Prediction method for residual service life of cutter

Abstract

The invention discloses a method for predicting the remaining service life of a tool. The method comprises the steps that 1, multi-source sensor signal data are obtained and preprocessed; step 2, constructing a time-frequency feature set for the obtained signal data by applying S transformation; step 3, a Kolmogorov-Arnold attention distribution network (KA-AAN) is built, and the KA-AAN is used for attention distribution; 4, predicting the residual service life RUL of the milling cutter through the KAN; and 5, model training and performance verification are carried out. By introducing the KAN, the feature importance is dynamically allocated in the time-frequency domain, and the accuracy and robustness of prediction of the remaining service life of the tool are improved. Through combination of an attention mechanism and a learnable spline function, the model can capture a complex non-linear relationship in a cutter degradation process, the adaptive capacity under different processing conditions is enhanced, the over-fitting risk is reduced, and the generalization energy of the prediction model is improved.

Description

Technical Field

[0001] This invention relates to a method for predicting the remaining service life of cutting tools, belonging to the field of cutting tool wear monitoring technology. Background Technology

[0002] In modern machining, efficient and accurate online prediction of remaining tool life (RUL) is crucial for improving production efficiency, reducing machining costs, and ensuring machining quality. Tool wear is one of the main causes of machining defects, chatter, and reduced machining efficiency. During the cutting process, it is necessary to predict the remaining tool life (RUL) based on the tool wear and replace the tool accordingly. Traditional tool RUL prediction mainly relies on manual experience and mathematical formulas. This method often fails to replace the tool in a timely manner, reducing machining quality, or increases costs due to premature tool replacement, making it difficult to fully utilize the remaining tool life. With the development of sensor technology, data-driven tool RUL prediction methods have gradually become a research hotspot. In recent years, deep learning methods have made significant progress in the field of tool RUL prediction. For example, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have been widely used to extract features from sensor signals and predict tool RUL. However, tool degradation and machining conditions complicate feature extraction from monitoring data, making the nonlinear mapping of these features to RUL challenging.

[0003] For example, monitoring signals during machining (such as force, vibration, and acoustic emission) are affected by both tool degradation and machining conditions (such as feed rate and depth of cut), resulting in complex nonlinear relationships. Traditional methods struggle to effectively extract features, leading to difficulties in feature extraction. Secondly, when training data cannot cover all complex working conditions, the model is prone to overfitting, resulting in decreased prediction accuracy and poor generalization ability under different working conditions. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing technologies, this invention provides a method for predicting the remaining service life of cutting tools. This invention proposes the Kolmogorov-Arnold Attention Allocation Network (KA-AAN) for tool RUL prediction, thereby overcoming the limitations of existing methods in terms of feature universality and cross-condition prediction accuracy.

[0005] Technical solution: A method for predicting the remaining service life of a cutting tool, comprising the following steps:

[0006] Step 1: Acquire multi-source sensor signal data and perform preprocessing;

[0007] Step 2: Apply the S-transform to the signal data obtained in Step 1 to construct a time-frequency feature set;

[0008] Step 3: Construct the Kolmogorov-Arnold attention allocation network KA-AAN, including the attention feature extraction network AFEN and the Kolmogorov-Arnold network KAN;

[0009] Step 3.1: Construct the attention feature extraction network AFEN based on the time-frequency feature sets of all sensors obtained in Step 2, and generate the final attention feature g;

[0010] Step 3.2: Construction of the Kolmogorov-Arnold network (KAN);

[0011] Step 4: Input the attention feature g generated in Step 3.1 into the KAN constructed in Step 3.2 for nonlinear regression, and predict the remaining service life (RUL) of the milling cutter through KAN;

[0012] Step 5: Model training and performance validation.

[0013] In a preferred embodiment, a force sensor is used to collect force signals during milling, an acceleration sensor is used to collect vibration signals during milling, and an acoustic emission sensor is used to collect acoustic emission signals during milling. After acquiring the multi-source sensor signal data, the data is preprocessed.

[0014] In the preferred embodiment, step 2 specifically includes:

[0015] Given the complexity of the time and frequency domains during tool degradation, time-frequency features are used as input. The S-transform (ST) is applied to transform the original data to obtain the time-frequency features for network input. For the time-domain signal of the c-th sensor... Its one-dimensional continuous ST is defined as follows:

[0016] (1)

[0017] The inverse transform of ST is:

[0018] (2)

[0019] Where f represents frequency, It is the center point of the time window function, where t represents the time variable;

[0020] wavelet function The normalization condition must be met:

[0021] (3)

[0022] Gaussian window function The definition of is:

[0023] (4)

[0024] According to the above definition, u c The ST of (t) is defined as:

[0025] (5)

[0026] The formulas for the discrete ST and its time-frequency characteristic complex matrix are as follows:

[0027] (6)

[0028] (7)

[0029] In formulas (6) and (7), k represents the time index, indicating that the current processing is the kth time window; j is the imaginary unit, n is the Fourier frequency component, N is the number of sampling points, and T is the sampling interval.

[0030] Based on the above formula, the window function of ST has significant adaptive characteristics, and its variation amplitude decreases as the frequency increases; at this time, the c-th... The amplitude of the time-frequency characteristic complex matrix obtained after discretizing the one-dimensional data of the sensor using ST is denoted as... And use it as the input to KA-AAN.

[0031] Preferably, step 3.1 specifically includes:

[0032] Step 3.1.1: Stack the time-frequency feature matrices of all the sensors obtained in Step 2 to form a three-dimensional time-frequency feature matrix, and perform feature embedding on this stacked matrix;

[0033] Step 3.1.2: Perform a multi-head attention mechanism on the feature matrix obtained in Step 3.1.1 after feature embedding;

[0034] Step 3.1.3: Concatenate and normalize the calculation results of all h attention heads in Step 3.1.2 to generate a single-layer attention output;

[0035] Step 3.1.4: Use the single-layer attention output obtained in step 3.1.3 as the input of the next layer KA-attention module, repeat the operations of steps 3.1.2 and 3.1.3, and cascade M KA-attention modules to extract deep attention features;

[0036] Step 3.1.5: Concatenate the outputs of the M KA-attention modules obtained in step 3.1.4 to generate the final attention feature g.

[0037] In the preferred embodiment, step 3.1.1 specifically comprises:

[0038] The c-th The time-frequency characteristic complex matrix of the sensor after ST processing is defined as X. c The time-frequency feature matrices of all sensors are stacked to form a three-dimensional time-frequency feature matrix: ; where X c The dimension is (F, R), where F represents the number of frequency bins and R represents the time step; feature embedding maps the original data into a fixed-size feature vector for subsequent attention processing and computation:

[0039] (8)

[0040] In formula (8), This is the feature matrix after feature embedding, where W0 is the weight matrix and B0 is the bias matrix, with dimensions as follows: , , , ,in The dimension of the embedded features.

[0041] In the preferred embodiment, step 3.1.2 specifically includes:

[0042] The attention distribution of a single attention head first requires calculating the Q, K, and V matrices:

[0043] (9)

[0044] In formula (9), It is the feature matrix after feature embedding. , and It is a mapping matrix with the following dimensions: , and ;

[0045] Attention is calculated as follows:

[0046] (10)

[0047] In formula (10), d k It is a hyperparameter that represents the dimension of the Key vector in the attention mechanism.

[0048] right A multi-head attention operation is performed, where the multi-head attention model linearly maps Q, K, and V through a projection matrix, then calculates h attention scores, and finally concatenates the results; the calculation of a single attention head is as follows:

[0049] (11)

[0050] In formula (11), , , and It refers to the query, key, and value in the q-th self-attention mechanism. , , and It is the mapping matrix of the q-th self-attention mechanism; the projection matrix projects Q, K, and V onto h different attention heads to learn different attention patterns, thereby improving model accuracy.

[0051] In the preferred embodiment, step 3.1.3 specifically comprises:

[0052] Concatenate the calculation results of all h attention heads in step 3.1.2:

[0053] (12)

[0054] In formula (12), Concat represents the matrix concatenation function. It is a linear mapping matrix used for splicing;

[0055] To accelerate network convergence and improve generalization, layer normalization is applied to each sublayer:

[0056] (13)

[0057] In formula (13), x is the output of the layer normalization; x is the input of the layer normalization. and It is a scaling parameter; and These are the mean and standard deviation of u, respectively.

[0058] In a preferred embodiment, step 3.1.5 specifically comprises:

[0059] The outputs of M KA-attention modules are concatenated to form the attention features of the tool health status:

[0060] (14)

[0061] In formula (14), It is the feature matrix after feature embedding, and F represents the network consisting of M layers of KA-attention modules. This represents the internal parameters of the KA-attention module in layer M, and Concat represents the matrix concatenation function.

[0062] Preferably, step 3.2 specifically includes:

[0063] Any multivariate continuous function defined on a bounded field It is represented as a finite combination of single-variable continuous functions, supplemented by binary addition operations. Represented as:

[0064] (15)

[0065] In formula (15), the right side represents KAN, where L represents the number of layers, and n j Indicates the first The number of nodes in the layer It is the first Layer-specific univariate activation functions; each specific function form The differences between different KAN architectures are defined. Defined as a weighted combination of the basic function and the B-spline function:

[0066] (16)

[0067] Among them, basic functions spline functions The definition is as follows:

[0068] (17)

[0069] (18)

[0070] Let represent the i-th B-spline basis function of order k. In formula (18), , and All of these are trainable parameters;

[0071] No. Step spline curve Its mesh size is g, defined by the DeBoor-Cox recurrence relation:

[0072] (19)

[0073] in, The pre-activation value is ; The post-activation value is denoted as The activation value of the (l+1, j)th neuron is the sum of the activation values ​​after all inputs.

[0074] (20)

[0075] Represented in matrix form, it can be written as:

[0076] (twenty one)

[0077] in, This corresponds to the function matrix of the l-th layer of the KAN network; a general KAN network consists of L layers: given an input vector The output of KAN is:

[0078] (twenty two)

[0079] In formula (22), It is a series of learnable linear transformation matrices (weight matrices), from layer 0 to layer L-1, with each layer corresponding to a transformation.

[0080] In the preferred embodiment, step 4 specifically includes:

[0081] The attention feature g generated in step 3.1.5 is input into the KAN constructed in step 8 for nonlinear regression, as follows:

[0082] (twenty three)

[0083] In formula (23), KAN represents a nonlinear mapping network from the tool attention feature g to the tool RUL, where These are the internal parameters of KAN.

[0084] Beneficial Effects: This invention, by introducing a Kolmogorov-Arnold attention allocation network, dynamically allocates feature importance in the time-frequency domain, effectively improving the accuracy and robustness of tool life prediction. This invention can automatically extract key features from multi-source sensor data, avoiding increased costs or decreased machining quality caused by premature or delayed tool replacement. Through the combination of attention mechanisms and learnable spline functions, the model can better capture the complex nonlinear relationships in the tool degradation process, enhancing its adaptability under different machining conditions, reducing the risk of overfitting, and thus significantly improving the generalization performance of the prediction model. This helps to improve production efficiency, reduce machining costs, and ensure machining quality. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0086] Figure 1 Here are the method flowchart (a) and method framework diagram (b) of the present invention;

[0087] Figure 2 This is a flowchart of the Kolmogorov-Arnold attention allocation network data processing of the present invention;

[0088] Figure 3 This is a framework diagram of the KAN layer of the present invention;

[0089] Figure 4 The diagram shows the test platform (a) and sensor layout (b) of the present invention.

[0090] Figure 5 The image shows the wear measurement results for T01, T11, and T21 of this invention.

[0091] Figure 6 The following are S-transform results of some machining signals according to the present invention: Fy time-frequency distribution diagram (a) for the first milling operation, Fy time-frequency distribution diagram (b) for the 35th milling operation, and VS for the first milling operation. y Time-frequency distribution diagram (c), VS of the 35th milling cut y Time-frequency distribution diagram (d);

[0092] Figure 7 Figures showing the RUL estimation results using the proposed method and the comparison method under the same operating conditions of the present invention: Case 1(a), Case 2(b), Case 3(c);

[0093] Figure 8 Figures showing the RUL estimation results using the proposed method and comparative method under different operating conditions of the present invention: Case 4(a), Case 5(b), Case 6(c);

[0094] Figure 9 The following is a comparison chart of the predictive performance of the present invention: predictive performance under the same operating conditions (a) and predictive performance under different operating conditions (b). Detailed Implementation

[0095] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0096] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0097] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0098] like Figure 1 As shown in (a) and (b), a method for predicting the remaining service life of a cutting tool includes the following steps:

[0099] Step 1: Acquire and preprocess multi-source sensor signal data: Use a force sensor to collect force signals during milling, an acceleration sensor to collect vibration signals during milling, and an acoustic emission sensor to collect acoustic emission signals during milling. After acquiring the multi-source sensor signal data, preprocess the data.

[0100] Step 2: Apply the S-transform to the signal data obtained in Step 1 to construct a time-frequency feature set:

[0101] Given the complexity of the time and frequency domains during tool degradation, time-frequency features are used as input. The S-transform (ST) is applied to transform the original data to obtain the time-frequency features for network input. The S-transform combines the advantages of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT), enabling adaptive adjustment of the time-frequency resolution and overcoming the limitations of traditional methods. For the time-domain signal of the c-th sensor... Its one-dimensional continuous ST is defined as follows:

[0102] (1)

[0103] The inverse transform of ST is:

[0104] (2)

[0105] Where f represents frequency, It is the center point of the time window function, where t represents the time variable;

[0106] wavelet function The normalization condition must be met:

[0107] (3)

[0108] Gaussian window function The definition of is:

[0109] (4)

[0110] According to the above definition, u c The ST of (t) is defined as:

[0111] (5)

[0112] The formulas for the discrete ST and its time-frequency characteristic complex matrix are as follows:

[0113] (6)

[0114] (7)

[0115] In formulas (6) and (7), k represents the time index, indicating that the current processing is the kth time window; j is the imaginary unit, n is the Fourier frequency component, N is the number of sampling points, and T is the sampling interval.

[0116] Based on the above formula, the window function of ST has significant adaptive characteristics, and its variation amplitude decreases as the frequency increases; at this time, the c-th... The amplitude of the time-frequency characteristic complex matrix obtained after discretizing the one-dimensional data of the sensor using ST is denoted as... And use it as the input to KA-AAN.

[0117] Step 3: Construct the Kolmogorov-Arnold attention allocation network KA-AAN, including the attention feature extraction network AFEN and the Kolmogorov-Arnold network KAN:

[0118] The structure of the Kolmogorov-Arnold attention allocation network KA-AAN is as follows: Figure 2 As shown, the attention feature extraction network consists of feature embeddings and M cascaded KA-attention modules. The attention feature extraction network extracts features and assigns importance to time-frequency features, thus obtaining attention features. Finally, the KAN network fuses these attention features to predict the tool's RUL.

[0119] Step 3.1: Construct the Attention Feature Extraction Network (AFEN) based on the time-frequency feature sets of all sensors obtained in Step 2, and generate the final attention feature g:

[0120] Step 3.1.1: Stack the time-frequency feature matrices of all sensors obtained in Step 2 to form a three-dimensional time-frequency feature matrix, and perform feature embedding on this stacked matrix:

[0121] The c-th The time-frequency characteristic complex matrix of the sensor after ST processing is defined as X. c The time-frequency feature matrices of all sensors are stacked to form a three-dimensional time-frequency feature matrix: ; where X c The dimension is (F, R), where F represents the number of frequency bins and R represents the time step; feature embedding maps the original data into a fixed-size feature vector for subsequent attention processing and computation:

[0122] (8)

[0123] In formula (8), This is the feature matrix after feature embedding, where W0 is the weight matrix and B0 is the bias matrix, with dimensions as follows: , , , ,in The dimension of the embedded features.

[0124] Step 3.1.2: For the feature matrix obtained in Step 3.1.1 after feature embedding, execute a multi-head attention mechanism in the KA-attention module:

[0125] The attention distribution of a single attention head first requires calculating the Q, K, and V matrices:

[0126] (9)

[0127] In formula (9), It is the feature matrix after feature embedding. , and It is a mapping matrix with the following dimensions: , and ;

[0128] Attention is calculated as follows:

[0129] (10)

[0130] In formula (10), d kIt is a hyperparameter that represents the dimension of the Key vector in the attention mechanism.

[0131] right A multi-head attention operation is performed, where the multi-head attention model linearly maps Q, K, and V through a projection matrix, then calculates h attention scores, and finally concatenates the results; the calculation of a single attention head is as follows:

[0132] (11)

[0133] In formula (11), , , and It refers to the query, key, and value in the q-th self-attention mechanism. , , and It is the mapping matrix of the q-th self-attention mechanism; the projection matrix projects Q, K, and V onto h different attention heads to learn different attention patterns, thereby improving model accuracy.

[0134] Step 3.1.3: Concatenate and normalize the calculation results of all h attention heads in Step 3.1.2 to generate a single-layer attention output:

[0135] Concatenate the calculation results of all h attention heads in step 3.1.2:

[0136] (12)

[0137] In formula (12), Concat represents the matrix concatenation function. It is a linear mapping matrix used for splicing;

[0138] To accelerate network convergence and improve generalization, layer normalization is applied to each sublayer:

[0139] (13)

[0140] In formula (13), x is the output of the layer normalization; x is the input of the layer normalization. and It is a scaling parameter; and These are the mean and standard deviation of u, respectively.

[0141] Step 3.1.4: Use the single-layer attention output obtained in step 3.1.3 as the input of the next layer KA-attention module, and repeat the operations of steps 3.1.2 and 3.1.3 to cascade M KA-attention modules to extract deep attention features. Through the cascaded stacking of M KA-attention modules, the network can extract deeper and more discriminative feature representations layer by layer, and dynamically allocate feature importance through the learnable activation function unique to KAN, and finally obtain key attention features that can simultaneously reflect the tool degradation state and machining conditions.

[0142] Step 3.1.5: Concatenate the outputs of the M KA-attention modules obtained in Step 3.1.4 to generate the final attention feature g:

[0143] The outputs of M KA-attention modules are concatenated to form the attention features of the tool health status:

[0144] (14)

[0145] In formula (14), It is the feature matrix after feature embedding, and F represents the network consisting of M layers of KA-attention modules. This represents the internal parameters of the KA-attention module in layer M, and Concat represents the matrix concatenation function.

[0146] Step 3.2: Construction of the Kolmogorov-Arnold network (KAN):

[0147] Any multivariate continuous function defined on a bounded field It is represented as a finite combination of single-variable continuous functions, supplemented by binary addition operations. Represented as:

[0148] (15)

[0149] In formula (15), the right side represents KAN, where L represents the number of layers, and n j Indicates the first The number of nodes in the layer It is the first Layer univariate activation functions; such as Figure 3 As shown, each specific function form The differences between different KAN architectures are defined. Defined as a weighted combination of the basic function and the B-spline function:

[0150] (16)

[0151] Among them, basic functions spline functions The definition is as follows:

[0152] (17)

[0153] (18)

[0154] Let represent the i-th B-spline basis function of order k. In formula (18), , and All of these are trainable parameters;

[0155] No. Step spline curve Its mesh size is g, defined by the DeBoor-Cox recurrence relation:

[0156] (19)

[0157] in, The pre-activation value is ; The post-activation value is denoted as The activation value of the (l+1, j)th neuron is the sum of the activation values ​​after all inputs.

[0158] (20)

[0159] Represented in matrix form, it can be written as:

[0160] (twenty one)

[0161] in, This corresponds to the function matrix of the l-th layer of the KAN network; a general KAN network consists of L layers: given an input vector The output of KAN is:

[0162] (twenty two)

[0163] In formula (22), It is a series of learnable linear transformation matrices (weight matrices), from layer 0 to layer L-1, with each layer corresponding to a transformation.

[0164] Step 4: Input the attention feature g generated in Step 3.1 into the KAN constructed in Step 3.2 for nonlinear regression, and predict the remaining service life (RUL) of the end mill using the KAN:

[0165] The attention feature g generated in step 3.1.5 is input into the KAN constructed in step 8 for nonlinear regression, as follows:

[0166] (twenty three)

[0167] In formula (23), KAN represents a nonlinear mapping network from the tool attention feature g to the tool RUL, where These are the internal parameters of KAN.

[0168] Step 5: Model training and performance validation;

[0169] Mean squared error (MSE) is used as the loss function, and the Adam optimizer is used to train and update all parameters of the entire KA-AAN model (including the attention feature extraction networks AFEN and KAN). The robustness and stability of the proposed method are verified by testing on experimental datasets under the same and different working conditions, demonstrating its high accuracy and strong adaptability.

[0170] In this embodiment, milling cutter life test data is used for verification:

[0171] The experiment was conducted on a DX650 CNC machine tool, and a schematic diagram of the test platform is shown below. Figure 4 As shown in (a), the platform is equipped with seven sensors: a triaxial accelerometer, three uniaxial accelerometers, a triaxial force sensor, a microphone, and an acoustic emission sensor, generating a total of 11 data channels. The sensor layout is as follows. Figure 4 (b) shows the specific types of milling cutters and the manufacturers and models of sensors listed in Table 1;

[0172]

[0173] The workpiece material and working conditions are set based on engineering practice, as detailed in Table 2. The tool wear and degradation trajectory is as follows: Figure 5 As shown, the wear width increases with the number of milling cycles. According to the tool failure criteria in ISO 8688-2, the tool is considered to have failed when the flank wear exceeds 300 μm, at which point the test is terminated. The ISO standard specifies the use of a 25 mm diameter end mill, while the tool used in this experiment has a diameter of 10 mm. The failure threshold for this test was set at 110 μm based on the phenomenon of red-hot and obvious sparks at the tool edge.

[0174]

[0175] The S-transform (ST) has proven effective in processing processed signals. On the one hand, the S-transform offers higher time resolution for high-frequency signals; on the other hand, it preserves lower amplitude and correlation for low-frequency signals. Figure 6(a), (b), and (c) compare the time-domain signals and their time-frequency representations of the Y-direction milling force (Fy) and the Y-axis spindle vibration signal (VSy) during the 1st and 35th milling cycles. The milling force is mainly concentrated in the low-frequency range with minimal noise. Its amplitude gradually increases with the number of milling cycles, and the red area in the time-frequency plot also strengthens accordingly. Conversely, the high-frequency component of the spindle vibration signal becomes sparser with increasing cycle count, while the amplitude of the low-frequency component gradually increases.

[0176] Seven sets of comparative experiments were conducted. The training and testing configurations are shown in Table 3, and the hyperparameter settings are shown in Table 4. The experiments aimed to evaluate the adaptability of the proposed method under the same and different operating conditions. Case 0 mainly tested the prediction accuracy of the proposed method under the assumption of sufficient known information. Cases 1, 2, and 3 focused on training and testing under the same conditions. Cases 4, 5, and 6 were used to evaluate the prediction accuracy and adaptability of the proposed network under unknown conditions.

[0177]

[0178]

[0179] To quantitatively and comprehensively evaluate model performance, mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and coefficient of determination (R²) are used as evaluation metrics. The formulas for each metric are as follows:

[0180] (twenty four)

[0181] (25)

[0182] (26)

[0183] (27)

[0184] in, This represents the c-th predicted value. This represents the c-th true value. This represents the sample mean.

[0185] To verify the effectiveness of the proposed method, it was compared with several commonly used and advanced prediction models, including Convolutional Neural Networks (CNN), CNN-Bi-LSTM, Spatiotemporal Attention (TSA), and CSBLSTM-TSAM. In Case 0, using an 8:2 random training-test set split, the proposed method achieved a mean absolute percentage error (MAPE) of 8.01%, the best performance among all models. In Cases 1, 2, and 3 under the same conditions, the MAPE values ​​of CNN and CNN-Bi-LSTM were 19.47% and 30.28%, respectively. Bi-LSTM struggles to capture nonlinear patterns, affecting its prediction accuracy. TSA and CSBLSTM-TSAM showed stable performance, with TSA's accuracy slightly lower than CSBLSTM-TSAM. The proposed method significantly improves prediction accuracy, reducing RMSE and MAPE by 41.04% and 49.29% respectively compared to TSA; and by 27.57% and 29.76% respectively compared to CSBLSTM-TSAM. Figure 7 As shown in (a), (b) and (c), the proposed method can effectively capture tool degradation patterns under the same working conditions and with sufficient historical data, providing better RUL prediction accuracy.

[0186] Figure 8 The prediction results for cases 4, 5, and 6 under multiple scenarios are presented. In the MSE comparison, KA-AAN has the lowest MSE (2.9148), outperforming CNN (23.9993), CNN-Bi-LSTM (23.5929), TSA (10.0663), and CSBLSTM-TSAM (7.9647). This indicates that the proposed method has the smallest prediction bias. The proposed method also achieves the best results in R², MAPE, and RMSE metrics. Compared to CNN, RMSE is reduced by 3.8756, and MAPE is reduced by 38.71%. KA-AAN's average MAPE is approximately 20% lower than TSA and 18% lower than CSBLSTM-TSAM.

[0187] The remaining useful life (RUL) prediction results of the five models in Cases 4, 5, and 6 are as follows: Figure 8 As shown in (a), (b), and (c), the results demonstrate that KA-AAN can more effectively capture tool degradation patterns and has a significant advantage in RUL prediction. In contrast, CNN and CNN-Bi-LSTM exhibit larger errors and fluctuations in early predictions. TSA, CSBLSTM-TSAM, and the proposed method show prediction trends closer to the actual RUL. However, TSA shows bias in later predictions: the bias is close to 0 in Case 4, but deviates from the true value in Cases 5 and 6.

[0188] Figure 9(a) and (b) show the evaluation metrics of the five methods under the same and different operating conditions, respectively. The height of the bar charts shows that CNN and CNN-Bi-LSTM have significantly higher errors, while the bar charts for TSA and CSBLSTM-TSAM are similar in height, but the proposed method's bar chart is significantly lower, indicating that its error is smaller. Figure 9 In (a), the proposed method shows generally better MAPE, especially in Case 2, where the MAPE is only 4.01%, demonstrating a significant improvement. The proposed method has the lowest average MAPE (8.27%), outperforming other models. And... Figure 9 In (b), the proposed method still has the lowest MAPE (18.63%), and even though the error is large in Case 6, it is still better than other models.

[0189] It is worth noting that, under the same operating conditions, the R² of CNN, CNN-Bi-LSTM, TSA, and CSBLSTM-TSAM are only slightly lower than that of the proposed method, indicating that they still possess strong predictive capabilities. However, under different operating conditions, the R² of CNN, CNN-Bi-LSTM, and TSA decreases significantly by 20.5%, 14.9%, and 16.7%, respectively, while the decrease of CSBLSTM-TSAM is smaller, at only 6.1%, demonstrating better adaptability to different operating conditions. The proposed method shows an R² decrease of only 1.4% under different operating conditions, exhibiting the best stability and predictive performance. Overall, the proposed method maintains higher stability and superior performance under different operating conditions, especially in complex environments.

[0190] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0191] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the remaining service life of a cutting tool, characterized in that: Includes the following steps: Step 1: Acquire multi-source sensor signal data and perform preprocessing; Step 2: Apply the S-transform to the signal data obtained in Step 1 to construct a time-frequency feature set; Step 3: Construct the Kolmogorov-Arnold attention allocation network KA-AAN, including the attention feature extraction network AFEN and the Kolmogorov-Arnold network KAN; Step 3.1: Construct the attention feature extraction network AFEN based on the time-frequency feature sets of all sensors obtained in Step 2, and generate the final attention feature g; Step 3.2: Construction of the Kolmogorov-Arnold network (KAN); Step 4: Input the attention feature g generated in Step 3.1 into the KAN constructed in Step 3.2 for nonlinear regression, and predict the remaining service life (RUL) of the milling cutter through KAN; Step 5: Model training and performance validation.

2. The method for predicting the remaining service life of a cutting tool according to claim 1, characterized in that: Step 1 specifically involves: using a force sensor to collect force signals during milling, an acceleration sensor to collect vibration signals during milling, and an acoustic emission sensor to collect acoustic emission signals during milling. After acquiring the multi-source sensor signal data, the data is preprocessed.

3. The method for predicting the remaining service life of a cutting tool according to claim 1, characterized in that: Step 2 specifically involves: Given the complexity of the time and frequency domains during tool degradation, time-frequency features are used as input. The S-transform (ST) is applied to transform the original data to obtain the time-frequency features for network input. For the time-domain signal of the c-th sensor... Its one-dimensional continuous ST is defined as follows: (1) The inverse transform of ST is: (2) Where f represents frequency, It is the center point of the time window function, where t represents the time variable; wavelet function The normalization condition must be met: (3) Gaussian window function The definition of is: (4) According to the above definition, u c The ST of (t) is defined as: (5) The formulas for the discrete ST and its time-frequency characteristic complex matrix are as follows: (6) (7) In formulas (6) and (7), k represents the time index, indicating that the current processing is the kth time window; j is the imaginary unit, n is the Fourier frequency component, N is the number of sampling points, and T is the sampling interval. Based on the above formula, the window function of ST has significant adaptive characteristics, and its variation amplitude decreases as the frequency increases; at this time, the c-th... The amplitude of the time-frequency characteristic complex matrix obtained after discretizing the one-dimensional data of the sensor using ST is denoted as... And use it as the input to KA-AAN.

4. The method for predicting the remaining service life of a cutting tool according to claim 1, characterized in that: Step 3.1 specifically includes: Step 3.1.1: Stack the time-frequency feature matrices of all the sensors obtained in Step 2 to form a three-dimensional time-frequency feature matrix, and perform feature embedding on this stacked matrix; Step 3.1.2: Perform a multi-head attention mechanism on the feature matrix obtained in Step 3.1.1 after feature embedding; Step 3.1.3: Concatenate and normalize the calculation results of all h attention heads in Step 3.1.2 to generate a single-layer attention output; Step 3.1.4: Use the single-layer attention output obtained in step 3.1.3 as the input of the next layer KA-attention module, repeat the operations of steps 3.1.2 and 3.1.3, and cascade M KA-attention modules to extract deep attention features; Step 3.1.5: Concatenate the outputs of the M KA-attention modules obtained in step 3.1.4 to generate the final attention feature g.

5. The method for predicting the remaining service life of a cutting tool according to claim 4, characterized in that: Step 3.1.1 specifically includes: The c-th The time-frequency characteristic complex matrix of the sensor after ST processing is defined as X. c The time-frequency feature matrices of all sensors are stacked to form a three-dimensional time-frequency feature matrix: ; where X c The dimension is (F, R), where F represents the number of frequency bins and R represents the time step; feature embedding maps the original data into a fixed-size feature vector for subsequent attention processing and computation: (8) In formula (8), This is the feature matrix after feature embedding, where W0 is the weight matrix and B0 is the bias matrix, with dimensions as follows: , , , ,in The dimension of the embedded features.

6. The method for predicting the remaining service life of a cutting tool according to claim 5, characterized in that: Step 3.1.2 specifically includes: The attention distribution of a single attention head first requires calculating the Q, K, and V matrices: (9) In formula (9), It is the feature matrix after feature embedding. , and It is a mapping matrix with the following dimensions: , and ; Attention is calculated as follows: (10) In formula (10), d k It is a hyperparameter that represents the dimension of the Key vector in the attention mechanism; right A multi-head attention operation is performed, where the multi-head attention model linearly maps Q, K, and V through a projection matrix, then calculates h attention scores, and finally concatenates the results; the calculation of a single attention head is as follows: (11) In formula (11), , , and It refers to the query, key, and value in the q-th self-attention mechanism. , , and It is the mapping matrix of the q-th self-attention mechanism; the projection matrix projects Q, K, and V onto h different attention heads to learn different attention patterns, thereby improving model accuracy.

7. The method for predicting the remaining service life of a cutting tool according to claim 6, characterized in that: Step 3.1.3 specifically involves: Concatenate the calculation results of all h attention heads in step 3.1.2: (12) In formula (12), Concat represents the matrix concatenation function. It is a linear mapping matrix used for splicing; To accelerate network convergence and improve generalization, layer normalization is applied to each sublayer: (13) In formula (13), x is the output of the layer normalization; x is the input of the layer normalization. and It is a scaling parameter; and These are the mean and standard deviation of u, respectively.

8. The method for predicting the remaining service life of a cutting tool according to claim 7, characterized in that: Step 3.1.5 specifically involves: The outputs of M KA-attention modules are concatenated to form the attention features of the tool health status: (14) In formula (14), It is the feature matrix after feature embedding, and F represents the network consisting of M layers of KA-attention modules. This represents the internal parameters of the KA-attention module in layer M, and Concat represents the matrix concatenation function.

9. The method for predicting the remaining service life of a cutting tool according to claim 8, characterized in that: Step 3.2 specifically involves: Any multivariate continuous function defined on a bounded field It is represented as a finite combination of single-variable continuous functions, supplemented by binary addition operations. Represented as: (15) In formula (15), the right side represents KAN, where L represents the number of layers, and n j Indicates the first The number of nodes in the layer It is the first Layer-specific univariate activation functions; each specific function form The differences between different KAN architectures are defined. Defined as a weighted combination of the basic function and the B-spline function: (16) Among them, basic functions spline functions The definition is as follows: (17) (18) Let represent the i-th B-spline basis function of order k; in formula (18), , and All of these are trainable parameters; No. Step spline curve Its mesh size is g, defined by the DeBoor-Cox recurrence relation: (19) in, The pre-activation value is ; The post-activation value is denoted as The activation value of the (l+1, j)th neuron is the sum of the activation values ​​after all inputs. (20) Represented in matrix form, it can be written as: (21) in, This corresponds to the function matrix of the l-th layer of the KAN network; a general KAN network consists of L layers: given an input vector The output of KAN is: (22) In formula (22), It is a series of learnable linear transformation matrices (weight matrices), from layer 0 to layer L-1, with each layer corresponding to a transformation.

10. The method for predicting the remaining service life of a cutting tool according to claim 9, characterized in that: Step 4 specifically involves: The attention feature g generated in step 3.1.5 is input into the KAN constructed in step 8 for nonlinear regression, as follows: (23) In formula (23), KAN represents a nonlinear mapping network from the tool attention feature g to the tool RUL, where These are the internal parameters of KAN.

Images