Metro depot building vibration response prediction method based on deep learning

Abstract

The application discloses a subway vehicle depot upper building vibration response prediction method based on deep learning, comprising the following steps: constructing a feature library containing vibration signals and working condition data, generating enhanced data by a mechanical model, and fusing the enhanced data into a data set; constructing a hybrid deep learning model embedded with physical priori, training and double-target optimizing parameters; outputting a prediction result after real-time data is identified by a light-weight model; periodically learning incrementally to fine-tune parameters, and migrating learning to adapt when a working condition suddenly changes; verifying accuracy and rationality, adjusting a regular term weight, or suggesting supplementing sensors; and the application compensates for sparse measured data by enhanced data fusion; conquers a deep nonlinear mapping problem by a double-branch structure, and avoids violating physical laws by physical constraints; reduces cost by incremental learning, and solves time-varying vibration capture problems by migration learning; and improves accuracy by closed-loop verification, realizes accurate and real-time vibration response prediction, and guarantees building safety and comfort.

Description

Technical Field

[0001] This invention relates to the field of subway engineering and building vibration analysis technology, specifically a deep learning-based method for predicting the vibration response of subway depot superstructures. Background Technology

[0002] Subway depot superstructures refer to building structures built directly above subway depots, a design that effectively improves land utilization. Due to the frequent entry and exit of subway trains from and from the depot, the vibrations generated are transmitted to the superstructure through the tracks and foundation, causing slight vibrations in components such as floor slabs, beams, and columns. While these long-term vibrations do not directly affect structural safety, they can lead to secondary problems such as wall cracking, equipment noise, and decreased human comfort. Traditional vibration analysis often relies on finite element simulation or on-site measurements; however, the complex subway operating environment, with factors such as track wear and changes in wheel-rail contact conditions significantly altering vibration characteristics, makes accurate predictions difficult using deterministic methods.

[0003] Currently, vibration response prediction methods based on physical models face the following challenges when dealing with nonlinear and time-varying vibration transmission problems. For example, track irregularities or changes in wheel-rail contact stiffness can cause shifts in vibration spectrum characteristics, while existing models typically assume constant parameters and cannot dynamically capture such instantaneous changes. Furthermore, while measured data can reflect real-world conditions, deploying sensors is costly and difficult to cover all critical areas, resulting in significant data sparsity. Although shallow machine learning methods can partially fit vibration patterns, their limited feature extraction capabilities lead to large prediction errors for high-frequency vibration components under multi-source excitation coupling, and they are particularly unable to effectively learn the deep nonlinear mapping relationship between abrupt excitation at the wheel-rail interface and the building's dynamic response. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a deep learning-based method for predicting the vibration response of subway depot superstructures, aiming to solve the problems in the background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a deep learning-based method for predicting the vibration response of subway depot superstructures, comprising the following steps:

[0006] Step S1: Construct a multi-dimensional working condition feature library, which contains direct vibration signals of buildings and vibration-related working condition data; simulate building vibration data under different working conditions based on the vibration transmission mechanics model to generate enhanced data; fuse the enhanced data, direct vibration signals and working condition data to form a hybrid dataset;

[0007] Step S2: Construct a hybrid deep learning model with embedded physical priors, train the model based on the hybrid dataset, and perform bi-objective optimization on the model parameters;

[0008] Step S3: Collect real-time direct vibration signals and corresponding working condition data. Based on the real-time direct vibration signals and corresponding working condition data, use a lightweight classification model to identify the current scene working condition. According to the identified current scene working condition, call the corresponding parameters and use a hybrid deep learning model to output the final vibration response prediction result.

[0009] Step S4: Periodically collect quantitative real-time direct vibration signals and corresponding working condition data, and fine-tune the parameter weights of the hybrid deep learning model using an incremental learning strategy; when the scene working conditions change significantly, use quantitative real-time working condition data to perform transfer learning fine-tuning on the hybrid deep learning model.

[0010] Step S5: Verify the accuracy and physical rationality of the vibration response prediction results; based on the verification results, adjust the weight of the regularization term in the physical prior or suggest supplementing the vibration sensor.

[0011] Furthermore, a hybrid deep learning model integrating physics priors is constructed, including:

[0012] This approach integrates physical laws and constraints into the training process of a hybrid deep learning model, achieved through a dual method of loss function regularization and prior parameter input.

[0013] Physical constraints are transformed into regularization terms of the loss function: The core physical laws governing vibration transmission are converted into constraints of the loss function, which are then jointly optimized with the prediction loss of the hybrid deep learning model. Specifically, this includes:

[0014] Energy conservation law constraint: Based on the principle of energy conservation in vibration systems, calculate the energy loss rate during vibration transmission and define the energy conservation regularization term. The relative error between the predicted vibration energy and the measured vibration energy is calculated using the following formula: , This represents the predicted vibrational energy. The measured vibration energy is obtained by integrating the acceleration signal. , Indicates equivalent mass. Indicates the sampling time. Indicates the acceleration of vibration over time The function of change; Indicates the integral;

[0015] Boundary condition constraints: Considering the displacement continuity condition of the foundation-subsoil interaction, define boundary condition regularization terms. The predicted deviation between the base vibration displacement of the building and the maximum allowable vibration displacement of the foundation is called the deviation. , This indicates the predicted vibration displacement at the bottom of the building foundation. Indicates the maximum permissible vibration displacement of the foundation; Based on the characteristic value of foundation bearing capacity Confirmed: If ≥150 , ,like <150 , ;

[0016] Wheel-rail excitation-response amplitude matching constraint: Based on the amplitude-frequency characteristic function of the wheel-rail system, an amplitude matching regularization term is defined. To determine the error between the predicted amplitude-frequency response and the theoretical amplitude-frequency response; the theoretical amplitude-frequency response function is expressed as: , This represents the natural angular frequency of the structure, which is a parameter representing the inherent vibration characteristics of the building's structure. Indicates the excitation angular frequency. Indicates the structural damping ratio; Represents the imaginary unit;

[0017] Vibration attenuation and transmission distance constraints: Defining the attenuation regularization term , Indicates the predicted vibration attenuation coefficient; Indicates the theoretical attenuation coefficient; Indicates the distance the vibration is transmitted;

[0018] The four types of regularization terms are combined with the mean squared error loss of the predicted value minus the true value in the hybrid deep learning model. By combining these, we obtain the total loss function of the hybrid deep learning model. :

[0019] ;

[0020] In the formula, , , , They represent the corresponding , , , Weighting coefficients;

[0021] Physical parameters, including wheel-rail contact stiffness, track irregularity, and building material elastic modulus, are directly used as fixed prior inputs to the deep learning model.

[0022] For wheel-rail contact stiffness, it is first normalized; the normalized wheel-rail contact stiffness is used as a prior input and directly input into the hybrid deep learning model, and multiplied element-wise with the fusion features to obtain the fusion features with the wheel-rail contact stiffness prior.

[0023] For track irregularities, they are first quantified as track irregularity amplitude. ; Amplitude of track irregularities Normalization is performed; the normalized track irregularity amplitude is used as a priori input and directly input into the hybrid deep learning model, where it is multiplied element-wise with the fusion features to obtain the fusion features with the prior track irregularity.

[0024] Furthermore, the hybrid deep learning model adopts a dual-branch feature extraction plus vibration response output architecture. The two branches process the direct vibration signal and the working condition data respectively. The vibration response output module decodes the high-dimensional feature vector fused from the two branches into specific vibration response prediction values, including:

[0025] Branch 1 of the hybrid deep learning model adopts a combination structure of convolutional neural network and Transformer encoder to extract the time-frequency domain features of vibration signal: a 3-layer convolutional neural network is used to extract the local time domain features of vibration signal; the vibration signal is converted into time-frequency map through short-time Fourier transform; the time-frequency map is input into the last two layers of convolutional neural network to capture frequency domain features; the frequency domain features are concatenated with the time domain features and then input into a 2-layer Transformer encoder to output time-frequency domain fused features;

[0026] Branch 2 of the hybrid deep learning model adopts a fully connected layer structure to extract low-dimensional vector features from the working condition data: the working condition data is normalized and then input into two fully connected layers to output low-dimensional vector features.

[0027] The time-frequency fusion features output by branch 1 of the hybrid deep learning model and the low-dimensional vector features output by branch 2 of the hybrid deep learning model are added element by element to obtain the fusion features. The fusion features are then input into the vibration response output module for vibration response prediction.

[0028] Furthermore, the dual-objective optimization of the model parameters includes:

[0029] With prediction accuracy and physical plausibility as dual optimization objectives, a non-dominated sorting genetic algorithm is used to optimize the network parameters of the hybrid deep learning model. Specifically:

[0030] To minimize With the goal, The coefficient of determination represents the ratio of the predicted response to the measured response of the hybrid deep learning model.

[0031] To minimize the loss of physical rationality With the goal, By the energy conservation regularity term Boundary condition regularization terms Amplitude matching regularization term We get the result by weighted summation;

[0032] Gradient descent-type optimization algorithms are used to simultaneously balance the loss of accuracy and the loss of physical constraints during each parameter update;

[0033] The non-dominated sorting genetic algorithm NSGA-II optimizes network parameters of hybrid deep learning models, including the kernel size of convolutional neural networks, the number of attention heads in Transformer encoders, and the number of neurons in fully connected layers.

[0034] Furthermore, the specific process of fine-tuning the parameter weights of the hybrid deep learning model using an incremental learning strategy is as follows: weekly, quantitative measured direct vibration signals and corresponding working condition data are collected regularly, and the parameter weights of the hybrid deep learning model are fine-tuned using an incremental learning strategy, including fine-tuning the attention weights of the Transformer encoder and the output weights of the fully connected layer.

[0035] When the operating conditions of the scenario change significantly, such as a significant change in the stiffness of the fasteners after track maintenance or a change in the train model, a quantitative amount of real-time operating condition data is collected. The hybrid deep learning model is used as a pre-trained model, and the collected real-time operating condition data is used for transfer learning fine-tuning.

[0036] Furthermore, the accuracy verification was performed by calculating the mean square error (MSE) and correlation coefficient between the predicted vibration response and the measured vibration response. Physical rationality verification includes: checking whether the vibration response prediction results meet the energy attenuation law of vibration transmission; and checking whether the vibration response prediction results meet the matching of the component vibration frequency and the structure's natural frequency.

[0037] Furthermore, based on the verification results, the specific process for adjusting the regularization term weights in the physical prior or suggesting the addition of vibration sensors is as follows: If the predicted vibration response at the floor corner has a large error and poor physical plausibility, adjust the regularization term weights in the physical prior and re-optimize the model parameters using a bi-objective approach; if the predicted vibration response at the floor corner has a large error but is physically plausible, add vibration sensors to the floor corner to increase data density; adjusting the regularization term weights in the physical prior includes increasing the variation function. To strengthen the constraint of energy conservation.

[0038] Furthermore, the vibration transmission mechanics model simulates building vibration data under different working conditions, and the specific process of generating enhanced data is as follows:

[0039] Based on the wheel-rail contact mechanics model, the mapping relationship between excitation signal and transmission path parameters under different working conditions is simulated. The wheel-rail contact mechanics model adopts Hertzian contact theory, and the excitation signal is the wheel-rail impact force. This indicates that the transmission path parameters are based on wheel-rail contact stiffness. Indicates wheel-rail impact force Represented as:

[0040] ;

[0041] In the formula, This represents the elastic modulus of the wheel and rail material; Indicates the equivalent radius of wheel-rail contact; This represents the Poisson's ratio of the wheel and rail materials. This indicates the amount of wheel-rail contact deformation;

[0042] By adjusting the wheel-rail contact deformation Wheel-rail contact stiffness Or, calculate the corresponding wheel-rail impact force based on the train's load. The mapping relationship between excitation signals and transmission path parameters under different working conditions is obtained, and multiple sets of excitation signal and transmission path parameter samples are generated.

[0043] Based on the vibration transmission wave equation, the mapping relationship between transmission path parameters and vibration response under different working conditions is simulated; the vibration transmission wave equation is:

[0044] ;

[0045] In the formula, express Time, location Vibration displacement response at the location; This indicates the speed at which a vibration wave propagates in the transmission medium. express The impact force of wheels and rails at any moment; Indicates the quality of the transmission medium; Represents the Dirac function; Indicates the sign of the partial derivative; Indicates wheel-rail impact force The coordinates of the position where the action takes place;

[0046] By adjusting the transmission path parameters, the vibration displacement response under different parameters can be obtained by solving the wave equation. This allows us to obtain the mapping relationship between transmission path parameters and vibration response under different working conditions, and generate multiple sets of vibration response samples, i.e., enhanced data.

[0047] Furthermore, in step S3, a working condition-model parameter mapping library is established based on the model parameters optimized by the dual objectives under different working conditions; according to the identified current scene working condition, the corresponding model parameters are called from the working condition-model parameter mapping library and input into the hybrid deep learning model, and the hybrid deep learning model outputs the vibration response prediction result.

[0048] Furthermore, direct vibration signal acquisition: Vibration sensors are deployed at key measuring points of the building to acquire the building's own raw vibration signals in real time;

[0049] Operating condition data acquisition: Interacting with three types of external systems to acquire vibration-related operating condition data:

[0050] Subway Operation System: Acquires operational data, including subway departure / arrival times, train speeds, and train schedules;

[0051] Track maintenance system: Acquires maintenance data, including track wear level, maintenance cycle, and track defects;

[0052] Environmental monitoring system: Acquires environmental data, including temperature, humidity, and wind speed in the monitored area.

[0053] Compared with existing technologies, this invention has the following advantages: It collects direct vibration signals by deploying sensors at key measuring points, combines this data with data from subway operation, track maintenance, and environmental monitoring systems to construct a multi-dimensional operating condition database, and generates enhanced data fusion based on a vibration transmission mechanics model to compensate for the sparsity of measured data. It employs a dual-branch deep learning architecture to overcome the challenges of weak feature extraction in shallow models and the inability to learn deep nonlinear mappings between wheel-rail excitation and building response. It embeds physical constraints of vibration transmission into the training process to avoid predictions that violate physical laws. Incremental learning fine-tunes model parameter weights to reduce computational costs, and transfer learning adapts to sudden changes in operating conditions, solving the problem of capturing time-varying vibrations. Closed-loop verification feedback adjusts the weights of regularization terms or supplements sensors to further improve accuracy, ultimately achieving accurate and real-time prediction of the vibration response of subway-covered buildings. Attached Figure Description

[0054] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0055] like Figure 1 As shown, the present invention provides a technical solution: a deep learning-based method for predicting the vibration response of subway depot superstructures, comprising the following steps:

[0056] Step S1: Construct a multi-dimensional working condition feature library, which contains direct vibration signals of buildings and vibration-related working condition data; simulate building vibration data under different working conditions based on the vibration transmission mechanics model to generate enhanced data; fuse the enhanced data, direct vibration signals and working condition data to form a hybrid dataset.

[0057] Step S1:11: Direct Vibration Signal Acquisition: A small number of vibration sensors are deployed at key measuring points of the building (such as load-bearing structural nodes, sensitive wall areas, etc.) to collect the original vibration signals of the building itself in real time. Specifically, a finite element model of the building structure is established using ANSYS software. Parameters such as concrete strength grade (C30-C40) and component cross-sectional dimensions are input. The mode shape nodes corresponding to the first 5 natural frequencies (1.2-8.5Hz) are extracted. These mode shape nodes, along with the beam-column nodes and weak areas of the floor slab, are used as key measuring points (mode shape nodes are preferentially selected at locations with amplitude ≥0.1mm). A small number of vibration sensors are deployed at the key measuring points to collect acceleration signals (unit: m / s²) and displacement signals (unit: mm). The acquisition frequency is set to 1000Hz to ensure that high-frequency vibration components can be captured.

[0058] Step S1.12: Operating Condition Data Acquisition: Interact with three types of external systems to acquire vibration-related operating condition data.

[0059] Subway Operation System: Acquires operational data such as subway departure / arrival times, train speeds, and train schedules;

[0060] Track maintenance system: Acquires maintenance data such as track wear level, maintenance cycle, and track defects (e.g., cracks, settlement);

[0061] Environmental monitoring system: Acquires environmental data such as temperature, humidity, and wind speed in the monitored area.

[0062] By classifying and summarizing direct vibration signals and operating condition data, a multi-dimensional operating condition feature library covering "building vibration - subway operation - track status - environmental conditions" is constructed.

[0063] The specific process of generating enhanced data by simulating building vibration data under different working conditions using the vibration transmission mechanics model is as follows:

[0064] Step S1.21: Based on the wheel-rail contact mechanics model, simulate the mapping relationship between the excitation signal and the transmission path parameters under different working conditions. The wheel-rail contact mechanics model adopts Hertzian contact theory, and the excitation signal is the wheel-rail impact force. (Unit: kN) indicates that the transmission path parameters are expressed in terms of wheel-rail contact stiffness. (Unit: kN / m) indicates wheel-rail impact force. Represented as:

[0065] ;

[0066] In the formula, The elastic modulus of wheel and rail materials (unit: GPa, steel) (approximately 206 GPa) This represents the equivalent radius of wheel-rail contact (unit: m, calculated based on wheel diameter and rail head curvature, e.g., when the wheel diameter is 840 mm). (Approximately 0.42m) This indicates the Poisson's ratio of the wheel and rail material (approximately 0.3 for steel). Indicates the amount of wheel-rail contact deformation (unit: mm);

[0067] By adjusting the wheel-rail contact deformation (Simulating different degrees of track wear; the more severe the wear, the better.) Larger), wheel-rail contact stiffness Or the train load (the greater the load, the greater the wheel-rail contact deformation). (The larger the value), the greater the corresponding wheel-rail impact force. The mapping relationship between "track wear degree / wheel-rail contact stiffness / train load - excitation signal - transmission path parameters" is obtained, and multiple sets of excitation signal and transmission path parameter samples are generated.

[0068] Step S1.22: Based on the vibration transmission wave equation, simulate the mapping relationship between transmission path parameters and vibration response under different working conditions. The vibration transmission wave equation is:

[0069] ;

[0070] In the formula, express Time, location Vibration displacement response at the location (unit: mm); This indicates the propagation speed of vibration waves in the transmission medium (unit: m / s; the longitudinal wave velocity in concrete is approximately 3000 m / s). express The impact force of wheels and rails at any moment; Indicates the mass of the medium being transferred (unit: kg, calculated based on the medium's volume and density). Represents the Dirac function; Indicates the sign of the partial derivative; Indicates wheel-rail impact force The coordinates of the position of the force determine the point of application of the excitation force in space;

[0071] By adjusting transmission path parameters (such as the wheel-rail contact stiffness corresponding to the degree of track wear) Wheel-rail impact force corresponding to train load Solving the vibration transmission wave equation yields the vibration displacement response under different parameters. This leads to the mapping relationship between "track wear degree / wheel-rail contact stiffness / train load - transmission path parameters - vibration response", generating multiple sets of vibration response samples, i.e., enhanced data.

[0072] The specific process of fusing augmented data with collected direct vibration signals and operating condition data to form a hybrid dataset is as follows: The augmented data, direct vibration signals, and operating condition data are normalized, and then the normalized augmented data, direct vibration signals, and operating condition data are mixed proportionally to form a hybrid dataset. This dataset can increase the sample size to 3-5 times the original measured sample size, effectively solving the problem of sparse measured data. Simultaneously, the simulated data is generated based on a mechanical model, ensuring physical rationality and avoiding distortion caused by pure data augmentation.

[0073] Step S2: Construct a hybrid deep learning model with embedded physical priors, train the model based on the hybrid dataset, and perform bi-objective optimization on the model parameters.

[0074] The hybrid deep learning model employs a dual-branch feature extraction and vibration response output architecture. The two branches process direct vibration signals and operational data separately, while the vibration response output module decodes the high-dimensional feature vector fused from the two branches into specific vibration response prediction values. The specific design is as follows:

[0075] 1. Branch 1 of the hybrid deep learning model uses a combination of convolutional neural network (CNN) and Transformer encoder to extract the time-frequency domain features of vibration signals:

[0076] A three-layer convolutional neural network (CNN) is used to extract local temporal features of vibration signals.

[0077] The first convolutional kernel size is set to 3×1, with 32 output channels, to capture local temporal details; the second convolutional kernel size is set to 5×1, with 64 output channels; and the third convolutional kernel size is set to 7×1, with 128 output channels.

[0078] The vibration signal is converted into a time-frequency diagram using a short-time Fourier transform (STFT). The formula for calculating the short-time Fourier transform is as follows:

[0079] ;

[0080] In the formula, Indicates the time-frequency diagram in Time, frequency The amplitude at that point; Indicates vibration signal; Represents the time variable of the vibration signal; Indicates the window function; Indicates the integral; The base of the natural logarithm; It represents the imaginary unit.

[0081] The time-frequency plot is input into the last two layers of the convolutional neural network to capture frequency domain features, and the frequency domain features are concatenated with the time domain features to form a feature vector with a dimension of 256.

[0082] The concatenated feature vector is input into a two-layer Transformer encoder, which outputs a time-frequency fused feature. The self-attention calculation formula of the Transformer encoder is as follows:

[0083] ;

[0084] In the formula, , , These represent the query matrix, key matrix, and value matrix, respectively, which are obtained by linear transformation of the concatenated feature vectors. express , The dimension; express transpose; express Activation function; This indicates a self-attention operation;

[0085] By capturing the dynamic correlation of vibration signals at different time steps through a self-attention mechanism, this branch ultimately outputs a time-domain-frequency domain fusion feature with a dimension of 256.

[0086] 2. Branch 2 of the hybrid deep learning model adopts a fully connected layer (FC layer) structure to extract low-dimensional vector features from the working condition data:

[0087] Normalize the operating data such as train load, track wear level, and foundation stiffness before inputting them into the two-layer fully connected layer. The calculation formula for the first fully connected layer is:

[0088] ;

[0089] In the formula, This represents the output of the first fully connected layer; This represents the weight matrix of the first fully connected layer; This represents the normalized operating condition data; Represents the ReLU activation function; This represents the bias vector of the first fully connected layer;

[0090] The second fully connected layer will process the output of the first fully connected layer. The feature is transformed into a low-dimensional vector with a dimension of 256, and the calculation formula is as follows:

[0091] ;

[0092] In the formula, This represents the output of the second fully connected layer; This represents the weight matrix of the second fully connected layer; This represents the bias vector of the second fully connected layer.

[0093] 3. The time-frequency domain fusion features output from branch 1 of the hybrid deep learning model and the low-dimensional vector features output from branch 2 of the hybrid deep learning model are added element-wise to obtain the fused features. These fused features are then input into the vibration response output module for vibration response prediction. The dual-branch architecture of the hybrid deep learning model solves the problem that traditional models cannot simultaneously process signal features and operating condition data, thus improving the completeness of feature representation.

[0094] The vibration response output module includes, in sequence:

[0095] One fully connected layer, employing the ReLU activation function, is used for advanced nonlinear fitting and feature dimensionality reduction. A linear output layer is also included, with the number of neurons configured according to the prediction task: one neuron for predicting single-point acceleration; two neurons for simultaneously predicting acceleration and displacement; and the number of neurons equal to the time step size for predicting responses at multiple future time steps. The input to this output module is the 256-dimensional fused features from the dual-branch architecture, and the output is the final predicted vibration acceleration (m / s²) or displacement (mm).

[0096] The construction of a hybrid deep learning model that incorporates embedded physical priors includes:

[0097] By integrating physical laws and constraints into the training process of hybrid deep learning models, and avoiding outputs that violate actual physical logic, this is achieved through a dual approach: loss function regularization and prior parameter input.

[0098] Step S2.21: Physical constraints are transformed into loss function regularization terms;

[0099] The core physical laws governing vibration transmission are transformed into constraints of the loss function, and jointly optimized with the prediction loss of the hybrid deep learning model (such as MSE loss). Specifically, this includes:

[0100] 1. Energy Conservation Law Constraint: Ensure that the vibration energy predicted by the hybrid deep learning model does not "appear out of thin air" or "disappear out of thin air" during the transmission process (e.g., the attenuation law of vibration energy as it is transmitted along the building structure conforms to energy conservation); specifically, based on the principle of energy conservation in vibration systems, calculate the energy loss rate during vibration transmission and define the energy conservation regularization term. The relative error between the predicted vibration energy and the measured vibration energy is calculated using the following formula: , This represents the predicted vibrational energy. The measured vibration energy is obtained by integrating the acceleration signal. , Indicates equivalent mass. Indicates the sampling time. Indicates the acceleration of vibration over time The change function; the regularization term constrains the energy predicted by the hybrid deep learning model to conform to the decay law, avoiding the physical inconsistency of "energy at distant measurement points being higher than that at nearby measurement points".

[0101] 2. Boundary Condition Constraints: The vibration response output of the hybrid deep learning model at building boundaries (such as the connection point between the foundation and the wall) and track boundaries (such as the wheel-rail contact point) must conform to the physical limitations of the boundaries in actual engineering (such as vibration displacement at the boundary not exceeding the material limit). Specifically, considering the displacement continuity condition of the foundation-subsidiary interaction, boundary condition regularization terms are defined. The predicted deviation between the base vibration displacement of the building and the maximum allowable vibration displacement of the foundation is called the deviation. , This indicates the predicted vibration displacement at the bottom of the building foundation. Indicates the maximum permissible vibration displacement of the foundation; Based on the characteristic value of foundation bearing capacity Confirmed: If ≥150 , ,like <150 , This regularization term ensures that the displacements predicted by the hybrid deep learning model at the constraints conform to the physical constraints, avoiding unreasonable predictions due to constraint failure.

[0102] 3. Wheel-rail excitation-response amplitude matching constraint: Ensure that the building vibration response amplitude predicted by the hybrid deep learning model is physically and logically matched with the wheel-rail excitation (such as the impact force generated by track irregularities) (e.g., when the excitation amplitude increases, the response amplitude must increase synchronously, and the proportion must conform to the vibration transmission coefficient); specifically, based on the amplitude-frequency characteristic function of the wheel-rail system, an amplitude matching regularization term is defined. To determine the error between the predicted amplitude-frequency response and the theoretical amplitude-frequency response; the theoretical amplitude-frequency response function is expressed as: , This represents the natural angular frequency of the structure, which is a parameter representing the inherent vibration characteristics of the building's structure. Indicates the excitation angular frequency. This represents the structural damping ratio (taken as 0.05-0.15); this regularization term constrains the matching between the predicted response amplitude and the excitation amplitude, avoiding unreasonable situations such as "small excitation, large response" or "large excitation, small response".

[0103] 4. Vibration attenuation and transmission distance constraints: Define attenuation regularization terms :

[0104] ;

[0105] In the formula, Indicates the predicted vibration attenuation coefficient; Indicates the theoretical attenuation coefficient; Indicates the distance the vibration is transmitted.

[0106] Among them, the predicted vibration attenuation coefficient Represented as:

[0107] ;

[0108] In the formula, Indicates the energy source of the excitation; This indicates the predicted energy at the measurement point.

[0109] Among them, the theoretical attenuation coefficient Determined based on soil type: When the soil type is silty clay... When the local soil type is sandy soil, .

[0110] 5. Combine the four types of regularization terms with the mean squared error loss of the predicted value minus the true value in the hybrid deep learning model. By combining these, we obtain the total loss function of the hybrid deep learning model. :

[0111] ;

[0112] In the formula, , , , They represent the corresponding , , , The weighting coefficients.

[0113] Step S2.22: Physical parameters are used as prior inputs to the hybrid deep learning model;

[0114] Known physical parameters such as wheel-rail contact stiffness (calculated based on the matching degree of the elastic modulus of wheel-rail materials, requiring a matching degree > 0.8), track irregularity (the maximum deviation value measured using the 30m chord method), and the elastic modulus of building materials are directly used as fixed prior inputs to the deep learning model. This eliminates the need for the model to "blindly learn" from the data, reducing the model's dependence on the amount of data. At the same time, it ensures that the output conforms to the vibration transmission characteristics corresponding to the physical parameters (e.g., the greater the contact stiffness, the higher the wheel-rail vibration transmission efficiency).

[0115] Among them, the wheel-rail contact stiffness is used as the prior input of the hybrid deep learning model to guide the network to learn nonlinear mapping relationships that conform to mechanical logic, thereby improving the model's ability to capture the response of sudden excitations at the wheel-rail interface.

[0116] For wheel-rail contact stiffness, first obtain its actual value (unit: kN / m). For example, when the rail wear level is 1, the wheel-rail contact stiffness is approximately 5000 kN / m; when the rail wear level is 5, the wheel-rail contact stiffness is approximately 3000 kN / m. Then normalize this value: , This represents the normalized wheel-rail contact stiffness (dimensionless, range [0,1]). Indicates the maximum wheel-rail contact stiffness. Indicates the minimum wheel-rail contact stiffness; As a priori input, it is directly fed into the hybrid deep learning model and multiplied element-wise with the fusion features to obtain fusion features that incorporate the prior knowledge of wheel-rail contact stiffness. This approach enables the network to prioritize the influence of wheel-rail contact stiffness when learning vibration response mapping. For example, when the wheel-rail contact stiffness decreases (severe track wear), the network will automatically adjust the prediction weights for high-frequency vibration components, improving its ability to capture responses to abrupt excitations at the wheel-rail interface (such as sudden wheel-rail impacts) and avoiding prediction biases caused by traditional models ignoring this parameter.

[0117] In this study, track irregularity is used as a prior input to the hybrid deep learning model to enhance the model's adaptability to vibration spectrum feature shifts.

[0118] For track irregularities, they are first quantified as track irregularity amplitude. (Unit: mm), for example, the unevenness amplitude after track maintenance is approximately 0.1 mm, and after long-term use, the unevenness amplitude is approximately 0.5 mm; regarding the unevenness amplitude of the track... Normalization is performed: , This represents the normalized amplitude of the track irregularity. This indicates the minimum track irregularity. Indicates the maximum track irregularity; As a priori input, it is directly fed into the hybrid deep learning model and multiplied element-wise with the fused features to obtain fused features incorporating the prior knowledge of track irregularity. Track irregularity causes a shift in vibration spectrum features (e.g., as irregularity increases, the dominant vibration frequency shifts to lower frequencies). This priori input allows the network to perceive this shift trend in advance, enhancing the model's adaptability to vibration spectrum feature shifts; for example, when... As the frequency domain features increase, the network adjusts their weights to ensure that the predicted spectral features are consistent with the actual offset patterns.

[0119] In this way, physical parameters are no longer ordinary inputs to the model, but are integrated into the feature fusion process as "guiding signals", enabling the network to learn nonlinear mapping relationships that conform to mechanical logic, thus avoiding the problem of the lack of physical meaning in purely data-driven models.

[0120] The dual-objective optimization of the model parameters includes:

[0121] With prediction accuracy and physical plausibility as dual optimization objectives, the non-dominated sorting genetic algorithm (NSGA-II) is used to optimize the model's network parameters (such as the kernel size of the convolutional neural network (CNN), the number of attention heads in the Transformer encoder, and the number of neurons in the fully connected layer (FC layer). Specifically:

[0122] 1. Improve prediction accuracy: minimize With the goal, The coefficient of determination represents the ratio of the predicted response to the measured response of the hybrid deep learning model. The closer the value is to 1, the higher the prediction accuracy of the hybrid deep learning model. The smaller the value, the better the prediction accuracy improvement effect of the hybrid deep learning model;

[0123] 2. Enhance physical plausibility: minimize the loss of physical plausibility. With the goal, By the energy conservation regularity term Boundary condition regularization terms Amplitude matching regularization term We get the weighted sum. The smaller the value, the more the model's predictions conform to the physical laws of vibration transmission; It can be represented as:

[0124] .

[0125] By employing gradient descent-type optimization algorithms (such as Adam and SGD), the "accuracy loss" and "physical constraint loss" are simultaneously balanced during each parameter update, ultimately obtaining the optimal network parameters that balance prediction accuracy and physical logic.

[0126] 3. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) optimizes the network parameters of the model (such as the kernel size of the Convolutional Neural Network (CNN), the number of attention heads in the Transformer encoder, and the number of neurons in the fully connected layer (FC layer):

[0127] Non-dominated sorting genetic algorithms simulate natural selection and genetic operations (selection, crossover, mutation) to search the parameter space for algorithms that simultaneously achieve... and The minimum parameter combination; during the iteration process, for the model corresponding to each parameter combination, calculate its... and Based on mechanisms such as non-dominated sorting and crowding distance, better parameter combinations are selected and iteratively optimized step by step.

[0128] Step S3: Collect real-time direct vibration signals and corresponding working condition data. Based on the real-time direct vibration signals and corresponding working condition data, use a lightweight classification model (such as support vector machine (SVM)) to identify the current scene working condition. According to the identified current scene working condition, call the corresponding parameters and use a hybrid deep learning model to output the final vibration response prediction result.

[0129] In step S3, a working condition-model parameter mapping library is established based on the model parameters optimized by the dual objectives under different working conditions. According to the identified current working condition, the corresponding model parameters are called from the working condition-model parameter mapping library and input into the hybrid deep learning model. The hybrid deep learning model outputs the vibration response prediction result. This process does not require retraining the model, improves the efficiency of real-time prediction, and solves the problem of long time consumption in traditional finite element simulation.

[0130] Step S4: Periodically collect quantitative real-time direct vibration signals and corresponding working condition data, and fine-tune the parameter weights of the hybrid deep learning model using an incremental learning strategy; when the scene working conditions change significantly, use quantitative real-time working condition data to perform transfer learning fine-tuning on the hybrid deep learning model.

[0131] The specific process of fine-tuning the parameter weights of the hybrid deep learning model using an incremental learning strategy is as follows: A small amount of measured data (such as direct vibration signals from 50 key measuring points and corresponding working condition data) is collected weekly. The parameter weights of the hybrid deep learning model are then fine-tuned using an incremental learning strategy. For example, only the attention weights of the Transformer encoder and the output weights of the fully connected layer are fine-tuned. The parameter update formula is:

[0132] ;

[0133] In the formula, This represents the updated parameter weights of the hybrid deep learning model; This represents the parameter weights of the hybrid deep learning model before the update. This represents the learning rate (values ​​from 0.001 to 0.01). This represents the loss function of the hybrid deep learning model on the new task; This represents the gradient symbol.

[0134] In this scenario, when significant changes occur in the operating conditions (such as a significant change in fastener stiffness after track maintenance or a change in train model), a small amount of real-time operating condition data is collected. The hybrid deep learning model is used as a pre-trained model, and transfer learning is performed to fine-tune it using this small amount of real-time operating condition data. The fine-tuning loss function is then implemented. for:

[0135] ;

[0136] In the formula, Indicates the amount of real-time operating data collected; Indicates the first The actual value corresponding to each real-time operating condition data; Indicates the first Predicted values ​​of real-time operating condition data; Represents the regularization coefficient; This represents the current parameters of the hybrid deep learning model during the fine-tuning process; This represents the parameters when the hybrid deep learning model is used as a pre-trained model.

[0137] Through transfer learning, the model can quickly adapt to new vibration transmission characteristics, solving the problem that traditional models need to be remodeled when faced with sudden changes in operating conditions.

[0138] Step S5: Verify the accuracy and physical rationality of the vibration response prediction results; based on the verification results, adjust the weight of the regularization term in the physical prior or suggest supplementing the vibration sensor.

[0139] Among them, the accuracy verification calculation includes the mean square error (MSE) and correlation coefficient between the predicted vibration response and the measured vibration response. Correlation coefficient The calculation formula is expressed as follows:

[0140] ;

[0141] In the formula, This represents the average value of the measured vibration response results; This represents the average value of the vibration response prediction results; This indicates the amount of data used for vibration response prediction; Indicates the first Measured results of the vibration response; Indicates the first The predicted results of the vibration response.

[0142] The physical rationality verification includes:

[0143] Check whether the vibration response prediction results meet the energy attenuation law of vibration transmission (i.e., the predicted response energy of the measuring point far away from the excitation source should be less than that of the measuring point close to the excitation source).

[0144] Check whether the vibration response prediction results meet the matching requirements between the component vibration frequency and the structure's natural frequency (i.e., the predicted component vibration frequency should be within a reasonable range of the structure's natural frequency, such as a deviation of no more than 5%).

[0145] Based on the verification results, the weights of the regularization terms in the physical priors are adjusted, or suggestions are made to add vibration sensors. Specifically: if the vibration response prediction results for a certain area (such as a corner of a floor slab) have large errors and poor physical plausibility (such as energy not decaying with distance), then the weights of the regularization terms in the physical priors are adjusted (e.g., increasing the change function). To strengthen the energy conservation constraint, the model parameters should be re-optimized in a bi-objective manner. If the vibration response prediction result in this area has a large error but is physically reasonable (e.g., the energy decay is in accordance with the law but the numerical deviation is large), it is recommended to add vibration sensors in this area to increase the data density and further reduce the prediction error.

[0146] Through the above implementation methods, the model can accurately capture time-varying vibration characteristics and has physical rationality. At the same time, it solves traditional problems such as data sparsity and poor real-time performance, and improves the reliability and practicality of vibration response prediction.

[0147] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A deep learning-based method for predicting the vibration response of subway depot superstructures, characterized in that, Includes the following steps: Step S1: Construct a multi-dimensional working condition feature library, which contains direct vibration signals of buildings and vibration-related working condition data; simulate building vibration data under different working conditions based on the vibration transmission mechanics model to generate enhanced data; fuse the enhanced data, direct vibration signals and working condition data to form a hybrid dataset; Step S2: Construct a hybrid deep learning model with embedded physical priors, train the model based on the hybrid dataset, and perform bi-objective optimization on the model parameters; Step S3: Collect real-time direct vibration signals and corresponding working condition data. Based on the real-time direct vibration signals and corresponding working condition data, use a lightweight classification model to identify the current scene working condition. According to the identified current scene working condition, call the corresponding parameters and use a hybrid deep learning model to output the final vibration response prediction result. Step S4: Periodically collect quantitative real-time direct vibration signals and corresponding working condition data, and fine-tune the parameter weights of the hybrid deep learning model using an incremental learning strategy; When the scene conditions change significantly, the hybrid deep learning model is fine-tuned by transfer learning using quantitative real-time condition data. Step S5: Verify the accuracy and physical rationality of the vibration response prediction results; Based on the verification results, adjust the weight of the regularization term in the physical prior or suggest adding a vibration sensor; Constructing a hybrid deep learning model that incorporates embedded physical priors includes: This approach integrates physical laws and constraints into the training process of a hybrid deep learning model, achieved through a dual method of loss function regularization and prior parameter input. Physical constraints are transformed into regularization terms of the loss function: The core physical laws governing vibration transmission are converted into constraints of the loss function, which are then jointly optimized with the prediction loss of the hybrid deep learning model. Specifically, this includes: Energy conservation law constraint: Based on the principle of energy conservation in vibration systems, calculate the energy loss rate during vibration transmission and define the energy conservation regularization term. The relative error between the predicted vibration energy and the measured vibration energy is calculated using the following formula: , This represents the predicted vibrational energy. The measured vibration energy is obtained by integrating the acceleration signal. , Indicates equivalent mass. Indicates the sampling time. Indicates the acceleration of vibration over time The function of change; Indicates the integral; Boundary condition constraints: Considering the displacement continuity condition of the foundation-subsoil interaction, define boundary condition regularization terms. The predicted deviation between the base vibration displacement of the building and the maximum allowable vibration displacement of the foundation is called the deviation. , This indicates the predicted vibration displacement at the bottom of the building foundation. Indicates the maximum permissible vibration displacement of the foundation; Based on the characteristic value of foundation bearing capacity Confirmed: If ≥150 , ,like <150 , ; Wheel-rail excitation-response amplitude matching constraint: Based on the amplitude-frequency characteristic function of the wheel-rail system, an amplitude matching regularization term is defined. To determine the error between the predicted amplitude-frequency response and the theoretical amplitude-frequency response; the theoretical amplitude-frequency response function is expressed as: , This represents the natural angular frequency of the structure, which is a parameter representing the inherent vibration characteristics of the building's structure. Indicates the excitation angular frequency. Indicates the structural damping ratio; Represents the imaginary unit; Vibration attenuation and transmission distance constraints: Defining the attenuation regularization term , Indicates the predicted vibration attenuation coefficient; Indicates the theoretical attenuation coefficient; Indicates the distance the vibration is transmitted.

2. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 1, characterized in that: The four types of regularization terms are combined with the mean squared error loss of the predicted value minus the true value in the hybrid deep learning model. By combining these, we obtain the total loss function of the hybrid deep learning model. : ； In the formula, , , , They represent the corresponding , , , Weighting coefficients; Physical parameters, including wheel-rail contact stiffness, track irregularity, and building material elastic modulus, are directly used as fixed prior inputs to the deep learning model. For wheel-rail contact stiffness, it is first normalized; the normalized wheel-rail contact stiffness is used as a prior input and directly input into the hybrid deep learning model, and multiplied element-wise with the fusion features to obtain the fusion features with the wheel-rail contact stiffness prior. For track irregularities, they are first quantified as track irregularity amplitude. ; Amplitude of track irregularities Normalization is performed; the normalized track irregularity amplitude is used as a priori input and directly input into the hybrid deep learning model, where it is multiplied element-wise with the fusion features to obtain the fusion features with the prior track irregularity.

3. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 2, characterized in that: The hybrid deep learning model employs a dual-branch feature extraction and vibration response output architecture. The two branches process direct vibration signals and operational data separately. The vibration response output module decodes the high-dimensional feature vector fused from the two branches into specific vibration response prediction values, including: Branch 1 of the hybrid deep learning model adopts a combination structure of convolutional neural network and Transformer encoder to extract the time-frequency domain features of vibration signal: a 3-layer convolutional neural network is used to extract the local time domain features of vibration signal; the vibration signal is converted into time-frequency map through short-time Fourier transform; the time-frequency map is input into the last two layers of convolutional neural network to capture frequency domain features; the frequency domain features are concatenated with the time domain features and then input into a 2-layer Transformer encoder to output time-frequency domain fused features; Branch 2 of the hybrid deep learning model adopts a fully connected layer structure to extract low-dimensional vector features from the working condition data: the working condition data is normalized and then input into two fully connected layers to output low-dimensional vector features. The time-frequency fusion features output by branch 1 of the hybrid deep learning model and the low-dimensional vector features output by branch 2 of the hybrid deep learning model are added element by element to obtain the fusion features. The fusion features are then input into the vibration response output module for vibration response prediction.

4. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 3, characterized in that: Bi-objective optimization of model parameters includes: With prediction accuracy and physical plausibility as dual optimization objectives, a non-dominated sorting genetic algorithm is used to optimize the network parameters of the hybrid deep learning model. Specifically: To minimize With the goal, The coefficient of determination represents the ratio of the predicted response to the measured response of the hybrid deep learning model. To minimize the loss of physical rationality With the goal, By the energy conservation regularity term Boundary condition regularization terms Amplitude matching regularization term We get the result by weighted summation; Gradient descent-type optimization algorithms are used to simultaneously balance the loss of accuracy and the loss of physical constraints during each parameter update; The non-dominated sorting genetic algorithm NSGA-II optimizes network parameters for hybrid deep learning models, including convolutional neural network kernel size, Transformer encoder attention head number, and number of neurons in fully connected layers.

5. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 4, characterized in that: The specific process of fine-tuning the parameter weights of the hybrid deep learning model using an incremental learning strategy is as follows: collect quantitative measured direct vibration signals and corresponding working condition data regularly every week, and fine-tune the parameter weights of the hybrid deep learning model using an incremental learning strategy, including fine-tuning the attention weights of the Transformer encoder and the output weights of the fully connected layer. When the operating conditions change significantly, such as when the stiffness of the fasteners changes significantly after track maintenance or when the train model is changed, a quantitative amount of real-time operating condition data is collected. The hybrid deep learning model is used as a pre-trained model, and the collected real-time operating condition data is used for transfer learning fine-tuning.

6. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 5, characterized in that: Accuracy verification calculations included the mean square error (MSE) and correlation coefficient between the predicted vibration response and the measured vibration response. Physical rationality verification includes: checking whether the vibration response prediction results meet the energy attenuation law of vibration transmission; and checking whether the vibration response prediction results meet the matching of the component vibration frequency and the structure's natural frequency.

7. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 6, characterized in that: Based on the verification results, the specific process for adjusting the regularization term weights in the physical prior or suggesting the addition of vibration sensors is as follows: If the predicted vibration response at the floor corner has a large error and poor physical plausibility, adjust the regularization term weights in the physical prior and re-optimize the model parameters using a bi-objective approach; if the predicted vibration response at the floor corner has a large error but is physically plausible, add vibration sensors to the floor corner to increase data density; adjusting the regularization term weights in the physical prior includes increasing the change function. To strengthen the constraint of energy conservation.

8. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 7, characterized in that: The specific process of generating enhanced data by simulating building vibration data under different working conditions using a vibration transmission mechanics model is as follows: Based on the wheel-rail contact mechanics model, the mapping relationship between excitation signal and transmission path parameters under different working conditions is simulated. The wheel-rail contact mechanics model adopts Hertzian contact theory, and the excitation signal is the wheel-rail impact force. This indicates that the transmission path parameters are based on wheel-rail contact stiffness. Indicates wheel-rail impact force Represented as: ； In the formula, This represents the elastic modulus of the wheel and rail material; Indicates the equivalent radius of wheel-rail contact; This represents the Poisson's ratio of the wheel and rail materials. This indicates the amount of wheel-rail contact deformation; By adjusting the wheel-rail contact deformation Wheel-rail contact stiffness Or, calculate the corresponding wheel-rail impact force based on the train's load. The mapping relationship between excitation signals and transmission path parameters under different working conditions is obtained, and multiple sets of excitation signal and transmission path parameter samples are generated. Based on the vibration transmission wave equation, the mapping relationship between transmission path parameters and vibration response under different working conditions is simulated; the vibration transmission wave equation is: ； In the formula, express Time, location Vibration displacement response at the location; This indicates the speed at which a vibration wave propagates in the transmission medium. express The impact force of wheels and rails at any moment; Indicates the quality of the transmission medium; Represents the Dirac function; Indicates the sign of the partial derivative; Indicates wheel-rail impact force The coordinates of the position where the action takes place; By adjusting the transmission path parameters, the vibration displacement response under different parameters can be obtained by solving the wave equation. This allows us to obtain the mapping relationship between transmission path parameters and vibration response under different working conditions, and generate multiple sets of vibration response samples, i.e., enhanced data.

9. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 8, characterized in that: In step S3, a working condition-model parameter mapping library is established based on the model parameters optimized by the dual objectives under different working conditions. According to the identified current working condition, the corresponding model parameters are called from the working condition-model parameter mapping library and input into the hybrid deep learning model. The hybrid deep learning model outputs the vibration response prediction result.

10. The method for predicting the vibration response of subway depot superstructures based on deep learning according to claim 1, characterized in that: Direct vibration signal acquisition: Vibration sensors are deployed at key measuring points of the building to collect the building's original vibration signals in real time. Operating condition data acquisition: Interacting with three types of external systems to acquire vibration-related operating condition data: Subway Operation System: Acquires operational data, including subway departure or arrival times, train speeds, and train schedules; Track maintenance system: Acquires maintenance data, including track wear level, maintenance cycle, and track defects; Environmental monitoring system: Acquires environmental data, including temperature, humidity, and wind speed in the monitored area.

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