Analysis and intelligent prediction of subway train-induced vibration in the building with pile foundation

The rapid development of subway construction inevitably leads to the subway lines traversing through or adjoining the buildings. However, current research primarily focuses on the train-induced ground-borne or building with shallow foundation vibrations, with a relatively limited investigation into the vibration pertaining to the building with pile foundation. A vibration analysis model of a building with pile foundation adjacent to a subway is established in this study using the finite element method, and the effects of various factors on the vibration of the building are analyzed, then the prediction of building vibration characteristics is also carried out by combining artificial intelligence methods. The results show that the building floor has an amplifying effect on the vibration acceleration level and Z-vibration level in the high frequency range, and the vibration energy attenuation at high frequencies is faster in the building with pile foundation compared to the building with shallow foundation. In the meantime, it shows that the GA-BP model is capable of effectively capturing the vibration characteristics of the building with pile foundation within the dominant frequency range. and the vibration of the building with pile foundation can be predicted not only by parameters such as train speed, soil and structure parameters but also by train-induced ground-borne vibration, which provides the possibility of simplifying the process of vibration prediction process and enhancing the practical application.


Introduction
Urban rail transit serves as the primary mode of transportation for city residents.By the end of 2022, a total of 55 cities in mainland China had operated urban rail transit, covering a vast network spanning 10,287.45kilometers, of which 77.84% were subway lines [1].With the rapid development of metro construction in cities, the expansion of metro lines inevitably leads to their proximity to or passing through densely populated areas, which in turn gives rise to the issue of vibration and noise in existing buildings along the subway lines.This phenomenon will interfere with the rest and work of residents and raise concerns about the structural safety of the building [2,3] Research regarding subway train-induced vibrations primarily focuses on the subway tunnels, the ground, and adjacent structures.Zhang et al. [4] conducted a study on the acceleration response of the track within the tunnel and the ground, and analyzed the train-induced vibration response of the tunnel under different operating conditions.The ground-borne vibration response of train operation in layered soils has also been analyzed based on different methods, such as 2.5D or 3D FE-BE [5,6].With the deepening research on train-induced vibrations, the refinement of the vehicle-track-soil-structure model 1337 (2024) 012052 IOP Publishing doi:10.1088/1755-1315/1337/1/012052 2 has been gradually progressing, accompanied by a stepwise enhancement in computational accuracy.On the other hand, with the development of artificial intelligence technology, an increasing number of researchers have adopted machine learning methods to carry out studies on the vibration prediction problem and compared the results with the traditional analysis methods.Machine learning methods have also been introduced to predict the environmental vibrations caused by urban rail transit.
To solve the problem mentioned above, this paper proposes a BP neural network machine learning model based on the optimization of the genetic algorithm (GA) to predict the subway train-induced vibration of buildings with pile foundation.Firstly, the loads generated by the subway train movement are simulated by UM software.Secondly, the simulated loads are applied to the finite element analysis model of the tunnel-soil-buildings system for further calculation.Finally, the calculation results are imported into the GA-BP neural network as a sample dataset for training, and the prediction of the subway train-induced vibration of buildings with pile foundation is performed.In the meantime, this paper establishes an approach for predicting the subway train-induced vibration of buildings with pile foundation through ground-borne vibration.In comparison to traditional analytical approaches, this approach demonstrates a good ability to rapidly predict vibrations in buildings adjacent to the subway during the preliminary engineering design phase, which helps to offer guideline suggestions for vibration control in the subsequent construction stage.

Finite element model for subway train-induced vibration
To solve the problem mentioned above, the genetic algorithm (GA) is introduced in the BP model to optimize the connection weights and biases of the neural network, which is called the GA-BP neural network.The GA, unconstrained by the limiting assumptions of the search space, can effectively obtain the optimal threshold and connection weights of a BP neural network with a high probability in discrete, multi-modal, and noisy high-dimensional problems.This helps to improve the reliability and accuracy of the model [7].

The vehicle-track analytical model
The trains operating in the Nanchang subway are taken as the research object [8], based on the theory of vehicle-rail coupling dynamics [9].The vehicle used in Nanchang subway is a B-type train, in which the carriage is a vibration system with 10 degrees of freedom composed of two bogies and four-wheel pairs, and connected by the main suspension and sub-suspension system [10].Considering the heavy load condition for the moving train, the static axle weight is 133.8kN, and the Hertz nonlinear contact theory is used to determine the interaction between the wheels and rails.The physical characteristics of the rail model were parameterized with reference to the CHN60 rail and DTVI2 fastener, and the rail gauge is 1435mm.

The tunnel-soil-buildings analytical model
A residential building with pile foundation adjacent to Nanchang Subway Line 2, which is a typical 7story frame structure, is taken as the research object.The distance S between the building and the center of the tunnel is approximately 21.6m.The storey height of the building h, the length l and the spacing d of the pile foundation are 3m, 10m and 4m, respectively.The diameter D and center embedded depth L of the tunnel are 5.4m and 10.8m, as shown in Figure 1, and the physical parameters of the soil are shown in Table 1.In calculating the train-induced environmental and building vibration response, research has pointed out that the simulation results of the two-dimensional (2D) finite element model are close to those of the three-dimensional (3D) finite element model, especially for the vibration response distribution pattern at different frequencies [12].Considering the numerical simulation results are used as the training dataset for machine learning, which needs to ensure the richness and accessibility of the training data, thus a 2D finite element model of the tunnel-soil-building is established for further analysis in this study.

The training dataset for the GA-BP model
To enrich the training dataset of subway train-induced vibration, a comprehensive parametric study was carried out in the numerical simulations.The work conditions specifically considered are listed in Table 2, and a total number of 64×7 datasets of train-induced building vibration responses under different working conditions were obtained by orthogonal design, which is a sufficient amount of data for machine learning training [13].  2 gives the framework of the prediction of the train-induced vibration model, in which the train speed, the embedded depth of the tunnel, the distance between the tunnel and the building, the elastic modulus of soil and soil damping were selected as the input layer, while the Z-vibration level VLz or the acceleration level VALi in the one-third octave band were selected as the output layer.

Implementation of the GA-BP model
In order to visualize the vibration characteristics of different floors of the building, the corresponding vibration acceleration levels in one-third octave band of each floor under different working conditions are given as shown in Figure 3.According to the Figure 3, the vibration frequencies of buildings caused by subway operation are mainly distributed within 80 Hz, where the dominant frequencies are in the range of about 1.0 Hz to 25 Hz.Compared with the building with shallow foundation, the vibration energy of the building with pile foundation decays faster, and the vibration acceleration level reaches a small value around 80 Hz, while the buildings with shallow foundation show a decrease in the vibration acceleration level around 80 Hz [14].This is attributed to the fact that vibration wave propagation across a building with pile foundation needs to pass through the pile body, pile cap and soil, while a building with shallow foundation only needs to pass through the soil and shallow foundation.Obviously, the increase in the transmission path increases the energy dissipation.The pile body also plays a role of vibration isolation, that is, the pile foundation is effective in reducing the propagation of reflected waves from the soil-pile contact surfaces to the superstructure, especially in the high frequency range [15,16].GA-BP model shows a high prediction accuracy when the vibration frequency is within the range of 20 Hz, and the prediction error gradually increases in the vibration frequency range of 20 Hz to 80 Hz.Nevertheless, it can be seen that the dominant frequency of the building with pile foundation is mainly distributed within 25 Hz in Figure 3, and the prediction results of GA-BP are sufficient to fulfill the computational needs.

Figure 5. Comparison of Root Mean Square Error (RMSE) of vibration acceleration levels
predicted by the BP and GA-BP models The tolerance between the predicted and simulated results for the BP and GA-BP models is also given in Figure 6. Figure 7 shows the sensitivity of optimized parameters using BP and GA-BP models.The regression values of each parameter for the BP and GA-BP models are given in Figure 7.A larger R 2 value is an indication of a better fitting, implying that the model is capable of capturing the features of the data, and the R 2 values of the GA-BP model are all greater than 0.95, demonstrating that the GA-BP model has a favorable prediction ability [17,18].This is due to the fact that the GA-BP model is able to globally search for optimal training weights and biases using the GA algorithm, which makes the GA-BP model more preferable in dealing with nonlinear relationships.

Discussion
The GA-BP model proposed above can rapidly predict the train-induced vibration of a building once the soil and structural parameters have been obtained; however, it is very time-consuming to get the soil parameters accurately and the efficiency and convenience of the proposed model will be limited.Therefore, the method of predicting train-induced vibration of the building with ground-borne vibration adjacent to the building is further constructed based on the proposed model, which is defined as the improved GA-BP model.Figure 10 gives the framework of the prediction. .The framework for predicting building vibration The improved GA-BP model is used to predict the train-induced building vibration under different operating conditions, and one-third octave vibration acceleration levels are given in Figure 11.The results show that the improved GA-BP model can well capture the vibration acceleration level distribution pattern of the building with pile foundation at different frequencies.According to Figure 12, the improved GA-BP model shows better prediction in the full frequency range compared to the original GA-BP model, especially for the dominant frequency.This may be attributed to the fact that vibration propagation in soil is a complex process involving the interaction of several factors, the use of the improved model avoids the influence of uncertainties and the train-induced building vibration is directly related to the vibration of the surrounding soil [20].

Summary and conclusions
This paper analyzes the vibration characteristics of the building with pile foundation adjacent to the subway based on the finite element method, and the influences of soil parameters, train speed, tunnel embedded depth, and distance of the building from the tunnel on the vibration response of the building were investigated.The train-induced vibration of the building was predicted by the artificial intelligence method, whose reliability was verified by comparing with the field measured data.The following conclusions can be drawn: (1) The dominant frequency of pile foundation building vibration is mainly in the range of 1-25Hz.The one-third octave vibration acceleration level of the building increases with the increase of the floor, especially when the vibration frequency is greater than 20Hz.Similarly, the Zvibration level tends to be amplified with the increase of floors, but the amplification effect is not significant.Compared with the building with shallow foundation, the vibration energy of the building with pile foundation decays faster, and the vibration acceleration level reaches a small value around 80 Hz, while the building with shallow foundation shows a decrease in the vibration acceleration level around 80 Hz (2) The GA-BP model shows a better prediction performance than the traditional BP model in terms of the number of training cycles, RMSE, and R 2 .The GA-BP model is capable of capturing the train-induced vibration response of the building with pile foundation adjacent to the subway line, especially for the dominant frequency range.(3) It is possible to predict the train-induced vibration of a building with pile foundation not only by the train operation parameters, soil parameters and structural parameters, but also by the ground-borne vibration surrounding the building, and the results show that it is more accurate to predict the train-induced vibration of a building by the ground-borne vibration, which provides the possibility of simplifying the vibration analysis.

Figure 1 .
Figure 1.Illustration of the relative positions of the building and the subway lineTable1.The physical parameters of the soil

Figure 2 .
Figure 2.The framework of the prediction of the train-induced vibration

Figure 3 .Figure 4 .
Figure 3. Vibration acceleration level in one-third octave band for the building with pile foundation at different floors

Figure 6 .Figure 7 .6
Figure 6.Tolerance between the predicted and simulated results for the BP and GA-BP models

Figure 8 .
Figure 8. Schematic diagram of field tests and soil parametersThen the acceleration data were converted to one-third octave vibration acceleration levels and compared to the predicted results, as shown in Figure9.The results show a slight fluctuation in the predicted values from 4 Hz to 25 Hz compared to the measured values.This may be due to the frequency range of 4 Hz to 25 Hz being the dominant frequency for the train-induced vibration of the buildings, and the train-induced vibration is also closely related to the vehicle, track, and the site conditions[19], which may lead to the fluctuation of the measured values in engineering practice.However, the onethird octave vibration acceleration levels predicted by the GA-BP model are overall similar to the measured values, which proves that it is feasible to use the GA-BP model to predict the train-induced vibration of the buildings with pile foundation adjacent to the subway line.

Figure 9 .
Figure 9.Comparison of predicted and measured results of vibration acceleration level Figure 10.The framework for predicting building vibrationThe improved GA-BP model is used to predict the train-induced building vibration under different operating conditions, and one-third octave vibration acceleration levels are given in Figure11.The results show that the improved GA-BP model can well capture the vibration acceleration level distribution pattern of the building with pile foundation at different frequencies.According to Figure12, the improved GA-BP model shows better prediction in the full frequency range compared to the original GA-BP model, especially for the dominant frequency.This may be attributed to the fact that vibration propagation in soil is a complex process involving the interaction of several factors, the use of the improved model avoids the influence of uncertainties and the train-induced building vibration is directly related to the vibration of the surrounding soil[20].

Table 1 .
The physical parameters of the soil

Table 2 .
Different work conditions for Pre-training