Research Article | Open Access
Smartphone’s Sensing Capabilities for On-Board Railway Track Monitoring: Structural Performance and Geometrical Degradation Assessment
Railway infrastructure managers run dedicated inspection vehicles to monitor the geometric quality of the track (among other aspects) to detect irregularities and ensure safe running conditions of railway lines, in accordance with specific regulations. Unfortunately, these inspections disturb the normal traffic operation, especially in networks with intense traffic; are generally carried out only a few times per year; and, consequently, do not provide prompt identification of critical situations. Considering the recent developments and cost reduction in sensing capabilities of smartphones, the authors present an approach to use these technologies to perform constant acceleration measurements inside in-service trains to complement the assessment of the structural performance and geometrical degradation of the tracks. Cross-correlation values above 0.85 were obtained between the standard deviations of the longitudinal level and the experimental vertical accelerations measured on-board a passenger train on an 11-km railway stretch. The results showed that the approach can be used to identify critical situations that affect the performance of the track, regarding passenger comfort, degradation rates, and risk of derailment. It may comprise a low-cost and crowdsourced complement to the general current practice of track geometric inspection by dedicated vehicles and contribute to an earlier detection of track malfunctions, consequently, to a more efficient maintenance planning and infrastructure management.
In ballasted railway tracks, the position of the rails changes with time, mostly caused by the development of differential settlements in the structure and by the accumulated railway traffic, which induces wear of components and plastic deformations in the supporting layers [1–3]. With time, this unwanted behaviour amplifies irregularities or faults in the position of the rails, causing the degradation of the geometric quality of the track. Eventually, this negatively affects the performance of this transport system, in terms of the running behaviour of trains, amplifying the dynamic response of the train-track system, promoting additional track degradation, noise and vibrations, poor ride comfort, and higher risk of derailment [4–8]. To prevent and minimise these consequences, railway infrastructure managers put significant effort into monitoring the track geometry and maintaining adequate track geometric quality, complying with specific requirements and standards [9, 10]. To that aim, dedicated inspection vehicles are used by infrastructure managers to perform the auscultation of the track geometry (among other aspects) to detect critical situations and to plan maintenance interventions requiring heavy machinery. The reconstruction of track geometry from track inspection cars is a well-established procedure and these vehicles are currently manufactured on an industrial basis by a few suppliers . Different approaches have been developed over the years, from contact-based (measuring axle principle) to non-contact-based, from chord measuring systems to inertial (absolute) systems. Modern inspection cars integrate inertial measurement that uses the known measuring technique by which the spatial position of a measuring sensor is determined by double integration of acceleration measurements. Commonly, the heart of these systems comprises an inertial measuring system (IMS), consisting of 3 high-precision gyro systems and accelerometers for three orthogonal spatial directions. Through the combination with optical track measuring systems, using laser distance sensors and location systems along the track (distance encoders and GNSS), the required longtime accuracies are established. In Europe, the requirements for these vehicles are standardized according to the European Norm EN 13848-2, since 2006 . A newer version of this norm is currently under discussion prEN 13848-2:2018.
Unfortunately, both the monitoring surveys by the inspection vehicles and the maintenance works are expensive activities that also hinder normal railway traffic. Given the importance of frequent monitoring of the railway track, particularly at critical locations, and taking into account the cost and increasing difficulty to conduct track geometry inspections throughout the rail networks, there is a need to develop alternative and expeditious methods to provide timely information on the performance and condition of the track , as implemented in recent years in world-leading railway networks .
Due to the increasing sensing capabilities and cost reduction of sensors for smartphones, in recent years, there has been significant development and increase in the application of micro-electro-mechanical systems (MEMS) that can be used to assess the performance of transport systems. Numerous applications can be found in the literature regarding its use to characterise the transport infrastructure and the vehicle’s motion [13–18]. Other applications evidence the potential of large-scale surveys to assess the performance of transport networks, in that they can be used to study mobility patterns  and to assess the ride quality of transport systems [20–24].
In this study, the authors present an approach for railway track monitoring using sensing capabilities of smartphones or other current low-cost inertial systems, as an alternative to more expensive and dedicated systems . A section of a railway line is used as case study to demonstrate the applicability of this approach. Acceleration measurements performed on-board a passenger train with a smartphone are analysed and compared against the longitudinal level of the track geometry records and its degradation with time. The study also demonstrates further applicability of the approach to assess the structural performance of railway tracks, by assessing how different wavelengths and amplitudes of the geometric irregularities affect degradation, running safety, and ride comfort, supported on dynamic train-track numerical simulations [25, 26].
The contribution of this approach, applied to condition and performance monitoring of the railway track, can provide valuable information for railway infrastructure managers as early detection of track faults and input data for asset management tools to optimise maintenance operations [27, 28].
2. Description of the Case Study
The stretch of track that was selected for this study is about 11 km long, located in the Northern Line of the Portuguese railway network. The track has Iberian gauge (1.668 m) and comprises continuously welded UIC 60E1 rails, Vossloh fastening system, monoblock concrete sleepers (spaced 0.6 m), and ballast layer with minimum thickness of 0.30 m under the sleepers, resting on a 0.20 m subballast layer. In the analysed stretch, the fastest passenger trains, the Alfa Pendular, normally travel at about 220 km/h.
Because this work focuses mainly on the vertical behaviour of the track, its geometric quality will be analysed in terms of the longitudinal level and its standard deviation. In general, this parameter is mostly associated to the track degradation and develops faster with traffic and time. In the scope of this study, it was possible to analyse the track geometry obtained in three different surveys: (i) July 2012, (ii) July 2013, and (iii) March 2016.
Although the stretch is in double line, only one of the tracks was considered in this study—the ascending track. Figure 1 shows the track longitudinal level measured in the third survey (March 2016), namely, the wavelength () ranges D1 () and D2 (), as established in the European Norm EN 13848-5 . It is visible that there are no relevant track defects and the longitudinal level records remain within the threshold values of the alert limits for D1 and D2, which indicates an overall good geometric quality of the track. It is also interesting to note that the locations denoting disturbances in the longitudinal level records of D1 do not match those of D2, which is expected given that the track defects of these two wavelength ranges normally have different sources [2, 29–31].
3. Smartphone Setup
To demonstrate the applicability of smartphone’s sensing capabilities for on-board railway track monitoring, the authors evaluated the accelerations inside the car body of the Portuguese Alfa Pendular passenger train, travelling along the stretch of track under analysis, using MEMS accelerometers (triaxial) found in modern and conventional smartphones. After previous validation tests using different smartphones , the measurements were performed with an Android™ smartphone, namely, the Samsung Galaxy®, SIII, GT-I9300, incorporating a MEMS accelerometer from STMicroelectronics®, model LSM330DLC. According to the manufacturer, the sensor is characterised by a power consumption of 0.23 mA, range of ±19.6133 m/s2 (±2 g), resolution of 0.009576807 m/s2, and median sampling frequency of 100 Hz. The LSM330DLC is a discontinued inertial module from late 2012, which comprises a revisited and downsized version of its predecessor module LSM330DL. It has a 12-bit resolution with selectable linear acceleration range of ±2/±4/±8/±16 g. It also offers fully programmable interrupt generator, power down mode for low-power operation and SPI/I2C digital interface. This module in particular has been used successfully in other studies demonstrating the smartphone’s sensing capabilities to characterise motion of structures and other bodies [33, 34]. After initial tests and following previous experience, the application “Sensor Log” (v1.04) was used to register the measurements (currently available at https://sensor-log.en.aptoide.com/). The selected application provided accelerometer and GNSS readings from the smartphone at faster sampling frequencies than other similar applications that were also available at the time. Although the GNSS position of the acceleration measurements is useful, its precision is not very critical, and the typical ±5 meter error  obtained with smartphones (under good atmospheric and multipath conditions) is sufficient for the proposed application, mainly because the data is analysed using sliding windows of variable length. Moreover, the approach is meant to be used on a regular basis on the same track, a few times per day; thus, significant positioning errors could be easily detected and discarded/corrected, particularly when compared with the last measurements performed by the inspection cars. Because the track layout in plan view is well-established, a method to validate the GNSS position could consist in confirming the strong correlation between the track curvature and the lateral accelerations measured on-board.
The measurements were performed inside the fifth coach car of the Alfa Pendular train, near the vertical alignment with the rear bogie, on the floor, under the seat, and at the location identified in Figure 2 and aligned with the car so that the orientation of the sensors’ axes (x, y, z) matched the transverse, longitudinal, and vertical alignments of the coach car, respectively (see Figure 2(c)).
The smartphone was used to record the accelerations in the three directions (x, y, and z) over a few minutes, as the train travelled along the 11 km stretch. At each measurement, the acceleration values in the three directions were recorded, and a timestamp was assigned. In the tests performed by the authors, the recorded data were stored internally in the smartphone memory, but other alternatives are possible, for example, transmitting the recoded data via on-board Wi-Fi or cell phone network. Because the sampling frequencies of the smartphone were not always constant, the measurements were resampled to 100 Hz.
4. Acceleration Measurements
Acceleration measurements and respective frequency content is presented in Figure 3, where it is clear the influence of the curvature of the track alignment in the lateral accelerations (x-direction) measured with the smartphone. It is also visible that most frequency content is below 15 Hz, which evidences the capabilities of the primary and secondary suspensions of the train in filtering higher-frequency contents from rolling contact [2, 4–7, 31, 36]. Nevertheless, it is noted a frequency peak at about 25.4 Hz, which is probably the consequence of a sleeper-spacing excitation: considering that the excitation frequencies of the train-track system, , can be estimated as , where is the train speed (220 km/h or 61.1 m/s) and is the sleeper spacing (equal do 0.6 m), we obtain a sleeper-spacing excitation frequency of . The frequency of 25.4 Hz is a submultiple of that frequency when multiplied by 4, thus corresponding to the span of 4 sleepers.
5. Correlation with the Track Geometry
It is common practice by railway infrastructure managers to calculate the standard deviation of the longitudinal level, to assess the track geometric quality, to study its degradation evolution, and to plan early maintenance operations, for which threshold values are established in European norms . To demonstrate that the vertical accelerations measured inside the coach car are correlated to the longitudinal level of the track, Figure 4 presents three plots, each comparing the standard deviation of the longitudinal level, , regarding wavelength rages D1 + D2, and with the standard deviation of the vertical accelerations, , considering three sliding-window sizes: 10 m, 75 m, and 200 m. The normalised cross-correlation () and dynamic time warping distance (DTW-norm dist) values [37, 38] between and are also indicated in the plots. It is visible the very good correlation between the variables, particularly for larger window sizes.
In order to justify the peak values of and in the three plots in Figure 4, the authors analysed the characteristics of the track, looking for any relevant structural aspect or sudden changes in the track structure (track discontinuity or singularities). In fact, about 30 relevant discontinuities were identified, including transition zones, rail joints, turnouts, bridges, underpasses, culverts, and stations, among others. Figure 5 presents examples of these discontinuities, and their location was also added to Figure 4. It is visible that, in general, they correspond to the location of peak values of and . This suggests that these locations experience higher geometric degradation and affect passenger comfort, which is in agreement with other studies [4–7, 36, 39].
Subsequently, to assess the actual track degradation rates, the authors analysed the evolution of the between the surveys of 2013 and 2016, . In Figure 6, it is visible that most of the locations denoting higher degradation rates (higher values of ) generally also correspond to the locations where higher values of are observed in Figure 4, for example, between km 3.5 and 4.5 and between km 9 and 10.5. It is also interesting to note that most of peaks are also centred on the track discontinuities identified above.
6. Track Geometry Data to Assess the Structural Performance
In addition to monitoring the condition of the track, the data obtained by smartphone-based or low-cost inertial systems may be analysed further to assess the structural performance of railway tracks. One possible application is its contribution to the early detection of critical locations in railway tracks that negatively affect the performance of this transport system. This approach can supported by a method proposed by the authors  that analyses how different wavelengths and amplitudes of the irregularities of the longitudinal level affect different critical aspects of the track performance, namely, (i) its degradation, (ii) the train running safety, and (iii) the passenger ride comfort. That method has been successful in anticipating the development of critical locations that affect the performance of the infrastructure in a previous railway line case study and, therefore, can be a valuable tool in maintenance and asset management activities of railway infrastructure managers. This is achieved by integrating the information concerning the track geometry records, the characteristics of the track superstructure and substructure, and the information from numerical train-track interaction simulations. The track geometry data, specifically the longitudinal level, can be obtained from normal inspection surveys or calculated by inverse analysis of the car-body acceleration obtained by smartphone-based or low-cost inertial systems, as demonstrated in other applications [40–42]. The effect of track irregularities (with different wavelengths and amplitudes), caused by differential settlements, on the dynamic train-track interaction is assessed by parametric numerical simulations, as in . Because the characteristics of the track and trains of this present case study are practically the same as those for which the method was firstly demonstrated , the results of that parametric numerical study may also be used here to identify possible critical situations, based on the information regarding the analysis of track geometry records.
The three criteria for the identification of the critical situations depicted in Figure 7 are as follows:(i)“Higher risk of train derailment”: situations of offload values (ratio of the offload vertical wheel-rail force to the static vertical wheel-rail force) lower than the threshold value of 0.6, considered in other studies (ii)“Rapidly increasing track degradation rates”: cases of higher vertical accelerations in the sleepers and in the trains’ axles, as well as increasing train-track forces and sleeper-ballast contact pressures [25, 44, 45](iii)“Lower passenger comfort”: situations of vertical accelerations inside the car body higher than the threshold of 1 m/s2 
Firstly, the authors calculated the longitudinal level (), depicted in Figure 8, as the sum of the wavelength ranges D1 () and D2 (), presented earlier in Figure 1. The figure also shows the position of transition zones and the other discontinuities mentioned in Figure 5.
Then, the longitudinal level was analysed, in terms of defect length and respective amplitude. In practice, for each position on the track, various amplitudes of the defects were calculated based on a range of overlapping chord lengths between 3 m and 35 m, as explained in detail in . Each pair of (amplitude and chord length), denoted here as an “occurrence,” was plotted in Figure 9 against the three critical regions described earlier (Figure 7).
From the analysis of Figure 9, most occurrences fall outside the three critical regions identified above (Figure 7). However, there were some occurrences associated with both higher risk of derailment and rapidly increasing track degradation rates, and even others with lower passenger comfort. To identify which locations in the track were associated with lower track performance, the method consists in intersecting the contour of the abovementioned regions with the list of occurrences in Figure 9.
Figure 10(a) shows the locations of the track discontinuities mentioned in Section 2 and the only location (a culvert at about 4.467 km mark) that was found to have a high number of the occurrences denoting lower passenger comfort. At that location, the results suggest vertical accelerations inside the coach car of the Alfa Pendular above 1 m/s2, a threshold value established in .
Figure 10(b) shows the locations of the track discontinuities mentioned in Section 2 and the only location (a turnout at about 3.821 km mark) that was found to have a high number of the occurrences denoting higher risk of derailment of the train. At that location, the results suggest offload values (ratio of the offload vertical wheel-rail force to the static vertical wheel-rail force) of the Alfa Pendular train lower than the threshold value of 0.6, considered critical in other studies .
Figure 11(a) also shows the locations of the track discontinuities mentioned in Section 2 and the location of the occurrences that fall inside the region associated with increasing degradation rates. Due to the large number of occurrences in this case, it was decided to remove the less relevant points to improve readability of the figure, namely, those denoting both amplitudes smaller than 1 mm and chord lengths smaller than 7.5 m. Some concentration of occurrences may be related to the presence of transition zones or other discontinuities, while many others seem to be of random nature or related to additional factors for which no obvious justification was found.
To assess the degradation rates, the authors also calculated the variation of the standard deviation along the track between two surveys (2016 and 2013) and compared the results against the locations with track discontinuities and concentrations of relevant occurrences (Figure 11(b)). Here, the authors used a shorter 10 m sliding window, instead of the 200 m sliding windows, for compatibility with the wavelength ranges analysed by the method and to be more sensitive to the influence of the track discontinuities. It is visible that most track discontinuities identified in Section 2 matched locations with concentration of occurrences and with higher rates of track degradation. These locations are listed in Table 1.
On the other hand, the two road underpasses at km 0.73 and 3.09 and the three culverts at km 3.1, 4.86, and 9.50 did not evidence poor track performance, which suggests that these structures are evidencing adequate structural behaviour.
The results presented in this study suggest that incessant and continuous monitoring of the vehicle’s motion, either using smartphones from crew/passengers or low-cost on-board sensing systems inside in-service trains, can provide valuable information for asset management activities of railway infrastructure managers.
The case study presented by the authors demonstrates that the standard deviations of the longitudinal level and the experimental vertical accelerations were very well correlated: cross-correlation values between 0.85 and 0.97 were obtained for sliding-window sizes of 10 m to 200 m. The study also showed that peaks of these two variables were often associated with sudden changes in the track, such as the presence of transition zones, rail joints, turnouts, bridges, underpasses, culverts, stations, and other track discontinuities. The track at these locations also evidenced higher degradation rates. Further analysis of the longitudinal level was performed in terms of how different wavelengths and amplitudes of the geometric irregularities affected the performance of the track, following a procedure established in , associating the results with numerical train-track interaction scenarios simulated in a previous parametric study . The approach allowed identifying scenarios along the track that suggested (i) higher risk of derailment, (ii) increasing degradation rates, and (iii) lower passenger comfort, based on established criteria. The results showed that many track discontinuities mentioned above seem to be associated with lower geometric quality of the track and with high degradation rates.
This approach may comprise a constant and daily monitoring complement to the general current practice of track geometric inspection by dedicated vehicles, which only performs a few surveys per year on a given railway line. In this way, this approach can contribute to an earlier detection of track malfunctions and, consequently, to a more efficient maintenance planning and asset management by implementing the system configuration diagram presented in Figure 12. For example, in the event of the identification of a critical location with a significant track defect, even if its position is not accurate, an alert could be triggered for the infrastructure maintenance team to analyse the situation and decide on further actions, such as visual inspection to the site to confirm the occurrence, performing precise track geometry measurements with the dedicated inspection car, and schedule corrective intervention to restore adequate track geometry if needed. World-leading railway networks seem to have implemented similar approaches in recent years , thought using more expensive and dedicated systems. Moreover, the current approach has the potential to be implemented as a smartphone- and crowdsourced-based system, similar to those presented by other authors [22, 23], but to monitor the track geometry and assess its structural performance.
The data used to support the findings of this study are available from the corresponding author upon request.
Part of the work was conducted in the framework of the TC202 National Committee of the Portuguese Geotechnical Society (SPG) “Transportation Geotechnics,” in association with the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE-TC202).
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The first author’s postdoctoral fellowship (SFRH/BPD/107737/2015) was supported by Fundação para a Ciência e a Tecnologia, through POCH cofinanced by the ESF and National Funds of MCTES, Portugal.
- E. T. Selig and J. M. Waters, Track Geotechnology and Substructure Management, Thomas Telford, London, UK, 1994.
- C. Esveld, Modern Railway Track, MRT-Productions, Zaltbommel, Netherlands, 2nd edition, 2001.
- B. Indraratna, W. Salim, and C. Rujikiatkamjorn, Advanced Rail Geotechnology—Ballasted Track, Taylor & Francis, Milton Park, UK, 2011.
- X. Lei and N.-A. Noda, “Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile,” Journal of Sound and Vibration, vol. 258, no. 1, pp. 147–165, 2002.
- T. Dahlberg, “Railway track dynamics—a survey,” Linköping University, Linköping, Sweden, 2003, RAILTRDY.DOC/2003-11-06/TD.
- K. Popp, K. Knothe, and C. Pöpper, “System dynamics and long-term behaviour of railway vehicles, track and subgrade: report on the DFG Priority Programme in Germany and subsequent research,” Vehicle System Dynamics, vol. 43, no. 6, pp. 485–521, 2005.
- I. I.-Y. Choi, J.-H. Um, J. S. Lee, and H.-H. Choi, “The influence of track irregularities on the running behavior of high-speed trains,” Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, vol. 227, no. 1, pp. 94–102, 2012.
- G. Kouroussis, D. P. Connolly, and O. Verlinden, “Railway-induced ground vibrations - a review of vehicle effects,” International Journal of Rail Transportation, vol. 2, no. 2, pp. 69–110, 2014.
- UIC, Best Practice Guide for Optimum Track Geometry Durability, Union Internationale des Chemins de Fer, Paris, France, 2008.
- CEN, “European Standard EN 13848-5:2017 Railway applications–track–Track geometry quality—Part 5: geometric quality levels–plain line, switches and crossings,” Comité Européen de Normalisation, Brussels, Belgium, 2017, CEN/TC 256–Railway Applications.
- CEN, “European standard EN 13848-2:2006 railway applications–track–track geometry quality—Part 2: measuring systems–track recording vehicles,” Comité Européen de Normalisation, Brussels, Belgium, 2006, CEN/TC 256–Railway Applications.
- P. Weston, C. Roberts, G. Yeo, and E. Stewart, “Perspectives on railway track geometry condition monitoring from in-service railway vehicles,” Vehicle System Dynamics, vol. 53, no. 7, pp. 1063–1091, 2015.
- H. Tsunashima, Y. Naganuma, A. Matsumoto, T. Mizuma, and H. Mori, “Condition monitoring of railway track using in-service vehicle,” in Reliability and Safety in Railway, X. Perpinya, Ed., vol. 12, pp. 334–356, IntechOpen, London, UK, 2012.
- O. Heirich, A. Lehner, P. Robertson, and T. Strang, “Measurement and analysis of train motion and railway track characteristics with inertial sensors,” in Proceedings of 14th International IEEE Conference on Intelligent Transportation Systems (ITSC), pp. 1995–2000, Washington, DC, USA, October 2011.
- A. Mednis, G. Strazdins, R. Zviedris, G. Kanonirs, and L. Selavo, “Real time pothole detection using Android smartphones with accelerometers,” in Proceedings of International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS), pp. 1–6, Barcelona, Spain, June 2011.
- R. Bhoraskar, N. Vankadhara, B. Raman, and P. Kulkarni, “Wolverine: traffic and road condition estimation using smartphone sensors,” in Proceedings of Fourth International Conference on Communication Systems and Networks (COMSNETS 2012), pp. 1–6, Bangalore, India, January 2012.
- O. Heirich, A. Steingass, A. Lehner, and T. Strang, “Velocity and location information from onboard vibration measurements of rail vehicles,” in Proceedings of 16th International Conference on Information Fusion (FUSION), pp. 1835–1840, Istanbul, Turkey, July 2013.
- S. Higuera de Frutos and M. Castro, “Using smartphones as a very low-cost tool for road inventories,” Transportation Research Part C: Emerging Technologies, vol. 38, pp. 136–145, 2014.
- P. Nitsche, P. Widhalm, S. Breuss, N. Brändle, and P. Maurer, “Supporting large-scale travel surveys with smartphones—a practical approach,” Transportation Research Part C: Emerging Technologies, vol. 43, pp. 212–221, 2014.
- C.-y. Lin, L.-j. Chen, Y.-y. Chen, and W.-c. Lee, “A comfort measuring system for public transportation systems using participatory phone sensing,” in Proceedings of International Workshop on Sensing for App Phones (PhoneSense’10, in Conjunction with ACM SenSys’10), Zurich, Switzerland, November 2010.
- L. Forslöf and H. Jones, “Roadroid: continuous road condition monitoring with smart phones,” Journal of Civil Engineering and Architecture, vol. 9, no. 4, pp. 485–496, 2015.
- H. Zhao, L.-L. Guo, and X.-Y. Zeng, “Evaluation of bus vibration comfort based on passenger crowdsourcing mode,” Mathematical Problems in Engineering, vol. 2016, Article ID 2132454, 10 pages, 2016.
- A. Azzoug and S. Kaewunruen, “RideComfort: a development of crowdsourcing smartphones in measuring train ride quality,” Frontiers in Built Environment, vol. 3, no. 3, 2017.
- P. Zoccali, G. Loprencipe, and R. C. Lupascu, “Acceleration measurements inside vehicles: passengers’ comfort mapping on railways,” Measurement, vol. 129, pp. 489–498, 2018.
- A. Paixão, E. Fortunato, and R. Calçada, “The effect of differential settlements on the dynamic response of the train-track system: a numerical study,” Engineering Structures, vol. 88, pp. 216–224, 2015.
- A. Paixão, E. Fortunato, and R. Calçada, “A contribution for integrated analysis of railway track performance at transition zones and other discontinuities,” Construction and Building Materials, vol. 111, pp. 699–709, 2016.
- C. Vale and S. M. Lurdes, “Stochastic model for the geometrical rail track degradation process in the Portuguese railway Northern Line,” Reliability Engineering & System Safety, vol. 116, pp. 91–98, 2013.
- A. R. Andrade and P. F. Teixeira, “Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models,” Reliability Engineering & System Safety, vol. 142, pp. 169–183, 2015.
- M. X. D. Li, E. G. Berggren, M. Berg, and I. Persson, “Assessing track geometry quality based on wavelength spectra and track-vehicle dynamic interaction,” Vehicle System Dynamics, vol. 46, no. 1, pp. 261–276, 2008.
- G. Kouroussis, D. P. Connolly, M. C. Forde, and O. Verlinden, “Train speed calculation using ground vibrations,” Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, vol. 229, no. 5, pp. 466–483, 2013.
- Z. Zhang, B. Zeng, C. Dai, and W. He, “Study on structural service performance of heavy-haul railway tunnel with voided base,” Advances in Civil Engineering, vol. 2018, Article ID 3510979, 12 pages, 2018.
- A. Paixão, “Transition zones in railway tracks: an experimental and numerical study on the structural behaviour,” Faculty of Engineering, University of Porto, Porto, Portugal, 2014, Ph.D. thesis.
- M. Benndorf, M. Garsch, T. Haenselmann, N. Gebbeken, and I. Videkhina, “Mobile bridge integrity assessment,” in Proceedings of IEEE Sensors, pp. 1–3, Orlando, FL, USA, October-November 2016.
- Q. Kong, R. M. Allen, M. D. Kohler, T. H. Heaton, and J. Bunn, “Structural health monitoring of buildings using smartphone sensors,” Seismological Research Letters, vol. 89, no. 2A, pp. 594–602, 2018.
- F. . v. Diggelen and P. Enge, “The world’s first GPS MOOC and worldwide laboratory using smartphones,” in Proceedings of the 28th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2015), pp. 361–369, Tampa, FL, USA, September 2015.
- G. Kouroussis, D. P. Connolly, G. Alexandrou, and K. Vogiatzis, “The effect of railway local irregularities on ground vibration,” Transportation Research Part D: Transport and Environment, vol. 39, pp. 17–30, 2015.
- A. William Anthony, Speech Recognition by Machine, Peter Peregrinus Ltd., London, UK, 1988.
- D. J. Berndt and J. Clifford, “Using dynamic time warping to find patterns in time series,” in Proceedings of KDD-94, Knowledge Discovery in Databases (AAAI-94), vol. 10, pp. 359–370, Seattle, WA, USA, July-August 1994.
- L. Ubalde, “La auscultación y los trabajos de vía en la línea del AVE Madrid—sevilla: análisis de la experiencia y deducción de nuevos criterios de mantenimiento,” Universitat Politècnica de Catalunya, Barcelona, Spain, 2004, Ph.D. thesis.
- T. Kobayashi, Y. Naganuma, and H. Tsunashima, “Condition monitoring of shinkansen tracks based on inverse analysis,” in Proceedings of Prognostic and System Health Management–PHM2013, vol. 33, pp. 703–708, Milan, Italy, September 2013.
- H. Tsunashima, Y. Naganuma, and T. Kobayashi, “Track geometry estimation from car-body vibration,” Vehicle System Dynamics, vol. 52, no. 1, pp. 207–219, 2014.
- M. Odashima, S. Azami, Y. Naganuma, H. Mori, and H. Tsunashima, “Track geometry estimation of a conventional railway from car-body acceleration measurement,” Mechanical Engineering Journal, vol. 4, no. 1, pp. 16–00498, 2017.
- H. Xia, Y. Han, N. Zhang, and W. Guo, “Dynamic analysis of train-bridge system subjected to non-uniform seismic excitations,” Earthquake Engineering & Structural Dynamics, vol. 35, no. 12, pp. 1563–1579, 2006.
- M. Baessler and W. Ruecker, “Track settlement due to cyclic loading with minimum pressure and vibrations,” in System Dynamics and Long-Term Behaviour of Railway Vehicles, Track and Subgrade, K. Popp and W. Schiehlen, Eds., pp. 337–356, Springer, New York, NY, USA, 2003.
- A. Kono and T. Matsushima, “Deformation characteristics of crushed-stone layer under cyclic impact loading from micro-mechanical view,” Journal of Japan Society of Civil Engineers, Ser. A1 (Structural Engineering & Earthquake Engineering (SE/EE)), vol. 68, no. 1, pp. 173–190, 2012.
- CEN, European Norm 1990:2005, Eurocode: Basis of Structural Design. Annex A2: Application for Bridges, Comité Européen de Normalisation, Brussels, Belgium, 2005.
Copyright © 2019 André Paixão et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.