Machine learning-based simulation and enhancement of vibration reduction effect of isolation trench

Abstract

This invention discloses a machine learning-based method for simulating and enhancing the vibration reduction effect of vibration isolation trenches, comprising the following steps: Step 1: Acquiring the time-domain vibration signal, geological parameters, and structural parameters of the vibration isolation trench from the disturbance source; Step 2: Performing continuous wavelet transform on the time-domain vibration signal using an improved Symlet wavelet function with edge window modulation to generate an energy spectrum; Step 3: Constructing a spectrum graph structure; Step 4: Constructing a frequency domain transfer graph neural network model and outputting frequency node features; Step 5: Introducing a time-varying spectrum absorption mechanism and outputting updated frequency node features; Step 6: Constructing a joint graph structure; Step 7: Introducing a frequency band residual shielding mechanism into the joint graph structure to iteratively evolve the structural parameters of the vibration isolation trench and obtain the optimal design parameters for the vibration isolation trench. This invention integrates the improved Symlet wavelet function and the frequency domain transfer graph neural network model to accurately simulate the vibration isolation response and intelligently optimize structural parameters.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and artificial intelligence, and in particular to a method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning. Background Technology

[0002] With increasing urban construction density and the widespread application of underground structures, foundation vibration reduction technology has become an important means of controlling the vibration response of ground structures. Among them, the foundation vibration isolation method based on vibration isolation trenches has been widely used in engineering practice due to its simple construction and stable effect. However, current design methods for vibration isolation trenches generally rely on empirical parameters or linear model simulations, making it difficult to accurately predict the multi-frequency disturbance response under complex geological conditions, resulting in the following problems:

[0003] Traditional analytical models and numerical simulation methods require simplification of geological parameters and vibration source characteristics, failing to fully consider the complex interactions between stratigraphic nonlinearity, frequency domain coupling, and structural parameters, resulting in limited simulation accuracy. Existing performance evaluations based on frequency response often focus on a single frequency point or narrow frequency band, lacking dynamic modeling and feedback optimization mechanisms across the entire frequency band for the target vibration reduction frequency band. In the parameter inversion stage, most methods employ optimization methods such as exhaustive search or gradient descent, which are computationally expensive, have slow convergence speeds, and are prone to getting trapped in local optima, making it difficult to achieve efficient search and global optimization of vibration isolation trench structural parameters. Furthermore, the lack of effective modeling methods for the time-varying characteristics and spectral evolution of disturbances makes it difficult for prediction results to adapt to the dynamic characteristics of multi-source vibration disturbances.

[0004] Therefore, how to provide a machine learning-based method for simulating and enhancing the vibration reduction effect of vibration isolation trenches is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] One objective of this invention is to propose a machine learning-based method for simulating and enhancing the vibration reduction effect of vibration isolation trenches. This invention integrates an improved Symlet wavelet function, frequency domain graph neural network modeling, and Bayesian optimization algorithm to construct a complete process from disturbance signal analysis to the inversion of structural parameters of the vibration isolation trench. It can achieve high-precision modeling of frequency domain response and frequency band targeted optimization under complex geological conditions. It has the advantages of high modeling accuracy, strong structural adaptability, and excellent optimization efficiency, effectively improving the simulation accuracy of vibration reduction effect of vibration isolation trenches and enhancing the ability of structural parameter design. It is suitable for vibration reduction design and effect evaluation in different scenarios.

[0006] A method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning, according to an embodiment of the present invention, includes the following steps:

[0007] Step 1: Collect time-domain vibration signals, geological parameters, and vibration isolation trench structural parameters of the disturbance source;

[0008] Step 2: The time-domain vibration signal is subjected to continuous wavelet transform using an improved Symlet wavelet function with edge window modulation to generate an energy spectrum, wherein the energy spectrum is plotted with frequency on the horizontal axis and time on the vertical axis.

[0009] Step 3: Divide the frequency axis of the energy spectrum into multiple non-overlapping frequency bands, construct a spectrum structure based on the frequency bands, where each frequency band corresponds to a frequency node, and establish edge connections and edge weights between frequency nodes based on the energy coupling relationship;

[0010] Step 4: Construct a frequency domain migration graph neural network model, generate intermediate feature vectors through frequency band attention graph convolutional layers, and introduce a modulation factor controlled by geological parameters into each frequency node to output frequency node features;

[0011] Step 5: Introduce a time-varying spectrum absorption mechanism to the frequency node features, and nonlinearly fuse the frequency response features at different time steps to output the updated frequency node features;

[0012] Step 6: Construct a joint graph structure based on the updated frequency node characteristics and vibration isolation trench structural parameters;

[0013] Step 7: Set the target vibration reduction frequency band, introduce a frequency band residual shielding mechanism into the joint diagram structure, and use a Bayesian optimization algorithm to iteratively evolve the structural parameters of the vibration isolation trench to obtain the optimal design parameters of the vibration isolation trench.

[0014] Optionally, the time-domain vibration signal includes the acceleration time series generated by ground motion, traffic load, and construction disturbance; the geological parameters include shear wave velocity and damping ratio; and the vibration isolation trench structural parameters include trench depth, trench width, and trench wall stiffness.

[0015] Optionally, the improved Symlet wavelet function with edge window modulation is used to perform continuous wavelet transform on the time-domain vibration signal, specifically as follows:

[0016] In the time domain of the original Symlet wavelet function, a start boundary interval and an end boundary interval are defined, and the length of each boundary interval is set to 10% to 20% of the total length of the time domain.

[0017] For any time point within the starting boundary interval, calculate the time difference between the current time point and the starting time point; for any time point within the ending boundary interval, calculate the time difference between the ending time point and the current time point; calculate the ratio of the time difference to the length of the corresponding boundary interval, and subtract the square of the ratio from 1 to generate a weighting coefficient;

[0018] Multiply the weighting coefficients by the value of the original Symlet wavelet function at the current time point to obtain the attenuated Symlet wavelet function value;

[0019] The starting boundary interval and the ending boundary interval are attenuated separately, and the attenuated starting boundary interval and the ending boundary interval are concatenated with the middle unmodulated segment of the original Symlet wavelet function to form a complete improved Symlet wavelet function.

[0020] The time-domain vibration signal is subjected to continuous wavelet transform using the improved Symlet wavelet function to generate an energy spectrum with frequency as the horizontal axis and time as the vertical axis.

[0021] Optionally, step three specifically includes:

[0022] The frequency axis of the energy spectrum is evenly segmented according to a preset bandwidth, and divided into multiple non-overlapping frequency bands, with each frequency band forming a frequency node;

[0023] For each frequency node, the energy distribution within the corresponding frequency band on the entire time axis is extracted from the energy spectrum. The energy distribution is the square of the magnitude of the frequency component of the frequency band at each moment after wavelet transform, and the energy distribution is sampled in time sequence to form an energy time series.

[0024] For any two frequency nodes, extract the corresponding energy time series, calculate the average of the two energy time series, calculate the product series of deviations from the average and sum them to obtain the deviation product sum; calculate the standard deviation of the two energy time series and multiply them to obtain the normalization factor; divide the deviation product sum by the normalization factor to obtain the Pearson correlation coefficient, which represents the linear consistency of the energy changes of the two frequency nodes.

[0025] The two energy time series are time-aligned and centered respectively. The data of each pair of corresponding positions in the centered series are multiplied and summed, and then divided by the length of the energy time series to obtain the cross covariance value, which reflects the degree of synchronization of energy fluctuations between frequency bands.

[0026] The Pearson correlation coefficient and the cross covariance value are linearly weighted with set weights to construct an energy coupling strength index between frequency nodes.

[0027] When the energy coupling strength index between any two frequency nodes exceeds a preset strength threshold, an edge connection is established between the corresponding two frequency nodes, and the energy coupling strength index is used as the edge weight.

[0028] A spectrum graph structure is constructed based on all frequency nodes, edge connections that meet the conditions, and their corresponding edge weights.

[0029] Optionally, the frequency domain transfer graph neural network model specifically includes a spectrogram input layer, a frequency band attention graph convolutional layer, a geomodulation fusion layer, and a frequency node feature output layer;

[0030] A feature vector is initialized for each frequency node in the spectrum graph structure. The feature vector consists of the maximum value, average value, and standard deviation of the energy time series corresponding to the frequency node, and is input into the spectrum graph input layer.

[0031] In the frequency band attention map convolutional layer, for each frequency node, the feature vectors of all neighboring frequency nodes are collected, the dot product between the feature vector of the current frequency node and the feature vectors of each neighboring frequency node is calculated as the similarity score, and the similarity score is normalized by the Softmax function to obtain the attention weight; the feature vectors of neighboring frequency nodes are weighted and aggregated using the attention weight to obtain the aggregated feature vector.

[0032] The aggregated feature vector is concatenated with the feature vector of the current frequency node, input into a linear mapping function and subjected to a nonlinear transformation by a ReLU activation function, and the intermediate feature vector of the current frequency node is output.

[0033] In the geological modulation fusion layer, a modulation factor is constructed based on geological parameters, and the intermediate feature vector is fused and modulated. The modulation factor is obtained by normalizing the ratio of the main frequency of the current frequency node to the shear wave velocity to between 0 and 1 and multiplying it with the damping ratio. The modulation factor is then multiplied into each feature component of the intermediate feature vector to generate frequency node features.

[0034] The frequency node feature output layer is used to output frequency node features.

[0035] Optionally, the time-varying spectral absorption mechanism is used to dynamically process the frequency node characteristics, specifically as follows:

[0036] For each frequency node, obtain the frequency node features at multiple consecutive time steps, initialize the frequency response feature sequence that changes with time, and each time step corresponds to a frequency response feature;

[0037] For each time step in the frequency response feature sequence, a time-weighted attenuation function is constructed to realize time-aware modulation. The time-weighted attenuation function is calculated by dividing the current time step number by the total number of time steps, and the attenuation factor is generated by subtracting the square of the calculated value from 1.

[0038] The attenuation factor is multiplied one by one with each dimension of the frequency response feature at the current time step to obtain the frequency response feature after time-weighted attenuation processing, forming a modulation response sequence that changes dynamically with time.

[0039] The modulation response sequence is input into a neural network structure for nonlinear fusion. The neural network structure is a gated recurrent unit with state memory capability, which dynamically controls the transmission relationship between historical response information and current input through a gating mechanism.

[0040] The output of the gated loop unit includes the final hidden state of historical evolution information, which serves as the updated frequency node feature.

[0041] Optionally, step six specifically includes:

[0042] Based on the updated frequency node features, the frequency nodes and edge connections in the spectrum graph structure are retained;

[0043] For each vibration isolation ditch structural parameter, a corresponding structural node is set, and all vibration isolation ditch structural parameters are normalized. The normalized vibration isolation ditch structural parameters are used as the feature vectors of each structural node.

[0044] Establish edge connections between each structural node and all frequency nodes;

[0045] For each pair of structural nodes and frequency nodes, the dot product of the feature vector of the structural node and the updated feature of the frequency node is calculated as the weight coefficient of the edge connection, forming an edge weight matrix.

[0046] A joint graph structure is constructed based on frequency nodes, structure nodes, and the edge weight matrix.

[0047] Optionally, the set target vibration reduction frequency band is achieved by introducing a frequency band residual shielding mechanism in the combined diagram structure, specifically as follows:

[0048] Extract the frequency value of each frequency node from the frequency node features, and set the frequency range of the target vibration reduction frequency band. Mark the frequency nodes within the target vibration reduction frequency band as target frequency band nodes, and mark the other frequency nodes as non-target frequency band nodes.

[0049] A residual vector is constructed between the output of the joint graph structure and the actual response of the target frequency band. In the residual vector, the residual values ​​of all non-target frequency band node positions are set to zero, and only the residual values ​​of the target frequency band node positions are kept unchanged, thus forming a frequency band residual shielding mechanism.

[0050] Optionally, the step of iteratively evolving the structural parameters of the vibration isolation trench using a Bayesian optimization algorithm to obtain the optimal design parameters for the vibration isolation trench specifically involves:

[0051] The residual vector after processing by the frequency band residual shielding mechanism is used as the optimization objective function, and the sum of squared residuals corresponding to all target frequency band nodes is used as the objective function value, which is defined as the performance evaluation index to be minimized.

[0052] The trench depth, trench width, and trench wall stiffness were selected as optimization variables in the structural parameters of the vibration isolation trench. The value range and step size accuracy were set respectively to form a three-dimensional continuous variable space.

[0053] Using the expectation function as the sampling criterion, the sample set of vibration isolation trench structure parameters is initialized, and then input into the joint graph structure for inference. The residual vectors corresponding to the sample parameters of each vibration isolation trench structure are obtained, and the residual values ​​at the target frequency band nodes are extracted and the objective function value is calculated.

[0054] Based on the initial sample set of vibration isolation ditch structural parameters, a response surface model of the optimization objective function is established through Gaussian process regression, and the mapping relationship between the sum of squared residuals and the vibration isolation ditch structural parameters is fitted.

[0055] The sampling point with the largest expected value is selected on the response surface as the sampling point for the next round, and the forward propagation is performed by inputting the joint graph structure to obtain a new residual vector and calculate the objective function value.

[0056] The newly obtained vibration isolation trench structural parameter samples are added to the vibration isolation trench structural parameter sample set, and the response surface model is retrained until the termination condition of the maximum number of iterations or the change in the objective function value is less than the set change threshold is met.

[0057] The final output is the structural parameters of the vibration isolation trench that minimize the objective function value, which are taken as the optimal design parameters for the vibration isolation trench.

[0058] The beneficial effects of this invention are:

[0059] This invention addresses the problems in existing vibration isolation trench design methods, such as insufficient multi-frequency response coupling modeling, low efficiency in structural parameter optimization, and difficulty in characterizing the dynamic evolution of vibration spectra, by constructing a frequency domain migration graph neural network model that integrates geological parameter modulation mechanisms and frequency band attention mechanisms. It employs a joint modeling and optimization strategy, utilizing Pearson correlation and cross-covariance to construct energy coupling edge weights in the spectrum graph structure, introducing frequency band attention graph convolution to achieve multi-band feature aggregation, and constructing a geological modulation factor by fusing the damping ratio with the ratio of the dominant frequency of the frequency band and the geological shear wave velocity, thereby modulating the stratigraphic environment of the frequency node features. During the time-frequency evolution stage, the model is constructed... A time-varying spectral absorption mechanism is implemented using a weighted gated cyclic unit, integrating the dynamic changes in response at each time step to enhance the modeling capability for non-stationary vibration signals. A joint graph structure is constructed by combining the structural parameters of the isolation trench, connecting frequency nodes with structural nodes to form a coupled modeling graph. A target vibration reduction frequency band is set during error backpropagation, and a frequency band residual shielding mechanism is introduced to ensure parameter feedback only occurs in the target frequency band. Finally, a Bayesian optimization strategy guided by Gaussian process regression and expectation function is used to perform global sampling and iterative updates on the residual response surface, achieving efficient optimization and inversion of key structural parameters such as trench depth, width, and wall stiffness. This invention achieves accurate prediction of the vibration reduction performance of isolation trenches and intelligent optimization design of structural parameters under multi-source disturbances and complex geological conditions. Attached Figure Description

[0060] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0061] Figure 1 This is an overall flowchart of a machine learning-based method for simulating and enhancing the vibration reduction effect of vibration isolation trenches proposed in this invention.

[0062] Figure 2 This is a flowchart of the improved Symlet wavelet function construction for a machine learning-based method for simulating and enhancing the vibration reduction effect of vibration isolation trenches proposed in this invention.

[0063] Figure 3 This is a schematic diagram of the frequency domain transfer graph neural network model structure of a vibration isolation trench vibration reduction effect simulation and enhancement method based on machine learning proposed in this invention. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0065] refer to Figures 1-3A method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning includes the following steps:

[0066] Step 1: Collect time-domain vibration signals, geological parameters, and vibration isolation trench structural parameters of the disturbance source;

[0067] Step 2: The time-domain vibration signal is subjected to continuous wavelet transform using an improved Symlet wavelet function with edge window modulation to generate an energy spectrum, wherein the energy spectrum is plotted with frequency on the horizontal axis and time on the vertical axis.

[0068] Step 3: Divide the frequency axis of the energy spectrum into multiple non-overlapping frequency bands, construct a spectrum structure based on the frequency bands, where each frequency band corresponds to a frequency node, and establish edge connections and edge weights between frequency nodes based on the energy coupling relationship;

[0069] Step 4: Construct a frequency domain migration graph neural network model, generate intermediate feature vectors through frequency band attention graph convolutional layers, and introduce a modulation factor controlled by geological parameters into each frequency node to output frequency node features;

[0070] Step 5: Introduce a time-varying spectrum absorption mechanism to the frequency node features, and nonlinearly fuse the frequency response features at different time steps to output the updated frequency node features;

[0071] Step 6: Construct a joint graph structure based on the updated frequency node characteristics and vibration isolation trench structural parameters;

[0072] Step 7: Set the target vibration reduction frequency band, introduce a frequency band residual shielding mechanism into the joint diagram structure, and use a Bayesian optimization algorithm to iteratively evolve the structural parameters of the vibration isolation trench to obtain the optimal design parameters of the vibration isolation trench.

[0073] In this embodiment, the time-domain vibration signal includes the acceleration time series generated by ground motion, traffic load, and construction disturbance; the geological parameters include shear wave velocity and damping ratio; and the vibration isolation trench structural parameters include trench depth, trench width, and trench wall stiffness.

[0074] In this embodiment, the continuous wavelet transform of the time-domain vibration signal using the improved Symlet wavelet function with edge window modulation is specifically as follows:

[0075] In the time domain of the original Symlet wavelet function, a start boundary interval and an end boundary interval are defined, and the length of each boundary interval is set to 10% to 20% of the total length of the time domain.

[0076] For any time point within the starting boundary interval, calculate the time difference between the current time point and the starting time point; for any time point within the ending boundary interval, calculate the time difference between the ending time point and the current time point; calculate the ratio of the time difference to the length of the corresponding boundary interval, and subtract the square of the ratio from 1 to generate a weighting coefficient;

[0077] Multiply the weighting coefficients by the value of the original Symlet wavelet function at the current time point to obtain the attenuated Symlet wavelet function value;

[0078] The starting boundary interval and the ending boundary interval are attenuated separately, and the attenuated starting boundary interval and the ending boundary interval are concatenated with the middle unmodulated segment of the original Symlet wavelet function to form a complete improved Symlet wavelet function.

[0079] The improved Symlet wavelet function is used to perform continuous wavelet transform on the time-domain vibration signal to generate an energy spectrum with frequency as the horizontal axis and time as the vertical axis.

[0080] In this invention, the original Symlet wavelet function is defined as follows:

[0081] ;

[0082] in, This represents the original Symlet wavelet function, used as the basis waveform for multi-scale decomposition in the time domain; This represents the coefficient of the k-th wavelet high-pass filter; Indicates the filter length, i.e. The total number of series; (t) represents the corresponding scaling function, used to construct an approximate signal for the low-frequency part; t represents a continuous-time variable.

[0083] To enhance the energy suppression capability of wavelets in the boundary region, this invention... An edge window modulation mechanism is introduced to construct a time-weighted decay function. And define the modulated Symlet wavelet function as:

[0084] ;

[0085] in, This represents the improved Symlet wavelet function modulated by an edge window; The edge weighting function is defined as follows:

[0086] ;

[0087] in, This represents the starting time point of the wavelet function. Indicates the end time point, Indicates the length of the initial boundary interval. This represents the length of the termination boundary interval, which is between 10% and 20% of the total time domain length. In the boundary region and The middle main section undergoes secondary attenuation processing according to time ratio. Keep the constant 1. The weighting method is to divide the distance between the current time point and the start (or end) of the boundary interval by the length of the corresponding boundary interval to obtain the ratio value, and then subtract the square of the ratio value from 1. The result is the weighting coefficient corresponding to that time point.

[0088] The modulation method described above is used to construct the following... Compared to the original It exhibits stronger energy control capabilities in the boundary region and is suitable for fine time-frequency analysis of non-stationary vibration signals within a finite time window.

[0089] In this embodiment, step three specifically includes:

[0090] The frequency axis of the energy spectrum is evenly segmented according to a preset bandwidth, and divided into multiple non-overlapping frequency bands, with each frequency band forming a frequency node;

[0091] For each frequency node, the energy distribution within the corresponding frequency band on the entire time axis is extracted from the energy spectrum. The energy distribution is the square of the magnitude of the frequency component of the frequency band at each moment after wavelet transform, and the energy distribution is sampled in time sequence to form an energy time series.

[0092] For any two frequency nodes, extract the corresponding energy time series, calculate the average of the two energy time series, calculate the product series of deviations from the average and sum them to obtain the deviation product sum; calculate the standard deviation of the two energy time series and multiply them to obtain the normalization factor; divide the deviation product sum by the normalization factor to obtain the Pearson correlation coefficient, which represents the linear consistency of the energy changes of the two frequency nodes.

[0093] The two energy time series are time-aligned and centered respectively. The data of each pair of corresponding positions in the centered series are multiplied and summed, and then divided by the length of the energy time series to obtain the cross covariance value, which reflects the degree of synchronization of energy fluctuations between frequency bands.

[0094] The Pearson correlation coefficient and the cross covariance value are linearly weighted with set weights to construct an energy coupling strength index between frequency nodes.

[0095] When the energy coupling strength index between any two frequency nodes exceeds a preset strength threshold, an edge connection is established between the corresponding two frequency nodes, and the energy coupling strength index is used as the edge weight.

[0096] A spectrum graph structure is constructed based on all frequency nodes, edge connections that meet the conditions, and their corresponding edge weights.

[0097] In this embodiment, the frequency domain transfer graph neural network model specifically includes a spectrum graph input layer, a frequency band attention graph convolutional layer, a geological modulation fusion layer, and a frequency node feature output layer;

[0098] A feature vector is initialized for each frequency node in the spectrum graph structure. The feature vector consists of the maximum value, average value, and standard deviation of the energy time series corresponding to the frequency node, and is input into the spectrum graph input layer.

[0099] In the frequency band attention map convolutional layer, for each frequency node, the feature vectors of all neighboring frequency nodes are collected, the dot product between the feature vector of the current frequency node and the feature vectors of each neighboring frequency node is calculated as the similarity score, and the similarity score is normalized by the Softmax function to obtain the attention weight; the feature vectors of neighboring frequency nodes are weighted and aggregated using the attention weight to obtain the aggregated feature vector.

[0100] The aggregated feature vector is concatenated with the feature vector of the current frequency node, input into a linear mapping function and subjected to a nonlinear transformation by a ReLU activation function, and the intermediate feature vector of the current frequency node is output.

[0101] In the geological modulation fusion layer, a modulation factor is constructed based on geological parameters, and the intermediate feature vector is fused and modulated. The modulation factor is obtained by normalizing the ratio of the main frequency of the current frequency node to the shear wave velocity to between 0 and 1 and multiplying it with the damping ratio. The modulation factor is then multiplied into each feature component of the intermediate feature vector to generate frequency node features.

[0102] The frequency node feature output layer is used to output frequency node features, which are used to characterize the response capability of each frequency band under the influence of geological conditions.

[0103] This invention constructs a frequency-domain-oriented transfer graph neural network model based on the spectrogram structure. It proposes a feature extraction structure combining a frequency band attention graph convolution mechanism with a geological modulation fusion method, which can more effectively characterize the response behavior of different frequency bands under complex geological conditions. Compared to traditional time-series modeling methods, this model not only utilizes the structural features in the frequency dimension of the spectrogram but also adaptively allocates coupling weights between adjacent frequency nodes through an attention mechanism, thereby strengthening information transmission between key frequency bands and improving the expressive power of spectral features.

[0104] By introducing modulation factors (shear wave velocity and damping ratio) that are closely related to geological conditions, physical-guided modulation of the eigenvectors of frequency nodes is achieved, making the frequency response characteristics of the model output more consistent with the vibration propagation characteristics in the actual geological environment. This modulation method uses the ratio of the dominant frequency of the frequency band to the shear wave velocity for normalization and combines it with the damping ratio as a dynamic modulation factor, which has a clear physical meaning and calculation path, and enhances the interpretability and generalization ability of the model.

[0105] In this embodiment, the time-varying spectral absorption mechanism is used to dynamically process frequency node characteristics, specifically as follows:

[0106] For each frequency node, obtain the frequency node features at multiple consecutive time steps, initialize the frequency response feature sequence that changes with time, and each time step corresponds to a frequency response feature;

[0107] For each time step in the frequency response feature sequence, a time-weighted attenuation function is constructed to realize time-aware modulation. The time-weighted attenuation function is calculated by dividing the current time step number by the total number of time steps, and the attenuation factor is generated by subtracting the square of the calculated value from 1.

[0108] The attenuation factor is multiplied one by one with each dimension of the frequency response feature at the current time step to obtain the frequency response feature after time-weighted attenuation processing, forming a modulation response sequence that changes dynamically with time.

[0109] The modulation response sequence is input into a neural network structure for nonlinear fusion. The neural network structure is a gated recurrent unit with state memory capability, which dynamically controls the transmission relationship between historical response information and current input through a gating mechanism.

[0110] The output of the gated loop unit includes the final hidden state of historical evolution information, which serves as the updated frequency node feature to reflect its absorption behavior and response characteristics over time.

[0111] In this embodiment, step six specifically includes:

[0112] Based on the updated frequency node features, the frequency nodes and edge connections in the spectrum graph structure are retained;

[0113] For each vibration isolation ditch structural parameter, a corresponding structural node is set, and all vibration isolation ditch structural parameters are normalized. The normalized vibration isolation ditch structural parameters are used as the feature vectors of each structural node.

[0114] Establish edge connections between each structural node and all frequency nodes;

[0115] For each pair of structural nodes and frequency nodes, the dot product of the feature vector of the structural node and the updated feature of the frequency node is calculated as the weight coefficient of the edge connection, forming an edge weight matrix.

[0116] A joint graph structure is constructed based on frequency nodes, structure nodes, and the edge weight matrix.

[0117] In this embodiment, the setting of the target vibration reduction frequency band involves introducing a frequency band residual shielding mechanism into the combined diagram structure, specifically as follows:

[0118] Extract the frequency value of each frequency node from the frequency node features, and set the frequency range of the target vibration reduction frequency band. Mark the frequency nodes within the target vibration reduction frequency band as target frequency band nodes, and mark the other frequency nodes as non-target frequency band nodes.

[0119] A residual vector is constructed between the output of the joint graph structure and the actual response of the target frequency band. In the residual vector, the residual values ​​of all non-target frequency band node positions are set to zero, and only the residual values ​​of the target frequency band node positions are kept unchanged, thus forming a frequency band residual shielding mechanism.

[0120] In this embodiment, the step of iteratively evolving the structural parameters of the vibration isolation trench using a Bayesian optimization algorithm to obtain the optimal design parameters for the vibration isolation trench specifically involves:

[0121] The residual vector after processing by the frequency band residual shielding mechanism is used as the optimization objective function, and the sum of squared residuals corresponding to all target frequency band nodes is used as the objective function value, which is defined as the performance evaluation index to be minimized.

[0122] The trench depth, trench width, and trench wall stiffness were selected as optimization variables in the structural parameters of the vibration isolation trench. The value range and step size accuracy were set respectively to form a three-dimensional continuous variable space.

[0123] Using the expectation function as the sampling criterion, the sample set of vibration isolation trench structure parameters is initialized, and then input into the joint graph structure for inference. The residual vectors corresponding to the sample parameters of each vibration isolation trench structure are obtained, and the residual values ​​at the target frequency band nodes are extracted and the objective function value is calculated.

[0124] Based on the initial sample set of vibration isolation ditch structural parameters, a response surface model of the optimization objective function is established through Gaussian process regression, and the mapping relationship between the sum of squared residuals and the vibration isolation ditch structural parameters is fitted.

[0125] The sampling point with the largest expected value is selected on the response surface as the sampling point for the next round, and the forward propagation is performed by inputting the joint graph structure to obtain a new residual vector and calculate the objective function value.

[0126] The newly obtained vibration isolation trench structural parameter samples are added to the vibration isolation trench structural parameter sample set, and the response surface model is retrained until the termination condition of the maximum number of iterations or the change in the objective function value is less than the set change threshold is met.

[0127] The final output is the structural parameters of the vibration isolation trench that minimize the objective function value, which are taken as the optimal design parameters for the vibration isolation trench.

[0128] To achieve automated optimization of the structural parameters of vibration isolation trenches, this invention introduces a Bayesian optimization algorithm based on the output of the joint graph structural model. The algorithm uses the sum of squares of the residuals in the target frequency band as the objective function to perform a global search within a continuous variable space for the three key structural parameters of the vibration isolation trench: trench depth, trench width, and trench wall stiffness. An optimization variable space is constructed, defining the search range for trench depth as 2.0 meters to 8.0 meters, trench width as 1.0 meter to 5.0 meters, and trench wall stiffness as... Pa to Pa, with step length accuracy set to 0.2 meters, 0.2 meters and 0.2 meters respectively. Pa.

[0129] The objective function is composed of the residuals between the frequency node features output by the joint graph structural model and the target response. Frequency nodes are extracted within the target vibration reduction frequency band, and their residual values ​​are squared and summed to form the objective function value. The initial sample set is generated using uniform Latin hypercube sampling to produce several sets of vibration isolation trench structural parameters, which are then input into the joint graph structural model for inference. The objective function value corresponding to each set of parameters is obtained and used as training data for constructing the response surface of the Gaussian process regression model.

[0130] The expectation function is one of the most commonly used sampling criteria in Bayesian optimization. Its core idea is to select the point that brings the greatest expected improvement under the uncertainty of the current Gaussian process model. This invention uses expected improvement as a sampling strategy, evaluating the improvement potential of each candidate parameter point on the constructed response surface, selecting the sample point with the largest expected value as the next round of sampling points, inputting it into the joint graph structure model, updating the objective function value and adding it to the sample set, and then retraining the Gaussian process regression model to fit the new residual-parameter mapping.

[0131] This process iterates continuously, dynamically adjusting the sampling strategy in each round based on the current model uncertainty and historical best results, until the set maximum number of iterations is reached or the change in the objective function value is less than a certain value for several consecutive rounds. The convergence condition is determined. Finally, the set of vibration isolation trench structural parameters that minimizes the objective function value is selected as the optimal design output to guide the actual engineering layout of the vibration isolation trench structure, improving vibration reduction effect and geological adaptability. This optimization process possesses automatic search capability, response surface interpretability, and convergence stability, making it suitable for inversion design problems involving complex structural parameters.

[0132] Example 1:

[0133] To verify the feasibility of this invention in practice, it was applied to a disturbance control project for an underground engineering project in a city. This project involved the construction of underground structures and vibration control of the surrounding environment. The geological conditions in the construction area were complex, with multiple layers of clay and sand structures. The disturbance sources mainly included construction machinery operations, traffic loads, and intermittent blasting, with vibration frequencies primarily concentrated between 0.5Hz and 50Hz. Due to the presence of precision experimental equipment and important municipal facilities in the vicinity, the area was highly sensitive to low- and mid-frequency vibrations. Traditional vibration isolation trench designs were significantly inadequate in terms of both vibration reduction effect and design efficiency.

[0134] In this embodiment, multiple triaxial vibration sensors are first deployed to collect time-domain signals of ground acceleration excited by disturbance sources. The sampling frequency is 200Hz, and multi-cycle typical operating condition data are continuously collected, with a total data point count exceeding 50 million. Subsequently, the improved Symlet wavelet function with edge window modulation proposed in this invention is used to perform continuous wavelet transform on the time-domain signals to generate an energy spectrum, and the frequency axis is divided into frequency bands at 1Hz intervals. Based on the frequency band division results, a spectrum graph structure is constructed, including multiple frequency nodes and edge connections and weights calculated based on coupling relationships.

[0135] Based on this spectrogram structure, a frequency domain transfer graph neural network model is constructed. The model input includes initial features of the frequency nodes (maximum, mean, and standard deviation of energy over time) and geological parameters of the site (shear wave velocity and damping ratio). Through a frequency band attention mechanism and a geological modulation fusion structure, a multi-scale perceived frequency node feature vector is output. This feature sequence is further input into a time-varying spectral absorption mechanism for multi-time-step fusion, generating the final frequency response features used for inference of the vibration isolation trench structure.

[0136] In the model optimization phase, the target vibration reduction frequency band was set at 4–10 Hz, and a frequency band residual shielding mechanism was introduced, calculating only the residual error within this frequency band. Trench depth (2–8 m), trench width (0.5–3 m), and trench wall stiffness (20–180 MPa) were selected as optimization variables to construct a three-dimensional continuous design space, and an iterative inversion using a Bayesian optimization algorithm was performed. The sum of squared residuals within the target frequency band was used as the objective function, and the expectation function was adopted as the sampling criterion. The response surface model was continuously updated through Gaussian process regression. A total of 50 rounds of iterative optimization were performed, and the final optimal structural parameters were: trench depth 6.5 m, trench width 2.2 m, and trench wall stiffness 95 MPa.

[0137] Table 1 Comparison of Vibration Response Before and After Optimization of Vibration Isolation Trench

[0138]

[0139] As can be seen from Table 1 above, the present invention has a significant vibration reduction effect within the target frequency range (4.0Hz to 10.0Hz). Under the original operating conditions, the acceleration response at a frequency of 4.0Hz is... 0.128m / s2 After optimization, it dropped to 0.039m / s2 The attenuation rate is as high as 69.5%. As the frequency increases, the attenuation effect remains stable; for example, at 7.0Hz... 0.176m / s2 Reduce to 0.058m / s2 The attenuation rate is 67.0%; at 10.0 Hz, it is... 0.121m / s2 Reduce to 0.043m / s2 The attenuation rate was 64.5%. The overall attenuation rate remained between 64.5% and 69.5%, indicating that the optimized method has a broad and stable suppression capability for vibrations over a wide frequency band.

[0140] Furthermore, this invention introduces a frequency band residual shielding mechanism, ensuring that error backpropagation focuses solely on the set target vibration reduction frequency band. Combined with a Bayesian optimization algorithm, iterative evolution of key structural parameters such as trench depth, trench width, and trench wall stiffness is performed, thereby precisely controlling the energy propagation path of the vibration response. This strategy effectively avoids interference from non-target frequency bands, improving the convergence efficiency and optimization accuracy of parameter adjustments. Based on the data comparison in Table 1 above, it not only exhibits significant attenuation at low frequencies (e.g., 4.0Hz) but also demonstrates good response control in mid-to-high frequency bands (e.g., 9.0Hz and 10.0Hz), verifying the versatility and practicality of the proposed method in multi-band vibration reduction design.

[0141] This embodiment achieves intelligent iterative optimization of vibration isolation trench structural parameters by constructing a frequency domain migration graph neural network model and introducing a frequency band residual shielding mechanism and a Bayesian optimization algorithm. Compared with traditional methods, this scheme fully utilizes the energy coupling relationship in the spectrum graph and the nonlinear correlation between geological parameters, enabling precise control of vibration response within a specified vibration reduction frequency band. Experimental results show that in the key frequency range of 4.0Hz to 10.0Hz, the optimized acceleration response is significantly reduced, with a maximum attenuation rate of 69.5% and a minimum rate above 64.5%, demonstrating stable and excellent broadband vibration reduction capabilities. This invention not only overcomes the sensitivity to non-target frequency band error interference in previous models but also significantly improves the efficiency and accuracy of structural parameter optimization. It is suitable for vibration control scenarios under complex geological conditions and has broad engineering application value in vibration isolation design for urban infrastructure and rail transit lines.

[0142] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A machine learning based simulation and enhancement method for vibration reduction effect of a trench, characterized in that, Includes the following steps: Step 1: Collect time-domain vibration signals, geological parameters, and vibration isolation trench structural parameters of the disturbance source; Step 2: The time-domain vibration signal is subjected to continuous wavelet transform using an improved Symlet wavelet function with edge window modulation to generate an energy spectrum, wherein the energy spectrum is plotted with frequency on the horizontal axis and time on the vertical axis. The improved Symlet wavelet function with edge window modulation is used to perform continuous wavelet transform on the time-domain vibration signal, specifically as follows: In the time domain of the original Symlet wavelet function, a start boundary interval and an end boundary interval are defined, and the length of each boundary interval is set to 10% to 20% of the total length of the time domain. For any time point within the starting boundary interval, calculate the time difference between the current time point and the starting time point; for any time point within the ending boundary interval, calculate the time difference between the ending time point and the current time point; calculate the ratio of the time difference to the length of the corresponding boundary interval, and subtract the square of the ratio from 1 to generate a weighting coefficient; Multiply the weighting coefficients by the value of the original Symlet wavelet function at the current time point to obtain the attenuated Symlet wavelet function value; The starting boundary interval and the ending boundary interval are attenuated separately, and the attenuated starting boundary interval and the ending boundary interval are concatenated with the middle unmodulated segment of the original Symlet wavelet function to form a complete improved Symlet wavelet function. The improved Symlet wavelet function is used to perform continuous wavelet transform on the time-domain vibration signal to generate an energy spectrum with frequency as the horizontal axis and time as the vertical axis. Step 3: Divide the frequency axis of the energy spectrum into multiple non-overlapping frequency bands, construct a spectrum structure based on the frequency bands, where each frequency band corresponds to a frequency node, and establish edge connections and edge weights between frequency nodes based on the energy coupling relationship; Step 4: Construct a frequency domain transfer graph neural network model. Generate intermediate feature vectors through frequency band attention graph convolutional layers, and introduce a modulation factor controlled by geological parameters into each frequency node to output frequency node features. The frequency domain transfer graph neural network model specifically includes a spectrum graph input layer, a frequency band attention graph convolutional layer, a geological modulation fusion layer, and a frequency node feature output layer. Step 5: Introduce a time-varying spectrum absorption mechanism to the frequency node features, and nonlinearly fuse the frequency response features at different time steps to output the updated frequency node features; Step 6: Construct a joint graph structure based on the updated frequency node characteristics and vibration isolation trench structural parameters; Step 7: Set the target vibration reduction frequency band, introduce a frequency band residual shielding mechanism into the joint diagram structure, and use a Bayesian optimization algorithm to iteratively evolve the structural parameters of the vibration isolation trench to obtain the optimal design parameters of the vibration isolation trench.

2. The method of claim 1, wherein the method is based on machine learning. The time-domain vibration signal includes the acceleration time series generated by ground motion, traffic load, and construction disturbance; the geological parameters include shear wave velocity and damping ratio; and the vibration isolation trench structural parameters include trench depth, trench width, and trench wall stiffness.

3. The method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning according to claim 1, characterized in that, Step three specifically involves: The frequency axis of the energy spectrum is evenly segmented according to a preset bandwidth, and divided into multiple non-overlapping frequency bands, with each frequency band forming a frequency node; For each frequency node, the energy distribution within the corresponding frequency band on the entire time axis is extracted from the energy spectrum. The energy distribution is the square of the magnitude of the frequency component of the frequency band at each moment after wavelet transform, and the energy distribution is sampled in time sequence to form an energy time series. For any two frequency nodes, extract the corresponding energy time series, calculate the average of the two energy time series, calculate the product series of deviations from the average and sum them to obtain the deviation product sum; calculate the standard deviation of the two energy time series and multiply them to obtain the normalization factor; divide the deviation product sum by the normalization factor to obtain the Pearson correlation coefficient. The two energy time series are time aligned and centered respectively. The data of each pair of corresponding positions in the centered series are multiplied and summed, and then divided by the length of the energy time series to obtain the cross covariance value. The Pearson correlation coefficient and the cross covariance value are linearly weighted with set weights to construct an energy coupling strength index between frequency nodes. When the energy coupling strength index between any two frequency nodes exceeds a preset strength threshold, an edge connection is established between the corresponding two frequency nodes, and the energy coupling strength index is used as the edge weight. A spectrum graph structure is constructed based on all frequency nodes, edge connections that meet the conditions, and their corresponding edge weights.

4. The method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning according to claim 1, characterized in that, A feature vector is initialized for each frequency node in the spectrum graph structure. The feature vector consists of the maximum value, average value, and standard deviation of the energy time series corresponding to the frequency node, and is input into the spectrum graph input layer. In the frequency band attention map convolutional layer, for each frequency node, the feature vectors of all neighboring frequency nodes are collected, the dot product between the feature vector of the current frequency node and the feature vectors of each neighboring frequency node is calculated as the similarity score, and the similarity score is normalized by the Softmax function to obtain the attention weight; the feature vectors of neighboring frequency nodes are weighted and aggregated using the attention weight to obtain the aggregated feature vector. The aggregated feature vector is concatenated with the feature vector of the current frequency node, input into a linear mapping function and subjected to a nonlinear transformation by a ReLU activation function, and the intermediate feature vector of the current frequency node is output. In the geological modulation fusion layer, a modulation factor is constructed based on geological parameters, and the intermediate feature vector is fused and modulated. The modulation factor is obtained by normalizing the ratio of the main frequency of the current frequency node to the shear wave velocity to between 0 and 1 and multiplying it with the damping ratio. The modulation factor is then multiplied into each feature component of the intermediate feature vector to generate frequency node features. The frequency node feature output layer is used to output frequency node features.

5. The method of claim 1, wherein, The time-varying spectral absorption mechanism is used to dynamically process frequency node characteristics, specifically as follows: For each frequency node, obtain the frequency node features at multiple consecutive time steps, initialize the frequency response feature sequence that changes with time, and each time step corresponds to a frequency response feature; For each time step in the frequency response feature sequence, a time-weighted attenuation function is constructed to realize time-aware modulation. The time-weighted attenuation function is calculated by dividing the current time step number by the total number of time steps, and the attenuation factor is generated by subtracting the square of the calculated value from 1. The attenuation factor is multiplied one by one with each dimension of the frequency response feature at the current time step to obtain the frequency response feature after time-weighted attenuation processing, forming a modulation response sequence that changes dynamically with time. The modulation response sequence is input into a neural network structure for nonlinear fusion. The neural network structure is a gated recurrent unit with state memory capability, which dynamically controls the transmission relationship between historical response information and current input through a gating mechanism. The output of the gated loop unit includes the final hidden state of historical evolution information, which serves as the updated frequency node feature.

6. The machine learning based vibration isolation trench damping effect simulation and enhancement method according to claim 1, characterized in that, Step six specifically involves: Based on the updated frequency node features, the frequency nodes and edge connections in the spectrum graph structure are retained; For each vibration isolation ditch structural parameter, a corresponding structural node is set, and all vibration isolation ditch structural parameters are normalized. The normalized vibration isolation ditch structural parameters are used as the feature vectors of each structural node. Establish edge connections between each structural node and all frequency nodes; For each pair of structural nodes and frequency nodes, the dot product of the feature vector of the structural node and the updated feature of the frequency node is calculated as the weight coefficient of the edge connection, forming an edge weight matrix. A joint graph structure is constructed based on frequency nodes, structure nodes, and the edge weight matrix.

7. The method for simulating and enhancing the vibration reduction effect of vibration isolation trenches based on machine learning according to claim 1, characterized in that, The set target vibration reduction frequency band introduces a frequency band residual shielding mechanism in the combined diagram structure, specifically as follows: Extract the frequency value of each frequency node from the frequency node features, and set the frequency range of the target vibration reduction frequency band. Mark the frequency nodes within the target vibration reduction frequency band as target frequency band nodes, and mark the other frequency nodes as non-target frequency band nodes. A residual vector is constructed between the output of the joint graph structure and the actual response of the target frequency band. In the residual vector, the residual values ​​of all non-target frequency band node positions are set to zero, and only the residual values ​​of the target frequency band node positions are kept unchanged, thus forming a frequency band residual shielding mechanism.

8. The method of claim 1, wherein, The optimal design parameters for the vibration isolation trench are obtained by iteratively evolving the structural parameters using a Bayesian optimization algorithm. Specifically: The residual vector after processing by the frequency band residual shielding mechanism is used as the optimization objective function, and the sum of squared residuals corresponding to all target frequency band nodes is used as the objective function value, which is defined as the performance evaluation index to be minimized. The trench depth, trench width, and trench wall stiffness were selected as optimization variables in the structural parameters of the vibration isolation trench. The value range and step size accuracy were set respectively to form a three-dimensional continuous variable space. Using the expectation function as the sampling criterion, the sample set of vibration isolation trench structure parameters is initialized, and then input into the joint graph structure for inference. The residual vectors corresponding to the sample parameters of each vibration isolation trench structure are obtained, and the residual values ​​at the target frequency band nodes are extracted and the objective function value is calculated. Based on the initial sample set of vibration isolation ditch structural parameters, a response surface model of the optimization objective function is established through Gaussian process regression, and the mapping relationship between the sum of squared residuals and the vibration isolation ditch structural parameters is fitted. The sampling point with the largest expected value is selected on the response surface as the sampling point for the next round, and the forward propagation is performed by inputting the joint graph structure to obtain a new residual vector and calculate the objective function value. The newly obtained vibration isolation trench structural parameter samples are added to the vibration isolation trench structural parameter sample set, and the response surface model is retrained until the termination condition of the maximum number of iterations or the change in the objective function value is less than the set change threshold is met; finally, the vibration isolation trench structural parameters that minimize the objective function value are output as the optimal vibration isolation trench design parameters.

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