Railway track inspection based on the vibration response to a ...

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Original Article

Railway track inspection based on the vibration response to a scheduled train and the Hilbert–Huang transform

Proc IMechE Part F: J Rail and Rapid Transit 0(0) 1–15 ! IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954409714527930 pif.sagepub.com

Hsin-Chu Tsai1, Chung-Yue Wang2, Norden E Huang3, Tsai-Wen Kuo1 and Wei-Hua Chieng1

Abstract With the development of high-density intercity railway networks, substantial investments are now required, in terms of labor and machinery, in order to be able to conduct safety inspections. This results in high operational costs. Highcapacity and high-speed operations have resulted in levels of damage and deterioration of railway system components that have surpassed all expected values. Thus, traditional methods of periodic inspection, though still necessary, are no longer sufficient to detect the rapid development of defects on railway systems. Therefore, the direct use of operational trains as inspection vehicles to detect defects in real-time has become a current trend in the development of inspection techniques. This study applies an inspection technique previously reported in the literature to on-site testing of track. The response to vibrations on railway bridges, track system components and track irregularities are also studied. The effects are analyzed using the Hilbert–Huang transform approach. It is shown that the proposed data analysis method can be used in conjunction with the routine operation of trains to create a method for the monitoring of track defects. Keywords Vehicle response characteristic, axle-box accelerometer, track irregularity, Hilbert–Huang transform, versine Date received: 15 August 2013; accepted: 8 January 2014

Introduction The inspection of railway systems is performed using various inspection methods and regulations that depend on the equipment being inspected. For example, elevated bridges undergo periodic visual inspections and traditional measurements conducted by assigned personnel to monitor if the bridge structure has deteriorated or settled. For bridges with structural safety concerns, further instrument-based tests and safety assessments are conducted. However, testing elevated railways distributed over long distances using periodic manual methods not only consumes substantial labor and time, but also potentially damaged bridges cannot be promptly identified during the inspection cycle. Currently, track systems mainly employ special and designated track inspection cars to conduct inspections during night-time non-operating hours. Track inspection cars typically employ contact-type measuring wheels to inspect if track irregularity offsets in a fixed chord length exist. Consequently, the speed of the vehicle during measurements is limited. To satisfy the inspection frequencies prescribed by regulations for long-distance railway networks, a specific number of inspection vehicles must be employed, increasing the financial

burden incurred by the railway management. In addition, track irregularity offsets obtained using chord-based measurement methods deviate to a certain proportion when compared with actual track irregularity offsets, and irregularities in all wavelength ranges cannot be fully detected.1,2 In the literature it has been shown that the measurement magnification Hðl, LÞ of a track irregularity is dependent on the chord length L of the instrument and the wavelength of the irregularity l. For example, the mid-chord offset method shows the measurement magnification is double (i.e. Hðl, LÞ ¼ 2) when the wavelength is equal to the chord length (i.e. l ¼ L), and when the wavelength is longer than the chord length (i.e. l 4 L), the measurement magnification decreases, and the mid-chord-based inspection system fails to measure the irregularities, due to the chord length 1

China Engineering Consultants, Inc., Taipei, Taiwan Department of Civil Engineering, National Central University, Taiwan 3 Research Center for Adaptive Data Analysis, National Central University, Taiwan 2

Corresponding author: Hsin-Chu Tsai, Institute of Railway Engineering, China Engineering Consultants, Inc., no. 185, Sec. 2, Sinhai Rd, Taipei 10637, Taiwan. Email: [email protected]

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being an even multiple of the irregularity wavelength (i.e. Hðl, LÞ ¼ 0 when l ¼ L=2n, n ¼ 1, 2, 3, . . .). Thus, numerous recent studies have investigated the development and installation of various sensors on scheduled trains or special vehicles for detecting dynamic responses to the vehicle as it passes along a route. These responses have been indirectly used to identify abnormalities in bridges, vehicles and tracks, and to modify previously employed fixed and periodic inspection methods. For example, Yang et al.3 and Yang and Lin4 examined highway bridges, and proposed two analytical solutions for the response of the vibration subsystem based on the equations of the vehicle/bridge interaction system. They explained that three types of frequency components (i.e. external force frequency, natural vibration frequency of the vehicle and bridge vibration frequency) existed in the vibration response to a vehicle on a bridge. On-site test results verified that the vibration frequencies of a bridge could be obtained based on the vibration responses to a vehicle on that bridge.5 When the vibration frequency of a bridge can be successfully obtained based on the vibration response to a train, this frequency can be rapidly obtained following a disaster (e.g. typhoons, floods and earthquakes). The vibration frequency of the bridge after its construction and after a disaster can be compared to detect bridge spans with abnormalities or defects. The majority of early studies reported in the literature installed accelerometers in carriages or on bogies to conduct measurements for railway systems. These studies integrated displacement measurements to test carriages and bogies, or used the relative displacement between bogies and axle boxes for the subsequent calculation of track irregularity displacements.6,7 To prevent the vehicle’s suspension systems from filtering high-frequency components and hindering the ability to inspect for the existence of short-wavelength defects in tracks, some studies have installed accelerometers on axle boxes and explored the effectiveness of measurement systems in identifying short-wavelength defects.8–10 To identify track irregularities with a long wavelength (e.g. more than 8 m), Waston et al.11,12 recommended installing gyroscopes on bogies to conduct track inspections for longitudinal and alignment irregularities. Compared with the axle-box acceleration measurement method, this technique provides superior inspection precision at low speeds. This measurement system is primarily known as the inertial measurement system. Although this system does not require complex instruments and can be easily installed on any scheduled train, the post-processing and analysis method used to examine the measured signals determine the success or failure of the system. Considering studies on detecting track irregularities using vehicle measurement systems, current commonly employed signal analysis and processing methods include statistical methods, such as

correlation, standard deviation and root mean square analyses8,9,11, and other methods including power spectrum density (PSD)13–15 and wavelet analysis16,17, which use responses to a vehicle to identify track irregularities. Although using statistical principles for identification is more intuitive and simpler for signal processing, it cannot accurately define or calculate the relationship between vehicle response and actual track irregularity offsets when processing vibration signals derived through sensors installed on the vehicle. Furthermore, the frequency content or the wavelength range of track irregularities cannot be determined. In contrast, the PSD processing method can be used to understand the frequency content (or wavelength range) of track irregularities and the possible extent of damage, although it cannot identify the road or track segment at which a defect is located. Because the frequency distribution within a vehicle-response frequency spectrum is complex and wide ranging, using a PSD approach to conduct inspections of unknown damage and accurately determine the frequency components caused by track damage is difficult. Generally, only the potential range (e.g. wavelength) and extent of damage can be determined, and the precision of qualitative and quantitative analyses remains inadequate. Time/ frequency analysis is a combination of the advantages of statistical processing principles and frequency spectrum analysis, and it can be used to directly observe signal frequency and amplitude changes based on a time series. The most frequently employed methods are the short-time Fourier transform and wavelet transform analysis. However, both methods possess common theoretical flaws. When analyzing signals, they require the designation of window functions and the selection of appropriate basis functions. Regardless of how data change, the same basis functions are used for approximation; thus, adaptive analysis cannot be conducted on data. When the preselected window or basis function characteristics do not match the frequency and waveform characteristics of the data, incorrect analysis results may occur. The most critical flaw of the Fourier type of analysis is the inherent problem imposed by the uncertainty principle on all integral transform methods: one cannot simultaneously determine time and frequency to the precision allowed by the data. Compared with traditional analysis methods, Huang et al.18 proposed empirical mode decomposition (EMD) in the Hilbert–Huang transform (HHT), which uses the timescale of a signal to conduct a decomposition. This is an adaptive function, and does not require predetermined basis functions. Therefore, it can be applied to the nonlinear and non-stationary characteristics of a vehicle response without the uncertainty limitation. Furthermore, it is a special dyadic filter capable of filtering measured data in the time domain.19 The authors of this study



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previously conducted measurements by installing velocimeters and accelerometers in carriages and on axle boxes in high-speed rail (HSR) track inspection cars in Taiwan. By coordinating HHT signal processing methods, longitudinal track irregularities were successfully identified based on vehicle responses.20 This paper briefly describes the developed inspection techniques and a portion of the on-site test results, and further explores the HHT identification of vehicle vibration response components and characteristics caused by railway bridges, track system components and track alignment irregularities. In addition, a rapid inspection system for assessing railway functionality is developed.

Measurement system installed on bridges For the bridge vibration test, velocimeters were used as the primary sensing units and they were placed equidistantly on the bottom of the box girder of the elevated bridge, as shown in Figure 3. The selected bridge was a pre-stressed concrete bridge that comprises a part of the Taiwan HSR. The selected test span was straight with a basic support and a span of 35 m. The sampling rate of the measurement system was 1 kHz, and the system could be used to measure the dynamic response characteristics of the bridge when a commercial train or a test vehicle (i.e. track inspection car) passed. The results can be used for comparison and verification of the on-board measurement system.

Measurement systems On-board measurement systems A real-time inertial measurement system was installed on a track inspection car of the Taiwan HSR. This was considered the pre-experiment, which was conducted before the formal test using a commercial high-speed train. Velocimeters, accelerometers and a GPS were installed inside the carriage to measure the vehicle’s responses, speed and position, as shown in Figure 1. Another two accelerometers were fixed to both sides of the leading axle boxes to ensure that the vibration path traveled directly from the track to the accelerometers without passing through the primary or secondary suspension system of the vehicle, as shown in Figure 2. The advantage of this configuration is that signal distortion due to the operation of the suspension systems is avoided and a true structural response can be identified in an effective manner. A more detailed description of the measurement system and specifications of the sensors installed in the vehicle can be found in Tsai et al.20

Figure 1. Composition of the on-board measuring device.

Data-processing techniques EMD The purpose of EMD is to empirically identify intrinsic oscillatory modes based on their characteristic timescales in the data, and then decompose the data. The sifting process can decompose data from high to low frequencies into several intrinsic mode function (IMF) components that possess good characteristics for the Hilbert transform. The EMD process is intuitive, direct and adaptive, and does not require predetermined basis functions.18 The decomposed IMFs of an EMD must satisfy the following conditions. 1. In the entire data set, the number of extrema and zero crossings must be either equal or differ by a maximum of one. 2. At any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. This means that the IMF is symmetric in regard to the time axis.

Figure 2. Axle-box accelerometer.



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Figure 3. The positions of the sensors on the tested bridge.

The first condition is obvious and similar to the traditional narrow-band requirements of a stationary Gaussian process. The second condition ensures that the Hilbert transform can lead to physically meaningful definitions of the instantaneous frequency for the IMFs. The sifting process for extracting the IMFs is as follows. 1. Identify all local extrema, then connect all local maxima by a cubic spline line and this is the upper envelope. Repeat the procedure for the local minima to produce the lower envelope. The mean of the upper and lower envelopes is designated m1 ðtÞ, and the difference between data xðtÞ and m1 ðtÞ is h1 ðtÞ ¼ xðtÞ m1 ðtÞ

ð1Þ

2. If h1 ðtÞ does not satisfy the IMF requirements, treat h1 ðtÞ as the data and repeat the first step until the requirements are satisfied. The final h1 ðtÞ is designated c1 ðtÞ, which is the first IMF component from the data c1 ðtÞ ¼ h1 ðtÞ

ð2Þ

3. By subtracting c1 ðtÞ from the original data, the residue r1 ðtÞ is obtained r1 ðtÞ ¼ xðtÞ c1 ðtÞ

ð3Þ

4. If r1 ðtÞ still contains information on longer-period components, it is treated as new data, and the

sifting process is repeated as in the previous steps to obtain the following IMF c2 ðtÞ. This process is repeated until the residue rn ðtÞ becomes a monotonic function from which no further IMFs can be extracted. Consequently, the data xðtÞ serves as the IMF ci ðtÞ and residue rn ðtÞ, that is xðtÞ ¼

n X

ci ðtÞ þ rn ðtÞ

ð4Þ

i¼1

The intermittent characteristic of signals in a certain scale does cause a mode-mixing problem.21 Mode mixing is defined as a single IMF consisting of either signals of widely disparate scales or a signal of a similar scale residing in different IMF components. This problem can cause serious aliasing in the time/frequency distribution, and also render the individual IMF devoid of physical meaning. Regarding the mode-mixing problem, the novel ensemble empirical mode decomposition (EEMD) method was proposed by Wu and Huang.22 The principle of EEMD involves adding n white-noise series in order to achieve the amplitude of the standard deviation for the target data xðtÞ. The ith amalgamation of signals and noise is xi ðtÞ. Using the original EMD to decompose data with added white noise into m IMFs is designated as Cm ; i ¼ 1, . . . , N . The (ensemble) i mean of the corresponding (ith) IMF of the decompositions is the final result. Therefore, a mode-mixing problem can be addressed using the new EEMD algorithm. This novel approach fully exploits the



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statistical characteristics of white noise to disrupt the signal in its true solution neighborhood, and to eliminate the signal after its purpose is served. Thus, it represents a substantial improvement to the original EMD and significantly reduces the likelihood of mode mixing.

Hilbert spectrum The energy/time/frequency representation method based on EMD has been summarized by Huang et al.23 as Hilbert spectral analysis. The essence of that paper is now briefly summarized. After applying the Hilbert transform to each IMF component, the data can be expressed in the following form, where aðtÞ is the instantaneous amplitude and !ðtÞ is the instantaneous frequency XðtÞ ¼

n X

aj ðtÞei

R

!j ðtÞdt

ð5Þ

j¼1

As the energy contained in the remainder rn may be considerable, and accounting for the uncertainties involved in long drifts and component information in lower and higher frequencies, the residual trend should not be included in the equation. However, it can be included if it possesses physical significance. Equation (5) provides both the amplitude and frequency of each component as functions of time. If expanded, the same data in the Fourier representation would be XðtÞ ¼

1 X

aj ei!j t

ð6Þ

j¼1

where both aj and !j are constants. Equations (5) and (6) show that the IMF is a generalized Fourier expansion that consists of a changing vibration amplitude and instantaneous frequency; it is thus capable of managing non-stationary data. In other words, it has none of the limitations of a traditional Fourier analysis regarding fixed amplitude and frequency expansion. Furthermore, equation (5) also enables the representation of amplitude and instantaneous frequency as functions of time in a three-dimensional plot, where the amplitude can be contoured onto the frequency/time plane. The frequency/time distribution of the amplitude is designated as the Hilbert spectrum Hð!, tÞ. With a defined Hilbert spectrum, the marginal spectrum can be defined as Z

T

hð!Þ ¼

Hð!, tÞdt

ð7Þ

0

The marginal spectrum offers a measure of the total amplitude (or energy) contributed by each frequency value, and represents the cumulative

amplitude over the entire data span in a probabilistic manner.18

Identification of a track irregularity The procedure proposed in Tsai et al.20 for processing the acceleration signal to facilitate identification of track irregularities is as follows. 1. Decompose the acceleration signal using EEMD and obtain a finite number of components, IMFi ðtÞ. 2. Determine the instantaneous frequency IFi ðtÞ of each component, and then transform the results into an instantaneous wavelength using the vehicle speed data li ðtÞ ¼ speed ðtÞ=IFi ðtÞ. 3. Select the acceleration components aj ðtÞ ak ðtÞ for specific wavelengths of interest, and integrate a high-pass filter of the individual components twice. The displacement components di ðtÞ of track irregularities can then be obtained from the acceleration ai ðtÞ. 4. The displacement of the track irregularities can be calculated by summing all displacement components using equation (8). Then the time domain t can be transferred into the space domain s DTR ðtÞ ¼

k X

di ðtÞ

ð8Þ

i¼j

5. To examine the validity of the offset for irregularities as compared with the track inspection car, the displacement of track irregularities can be transferred into a 10-m-chord versine through the transform function included in equation (9), where VðsÞ is the (10-m chord) versine, DTR ðsÞ is the displacement of track irregularities and L is the chord length (L ¼ 10 m). VðsÞ ¼ DTR ðsÞ

DTR ðs ðL=2ÞÞ þ DTR ðs þ ðL=2ÞÞ 2 ð9Þ

Signal characteristics of the vehicle response Original signal characteristics Track irregularities, corrugation, weld depressions and other track irregularity defects can cause abnormal vibrations in vehicles and produce defect-induced damage characteristics in the measured vehicle vibration signals. This section presents a discussion on the measured signal variations in carriages and on axle boxes, and explores the physical significance implied by the surface characteristics and waveforms of the raw signal. Figure 4 shows the lateral acceleration



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Proc IMechE Part F: J Rail and Rapid Transit 0(0) acceleration signals show numerous smaller fixed interval peak values within the 1-km intervals, as displayed in Figure 5. The time interval is 1.13 s. When multiplied by the vehicle speed, the intervals are approximately 25 m. This phenomenon was caused by the fixed welds that were spaced at 25-m distances

Axle-box lateral acceleration A1y 30

20

Acceleration (g)

signals from the carriage and the bilateral axle boxes, which were measured using the on-board measurement system as the track inspection car traveled on a railway viaduct at 78.5 km/h. The figure clearly shows that lateral acceleration in the carriage had a significant square-wave offset, which primarily occurred due to the inclined lateral accelerometer being affected by the gravitational force g as the train passed over curved sections that had a cant. The same phenomenon should have occurred in the lateral acceleration of the axle boxes. However, because the response of wheel/track contact in axlebox acceleration was significantly higher than the acceleration offset caused by the cant, the offset could not be directly observed in the original signal. If the signal was processed using a 1-Hz low-pass filter, the offset in the axle-box lateral acceleration could be easily observed. Further observation of the axle-box lateral acceleration signals showed that the amplitudes of the equalinterval impulse responses could reach over 20 g, and the peak time interval was approximately 45.9 s. Based on vehicle speed conversion, this is an approximately 1-km interval. Railway inspection personnel have confirmed that this is the fixed interval between insulated joints. In addition, the above lateral

Insulated joint

10

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Figure 5. Equidistant impulse of the lateral axle-box acceleration.

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6600 Time (sec)

6800

Figure 4. Lateral acceleration signals measured in the carriage and axle box.


7000

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when the continuous welded rail was laid. However, not all track sections displayed this distinctive situation, which indirectly indicates that the quality of the weld tread in the track section demonstrating the discussed impulse response was lower than that in other sections. The velocimeter signals in the carriage (Figure 6) showed similar responses with equal-interval peak values. The frequency spectrum obtained using the fast Fourier transform demonstrated that the frequency of the equal-interval peak values was approximately 0.72 Hz. Conversion using this frequency and the vehicle speed (21.8 m/s) yielded an interval distance of approximately 30 m, which is the same distance as the span in this viaduct section. Thus, the equal-interval peak value response was initially determined to have resulted from varying levels of structural stiffness as the train passed over bridge piers. However, this inference was found to be inaccurate following verification efforts. For example, Figure 7(a) shows the signal measured by the track inspection car when passing other viaduct sections. The data in the figure demonstrate that instead of fixed peak values occurring along the entire route, they only occur in the 298 k and 298k500 sections. This indicates that the initial determination was inaccurate. Further comparisons of 40-m chord longitudinal irregularity data from the track inspection car measurements showed that the peak values in the velocimeter signals were responses to longitudinal irregularities in this section, as shown in Figure 7(b). Hence, the fixed interval peak value response in Figure 6 was not a response resulting from the bridge structure, but rather the longitudinal irregularities of the track. This discussion indicates that, even without data analysis, a portion of the original data characteristics in the dynamic signal responses measured using

Vertical velocity signal measured at 293k136-292k131. 20 15 10

Theoretically, track fasteners can be considered a continuous elastic foundation beam. If track fasteners and other components are damaged or fail, they alter the support stiffness of the track. In principle, this can be detected from the train’s vibration response. Wu and Thompson indicated that wheel/ track interaction and vibration responses are influenced by changes in the stiffness of discrete distribution supports.24 Therefore, this section adopts EEMD to decompose the acceleration signal of the axle boxes and explore if the decomposed components possess vibration responses and frequencies caused by the track inspection car passing over fixed interval fasteners. The fastener interval of the railway structure is 0.625 m, and the case analysis is shown in Table 1. The frequency of the vehicle’s vibration response induced by fasteners is similar to the ratio of the its speed to the fastener interval. Consequently, when the fastener interval is fixed, the vibration frequency is determined by the train’s speed. The Ftheory included

(a) 30

5

(b)

-5 -10 -15 -20 -25

10 0 -10 -20

293

298

10

298.5

299

40m versine of Track inspection car

5 0 -5 -10 297.5

292.2 292.3 292.4 292.5 292.6 292.7 292.8 292.9

Velocity data

20

297.5

0

Versine (mm)

Velocity (mm/s)

Vehicle vibration responses caused by fasteners

Velocity (mm/s)

25

vehicles can show the existence of short-wave track irregularities, corrugation, weld depressions and other track irregularities or alignment changes. Medium- and long- wavelength irregularities can be observed using the original signal characteristics produced by the carriage’s interior sensors. This is the reason why numerous studies extract window function statistics from time-series signals (e.g. root mean square, moving standard deviation, and other signal processing methods) to identify rail sections with potential defects. This also suggests that any defects or damage in the track system can cause abnormal forced vibrations in the vehicle system. Nevertheless, in order to quantify the anomalies further, signals also typically require further analysis.

298

298.5

299

Mileage (km)

293.1

Mileage (km)

Figure 6. Vertical signal of the velocimeter measured in the carriage.

Figure 7. (a) The vertical signal measured by the velocimeter and (b) the versine of the 40-m chord length measured by the track inspection car.




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in the table is the frequency value of the theoretical calculation, and Fexperiment is the frequency value obtained in an experiment, which represents the main vibration frequency of one of the components ci after the axle-box acceleration signals were processed using EEMD. Figure 8 shows the frequency spectrum for c2 to c7 after the vertical acceleration signals were decomposed in case 1. The figure clearly indicates that the main frequency of vibration component c7 matches the fastener’s excitation frequency. This verifies that the vehicle’s vibration responses were affected by changes in the stiffness of the continuously distributed supports, suggesting that changes in the structural stiffness in the locations at

Table 1. The excitation response of the fasteners. Speed (m/s)

Ftheory (Hz)

Fexperiment (Hz)

1 2 3 4

21.97 22.8 12.4 12.5

35.15 36.48 19.84 20

35.10 36.49 19.80 20.01

0.05

0

amp. of c7

0

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0.2 0.1 0

0.5 0

20 10 0

amp. of c6

amp. of c5

amp. of c4

amp. of c3

amp. of c2

Case

which the vehicle passed were reflected in the vehicle’s vibration responses. The Ftheory and Fexperiment from other cases are also consistent with these results. In addition, the analytical process shows that compared with past analytical methods, EEMD does not require assumptions about the vehicle’s response frequency range and bandwidth. EEMD can adaptively separate the potential physical characteristics and frequency content contained within responses. In addition to being affected by changes in the track’s configuration, irregularities and alignment changes, and abnormalities in the vehicle, the vibration response of a vehicle are affected by the response of lower bridge supports. The excitation of specific driving speeds or fixed-interval wheel sets may even result in vehicle/bridge resonance.3,25 Thus, this study examined whether the response of a train passing over a viaduct contained vibration components and frequency content caused by bridge vibrations. For analysis, data from velocimeter signals of the mid-span box girder, the acceleration signals of the axle boxes and velocity signals from inside the carriage were employed. The sampling rate of the bridge measurement system was 500 Hz, and the sampling rate of the track inspection car measurement system was 5 kHz.

5

99.91 75.99

0

0

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50 Frequency, Hz

60

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50 Frequency, Hz

60

70

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35.10

10 0 0

10

20

30

40

Figure 8. Case 1 vertical acceleration signal for c2 (top plot) to c7 (bottom plot) frequency spectra.



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The data length was sourced from the signals of the two bridge spans at the start and end of the location at which the track inspection car entered and exited the test span, which resulted in a three-span (three spans of 35 m) data length. This data was employed to facilitate observation of the instantaneous frequency change when the track inspection car entered and exited the test span, and to enhance the resolution of frequency analysis. Figure 9 shows the original signal and the speed of the track inspection car passing over the test span. A1z and A2z are vertical accelerometer signals from the bilateral axle boxes, and V1z is the vertical velocimeter signal from inside the carriage. To reduce noise and random high-frequency impulses, and to highlight the bridge vibration frequency, resampling of the original data measured from the vehicle was performed. This data was transformed into 10 500-Hz signals that were summed and averaged into one signal for EEMD processing. The obtained high-to-low frequency IMFs underwent the Hilbert transform to yield the marginal spectrum of each IMF, which was used to understand the distribution range of each component frequency. Next,

components that could potentially cover the bridge vibration frequency range were selected to observe if the vehicle response contained bridge vibration frequencies. Figure 10 shows the marginal spectrum plotted according to the acceleration signals IMF6 obtained from the bilateral axle boxes after conducting the Hilbert transform. The figure demonstrates that the distribution of the two acceleration frequency peak values is similar. Specifically, the frequency peak values 4.3, 5.4 and 6.8 Hz are almost identical to the 4.4, 5.5 and 6.8 Hz frequencies obtained in the vehicle’s ambient-vibration test conducted in this study, and should have been part of the vibration response of the vehicle system. In addition, the figure shows that both accelerometers demonstrate a response with a frequency of approximately 6.5 Hz. This frequency and the 6.6 Hz vertical vibration frequency measured by the box girder velocimeter are similar. Further observations of the marginal spectrum from the velocimeter in the interior of the carriage indicated that the vibration component IMF4 provided a similar response to that of the bridge frequency, as shown in Figure 11. To facilitate the comparison of the frequency spectra obtained from the acceleration and

Velocity (mm/s)

5 V1z 0

-5 137.16

137.17

137.18

137.19

137.2

137.21

137.22

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A1z 0

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137.17

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137.21

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2 Acc. (g)

A2z 0

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8 Vehicle speed 6 4

2 137.16

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137.18

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137.2

137.21 137.22 Mileage (km)

137.23

137.24

137.25

137.26

Figure 9. The vertical vibration signals from various sensors and the vehicle speed as the track inspection car passed over the bridge span.




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V3z-IMF4 Hilbert Spectrum

IMF 6 Marginal Hilbert Spectrum (137k195-137k230) 0.9

20 A1z A2z

X: 5.44 Y: 0.7342

0.8

0.5 15

0.6 0.5

X: 7.945 Y: 0.5378

X: 6.458 Y: 0.5172

Frequency (Hz)

Spectral Density

0.7

X: 4.344 Y: 0.3984 X: 6.849 Y: 0.4472

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Figure 10. IMF6 marginal spectrum of the axle-box vertical accelerometer.

V1z and A2z Marginal Hilbert Spectrum (137k195-137k230) X: 5.44 Y: 1

V1z-IMF4 A2z-IMF6

X: 6.497 Y: 1

Spectral Density

1 X: 7.945 Y: 0.7325

0.8

0.6

X: 4.344 Y: 0.5426

0.4

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Frequency, Hz

Figure 11. Marginal spectra of the vertical velocimeter IMF4 and of the axle-box accelerometer IMF6.

velocity signals, the frequency spectra obtained from two sensor signals were normalized. The figure shows that the frequency spectrum obtained from the velocimeter also possesses a 6.5-Hz frequency component, which is very close to the vertical vibration frequency of the bridge. Nevertheless, because the energy of this peak value of the frequency was the highest of all the peak values, and the vibration component (IMF4) exhibited the highest energy of all the IMFs, this study still questioned if the discussed frequency peak value was actually the bridge-induced vehicle response. The vehicle response energy resulting from bridge vibrations should be smaller than the vibration response of the vehicle’s suspension system under external excitation. Thus, this study initially determined that this frequency component should represent the vibration response of the vehicle itself. To confirm the physical significance of this frequency component, the time/

137.18

137.2 137.22 Mileage (km)

137.24

137.26

0

Figure 12. Hilbert spectrum of the IMF4 velocimeter in the box girder span.

frequency changes of the velocimeter signals on the box girder span were observed when the track inspection car passed. This observation was conducted to explore whether the components of the bridge response after EEMD contained vibration responses with an evident characteristic main frequency, and whether neighboring test spans exhibited similar frequency changes to those of the measured span when vehicles passed. The Hilbert spectrum of velocimeter IMF4 on the box girder span plotted in Figure 12 shows that when the track inspection car was on the north-side neighboring span (137k160–137k195), the test span (137k195–137k230) produced a stable vibration response under the effect of excitation of the neighboring span. This response was clearly the main frequency response (6.5 Hz) of the bridge’s vibration. When the track inspection car entered the test span, its relative position was approximately 137k195–137k205. The bridge produced frequency vibrations and disturbances before gradually stabilizing. When the track inspection car left the test span (the relative position of approximately 137k230), the same frequency disturbance situation was produced. Thus, this vibration component was obviously the response of the main frequency of the vibration of the bridge. A simultaneous observation of the velocimeter signal IMF4 inside the carriage (see Figure 13(a)) and the time/frequency distribution of the box girder span velocimeter signal IMF4 (see Figure 13(b)) clearly shows that a frequency disturbance occurred when the track inspection car entered and exited the bridge span (e.g. at the 137k160, 137k200 and 137k230 marks). The frequency distribution of the other track sections for these two signals was similar. Because the velocimeter inside the carriage was affected by the vehicle’s suspension system, the frequency disturbances and the frequency components were more complex.



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10m-chord Versine of Track Irregularity 4

versine (mm)

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Figure 13. Hilbert spectrum of the IMF4 (a) velocimeter in the carriage and (b) velocimeter in the box girder span.

This discussion indicates that the frequency spectrum for the accelerometer on the axle boxes and the velocimeter inside the carriage demonstrated an approximately 6.5-Hz vehicle vibration response component that was caused by bridge vibrations. The energy from the frequency component measured by the velocimeter inside the carriage was higher, which may have been due to the resonance effects created by the vehicle and main bridge vibration frequencies being close to one another (fv ¼ 6.8 Hz, fb ¼ 6.5 Hz). However, this phenomenon may simply represent a larger response produced by the vehicle when the vehicle drove over bridge spans along the route at a specific speed.3 The HHT approach can be very effective for structural health monitoring, as reported by Huang et al.26, if sensors are deployed on the structure. However, this method would be ineffective for HSR systems if there are too many bridges along a line. Therefore, developing a moving vehicle-borne system is necessary. The method presented here is an initial trial. Other challenging issues such as the sensitivity of the sensor and the speed of the vehicle all need further research.

Track irregularity identification results Tsai et al.20 proposed a track irregularity identification system based on the HHT, which was verified by accurately measuring longitudinal track irregularities based on on-site measurements and analysis results. To make this paper more complete, the results presented in that paper will be briefly summarized and the effectiveness of this method for identifying alignment irregularities will be further explored.

Results on the identification of longitudinal track irregularities Figure 14 displays the displacement curve obtained from a velocimeter inside a carriage analyzed using

Figure 14. The displacement data determined from the velocimeter inside a carriage analyzed using the method proposed in this study and the 10-m-chord versine measured by the track inspection cars.20

the method proposed in this study and the 10-m-chord versine measured by the track inspection cars. The figure shows that regardless of the irregularity or irregularity wavelength of the section of track, the track irregularity displacement curve obtained from the velocimeter inside the carriage is consistent with the result measured using the track inspection car. For example, the three wavelengths at 310k þ 600 310k þ 700 are for a 30-m vertical irregularity, and seven vertically irregular waveforms are located at 310k þ 800 311k. However, a proportional deviation exists between the displacement curve of the actual track irregularities and the versine measured by the track inspection car.2 Thus, the amplitude of the displacement curve obtained from the velocimeter in the figure does not match the versine measured by the track inspection car. Figure 15 demonstrates the results after the track irregularity displacement curve was converted into the 10-m-chord versine using equation (9). The dashed blue line is the 10-m-chord versine measured using the track inspection car, and the solid red line is the 10-m-chord versine obtained from the velocimeter in the carriage. The analysis results show that the versine obtained using this system is similar to the results obtained using the track inspection car both in terms of waveform and phase. However, the size of the versine is significantly smaller than the result obtained using the track inspection car. The primary factor that caused this deviation was that the measured response inside the carriage was affected by the vehicle. Conversely, the effects of the suspension system were mitigated in the axle-box acceleration signals, and the obtained versine possessed a waveform, phase, and irregularity offsets (i.e. amplitude) similar to the measurements obtained using the track inspection car. Slightly smaller




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10m-chord versine of track irregularities (velocimeter)

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Mileage (km)

Figure 15. Comparison of 10-m-chord versines from the velocimeter in the carriage and track inspection car (case 1).20

Figure 17. Comparison of the 10-m-chord versines from the right-side axle-box accelerometer and track inspection car (case 2).

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10m-chord versine of right track irregularities 6

Vehicel speed Track inspection car

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-6 309.8

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-2 -4 -6 309.8

66 295.5 309.85

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Mileage (km)

Figure 16. Comparison of the 10-m-chord versines from the right-side axle-box accelerometer and track inspection car (case 1).20

amplitudes were measured for only parts of the track sections. The majority of the track sections could control the error range to less than 1 mm, as shown in Figure 16. To verify that this method can obtain accurate inspection results when the vehicle’s speed is not fixed, this study selected measurement signals for a non-stationary driving speed to conduct further analysis. Figure 17 shows the identification results from the right-side track of the same track section. Figure 18 shows the vehicle’s driving speed for this test section. The data in the figures indicate that using the axle-box accelerometer measurement system in coordination with HHT signal processing technology can effectively identify sections with vertical track irregularities and irregular wavelengths and offsets even when measuring at varying vehicle speeds.

296

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Mileage (km)

Figure 18. Train speed for case 2.

Results on the identification of track alignment irregularities To explore the identification of track alignment irregularities using the measurement system and identification method employed in this study, measured signals from straight and curved sections traveled on by track inspection cars were selected and analyzed, and the identifications of alignment irregularities for various track sections were compared. Figure 19 demonstrates a comparison of the 10-m-chord versine from the left-track axle-box lateral accelerometer and the results obtained using the track inspection car. Although the variation range of the overall track irregularity amplitude is similar (approximately 1:5 mm), a partial amplification of the curve distribution showed that regardless of the wavelength or the size of the irregularity offset, the accelerometer




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2 Track Inspection Car Axle-box Accelerometer

1 0 -1 -2 231

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Figure 19. A comparison of the 10-m-chord versines from the left-side axle-box accelerometer and track inspection car in a straight section.


Versine (mm)

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191

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Zoom in (190k500-190k) 3 Track Inspection Car Axle-box Accelerometer

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190.25 190.2 Mileage (km)

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Figure 20. A comparison of the 10-m-chord versines from the left-side axle-box accelerometer and track inspection car in a curved section.

results varied significantly from the measurement results for the track inspection car. The possible reasons causing this phenomenon are as follows. 1. A lower signal-to-noise ratio. As regulations for HSR track alignment irregularities are strict (e.g. only 4 mm is allowed for the 10-m-chord alignment irregularity), this leads to a

lower vibration response signal-to-noise ratio caused by alignment irregularities. This problem was especially severe when the track inspection car was moving at low speeds, which affected identification results. 2. Wheel/track gap. Because of limitations in the gauge and wheel flange design, a fixed gap exists between the two,



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unlike vertical wheel treads that completely fit the railhead. Thus, actual track irregularities cannot be reflected, which is the primary reason for poor alignment irregularity identification results. A reasonable explanation based on analysis of acceleration signals for curved sections can also be provided. Figure 20 shows the results of the analysis on curved sections. The alignment irregularity variation range in the figure is similar to the analysis results for straight track sections. However, a partial magnification of the identification results shows that the inspection results for curved sections are more similar to the track inspection car results, regardless of whether wavelength or amplitude were measured. The primary reason causing this phenomenon is that the speed of the track inspection car was slow; therefore, when it passed a curve, the wheels may have adhered more tightly to the track surface because of rail cant and the influence of the gravitational force g. This facilitated a more realistic reflection regarding track alignment irregularities. Nevertheless, the wheels did not always roll tightly against the side of the track even in curved sections, which explains the analysis results for curved sections derived by the proposed system. Sections of the track showed extremely accurate results, and other sections could not be successfully inspected with regard to track irregularities. 3. Trajectory differences. Because of the wheel/track gap, even if a vehicle was driven on the same track section, wheel trajectories that had passed over the railhead tread can show differences, which could possibly lead to varying test and measurement results for each iteration and low repeatability.

response, the short duration of a vehicle passage over a single bridge span, similar vehicle systems and bridge vibration frequencies, and the limitations of the sensors increase the difficulties for the on-board measurement system to accurately identifying bridge responses. Many of these difficulties have not been fully addressed here. They will be the subject of future research. The proposed method can do a good job on identifying track anomalies. The identification method and analysis procedure for track irregularities proposed in this study can accurately calculate if longitudinal track irregularities exist, as well as the corresponding wavelengths and amplitudes along the track route, even under varying vehicle speeds. Although signals from a velocimeter inside a carriage can be used to conduct inspections regarding longitudinal track irregularities and wavelength range, the calculation of the track irregularity offset (versine) is affected by the vehicle’s suspension system and can lead to major levels of error. The identification of track alignment irregularities is limited by the design of the track gauge and the wheel flange interval, which might lead to inaccurate identifications and reflection of track alignment irregularity in the lateral vibration acceleration responses. This problem is exacerbated on curved sections, the precision and stability of the overall identification remains problematic. Further research is still needed. The difficulties notwithstanding, the analysis and examination results of these sample cases indicate that constructing a rapid inspection and identification method for railway systems based on the HHT is feasible. This can facilitate monitoring of the physical and potential defect characteristics from operational trains and vehicles.

Conclusions

Funding

Dynamic signal measurements for vehicles can be used to detect certain track irregularities, defects and alignment changes without signal treatments by using parts of the original signal’s characteristics. To quantify the anomalies, however, analysis of the data is necessary. The use of adaptive EEMD processing can allow separation of the vibration signals measured on vehicles into finite IMFs from high to low frequency, from which quantitative information can be obtained. This information includes the vehicle’s vibration responses caused by fixed interval fasteners and bridge structures, and the response of the vehicle system itself. Caution must be exercised, however, as on-site test results show that the signal response measured by a moving vehicle cannot easily and clearly identify bridge vibration responses and frequencies unless a sophisticated analysis method is used. In addition to processing the wide-range and complex frequency components of the vehicle’s vibration

This study was partially sponsored by the Taiwan High-Speed Rail Corporation (THSRC) under contract no. C611.

Acknowledgments The authors thank the THSRC for their assistance in the experimental research that was performed between 2009 and 2011 and is described in this paper. This paper is based on a research report entitled ‘‘Development of a Health diagnosis system for the Taiwan high speed rail,’’ whose copyright is held by the THSRC.

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