Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform

Transcription

1 Tamkang Journal of Science and Engineering, Vol. 13, No. 3, pp (2010) 267 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform Huan-Hsuan Ho 1 *, Po-Lin Chen 2, Dave Ta-Teh Chang 2 and Chih-Hao Tseng 2 1 Department of Traffic Science, Central Police University, Taoyuan, Taiwan 333, R.O.C. 2 Department of Civil Engineering, Chung Yuan Christian University, Taoyuan, Taiwan 320, R.O.C. Abstract The main purpose of this study is to explore the feasibility and applicability of using EMD and HHT on the analysis of track structure system through laboratory testing and vibration testing. The research process is divided into two phases, the first section is rail vibration frequency testing, It was measured the vertical (Z direction) natural frequency of a single span rail in the laboratory. The analysis methods use EMS and HHT spectrum analysis theory, as well as on FFT, in order to know the different results of the two methods. The results of interval rail vibration frequency test showed that Z direction range is 720 Hz, and is roughly the same as the scope defined by existent documentations. The significant results obtained by the analysis of EMD and HHT, and percepts the different self-vibration frequencies of injury and normal rail; as is known from the simulation results, for the different vertical support conditions of standard section and hollowed out section, the vibration frequency of the track structure decreased from standard section s 700 Hz to 400 Hz, this phenomenon is very clear for the application of EMD and HHT, and further confirmed the feasibility and applicability of EMD and HHT used in track structure. In addition, the accelerometer at rail effective on quantity examine laying ranging interval between 8 m, so it is not good for the economic benefits, vibration signals obtained by setting up the accelerometer on the top of the locomotive is complicated, but remain valid by doing HHT spectrum analysis after EMD signal decomposition, and can help to further targeting the damage location. Finally, by comparing the results of HHT and FFT analysis, we confirmed that FFT can only get the average natural frequency which has nothing to do with time, it can not be used to calculate the possible damaged location of the track structure, while HHT can obtain time-varying frequency and energy calibration, then we can effectively calculate the possible damaged location of the track structure. By comprehensively analyzing the results, EMD and HHT has the practical advantage and broader applicability than FFT. Key Words: Empirical Mode Decomposition, Fast Fourier Transform Analysis, Hilbert-Huang Transform 1. Introduction Rail transport road network has been actively promoted in Taiwan recently years. The Taiwan Railway *Corresponding author. hohuanh@gmail.com Administration developed from the traditional longdistance passenger transport system to the Mass Rapid Transit System of Taipei metropolitan area and Kaohsiung metropolitan area, as well as high-speed railway currently under construction. In order to track a longer life, the safety maintenance and inspection technology

2 268 Huan-Hsuan Ho et al. applied to track structural are increasingly receiving more attentions. There are various kinds of track inspection technologies, and one of which is track vibration modal analysis, this study investigated vibration frequency characteristics of the track by using the new detection technology-hht (Hilbert-Huang Transform), the vibration analysis method was published in UK Royal Society journal by Dr. Huang E in 1988, and the paper referred to an innovative signal decomposition method called empirical mode decomposition method (Empirical Mode Decomposition, hereinafter referred to as EMD) [1], this method has the advantage of effective decomposition of vibration of signals, complex original signal is decomposed into a limited number of intrinsic mode function with different times scales (Intrinsic Mode Function, hereinafter referred to as IMF), this advantage makes the non-linear and non-steady state of diachronic vibration signal to get a better spectrum analysis. Users can extract original real vibration signal from the tested structure, carry out HHT conversion with IMFs as a launch base and get a variety of graphical spectrum analysis. In 2003, to perfecting EMD technology, Dr. Huang E further proposed concept of Intermittent Criterion in a paper publishe [2], the establishment of this criterion makes EMD technology more comprehensive and accuracy in use, and makes IMFs which is from EMD more cleaner and clearer. Currently, dynamic test analysis if track structure are mainly made of fast Fourier transform (Fast Fourier Transform, hereinafter referred to as FFT) and Wavelet analysis, majority of research explore track vibration by numerical simulation methods. Therefore, this study used dynamic measurements and applied EMD HHT for signal decomposition and spectral resolution, hoping to obtain better research results through this new research method. 2. Empirical Mode Decomposition Method (EMD) EMD can decomposed diachronic signals into a fitness of IMF component, together with HHT which provides meaningful time-varying frequency, thus dealt with nonlinear and non steady state signals. Since the basement of EMD is derived from original vibrations-diachronic signals, the following underlying assumptions exist when dealing with nonlinear and non resident state data: There must be two extremes of the signal: a maximum and a minimum. Signal characteristic time scale is defined as the time difference between the two extremes. If the data contains no extreme but inflection points, we do once or more times of differential with the signal until finding the extreme. The final results can be obtained from integral component differential. This method is based on experience, using characteristic time scale of signal to define the vibration mode, and then decomposed signals according to it. According to Dazin [3] data analysis, the first step is using visual inspection of the data, replying on inspections, there will be two ways immediately and directly ascertain the different time scales: First, time difference between two consecutive local maximums or minimums; Second, time difference between two consecutive cross-zeros. Here, time difference between two consecutive extremes was the intrinsic time scale of vibration mode, so a very good resolution of vibration mode was provided and this definition can also be applied to non-zero mean data or even data without zero that is all positive or negative. This is a systematic approach used to parse out the IMF, may also be called a shifting process, the decomposition method used envelope defined by local maximum and minimum respectively, firstly we find out all of the local maximums in the signal, connect all the maximum points to be the upper envelope with cubic spline and then, find out all of the local minimums in the signal, connect all the minimum points to be the inferior envelope. The upper and inferior envelop will contain the entire data. The average of maximum envelope and minimum envelope is called mean envelope, an alias m1 for it, and the difference value between original signal and mean envelope is the first component, an alias h 1 for it shall be: X(t) m 1 = h 1 (1) In theory, h 1 should be an IMF, for the establishment of the above-mentioned h 1 seems to meet all requests that IMF should have. But in fact, it is not the case, it is normal that the original data is high or low suddenly, and they will re-generate new extremes and translate or exaggerate pre-existing extreme, for the original data is directly used for extreme envelope, the impact to extreme envelope is

3 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform 269 direct while the impact to mean envelope is indirect, thus the transfer process is entered. But even the cubic curve is approximately perfect, a slight bump of the slope will enlarge into a local extreme, and makes local zero change from a rectangular coordinate system into a curve coordinate system, in the other word, the mean envelope and y-axis are regarded as new coordinate system. In the second transfer process, h 1 is the original signal, and then h 1 m 11 = h 11 (2) Repeating the process of transferring for k times until is h 1k an IMF, that means h 1(k 1) m 1k = h 1k (3) component, so it is considered as a new data and is dealt using the same transfer process aforesaid. This method can be applied very widely. Then the result of the subsequent r 1 should be r1 c2 r2 r 1 c r n n n (6) The transfer process can stop relying on any predetermined specification, it is not the meaning that when the components c n or r n become far more smaller than general results intended, instead, when the remainder r n turns to be a monotonous function, thus there is no IMF that can be resolved out, then the process can stop. Even Finally, designating it as c 1 = h 1k (4) As noted above, this process decomposes optimal modes from original signal, through their characteristic time scales, the transfer process can eliminate the carrier and sooth the uneven amplitude. Although eliminating the carrier and soothing the rough amplitude is meaningful and absolutely necessary, it will rub out part of the amplitude disturbance with some physical meaning while this process is used to a certain limit. In order to ensure that the amplitude and frequency changes of IMF component can be sufficient to maintain the physical meaning, a convergence conditions must be decided for the transfer process to be cut-off automatically. The condition is that in IMF, if the number of cross-zero points is the same as the total number of local extreme points (the number of local maximum plus the number of local minimum) are equal, the transfer process of this mode will stop and the next process will begin, the process is detailed in Figures 1~2. On the whole, c 1 should be the best time scale contained in signal or shortest cycle component, c 1 can be separated from original signal as Figure 1. Original vibration signal. X(t) c 1 = r 1 (5) Because the remainder r 1 still contains long period Figure 2. Indication of IMFs after N times of transfer process.

4 270 Huan-Hsuan Ho et al. if the signal is zero mean, the last remainder still may not be zero; because the signals have a trend, the last remainder is the trend. Totalizing equations (5) and (6) to be equation (7): X () t c r n i 1 i n (7) Accordingly, we can complete to decompose a data to n-empirical modes and a remainder regarded as the mean trend or a constant. The application of EMD don t need any mean or zero value reference axis, only needs to know the position of local maximum. For each component concerned, zero reference axis will be generated automatically relying on the transfer process. And for EMD don t need a zero reference axis, to a non-zero mean data, EMD will remove the troublesome step of mean. 3. Research Program and Test Methods 3.1 Research Program The research program can be divided into two phases, the first test is a preliminary study and comparison of the vertical (Z direction) rail frequency after simple laboratory vibration simulation as well as in-situ dynamic load test of standard segment. In this stage, not only the frequency interval was confirmed, but also in cases of, if the difference of vertical (Z) frequency of the track can obtain significant results by application of EMD and HHT; In the second phase, ballasted track structure system was chosen in Taoyuan Taiwan Railway proving ground, and the ballast was hollowed artificially at a special section, we changed its vertical (Z) supporting conditions in order to explore the different vertical (Z) frequency while the track structure was in the state of ballast hollowed out, and tried to define an effective measurement distance of laying accelerometers and knew whether we could ensure the damaged location with vibration diachronic signals. The signal analysis methods adopted EMD and HHT vibration modal analysis as well as FFT, through comparing the differences of the result obtained, the feasibility and applicability of using EMD and HHT in track structure vibration testing can also be verified [4,5]. 3.2 Vibration Testing of Rail Section As the natural vibration frequency of current orbit is not always the same as theory, the reason is that the interior of the rail material may not that homogeneous and the track components may also cause natural frequency changes. Therefore, in the testing ground, vibration signal was measured to verify that the vertical (Z) frequency range from Hz [6]. The following content, considering the operation of this test, was divided into two parts to illustrate due to the different test sites: First, proving ground for civil engineering of Chung Yuan Christian University; Second, Taoyuan Taiwan Railway testing ground Proving Ground for Civil Engineering of Chung Yuan Christian University Vibration source selection The main purpose of the simulate test in proving ground for civil engineering is to find the range of the rail s natural vibration frequency, so a percussion hammer with single frequency was used as the source of vibration, it is conducive to analysis and can be reference for future analysis The layout of measurement points and establishing measurement interval In order to simulate current rails, we chose two sleepers and a short rail in the testing ground, its configuration was shown in Figure 3. Using a hammer as the source of vibration (shown as Figure 4), we did the test in order to understand the changing state of natural vibration frequency. The trial section simulated ballast section, with rail weight 50 kg, sleeper spacing 60 cm Measurement operation Firstly, we measured vibration signal data of normal rail while being knocked, then drilled a diameter of 2 cm hole on the rail near the accelerometer to simulated rail damaged state, and measured vibration signal data after knocking, as is shown in Figures 5 and 6. Generally speaking, the higher the sampling frequency, the more robust and complete the data would be, but considering that large amount of data might take a long time, and because the vertical (Z) vibration frequency of the rail was about Hz, we defined the sampling frequency as 5000 Hz, that is, took a point every s.

5 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform l Figure 3. Measurement point. Figure 4. Vibration source (hammer) percussion. Figure 5. Schematic diagram of normal rail. Figure 6. Schematic diagram of damaged rail. The process was divided into two parts: normal section and damaged section, we could tell the difference by test analysis and found the location where the energy concentration transmitted by vibration wave, if the rail was damaged, there would be phenomenon of stress concentration, according to this, we could tell the range of natural vibration frequency, also we can tell if the frequency has a downward trend after the rail structure being damaged Taoyuan Taiwan Railway Proving Ground Vibration source selection The main purpose of testing was to understand the natural vibration frequency of the rail, so we used hammers as the source of vibration The layout of measurement points and establishing measurement interval A cross-section (the distance-60 cm between two adjacent fasteners in the rail is called a cross) or twocross sections of a standard segment were chosen for the on-site testing. Using the hammers as a vibration source, we could understand the changes in the state of the actual natural vibration frequency by testing. The testing area 271 is 50 kg ballast section, gauge m, sleepers spacing 60 cm Measurement operation Generally speaking, the higher the sampling frequency, the more robust and complete the data would be, but considering that large amount of data might take a long time, and because the vertical (Z) vibration frequency of the rail was about Hz according to literatures, we defined the sampling frequency as 5000 Hz, that is, took a point every s. 3.3 Simulation Experiment of Ballast Hollowed Out Ballast hollowed out resulted in extinct difference of supporting conditions between the plumb direction of the track structure and the standard segment, which would lead to the change of the track s vibration frequency in plumb direction (Z). Therefore, the ballast under the special section s track structure would be excavated and the situation of ballast hollowed out would be simulated artificially during the trial. From the different forms caused by the locomotive s traveling on the top of the track, the wave propagation distance of the track s vibration could be understood exactly, and the effective measurement range and the laying location of the accelerometer could

6 272 Huan-Hsuan Ho et al. be determined by changing the laying location of it. Another try was that the accelerometer was installed on the locomotive in a more complex environment in order to see if the complex vibration signal could be decomposed. HHT and FFT were separately used for signalanalyzing tools to compare the difference in signal analysis and confirm its applicability. bration signal can be obtained from the accelerometer installed on the locomotive after disturbance. In addition, in order to avoid the interference caused by the vibration of the locomotive s engine, the installing position of the accelerometer should be away from the engine and close to the upside of the axle, as shown in Figure Selection of the Vibration Sources Owing to the need to create a continuous load on the top of the track and the different vibration shapes of the locomotive s running on the top of the ballast hollowed out, the heavier locomotive was used for a source of vibration. Because of the different energy inspired by the different weight of locomotive, the area range of the ballast hollowed out was calculated by analyzing the speed and the cut-time, using the two kinds of locomotives which weighted 10 tons and 15 tons. 4. Signal Data Analysis Result Layout of the Measurement Points and Establishment of the Measurement Range The establishment of layout range when measurement points on the rail Selecting a specific section and excavating three ballasts under PC pillow caused non-support state at the bottom of the PC pillow, which was used to simulate the situation of the ballast hollowed out. The area of hollowing out and the layout location of the measurement points were shown in Figure The layout of measurement points on the locomotive Also, by trying to install the accelerometer on the top of the locomotive, we could know whether the vi- Figure 7. Hollowed out regional and placement of measuring points. 4.1 Vibration Data Analysis of Rail Section Analysis Results of Testing Ground for Civil Engineering of Chung Yuan Christian University l The test analysis showed the vertical (Z) of the selfvibration frequency of the rail without damage could range of about 720 Hz; those are damaged could range of about 680 Hz. These results indicated that, due to the structure of rail damaged, original structure was weakened in stiffness. This caused vibration frequency was significantly decreased from 720 Hz to 680 Hz and generate energy was dissipated. The results were shown in Figure 9. l Test results also confirmed that the vertical (Z) vibration frequency difference of the structure of rail without any damage and with damage can vary by the application of EMD and HHT to obtain significant results Comparison of Analysis Results of the Section of the Taiwan Railway Administration Test Sites From Figure 10 that the analysis results of Marginal Figure 8. Measurement of accelerometers on the head of the locomotive.

7 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform 273 Figure 9. Comparison of HHT energy frequency spectrum of normal and damaged rail in Z direction. we can get the exact understanding the wave propagation distance of orbital vibration and conclude the effective measurement range of the accelerometer through changing the location of accelerometer. The methods of EMD and HHT, as well as FFT, was adopted to achieve the response spectrum of track structure, and the analysis results were compared. Figure 10. Comparison of marginal frequency spectrum in Z direction of Taiwan Ballast Railway section and laboratory Analysis Results of Decomposition Mode of EMD The original vibration acceleration time-curve got in simulation experiment is shown in Figure 11. Because the vibration mode contained in the figure is rather complicated and not single, we can t find out directly the real vibration signals of the track structure from the diagram. If the signals can t be decomposed effectively to restore the real original appearance of track structure, we will not judge from the follow-up analysis of the results. Spectrum, we can see the frequency difference between two sets of tests, one is the vertical (Z) self-vibration frequency of the no damaged structural and another is in the laboratory simulation test with the Taiwan Railway ballast segment Proving Ground. 4.2 Analysis of Simulation Experiment Data with Ballast Hollowed In the experiment, with the approach of excavating widely about two meters beneath the ballast track system and simulating the situation of ballast scouring, the selfvibration frequency difference of track structure s vertical direction (Z) was discussed from the circumstances of changing uprightness to supporting. In the same time, Figure 11. Duration curve of original vibration acceleration.

8 274 Huan-Hsuan Ho et al. Therefore, in the analysis process, the original signals were decomposed into a finite number of modeling functions of IMFs in which one component was the mode of rail vibration with the method of EMD, coupled with the spectrum analysis with HHT, to obtain the energy spectrum diagram of HHT and the marginal spectrum map and compare them. The following points are the raw data for each of the EMD signal decomposition results, as shown in Figures 12~ Analysis Results of HHT After decomposing the track s original vibration acceleration signals in the way of EMD and obtaining the Figure 12. IMFs-D02Z1 (the first point). Figure 14. IMFs-D23Z3 (the third point). main components of vibration mode, we converted the data of vibration time to frequency domain by HHT and got the rail s HHT frequency spectrum graph of energy and the marginal spectrum graph, then we could judge the change of frequency and the position of ballast scouring in track structure from the time took by a block vibration. The results of the analysis are laid according to the location of accelerometers were as follows: Analysis results of measurement with accelerometer located in orbit l Analysis results of the first point The first point is located in the excavation area, the Figure 13. IMFs-D30Z (the first point with heavy trucks). Figure 15. IMFs-D24Z (the fifth point).

9 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform 275 different, resulting in the different stiffness of two sections of track structure as a whole, so the real-time frequency range presented a sharp decline in the trend. Figure 18 shows the results of the marginal frequency spectrum graph.from the Figure we can see the frequency peak of its accumulated energy in the hollowed out section frequency range of 300~600 Hz is 400 Hz,while in the standard segment with frequency range of 500~800 Hz is 700 Hz. In the two segments, the peak frequency is from high frequency to low frequency, obviously, resulting from the different supporting conditions of vertical direction, this phenomenon shows the same trend obtained in Figure 17. l results of spectral analysis is shown in Figure 17~18. As is shown in Figure 17, the complete vibrating time, namely, the HHT energy frequency spectrum graph, from the graph we can see the vibration frequency of standard section ranges between 500~800 Hz and the vibration frequency of hollowed out section ranges between 300~600 Hz. The difference shows that the intensity of the spectrum caused when the first locomotive passed the digging Space Department was larger, which lasted about t = 1.5 s to 2.5 s. The reason for the situation above is that the supporting conditions of the vertical direction (Z) of the standard section and hollowed out section are Analysis results of the third point The third point was laid on the rail 4.1 m away from the excavation area, the results of spectral analysis were shown in Figures Figure 19 was the full duration of the HHT vibrating energy frequency spectrum graph, because the third point was about 4.1 m away from the hollowed area, the time range during which spectrum intensity was larger was divided into two sections, namely, t = 2.4 s-2.6 s (range in the hollowed area ) and t = 3 s3.2 s (above measured point). The frequency of measurement point was about 550 Hz and dropped sharply to about 450 Hz in the hollowed area, which showed that accelerometer was within the range of effective measurement. From Figure 20 (Marginal spectrum graph), we Figure 17. Energy spectrogram (the first point). Figure 18. Marginal spectrogram (the first point). Figure 16. IMFs-D45Z (measured on the locomotive).

10 276 Huan-Hsuan Ho et al. Figure 19. Energy spectrogram (the third point). Figure 20. Marginal spectrogram (the third point). could know exactly the change of the frequency of measured point and that the two frequency peaks of higher frequency spectrum intensity were just at 550 Hz and 450 Hz Analysis results of measurement with accelerometer laid on the locomotive head When measurement point was laid on the locomotive head, for the vibration signal of track structure was transmitted through the track rails, wheels, shock absorbers and then to the accelerometer on the head of locomotive, the vibration mode contained in the signal was rather complex (for example, the vibration of locomotive engine, shock absorbers and other various components). But, with signal decomposed by EMD, we can still obtain the IMF component containing the main mode of rail vibration, and then find out the main frequency range of rail by HHT analysis. The changes of frequency during the whole process were shown in the Figure 21, namely, HHT energy spectrum graph. It was clear to see the spectrum intensity was large in the whole duration, which was maybe caused by the steel wheels contacting with rail due to directly affected by the force. During the interval t = 4 s to 4.7 s, the frequency had a sharp decline in the trend and dropped about 400 Hz. With the known speed of about 20 km/h and the distance, about 21 m, from the starting position to the hollowed area, we could estimate the time of arriving at the hollowed area is about 3.78 seconds, calculated as follows: Speed of car per second V 1000/3600 (m/s); time of passing track T = (L + a)/s (s); accelerometer recorded 5000 data per second, so every 5000 points, namely, one second. There were 5000T points in T seconds. Therefore, it was confirmed that the time points estimated approached those on which frequency dropped sharply in the frequency spectrum graph. Figure 22 showed that the natural vibration frequency lasted from the original 700 Hz down to 400 Hz in the whole vibration time of the measuring point. The reasons for error were summarized as: (1) the error caused by human factors; (2) speed control error. Therefore, avoiding the reasons that cause error will be able to effectively achieve the effect of damage location The Analyzing and Comparing Results of FFT In order to compare the differences of results obtained from the HHT and FFT analysis methods, so the data of point one, three, and measurement point on locomotive

11 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform 277 head was analyzed by FFT, the results of the analysis were shown in Figures 23, 25, 27. By analyzing the frequency spectrum of FFT, we can know the frequency, under the disturbing of vibrating source, corresponding to its max vibration amplitude was the main frequency inspired by the measured component. Compared with the frequency spectrum of non-logarithmic HHT, as were shown in Figures 24, 26, 28, the analysis results of the main frequency range inspired by rail were the same, the frequency range at point 1 is about 700 Hz, the frequency range at point 3 is about 500~600 Hz and the frequency range at the measuring point above locomotive is about 700 Hz. Figure 21. HHT energy spectrogram (measured on the locomotive). Figure 22. Marginal spectrogram (measured on the locomotive) Figure 23. FFT energy spectrogram (the first point). Figure 24. HHT energy spectrogram (the first point). Figure 25. FFT energy spectrogram (the third point). Figure 26. HHT energy spectrogram (the third point).

12 278 Huan-Hsuan Ho et al. Figure 27. FFT energy spectrogram (measured on the locomotive). Figure 28. HHT energy spectrogram (measured on the locomotive). In fact, by comparing the energy spectrum graphs of HHT in Figures 17, 19, 21, we learned that the response spectrums of the above-mentioned measurement points were non-steady state response, their response spectrums distributed separately, and the frequency would drop when the structure of the track was damaged. Therefore, we could determine whether the vibration response was steady-state or not by HHT spectrum; if the steady-state response, the Hilbert spectrum response was concentrated; if the non-steady-state response, the Hilbert spectrum response was scattered. The frequency obtained from FFT spectral diagram was the average natural frequency which just got nothing to do with time, so that the real damage position of the track couldn t be known effectively. However, the real-time frequency and energy calibration changing with time could be obtained through the analysis of HHT, as was shown in former section. We could judge the time-scale location of damage points by the changes of real-time frequency and energy, and then calculate the damage location of orbit by the known speed and the starting position of vehicles. It can be seen, HHT is indeed one analytical method with rather advantages. 5. Conclusions and Suggestions The results of the study can be summed up as the following conclusions and suggestions: (1) The analysis results of the experiment showed that the self-vibration frequency range in vertical (Z) of the rail undamaged is about 720 Hz, while that of the rail damaged is about 680 Hz. These results indicate that, due to the damage of the rail structure, the stiffness of original structure is weakened, which cause self-vibration frequency to drop significantly from 720 Hz down to 680 Hz and produce energy dissipating. Test results also confirm that the difference of the vibration frequency in vertical direction (Z) of rail structure undamaged or damaged can be obtained obviously by the application of EMD and HHT. (2) From the results of simulation experiment of ballast hollowing, we can understand exactly the wave propagation distance of orbital vibration. When the speed is about 25~30 km/hr, the measuring scale of the accelerometer is 4 m approximately and the total effective measuring scale is within about 8 m, the vibration energy caused by locomotive head dissipated in just a few seconds due to the high strength of track system, so the measuring range is limited. Therefore, as for the test of track vibration, it is not economical to set a group of accelerometers at intervals of 8 m. (3) According to the analysis results of data measured on the locomotive head, we can see EMD can decompose the complex vibration signals, the trend of rail s real-time frequency throughout the duration and the energy changes of various real-time frequency can be clearly presented by HHT frequency spectrum graph. The damage location of track structure can be judged by the time point on which frequency declines and the speed, achieving the effect of damage location effectively. (4) By comparing the analysis results of HHT and FFT, we can only obtain the average natural frequency

13 Rail Structure Analysis by Empirical Mode Decomposition and Hilbert Huang Transform 279 which has nothing to do with time by FFT, so we can t estimate the real damage position of the track structure. However, we can get the real-time frequency and energy calibration changing with time by HHT, and estimate the real damage position of the track structure. On the whole, EMD and HHT are indeed two signal analysis methods with advantages. (5) To improve the comparison basis of the vibration detection in the future, it is suggested that, aiming at 60 kg road section in high-speed rail track structure, the vibration behavior be understood by vehicles with different weight. (6) For HHT has the feature of simplicity and rapidity and the advantage of damage location, we suggest that in the future studies, HHT track vibration detection technology can be used as comprehensive vibration testing by trying installing accelerometers on rail inspection car. As the detection vehicle of track can only detect the condition that the track is not integrated outside it, the damage inside can t be detected, so ultrasonic flaw detector vehicle is added to detect internal rail flaws. But it will cost so much to inspect the whole line with ultrasonic flaw detector vehicle. Therefore, in the future studies, it will improve the whole line track inspection work if the advantage of damage location of the HHT vibration-analyzing method can be combined with the track geometry data, ultrasonic detection deformation data and other data. References [1] Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C. and Liu H. H., The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis, Proc. R. Soc. Lond. A, Vol. 454, pp (1998). [2] Huang, N. E., Wu, M. C., Long, S. R., Shen, S. S. P., Qu, W., Gloersen, P. and Fan, K. L., A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis, Proc. R. Soc. Lond. A, Vol. 4549, pp (2003). [3] Dazin, P. G., Nonlinear Systems, Cambridge University Press, Cambridge (1992). [4] Chang, D. T.-T., Safety Inspection and Construction Reinforcement Quality Control and Inspection Technology Research of High-speed Railway Prestressed Concrete Bridge, Plan Case Report Commissioned by High-speed Rail Bureau of Transportation Ministry (2004). [5] Chen, P.-L., Chang, D. T.-T. and Chen, M.-X., HHT Vibration Analytical Method Applied to the Track Fastening Research, Advanced Engineering Journal, Vol. 3, pp (2008). [6] Chen, X., Rail Vehicle Noise Measurement Analysis and Improvement - Series 1: Wheel-rail, Sleepers, GRC Wall Resonance Frequency Measurement and Analysis, Measuring Information, Vol. 101, pp (2005). Manuscript Received: Nov. 27, 2009 Accepted: May 6, 2010