^{1}

^{1}

^{1}

^{1}

^{1}

^{2}

^{1}

^{2}

In this study, a data-driven interior noise prediction model is developed for vehicles on an urban rail transit system based on random forest (RF) and a vehicle/track coupling dynamic model (VTCDM). The proposed prediction model can evaluate and optimize the sustainability of railway alignment from the perspective of interior noise. First, a data collection framework via embedded sensors of onboard smartphones was developed. Then, for establishing the mapping relationship between the dynamic responses of the car body and interior noise, the collected dataset was fed to the RF. Parameter, error distribution, and feature importance analyses were conducted for evaluating and optimizing the performance of the RF. With the optimized parameters, the probability of prediction errors being within 5 dB was 86.9%. Next, the VTCDM was established using an existing industry multibody simulation tool and verified through a comparison between the simulated and field dynamic responses. Finally, a case study that extends the application of this interior noise prediction model to railway alignment design is presented.

By the end of 2018, 35 cities in mainland China had opened 180 urban rail transit (URT) lines, with a total operation mileage of more than 5700 km. Moreover, the length of subway lines was approximately 4350 km, accounting for 75.6% of all URT lines. The rapidly expanded URT networks offered great convenience to the citizen and were highly advantageous in solving traffic congestions. As a critical URT component, the subway is crucial in people’s daily life. However, owing to the unreasonable design of railway alignments and the degradation of track infrastructures, the running quality of trains worsens with the increase in service time. Furthermore, these issues caused abnormal interior noise and vibration, which severely affected passengers’ ride comfort. The interior noise of subway vehicles significantly affected passengers’ experience; therefore, the design, construction, and operation of subway lines must be emphasized [

Generally, train noise can be divided into two categories: external and interior noises [

Wheel-rail noise, including rolling noise, impact noise, and curve squeal, is primarily affected by the wheel-rail relationship when trains move along a track. However, the wheel-rail interaction not only affects the generation of noise but also affects the dynamic responses of vehicles. For example, when rail corrugation occurs, a series of dynamic problems as well as serious train interior noise are likely to appear. Hence, onboard devices to detect track faults from cabin vibrations and interior noise have been developed [

Because RF is a supervised learning algorithm, a large amount of training datasets is required when modeling. For acquiring these datasets, an onboard smartphone application was developed to collect the dynamic responses and interior noise of the subway vehicle. With the development of microelectromechanical system technologies, smartphones with built-in sensors exhibit excellent properties in terms of portability and practicability. Moreover, several applications regarding transport infrastructure condition monitoring and vehicle motion pattern recognition have been reported [

The goal of this study was to develop a data-driven method for forecasting vehicle interior noise for the optimization of URT railway alignments. Hence, a large number of train operation status data were collected using the embedded sensors of an Android smartphone. Subsequently, the relationship between car body dynamic responses and interior noise of subway trains was established using RF. For obtaining the simulated dynamic responses of the car body under specific railway alignments, we built a vehicle/track coupling dynamic model (VTCDM) via the Universal Mechanism (UM) software.

Finally, based on the mapping relationship learning from data and dynamic responses from the simulated model, the interior noise under specific railway alignments can be predicted. Further, the prediction results can be applied for optimizing railway alignments at the design stage. The key contributions of this study are as follows:

Propose a data-driven prediction framework for subway vehicle interior noise based on the smartphone-collected dataset, RF, and VTCDM

Establish a VTCDM via the UM software based on multibody system dynamics

Validate the VTCDM and the proposed interior noise prediction model using the field test data from Chengdu Subway Line 7

Develop an application scenario for optimizing railway alignments with the prediction model of vehicle interior noise

The remainder of this study is organized as follows. Section

Because train interior noise directly affects passengers’ ride comfort, noise control becomes a challenging technology in the design and construction of railway lines. Many factors have an impact on vehicle interior noise. The potential sources of interior noise can be categorized into two groups according to the characteristics of sound: the airborne and structure-borne noise sources [

The composition of vehicle interior noise and some critical influencing factors.

Currently, numerous investigations have been conducted regarding the analysis of noise characteristics [

In 1966, Gladwell et al. first proposed formulating acoustic problems in terms of displacements, similar to a continuous elastic structure [

Unlike the FEM, the BEM does not require the acoustic space to be discretized; only the boundary conditions require discretization, which can reduce the calculation time and minimize the calculation error. Owing to the superiority of the boundary element method, it has been widely promoted recently. Similar to the FEM, the BEM was also first used to predict the interior noise of cars [

The SEAM is entirely different from the two methods above. It utilizes energy as a variable to describe the state of a system, and its core is energy conservation. By constructing the energy flow equation between the cavity subsystems, the energy stored in the relevant acoustic cavity subsystem is available, which can be used to predict the acoustic and dynamic responses. In 1997, Radcliff used the SEAM to predict the interior noise caused by automobile engines. In 2003, James predicted the aerodynamic noise of high-speed trains based on the SEAM, and the feasibility and accuracy of the SEAM for predicting the high-frequency train interior noise were verified by comparison with wind tunnel test results [

The methods above are numerical methods. Although they can yield more accurate results under specific conditions, the requirements for complex model parameters and a large amount of computing capacity render them challenging for practical applications. Recently, data-driven approaches have provided insight for different areas in railway transportation fields [

Herein, a data-driven interior noise prediction method is proposed, which is different from the traditional numerical model, as shown in Figure

Research methodology.

Figure

Data collection framework for this study.

Parameters about the smartphone and sensors.

Device | Item | Parameter |
---|---|---|

Smartphone | Model | FRD-AL00 |

Operating system | Android 8.0 | |

Chipset | HiSilicon Kirin 950 | |

CPU | Octa-core (4 × 2.3 GHz and 4 × 1.8 GHz) | |

GPU | Mali-T880 MP4 | |

Memory | 4 GB RAM | |

Inertial measurement unit | Model | LSM6DS3 |

Acceleration range | ±2/±4/±8/±16 g | |

Angular rate range | ±25/±250/±500 dps | |

Analog supply voltage | 1.71 V to 3.6 V | |

Power consumption | 1.25 mA | |

Microphone sensors | Model | MP34DB02 |

Frequency range | 20 Hz to 20 kHz | |

Supply voltage range | 1.64 V to 3.6 V | |

Acoustic overload point | 120 dBSPL | |

Signal-to-noise ratio | 62.6 dB | |

Sensitivity | −26 dBFS |

By reading the embedded sensors of the smartphone with the developed application, the data required, that is, seven types of signals, were readily available. The audio signal was acquired using the microphone sensors of the smartphone, and the dynamic responses of the car body including the vibration accelerations (horizontal, vertical, and longitudinal accelerations) and rotational angular velocities (pitch angular, yaw angular, and roll angular velocities) were available with the built-in inertial sensors. In our study, the sampling frequency of the audio signal was 22,050 Hz and that of all the inertial sensors was set as 100 Hz.

The sound pressure recorded by using the microphone differed from that perceived by the human ear (even in the same field) owing to various factors, such as psychological effects, presence of outer ear, and cochlear health status. To objectively reflect the passenger’s hearing experience, we employed the A-weighting sound pressure level (SPL(A)) in this study to evaluate the interior noise. The SPL(A) can be calculated as follows:^{−6} Pa. The data, including horizontal, vertical, and longitudinal accelerations and pitch angular, yaw angular, and roll angular velocities collected by the smartphone, were used to describe the dynamic responses of the car body. However, using only the data collected by the vehicle-carried smartphone may not be sufficient to explain the causes of the interior noise. For better prediction results, we considered the rotational angular accelerations of the car body obtained by calculating the first derivative of the rotational angular velocity. The effects of the trains’ running speed on the generation of interior noise were nonnegligible. As a crucial parameter, the train speed was introduced to the prediction model. Because the subway tunnels are a GPS-free environment, the location and running speed information were not available through the GPS module embedded in the smartphones. The first-order integration of the longitudinal acceleration was used to overcome the problem. The running velocity of the train can be calculated by the following equation [

Features involved in the prediction model.

Collected signal | Used signal | Selected features | |
---|---|---|---|

1 | Audio signal | SPL(A) | RMS |

2 | Horizontal acceleration | Horizontal acceleration | Mean value |

3 | Vertical acceleration | Vertical acceleration | RMS |

4 | Longitudinal acceleration | Longitudinal acceleration | Variance |

5 | Pitch angular velocity | Pitch angular velocity | Standard deviation |

6 | Yaw angular velocity | Yaw angular velocity | Peak value |

7 | Roll angular velocity | Roll angular velocity | Skewness |

8 | Pitch angular acceleration | Kurtosis | |

9 | Yaw angular acceleration | Shape factor | |

10 | Roll angular acceleration | Crest factor | |

11 | Operating velocity of trains | Clearance factor |

A disadvantage of using raw signals collected by smartphones is that they show track quality problems in only single points, which complicates the generation of a reasonable section length for optimization. Additionally, the sampling frequencies of the inertial sensors and microphone are different, which renders it challenging to build a point-to-point relationship directly. Hence, a moving time window method was employed in this study. For confirming the optimal time window, the size of the time window was varied from 0.5 to 10 s, and the hop length of the window was half the size of the time window. Additionally, a series of features was selected to reflect the characteristics of the signals inside the window. We selected the root mean square (RMS) of the SPL(A) in the windows as the index of the interior noise. As for the dynamic responses of the car body, the following features were used: (1) mean value, (2) RMS, (3) variance, (4) standard deviation, (5) peak value, (6) skewness, (7) kurtosis, (8) shape factor, (9) crest factor, and (10) clearance factor. In each frame of the dynamic response signals of the car body, these features were calculated as input parameters for our prediction model.

RF is an ensemble learning approach comprising hundreds of decision trees for performing classification or regression tasks independently. Using the average of all the trees’ results as the final output can significantly improve the predictive accuracy. RF was developed based on the decision tree structure; however, two additional characteristics, including bagging and random subspace methods, were added to improve the accuracy and robustness. First, by creating a series of bootstrap samples, the bagging algorithm is fundamental for improving the accuracy and stability of machine-learning models. The introduction of the bagging method helps reduce variance and control overfitting. Next, the random subspace method is designed to increase tree independence by generating trees with a random sample of features rather than the entire feature set [

As a data-driven method, RF relies more on a tremendous amount of data to perform interior noise prediction. Compared with mathematical and physical models, data-driven prediction models do not require complex parameters, strict conditions, or hypotheses. Furthermore, this method can potentially reduce computational time and require less computer memory compared with numerical models. The mapping relationship between the dynamic responses of the car body and interior noise exhibits a strong nonlinear characteristic. Because the RF is a combination of a series of decision trees, it exhibits an outstanding performance for fitting nonlinear relationships. Therefore, RF was selected in this study to fit the mapping relationship between the dynamic responses of the car body and the interior noise.

In RF, one dependent variable exists, that is, the RMS of SPL(A) for each moving window. Moreover, 100 independent variables (10 dynamic response signals × 10 selected features; 10 dynamical response signals are items 2 to 11 of Column 3, Table

Using RF, we established the mapping relationship between the dynamic response of the car body and the subway vehicle interior noise. However, it is difficult to exert its value using only such a mapping relationship. To expand its application scenario, we propose applying the mapping relationship for evaluating the design of the URT railway alignments based on the simulated dynamic responses of the vehicles. Hence, a VTCDM was constructed, with which the required simulated dynamic response signals could be obtained.

Vibrations of the vehicle can be transmitted to the track via the wheel-rail contact and cause vibrations of the track structure. However, the vibrations of the vehicle are also affected by the track in reverse [

Key parameters of type A subway vehicle.

Parameters | Value | |
---|---|---|

1 | Length between bogie pivot centers (m) | 15.7 |

2 | Wheelbase (m) | 2.5 |

3 | Lateral distance of the rolling circle (m) | 1.493 |

4 | Nominal rolling circle radius (m) | 0.84 |

5 | Mass of car body (kg) | 50 877 |

6 | Mass of bogie (kg) | 2 721.5 |

7 | Mass of wheel (kg) | 1900 |

8 | Wheel tread type | LMA |

After RF and the VTCDM were established, a series of analyses were implemented. First, the performance of the RF regression model was analyzed in terms of parameter tuning, feature importance, and error distribution. Next, the VTCDM and the interior noise prediction model were verified through the field test data. Subsequently, an application scenario for evaluating the railway alignments from the perspective of interior noise was presented.

To obtain the optimal parameters of RF, the effects of the number of decision trees, size of time windows, and mode of the max feature numbers on the performance were studied. It is noteworthy that the Out-of-Bag

Effect of number of estimators on OOB

The number of features considered when forming the random forests significantly affects the goodness of fit. Three max feature modes, “auto,” “sqrt,” and “log2,” are discussed from the perspective of computation time and goodness of fit, as shown in Figure

From the analysis above, the optimal parameters of the RF were confirmed. The RF with 200 trees and “auto” max feature mode was selected in our study to obtain better fitting results with less computing capacity. Figure

Additionally, we studied the distribution characteristics of prediction errors of the RF regression model (RFRM). The prediction error distribution of the RFRM was compared with that of the linear regression model (LRM), radial-basic-function-based support vector regression model (rbf-SVRM), and gradient boosting regression model (GBRM). Figure

Comparison of the prediction error distributions.

The essence of feature importance assessment in RF is to calculate the average of each feature’s contribution to all trees in the forest and subsequently compare the contributions among those features. The mean decrease impurity method was adopted in this study to perform feature importance analysis and variance was used as the impurity measure [

Feature importance analysis.

Not only the RF but also the VTCDM significantly affects the performance of the interior noise prediction model. In Figure

Verification of the VTCDM and interior noise prediction model.

We developed an application case of the interior noise prediction model for evaluating railway alignments in the design stage. In this study, we designed three types of railway alignments, as shown in Figure

Evaluation of railway alignments considering interior noise.

In Figure

In this case, we did not consider different vehicles, as only one type of vehicle was selected for a specific subway line in general. For simplifying the model of the cases, the impact of travel speeds of the train on the noise level was not considered, whereas in practical operation, trains usually repeatedly go through the process of starting-speeding up—keeping a high travel speed—speeding down-stopping. In the section with small-radius curves, the higher the speed of the train is, the more likely it causes noise issues, such as squeal. Therefore, the sections where trains have a high travel speed should avoid small-radius curves or reverse curves as much as possible in the design of rail alignments.

The interior noise of subway vehicles based on RF and VTCDM was forecasted herein using data collected from onboard smartphones. Through parameter study, we confirmed the optimal parameters of the RF model: number of trees, 200; size of time window, 0.5 s; “auto” max feature mode selected. With such parameters,

Feature importance analysis demonstrated that the running velocity of the train affected the interior noise the most. Additionally, the yaw rate and longitudinal acceleration of the car body affected the vehicle interior noise significantly. The effectiveness of the VTCDM was verified through comparisons between the simulated and measured dynamic responses of the car body. From the comparison with the field-test vehicle interior noise, it was evident that the proposed prediction method could accurately predict the trend of subway train interior noise. However, the local fluctuations of the interior noise caused by some nonwheel-rail noise, such as the sounds of broadcast and electrical devices, could not be forecasted correctly. The case study demonstrated that the proposed interior noise forecasting method could be used for evaluating and optimizing railway alignment designs in the early stage from the perspective of interior noise.

Next, to improve the performance of the prediction model, we could categorize the training data in detail according to different characteristics, such as track type, train type, and service time of the track system. Because the simplification of the vehicle track into a multirigid-body system in the current model reduced the forecasting accuracy, the flexibility of the car body and track shall be considered in future studies.

Noise data will be available upon request to the corresponding author.

The authors declare that they have no conflicts of interest.

This study was funded by the China Scholarship Council (ID: 201907000077) and National Natural Science Foundation of China (Grant no. 51878576).