A milling chatter monitoring method based on manifold learning and dynamic graph neural network

Abstract

The present application belongs to the field of online monitoring of machining process, and provides a milling chatter monitoring method based on manifold learning and dynamic graph neural network. The cutting force signals and acoustic emission signals in the milling process are collected, synchronized and divided by sliding window to construct windowed multi-source signal samples; the manifold learning is used to obtain a manifold geometry target representing the evolution of the milling state, and the target is used as a constraint to screen chatter-sensitive key features in combination with mutual information and minimum redundancy maximum correlation criterion; further, the chatter-sensitive key features are mapped to graph nodes to construct a milling chatter dynamic graph; a milling chatter monitoring model including a graph attention encoding module, a graph-level readout module, a timing enhancement module and a classification module is established to extract cross-window chatter evolution enhancement features and realize real-time monitoring of milling chatter. The method can improve the early weak chatter feature recognition ability, monitoring accuracy and robustness.

Description

Technical Field

[0001] This invention belongs to the field of online monitoring of machining processes, and relates to a method for monitoring milling chatter based on manifold learning and dynamic graph neural networks. Background Technology

[0002] Large, thin-walled parts are widely used in aerospace and high-end equipment manufacturing, characterized by their large size, thin wall thickness, and low rigidity. During milling, the relative vibration between the tool and workpiece under the cyclic excitation of cutting forces and the effects of material removal easily lead to milling chatter, resulting in decreased surface quality, deterioration of machining texture, and in severe cases, tool breakage, workpiece scrapping, or even production safety accidents. Therefore, real-time online monitoring of milling chatter in thin-walled parts is of great significance. Existing online chatter monitoring methods typically collect signals such as vibration, cutting force, and acoustic emission, extract time-domain, frequency-domain, or time-frequency-domain features, and combine them with threshold discrimination, support vector machines, random forests, or neural networks to achieve state recognition. However, these methods rely on manual feature design, empirical thresholds, and model parameter settings. When faced with non-stationary signals and strong noise interference during the milling process of thin-walled parts, they are prone to problems such as unclear early chatter characteristics, insufficient state discrimination ability, and weak generalization ability.

[0003] In 2023, Ma Haifeng et al. proposed an online flutter monitoring method and system based on adaptive variational mode decomposition in patent CN115555920A. This method determines the flutter frequency band by obtaining the natural frequency of the processing system, extracts modal components of different frequency bands using adaptive variational mode decomposition, calculates the flutter mode energy ratio and scattering entropy, and combines it with support vector machines to achieve processing state identification. However, this method still relies primarily on flutter frequency band determination, signal decomposition, and artificial feature construction. The monitoring effect is easily affected by frequency band selection, decomposition parameters, and feature design, making it difficult to fully adapt to early flutter monitoring under complex working conditions. In 2025, Bo Qile et al. proposed an adaptive flutter monitoring method based on working mode identification and capsule networks in patent CN121018272A. This method extracts time-varying flutter fundamental frequency features through data-driven random subspace identification and combines it with capsule networks to achieve flutter state identification. However, this method has the problems of relatively concentrated feature sources and insufficient description of the synergistic change relationship of multi-domain features. It is difficult to explicitly characterize the coupling relationship between flutter-sensitive features that are dynamically reconstructed as the processing window progresses, which limits its sensitivity to early weak flutter features and its adaptability to cross-window state evolution under complex working conditions.

[0004] None of the above studies mentioned a method for monitoring milling chatter based on manifold learning and dynamic graph neural networks. Summary of the Invention

[0005] This invention primarily addresses the problems of existing milling chatter monitoring methods, such as heavy reliance on manual features, insufficient extraction of early weak chatter features, and inadequate representation of the dynamic coupling relationship of key chatter-sensitive features. It proposes a milling chatter monitoring method based on manifold learning and dynamic graph neural networks. This method constructs a manifold geometric target representing the evolution of the milling state by acquiring and windowing cutting force and acoustic emission signals, and uses this target as a constraint to select key chatter-sensitive features. Furthermore, it maps these key features to graph nodes, constructing a dynamic graph of milling chatter and establishing a milling chatter monitoring model to achieve real-time monitoring of milling chatter.

[0006] The technical solution of the present invention: A method for monitoring milling chatter based on manifold learning and dynamic graph neural networks includes the following steps: Step 1, Extraction and Screening of Key Flutter-Sensitive Features: Step 1.1: Collect cutting force signals and acoustic emission signals during the milling process to form multi-source sensing signals. Perform synchronization and sliding window segmentation on the multi-source sensing signals to construct windowed multi-source signal samples. Step 1.2: Extract candidate features from the windowed multi-source signal samples and standardize the candidate features; Step 1.3: Based on the windowed multi-source signal samples, perform manifold learning to obtain the manifold geometric target that characterizes the milling state evolution; using the manifold geometric target as a constraint, select the flutter-sensitive key features from the standardized candidate features to obtain the flutter-sensitive key features in the offline training stage.

[0007] Step 2, Construction of the dynamic diagram of milling chatter during the milling process: Each identified chatter-sensitive key feature is set as a graph node. The current value, first difference, rolling mean, and rolling standard deviation of the chatter-sensitive key feature corresponding to each graph node are extracted and combined into a four-dimensional node feature vector. The node feature vectors of each graph node are arranged in order to form a node feature matrix. Furthermore, the dynamic edge weights between graph nodes are calculated based on the dynamic correlation between each chatter-sensitive key feature within a continuous historical window to form a window-level dynamic adjacency matrix, thereby constructing a milling chatter dynamic graph.

[0008] Step 3, Construction and offline training of milling chatter monitoring model: A milling chatter monitoring model is constructed, comprising a graph attention encoding module, a graph-level readout module, a temporal enhancement module, and a classification module. The dynamic graph of milling chatter is input into the graph attention encoding module to encode the node feature vectors and the connection relationships between graph nodes, obtaining a node update representation matrix. This node update representation matrix is ​​then input into the graph-level readout module to obtain a graph-level representation. The graph-level representations of multiple consecutive windows are input into the temporal enhancement module to extract cross-window chatter evolution enhancement features. Finally, the classification module outputs the stable state probability and the chatter state probability. The milling chatter monitoring model is then trained offline using labeled training samples.

[0009] Step 4, Real-time monitoring of milling chatter: Cutting force signals and acoustic emission signals during the milling process are acquired in real time and processed according to step 1.1 to obtain real-time windowed multi-source signal samples. Based on the chatter-sensitive key features identified during the offline training phase, the corresponding real-time chatter-sensitive key features are extracted from the real-time windowed multi-source signal samples, and the real-time chatter-sensitive key features are standardized using the mean and standard deviation of the chatter-sensitive key features identified during the offline training phase. Further, a real-time milling chatter dynamic graph is constructed according to step 2, and the real-time milling chatter dynamic graph is input into the milling chatter monitoring model that has been trained offline. When the output chatter state probability is higher than the steady state probability, the current window is determined to be in a chatter state.

[0010] Furthermore, step 1.1 includes the following specific steps: A toolholder-type force sensor is clamped to the spindle end via the machine tool spindle toolholder interface, and an acoustic emission sensor is installed near the workpiece to collect cutting force and acoustic emission signals during the milling process, forming a multi-source sensing signal. The collected multi-source sensing signals are synchronized and segmented into a sliding window to obtain windowed multi-source signal samples. (1) in, For the first Windowed multi-source signal samples for each window For window number, Represents the real number field. Number of signal channels The number of sampling points within a single window. For the first The first window Windowed multi-source signals under one signal channel.

[0011] Step 1.2 includes the following specific steps: Based on the time-frequency characteristics of the signals during the milling process, the workpiece surface quality, and the vibration state at the machining site, windowed multi-source signal samples are labeled as either stable or fluttering states. The labeling results are then used as the true state labels for these windowed multi-source signal samples. The real state label corresponding to the windowed multi-source signal sample of each window is denoted as . , Assign a status category number, For a stable state, The true state label is used for offline training of the milling chatter monitoring model.

[0012] For the Candidate features are extracted from windowed multi-source signal samples. These candidate features are categorized into three types: time-domain, frequency-domain, and time-frequency-domain features. A candidate feature set is then constructed. The candidate features in the candidate feature set are then standardized using the following expression: (2) in, For the first The first window One candidate feature, For the offline training phase The mean of each candidate feature, For the offline training phase The standard deviation of each candidate feature For the first The standardized first window One candidate feature, Let be the number of candidate features. Therefore, a standardized candidate feature set is constructed: (3) Furthermore, the values ​​of the same candidate feature in all windows are aggregated to form the first... The feature sequence of candidate features across all windows This is used for subsequent screening of key flutter-sensitive features.

[0013] Furthermore, step 1.3 includes the following specific steps: Step 1.3.1: The first windowed multi-source signal sample constructed in Step 1.1... Cutting force signal within a window Perform phase space reconstruction: Let the embedding dimension of the phase space reconstruction be... The time delay is The reconstructed state vector of the phase space is then expressed as: (4) in, For the first Within the window, the first The state vector is obtained by reconstructing the phase space from the sampling points as the starting positions. , , The number of sampling points within a single window. For the first The cutting force signal within the window is at the... The amplitude at each sampling point.

[0014] Subsequently, using the state vectors obtained from the phase space reconstruction as graph nodes, the Euclidean distance between any two state vectors is calculated: (5) in, For the first State vector within a window With state vector The Euclidean distance between them For each state vector, select several state vectors with the smallest Euclidean distance to establish graph edges, determine the nearest neighbor connections, and thus construct the first... The state vector nearest neighbor graph corresponding to the nth window is generated. Similarity weights are assigned to state vectors with nearest neighbor connections in the state vector nearest neighbor graph. For the nth window... State vector in each window With state vector The similarity weight between the two is defined as: (6) in, State vector With state vector Similarity weights between them It is an exponential function. The kernel width controls the influence of the Euclidean distance between state vectors on the similarity weights. For state vectors without nearest neighbor connections, the similarity weights are reset to 0.

[0015] Construct the first [structure] based on similarity weights. The similarity weight matrix corresponding to each window And construct the degree matrix from the similarity weight matrix. And the Laplace matrix Among them, the degree matrix It is a diagonal matrix, the degree matrix The The diagonal element and the first The state vector obtained by reconstructing the phase space starting from each sampling point is... Correspondingly, it is represented as . No. The graph Laplace matrix corresponding to each window is represented as follows: Further solve the following generalized eigenvalue problem: (7) in, For eigenvalues, Let be the feature vector. Select several small non-zero eigenvalues ​​and their corresponding feature vectors to construct a low-dimensional embedding representation. Then, perform statistical aggregation on the low-dimensional embedding representation (including mean, standard deviation, maximum, and minimum value statistics) to obtain the ... Temporal manifold embedding of the cutting force signal in a window .

[0016] Step 1.3.2: Simultaneously, analyze the acoustic emission signal of each window in the windowed multi-source signal sample constructed in Step 1.1. Perform a short-time Fourier transform to obtain the local time-spectral representation; calculate the power spectrum based on the local time-spectral representation, and use a Mel filter bank to perform a weighted summation of the power spectrum to obtain the Mel filter bank energy; perform logarithmic compression on the Mel filter bank energy to obtain the th... The spectral feature vectors corresponding to each short-time analysis frame within each window: (8) in, For the first The first window The spectral feature vector corresponding to each short-time analysis frame For the first The short-time analysis frame in the first Energy under a Mel filter , This represents the number of Mel filters in the Mel filter bank. To prevent positive numbers from having zero values ​​in logarithmic operations.

[0017] The first The spectral feature vectors corresponding to all short-time analysis frames within a window are arranged in chronological order to form a spectral feature sequence: (9) in, For the first Number of short-time analysis frames within a window.

[0018] Furthermore, using the spectral feature vectors in the spectral feature sequence as graph nodes, the Euclidean distance between any two spectral feature vectors is calculated: (10) in, For the first The first window spectral feature vectors With the spectral feature vectors The Euclidean distance between them. Based on the Euclidean distance, for each spectral feature vector, select several spectral feature vectors with the smallest distance and connect them to obtain the graph edges, thus constructing the first... The spectral nearest neighbor graph corresponding to each window.

[0019] In the spectral nearest neighbor graph, the edge lengths between spectral feature vectors with graph edges are defined as the corresponding Euclidean distance. For any two spectral feature vectors, a path connecting them is searched along the spectral nearest neighbor graph, and the sum of the edge lengths of each path is calculated. The minimum path length is defined as the geodesic distance between them, denoted as... For the first The first window The spectral eigenvector and the first The geodesic distances between each pair of spectral feature vectors on the spectral nearest neighbor graph are used to construct the first spectral feature vector. The geodesic distance matrix corresponding to each window The Isomap method is used to perform low-dimensional mapping on the geodesic distance matrix to obtain the first... Frequency domain manifold embedding of the acoustic emission signal of a window .

[0020] Step 1.3.3, the first Temporal manifold embedding of the cutting force signal in a window Frequency domain manifold embedding of acoustic emission signals By splicing and merging, the first... The manifold geometric representation corresponding to each window: (11) in, For the first The manifold geometric representations corresponding to each window are arranged in window order to form a manifold geometric objective representing the evolution of the milling state from steady to chattering: (12) in, This represents the total number of windows.

[0021] manifold geometry target To constrain this process, the mutual information between the standardized candidate features and the manifold geometry is calculated to characterize the correlation between the candidate features and the milling state evolution process. Simultaneously, the mutual information between the candidate features and the selected features is calculated to characterize the redundancy among the candidate features. The minimum redundancy maximum correlation criterion is then used to screen chatter-sensitive key features. The scoring function is as follows: (13) in, For the first The score value of each candidate feature, Indicates mutual information, For the selected feature set, The redundancy penalty coefficient is... For the first The feature sequence of each selected feature across all windowed multi-source signal samples. For the first Redundancy between candidate features and selected features. According to the scoring function, select from all candidate features... A key feature sensitive to flutter.

[0022] Furthermore, step 2 includes the following specific steps: The flutter-sensitive key features obtained in step 1 are used as graph nodes, with each flutter-sensitive key feature corresponding to one graph node; for the first... Each window displays the current value of the flutter-sensitive key feature corresponding to each graph node. First-order difference rolling average and rolling standard deviation Combined into node feature vectors: (14) Among them, the rolling mean and rolling standard deviation are based on the most recent Calculate within a window. Arrange all node feature vectors in order to obtain the node feature matrix: (15) After obtaining the node feature matrix, the dynamic edge weights between graph nodes are further calculated based on the dynamic correlation of each flutter-sensitive key feature within a continuous historical window. First, a rolling historical sequence of flutter-sensitive key features is established for each graph node, denoted as the first... The graph node at the th ... The standardized current value of the key flutter sensitivity feature corresponding to each window is: Then the first The first window The flutter-sensitive key feature rolling history sequence corresponding to each graph node is as follows: (16) in, For the first The first window The scrolling history sequence of flutter-sensitive key features corresponding to each graph node The length of the scrolling history window. When the number of available history windows is less than At any given time, the existing continuous historical window is used to construct the rolling historical sequence of the flutter-sensitive key features. Then, the dynamic edge weights between graph nodes are calculated based on the dynamic correlation between the rolling historical sequences of the flutter-sensitive key features corresponding to any two graph nodes. (17) in, For the first The first window The graph node and the first Dynamic edge weights between nodes in a graph , This represents the Spearman rank correlation operator.

[0023] Construct the first based on the dynamic edge weights The original adjacency matrix of the windows: (18) The original adjacency matrix is ​​sparsified by retaining several large dynamic edge weights between each graph node and other graph nodes, and setting the remaining dynamic edge weights to 0, resulting in a sparse adjacency matrix. This sparse adjacency matrix is ​​then symmetricized and smoothed using an exponential moving average method to obtain the ... The smooth adjacency matrix corresponding to each window Adding self-connections to the smooth adjacency matrix yields: (19) in, for An identity matrix of order 1. For the matrix after adding a self-join... After symmetric normalization, the window-level dynamic adjacency matrix is ​​obtained: (20) in, for The corresponding adjacency matrix.

[0024] The first is composed of the node feature matrix and the window-level dynamic adjacency matrix. Milling chatter dynamics under one window The milling chatter dynamic diagram is used to characterize the evolution of key chatter-sensitive features and their dynamic coupling relationships as the milling process progresses.

[0025] Furthermore, step 3, which involves constructing a milling chatter monitoring model, includes the following specific steps: A milling chatter monitoring model was constructed, including a graph attention encoding module, a graph-level readout module, a time-series enhancement module, and a classification module.

[0026] Compare the milling chatter animation with the actual state labels As training samples, they are input into the graph attention encoding module. In the graph attention encoding module, according to the first... The window-level dynamic adjacency matrix corresponding to each window Define the connection relationships between graph nodes. When the window-level dynamic adjacency matrix... The Middle The graph node and the first The elements corresponding to each graph node At that time, it is determined that there is a connection between the two, and it will be connected with the first The node numbers of graph nodes that have connections are denoted as follows: , by all Constituting the first The first window The set of neighboring graph nodes of each graph node ;when At that time, it is determined that there is no connection between the two. For the first... Each graph node and its set of neighboring graph nodes. The first in For each graph node, calculate the unnormalized attention score based on the node feature vectors of both nodes: (twenty one) in, For the unnormalized attention score function, The learnable weight matrix in the graph attention encoding module, and The first The graph node and the first The feature representation of a graph node after linear transformation.

[0027] Subsequently, in the The first window The set of neighboring graph nodes of each graph node Internally, the unnormalized attention score is Softmax normalized: (twenty two) in, This indicates that the update is in progress. The first window When there are one graph node, the neighboring graph node is... For the The normalized attention weights of each graph node satisfy the following: .

[0028] The graph node update process is as follows: (twenty three) in, It is a non-linear activation function. For the first The first window The updated representation of each graph node.

[0029] The first The update representations of all graph nodes in each window are arranged in order, forming a node update representation matrix: (twenty four) Subsequently, the graph-level readout module pools the node update representation matrix to obtain the graph-level representation of the current window: (25) in, For the first The graph-level representation corresponding to each window This is a pooling operation. The graph-level representations of multiple consecutive windows are input into the time-series enhancement module to extract flutter evolution enhancement features across windows: (26) in, The number of consecutive windows input to the timing enhancement module. This is a timing enhancement module that includes a time attention mechanism, a gated loop unit, and a residual fusion structure. For the first Each window corresponds to a flutter evolution enhancement feature.

[0030] Finally, the flutter evolution enhancement features are input into the classification module, which outputs the stable state probability and the flutter state probability: (27) in, For the learnable weight matrix in the classification module, This is the bias vector in the classification module. Output a predicted probability vector for the milling chatter monitoring model. For the steady state probability, Let flutter state probability be , This is a normalized exponential function used to convert classification scores into a probability distribution.

[0031] Furthermore, in step 3, the milling chatter monitoring model is trained offline, and the cross-entropy loss function is used during the offline training process: (28) in, To predict the probability of milling chatter monitoring model.

[0032] The beneficial effects of this invention are: the method effectively improves the accuracy, robustness and real-time performance of milling chatter monitoring, enhances the adaptability to non-stationary machining processes and early weak chatter characteristics, and is a chatter monitoring method with good application prospects. Attached Figure Description

[0033] Figure 1 Flowchart for screening key features sensitive to flutter.

[0034] Figure 2 A flowchart is constructed to visualize the chatter dynamics during the milling process.

[0035] Figure 3 This is a schematic diagram of the milling chatter monitoring model.

[0036] Figure 4 This is a schematic diagram of a timing enhancement module that includes a time attention mechanism, a gated loop unit, and a residual fusion structure.

[0037] Figure 5 This is a schematic diagram of the multi-source sensor signals collected, where (a) is the cutting force signal and (b) is the acoustic emission signal.

[0038] Figure 6 The diagrams are visualizations of the stable and flutter states at different stages of the present invention. (a) is a visualization of the state distribution corresponding to the multi-source sensing signals, (b) is a visualization of the state distribution after screening the key flutter-sensitive features, (c) is a visualization of the state distribution corresponding to the output of the graph attention coding module, and (d) is a visualization of the state distribution corresponding to the output of the timing enhancement module. Detailed Implementation

[0039] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0040] Step 1, flutter-sensitive key feature extraction and screening, such as Figure 1 As shown: In this embodiment, the spindle speed for the milling experiment was set to 2000 r / min, the feed rate to 400 mm / min, the axial depth of cut to 1 mm, and the radial depth of cut to 0.3 mm. A carbide end mill with a diameter of 18 mm and 4 teeth was used. The workpiece material was a thin-walled 7075 aluminum alloy part. A tool holder-type force sensor was mounted on the spindle end via the machine tool spindle tool holder interface, and an acoustic emission sensor was installed near the workpiece to collect cutting force signals and acoustic emission signals during the milling process, forming a multi-source sensing signal, such as... Figure 5 As shown, in this embodiment, the sampling frequency of the cutting force signal is set to 2.5kHz, and the sampling frequency of the acoustic emission signal is set to 2.5kHz. The acquired multi-source sensor signals are synchronized and segmented using a sliding window to obtain windowed multi-source signal samples: (1) in, For the first Windowed multi-source signal samples for each window For window number, Represents the real number field. Number of signal channels The number of sampling points within a single window. For the first The first window Windowed multi-source signals under a single signal channel. Set the number of signal channels. =2, the number of sampling points in a single window =1000.

[0041] Based on the time-frequency characteristics of the signals during the milling process, the workpiece surface quality, and the vibration state at the machining site, windowed multi-source signal samples are labeled as either stable or fluttering states. The labeling results are then used as the true state labels for these windowed multi-source signal samples. The real state label corresponding to the windowed multi-source signal sample of each window is denoted as . , Assign a status category number, For a stable state, The true state label is used for offline training of the milling chatter monitoring model.

[0042] For the Candidate features are extracted from windowed multi-source signal samples. These candidate features are categorized into three types: time-domain, frequency-domain, and time-frequency-domain features. A candidate feature set is then constructed. The candidate features in the candidate feature set are then standardized using the following expression: (2) in, For the first The first window One candidate feature, For the offline training phase The mean of each candidate feature, For the offline training phase The standard deviation of each candidate feature For the first The standardized first window One candidate feature, The number of candidate features is set to [value]. =60, including 20 time-domain features, 20 frequency-domain features, and 20 time-frequency-domain features. Therefore, a standardized candidate feature set is constructed: (3) Furthermore, the values ​​of the same candidate feature in all windows are aggregated to form the first... The feature sequence of candidate features across all windows This is used for subsequent screening of key flutter-sensitive features.

[0043] For the constructed windowed multi-source signal samples, the first Cutting force signal within a window Perform phase space reconstruction: Let the embedding dimension of the phase space reconstruction be... The time delay is The reconstructed state vector of the phase space is then expressed as: (4) in, For the first Within the window, the first The state vector is obtained by reconstructing the phase space from the sampling points as the starting positions. , , The number of sampling points within a single window. For the first The cutting force signal within the window is at the... The amplitude at each sampling point is set in this embodiment, and the embedding dimension is set. =3, time delay =2.

[0044] Subsequently, using the state vectors obtained from the phase space reconstruction as graph nodes, the Euclidean distance between any two state vectors is calculated: (5) in, For the first State vector within a window With state vector The Euclidean distance between them For each state vector, select the 10 state vectors with the smallest Euclidean distance to establish graph edges, determine the nearest neighbor connections, and thus construct the first... The state vector nearest neighbor graph corresponding to the nth window is generated. Similarity weights are assigned to state vectors with nearest neighbor connections in the state vector nearest neighbor graph. For the nth window... State vector in each window With state vector The similarity weight between the two is defined as: (6) in, State vector With state vector Similarity weights between them It is an exponential function. The kernel width controls the influence of the Euclidean distance between state vectors on the similarity weights. In this embodiment, the kernel width of the similarity weights in the near-neighbor graph of state vectors is set to the median of the pairwise Euclidean distances between the state vectors reconstructed in the phase space. The similarity weights of state vectors without near-neighbor connections are reset to 0.

[0045] Construct the first [structure] based on similarity weights. The similarity weight matrix corresponding to each window And construct the degree matrix from the similarity weight matrix. And the Laplace matrix Among them, the degree matrix It is a diagonal matrix, the degree matrix The The diagonal element and the first The state vector obtained by reconstructing the phase space starting from each sampling point is... Correspondingly, it is represented as . No. The graph Laplace matrix corresponding to each window is represented as follows: Further solve the following generalized eigenvalue problem: (7) in, For eigenvalues, Let be the feature vector. Select the feature vectors corresponding to the three smallest non-zero feature values ​​to construct a low-dimensional embedding representation, and perform statistical aggregation on the low-dimensional embedding representation (including mean, standard deviation, maximum, and minimum value statistics) to obtain the _th _ ... Temporal manifold embedding of the cutting force signal in a window .

[0046] Simultaneously, the acoustic emission signal of each window in the constructed windowed multi-source signal sample... Perform a short-time Fourier transform to obtain the local time-spectral representation; calculate the power spectrum based on the local time-spectral representation, and use a Mel filter bank to perform a weighted summation of the power spectrum to obtain the Mel filter bank energy; perform logarithmic compression on the Mel filter bank energy to obtain the th... The spectral feature vectors corresponding to each short-time analysis frame within each window: (8) in, For the first The first window The spectral feature vector corresponding to each short-time analysis frame For the first The short-time analysis frame in the first Energy under a Mel filter , This represents the number of Mel filters in the Mel filter bank. To prevent zero-valued positive constants from occurring in logarithmic operations, in this embodiment, a Hamming window is used as the window function in the short-time Fourier transform of the acoustic emission signal. The window length is set to 256 points, the frame shift to 128 points, and the number of FFT points to 512 points. The number of Mel filters is set to 40, and the positive constant to prevent zero-valued positive constants from occurring in logarithmic operations is set to 1. 10 -6 .

[0047] The first The spectral feature vectors corresponding to all short-time analysis frames within a window are arranged in chronological order to form a spectral feature sequence: (9) in, For the first Number of short-time analysis frames within a window.

[0048] Furthermore, using the spectral feature vectors in the spectral feature sequence as graph nodes, the Euclidean distance between any two spectral feature vectors is calculated: (10) in, For the first The first window spectral feature vectors With the spectral feature vectors The Euclidean distance between them. Based on the Euclidean distance, for each spectral feature vector, select the 10 spectral feature vectors with the smallest distance and connect them to obtain the graph edges, thus constructing the first... The spectral nearest neighbor graph corresponding to each window.

[0049] In the spectral nearest neighbor graph, the edge lengths between spectral feature vectors with graph edges are defined as the corresponding Euclidean distance. For any two spectral feature vectors, a path connecting them is searched along the spectral nearest neighbor graph, and the sum of the edge lengths of each path is calculated. The minimum path length is defined as the geodesic distance between them, denoted as... For the first The first window The spectral eigenvector and the first The geodesic distances between each pair of spectral feature vectors on the spectral nearest neighbor graph are used to construct the first spectral feature vector. The geodesic distance matrix corresponding to each window The Isomap method is used to perform low-dimensional mapping on the geodesic distance matrix to obtain the first... Frequency domain manifold embedding of the acoustic emission signal of a window .

[0050] The first Temporal manifold embedding of the cutting force signal in a window Frequency domain manifold embedding of acoustic emission signals By splicing and merging, the first... The manifold geometric representation corresponding to each window: (11) in, For the first The manifold geometric representations corresponding to each window are arranged in window order to form a manifold geometric objective representing the evolution of the milling state from steady to chattering: (12) in, This represents the total number of windows.

[0051] manifold geometry target To constrain this process, the mutual information between the standardized candidate features and the manifold geometry is calculated to characterize the correlation between the candidate features and the milling state evolution process. Simultaneously, the mutual information between the candidate features and the selected features is calculated to characterize the redundancy among the candidate features. The minimum redundancy maximum correlation criterion is then used to screen chatter-sensitive key features. The scoring function is as follows: (13) in, For the first The score value of each candidate feature, Indicates mutual information, For the selected feature set, As a redundancy penalty coefficient, this embodiment sets =0.5. For the first The feature sequence of each selected feature across all windowed multi-source signal samples. For the first Redundancy between candidate features and selected features. According to the scoring function, select from all candidate features... A key feature sensitive to flutter, set =12.

[0052] Step 2, constructing a dynamic diagram of the milling process, such as Figure 2 As shown: The flutter-sensitive key features obtained in step 1 are used as graph nodes, with each flutter-sensitive key feature corresponding to one graph node; for the first... Each window displays the current value of the flutter-sensitive key feature corresponding to each graph node. First-order difference rolling average and rolling standard deviation Combined into node feature vectors: (14) Among them, the rolling mean and rolling standard deviation are based on the most recent Calculate per window, set =6. Arrange all node feature vectors in order to obtain the node feature matrix: (15) After obtaining the node feature matrix, the dynamic edge weights between graph nodes are further calculated based on the dynamic correlation of each flutter-sensitive key feature within a continuous historical window. First, a rolling historical sequence of flutter-sensitive key features is established for each graph node, denoted as the first... The graph node at the th ... The standardized current value of the key flutter sensitivity feature corresponding to each window is: Then the first The first window The flutter-sensitive key feature rolling history sequence corresponding to each graph node is as follows: (16) in, For the first The first window The scrolling history sequence of flutter-sensitive key features corresponding to each graph node Set the scroll history window length. =6, When the number of available history windows is less than At any given time, the existing continuous historical window is used to construct the rolling historical sequence of the flutter-sensitive key features. Then, the dynamic edge weights between graph nodes are calculated based on the dynamic correlation between the rolling historical sequences of the flutter-sensitive key features corresponding to any two graph nodes. (17) in, For the first The first window The graph node and the first Dynamic edge weights between nodes in a graph , This represents the Spearman rank correlation operator.

[0053] Construct the first based on the dynamic edge weights The original adjacency matrix of the windows: (18) The original adjacency matrix is ​​sparsified by retaining the four largest dynamic edge weights between each graph node and other graph nodes, and setting the remaining dynamic edge weights to 0, resulting in a sparse adjacency matrix. This sparse adjacency matrix is ​​then symmetricized and smoothed using an exponential moving average method to obtain the [missing information - likely a specific graph element]. The smooth adjacency matrix corresponding to each window In this embodiment, the smoothing coefficient is set to 0.8. Adding self-connections to the smoothed adjacency matrix yields: (19) in, for An identity matrix of order 1. For the matrix after adding a self-join... After symmetric normalization, the window-level dynamic adjacency matrix is ​​obtained: (20) in, for The corresponding adjacency matrix.

[0054] The first is composed of the node feature matrix and the window-level dynamic adjacency matrix. Milling chatter dynamics under one window The milling chatter dynamic diagram is used to characterize the evolution of key chatter-sensitive features and their dynamic coupling relationships as the milling process progresses.

[0055] Step 3, Construction and offline training of milling chatter monitoring model: A milling chatter monitoring model is constructed, including a graph attention encoding module, a graph-level readout module, a time-series enhancement module, and a classification module, such as... Figure 3 As shown.

[0056] Compare the milling chatter animation with the actual state labels As training samples, they are input into the graph attention encoding module. In this embodiment, there are 3000 training samples, including 1600 stable state samples and 1400 flutter state samples; these are divided into training, validation, and test sets in a 7:2:1 ratio, with 2100 training samples, 600 validation samples, and 300 test samples. In the graph attention encoding module, according to the... The window-level dynamic adjacency matrix corresponding to each window Define the connection relationships between graph nodes. When the window-level dynamic adjacency matrix... The Middle The graph node and the first The elements corresponding to each graph node At that time, it is determined that there is a connection between the two, and it will be connected with the first The node numbers of graph nodes that have connections are denoted as follows: , by all Constituting the first The first window The set of neighboring graph nodes of each graph node ;when At that time, it is determined that there is no connection between the two. For the first... Each graph node and its set of neighboring graph nodes. The first in For each graph node, calculate the unnormalized attention score based on the node feature vectors of both nodes: (twenty one) in, For the unnormalized attention score function, The learnable weight matrix in the graph attention encoding module, and The first The graph node and the first The feature representation of a graph node after linear transformation.

[0057] Subsequently, in the The first window The set of neighboring graph nodes of each graph node Internally, the unnormalized attention score is Softmax normalized: (twenty two) in, This indicates that the update is in progress. The first window When there are one graph node, the neighboring graph node is... For the The normalized attention weights of each graph node satisfy the following: .

[0058] The graph node update process is as follows: (twenty three) in, In this embodiment, the nonlinear activation function is the ELU activation function. For the first The first window The updated representation of each graph node.

[0059] The first The update representations of all graph nodes in each window are arranged in order, forming a node update representation matrix: (twenty four) In this embodiment, the graph attention encoding module sets up two graph attention layers. The first graph attention layer has an input dimension of 4, a hidden dimension of 128, and an output dimension of 12. 128; The second graph attention layer has an input dimension of 128, an output dimension of 64, and an output node update representation matrix dimension of 12. 64; The random deactivation layer ratio in the graph attention encoding module is set to 0.1. Subsequently, the graph-level readout module pools the node update representation matrix to obtain the graph-level representation of the current window: (25) in, For the first The graph-level representation corresponding to each window This is a pooling operation. In this embodiment, the graph-level representation dimension is 64. The graph-level representations of multiple consecutive windows are input into the time-series enhancement module to extract cross-window flutter evolution enhancement features: (26) in, The number of consecutive windows input to the timing enhancement module is set to 6; For the first The flutter evolution enhancement features corresponding to each window; For a timing enhancement module that includes a time attention mechanism, a gated loop unit, and a residual fusion structure, such as Figure 4As shown. In this embodiment, a temporal attention mechanism is used to calculate the temporal attention weights corresponding to the graph-level representations of multiple consecutive input windows, and these temporal attention weights are used for attention weighting calculation to obtain attention-weighted features. Subsequently, the attention-weighted features are sequentially input into a linear layer and a gated recurrent unit, and are regularized through a random deactivation layer of the gated recurrent unit. Simultaneously, the temporal attention weights are output as attention pooling features through an attention pooling layer, highlighting graph-level representation windows that contribute significantly to the current flutter state and suppressing graph-level representation windows that are weakly correlated with the current flutter state. Further, the processed attention-weighted features, attention pooling features, and the current window's graph-level representation are jointly input into a residual fusion structure, ultimately outputting the corresponding flutter evolution enhancement features. The temporal enhancement module has an input dimension of 6. 64. The hidden layer dimension of the time attention mechanism is set to 256, and the time attention weight dimension of the output of the time attention mechanism is 6. 1. The attention-weighted feature dimension is 6. 64, the attention pooling feature dimension is 6. 64. The hidden layer dimension of the gated loop unit is set to 256, and the output dimension of the gated loop unit is 1. 256, the random deactivation layer of the gated recurrent unit is set to 0.1, and the flutter evolution enhancement feature dimension is 1. 256.

[0060] Finally, the flutter evolution enhancement features are input into the classification module, which outputs the stable state probability and the flutter state probability: (27) in, For the learnable weight matrix in the classification module, This is the bias vector in the classification module. Output a predicted probability vector for the milling chatter monitoring model. For the steady state probability, Let flutter state probability be , This is a normalized exponential function used to convert classification scores into a probability distribution.

[0061] The cross-entropy loss function is used during offline training: (28) in, To predict the probability of milling chatter monitoring model.

[0062] The model training parameters were set as follows: batch size was 32, learning rate was 0.001, weight decay coefficient was 0.0005, number of training epochs was 40, the optimizer was AdamW, the learning rate scheduling strategy was StepLR, where the StepLR step size was 5, the decay coefficient was 0.98, the gradient clipping threshold was 3.0, and the number of early stopping patience epochs was 10. In this embodiment, the model achieved an accuracy of 98.3%, a precision of 97.8%, a recall of 98.9%, and an F1 score of 98.4% on the test set, indicating that the milling chatter monitoring model can effectively distinguish between stable and chattering states. After training, a milling chatter monitoring model for real-time monitoring was obtained.

[0063] To verify the ability of this invention to distinguish between steady-state and flutter states at different stages, principal component analysis (PCA) was performed on the multi-source sensor signals, the selected flutter-sensitive key features, the output of the graph attention coding module, and the output of the time-series enhancement module for dimensionality reduction. A two-dimensional visualization space was then constructed using the first principal component PCA1 and the second principal component PCA2, resulting in the following... Figure 6 The state distribution results are shown. Figure 6 This is a visual diagram illustrating the distribution of stable and flutter states at different stages of the present invention. Figure 6 (a) in the diagram is a visualization of the state distribution corresponding to the multi-source sensing signals; Figure 6 (b) in the diagram is a visualization of the state distribution after screening key flutter-sensitive features; Figure 6 (c) in the diagram is a visualization of the state distribution corresponding to the output of the graph attention encoding module; Figure 6 In the diagram, (d) is a visualization of the state distribution corresponding to the output of the timing enhancement module. Figure 6 As can be seen, with the gradual implementation of flutter-sensitive key feature screening, graph attention encoding, and temporal enhancement processing, the distribution differentiation between steady state and flutter state gradually increases, indicating that the present invention improves the separability between steady state and flutter state.

[0064] Step 4, Real-time monitoring of milling chatter: Cutting force signals and acoustic emission signals during the milling process are acquired in real time and processed according to step 1.1 to obtain real-time windowed multi-source signal samples. Based on the chatter-sensitive key features identified during the offline training phase, the corresponding real-time chatter-sensitive key features are extracted from the real-time windowed multi-source signal samples, and the real-time chatter-sensitive key features are standardized using the mean and standard deviation of the chatter-sensitive key features identified during the offline training phase. Further, a real-time milling chatter dynamic graph is constructed according to step 2, and the real-time milling chatter dynamic graph is input into the milling chatter monitoring model that has been trained offline. When the output chatter state probability is higher than the steady state probability, the current window is determined to be in a chatter state.

[0065] In this embodiment, the real-time sliding window segmentation length is set to 0.4s, and the window step size is set to 0.02s, meaning the model outputs monitoring results every 0.02s, ultimately achieving an accuracy rate of over 98%. The specific implementation examples described above further illustrate the purpose, technical solution, and beneficial effects of this invention. It should be understood that the above descriptions are merely specific implementation examples of this invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for monitoring milling chatter based on manifold learning and dynamic graph neural networks, characterized in that, Includes the following steps: Step 1, Extraction and Screening of Flutter-Sensitive Key Features: Step 1.1: Collect cutting force signals and acoustic emission signals during the milling process to form multi-source sensing signals. Perform synchronization and sliding window segmentation on the multi-source sensing signals to construct windowed multi-source signal samples. Step 1.2: Extract candidate features from the windowed multi-source signal samples and standardize the candidate features; Step 1.3: Based on the windowed multi-source signal samples, perform manifold learning to obtain the manifold geometric target characterizing the milling state evolution; using the manifold geometric target as a constraint, select the chatter-sensitive key features from the standardized candidate features to obtain the key features for offline training. Step 2, Construction of the dynamic diagram of milling chatter during the milling process: Each flutter-sensitive key feature identified through screening is set as a graph node; the current value, first difference, rolling mean, and rolling standard deviation of the flutter-sensitive key feature corresponding to each graph node are extracted and combined into a four-dimensional node feature vector; the node feature vectors of each graph node are arranged in order to form a node feature matrix. Furthermore, based on the dynamic correlation between each chatter-sensitive key feature within a continuous historical window, the dynamic edge weights between graph nodes are calculated to form a window-level dynamic adjacency matrix, thereby constructing a milling chatter dynamic graph. Step 3, Construction and offline training of milling chatter monitoring model: A milling chatter monitoring model is constructed, comprising a graph attention encoding module, a graph-level readout module, a temporal enhancement module, and a classification module. The dynamic graph of milling chatter is input into the graph attention encoding module to encode the node feature vectors and the connection relationships between graph nodes, and to obtain the node update representation matrix. The node update representation matrix is ​​input into the graph-level readout module to obtain the graph-level representation. The graph-level representations of multiple consecutive windows are input into the temporal enhancement module to extract the chatter evolution enhancement features across windows. Finally, the classification module outputs the stable state probability and the chatter state probability; the milling chatter monitoring model is trained offline using the labeled training samples; Step 4, Real-time monitoring of milling chatter: Real-time acquisition of cutting force signals and acoustic emission signals during the milling process, processing according to step 1.1, to obtain real-time windowed multi-source signal samples; Based on the key features sensitive to chatter identified during the offline training phase, the corresponding real-time chatter sensitive features are extracted from the real-time windowed multi-source signal samples. The real-time chatter sensitive features are then standardized using the mean and standard deviation of the key features sensitive to chatter identified during the offline training phase. Furthermore, a real-time milling chatter dynamic graph is constructed according to step 2, and the real-time milling chatter dynamic graph is input into the milling chatter monitoring model that has been trained offline. When the output chatter state probability is higher than the steady state probability, the current window is determined to be in a chatter state.

2. The milling chatter monitoring method based on manifold learning and dynamic graph neural networks as described in claim 1, characterized in that, Step 1.1 includes the following specific steps: A toolholder-type force sensor is clamped to the spindle end via the machine tool spindle toolholder interface, and an acoustic emission sensor is installed near the workpiece to collect cutting force signals and acoustic emission signals during the milling process, forming a multi-source sensing signal. The collected multi-source sensing signals are synchronized and segmented into a sliding window to obtain windowed multi-source signal samples. （1） in, For the first Windowed multi-source signal samples for each window For window number, Represents the real number field. Number of signal channels The number of sampling points within a single window. For the first The first window Windowed multi-source signals under one signal channel; Step 1.2 includes the following specific steps: Based on the time-frequency characteristics of the signals during the milling process, the workpiece surface quality, and the vibration state at the machining site, windowed multi-source signal samples are labeled as either stable or fluttering states. The labeling results are then used as the true state labels for these windowed multi-source signal samples. The real state label corresponding to the windowed multi-source signal sample of each window is denoted as . , Assign a status category number, For a stable state, The true state label is used for offline training of the subsequent milling chatter monitoring model, representing the chatter state. For the first Candidate features are extracted from windowed multi-source signal samples. These candidate features are categorized into three types: time-domain, frequency-domain, and time-frequency-domain features. A candidate feature set is then constructed. The candidate features in the candidate feature set are then standardized using the following expression: （2） in, For the first The first window One candidate feature, For the offline training phase The mean of each candidate feature, For the offline training phase The standard deviation of each candidate feature For the first The standardized first window One candidate feature, The number of candidate features is given; therefore, a standardized candidate feature set is constructed: （3） Furthermore, the values ​​of the same candidate feature in all windows are aggregated to form the first... The feature sequence of candidate features across all windows This is used for subsequent screening of key features sensitive to flutter.

3. The milling chatter monitoring method based on manifold learning and dynamic graph neural networks as described in claim 2, characterized in that, Step 1.3 includes the following specific steps: Step 1.3.1: The first windowed multi-source signal sample constructed in Step 1.1... Cutting force signal within a window Perform phase space reconstruction: Let the embedding dimension of the phase space reconstruction be... The time delay is The reconstructed state vector of the phase space is then expressed as: （4） in, For the first Within the window, the first The state vector is obtained by reconstructing the phase space from the sampling points as the starting positions. , , The number of sampling points within a single window. For the first The cutting force signal within the window is at the... The amplitude at each sampling point; Subsequently, using the state vectors obtained from the phase space reconstruction as graph nodes, the Euclidean distance between any two state vectors is calculated: （5） in, For the first State vector within a window With state vector The Euclidean distance between them For each state vector, select several state vectors with the smallest Euclidean distance to establish graph edges, determine the nearest neighbor connections, and thus construct the first... The state vector nearest neighbor graph corresponding to the nth window is used; and similarity weights are assigned to state vectors with nearest neighbor connections in the state vector nearest neighbor graph, for the nth window... State vector in each window With state vector The similarity weight between the two is defined as: （6） in, State vector With state vector Similarity weights between them It is an exponential function. The kernel width controls the influence of the Euclidean distance between state vectors on the similarity weights; for state vectors that do not have nearest neighbor connections, the similarity weights are reset to 0. Construct the first [structure] based on similarity weights. The similarity weight matrix corresponding to each window And construct the degree matrix from the similarity weight matrix. And the Laplace matrix Among them, the degree matrix It is a diagonal matrix, the degree matrix The The diagonal element and the first The state vector obtained by reconstructing the phase space starting from each sampling point is... Correspondingly, it is represented as ;No. The graph Laplace matrix corresponding to each window is represented as follows: Further solve the following generalized eigenvalue problem: （7） in, For eigenvalues, Let be the feature vector; select several small non-zero feature values ​​corresponding to the feature vectors to construct a low-dimensional embedding representation, and perform statistical aggregation on the low-dimensional embedding representation to obtain the th . Temporal manifold embedding of the cutting force signal in a window ; Step 1.3.2: Simultaneously, analyze the acoustic emission signal of each window in the windowed multi-source signal sample constructed in Step 1.

1. Perform a short-time Fourier transform to obtain the local time-spectral representation; calculate the power spectrum based on the local time-spectral representation, and use a Mel filter bank to perform a weighted summation of the power spectrum to obtain the Mel filter bank energy; perform logarithmic compression on the Mel filter bank energy to obtain the th... The spectral feature vectors corresponding to each short-time analysis frame within each window: （8） in, For the first The first window The spectral feature vector corresponding to each short-time analysis frame For the first The short-time analysis frame in the first Energy under a Mel filter , This represents the number of Mel filters in the Mel filter bank. To prevent positive constants from having zero values ​​in logarithmic operations; The first The spectral feature vectors corresponding to all short-time analysis frames within a window are arranged in chronological order to form a spectral feature sequence: （9） in, For the first Number of short-time analysis frames within a window; Furthermore, using the spectral feature vectors in the spectral feature sequence as graph nodes, the Euclidean distance between any two spectral feature vectors is calculated: （10） in, For the first The first window spectral feature vectors With the spectral feature vectors The Euclidean distance between them; based on the Euclidean distance, select several spectral feature vectors with the smallest distance to each spectral feature vector and connect them to obtain the graph edges, thus constructing the first... The spectral nearest neighbor graph corresponding to each window; In the spectral nearest neighbor graph, the edge lengths between spectral feature vectors with graph edges are defined as the corresponding Euclidean distances. For any two spectral feature vectors, a path connecting them is searched along the spectral nearest neighbor graph, and the sum of the edge lengths of each path is calculated. The minimum path length is defined as the geodesic distance between them. For the first The first window The spectral eigenvector and the ... The geodesic distances between each pair of spectral feature vectors on the spectral nearest neighbor graph; the geodesic distances between all pairwise spectral feature vectors constitute the first... The geodesic distance matrix corresponding to each window The Isomap method is used to perform low-dimensional mapping on the geodesic distance matrix to obtain the first... Frequency domain manifold embedding of the acoustic emission signal of a window ; Step 1.3.3, the first Temporal manifold embedding of the cutting force signal in a window Frequency domain manifold embedding of acoustic emission signals By splicing and merging, the first... The manifold geometric representation corresponding to each window: （11） in, For the first The manifold geometric representations corresponding to each window are arranged in window order to form a manifold geometric target representing the evolution of the milling state from stable to chattering: （12） in, Total number of windows; manifold geometry target To constrain this process, the mutual information between the standardized candidate features and the manifold geometry is calculated to characterize the correlation between the candidate features and the milling state evolution process. Simultaneously, the mutual information between the candidate features and the selected features is calculated to characterize the redundancy among the candidate features. The minimum redundancy maximum correlation criterion is then used to screen chatter-sensitive key features. The scoring function is as follows: （13） in, For the first The score value of each candidate feature, Indicates mutual information, For the selected feature set, The redundancy penalty coefficient is... For the first The feature sequence of each selected feature across all windowed multi-source signal samples. For the first Redundancy between candidate features and selected features; selecting from all candidate features according to the scoring function. A key feature sensitive to flutter.

4. The milling chatter monitoring method based on manifold learning and dynamic graph neural network as described in claim 3, characterized in that, Step 2 includes the following specific steps: The flutter-sensitive key features obtained in step 1 are used as graph nodes, with each flutter-sensitive key feature corresponding to one graph node; for the first... Each window displays the current value of the flutter-sensitive key feature corresponding to each graph node. First-order difference rolling average and rolling standard deviation Combined into node feature vectors: （14） Among them, the rolling mean and rolling standard deviation are based on the most recent Calculate within a window; arrange all node feature vectors in order to obtain the node feature matrix: （15） After obtaining the node feature matrix, the dynamic edge weights between graph nodes are further calculated based on the dynamic correlation of each flutter-sensitive key feature in a continuous historical window. First, a rolling historical sequence of flutter-sensitive key features is established for each graph node, assuming the th... The graph node at the th ... The standardized current value of the key flutter-sensitive features corresponding to each window is [value]. Then the first The first window The flutter-sensitive key feature rolling history sequence corresponding to each graph node is as follows: （16） in, For the first The first window The scrolling history sequence of flutter-sensitive key features corresponding to each graph node The length of the scrolling history window. When the number of available history windows is less than At any given time, the existing continuous historical window is used to construct the rolling historical sequence of the flutter-sensitive key features; then, the dynamic edge weights between graph nodes are calculated based on the dynamic correlation between the rolling historical sequences of the flutter-sensitive key features corresponding to any two graph nodes. （17） in, For the first The first window The graph node and the first Dynamic edge weights between nodes in a graph , This represents the Spearman rank correlation operator; Construct the first based on the dynamic edge weights The original adjacency matrix of the windows: （18） The original adjacency matrix is ​​sparsified by retaining several large dynamic edge weights between each graph node and other graph nodes, and setting the remaining dynamic edge weights to 0, resulting in a sparse adjacency matrix. This sparse adjacency matrix is ​​then symmetricized and smoothed using an exponential moving average method to obtain the ... The smooth adjacency matrix corresponding to each window Adding self-connections to the smooth adjacency matrix yields: （19） in, for An identity matrix of order 1; for the matrix after adding a self-join After symmetric normalization, the window-level dynamic adjacency matrix is ​​obtained: （20） in, for The corresponding adjacency matrix; The first is composed of the node feature matrix and the window-level dynamic adjacency matrix. Milling chatter dynamics under a window The milling chatter dynamic diagram is used to characterize the evolution of key chatter-sensitive features and their dynamic coupling relationships as the milling process progresses.

5. The milling chatter monitoring method based on manifold learning and dynamic graph neural network as described in claim 4, characterized in that, Step 3, which involves constructing a milling chatter monitoring model, includes the following specific steps: A milling chatter monitoring model was constructed, including a graph attention encoding module, a graph-level readout module, a time-series enhancement module, and a classification module; Compare the milling chatter animation with the actual state labels As training samples, they are input into the graph attention encoding module. In the graph attention encoding module, according to the first... The window-level dynamic adjacency matrix corresponding to each window Limiting the connection relationships between graph nodes; when the window-level dynamic adjacency matrix The Middle The graph node and the first The elements corresponding to each graph node At that time, it is determined that there is a connection between the two, and it will be connected with the first The node numbers of graph nodes that have connections are denoted as follows: , by all Constituting the first The first window The set of neighboring graph nodes of each graph node ;when When, it is determined that there is no connection between the two; for the first Each graph node and its set of neighboring graph nodes. The first in For each graph node, calculate the unnormalized attention score based on the node feature vectors of both nodes: （21） in, For the unnormalized attention score function, The learnable weight matrix in the graph attention encoding module, and The first The graph node and the first Feature representation of a graph node after linear transformation; Subsequently, in the The first window The set of neighboring graph nodes of each graph node Internally, the unnormalized attention score is Softmax normalized: （22） in, This indicates that the update is in the... The first window When there are one graph node, the neighboring graph node is... For the first The normalized attention weights of each graph node satisfy the following: ; The graph node update process is as follows: （23） in, It is a non-linear activation function. For the first The first window The updated representation of each graph node; The first The update representations of all graph nodes in each window are arranged in order, forming a node update representation matrix: （24） Subsequently, the graph-level readout module pools the node update representation matrix to obtain the graph-level representation of the current window: （25） in, For the first The graph-level representation corresponding to each window For pooling operations; input the graph-level representations of multiple consecutive windows into the time-series enhancement module to extract flutter evolution enhancement features across windows: （26） in, The number of consecutive windows input to the timing enhancement module. This is a timing enhancement module that includes a time attention mechanism, a gated loop unit, and a residual fusion structure. For the first The flutter evolution enhancement features corresponding to each window; Finally, the flutter evolution enhancement features are input into the classification module, which outputs the stable state probability and the flutter state probability: （27） in, For the learnable weight matrix in the classification module, This is the bias vector in the classification module. Output a predicted probability vector for the milling chatter monitoring model. For the steady state probability, Let flutter state probability be , This is a normalized exponential function used to convert classification scores into a probability distribution.

6. The milling chatter monitoring method based on manifold learning and dynamic graph neural networks as described in claim 5, characterized in that, In step 3, the milling chatter monitoring model is trained offline, and the cross-entropy loss function is used during the offline training process. （28） in, To predict the probability of milling chatter monitoring model.

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