978-1-4799-0036-7/13/$31.00 ©2013 IEEE 345 36th Int. Spring Seminar on Electronics Technology

Inertial Measurement System for Evaluation of the Bogie–Railway System Dynamics

Emil Iontchev1), Radostin Kenov2), Rossen Miletiev2) 1) Higher School of Transport “T. Kableshkov”, Sofia, Bulgaria

2) Technical University of Sofia, Faculty of Telecommunication, Sofia, Bulgaria

Abstract: The paper discusses the application of the electronic measurement system based on MEMS inertial sensors and GPS receiver which is capable to measure and record the dynamic parameters of the interaction of the bogie-railway system. The inertial data are combined with the GPS navigation data by Kalman filter to establish the tram bogie rotation angles. The derailed probability is calculated for all railway places on the basis of the frequency analysis.

1. INTRODUCTION

The derailment of the railway vehicles is caused by the loss of the lateral guidance at the wheel and rail interface. There are several criteria for discovering of the derailment reasons. The base of the most of the proposed criteria is the Nadal criteria which defines the relationship between vertical (V) and lateral (L) forces [1].

The second group of derailment reasons is directed to the gauge widening due to the great lateral forces which may be generated by the bogie suspension failures, irregular shape of the wheels or/and rails. These forces may even turn upside down the rail. The proposed criteria are also based on the relation L/V which has not to exceed the limitation.

The third reason is caused by the displacement of the track under the influence of the great lateral forces generated by the vehicle and insufficient lateral strength and railway stiffness. The other derailment reason is caused by the huge dynamic lateral displacement of the wheelset. That circumstance causes a harmonic vehicle movement across the railway center line with specific frequency and length. The oscillation vehicle movement is also provoked by the rail asymmetry even when the vehicle moves at a straight line. These oscillations attenuate due to the conical wheel shape only if their frequency is under the critical frequency. The relation between the

critical frequency, the vehicle speed, the railway and the vehicle geometry is given at [2].

The current paper proposed a method for discovering of the vehicle hunting oscillation based on the determination of the wheelset or bogie spin angle around the vertical axis and the frequency analysis of the of corresponding signal and inertial data of the interaction bogie–rail.

2. MEASUREMENT SYSTEM DESCRIPTION AND SIGNAL PROCESSING

The MEMS based inertial system is built to measure the linear accelerations and to calculate the dynamic characteristics especially the rotation angle of the bogie. The system is recognized as 9 DoF (Degrees of Freedom) and it is based on 3D linear accelerometer, 3D digital gyroscope and 3D digital magnetometer. The localization of the vehicle is obtained by build-in GPS receiver with a refresh rate up to 10 Hz.

The system reads the inertial and magnetic data 240 times per second and stores the navigation and inertial data in the internal FLASH memory (SD card) with a capacity up to 4 GB. The navigation data are transmitted also to the remote server via GPRS connection.

Block diagram of the system and the installation place are shown at Figure 1.

978-1-4799-0036-7/13/$31.00 ©2013 IEEE 346 36th Int. Spring Seminar on Electronics Technology

SDcard

US

AR

T 1

SPI 1

SP

I 2

IMU system

Powersupply

+3,3 V

+3

,8 V

+ V

5

US

AR

T 2

μC

GPSreceiver

GSM/GPRS modem

Xmagn

Xgyro

Ygyro

Zgyro

Ym

agnY

accl

Zaccl

Zm

agn

Z

Y

XXaccl

Fig. 1. The measurement system and its orientation relative to the vehicle axes.

The rotation angle of the bogie is calculated by the signal processing of the stored data according to the algorithm shown at Figure 2.

XacclYacclZaccl

Xgyro KalmanfilterLPF

LPFKalman

filter

XmagnRoll Pitch Results

Yaw

PSD Plot

Ygyro

Ymagn

Zgyro

Zmagn

GPS data

SD card

Fig. 2. Data processing algorithm.

The inertial data are filtered to remove high frequency noise and the bias offset and are fed into Kalman filter to calculate the bogie pitch and roll angle. These rotation angles are used by the magnetometer Kalman filter to establish the yaw angle (heading) according to equations [3]:

ndeclinatio

H

H

magnmagnH

magnmagnmagnH

M

Yarctg

ZYY

ZYXX

0

0

sincos

sincossinsincos

(1)

where rollpitch , (Figure 3).

Pitch

Roll

X

Y

Horizontal plane

Fig. 3. Definition of bogie pitch and roll angles.

The declination angle for Sofia (Bulgaria) is equal to +422 [4]. The 3D magnetometer is also preliminary calibrated towards soft-iron and iron-iron effects according to the algorithm described at [5].

The data processing algorithm is based on dual two-states Kalman filters which algorithms are shown at Figure 4

The second Kalman filter integrates the GPS and inertial data. The Kalman filter updates its state on the bases of the shown steps [6]:

Prediction of the state at time step k

and the corensponding covariance

Correction of the state at time step k

and the corensponding covariance

Measurementsat time step k

Previousat time step k-1

state

Fig. 4. Kalman filter algorithm.

The output signal is processed in time and frequency domain by short-time Fourier transform (STFT) [7] and wavelet analysis [8]. The wavelet analysis is preferred due to its better frequency and time resolution. The transformation coefficients are calculated according to the equation [9]:

dttxa

btabaW x

2

1

, (2)

The wavelet transformation uses a wavelet

function

a

bt as a base and variables а (scale) and

b (position). The wavelet functions may be considered as windows, which parameters depend on the signal. The time-frequency resolution of the windows is estimated by the equation [10]:

4

1t (3)

978-1-4799-0036-7/13/$31.00 ©2013 IEEE 347 36th Int. Spring Seminar on Electronics Technology

The choice of the wavelet function specifies the approach to this boundary. This task could not be solved in a simple way and there are lots of methods to solve it. One of the possible ways is described at [11].

The output signal is processed on the bases of the wavelet packets which use the similar signal decomposition as a fast wavelet transform, but the details are decomposed to two parts. In this way we obtain a complete binary tree and deeper analysis may be accomplished. The level decomposition choice is based on the signal parameters or other specific criteria such as entropy of the calculated coefficients [12].

3. EXPERIMENTATION AND DATA ANALYSIS

The measurement system and signal processing algorithms are tested in a real world. The system is installed on tram without passengers. The tram test route is shown at Figure 5. The test route was crossed only one time because of the some limitations.

Fig. 5. Tram route graph.

The experimental data are recorded on SD card and are processed by MATLAB routine. The critical frequency of each point is calculated on the basis of GPS data, parameters of railway and tram according to equation at [2]. The results are shown at Figure 6.

0 180 360 540 720 900 1080 1260 1440 1620 18000

0.5

1

1.5

2

2.5

3A critical frequency

Time [s]

Fre

quen

cy [

Hz]

Fig. 6. Evaluated frequency.

The derailment is caused by the low frequency harmonics, therefore the cut-off frequency for the low pass filters are set to 20 Hz for the gyroscope and magnetometer data while for the accelerometer data cut-off frequency is set to 1 Hz.

0 180 360 540 720 900 1080 1260 1440 1620 1800-30

-20

-10

0

10

20

30Yaw angle

Time [s]

Ang

le

Fig. 7. Yaw angle (heading).

The rotation angle of the bogie is calculated using the algorithm described at Figure 2. The results are shown at Figure 7. We may define five rotation angle peaks, which are caused by the collisions between the wheels and rails.

The frequency analysis results are shown at Figure 8 and Figure 9. The results from Figure 8 are obtained on the basis of STFT and Hamming window with frequency resolution of 1 Hz and overlap equal to 50 %. The previously defined five places with high amplitudes of oscillation are well seen, but their frequencies are below the critical frequency value.

978-1-4799-0036-7/13/$31.00 ©2013 IEEE 348 36th Int. Spring Seminar on Electronics Technology

Fig. 8. PSD of yaw angle.

The similar results are obtained by the wavelet analysis. The signal is decomposed to sixth level with db3 wavelet function.

Power spectral density

Fre

quen

cy [

Hz]

Time [s]

0 180 360 540 720 900 1080 1260 1440 1620 1800

8

6

4

2

20 40 60 80 100 120

Fig. 9. PSD of yaw angle.

The previously defined places with high amplitudes of oscillation are also well seen but the better frequency resolution of the wavelet function indicates a frequency in the frequency range of the critical frequencies (4 Hz). Its amplitude is significantly smaller than the others but its value is higher than the critical frequency level defined by the Figure 6 plot. This defines this point as a potential dangerous place if the local speed is much higher rather than the test speed.

4. CONCLUSION

The current paper discusses the MEMS based inertial measurement system with 9 degrees of freedom which is capable to store and calculates the bogie-railway system dynamics. It is shown that the analysis in the time and frequency domain of the rotation angle of the bogie may be used as a diagnostic parameter for the derailment ability of the railway vehicles.

ACKNOWLEDGEMENT

The paper is published with the support of the project BG051PO001-3.3.06-0043 “Increasing, Improving and Extending the Scientific Potential of the University in Transport by Support to Development of PhD Students, Postdocs, Trainees and Young Researchers in the Field of Transport, Power Engineering and ICT in Transport” within the Human Resources Development Operational Programme co-funded by the European Social Fund of the European Union.

REFERENCES

[1] Iwnicki Simon, “Handbook of Railway Vehicle Dynamics”, Taylor &Francis Group, 2006, Chapter VIII.

[2] Michael DeLorenzo, “NUCARS Modeling of a Freight Locomotive with Steerable Trucks”, Blacksburg, Virginia Polytechnic Institute and State University, May 20, 1997, pp 12.

[3] Valenti Chris, “AN996, Designing a Digital Compass Using the PIC18F2520 microcontroller”, Microchip Technology Inc., 2005.

[4] http://magnetic-declination.com/.

[5] Thomas Stork, “AN00022 - Electronic Compass Design using KMZ51 and KMZ52”, Philips Semiconductors, 2000.

[6] Welch Greg, Gary Bishop, “An Introduction to the Kalman Filter, TR 95-041”, Department of Computer Science University of North Carolina at Chapel Hill, NC 27599-3175, April 5, 2004.

[7] S. Lawrence Marple, Jr., “Digital Spectral Analysis with applications”, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

[8] Misiti Michel, Misiti Yves, Oppenheim Georges, Poggi Jean-Michel, “Wavelet Toolbox™ 4, User’s Guide”, The MathWorks, Inc., 1997-2009.

[9] Mallat Stephane, “A wavelet tour of signal processing, Second Edition”, Academic Press, 1999.

[10] Rioul Oliver, Vetterli Martin, “Wavelets and signal processing”, IEEE SP Magazine, October, 1991.

[11] Iontchev Emil, “А choice of a wavelet for the noise reduction of the signals from inertial sensors”, Mechanics, Transport, Communications, Volume 2, 2011, pp. 5.1-5.9.

[12] Sang Yan-Fang, Wang Dong, Wu Ji-Chun, “Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising”, Entropy 2010, 12, pp.1499-1513.