Acceleration Measurements Inside Vehicles: Passengers’ Comfort Mapping on Railways. Pablo Zoccali1, Giuseppe Loprencipe 1* and Robert Cristian Lupascu1

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Acceleration Measurements Inside Vehicles: Passengers’ Comfort Mapping on Railways.

Pablo Zoccali1, Giuseppe Loprencipe 1* and Robert Cristian Lupascu1

1 Department of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy; (P.Z.); (R.C.L.)

* Corresponding author:; Tel.: +39-064-458-5112

Abstract: Monitoring the status of infrastructural networks along their service life is fundamental to ensure a safe and good service quality. Due to the length and extension of infrastructures, it is fundamental to develop effective and low cost approaches that can allow a continuous monitoring. In this paper, an assessment method based on the ride comfort evaluation inside vehicles according to ISO 2631 (i.e. frequency weighted acceleration) was developed and tested on an Italian railway. In particular, the frequency weighted acceleration was calculated along the whole trip between two consecutive stops. In order to identify and localize the most critical areas along the traveling path, the vertical frequency weighted acceleration was also calculated for sub-sections of fixed lengths (i.e. 10 m) and then mapped on geographic information systems (GIS). In this way, it is also possible to determine, for example considering a railway infrastructure, whether the eventual discomfort may be due to localized irregularities or due to the passage on worn switches. Once proper threshold limit values are defined, early interventions can be planned in order to restore adequate comfort and safety levels. To test the proposed procedure, it was applied to a surface metropolitan railway characterized by an automatic guide, which granted the chance of evaluating the repeatability of the present approach. During the in-situ measurements, an inertial measurement unit (IMU) integrated together with a GPS receiver was used.

Keywords: Transport monitoring; Ride comfort; Vertical acceleration; ISO 2631.

1. Introduction

Ensuring a good service quality to the passengers is one of the main tasks and purposes of a transport operator. Several approaches have been investigated and proposed in order to estimate the service and ride quality of public transports perceived by passengers [1-4]. In the aforementioned works, it was underlined that passengers’ perception of the service quality depends on several characteristics, such as accessibility, safety, comfort and service. In addition, passengers’ age, behavior and position inside the vehicle can significantly influence the service quality perception.

Ride comfort, in particular, includes different aspects such as: air-condition on board, inside vehicle temperature, seat comfort, noise and vibration exposure. About the latter issue, many researchers dealt with this topic with regard to both railway and road transport systems [5]. Johanning et al. [6] evaluated whole-body vibration exposure inside railroad locomotives according to ISO 2631 [7]. In [8] the correlation between different ride comfort evaluation methods (i.e. Statistical [9-11], Root mean square – r.m.s. [7] and Sperling’s methods) for railway vehicles was investigated. The main difference in each method concerns the frequency weighting adopted to take account of human sensation. In this study [8], a correlation factor (R2) greater than 0.88 was found in all cases. Kim et al. [12] performed an experimental study on the ride comfort of the high-speed train using the statistical method. In particular, they decided to use the UIC 513R approach rather than the ISO 10056 one because the first emphasizes the low-frequency vibration of the train. In [13], the ISO 2631 evaluating method was used to assess whole-body vibration exposure in trains, considering different measurement location: seat pan, seat back and floor.

Similar studies, related to the evaluation of whole-body vibration exposure, were also carried out for road vehicles using the ISO 2631 approach [14-17]. With regard to ride comfort evaluation on road infrastructures, many authors investigated the chance of using the frequency weighted vertical acceleration (awz) described in the ISO 2631 to assess and estimate road pavement condition in terms of distresses [18] and/or longitudinal roughness [19-21]. In addition, many studies assessed the capability of performing such acceleration measurements by means of smartphones [22-26], in order to reduce monitoring costs of road pavement condition.

In the last years, many researchers investigated the chance of using Inertial Navigation System (INS) to measure and analyze road and railway track geometry condition from in-service vehicles [27-30].

In the field of rail transportation, the quality of rail track can be checked by means of inertial measurement unit (IMU) integrated together with a GPS receiver to prevent the generation of noise and vibration [31-34], but also acceleration measurements can be used to properly identify track singularities [35].

In this paper, the use of an IMU integrated together with a GPS receiver was investigated to evaluate ride comfort on railway vehicles adopting the ISO 2631 approach. In particular, the ride quality assessment was carried out considering the whole path between two following stations, but also dividing it in several shorter segments. In this way, the most critical areas can be detected (e.g. presence of a switch) and properly visualize on specific geographic information systems (GIS). In addition, the characteristics of the railway line chosen as case study, were selected in order to test the repeatability of the measurements.

The final aim is to provide a method to assess the current condition/anomalies of several type of infrastructures (such as railway, highways, minor roads, etc.) by means of estimating passengers’ comfort and mapping the results in order to easily localize the most critical areas. In particular, a system installation to be used on different infrastructures and vehicles was tested. The proposed method can allow to monitor the infrastructure condition during its service life, also taking into account the several parameters affecting the system such as speed and vehicle type.

2. Methodology and equipment

To perform the evaluation of the ride comfort on railway tracks the ISO 2631 approach was adopted, using inertial sensors and GPS receiver to collect acceleration and position data. In particular, the frequency range of interest for comfort and perception, as provided in ISO 2631-1, goes from 0.5 Hz to 80 Hz.

2.1. Frequency weighted acceleration—ISO 2631

This method is based on the measurement of acceleration inside road vehicles along three axes (x, y, z) defined in the ISO 2631 according to the position considered (Figure 1). The acceleration measurements are then used to determine root mean square (RMS) accelerations through the evaluation of the Power Spectral Density (PSD) with regard to all 23 one-third-octave bands that represent the frequency range of interest for human response to vibrations (0.5–80 Hz) described in the ISO 2631.

Figure 1. Basicentric axes of the human body for the different position during vibration exposure.

Once the RMS accelerations are known, it is possible to calculate the weighted RMS acceleration for each axis using the following Equation (1):


where Wi is the frequency weightings in one-third octaves bands to be chosen based on the position considered (Table 1) and provided by the standard (Figure 2). aij is the RMS acceleration for the i-th one-third octave band for axis j (j=x, y, z). Once the RMS values are calculated for each axis, the vibration total value (av) is obtained using the following equation (2):


where awx, awy and awz are the RMS values along the three coordinate axes, and kx, ky and kz are combination factors provided by ISO 2631, which are equal to 1 for seated and standing positions. In particular, in this paper, the observation point was placed on the floor along the centerline, considering then the standing position.
Table 1. Guide for the application of frequency-weighting curves provided by ISO 2631

Frequency weighting




Motion sickness


z-axis, seat surface

z-axis, seat surface

z-axis, seat surface


z-axis, standing vertical recumbent (except head)

z-axis, standing vertical recumbent (except head)

x-, y-, z-axes, feet (sitting)


x-axis, seat surface

x-axis, seat surface

x-axis, seat surface


y-axis, seat surface

y-axis, seat surface

y-axis, seat surface

x-, y-axes, standing horizontal recumbent

x-, y-axes, standing horizontal recumbent

y-,z-axes, seat-back






Figure 2. Frequency weighting curves.
In particular, many authors proposed the use of vertical frequency weighting accelerations (awz) to assess ride quality on road pavements [19-21]. These values, in fact, can be compared with the threshold ones proposed by ISO 2631 for public transport (Table 2) to estimate the corresponding comfort level perceived by users traveling along the examined road sections. The same comparison can also be done dealing with vibration exposure inside railway vehicles.
Table 2. Comfort levels related to awz threshold values proposed by ISO 2631 for public transport.

awz values (m/s2)

Comfort level


Not uncomfortable


A little uncomfortable


Fairly uncomfortable




Very uncomfortable


Extremely uncomfortable

2.2. Equipment

As already stated in the previous section, an inertial measurement unit (IMU) integrated together with a GPS receiver was used to perform the in-situ measurements. Specifically, the equipment was the LandMarkTM 10 GPS/AHRS (Figure 3), whose main specifications for inertial and GPS/AHRS system performances are reported, respectively, in Table 3 and Table 4.

Table 3. LandMarkTM 10 GPS/AHRS main specifications for inertial performance.


Rate Axes

Accel. Axes

Standard Full-Scale Ranges

± 150°/sec

± 2g's

Bias (In-Run Stability), 1σ


0.1 mg

Angle Random Walk, 1σ


0.07 mg/√Hz

Bias Over Temp, 1σ

< 0.1°/sec

< 3 mg

Sensor Resolution


0.035 mg


1 mrad, 1σ


≤ 0.03°/sec/g, 1σ

Table 4. LandMarkTM 10 GPS/AHRS main specifications for GPS/AHRS system performance.

GNSS Receiver




Max Navigation Update Rate

Up to 18 Hz

GPS Horizontal Position Accuracy

Autonomous 2.5 m


2.0 m

Speed Accuracy

0.05 m/s

Heading Accuracy (GPS)

0.3 degrees

Pitch & Roll Angles (Inertial)

± 0.25° stationary

Altitude (Barometric)

± 3 m, 1σ

Update Rate (synced inertial) GPS

100 Hz

Although the frequency range of interest specified by ISO 2631 [7] and ISO 8041 [36] for human response to vibrations goes from 0.5 Hz to 80 Hz, it was decided to use an instrumentation having a frequency-sampling rate of 100 Hz since the weighting curves depicted in Figure 2 show that human feeling is mostly sensitive to vibration within the range 4-16.5 Hz in the vertical direction and from 0.6 to 2 Hz in the longitudinal and lateral ones. According to the Nyquist-Shannon sampling theorem, the frequency-sampling rate should be at least equal to the double of the maximum frequency content of sampled signal, in order to avoid loss of information and aliasing. In [12], it was found that the vibration level is high at low frequency range, specifically below 20 Hz, for both the high-speed and conventional lines. In particular, they showed that for conventional lines (mean speed 143.6 km/h) the PSD of vertical acceleration above 20 Hz is close to zero and thus no meaningful errors (considering also the use of the ISO 2631 weighting curves) are made by using a frequency-sampling rate of 100 Hz. In addition, the final purpose of this choice was also to test the effectiveness of the maximum frequency sampling rate settable on smartphones [23,37], which will be the object of future investigations.



Figure 3. LandMarkTM 10 GPS/AHRS instrument: (a) IMU and (b) GPS receiver.
3. Case of study

The choice of the railway infrastructure was mainly done because it ensures to travel on the same trajectories at different passages, which is a very important aspect of the repeatability analysis of the acceleration measurements. Furthermore, the line chosen for this experiment features Automatic Train Operation rather than manually-driven trains, which should provide more consistent speed profiles. Specifically, the trains on which the measures were collected consists of 6 articulated cars for an overall length of about 109 m, a height of 3.64 m and a width equal to 2.85 m. The maximum speed is 90 km/h.

The in-situ measurements were performed along 7 sections traveled in both directions (double-track line) (whose lengths and geometry are described in Table 5) and belonging to an Italian metropolitan placed on the surface (track gauge of 1435 mm). The line is characterized by an electric overhead system (1,500 V).

For each section and traveling direction, a total number of 14 measures were carried out and then analyzed. In particular, based on the GPS signal quality the measures were accepted or discarded.

Table 5. Length and geometry of the examined sections.

Section ID.

Direction WE - Length (m)

Direction EW - Length (m)

Number of Curves

Mean Curvature Radius





R1 = 800 m; R2 = 1090 m





R1 = 1020 m





R1 = 360 m; R2 = 580 m





R1 = 300 m; R2 = 660 m; R3 = 560 m





R1 = 410 m; R2 = 3000 m





R1 = 590 m; R2 = 530 m





R1 = 1010 m

The vibration total value (av) was calculated for each section (whole length) and direction, evaluating then the repeatability of the measurements. In addition, in order to assess the capability of the proposed approach to localize irregular and distress areas along the path, the av values on 10 m length segments were also calculated. This aspect, in particular, may be mostly important for road application and, for this reason, it was decided to consider the distance (i.e. 10 m) recommended by Italian highways agency [38] for road roughness evaluation using the International Roughness Index (IRI) [39].

In general, it is useful to remark that the final aim of this work is to characterize and assess the infrastructure. To perform such analysis, it should be necessary to consider sub-sections with very small length; however, the length choice must take into account also the traveling speed. In fact, the total time necessary to cover the chosen distance affects the frequency resolution.

The length of 10 m, suitable for some application on road infrastructures, allows to fully cover the comfort and perception frequency range of interest (0.5-80 Hz) for speed lower than 20 km/h.

However, for speed until 90 km/h such length grants to capture the most critical frequency range (4-16.5 Hz) mainly for vertical direction. In addition, keeping the sub-section length as small as possible also allows to analyze acceleration signals referred to traveling speed with reduced variability. The maximum speed reached for a very short time during all the tests considered in this paper was always lower than 90 km/h.

The equipment used in this paper does not directly provide distance measurements, thus, they were calculated starting from speed measures and time references (Δt=0.01 s). To evaluate the accuracy of the distance values obtained, a statistical analysis of the whole length of each section calculated for all the passages were carried out.

The installation system was developed in order to be used on different vehicles and infrastructures, also allowing a fast installation. The IMU platform was placed inside a case (Figure 4), which was then fixed on the train floor (along the centerline) during the measurements applying both a rough adhesive tape and a double-sided adhesive tape on its bottom surface. The x axis of the platform was directed along the longitudinal axis of the train, axis y as the transverse axis and z axis as the vertical one. The GPS receiver, instead, was attached to a window by means of a suction cup.

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