as follows: , In the formula, For the Group key feature vector, For the The mean of the group key eigenvectors, C is a constant.

[0010] Furthermore, the covariance function used by the Gaussian process regression model is an isotropic rational quadratic covariance function, as shown in the following formula: , In the formula, For the Group key feature vector, For the Group key feature vector, For the The key feature vector and The covariance matrix of the group's key eigenvectors, is the standard deviation of the key feature, is the shape parameter, is the characteristic length scale, For the The key feature vector and The Euclidean distance between the key feature vectors of a group.

[0012] The beneficial effects of the present invention are as follows: the present invention first fits the residual stress data by establishing a mathematical model of the residual stress gradient distribution curve of the surface layer of the high-temperature alloy to obtain the optimal values ​​of the model parameters, and then uses a Gaussian process regression model to construct the relationship between the key features of the multi-source signal and the optimal values ​​of the model parameters, thereby establishing a correlation relationship between the key features-the optimal values ​​of the model parameters-the residual stress gradient distribution curve of the workpiece surface. The method of the present invention can directly use the multi-source signals in the high-temperature alloy milling process to directly predict the gradient distribution of the residual stress on the surface layer of the high-temperature alloy, thereby achieving the purpose of online monitoring of the residual stress on the surface layer of the high-temperature alloy during the processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the method of the present invention; Figure 2 is a time domain diagram of the cutting force signal in the present invention; Figure 3 is a frequency domain diagram of the cutting force signal in the present invention; Figure 4 It is a schematic diagram of the principal component contribution rate and the principal component cumulative contribution rate in the present invention; Figure 5It is a schematic diagram of the fitting effect of the mathematical model in the present invention; Figure 6 It is a schematic diagram of the iterative process of optimizing the model parameters of the mathematical model in the present invention; Figure 7 It is a schematic diagram of the predicted curve of the surface residual stress distribution in the feed direction of the fifth set of data sets in the present invention; Figure 8 It is a schematic diagram of the predicted curve of the surface residual stress distribution in the vertical feed direction of the fifth set of data sets in the present invention; Fig. 9 It is a schematic diagram of the predicted curve of the surface residual stress distribution in the feed direction of the 18th data set in the present invention; Fig.10 It is a schematic diagram of the predicted curve of the surface residual stress distribution in the vertical feed direction of the 18th data set in the present invention; Fig.11 It is a schematic diagram of the prediction curve of the surface residual stress distribution in the feed direction of the 23rd data set in the present invention; Fig.12 It is a schematic diagram of the predicted curve of surface residual stress distribution in the vertical feed direction of the 23rd data set in the present invention. DETAILED DESCRIPTION

[0014] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0015] At present, most machine learning prediction models are used to characterize the gradient distribution of residual stress on the surface of high-temperature alloys. However, the input parameters of machine learning prediction models are mostly static process parameters, which cannot reflect the dynamic changes of surface residual stress during milling of high-temperature alloys, and thus cannot predict the gradient distribution of residual stress on the surface of high-temperature alloys in real time. The residual stress distribution generated during the cutting process is the main reason for the deformation and scrapping of thin-walled parts after processing. Therefore, in order to meet the needs of intelligent manufacturing, it is urgent to study the online prediction of surface residual stress distribution.

[0016] The present invention provides a method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals. Figure 1 As shown, the following steps are included: S110, obtaining residual stress data along the depth direction of the workpiece surface after high-temperature alloy milling layer by layer.

[0017] Firstly, a 3-factor 3-level full factorial experiment was designed, and a total of 27 groups of milling experimental schemes with different milling parameters were used to mill the workpiece, which was a high-temperature alloy workpiece. The multi-source signals monitored during the milling process were collected to obtain 27 groups of multi-source signals, including cutting force signals, cutting vibration signals, cutting noise signals, and cutting temperature signals during the milling process of high-temperature alloys.

[0018] Specifically: The cutting force signal is collected by Kistler 9257B force measuring platform, and the sampling frequency is set to 10000Hz. The cutting force signal is amplified by Kistler 5080 multi-channel charge amplifier to form cutting force data along the x-axis, y-axis and z-axis. The cutting vibration signal is collected by the acceleration sensor, and the sampling frequency is set to 25600Hz. The cutting noise signal is collected by the acoustic test microphone sensor, and the sampling frequency is set to 25600Hz. The cutting temperature signal is collected by the infrared thermal imager, and the temperature data is recorded every 0.2 seconds. Among them, the cutting force signal, cutting vibration signal, cutting noise signal and cutting temperature signal are all generated by the workpiece and the tool during the processing. Table 1 shows the processing parameter levels.

[0019] Table 1 Processing parameter levels

[0020] Secondly, the time domain features and frequency domain features of 27 groups of multi-source signals are extracted respectively, and the time domain features and frequency domain features of the 27 groups of multi-source signals are normalized and then reduced in dimension. Several key features are obtained for each group, and 10 key features are selected from the several key features to form a key feature set for each group, and a total of 27 key feature sets are obtained. Among them, Figure 2 It is the time domain diagram of the cutting force signal. In the figure, the horizontal axis is time and the vertical axis is the cutting force signal. Figure 3 It is the frequency domain diagram of the cutting force signal. In the figure, the horizontal axis is frequency and the vertical axis is energy.

[0021] Specifically: The multi-source signals collected by various sensors during the workpiece milling process are uniformly characterized and processed, and then the multi-source signals are preprocessed and feature extracted.

[0022] Filter multi-source signals. Use low-pass, high-pass or band-pass filters to filter cutting force signals, cutting vibration signals and cutting noise signals to improve signal stability; on this basis, use wavelet transform algorithm to perform noise reduction and detrending processing.

[0023] Feature extraction is performed on the multi-source signals after noise reduction and detrending. Time domain features and frequency domain features are obtained through time domain processing and frequency domain processing respectively. The time domain features include 13 time domain features, including maximum value, minimum value, root mean square value, average value, variance, peak-to-peak value, absolute average value, skewness value, kurtosis value, margin factor, waveform factor, pulse factor and peak factor; the frequency domain features include 5 frequency domain features, including centroid frequency, average frequency, root mean square frequency, frequency variance and band energy.

[0024] The extracted time domain features and frequency domain features are normalized to obtain normalized features. The present invention uses a maximum-minimum normalization method. The purpose of normalization is to convert data of different dimensions to the same dimension so that each signal feature can be compared and calculated at the same scale to improve the accuracy and stability of the prediction results.

[0025] The principal component analysis method is used to reduce the dimension of data and determine the top 10 key features. Too many features will cause feature data redundancy, resulting in a decrease in the accuracy of the mathematical model and failure to meet the prediction requirements. Since there is no significant correlation between these redundant features and the surface residual stress, they need to be removed. The present invention uses the principal component analysis method to reduce the dimension of the normalized features and construct new low-dimensional features. The purpose of the principal component analysis is to convert the data from the original feature space (high-dimensional space) to the new feature space (low-dimensional space). The new feature space is composed of a linear combination of the original features. The advantage is that it can automatically assign weights to the extracted feature set by analyzing the correlation between the features, thereby obtaining key features, so as to reduce the feature dimension, enhance the generalization ability of the mathematical model, simplify the complexity of the mathematical model, and ensure the value of the original information, more comprehensively characterize the intrinsic information of the data, thereby improving the prediction accuracy and prediction efficiency of the mathematical model. According to the standard of principal component analysis, when the cumulative contribution rate of each principal component exceeds 90%, these principal components can fully characterize all the information of the original features. It is found by calculation that when the 10th principal component is accumulated, the cumulative contribution rate exceeds 90%. Therefore, the first 10 principal components are determined as the key feature set for surface residual stress prediction. The principal component contribution rate and the principal component cumulative contribution rate in the present invention are as follows: Figure 4 shown.

[0026] Finally, the X-ray diffraction method was used, combined with the electrolytic polishing method to remove materials layer by layer, to measure the residual stress of the milled surface of the workpiece after milling and along the depth direction of the surface. A portable X-ray stress tester (DS-21P) was used to test the residual stress of the milled surface of the workpiece. Since the X-ray diffraction method can only measure the surface stress of the workpiece, it is necessary to use an electrolytic polishing instrument to gradually corrode the workpiece surface and measure the residual stress data along the depth direction of the workpiece processing surface, and 27 sets of residual stress data sets were obtained. The residual stress includes the residual stress in the feed direction and the residual stress in the perpendicular feed direction.

[0027] Specifically: The workpiece is corroded and polished along the depth direction of the workpiece processing surface. The polishing thickness is 5-20um each time. After each polishing, the residual stress is measured once using the X-ray diffraction method until the residual stress decays and tends to be stable.

[0028] S120, constructing a mathematical model of the residual stress gradient distribution curve of the surface layer of the high-temperature alloy, inputting the residual stress data into the mathematical model, and fitting to obtain the optimal values ​​of the model parameters of the mathematical model.

[0029] The 27 sets of residual stress data sets were input into the mathematical model in turn and fitted to obtain the optimal values ​​of the 27 sets of model parameters.

[0030] The fitting process is as follows: input the residual stress data into the mathematical model and initialize the model parameters; initialize the firefly algorithm and perform fitting calculations on the model parameters to obtain the correlation coefficients; at the end of the firefly algorithm N In the iterations, if the change in the correlation coefficient is less than , the fitting is successful, and the current model parameters are selected as the optimal values ​​of the model parameters. Otherwise, the model parameters are updated and the fitting calculation is performed again. N is the last several iterations of the firefly algorithm. N Take 50, is the threshold value of the correlation coefficient change value, in the present invention Take 0.01.

[0031] Specifically: By observing and analyzing the residual stress data measured in each group of experiments, it can be seen that the gradient distribution of the residual stress on the surface of the workpiece shows a trend of first decreasing, then increasing, and finally tending to the matrix stress. That is, as the depth of the workpiece processing surface continues to increase, the residual stress first gradually increases, then gradually decreases, and finally tends to the matrix stress. Therefore, the gradient distribution curve of the residual stress on the surface of the workpiece is spoon-shaped as a whole. Therefore, its distribution characteristics can be described by establishing a mathematical model of the residual stress gradient distribution curve on the surface of the high-temperature alloy. Traditional polynomial fitting needs to adjust the polynomial order when fitting different residual stress gradient distribution curves, and there are too many undetermined coefficients and they are not fixed. The exponential decay cosine function has fixed undetermined coefficients. Therefore, it is more suitable as a mathematical model to describe the residual stress gradient distribution curve on the surface of the high-temperature alloy. The mathematical model of the residual stress gradient distribution curve on the surface of the high-temperature alloy is shown in the following formula: , In the formula, The depth from the workpiece surface is The residual stress at is the amplitude constant of the mathematical model, is the damping coefficient of the mathematical model, is the damping frequency of the mathematical model, is the phase angle of the mathematical model, and are constants, =1000, =100, where , , and are the model parameters to be optimized.

[0032] Based on the obtained residual stress data, the mathematical model of the residual stress gradient distribution curve of the surface layer of the high-temperature alloy is used to fit the residual stress data. The fitting process is regarded as the optimization process of the model parameters, so that the fitted curve is closest to the surface residual stress gradient distribution of the workpiece after milling. At the same time, the firefly algorithm is selected to optimize the parameters of the mathematical model, and the correlation coefficient is used as the optimization objective function to obtain the optimal value of the model parameters.

[0033] Among them, for the model parameters to be optimized, the optimization space should cover all residual stress data. Therefore, by analyzing the measured residual stress data and combining the characteristics of the exponential decay cosine function, The value range is (0, 10], The value range of is [0, 1], The value range is (0, 10], The value range of is [0, 2π], then the correlation coefficient can be expressed as follows: , In the formula, R 2 is the correlation coefficient, is the fitted value of the exponentially decaying cosine function, is the residual stress test value, is the average value of residual stress test values.

[0034] When the firefly algorithm is used to solve the optimal values ​​of the model parameters, the parameters of the firefly algorithm are set as follows: the population size is set to 300, the number of iterations is set to 200, the light intensity absorption factor is set to 1, the maximum attraction constant is set to 1, and the position update constant is set to 0.2.

[0035] Figure 5 It is a schematic diagram of the fitting effect of the mathematical model in the present invention, Figure 6 This is a schematic diagram of the iterative process of model parameter optimization of the mathematical model in the present invention. It can be seen that the firefly algorithm has converged after about 50 iterations, and finally, the correlation coefficient is 0.986. The correlation coefficient in the feed direction is distributed between 88.3% and 99.8%, and the correlation coefficient in the vertical feed direction is distributed between 86.0% and 99.5%, indicating that the mathematical model based on the exponential decay cosine function has a high accuracy and can effectively characterize the surface residual stress gradient distribution of the workpiece after milling.

[0036] S130, constructing a Gaussian process regression model, taking the key features of the multi-source signals as the input of the Gaussian process regression model, taking the optimal values ​​of the model parameters as the theoretical output of the Gaussian process regression model, training the Gaussian process regression model, and obtaining a trained Gaussian process regression model; the multi-source signals include cutting force signals, cutting vibration signals, cutting noise signals, and cutting temperature signals in the high-temperature alloy milling process.

[0037] Among them, for the regression problem, Gaussian noise needs to be considered. is the standard deviation of the Gaussian noise signal.

[0038] The mean function used in the Gaussian process regression model is as follows: , In the formula, For the Group key feature vector, For the The mean of the group key eigenvectors, C is a constant.

[0039] The covariance function used by the Gaussian process regression model is an isotropic rational quadratic covariance function, as shown below: , In the formula, For the Group key feature vector, For the Group key feature vector, For the The key feature vector and The covariance matrix of the group's key eigenvectors, is the standard deviation of the key feature, is the shape parameter, is the characteristic length scale, For the The key feature vector and The Euclidean distance between the key feature vectors of a group.

[0040] The performance of the Gaussian process regression model is affected by the hyperparameters The influence of initializes the hyperparameters of the Gaussian process regression model, where c Initialized to 1, Set to 1, The value range of is (0, 2], is the standard deviation of the Gaussian noise signal, The value range of is [0.01,10], is the standard deviation of the key feature, The value range of is [0.01,10]. Then, the maximum likelihood estimation method is used to calculate the hyperparameters. Finally, the gradient descent algorithm is used to obtain the optimal hyperparameters.

[0041] Specifically: According to the same milling parameters, 27 groups of key feature sets and 27 groups of optimal values ​​of model parameters are matched to obtain 27 groups of data sets, each of which includes the key feature sets and the optimal values ​​of model parameters under the same milling parameters.

[0042] The 5th, 18th and 23rd data sets of the 27 data sets were randomly selected as validation sets, and the remaining 24 data sets were used as training sets. The key feature set of each data set in the training set was used as input, and the optimal values ​​of the model parameters were used as output. The Gaussian process regression model was trained to establish a mapping relationship between the key features and the optimal values ​​of the model parameters.

[0043] The key feature set of each data set in the validation set is used as the input of the trained Gaussian process regression model to predict the model parameters. The model parameters are input into the mathematical model. The surface residual stress distribution curve predicted by the fifth data set in the validation set and the experimental measurement results are shown in Figure 2. Figure 7 and Figure 8 As shown in the figure, the surface residual stress distribution curve predicted by the 18th data set in the validation set and the experimental measurement results are shown in Fig. 9 and Fig.10 As shown in the figure, the surface residual stress distribution curve predicted by the 23rd data set in the validation set and the experimental measurement results are shown in Fig.11 and Fig.12 As shown in the figure, it can be seen that the prediction method of the present invention can accurately predict the residual stress distribution on the surface of the high-temperature alloy.

[0044] As shown in Table 2, in the table, No. 5, No. 18 and No. 23 are validation sets, where No. 5 is the 5th set of data, No. 18 is the 18th set of data, and No. 23 is the 23rd set of data. σ represents the residual stress, σ x It represents the surface residual stress in the feeding direction, σ y represents the surface residual stress in the vertical feed direction, R 2 It represents the correlation coefficient. The highest correlation coefficient can reach 97.62%, the lowest correlation coefficient can reach 91.16%, and the average value is 94.39%.

[0045] Table 2 Correlation coefficients for prediction of residual stress gradient distribution in milling surface of high-temperature alloy

[0046] The isotropic rational quadratic covariance function used in the present invention introduces a shape parameter, which can regulate the multi-scale characteristics of the covariance function. In essence, the isotropic rational quadratic covariance function used in the present invention can be regarded as the superposition of multiple square exponential covariance functions of different scales. When , the isotropic rational quadratic covariance function can be degenerated into a squared exponential covariance function. Usually, The value range is (0, 2]. The isotropic rational quadratic covariance function adopted in the present invention can effectively balance the global and local characteristics, enhance the anti-interference ability of local fluctuations, and is suitable for modeling data with complex dynamic changes.

[0047] In order to predict the residual stress gradient distribution of the milled surface of high-temperature alloy, the present invention establishes a mapping relationship between key features and model parameters based on the Gaussian process regression model, thereby establishing a correlation relationship between key features, optimal values ​​of model parameters, and residual stress gradient distribution curves on the workpiece surface. The Gaussian process regression model is a generalization of the multivariate Gaussian distribution. Since the Gaussian process regression model is a quantitative modeling, its prediction accuracy is not affected by Gaussian noise. Therefore, the Gaussian process regression model has better prediction performance than other traditional machine learning models.

[0048] S140, inputting the key features of any group of multi-source signals into the trained Gaussian process regression model to obtain model parameters corresponding to the key features of any group of multi-source signals.

[0049] By inputting the model parameters corresponding to the key features of any set of multi-source signals into the mathematical model, the surface residual stress gradient distribution curve of the workpiece corresponding to the key features of any set of multi-source signals can be obtained.

[0050] In summary, the method for predicting residual stress gradient distribution on the surface of high-temperature alloys based on multi-source signals proposed in the present invention first fits the residual stress data by establishing a mathematical model of the residual stress gradient distribution curve on the surface of high-temperature alloys to obtain the optimal value of the model parameters, and then uses the Gaussian process regression model to construct the relationship between the key features of the multi-source signals and the optimal value of the model parameters, thereby establishing the correlation between the key features, the optimal value of the model parameters, and the residual stress gradient distribution curve on the surface of the workpiece, which provides a basis for online monitoring of the residual stress gradient distribution on the surface of the workpiece. Experimental verification shows that the prediction accuracy of the present invention is above 0.9, with the highest reaching 0.976, which can meet the monitoring requirements of the residual stress on the surface of high-temperature alloy workpieces in production and manufacturing. Compared with the prior art, the present invention improves the prediction accuracy of the residual stress on the surface of the workpiece; the average running time of the prediction process is 5 seconds, which meets the requirements of online monitoring, greatly reduces the prediction time of traditional residual stress prediction methods (such as finite element method), and improves efficiency. The residual stress distribution on the surface of the workpiece during machining is the main reason for the excessive deformation of the workpiece after machining. Since the present invention can predict the residual stress distribution on the surface of the workpiece during machining, when the surface residual stress exceeds the expected range, the process parameters can be changed in time to adjust the distribution of the residual stress, thereby avoiding excessive deformation of the workpiece after machining and causing the workpiece to be scrapped, saving machining costs, and providing a solution for monitoring the residual stress on the surface of high-temperature alloys using online data, making it possible to monitor the residual stress on the surface of high-temperature alloys online and meeting the needs of intelligent manufacturing.

Claims

1. A method for predicting residual stress of surface layer of high temperature alloy milling based on multi-source signals, characterized in that: The following steps are involved: Obtain residual stress data along the depth direction of the workpiece surface after milling of high-temperature alloy layer by layer; Constructing a mathematical model of a residual stress gradient distribution curve of a high-temperature alloy surface layer, inputting the residual stress data into the mathematical model, and fitting to obtain optimal values ​​of model parameters of the mathematical model; A Gaussian process regression model is constructed, key features of multi-source signals are used as inputs of the Gaussian process regression model, optimal values ​​of the model parameters are used as theoretical outputs of the Gaussian process regression model, and the Gaussian process regression model is trained to obtain a trained Gaussian process regression model; the multi-source signals include cutting force signals, cutting vibration signals, cutting noise signals, and cutting temperature signals in a high-temperature alloy milling process; The key features of any group of multi-source signals are input into the trained Gaussian process regression model to obtain the model parameters corresponding to the key features of any group of multi-source signals.

2. The method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals according to claim 1 is characterized in that: The key feature extraction process includes: Respectively extracting time domain features and frequency domain features of the multi-source signals; Normalizing the time domain features and the frequency domain features to obtain normalized features; The normalized features are reduced in dimension to obtain key features.

3. The method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals according to claim 2 is characterized in that: The mathematical model is constructed based on an exponentially decaying cosine function and is expressed as: ， In the formula, The depth from the workpiece surface is The residual stress at is the amplitude constant of the mathematical model, is the damping coefficient of the mathematical model, is the damping frequency of the mathematical model, is the phase angle of the mathematical model, and are all constants, among which, , , and are the model parameters to be optimized.

4. The method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals according to claim 3 is characterized in that: Inputting the residual stress data into the mathematical model and fitting to obtain the optimal values ​​of the model parameters of the mathematical model comprises: Inputting the residual stress data into the mathematical model and initializing the model parameters; Initialize the firefly algorithm and perform fitting calculation on the model parameters to obtain the correlation coefficient; At the end of the firefly algorithm N In the iterations, if the change in the correlation coefficient is less than , the fitting is successful and the current model parameters are selected as the optimal values ​​of the model parameters. Otherwise, the model parameters are updated and the fitting calculation is performed again.

5. The method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals according to claim 4 is characterized in that: The mean function used in the Gaussian process regression model is as follows: ， In the formula, For the Group key feature vector, For the The mean of the group key eigenvectors, C is a constant.

6. The method for predicting residual stress of high-temperature alloy surface during milling based on multi-source signals according to claim 5, characterized in that: The covariance function used in the Gaussian process regression model is an isotropic rational quadratic covariance function, as shown in the following formula: ， In the formula, For the Group key feature vector, For the Group key feature vector, For the The key feature vector and The covariance matrix of the group's key eigenvectors, is the standard deviation of the key feature, is the shape parameter, is the characteristic length scale, For the The key feature vector and The Euclidean distance between the key feature vectors of a group.

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