ieeepro techno solutions 2013 ieee embedded project study of the track–train continuous...

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1

Study of the Track–Train Continuous InformationTransmission Process in a High-Speed Railway

Linhai Zhao, Baigen Cai, Senior Member, IEEE, Junjie Xu, and Yikui Ran

Abstract—In the experiments and practical applications in ahigh-speed railway, it is observed that the carrier frequency ofthe sampled signal in a track circuit reader (TCR) is changedwith train speed and goes beyond the upper permissive rangeprescribed for a jointless track circuit (JTC) in some cases. Thiscan directly affect the availability of train target speed in traincontrol systems and thus has an effect on the generation of thedistance-to-go profile. It not only reduces the safety and efficiencyof train traveling but also limits the improvement of train speed.To find the primary cause of the deviation in carrier frequencyof the sampled signal in TCR (CFSST), this paper models thetrack-to-train continuous information transmission process usingthe transmission line theory based on the structures and principlesof JTC and TCR. Then, the relation between the deviation inCFSST and the train speed is derived. Experimental results inhigh-speed railway have verified the correctness of the analysis,and the study can provides a strong theoretical basis for improvingthe safety level of railway traffic. Moreover, it can be a goodreference for other countries where the similar track circuits areapplied.

Index Terms—High-speed railway, jointless track circuit (JTC),track circuit reader (TCR), track–train continuous informationtransmission (TTCIT), traffic control, transmission line theory.

I. INTRODUCTION

A T PRESENT, train control systems are widely used inrailways for the safety of train operation all over the

world, and these control systems are almost the same in aspectsof the structure and the system function. Fig. 1 shows theChina Train Control System (CTCS) [1], which is the dominantequipment for train speed supervision and train protection,particularly in the booming high-speed railway in China.

In CTCS, the distance-to-go profile formed in the systemis critical for ensuring train safety during the operation. Theprofile is used for performing the task of train running speed su-pervision, and some specific measures can be taken to prevent a

Manuscript received October 17, 2012; revised March 24, 2013; acceptedJuly 10, 2013. This work was supported by the China Ministry of Railwayproject: The research of basic theory of high-speed railway—Research onbasic theory of reliable transmission information of track circuit and balisein high-speed railway (2011X021-C). The Associate Editor for this paper wasB. De Schutter.

L. Zhao is with the School of Electronic and Information Engineering, Bei-jing Jiaotong University, Beijing 100044, China (e-mail: [email protected]).

B. Cai is with the Scientific and Technical Department, Beijing JiaotongUniversity, Beijing 100044, China (e-mail: [email protected]).

J. Xu is with Xiamen Tobacco Industrial Co., Ltd., Xiamen 361022, China(e-mail: [email protected]).

Y. Ran is with Zhejiang Insigma Supcon Information Technology Co., Ltd.,Zhejiang 310051, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITS.2013.2274617

Fig. 1. Structure and principle diagram of the TTCIT system.

traffic accident when the train is going too fast according to thecurve. The target speed of the train is essential for generatingthe profile, and the process of obtaining the speed in the CTCScomputer is shown in Fig. 1. When the track circuit is idle, thetrack circuit signal coded with train target speed is generatedby the transmitter and then flows into the receiver through thetransmission cable, the tuning, the compensation capacitor C,and the rails. However, the first axle and wheels short-circuitthe track circuit signal when a train enters the track section,and the induced voltage can be produced in the antennas ofthe track circuit reader (TCR) on-board by the electromagneticinduction between the short-circuit current and the antennas.Then, the target speed can be extracted in TCR by analog-to-digital (A/D) sampling, signal demodulation, and decoding.Furthermore, the speed can be input to the CTCS computer. Ingeneral, the information transmission from the transmitter ofthe track circuit to the TCR is defined as track–train continuousinformation transmission (TTCIT), and the process is calledthe TTCIT process (TTCITP) accordingly. For track circuit,the signal applied is kind of frequency-shift keying (FSK) withcontinuous phase, which can be [2]

Ufs(t) = Afs cos

(2πfct+ 2πΔfp

∫sm(t)dt+ φfs

)(1)

where Afs is the amplitude of the track circuit signal and withinconstant bounds for a specific track circuit; fc, Δfp, and φfs

are the carrier frequency, frequency offset, and the initial phaseof the signal, respectively. sm(t) is a 50% duty cycle square-wave modulated signal with a modulated frequency fd, whichcorresponds to a specific train target speed. Fig. 2 graphicallyshows the track circuit signal and its spectrum, which explic-itly illustrates that the spectrum is one discrete spectrum thatspreads out symmetrically in the frequency domain, with fc asthe frequency center and fd as the frequency interval.

Fig. 3 shows the carrier frequencies fc and modulated lowfrequencies fd in different track sections for the minimum trainheadway. As for the following train 2, the CTCS computercan determine that there are at least eight free blocks ahead,according to the modulated low frequency of 21.3 Hz in this

1524-9050 © 2013 IEEE

mailto: [email protected]





2 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS

Fig. 2. Schematic diagram of JTC signal and its spectrum. (a) Schematic dia-gram of JTC signal. (b) Schematic diagram of the spectrum of the signal in (a).

section, getting from TCR. That is, the target speed at the exitpoint A of the eighth block is 0.

However, an undetected phenomenon is observed in the high-speed railway operation tests; that is, the final signal obtainedin the TTCITP (CFSST) changes with train speed. Fig. 4 showsthe deviations in CFSST from the nominal values, using thedata collected from a through express from Beijing to Tianjinin the Jing-Jin intercity high-speed railway.

It can be seen that the deviation in the carrier frequencybecomes greater with the increase of train speed in train acceler-ation phase while leaving the departure station. When the trainreaches the ceiling speed of 350 km/h and runs in the constant-speed cruise phase, the deviation in carrier frequency reachesthe maximum and remains unchanged. In the decelerationphase that train arrives at the target station ahead, the deviationin carrier frequency decreases due to the decline of the trainspeed, and no deviation is introduced when train stops.

It should be noted that the deviation in the carrier frequencyof the sampling signal has a bearing on the train safety. Themost used method for the track circuit signal demodulationin TCR currently is the combination of the double-detuningfrequency discrimination method in the domain and the spectralline analysis method in the frequency domain [3]. The formeruses two filters with different center frequencies, namely, theupper side frequency (fc +Δfp) and the lower side frequency(fc −Δfp) of track circuit signal, to divide the FSK signalinto two components for obtaining the modulated frequency.To the end, the latter makes use of the characteristics that thefrequency difference in the spectrum between the two spectrallines of the carrier frequency and of the first side frequencyis the modulated frequency. However, the deviation in carrierfrequency causes the real signal to deviate from the centralfrequency bands of the filters and also leads to spectral linelocation problems due to a right shift in the spectrum for thetwo methods respectively, affecting the result of modulatedfrequency extraction.

At present, the permissive deviation range of the carrier fre-quency of the track circuit for TCR demodulation is [−0.15 Hz,0.15 Hz]. To obtain the real-time demodulation, TCR canmerely reach the best resolution of 0.1 Hz for carrier frequencycalculation. In addition, the permissive deviation range is[−0.2 Hz, 0.2 Hz] in practice. As shown in Fig. 4, the maximum

Fig. 3. Carrier frequencies and modulated low frequencies in different tracksections for the minimum train headway and the profile in different conditions.

Fig. 4. Deviation of carrier frequencies of SST in the Jing-Jin intercity high-speed railway.

deviation is about 0.15 Hz when the train runs through a normaltrack circuit with a high speed of 350 km/h. Furthermore, ifa positive frequency deviation presents in the output signal ofthe transmitter, the deviation in CFSST is very likely to go outof the permissive range. Thus, the modulated low frequencycannot be extracted to the CTCS computer according to the“fault-safety” principle and can shorten the stop target distance,and the normal braking is taken, as shown in Fig. 3, that thedistance is changed from A to B for the following train 2. Thiscannot only reduce the safety and efficiency but also lowerpassenger’s ride comfort. Therefore, it is necessary to study theprincipal causes for the deviation in frequency to ensure trainsafety and enhance the development of high-speed railway.

Since the phenomenon is hardly found and only becomesprominent relatively when the train runs at high speed, norelevant researches have been done presently. Although it canbe seen that it is associated with train speed apparently, itneeds to deeply study the TTCITP to analyze this phenomenoncomprehensively. At present, the TTCITP is not taken as awhole for study and is divided into two parts, namely, thetransmission process of track circuit signal and the receivingand demodulating process of the induced voltage in TCR. Withrespect to a jointless track circuit (JTC), the track resistance andadjacent track interference were modeled using a finite-elementmethod [4], [5]. On this basis, Nleva [6] has done the researchon the design and simulation of the JTC model. Nedelchev [7]proposed a mathematical model for JTC using a transmissionline, and the maximum length of the JTC was found based onthe model. In addition, the transmission line theory was appliedfor the modeling of the center-fed boundless track circuit in [8].The amplitude of the short-circuit current of track circuit wasused for fault diagnosis of capacitors in track circuits in [9] and[10] based on the model of track circuit using the transmissionline theory. In addition, Chen and Chen [11] proposed a methodfor calculating distributive parameters of track circuit usinga semidiagonal matrix of finite elements. Furthermore, Zhaoand Zhang [12] applied a boundary condition analysis methodto the digitalized simulation of track circuit. However, themain efforts of these studies are dedicated to the modeling ofthe track circuit and/or the transmission interference analysis,


ZHAO et al.: STUDY OF THE TTCITP IN HIGH-SPEED RAILWAY 3

Fig. 5. Model of TTCITP based on transmission line and electromagneticinduction theories.

which are all based on the static model without considerationfor the train dynamic process.

As for TCR, Su et al. [13] studied the static model of theelectromagnetic induction process between the short-circuitcurrent of JTC and the induced voltage in TCR. The model wasbuilt on the assumption that the magnetic field distribution ofthe track circuit is generated by the constant-current circuit withinfinite length. This is inconsistent with real operating condi-tions, physical structures, or information transmission processof JTC and TCR, and the results need a further verification inuse. The study on the complete theoretical dynamic model ofsignal reception process for TCR at train running state is stilllacking.

In a word, no models of the TTCITP have been built in theseworks and that is why the deviation in carrier frequency that isgenerated cannot be explained in a theoretical perspective. Tosolve the problem, this paper models the TTCITP based on thetransmission line. The relation between the deviation in carrierfrequency and the train speed can be expressed mathematicallyusing the model and experimental results in high-speed railwaythat have verified the correctness of the analysis. The study canprovide a theoretical support for improving railway traffic speedand the optimization of the existing signal decoding algorithmin TCR. Moreover, it can be a good reference for other countrieswhere the similar track circuits are applied.

This paper is organized as follows: Section II models theTTCITP in detail. Then, the analysis of the influence on thesampled signal in TCR (SST) is conducted based on the modelin Section III. Section IV is the experimental results. Section Vis the discussion followed by the conclusions in Section VI.

II. MODEL OF TTCITP

The TTCITP can be modeled using the transmission line andelectromagnetic induction theories based on its basic transmis-sion principle. The model is shown in Fig. 5, which includesfour parts: the rail short-circuit current, the induced voltage inTCR antennas, the voltage in the TCR transmission cable, andthe sampling voltage in the TCR host computer [14].

1) Model of the Rail Short-Circuit Current: According tothe transmission line theory, the short-circuit current �Isc(x)shown in Fig. 4 can be expressed as

�Isc(x) = �Ufs

/[�Nsf11(x)Rf + �Nsf12(x)

](2)

where �Ufs is the phasor representation of Ufs(t) in (1). Rf isthe equivalent shunt resistance of train. �Nsf11(x) and �Nsf12(x)are the characteristic parameters of the equivalent four-terminalnetwork (EFTN) �Nsf (x) from the transmitter of the trackcircuit to the train shunting point x. Here, the EFTN �Nsf (x)satisfies

�Nsf (x)=

[�Nsf11(x) �Nsf12(x)�Nsf21(x) �Nsf22(x)

]= �Np× �Nb× �Ng(x) (3)

where �Np and �Nb are the EFTN of the cable and tuning inthe sending end, respectively, and �Ng(x) is the EFTN of therails from the tuning in the sending end to the shunting point x.Suppose that a track circuit with rail length lg between the twotunings at both ends has M compensation capacitors. Accord-ing to the requirement that all capacitors should be uniformlyspaced in the track circuit [15], the interval of neighboringcapacitors lT can be given by

lT = lg/M. (4)

In this paper, a capacitor and the rails with the length of halfthe distance between the adjacent capacitors (lT ) on its bothsides are treated as a basic compensation unit [12], and thus, xcan be expressed as

x = m · lT + ly (5)

where m denotes the number of complete compensation unit,and ly denotes the remaining part which cannot constitute acompensation unit in the rails of length x. Therefore, �Ng(x)can be given by

�Ng(x) = ( �Nt)m × �Ny(ly). (6)

Here, �Nt and �Ny(ly) are the EFTN of the compensation unitand the remaining part ly , respectively. That is

�Nt =

[�Nt11

�Nt12�Nt21

�Nt22

]= �Ngg(lT /2)× �Ncp × �Ngg(lT /2) (7)

�Ny(ly) =

⎧⎨⎩

�Ngg(ly), 0 � ly < lT /2�Ngg(lT /2)× �Ncp

× �Ngg(ly − lT /2), lT /2 � ly < lT

(8)

where �Ncp and �Ngg(lT /2) are the EFTN of the capacitor andthe rails of length lT /2 [2], respectively. That is

�Ncp=

[1 0

1/�Zcp 1

](9)

�Ngg(lT /2)=

[cosh(�γg ·lT /2) �Zg sinh(�γg ·lT /2)

sinh(�γg ·lT /2)/�Zg cosh(�γg ·lT /2)

]. (10)

Here, �Zcp is the impedance of the capacitor. �Zg and �γg arethe characteristic impedance and propagation constant of therail, respectively, and both are dependent on the rail impedance�Zd and the ballast resistance of track circuit rd [2]. That is

�Zg =

√�Zdrd, �γg =

√�Zd/rd. (11)



Using (1) and (2), �Isc(x) at the shunting point x can bedenoted by Isc(x, t) in the time domain, i.e.,

Isc(x, t)=Asc(x) cos

(2πfct+ 2πΔfp

∫sm(t)dt+φsc(x)

)(12)

where the amplitude Asc(x) and the initial phase φsc(x) ofIsc(x, t) can be given as

Asc(x) =Afs

/(∣∣∣ �Nsf11(x)Rf + �Nsf12(x)∣∣∣) (13)

φsc(x) =φfs − arg(�Nsf11(x)Rf + �Nsf12(x)

). (14)

Here, | · | is the complex modulus operator, and arg(·) thephase calculation operator.

2) Model of the Induced Voltage in TCR Antennas: As forthe induction in TCR antennas shown in Fig. 5, the inducedvoltage in TCR antennas �Ucv(x) and the short-circuit current�Isc(x) can approximately satisfy [3], [16]

�Ucv(x) = �Isc(x)× �kjg (15)

where �kjg is the complex constant given by

�kjg = ajg∠φjg. (16)

Here, ajg denotes the modulus of �kjg and φjg the phase. Thevalue of �kjg is related to many factors such as TCR antennacharacteristics, the mounting position of the antennas, and theparameters of track circuit signal. Substituting (12) and (16)into (15), it arrives at

Ucv(x, t) = ajgAsc(x)

· cos(

2πfct+ 2πΔfp

∫sm(t)dt+ φsc(x) + φjg

). (17)

It can be seen in (17) that Ucv(x, t) is approximately linearto Isc(x, t), concerning the amplitude with a scale factor ajg ,however, differing a constant φjg in phase.

3) Model of the TCR Transmission Cable: The EFTN of theTCR transmission cable �Ncs shown in Fig. 5 can be expressedas

�Ncs =

[�Ncs11

�Ncs12�Ncs21

�Ncs22

]. (18)

Here, �Ncs11, �Ncs12, �Ncs21 and �Ncs22 are the parameters of theEFTN of TCR transmission cable, which is mainly dependenton the internal structure and length of the cable. According tothe function design of the TCR device, it allows slight distortionon the signal when transmitting in the cable. According to thetransmission line theory, the relation among the induced voltagein TCR antennas can be expressed as⎧⎨

⎩[�Ucv(x)�Icv(x)

]= �Ncs ×

[�Ucs(x)�Ics(x)

]�Ucv(x) = j2πfc(2Ljg) · �Icv(x)

(19)

where �Ucv(x) is the induced voltage in TCR antennas, and�Icv(x) is the induced current. �Ucs(x) is the output voltage ofthe TCR transmission cable, and �Ics(x) is the output current.Ljg is the inductance of TCR antennas, and fc is the carrierfrequency of �Ucv(x). j is the imaginary unit, and j2 = −1. Itcan be derived from (19) that

�Ucs(x)=

(�Ncs22− �Ncs12/(j4πfcLjg)

�Ncs11× �Ncs22− �Ncs12× �Ncs21

)× �Ucv(x). (20)

Therefore, if acs and φcs denote the amplitude gain and phasechange of the TCR cable, according to (20), it arrives at⎧⎨

⎩acs =

∣∣∣ �Ncs11− �Ncs12/(j4πfcLjg)�Ncs11× �Ncs22− �Ncs12× �Ncs21

∣∣∣φcs = arg

(�Ncs11− �Ncs12/(j4πfcLjg)

�Ncs11× �Ncs22− �Ncs12× �Ncs21

).

(21)

Using (20) and (21), �Ucs(x) in the time domain can berewritten as

Ucs(x, t) = acsajgAsc(x)

· cos(

2πfct+ 2πΔfp

∫sm(t)dt+ φsc(x) + φjg + φcs

).

(22)

4) Model of the Sampled Voltage in the TCR Host Computer:As shown in Fig. 5, the sampled signal Ucy(x(n), n) is thesampled result of the signal Ucs(x, t) in the TCR host computerwith a constant sampling frequency fs. Suppose that x(n) isthe sampled result of x in (5) at the sampled time n/fs (n =1, . . . , N). Here, N is the number of the total sampling pointscollected when the train passes through the track circuit. Then,(22) can be rewritten as

Ucy (x(n), n)

= Acy (x(n)) · cos(

2πfcn

fs+ 2π

Δfpfs

n∑i=1

sm

(i

fs

)

+ φcy (x(n))

), n = 1, . . . , N (23)

Acy (x(n))

= ajgacsAfs

/(∣∣∣ �Nsf11 (x(n))Rf

+ �Nsf12 (x(n))∣∣∣) , n = 1, . . . , N (24)

φcy (x(n))

= φfs + φjg + φcs

− arg(�Nsf11 (x(n))Rf+ �Nsf12 (x(n))

), n=1, . . . , N.

(25)

Here, Acy(x(n)) and φcy(x(n)) are the amplitude envelopeand the initial phase of Ucy(x(n), n) in TCR, respectively. Inaddition, (23) describes the model of the sampling signal in theTCR host computer in the way of the train shunting point.



Fig. 6. Diagrams of the sampling process for SST at speed v1 and 2v1.(a) Diagram of the sampling process for SST at train speed v1. (b) Diagramof the sampling process for SST at train speed 2v1.

III. ANALYSIS OF THE INFLUENCE

ON SST FROM TRAIN SPEED

It shows that train speed has no bearing on the naturalamplitude Acy(x(n)) and the initial phase φcy(x(n)) at anyshunting point x(n) for a specific TCR based on the TTCITPmodel, as described in (23). At any train speed, the amplitudeand the initial phase keep the relations unchanged, as shownin (24) and (25), respectively. To find out the reason for thedeviation in the carrier frequency of the SST when train is atrunning state, therefore, it has to take the sampling data set inTCR obtained from a JTC into account in macroscopic view.

For simplicity, this paper focuses on the case that the trainruns at a constant speed. Therefore, the shunting point x(n) in(23)–(25) can be written as

x(n) = lg − νsn/fs, n = 1, . . . , Nνs = νs1 = νs2 = · · · = νsN . (26)

Since the sampling rate for the SST is constant, the shuntingpoint x(n) corresponding to the sampling time n/fs, n =1, . . . , N depends on train speed, according to (26). Fig. 6shows the sampling process for the SST. Suppose a train runsat speed ν1 through the track section. The sampled data set{Ucy(x(n), n)} can be expressed as

{Ucy (x(n), n)}= {Ucy (x(n), n) |x(1) = x1, x(2) = x2, x(3)=x3,

x(4)=x4, x(5)=x5, . . . ;n=1, 2, 3, . . . , N} . (27)

If the train runs at speed 2ν1 and the first shunting point isthe same, then it has

{Ucy (x(n), n)} = {Ucy (x(n), n) |x(1) = x1, x(2) = x3,x(3) = x5, . . . ;n = 1, 2, 3, . . . , N/2} . (28)

It can be seen in (27), (28), and Fig. 6 that, although thesampling points Ucy(x(n), n), n = 1, . . . , N in the sampleddata set {Ucy(x(n), n)} are collected at constant time interval1/fs, the shunting point x(n) is changed with different trainspeeds. Therefore, the amplitudes Acy(x(n)) and the initialphases φcy(x(n)) of the sampling points collected are changedaccordingly.

As for the impact of train speed on the amplitude, althoughnot the focus of the paper, it can be seen that amplitudeAcy(x(n)) is determined by the shunting point x(n), sinceparameters fs, ajg , acs, and Afs are essentially constant,and Rf with slight fluctuation. Suppose that {Acy(x(n)), n =1, 2, . . . , N} is the amplitude set of the sampled data set{Ucy(x(n), n), n = 1, 2, . . . , N} and {Acy(x)|x ∈ [0, lg]} isthe whole amplitude set of the signal in TCR, the amplitude setof the sampled data set can be considered as the set extractedfrom the set {Acy(x)|x ∈ [0, lg]} at speed νs based on theshunting point. That is

{Acy(lg−nνs/fs)| n = 1, 2, . . . , N}⊆{Acy(x)| x ∈ [0, lg]} .(29)

If the amplitudes of the sampled signal {Acy(x)|x ∈ [0, lg]}at all sampling points meet the requirement of the TCR, thenno effect is made by train speed with respect to the amplituderequirement.

For φcy(x(n)), the conclusions in the Appendix can befurther generalized to the case that the train shunts at arbitrarypoints, which can be written as

φcy (x(n)) = −Im(�γcu)x(n) + (B1 +B2)/2, x(n) ∈ [0, lg](30)

where �γcu is associated with the composite structure of thecompensation unit in JTC and determined mainly by railimpedance, ballast resistance, and compensation capacitor, asshown in (36). Since the ballastless track is applied in high-speed railways, the ballast resistance and rail impedance remainessentially constant, and the component Im(�γcu) can be con-sidered as constant in normal condition. Here, Im(�γcu) > 0. Inconsequence, the initial phase φcy(x(n)) of the sampling signalis approximately proportional to the position of the shuntingpoint x(n). In this paper, the constant speed is considered.Substituting (26) into (28), it becomes

φcy(n, νs) = Im(�γcu)νsn/fs + (B1 +B2)/2 − Im(�γcu)lg,

n = 1, 2 . . . , N ; νs = νs1 = νs2 = · · · = νsN . (31)

Furthermore, substituting (26) and (31) into (23), it becomes

Ucy(n, νs)

= Acy(lg − νsn/fs)

· cos((2πfc + Im(�γcu)νs)

n

fs+ 2π

Δfpfs

n∑i=1

sm

(i

fs

)

+ (B1 +B2)/2 − Im(�γcu)lg

),

n = 1, 2 . . . , N ; νs = νs1 = νs2 = · · · = νsN .

(32)



Fig. 7. Diagram of the experiment plan.

Equation (32) shows the model for the SST when the trainruns at constant speed νs. Here, Acy(lg − νsn/fs) can beexpressed by (24) and (31). That is

Acy(lg − νsn/fs)

= ajgacsAfs

/(∣∣∣ �Nsf11(lg − νsn/fs)Rf

+ �Nsf12(lg − νsn/fs)∣∣∣) , n = 1, . . . , N.

(33)

According to (32) and (1), the relation between the carrierfrequency fcy of SST and the carrier frequency fc of the outputsignal by the JTC transmitter can be written as

fcy = fc + Im(�γcu)νs/2π. (34)

It shows that a positive deviation in CFSST is generated andthe deviation is approximately linear with the train speed underthe condition of the constant speed. This is consistent with thedeviation polarity and the change rule against the train speed,as shown in Fig. 4. In addition, the parameters, such as fd andΔfp, are not affected by train speed, according to (32) and (1).

IV. EXPERIMENTAL VERIFICATION

The on-site experiment in high-speed railway is applied toverify the correctness of the conclusions based on the TTCITPmodel built in this paper, about the influences on the CFSST, themodulated low frequency, the frequency offset, and the ampli-tude of SST from train speed. The diagram of the experimentdesign is shown in Fig. 7, and the parts of the experimentaldevices are shown in Fig. 8.

To verify the relation between the deviation in CFSST andthe train speed presented in this paper, a train runs through aspecific JTC back and forth at different train speeds of 300, 330,350, and 370 km/h. In this way, the discreteness of parametersof the train and rail tracks and the fluctuation of parameters ofthe equipment caused by the long experiment interval can beessentially eliminated. Therefore, main parameters, such as railimpedance, ballast resistance, train shunting resistance, and thevalue of compensation capacitor, are relatively stable due to theconstraints of the experiment, and it can provide the most effec-tive support for guaranteeing a correct analysis of the relation.

In the experiment, parameters of the output signal by thetransmitter of the JTC, such as carrier frequency, modulated lowfrequency, and frequency offset, are measured by a microcom-puter monitoring system on ground. The rail impedance, ballastresistance, and the value of the compensation capacitor can beobtained by the measurement method shown in [17] and [18],

Fig. 8. Parts of experiment devices. (a) Monitor for the transmitter of the JTC.(b) Ballast resistance monitor. (c) JTC parameter measurement. (d) TCR and therecorder.

and the equivalent train shunting resistance is set accordingly.These parameters are used to calculate the theoretical valuesof the deviations using (34) at different train speeds. On theother hand, the TCR recorder on-board stores the samplingsignals during train passing the JTC, and these signals are usedto calculate the real deviation in CFSST. In addition, the tworesults can be compared to obtain the final assessment.

Fig. 9 shows the real output signal by the transmitter (a) andthe real SST collected when the train passed through the JTCat 370 km/h (b). In (c) and (d), the real envelope and phase arecompared with the simulated envelope and phase obtained bythe models proposed in this paper, with the same parametersmeasured, respectively.

As in (c), the assessment shows that the coefficient of de-termination is 0.9868, the root-mean-square error is 0.02135and the sum of squares due to error is 2.083, indicating that(24) is correctly. The initial phase of the signal shown in(c) is extracted by the Hilbert–Huang transform [19] and thetime–frequency analysis method [20]. The slope of the theoret-ical phase is 0.942 and the real slope is 0.958, and the relativeerror is 1.67%. It shows that the phase model proposed in thispaper can well describe the real situation.

The carrier frequency of the output signal given by the micro-computer monitoring system is 2298.70 Hz, the modulated lowfrequency is 21.30 Hz, and the frequency offset is 11 Hz. Thespectral analysis on the signals shows that the carrier frequencyfor the output signal is 2298.70 Hz and 2298.85 Hz for the SST[see Fig. 8(c)].

Deviations in CFSST at different speeds can be obtainedsimilarly. The results and the corresponding linear fitting areshown in Fig. 10.

It shows that the deviation in CFSST is approximatelylinear with train speed. The slope of the fitting in Fig. 10is 0.00116, and Im(�γcu) = 0.00768 rad/m according to (36).Thus, Im(�γcu)/(2π) = 0.00122 rad/m, and the relative error is4.9%. It can be concluded that (34) can very well describe therule of deviation in CTSST when train runs at a constant speed.



Fig. 9. Specific signal and its verification (vs = 370 km/h). (a) Output signal by the transmitter of the JTC. (b) SST obtained when a train passed through theJTC. (c) Amplitude envelopes of signal in (b) and its simulated signal. (d) Initial phases of the real signal in (b) and the simulated signal. (e) Spectra of signals in(a) and (b).

Fig. 10. Deviations of carrier frequency of SST at different train speeds andthe corresponding linear fitting.

Fig. 11. Time–frequency distributions of the signal in Fig. 9(b).

Fig. 8(b) is also used to show the effect by train speed onparameters of the SST, such as the modulated low frequency,the frequency offset, and the amplitude. Fig. 9 shows theupper and lower side frequencies of the SST extracted by thetime–frequency analysis [19]. The corresponding amplitudeenvelope of the SST is shown in Fig. 11.

The frequency offset can be determined by the upper andlower side frequencies based on (1), and the modulated lowfrequency can be obtained by calculating the alternation periodof the upper side frequency and the lower side frequency. The

Fig. 12. Amplitudes of SST at different speeds for the JTC, with train speedof 300 and 370 km/h.

low frequency and the frequency offset of the SST are 21.30and 11 Hz by calculation, which are the same as those of theoutput signal. As for the amplitude, it is shown in Fig. 12 thatthe increase in train speed leads to the amount reduction of datasampled in TCR during train passing the same JTC. However,at the same shunting point, as the point “a” shows in Fig. 12,the natural amplitude of the sampled data corresponding to theshunting point is not changed with train speed, which is also inaccordance with the analysis. It further shows the correctness ofthe analysis based on the TTCITP model proposed in this paper.

V. DISCUSSIONS

It should be noted that the ballastless track is universallyapplied in high-speed railways, and the parameters of the trackcircuit are relatively stable in normal circumstances. As a result,the transmission phase shift of the compensation unit has slightfluctuation in value, and the positive deviation in CFSST can beregarded as essentially proportional to train speed, according to(32). Based on this conclusion, the decoding algorithm in TCRcan be optimized. An alternation bandwidth for the deviation is



added for the double-detuning frequency discrimination and theupper search limit of carrier and side frequencies is increasedaccording to the deviation for the spectral line analysis.

In considering that the train runs at constant speed approx-imately, the paper focuses on train uniform motion state, onthe assumption that JTC is in normal condition. Furthermore,it shows that the deviation will be caused when in the motionstate and also in the condition of the variable speed in a trackcircuit of course. The variable speed case can be consideredas several constant speed phrases, and it is the combination ofdifferent deviations at different constant speeds.

As for faults in JTC, for example, the broken-wire fault in thecapacitor of a compensation unit can change the transmissionstructure of the JTC. It affects the short-circuit current at thesampling point between the faulty capacitor and the receiver[21], and the deviation in CFSST is influenced accordingly.A deviation in CFSST in one track section is out of thepermissive range, and the on-site measurement has shown thatthere is one faulty compensation capacitor in the track circuit. Inaddition, the deviation becomes normal after the maintenance.The analysis on this situation is more complicated, and it needsa further study on the influences by fluctuation of transmissioncharacteristic parameters and faults in railway equipment inhigh-speed condition. This can contribute to the completenessof the TTCITP model.

VI. CONCLUSION

TTCIT consists of JTC and TCR, taking an important rolein the CTCS. The track circuit signal with modulated lowfrequency coded by train target speed is transmitted from JTCto TCR, and the target speed is extracted to the CTCS computerfor speed supervision. The CFSST is found to change with trainspeed, and this directly affects the availability of modulated lowfrequency. In consequence, the travel safety and transportationefficiency are reduced and also the increase of train speed isprevented. To analyze this problem, the paper proposes themodel of TTCITP based on the transmission line theory, andthe mathematical relation between the change of CFSST andthe train speed is analyzed in the condition of uniform trainspeed and normal working state.

Theoretical studies and experimental results show that trainspeed only has a bearing on the position of train shuntingpoint at each sampling time, but with no change on the naturalamplitude and initial phase of the signal at this shunting point.The conclusion obtained in this paper shows that the deviationin CFSST is decided by the train speed and the equivalenttransmission phase-shift, whereas the modulated low frequency,the frequency offset, and the amplitude are not influenced innormal condition.

The study in this paper can be of great importance to theoptimization of the decoding algorithm in TCR and also atheoretical support for high-speed railway development and theincrease of train speed. Further studies are being carried outto analyze the influences from compensation capacitor faultsystematically. This will contribute to the further completionof the analysis of TTCITP in high-speed railway.

Fig. 13. Equivalent uniform transmission line for the compensation unitin JTC.

APPENDIX

INITIAL PHASE MODELS OF SST WHEN

TRAIN SHUNTS AT THE CENTER AND THE

BOUNDARY OF COMPENSATION UNIT

As for JTC and TCR, the parameters φfs, φjg , and φcs in(25) are essentially constant, and thus, arg( �Nsf11(x(n))Rf +�Nsf12(x(n))) becomes the main part to analyze. It isdenoted by

φzy (x(n)) = arg(�Nsf11 (x(n))Rf + �Nsf12 (x(n))

). (35)

The transmission characteristics of compensation unit de-picted in (7) can be equivalent to a uniform transmission linenetwork, as shown in Fig. 13.

In addition, the characteristic impedance �Zcu and propagationconstant �γcu of the equivalent network can be represented by

�Zcu=

√�Nt12/ �Nt21, �γcu=ln( �Nt11+

√�Nt12 · �Nt21)/lT . (36)

Therefore, (14) can be further simplified as

�Nt =

[cosh(�γculT ) �Zcu × sinh(�γculT )

sinh(�γculT )/�Zcu cosh(�γculT )

]. (37)

Here, suppose that

�Ngd =

[�Ngd11

�Ngd12

�Ngd21�Ngd22

]= �Np × �Nb (38)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

�θ = artanh( �Ngd12/ �Ngd11�Zcu)

�ε1 = artanh(Rf/�Zcu)

�ε2 = artanh(Rf�Zcu/�Z

2g )

�α1 = artanh(�Zg/�Zcp + �Zg/Rf )

�α2 = artanh(�Zg/�Zcp +Rf/�Zg)

�ε3 = artanh(�Zg/

(�Zcu tanh(�γglT /2 + �α1)

))�ε4 = artanh

(�Zcu tanh(�γglT /2 + �α2)/�Zg

)�A1 = �Ngd11

�Zcu/(cosh �θ cosh �ε1)�A2 = �Ngd11

�Zg/(cosh �θ cosh �ε2)

�A3 =�Ngd11Rf

�Zcu sinh(�γglT /2+�α1)�Zg cosh �θ cosh �α1 cosh�ε3

�A4 =�Ngd11

�Zg cosh(�γglT /2+�α2)

cosh �θ cosh �α2 cosh�ε4

(39)



φzy(m, ly)=

⎧⎪⎪⎪⎨⎪⎪⎪⎩

arg(�A1 cosh(�γgly) sinh(�γculTm+�θ+�ε1)+ �A2 sinh(�γgly) cosh(�γculTm+�θ+�ε2)

), 0 � ly<lT /2

arg(�A3 cosh (�γg(ly−lT /2)) sinh(�γculTm+�θ+�ε3)

+�A4 sinh (�γg(ly−lT /2)) cosh(�γculTm+�θ+�ε4)), lT /2� ly<lT

(40)

where �θ, �ε1, �ε2, �α1, �α2, �ε3, �ε4, �A1, �A2, �A3, and �A4 are allcomplex constants. Using (5) and (39), (35) can be rewritten as(40), shown on the top of the page.

Let ly = 0, ly = lT /2, then it arrives at

φzy(m, ly)

=

⎧⎨⎩

arg( �A1) + arg(sinh(�γculTm+ �θ + �ε1)

), ly = 0

arg( �A3) + arg(sinh(�γculTm+ �θ + �ε3)

), ly = lT /2.

(41)

Here, let

�γcu=η1+jη2; �θ+�ε1=ξ1+jξ2; �θ+�ε3=ρ1+jρ2. (42)

Substituting (42) into (41) and using the Euler formula, then

arg(sinh(�γculTm+ �θ + �ε1)

)= arctan 2

((e2(η1m+ξ1)lT + 1) sin ((η2m+ ξ2)lT )

(e2(η1m+ξ1)lT − 1) cos ((η2m+ ξ2)lT )

)≈ (η2m+ ξ2)lT (43)

arg(sinh(�γculTm+ �θ + �ε3)

)= arctan 2

((e2(η1m+ρ1)lT + 1) sin ((η2m+ ρ2)lT )

(e2(η1m+ρ1)lT − 1) cos ((η2m+ ρ2)lT )

)≈ (η2m+ ρ2)lT . (44)

Here, arctan 2(·) is the four-quadrant arctangent functionafter unwrapping operation. Using (43) and (44), (25) can berewritten as

φcy(x(n))=

{−Im(�γcu)x(n)+B1, x(n)=mlT−Im(�γcu)x(n)+B2, x(n)=mlT +lT /2.

(45)

Here, Im denotes the operator of getting the imaginary part. Inaddition, B1 and B2 can be expressed

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

B1=φfs+φcs+φjg−arg( �A1)

−(Im(�θ+�ε1)

)lT , ly=0

B2=φfs+φcs+φjg−arg( �A3)

−(Im(�θ+�ε3)

)lT +Im(�γcu)lT /2, ly= lT /2.

(46)

It could be known that the slope of phase φcy(x(n)) willbe the same but with two different intercepts (B1 and B2) inboth cases that train shunts at the common boundary of com-pensation unit (x(n) = mlT ) and the compensation capacitorlocation (x(n) = mlT + lT /2).

REFERENCES

[1] H. R. Dong, B. Ning, B. G. Cai, and Z. S. Hou, “Automatic train con-trol system development and simulation for high-speed railways,” IEEECircuits Syst. Mag., vol. 10, no. 2, pp. 6–18, 2nd Quart., 2010.

[2] X. K. Fei, Principle and Analysis of Jointless Track Circuit. Beijing,China: China Railway Publishing House, 1993.

[3] K. M. Qiu, JT1-CZ2000 Type Cab Signal On-Board System. Beijing,China: China Railway Publishing House, 2007.

[4] D. C. Carpenter and R. J. Hill, “Railroad track electrical impedance andadjacent track crosstalk modeling using the finite-element method of elec-tromagnetic systems analysis,” IEEE Trans. Veh. Technol., vol. 42, no. 4,pp. 555–562, Nov. 1993.

[5] R. J. Hill and D. C. Carpenter, “Rail track distributed transmissionline impedance and admittance: Theoretical modeling and experimen-tal results,” IEEE Trans. Veh. Technol., vol. 42, no. 4, pp. 225–241,Nov. 1993.

[6] B. Nleya, “Model of a laser-frequency measuring device,” in Proc. IEEEISIE, Pretoria, South Africa, pp. 639–642.

[7] N. Nedelchev, “Jointless track circuit length,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 146, no. 1, pp. 69–74, Jan. 1999.

[8] N. Nikolov and N. Nedelchev, “Study on centre-fed boundless trackcircuits,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 152, no. 5,pp. 1049–1054, Sep. 2005.

[9] L. Oukhellou, P. Aknin, and F. Vilette, “Classification and localization ofdefects by combined use of internal and external modelings,” in Proc. Int.Conf. PSIP, Grenoble, France, 2003, pp. 165–168.

[10] L. Oukhellou, A. Debiolles, T. Denoeux, and P. Aknin, “Faultdiagnosis in railway track circuits using Dempster–Shafer classi-fier fusion,” Eng. Appl. Artif. Intell., vol. 23, no. 1, pp. 117–128,Feb. 2010.

[11] Y. S. Chen and L. A. Chen, “Semi diagonal matrix method of finiteelements for calculation of track circuit,” J. China Railway Soc., vol. 21,no. 6, pp. 54–57, Dec. 1999.

[12] H. B. Zhao and Y. Z. Zhang, “Study on some problems of track circuit withcompensating capacitors,” J. China Railway Soc., vol. 20, no. 4, pp. 77–81, Aug. 1998.

[13] J. Su, D. Y. Jiang, and P. X. Du, “The dynamic test method on trackcircuits,” Appl. Electron. Tech., vol. 32, no. 11, pp. 7–10, 2006.

[14] L. H. Zhao, J. P. Wu, and Y. K. Ran, “Fault diagnosis for track circuit usingAOK-TFRs and AGA,” Control Eng. Practice, vol. 20, no. 12, pp. 1270–1280, Dec. 2012.

[15] ZPW-2000 Track Circuit Technology Conditions. Beijing, China: ChinaRailway Publishing House, 2008, p. 6, TB/T 3206-2008.

[16] A. M. Bryleyev, Analysis and Synthesis of Track Circuit,M. P. Sun, Ed. Beijing, China: China Railway Publishing House,1981, pp. 53–54.

[17] J. S. Qi, “ZPW-2000A jointless track circuit adjustment and analysisof ballast bed resistance,” Railway Signalling Commun., vol. 46, no. 2,pp. 30–32, Feb. 2010.

[18] CD96 Type Series Frequency Shift Measuring Instrument, Beijing Rail-way Signal Co., Ltd., Beijing, China, Mar. 20, 2013. [Online]. Available:http://www.brsf.com.cn/product_detail.asp?id=445

[19] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng,N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposi-tion and the Hilbert spectrum for nonlinear and non-stationary time seriesanalysis,” Philos. Trans. Roy. Soc. London A, Math. Phys. Sci., vol. 454,no. 1971, pp. 903–995, Mar. 1998.

[20] Y. Y. Zhen, R. J. Ma, and X. Y. Wei, “Study on FSK signal demodulationbased on time-frequency distribution,” J. China Railway Soc., vol. 28,no. 2, pp. 95–99, Apr. 2006.

[21] L. H. Zhao, J. J. Xu, W. N. Liu, and B. G. Cai, “Compensation capacitorfault detection method in jointless track circuit based on Levenberg–Marquardt algorithm and generalized S-transform,” Control Theory Appl.,vol. 27, no. 12, pp. 1612–1617, Dec. 2010.

http://www.brsf.com.cn/product_detail.asp?id=445



Linhai Zhao received the Ph.D. degree in intelli-gent transportation engineering from Beijing Jiao-tong University, Beijing, China, in 2011.

He is an Associate Professor and a Master’sSupervisor with the School of Electronic and In-formation Engineering, Beijing Jiaotong University,Beijing, China. His main research interests includeresearch on track–train information reliable transmis-sion, train intelligent control theory, and intelligentcooperative vehicle infrastructure system simulation.

Prof. Zhao received the second prize for the Na-tional Science and Technology Advancement Award twice in 1998 and 2009,respectively, due to his scientific contributions to train control in railways,

Baigen Cai (SM’13) received the B.S. and M.S. de-grees in traffic information engineering and controlfrom Beijing Jiaotong University, Beijing, China, in1987 and 1990, respectively.

He is a Professor with Beijing Jiaotong Univer-sity, Beijing, China, where he is the Director of theScientific and Technical Department. His researchinterests include intelligent transportation systems,the Global Navigation Satellite System and its ap-plications in transportation, multisensor fusion andintegration, and intelligent control.

Mr. Cai serves as a Reviewer for many international journals.

Junjie Xu received the M.S. degree in traffic in-formation engineering and control from BeijingJiaotong University, Beijing, China, in 2012.

He is with Xiamen Tobacco Industrial Co., Ltd.,Xiamen, China, working on mechanical automaticcontrol.

Yikui Ran received the M.S. degree in traffic infor-mation engineering and control from Beijing Jiao-tong University, Beijing, China, in 2012.

He is with Zhejiang Insigma Supcon InformationTechnology Co., Ltd., Zhejiang, China, devoted toresearch on railway signal control and intelligenttransportation control, working on software develop-ment for train control.