A method for predicting self-excited vibration of a roadway repair robot based on noise reduction empowerment space-time feature fusion

Abstract

This invention discloses a method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion. The method includes: acquiring raw vibration signals from multiple channels on the robotic arm; processing the multi-channel vibration signals using a frequency domain filtering signal reconstruction method to filter out high-frequency noise and achieve complete signal reconstruction after setting the frequency point to 0 in the frequency domain filtering; dividing the reconstructed multi-channel vibration signals into multiple samples, calculating the self-excited vibration intensity-time series for each sample over a period of time, and calibrating the samples accordingly; dividing the multiple samples into a training set and a test set at an 8:2 ratio; constructing a self-excited vibration prediction model based on spatial information fusion and temporal feature extraction; training the prediction model using the training set to establish a nonlinear mapping relationship between vibration features and self-excited vibration intensity; inputting the test set data into the trained self-excited vibration prediction model to verify model performance, and calculating and outputting the predicted self-excited vibration of the robotic arm in the near future.

Description

Technical Field

[0001] This invention belongs to the field of load prediction technology, and relates to a method for predicting the self-excited vibration of a roadway repair robot based on noise reduction and spatiotemporal feature fusion. Background Technology

[0002] Roadways are critical passageways in underground engineering projects, facilitating personnel movement, material transport, ventilation, drainage, and power supply. Their structural condition directly impacts the safety of production operations. However, during actual service, roadways are susceptible to structural damage such as roof falls due to geological changes and construction vibrations. Given the extremely high safety risks associated with manually performing roof fall repairs, the use of robots to replace manual labor in roadway roof fall repair has become an inevitable trend.

[0003] Deep underground tunnels are typically long and narrow with limited working space. Their great depth, high surrounding rock stress, high temperature, high humidity, and poor ventilation create extreme working environments. The tunnel walls have complex rock compositions with densely developed joints and fissures, widespread weak interlayers and soft-hard rock interfaces, and extremely uneven stress distribution. This results in significant heterogeneity and anisotropy in the surrounding rock, a key factor inducing self-excited vibrations. Tunnel repair robots are primarily used for rapid and precise milling repair of deformed areas such as floor bulges, side bulges, and roof fractures. During operation, the robotic arm first positions the milling head to the area to be repaired through multi-joint coordinated motion. Then, the milling head rotates at high speed to contact the rock wall, achieving material crushing and stripping through a combination of impact, compression, and cutting actions between the cutting teeth and the rock mass. In actual operation, during the initial contact stage, the milling head lightly cuts into the surface of the rock wall, mainly bearing the instantaneous impact load. After entering the steady-state cutting stage, as the cutting depth increases, the milling head continuously squeezes and breaks the rock mass, and the cutting load exhibits complex characteristics of periodic fluctuations and random impact superposition. To adapt to the working space constraints of narrow underground tunnels in deep mines, tunnel repair robots mostly adopt a lightweight, slender, and weakly rigid series cantilever structure design. The cutting load induces self-excited vibration, forming a positive feedback closed loop between the load and the robotic arm structure. The intensity of the self-excited vibration increases rapidly, seriously affecting the robot's normal repair operation.

[0004] During the operation of tunnel repair robots, severe broadband noise is generated due to multiple factors such as rock mass anisotropy, abrupt changes in cutting load, and transient release of surrounding rock stress. The vibration response of the robotic arm exhibits complex dynamic characteristics with strong non-stationarity, nonlinearity, and non-Gaussian distribution. Therefore, the acquired multi-channel vibration signals contain a large number of transient impacts, amplitude spikes, and fixed-frequency interference components, accompanied by data loss and distortion, zero-point drift, and high signal-to-noise ratio data quality issues. Conventional filtering techniques are insufficient to properly handle such severely degraded vibration signals, causing the effective self-excited vibration characteristics to be submerged by strong noise and distorted within the complex robotic arm structure of the tunnel repair robot. The prediction model cannot establish an accurate mapping relationship, seriously affecting the prediction accuracy and stability of the self-excited vibration of the tunnel repair robot.

[0005] Current signal preprocessing techniques can be divided into time-domain filtering and frequency-domain filtering. Time-domain filtering typically employs convolution calculations. This calculation method is simple and can effectively suppress noise for small-scale, simple signals with low sampling rates. However, it has the following drawbacks when processing complex signals:

[0006] (1) Limited filtering effect: Time-domain filtering has poor selectivity for frequency components and is difficult to effectively suppress noise at specific frequencies, which may lead to signal distortion; (2) Low computational efficiency: For large-scale data, time-domain filtering has high computational complexity and slow processing speed, which affects real-time monitoring capabilities; (3) Artifact problem: The use of window functions may introduce artifacts, affecting the accuracy of signal analysis.

[0007] Compared to time-domain filtering, frequency-domain filtering offers significant advantages such as precise selectivity, high processing efficiency, and intuitive spectral analysis. However, when reconstructing vibration signals after filtering, time-domain filtering, which uses convolution calculations, only requires deconvolution to recover the original signal. Frequency-domain filtering, on the other hand, performs multiplication calculations in the frequency domain. Furthermore, to limit specific frequency ranges, frequency-domain filters perform zero-taking operations, which may result in division by zero during the reconstruction of nodal vibration signals. This renders the reconstructed vibration signal process meaningless. Summary of the Invention

[0008] To address the aforementioned technical problems, the purpose of this invention is to provide a method for predicting the self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion.

[0009] This invention provides a method for predicting the self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion, comprising:

[0010] Step 1: Collect raw vibration signals from multiple channels on the robotic arm;

[0011] Step 2: Based on the frequency domain filtering signal reconstruction method, the multi-channel vibration signal is processed to filter out high-frequency noise and achieve complete reconstruction of the signal after the frequency point is set to 0 in the frequency domain filtering.

[0012] Step 3: Divide the reconstructed multi-channel vibration signal into multiple samples, calculate the self-excited vibration intensity-time series of each sample over a period of time, and use this to calibrate the samples. Divide the multiple samples into training set and test set in an 8:2 ratio.

[0013] Step 4: Construct a self-excited vibration prediction model based on spatial information fusion and temporal feature extraction, train the prediction model using the training set, and establish a nonlinear mapping relationship between vibration characteristics and self-excited vibration intensity.

[0014] Step 5: Input the test set data into the trained self-excited vibration prediction model, verify the model performance, and calculate and output the prediction results of the robot arm's self-excited vibration in the near future.

[0015] The self-excited vibration prediction method for a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion, as proposed in this invention, has the following beneficial effects:

[0016] (1) Solving the "division by zero" problem in frequency domain filtering, achieving accurate signal reconstruction. Combining the frequency domain filtering signal reconstruction principle with partial frequency zeroing and the principle of averaging multiple reconstructed signals, while retaining the efficient noise reduction capability of frequency domain filtering, it avoids problems such as numerical instability and distortion during signal reconstruction, ensuring that the signal on which subsequent feature extraction is based is complete, real, and accurate. Moreover, it retains the core features of the original signal, which can directly support applications such as machine learning and sparse measure extraction, providing high-quality data support for equipment life prediction and fault diagnosis.

[0017] (2) The proposed method has strong generalization ability, establishes a data-driven deep learning framework, adaptively learns the self-excited vibration characteristics in multi-source signals, does not overly rely on accurate physical models or prior knowledge of specific models, and enhances the potential adaptability of the method to different robot configurations and working conditions.

[0018] (3) It can effectively extract the self-excited vibration prediction features. The model accurately adapts to the nonlinear mapping relationship between the vibration features of key nodes and the future self-excited vibration intensity, ensuring the prediction accuracy and stability, and meeting the reliability requirements of the roadway repair robot operation.

[0019] (4) The model is lightweight and has low computational requirements. It allows the robot body to deploy a self-excited vibration prediction model that integrates a spatial information fusion module and a temporal feature extraction module through a lightweight design. It can adaptively learn the mapping characteristics between the self-excited vibration intensity and multi-source vibration signals and quickly output short-term self-excited vibration prediction results. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for predicting the self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion, according to the present invention. Detailed Implementation

[0021] like Figure 1 As shown, the present invention provides a method for predicting the self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion, comprising:

[0022] Step 1: Collect raw vibration signals from multiple channels on the robotic arm, specifically:

[0023] Three-dimensional vibration sensors were installed on the milling head housing near the main spindle bearing, the front support of the drive shaft, the rear support of the drive shaft, the robot forearm rotation joint, the robot upper arm pitch joint, and the robot chassis and arm connection base to collect vibration signals from 18 channels. , i represents the sensor serial number, and x, y, z represent the axial direction.

[0024] Step 2: Based on the frequency domain filtering signal reconstruction method, the multi-channel vibration signal is processed to filter out high-frequency noise, achieving complete reconstruction of the signal after setting the frequency point to 0 in the frequency domain filtering. Specifically:

[0025] Step 2.1: Input signal Mapping to the frequency domain using Fast Fourier Transform:

[0026]

[0027] Where f is the frequency and N is the input signal. The length of the signal is determined by the multi-channel vibration signal acquired in step 1.

[0028] Step 2.2: Design a frequency domain filter At low frequencies below 100Hz The frequency point is set to 0, and the frequency is filtered by a frequency domain filter. right Perform frequency domain filtering:

[0029]

[0030] Step 2.3: Construct the extended filter and the equivalent filter. First, for... and Performing inverse fast Fourier transform yields and ,set up ,in and They are and Let the length of be:

[0031]

[0032]

[0033] in, For extended filters, This is an equivalent filter.

[0034] Step 2.4: Reconstruction of the frequency-domain filtered signal with some frequencies set to zero. First, calculate:

[0035]

[0036] right Performing an inverse fast Fourier transform yields:

[0037]

[0038] In the formula, It is by Reconstruction , ,..., , of Reconstructed signals on each interval.

[0039] Step 2.5: Reconstruct the frequency-domain filtered signal by setting some frequencies to zero as described above, and obtain the reconstructed signal after frequency-domain filtering. Group Reconstructing the signal, for this The output is after the group reconstruction signal is accumulated:

[0040]

[0041] Performing a Fast Fourier Transform on both sides of the above equation yields:

[0042]

[0043] The derivation results show that the average solution of multiple reconstructed signals obtained from the reconstruction process of frequency domain filtered signals with some frequencies set to zero is actually the result obtained by the traditional fast Fourier transform. In other words, by combining the reconstruction principle of frequency domain filtered signals with some frequencies set to zero and the averaging principle of multiple reconstructed signals, the complete reconstruction of the signal after some frequency points are set to zero in the frequency domain filtering method can be achieved.

[0044] Step 3: Divide the reconstructed multi-channel vibration signal into multiple samples, calculate the self-excited vibration intensity-time series for each sample over a period of time, and use this to calibrate the samples. Divide the multiple samples into a training set and a test set in an 8:2 ratio, specifically:

[0045] The reconstructed multi-channel vibration signals output from step 2 are stitched together into a matrix X:

[0046]

[0047] In the above formula, i represents the sensor number of the multi-channel vibration signal source, and x, y, z represent the axial direction of the multi-channel vibration signal source. X is divided into multiple samples with a length of 1024. The self-excited vibration intensity magnitude sequence of length 32 after the last moment of each sample is calibrated. Data during periods without load, such as equipment start-up and shutdown, are removed. The dataset is randomly divided into training set and test set in a ratio of 8:2 for model training and performance verification.

[0048] Step 4: Construct a self-excited vibration prediction model based on spatial information fusion and temporal feature extraction. Train the prediction model using the training set and establish a nonlinear mapping relationship between vibration characteristics and self-excited vibration intensity.

[0049] The self-excited vibration prediction model includes a spatial information fusion module and a temporal feature extraction module. The spatial information fusion module is used to extract multi-scale contextual information and local detail features from the data and fuse them to obtain self-excited vibration intensity features. The temporal feature extraction module uses the self-excited vibration intensity prediction features as input and performs weighted fusion of forward and backward propagation hidden states through a learnable weight matrix. It fuses the bidirectional hidden states and outputs the final predicted value of self-excited vibration intensity.

[0050] The calculation process of the spatial information fusion module includes the following steps:

[0051] Step 4.1: The reconstructed multi-channel vibration signal, used as input data, is segmented into multiple heads for parallel and recursive processing.

[0052]

[0053] Where X is the input feature map; It is the main source of recursive processing. arrive These are auxiliary heads; each segmented head represents a vibration signal collected by a different sensor, which has been filtered and reconstructed. n is the number of recursion layers. This is a channel-sharing operation.

[0054] Step 4.2: The main head and the output of each recursive layer are processed by two convolutional kernels. The auxiliary head is projected through a 1x1 convolution before being fed into the layer operator to enhance feature diversity.

[0055]

[0056]

[0057]

[0058] In the formula, , These are the feature representations of the main head after different 1×1 convolution projections. It is the feature representation after the auxiliary head projection; It is the input of the nth layer, which comes from the output of the previous layer or the main head in the initial segmentation result.

[0059] Step 4.3: For each recursive operation layer, the projected features are fed into the layer operator, which consists of an amplifier and a discriminator.

[0060]

[0061]

[0062] Here, Amp represents the amplifier's output, and this process uses progressively larger convolution kernels. DWConv represents depthwise convolution of the input data. This indicates the size of the convolution kernel, which increases the receptive field as the number of layers increases. Multiply the preceding and following data element by element to highlight key regional features; Dis represents the output of the discriminator, which uses GELU as the activation function of the module. The discriminator introduces local detail information through parallel convolution kernels of different sizes, ensuring that the model is lightweight enough and improving the real-time performance of self-excited vibration prediction.

[0063] Step 4.4: Concatenate the outputs of the amplifier and discriminator along the channel dimension to form an output head with a dual-layer discriminative receptive field:

[0064]

[0065] in, This is a concatenation operation; after recursive calculation, the first level input... , Output After n recursions, the final output is... That is, the feature matrix output by the nth layer operator.

[0066] Step 4.5: For the output feature matrix, process it using a convolution kernel of length n+1 columns:

[0067]

[0068] in, The final output of the spatial information fusion module is the self-excited vibration intensity characteristic with dimensions (1, 1024).

[0069] The calculation process of the time-series feature extraction module includes the following steps:

[0070] Step 4.6: Initialize the forward propagation state at time 0 to zero. At the final moment T, the backpropagation state is zero. Based on the current input and the hidden states of the previous and next time steps, update the forward and backward propagation states at the current time step:

[0071]

[0072] In the formula, Self-excited vibration intensity characteristics Element; These represent the hidden states during forward and backward propagation, respectively. This represents the forward and backward input weight matrices. These represent the hidden state weight matrices for forward and backward propagation, respectively. , These represent the bias values ​​for forward and backward propagation, respectively.

[0073] Calculate the overall hidden state at time t:

[0074]

[0075] In the formula, This represents the final hidden state at the current moment. This is the overall bias.

[0076] Step 4.7: Calculate the weighted sum based on the input features and the final hidden state at the previous time step:

[0077]

[0078] In the formula, This represents the weighted sum at the current moment and is the input for the gating calculation; It is the overall hidden state of the previous moment, calculated from the previous step; These are the weight parameters determined through model training, which assign weights to historical states and current inputs. It is a weighted bias term, which is also determined through model training.

[0079] Step 4.8: Use the Sigmoid activation function to process the weighted sum and calculate the input gate state:

[0080]

[0081] In the formula, The input gate state is represented by a value of [0,1], which determines whether the historical state and the current input are retained or forgotten. It is the Sigmoid activation function, which compresses the input to [0,1] and introduces nonlinearity, enhancing the model's ability to fit self-excited vibration predictions.

[0082] Step 4.9: Calculate the candidate hidden state:

[0083]

[0084] In the formula, represents the candidate hidden state, which is a new undetermined state generated based on the current input and the historical state after gating; tanh represents the double tangent activation function, which compresses the input to the interval [-1,1] while adding nonlinearity; These are all parameters obtained from model training. The first two are weight parameters, and the last one is used to calculate the bias in the candidate hidden state.

[0085] Step 4.10: Calculate the weighted hidden state:

[0086]

[0087] In the formula, This part indicates the situation where newly generated data is included in the loop. This indicates the retention status of historical information.

[0088] Step 4.11: Map the final extracted hidden states to the output space:

[0089] The output layer performs a linear transformation and activation on the hidden state to generate the predicted output for the current time step:

[0090]

[0091] In the formula, This represents the final output sequence, i.e., the predicted value of self-excited vibration intensity; To output the weight matrix, This represents the Sigmoid function, which is suitable for predicting self-excited vibrations.

[0092] Step 5: Input the test set data into the trained self-excited vibration prediction model, verify the model performance, and calculate and output the prediction results of the robot arm's self-excited vibration in the near future.

[0093] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion, characterized in that, include: Step 1: Collect raw vibration signals from multiple channels on the robotic arm; Step 2: Based on the frequency domain filtering signal reconstruction method, the multi-channel vibration signal is processed to filter out high-frequency noise and achieve complete reconstruction of the signal after the frequency point is set to 0 in the frequency domain filtering. Step 3: Divide the reconstructed multi-channel vibration signal into multiple samples, calculate the self-excited vibration intensity-time series of each sample over a period of time, and use this to calibrate the samples. Divide the multiple samples into training set and test set in an 8:2 ratio. Step 4: Construct a self-excited vibration prediction model based on spatial information fusion and temporal feature extraction, train the prediction model using the training set, and establish a nonlinear mapping relationship between vibration characteristics and self-excited vibration intensity. Step 5: Input the test set data into the trained self-excited vibration prediction model, verify the model performance, and calculate and output the prediction results of the robot arm's self-excited vibration in the near future.

2. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion as described in claim 1, characterized in that, Step 1 specifically involves: Three-dimensional vibration sensors were installed on the milling head housing near the main spindle bearing, the front support of the drive shaft, the rear support of the drive shaft, the robot forearm rotation joint, the robot upper arm pitch joint, and the robot chassis and arm connection base to collect multi-channel vibration signals. , i represents the sensor serial number, and x, y, z represent the axial direction.

3. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion as described in claim 1, characterized in that, Step 2 specifically involves: Step 2.1: Input signal Mapping to the frequency domain using Fast Fourier Transform: Where f is the frequency and N is the input signal. The length of the signal is the multi-channel vibration signal acquired in step 1; Step 2.2: Design a frequency domain filter At low frequencies below 100Hz The frequency point at that location is set to 0, and then filtered by a frequency domain filter. right Perform frequency domain filtering: Step 2.3: Construct the extended filter and the equivalent filter. First, for... and Performing inverse fast Fourier transform yields and ,set up ,in and They are and Let the length of be: in, For extended filters, For equivalent filters; Step 2.4: Reconstruction of the frequency-domain filtered signal with some frequencies set to zero. First, calculate: right Performing an inverse fast Fourier transform yields: In the formula, It is by Reconstruction , ,..., , of Reconstructed signals over each interval; Step 2.5: Reconstruct the frequency-domain filtered signal by setting some frequencies to zero as described above, and obtain the reconstructed signal after frequency-domain filtering. Group Reconstructing the signal, for this The output is after the group reconstruction signal is accumulated: Performing a Fast Fourier Transform on both sides of the above equation yields: The derivation results show that the average solution of multiple reconstructed signals obtained from the reconstruction process of frequency domain filtered signals with some frequencies set to zero is actually the result obtained by the traditional fast Fourier transform. In other words, by combining the reconstruction principle of frequency domain filtered signals with some frequencies set to zero and the averaging principle of multiple reconstructed signals, the complete reconstruction of the signal after some frequency points are set to zero in the frequency domain filtering method can be achieved.

4. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion as described in claim 1, characterized in that, Step 3 specifically involves: The reconstructed multi-channel vibration signals output from step 2 are stitched together into a matrix X: In the above formula, i represents the sensor number of the multi-channel vibration signal source, and x, y, z represent the axial direction of the multi-channel vibration signal source. X is divided into multiple samples with a length of 1024. The self-excited vibration intensity magnitude sequence of length 32 after the last moment of each sample is calibrated. Data during periods without load, such as equipment start-up and shutdown, are removed. The dataset is randomly divided into training set and test set in a ratio of 8:2 for model training and performance verification.

5. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion as described in claim 4, characterized in that, The self-excited vibration prediction model in step 4 includes a spatial information fusion module and a temporal feature extraction module. The spatial information fusion module is used to extract multi-scale contextual information and local detail features from the data and fuse them to obtain self-excited vibration intensity features. The temporal feature extraction module uses the self-excited vibration intensity prediction features as input and performs weighted fusion of forward and backward propagation hidden states through a learnable weight matrix. It fuses the bidirectional hidden states and outputs the final self-excited vibration intensity prediction value.

6. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion according to claim 5, characterized in that, The calculation process of the spatial information fusion module includes the following steps: Step 4.1: The reconstructed multi-channel vibration signal, used as input data, is segmented into multiple heads for parallel and recursive processing. Where X is the input feature map; It is the main source of recursive processing. arrive These are auxiliary heads; each segmented head represents a vibration signal collected by a different sensor, which has been filtered and reconstructed. n is the number of recursion layers. This is a channel-sharing operation; Step 4.2: The main head and the output of each recursive layer are processed by two convolutional kernels. The auxiliary head is projected through a 1x1 convolution before being fed into the layer operator to enhance feature diversity. In the formula, , These are the feature representations of the main head after different 1×1 convolution projections. It is the feature representation after the auxiliary head projection; It is the input of the nth layer, which comes from the output of the previous layer or the main head in the initial segmentation result; Step 4.3: For each recursive operation layer, the projected features are fed into the layer operator, which consists of an amplifier and a discriminator. Here, Amp represents the amplifier's output, and this process uses progressively larger convolution kernels. DWConv represents depthwise convolution of the input data. This indicates the size of the convolution kernel, which increases the receptive field as the number of layers increases. Multiply the preceding and following data element by element to highlight the features of key regions; Dis represents the output of the discriminator, which uses GELU as the activation function of the module. The discriminator introduces local detail information through parallel convolutional kernels of different sizes, ensuring that the model is lightweight enough and improving the real-time performance of self-excited vibration prediction. Step 4.4: Concatenate the outputs of the amplifier and discriminator along the channel dimension to form an output head with a dual-layer discriminative receptive field: in, This is a concatenation operation; after recursive calculation, the first level input... , Output After n recursions, the final output is... , that is, the feature matrix output by the nth layer operator; Step 4.5: For the output feature matrix, process it using a convolution kernel of length n+1 columns: in, The final output of the spatial information fusion module is the self-excited vibration intensity characteristic with dimensions (1, 1024).

7. The method for predicting self-excited vibration of a roadway repair robot based on noise reduction-enabled spatiotemporal feature fusion according to claim 6, characterized in that, The calculation process of the time-series feature extraction module includes the following steps: Step 4.6: Initialize the forward propagation state at time 0 to zero. At the final moment T, the backpropagation state is zero. Based on the current input and the hidden states of the previous and next time steps, update the forward and backward propagation states at the current time step: In the formula, Self-excited vibration intensity characteristics Element; These represent the hidden states during forward and backward propagation, respectively. This represents the forward and backward input weight matrices. These represent the hidden state weight matrices for forward and backward propagation, respectively. , These represent the bias values ​​for forward and backward propagation, respectively. Calculate the overall hidden state at time t: In the formula, This represents the final hidden state at the current moment. This is the overall bias. Step 4.7: Calculate the weighted sum based on the input features and the final hidden state at the previous time step: In the formula, This represents the weighted sum at the current moment and is the input for the gating calculation; It is the overall hidden state of the previous moment, calculated from the previous step; These are the weight parameters determined through model training, which assign weights to historical states and current inputs. It is a weighted bias term, which is also determined through model training; Step 4.8: Use the Sigmoid activation function to process the weighted sum and calculate the input gate state: In the formula, The input gate state is represented by a value of [0,1], which determines whether the historical state and the current input are retained or forgotten. It is the Sigmoid activation function, which compresses the input to [0,1] and introduces nonlinearity to enhance the model's ability to fit self-excited vibration prediction; Step 4.9: Calculate the candidate hidden state: In the formula, represents the candidate hidden state, which is a new undetermined state generated based on the current input and the historical state after gating; tanh represents the double tangent activation function, which compresses the input to the interval [-1,1] while adding nonlinearity; These are all parameters obtained from model training. The first two are weight parameters, and the last one is used to calculate the bias in the candidate hidden state. Step 4.10: Calculate the weighted hidden state: In the formula, This part indicates the situation where newly generated data is included in the loop. Indicates the retention status of historical information; Step 4.11: Map the final extracted hidden states to the output space: The output layer performs a linear transformation and activation on the hidden state to generate the predicted output for the current time step: In the formula, This represents the final output sequence, i.e., the predicted value of self-excited vibration intensity; To output the weight matrix, This represents the Sigmoid function, which is suitable for predicting self-excited vibrations.

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