Study on the Scoping prediction of Railway-induced environmental vi- bration based on Transfer learning Ruihua Liang 1 , Weifeng Liu 2 Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong Uni- versity Beijing 100044, China

ABSTRACT While the urban rail transit infrastructures provide convenience to people, environmental vibrations and radiated noise generated by its operation can also affect the residents in the surrounding build- ings. Therefore, during the preliminary design stage of railway lines, extensive vibration scoping prediction needs to be carried out, which can promote reasonable vibration mitigation design, thus minimizing the impact of the railway induced environmental vibration. Considering the limitations in the accuracy of existing methods, a deep learning-based vibration scoping prediction model is proposed in this paper. Moreover, the transfer learning strategies are used to enable the model to be trained with the railway induced vibration data obtained from both numerical simulations and field measurements, which allows the model to be trained more sufficiently and thus achieve higher pre- diction accuracy while keeping high efficiency. To validate the performance of the proposed method, a case study is presented. Specifically, vibration data under different conditions obtained from nu- merical simulations and measurements are used to train and test the deep learning-based models using transfer learning strategies. Then, by comparing the performance of the trained model with the existing scoping methods, the feasibility and advancement of the proposed method are demonstrated.

1. INTRODUCTION

In recent years, urban rail transit infrastructure has been widely developed in major cities around the world. However, while rail transit provides convenience for the travel of urban residents, it also brings severe environmental vibration impacts. Excessive vibration and the structure-radiated noise it causes could affect the normal life of residents around the railway line [1, 2]. Therefore, scoping prediction of environmental vibration is necessary during the design phase of a new railway line, which could ensure that the environmental vibration impact on the buildings surrounding the line is acceptable after construction is completed.

In recent decades, various models have been developed to predict the environmental vibration caused by trains, which can be broadly classified into numerical [3], empirical [4], and hybrid meth- ods [5]. Due to the different demands on the efficiency of vibration prediction, different methods are often used to carry out vibration prediction at different stages of railway construction. In particular, the empirical models, as fitting models based on existing vibration data, are able to achieve very efficient environmental vibration prediction and therefore are usually used for scoping prediction during the design phase of a new railway line. Currently, this vibration prediction method has been widely adopted by the standards of countries all over the world.

1 18115029@bjtu.edu.cn

2 wfliu@bjtu.edu.cn

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Recently, data-driven machine learning (ML) techniques have been rapidly developed, which are able to create adaptive fitting relationships between conditions and responses, thus reducing the prediction errors caused by fixed fitting relationships in empirical methods [6]. These techniques have been widely used in studies related to prediction and classification in various engineering fields. Spe- cifically, Connolly [7] and G. Paneiro [8] have conducted studies on the scoping prediction of train- induced vibrations based on the artificial neural network (ANN) models, and both achieved good prediction performance.

However, one significant drawback of ML-based train-induced vibration prediction is that it is very dependent on the quantity and quality of actual vibration measurement data. In engineering, it is very expensive to perform vibration measurements and even more difficult to collect vibration data under complex condition variables, this situation leads to the inability to train ML-based models with sufficient vibration samples, which limits the accuracy of the method for scoping prediction of rail- way-induced vibration.

To deal with the over-reliance of ML methods on data from a particular domain, transfer learning (TL) techniques have been introduced in recent years and are widely used in many tasks in various engineering fields [9]. The concept of TL is to transfer the prior knowledge obtained in a source domain with sufficient data to a target domain with fewer data, thus improving the prediction accu- racy of ML-based models in the target domain [10].

In the field of train-induced environmental vibration, measured vibration data are accurate but also costly, while simulated vibration data generated using numerical models are low cost but with discounted accuracy. Therefore, the application of TL techniques to enable ML-based models to con- sider simulated vibration data when optimizing with measured vibration data is a promising concept, which can reduce the overdependence of the method on costly measurement data and improve the accuracy of the method. In this paper, a TL-based method for predicting train-induced environmental vibration is presented, and a case study is presented to demonstrate the performance of the proposed method.

2. METHODOLOGY

2.1. Related Background Knowledge

In these developed ANN-based train-induced environmental vibration prediction models, the inputs of the model are various condition variables related to the vibration magnitude, such as train speed, tunnel burial depth, and soil parameters. The output of the model is the magnitude of the en- vironmental vibration induced by trains, e.g., vibration decibels VdBmax. The mathematical relation- ship between model inputs and outputs is modelled by a large number of weight parameters in the ANN model, the values of which can be obtained in the optimization using vibration data, this process is also known as the training of the ANN model. In the traditional ANN-based model, the model is trained from scratch based on the measured vibration data, as shown in Figure 1 (a).

As mentioned in the previous section, this paper proposes to use the TL technique to consider the prior knowledge obtained from the numerically simulated vibration data in the model training. There are two common TL strategies, the first one is to pre-train the weight parameters of the model using vibration simulation data, and then fine-tune the pre-trained model weight parameters using the measured vibration data, as shown in Figure 1 (b). The second one is to freeze the weight parameters in the first few layers of the model after the model is pre-trained, and then retrain the weight param- eters in the latter layers of the model, as shown in Figure 1 (c).

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Figure 1: Schematic diagram of the model training process under various strategies

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2.2. The Research Framework

The basic framework of the proposed method is shown in Figure 2. Specifically, vehicle-track coupled numerical models and tunnel-soil coupled numerical models are developed to simulate the train-induced environmental vibration data under various conditions, and these data are used to pre- train the ANN models. Subsequently, the measured data collected by the research team would be used to retrain the pre-trained models based on various TL strategies. Finally, the retrained model can be used to predict the train-induced environmental vibrations.

Random initialization of all weights Initialization with pre-trained weights Initialization with pre-trained weigl Tem ; ok ; Bed > 4 : Bias EN ( ia WEX UO OS (a) Train the model from seratch (b) Fine-tune the pretrained model (©) Train the last layers of model

Figure 2: Basic framework of the proposed method

3. MODEL IMPLEMENTATION

‘Vain propeatin sito Freuerey 2) Preto of ition slertinee yration measurement data 4. Fine-tunning model in target domain

3.1. The Vibration Simulation Data

In this paper, the simulation of the train-induced environmental vibrations is considered as the simulation of two subsystems. Specifically, the vehicle-rail interaction forces are solved by an ana- lytical vehicle-rail coupling model, in which the vehicle is considered as a multi-rigid body system and the rail is considered as a discrete supported Euler beam, as shown in Figure 3. The support re- action forces of the fasteners during train travel are solved and fed into the tunnel-soil system as ex- citation forces, details of the vehicle-rail coupling model can be found in the literature [5]. In addi- tion, the finite element method was used to simulate the transmission of train-induced vibration in the tunnel-soil system, and the model established is shown in Figure 4. Details of the simulation of train-induced vibration transmission using the finite element method can be found in the literature [11].

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Figure 3: Schematic diagram of the vehicle-track coupling model

i | Ral v Me Ie oe — Carriage Reps i] mo i 5.8 —_ <= ait | sippons or Sos Srl Neo TE BOE “ide

Note: ¥ Train induced dynamic excitation + Vibration observation points

Figure 4: Schematic diagram of the finite element model built in this study

Using the numerical method described above, the train-induced environmental vibration data for various condition variables can be computed and used for subsequent pre-training of the model. For the numerical calculation, the condition variables considered in this paper are train speed, average dynamic modulus of elasticity of the soil, burial depth of the tunnel vault and horizontal distance between the surface measurement point and the track. Specifically, four typical train speeds of 30km/h, 45km/h, 60km/h and 75km/h, four typical burial depths of 10m, 15m, 20m and 25m, six typical dynamic modulus of the soil of 100MPa, 200MPa, 300MPa, 400MPa, 500MPa and 600MPa, and 21 measurement points in the range of 0-100m from the track centerline are considered in this paper. Since the vibration response at various positions can be calculated in the same model, 4×4×6=96 numerical models need to be calculated, and 96×21=2016 vibration response data under different condition variables are finally obtained. In addition, other parameters in these numerical calculations are adopted from the typical parameters of trains and ground of the Beijing subway, and the details can be found in the literature [12].

3.2. Pre-training of Model

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Figure 5: The ANN model for predicting the train-induced environmental vibration

In this paper, the acceleration level in the one-third octave band is used to describe the vibration magnitude at each frequency, which is defined as follows.

𝑎 𝑟𝑚𝑠 (𝑓 𝑖 )

𝑎 0 ) , (1)

𝑉 𝑎 𝐿(𝑓 𝑖 ) = 20lg (

where a rms ( f i ) is the root-mean-square value of the acceleration at the centre frequency f i , and a 0 = 10 -

6 m/s 2 is the reference acceleration.

Specifically, the neural network for simulating train-induced environmental vibrations is imple- mented using the Keras platform with TensorFlow as the backend. The model is shown in Figure 5. With reference to existing studies, the model in this study uses three hidden layers, each containing 1024 neurons, and the activation function of the model output layer is chosen as the Tanh function, which is a common setting for neural networks in prediction tasks, while the activation function of the other layers is chosen as the ReLU function, which provides higher efficiency in the training

Train speed » ‘Tunnel depth Soil elastic modulus Es ‘aecdleration Tove Vals Distance d

process. The training of the model is performed by optimizing the root mean square error loss using the Adam optimizer with a learning rate set to 10e-3, which provides a faster convergence rate. To prevent overfitting problems during training, a dropout technique was used in the model, whose drop- out rate was taken as 50%. In addition, a mini-batch technique was used with a batch size of 64, and the number of training iterations was 10,000.

3.3. Fine-tuning of Model

The authors' research team performed a large number of train-induced vibration measurements along the railway lines in Beijing, and these measured data will be used to retrain and test the pre- trained neural network based on TL. In this paper, retraining techniques are used to fine-tune the model, and the method is illustrated in Figure 1 (c). Specifically, the parameters of the first three pre- training layers are frozen to be kept constant, and the measured data are used to retrain the weight parameters of the last layer of the model.

3.4. Model Performance

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Figure 6: Performance of models on prediction of vibration acceleration levels

Some of the measured train-induced environmental vibration data were used as test data for the model, which was not used for model training and tuning. The prediction results of the TL strategy- based model and the ML-based model for the vibration acceleration levels at these typical measure- ment points are shown in Figure 6. It can be seen that the trends of acceleration levels at different frequencies predicted by the two models are consistent with the measured results, demonstrating the feasibility of the fast prediction method based on the ML technique for frequency-dependent vibration level prediction. In addition, the TL-based model achieves better accuracy at most measurement points, which is clearly shown in Figures 6 (c) and (g). At measurement points far from the vibration

20) meee teasucemnent 90 ee Measurement 2) ee eanrement BS meccen oy Q) pesca BP] Srescamey ee z, Se Ba Ei 8. S00 ge Es a is spe-stnn | sinnh = Distance=50m ° Distance=100m a % % (a) Frequency (Hz) (b) Frequency (Hz) (o) Frequency (Hz) 7 te Measicement oe Neasurnmet 1 te Measurement Tec hescondy Mt, Gr Scene 3) —Spescsonty te 3° a Se. 80. 50 Sa. ge ge Speed-35km/h | 3" 3 Distance=Om Distance=30m Distance=60m Frequency (Hz) Frequency (Hz) Frequency (H2)

source, the ML-based model exhibits a large error in vibration prediction in some frequency bands, which may be caused by the small amount of data with similar conditions in the training set, and this is a problem that is often encountered when using traditional ML-based models for prediction. How- ever, the TL technique proposed in this paper compensates for this problem well and proves its supe- riority in train-induced vibration prediction.

4. CONCLUSIONS

In this paper, a TL-based train-induced environmental vibration scoping prediction method is proposed, which can improve the accuracy of vibration scoping prediction in the planning stage of railway lines. In this method, an ANN model is built to simulate the complex relationship between the condition variables and the environmental vibration response. The model was first required to be pre-trained on the source domain, which contains a large amount of vibration simulation data obtained through numerical calculations, and then the model was required to be retrained on the target domain based on the TL strategy, which contains the measured train-induced vibrations. After this process, the prior knowledge in the numerical model can be transferred to the neural network model trained on the measured vibration data, which improves the accuracy of the prediction while achieving rapid scoping prediction.

In addition, this paper presents a case study of model implementation, in which a theoretical vehicle-rail coupling model and a tunnel-soil coupling model based on the finite element method is used to calculate train-induced environmental vibrations under various condition variables, and the data results of these numerical calculations are considered as the source domain. Furthermore, the vibration data measured along the Beijing subway were used as the target domain. After comparing the model prediction results with the measured train-induced environmental vibration, it is found that the accuracy of the TL-based environmental vibration prediction model proposed in this paper is better than that of the traditional ML-based environmental vibration prediction model, which can compensate for the poor accuracy of the traditional ML-based model in predicting the train-induced vibration under rare combinations of condition variables.

5. ACKNOWLEDGEMENTS

Financial support from the Fundamental Research Funds for the National Natural Science Foundation of China (Grant No. 52178404) is gratefully acknowledged. 6. REFERENCES

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