Railway infrastructure damage detection using ...

STRUCTURAL CONTROL AND HEALTH MONITORING

Struct. Control Health Monit. 2014 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.1660

Railway infrastructure damage detection using wavelet transformed acceleration response of traversing vehicle Daniel Cantero*,† and Biswajit Basu Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin 2, Ireland

SUMMARY This paper proposes the use of vertical accelerations of a moving train to detect local track irregularities produced by weaker sections of the infrastructure. By analysing the vehicle accelerations using the wavelet transform, it is possible to clearly identify the location of damaged sections. A wavelet-based indicator is proposed to facilitate an algorithm for recognition of deteriorated segments. The proposed indicator is validated by means of a 2-DOF vehicle model excited by randomly generated track irregularities together with the presence of various local track defects. A Monte Carlo analysis is performed to evaluate the performance of the proposed indicator for a variety of model parameters, including vehicle mechanical properties, shape of isolated track irregularities and levels of damage. Copyright © 2014 John Wiley & Sons, Ltd. Received 10 March 2013; Revised 9 January 2014; Accepted 28 February 2014 KEY WORDS:

railway infrastructure; damage detection; moving vehicle; wavelet-based indicator

1. INTRODUCTION The assessment of railway infrastructure is expensive and difficult, mainly due to the sheer length of the network. Additionally, the intense use of these structures by frequent and heavy traffic makes the task of detection and possible repair of damaged sections problematic. Early warning systems that minimize the disruption of the network are desirable and useful. Over the past decade, various research groups have been investigating this indirect rail track assessment technique where the response of the structure is not studied directly but the response of the traversing vehicle is used instead. Mizuno et al. [1] present experimental results concluding that the acceleration response of the floor of a passenger vehicle is a promising index to capture railway track disorders in vertical direction. Ishii et al. [2] confirm the close correlation between vehicle acceleration and track irregularity. With and Bodare [3] use a special towed measuring car to investigate track conditions, by means of the flexibility frequency response function. Alternatively, Tsunashima et al. [4] use microphones to detect high frequency damage, such as rail corrugation. Indirect assessment of structures by moving vehicles is also investigated in highway engineering to estimate the natural frequencies of traversed bridges [5]. An inexpensive possibility by which damage can be identified involves monitoring the accelerations on vehicles while operating at normal speeds. Damaged rail infrastructure generally translates into additional localized deformations of the track, which then are reflected on the acceleration signal of the traversing vehicle. This information is captured in the low frequency content of the signal. Low frequency detection generally requires heavy and relatively immobile equipment [3]. However, it is also possible to accurately analyse the low frequency range in a signal with an appropriate time-frequency tool. *Correspondence to: Daniel Cantero, Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin 2, Ireland. † E-mail: [email protected]

Copyright © 2014 John Wiley & Sons, Ltd.

D. CANTERO AND B. BASU

In this paper, the use of the continuous wavelet transform (CWT) is proposed that, among other advantageous properties, features a variable resolution in frequency domain. By studying the low frequency component of the acceleration signal using CWT, it is possible to accurately locate isolated irregularities caused by infrastructure damage. Appropriate management of repeated measurements of vehicle accelerations in combination with spatial positioning techniques (e.g. GPS) should lead to an up to date state report of the existing railway network. Most of the existing literature analyse urban railways, at lower speeds, and small radius curves with particular emphasis on rail corrugation, which typically features medium to high frequency responses. Here, the authors focus on the inspection of long and shallow track damages that feature low frequency responses of the vehicle’s acceleration. Also long distance trains, which travel at considerable high speed, are also considered in this study. Additionally, this paper aims to propose an indicator from the CWT analysis to facilitate the automatic detection of damage. Existing literature on similar topics usually rely on visual inspection of wavelet coefficients, there is no clear recommendation available on how to analyse the information provided by the CWT using qualitative indicators. The paper is divided into the following sections. First, a brief overview of signal processing tools is presented while highlighting the advantages of wavelet transform. The next section explains the numerical model used for simulations. Thereafter, a step-by-step example is illustrated explaining the proposed approach. It is followed by the results of a Monte Carlo simulation that validates the methodology for a range of irregularities and vehicle properties. Finally, in the conclusion section, an overview of the monitoring methodology and results is presented.

2. ANALYSING IN TIME-FREQUENCY DOMAIN The standard approach for analysing signals in frequency domain is the FFT. This provides excellent information of stationary signals by means of an efficient algorithm. The disadvantage of this tool is that the information obtained is for the whole signal and localized variations in time vanish within the noisy results. To overcome this limitation, the next logical step is to perform a windowed FFT, which is generally termed as short-term Fourier transform. This provides information in timefrequency domain but lacks sufficient accuracy because of its constant frequency resolution. [4,6,7] An excellent time-frequency tool is the CWT that has been developed over the last three decades. This transform decomposes the analysed signal in a set of coefficients in two dimensions, shift and scale, where scale is inversely proportional to frequency. A basis function is translated (shift) and stretched (scale) and compared against the signal. High coefficients indicate a good match between signal and wavelet at a particular instant in time and associated frequency. This tool offers variable resolution providing a map of energy content of the signal in time and frequency. It is particularly interesting for the research presented in this paper to note that CWT features a high frequency resolution at low frequencies. Mathematical description of the CWT has been presented in many publications, and the reader can refer to [8–12] amongst others. In this paper, the wavelet coefficients are normalized against the signal’s total energy. The signal under investigation is the vehicle’s vertical acceleration, which strongly depends on the traversing speed of the train. Thus, the total energy of the signal varies too. However, by normalizing the wavelet coefficients, the proposed methodology in this paper becomes independent of any vehicle speed. It is also important to note that the actual values of the coefficients depend on the chosen wavelet basis, the considered scales and the sampling frequency of the signal. The maximum scale to be considered is directly related to the maximum damage wavelength of interest.

3. MODEL DESCRIPTION The numerical model developed for this investigation allows the dynamic response of a moving vehicle over rail track irregularities to be studied. The vehicle model is a 2-DOF system as shown in Figure 1a. The main body and suspension masses are connected by spring and dashpot systems. The ranges of mechanical properties used for the vehicle model are listed in Table I. The chosen model and parameters aim to qualitatively describe the dynamic behaviour of a train wagon. The vibrations of the main Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

RAILWAY INFRASTRUCTURE DAMAGE DETECTION USING VEHICLE ACCELERATION

a)

b)

Figure 1. (a) Sketch of vehicle model and (b) track irregularity PSD (Federal Railroad Administration Class 6).

Table I. Vehicle model properties. Property k1 k2 c1 c2 m1 m2 v

Minimum 6

0.73 · 10 0.50 · 106 15.00 · 103 5.00 · 103 7.90 · 103 512.50 30

Maximum

Unit 6

2.90 · 10 2.00 · 106 60.00 · 103 20.00 · 103 31.60 · 103 2050 220

N/m N/m N/m2 N/m2 kg kg km/h

vehicle body mass depend on the primary (wheel to bogie) and secondary (bogie to frame) suspension systems, which are approximated by the presented model. Similar simplified vehicle descriptions are commonly in use [13]. Random track irregularities are defined following the Federal Railroad Administration recommendations as given in [13]. Class 6 profile track irregularities are generated from the PSD presented in Figure 1b, and the maximum and minimum wavelengths considered are 300 and 0.5 m, respectively as suggested in [14]. Garg and Dukkipati [15] give the analytical expressions of various typical isolated irregularities that have been reported during extensive field measurements. In this paper, five of the most representative irregularities are chosen; their shapes are shown in Figure 2, and their typical range of values is given in Table II. These shapes feature in a variety of situations, and they might represent piers at bridges (cusp), soft spots (bump), bridges (jog), areas of spot maintenance (plateau) and soft and unstable subgrades (trough). Each of these irregularity shapes might also be appropriate to describe other local irregularities (further information in [15]). The equations of motion of the presented model are solved numerically by direct integration using the Newmark-β scheme. The system is excited by the random track irregularities together with the isolated irregularities while moving at constant speed. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

D. CANTERO AND B. BASU

b)

a)

1/k

1/k

A

A

c)

d) 1/k

A

A

1/k

e) 1/k

A

Figure 2. Sketch of isolated irregularities; (a) cusp, (b) bump, (c) jog, (d) plateau and (e) trough. Table II. Range of analytical parameters for considered isolated irregularities. Type Cusp Bump Jog Plateau Trough

A (m)

k (m-1)

0.0229–0.0762 0.0127–0.1016 0.0127–0.1270 0.0229–0.0762 0.0178–0.0508

0.0525–0.3117 0.0427–0.2133 0.0262–0.1476 0.0295–0.1083 0.0656–0.0820

4. DAMAGE DETECTION METHODOLOGY

Track Irregularity (mm)

In this section, the methodology to identify and locate an isolated irregularity is illustrated by means of a numerical simulation. The vehicle model described in Section 3 traverses over two tracks of 3000-m length each. The only difference between the tracks is the addition of an isolated irregularity in one of them. The track without the irregularities termed as undamaged track and the other with an irregularity will be termed as a damaged track. The tracks are shown in Figure 3. The isolated irregularity added to the damaged track consists of a bump type irregularity located at the centre. Parameters A (0.0127) and k (0.0427) are chosen from Table II to represent a wide and shallow irregularity, which is generally more difficult to detect. The vertical dotted line indicates the centre of the isolated irregularity. 0 −5 −10 0

0.5

1

1.5

2

2.5

3

Distance (km)

Figure 3. Class 6 track irregularity; solid line = undamaged track; dashed line = damaged track by addition of wide and shallow bump; and dotted line = centre of isolated irregularity. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

RAILWAY INFRASTRUCTURE DAMAGE DETECTION USING VEHICLE ACCELERATION

Acceleration (m/s2)

Figure 4 shows the vertical acceleration €x 1 of mass m1 for the vehicle traversing the two tracks at 50 m/s (180 km/h). The mechanical properties of the vehicle are taken from the average values given in Table II. Acceleration responses in both cases are very similar, and no obvious feature distinguishes the two that would indicate the presence of a bump. The CWT of the acceleration signals W Ψ€x 1 ða; bÞ provides information about their frequency content and evolution over time, at particular scales a and shift parameters b for the wavelet basis Ψ. Figure 5 shows the absolute value of the CWT normalized with respect to the total energy of the signal of the undamaged case using Morlet basis function. A band with high energy concentration can be observed near scale 700, which corresponds to the lowest natural frequency of the vehicle. The undamaged track excites the vehicle showing some variability in time due to local roughness that leads to higher concentration of energy in the signal. Performing the same wavelet analysis on the vehicle’s acceleration for the case of damaged track displays clear differences. Figure 6 gives a similar map of time-scale distribution of the wavelet coefficients but with a significant difference at the centre of the signal. The wavelet coefficients show high values concentrated in the low frequency (high-scales) range that corresponds to the presence of the bump. The presence of the bump has thus introduced some low frequency energy in the response, which is reflected in the values of jW Ψ€x 1 ða; bÞj. Visual inspection of the coefficients in Figure 6 clearly alerts us about the presence of a local and significant irregularity. However, graphically analysing the results might be subjective and will have to be done offline. Thus, an automatic algorithm to detect these irregularities is presented. It was found that the sum of the coefficients for all analysed scales gives a clear indication of the local singularities in time. Also the maximum thereof or peak value is a good indicator to estimate the presence and location of isolated irregularities.

0.05 0 −0.05 −0.1 15

20

25

30

35

40

45

Time (s)

Figure 4. Vertical acceleration of mass m1 for undamaged (solid line) and damaged (dashed line) tracks.

Figure 5. jW Ψ€x 1 ða; bÞj for the case of undamaged track.

Figure 6. jW Ψ€x 1 ða; bÞj for the case of damaged track. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

D. CANTERO AND B. BASU

Figure 7 shows the coefficients summed for the case of undamaged and damaged tracks. Near the bump, concentration of high values can be found, and the peak value occurs at the centre of the irregularity. Thus, for any given track on successive acceleration recordings over time, it is possible to define a functional of the absolute value of the wavelet coefficients. This functional is the absolute value of the wavelet coefficients summed over all scales and defined in Equation 1 where n is the number of scales considered. F ðbÞ ¼

n  X   W Ψ€x 1 aj ; b 

(1)

j¼1

A threshold Fth can be defined from this functional. Vehicles traversing over undamaged tracks will result in values of the functional below the threshold, whereas instances surpassing the threshold might indicate the presence of an isolated irregularity or damage. The local energy at t = b and at scale aj has the relation E j ðbÞ∝

1 ðW Ψ€x i Þ2 : aj

(2)

Hence, we have the relation F ðbÞ∝

qffiffiffiffiffiffiffiffiffiffiffi n X pffiffiffiffi aj E j ðbÞ

(3)

j¼1

which shows that the functional F(b) is proportional to the sum of the squared root of local energy with pffiffiffiffi a scale dependant multiplier aj. The reason why the proposed indicator is able to detect the damage is as follows. When there is damage or an irregularity, the local energy is distributed more evenly over a broad range of frequencies including those contributing to lower frequencies (high value of aj). This pffiffiffiffi contribution gets amplified by a large factor of aj , and hence the sum over all scales leads to a significantly high value. Also, the square root of the local energy increases the relative contribution to the values at low frequency as compared with the dominant frequency, which is desirable for detecting the presence of the low frequency components. This forms the basis of detection of the damage on the irregularity in the track. In this section, a 1000 Hz sampling frequency of the signal was used for representation purposes. However high sampling rate is not necessary, a much smaller sampling frequency can be used since we are only interested in the low frequency range of the response. The signal can be down-sampled to 10 Hz achieving similar results and has been done in following section. This reduces CWT computation time and the amount of information to be stored.

5. MONTE CARLO SIMULATION

Sum of coefficients

In this section, a Monte Carlo simulation is performed to demonstrate the applicability of the method and the indicator presented in the previous section. The same model is simulated repeatedly while randomly changing some of its features. For every run in the simulation following properties were randomly varied: 50 40 30 20 10 0

15

20

25

30

35

40

45

Time (s)

Figure 7. Sum of continuous wavelet transform coefficients (absolute value) for undamaged (solid line) and damaged (dashed line) track. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

RAILWAY INFRASTRUCTURE DAMAGE DETECTION USING VEHICLE ACCELERATION

-

Track irregularity, one different Class 6 profile for every run Vehicle mechanical properties (Table I) Vehicle velocity (Table II) Six track conditions (five isolated irregularities and the undamaged case) Properties of isolated irregularity ◯ Width and depth (Table II) ◯ Location (anywhere along the track)

A vast amount of runs could be generated numerically. However, for clarity, in Figure 8, only 100 events for each irregularity type are shown. For every event in the simulation, the peak value is presented in Figure 8 clearly indicating that higher irregularity amplitudes result in higher concentrations of energy. Peak values for events with undamaged tracks present some small variability but are smaller than for the rest of the events. On the basis of this simulation results, in this case, the threshold can be set at 3.

80

Peak Value

70 60 50 40 30 20 10 0

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Damage A

Figure 8. Peak values for undamaged track (o), cusp (▼), bump (*), jog (+), plateau(x), trough (•) and threshold (dashed line).

a)

60 40 20 0 40

50

80 60 40 20 0 -20 30

60

Vehicle velocity (m/s)

d)

40

50

60

Vehicle velocity (m/s)

80 60 40 20 0 -20 30

40

50

60

Vehicle velocity (m/s)

e) 100

Prediction Error (m)

100

Prediction Error (m)

Prediction Error (m)

80

-20 30

100

100

Prediction Error (m)

Prediction Error (m)

c)

b) 100

80 60 40 20 0 -20 30

40

50

60

Vehicle velocity (m/s)

80 60 40 20 0 -20 30

40

50

60

Vehicle velocity (m/s)

Figure 9. Isolated irregularity localization prediction error; (a) cusp, (b) bump, (c) jog, (d) plateau, (e) trough. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

D. CANTERO AND B. BASU

Once the threshold is selected, it is possible to locate the point at the track associated with high energy concentrations. In the following results, the location of the damage is randomly changed along the 3000 m of the track. However, it is possible to predict and detect damaged sections by performing the CWT of the acceleration signal and locating the peak values that exceed the threshold. Figure 9 shows the irregularity location prediction error for 300 events for different irregularity types using the same symbol notation as in Figure 8. In general, the results show acceptable damage localization predictions and variable accuracies for each irregularity shape. It also becomes clear that the prediction error depends on vehicle’s speed. This is because the vehicle takes some amount of time to ‘feel’ the irregularity, but travelling at faster speeds, the location error becomes larger. The errors presented in Figure 9 might seem excessive in some cases. It is important to note that the location of the irregularities was estimated using the peak value location. However, a closer look at wavelet coefficients will show that there is a range of very high values near the detected peak value and of similar magnitude. Therefore, peak values indicate the existence of an irregularity and give only a first estimate of the damage location. A closer inspection of the CWT coefficients will clearly indicate the extent and the location of the damage. Once detected, a manual insight of the track area in the vicinity (over a length of 60–80 m) will be necessary. Not shown here, but very similar results were found using other wavelet basis. In addition to the Morlet basis presented here, other bases used include the following: Haar, Mexican Hat, Shannon, Littlewood-Paley and Modified Littlewood-Paley. Even though similar results were obtained for any of the basis, Morlet wavelet was selected for its slightly better performance in the results.

6. CONCLUSION This paper proposes a wavelet-based automatic assessment methodology that can be implemented on rail networks. This algorithm uses wavelet signal processing of acceleration signals from vehicles moving on tracks. The system would need accelerometers on some of the operating vehicles together with positioning systems. This would provide periodic records of accelerations obtained at a regular spatial resolution track network. To reduce data and computational calculations, records could be downsampled. Signals are then analysed by means of CWT and the sum of normalized coefficients (absolute value) are computed. With every repetition of this process a more stable baseline condition can be defined for the network under consideration. Appropriate thresholds can be selected for segments of the infrastructure. Peak values that exceed the threshold indicate high concentration of energy due to an isolated irregularity associated with a degrading or damaged section of the track. ACKNOWLEDGEMENT

This research is carried out under the EU FP7 funding for the Marie Curie IAPP project NOTES (grant no. PIAPGA-2008-230663). The authors are grateful for the support. REFERENCES 1. Mizuno Y, Fujino Y, Kataoka K, Matsumoto Y. Development of a mobile sensing unit and its prototype implementation. Tsinghua Science and Technology 2008; 13:223–227. 2. Ishii H, Fujino Y, Mizuno Y, Kaito K. The study of train intelligent monitoring system using acceleration of ordinary trains. Proceedings of Asia-Pacific Workshop on Structural Health Monitoring, Yokohama Japan (CD), 2006. 3. With C, Bodare A. Evaluation of track stiffness with a vibrator for prediction of train-induced displacement on railway embankments. Soil Dynamics and Earthquake Engineering 2009; 29:1187–1197. doi:10.1016/j.soildyn.2008.11.010. 4. Tsunashima H, Naganuma Y, Matsumoto A, Mizuma T, Mori H. Condition monitoring of railway track using in-service vehicle. In Reliability and Safety in Railway, Perpinya X (ed.). Intech, 2012; 333–356. doi:10.5772/35205. (Available from: http://www. intechopen.com/books/reliability-and-safety-in-railway/condition-monitoring-of-railway-track-using-in-service-vehicle) 5. Siringoringo DM, Fujino Y. Estimating bridge fundamental frequency from vibration response of instrumented passing vehicle: Analytical and experimental study. Advances in Structural Engineering 2012; 15:443–459. 6. Kunpeng Z, San WY, Soon HG. Wavelet analysis of sensor signals for tool condition monitoring: a review and some new results. International Journal of Machine Tools and Manufacture 2009; 49:537–553. doi:10.1016/j.ijmachtools.2009.02.003. 7. Caprioli A, Cigada A, Raveglia D. Rail inspection in track maintenance: a benchmark between the wavelet approach and the more conventional Fourier analysis. Mechanical Systems and Signal Processing 2007; 21:631–652. doi:10.1016/j. ymssp.2005.12.001. Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc

RAILWAY INFRASTRUCTURE DAMAGE DETECTION USING VEHICLE ACCELERATION 8. Basu B. Identification of stiffness degradation in structures using wavelet analysis. Construction and Building Materials 2005; 19:713–721. doi:10.1016/j.conbuildmat.2005.02.018. 9. Kim H, Melhem H. Damage detection of structures by wavelet analysis. Engineering Structures 2004; 26:347–362. doi:10.1016/j.engstruct.2003.10.008. 10. Robertson AN, Basu B. Wavelet analysis. In Encyclopaedia of Structural Health Monitoring, Boller C., Chang F-K, Fujino Y. (eds.). John Wiley & Sons: Chichester, UK, 2009; 1–29. doi:10.1002/9780470061626.shm048. 11. Nagarajaiah S, Basu B. Output only modal identification and structural damage detection using time frequency & wavelet techniques. Earthquake Engineering and Engineering Vibration 2009; 8:583–605. doi:10.1007/s11803-009-9120-6. 12. Basu B, Gupta VK. Seismic response of SDOF systems by wavelet modeling of nonstationary processes. Journal of Engineering Mechanics 1998; 124:1142–1150. 13. Frýba L. Dynamics of Railway Bridges. Thomas Telford: London, 1996. 14. Van Nguyen D, Kim KD, Warnitchai P. Simulation procedure for vehicle–substructure dynamic interactions and wheel movements using linearized wheel–rail interfaces. Finite Elements in Analysis and Design 2009; 45:341–356. doi:10.1016/j.finel.2008.11.001. 15. Garg VK, Dukkipati RV. Dynamics of Railway Vehicle Systems. Academic Press: Ontario, 1984.

Copyright © 2014 John Wiley & Sons, Ltd.

Struct. Control Health Monit. 2014; DOI: 10.1002/stc