Measurement of railroad track irregularities using an automated recording vehicle

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Measurement, Vol. 183, on October 2021, available at: https://doi.org/10.1016/j.measurement.2021.109765 Copyright 2021 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND Measurement of railroad track irregularities using an automated recording vehicle Pedro Urdaa,∗ , Javier F. Aceitunob, Sergio Mu˜nozc, Jos´e L. Escalonaa aDepartment of Mechanical and Manufacturing Engineering, University of Seville, Spain bDepartment of Mechanical and Mining Engineering, University of Ja´en, Spain cDepartment of Materials and Transportation Engineering, University of Seville, Spain Abstract This paper presents the design, construction and experimental validation of a scaled railway vehicle for the automated and quick survey of the geometry of an experimental scaled track. The method, that can be extended to full scale tracks, validates the measurements of the automated recording vehicle (ARV) by comparison with respect to a precise but slow manual measuring method (MMM). The two-axle vehicle, which is powered by a brushless DC motor, has its leading axle instrumented with a LVDT, an inclinometer, a reflector and a precision encoder. These sensors, together with the help of a total station, allow the measurement of the scaled track geometry and its irregularities following an optimization procedure that first determines the ideal track centreline. The ARV has been tested on a scaled track and its measurements are validated with the MMM results showing a good agreement between both approaches. Keywords: Track surveying, instrumented railway vehicle, scaled track, track irregularities, experimental validation, automated recording vehicle. 1. Introduction1 An accurate knowledge of the track geometry is essential to guarantee the safety of the rolling stock.2 This is because the dynamic response of a railway vehicle [1] is highly influenced by track irregularities3 [2, 3]. Thus, operator companies are continuously investing human and material resources on the survey4 and maintenance of their railway infrastructures. Large track irregularities result on larger wheel-rail5 contact forces, that end up compromising the integrity of the track and, the most important, the safety6 of the passengers. These irregularities can also produce disturbing sounds for the nearby towns to the7 track [4] and reduce the comfort of the vehicle [5, 6].8 Rail irregularities can be understood as geometrical deviations of the rail cross-sections from an ideal9 track geometry. They can be divided into two general groups: (1) distributed track irregularities and (2)10 isolated track defects. The first group appears as regular patterns along the track with multiple wave-11 lengths that depend on the damage mechanism, i.e. rail wear [7] or rolling contact fatigue (RCF). This12 group of irregularities is usually quantified by the four well-known variables used in the industry: track13 gauge, cross level, vertical profile, and alignment. The isolated track defects, which are the responsible14 of many of the unsafe vehicle responses, appear more rarely but may also have regular patterns. They15 ∗Corresponding author: [email protected] Preprint submitted to Measurement April 18, 2021 account for changes in the rail cross section at specific locations, such as in poor drain areas, bridges, or16 turnouts [8].17 Engineers have been working for decades on the development of new methodologies and measuring18 apparatus for the precise measurement of track irregularities and simulation models and procedures that19 help to determine and improve the comfort of the ride [9, 10, 11]. This is evidenced by the numerous20 patented ideas and scientific studies found in the literature. Some of the oldest inventions are based on21 simple mechanical measuring methods [12] or instrumented wheelsets [13] and others more recent use22 sensorized trailed vehicles [14] or computer vision techniques [15]. Nowadays, there are also laboratory23 vehicles such as the Taiwanese EM-50 for the inspection of high-speed lines, the Bulgarian EM-120 for24 the inspection of the catenaries [16] or the Spanish Seneca track and catenary inspection vehicle. These25 are just a small sample of the numerous measuring systems that have been and are currently being used26 in the railway industry for surveying the track.27 In general, track measuring methods can be classified into manual surveys and automated or dynamic28 surveys. On one hand, manual methods are normally based on the use of an instrumented trolley that29 is manually pushed by a human operator along the track under analysis. On the other hand, automated30 methods are based on the use of a laboratory vehicle. This one can be instrumented with inertial and31 navigational sensors for a measurement of the track based on the dynamic response of the vehicle or32 distance measuring devices. The latter are used in the so-called chord methods which are applied in33 the horizontal and vertical versine measurement of rails [17]. An extended survey of track irregularity34 measuring methods can be found in [18]. The European standard EN-13848-3:2009 [19] regulates the35 measuring features and requirements for track measuring systems.36 For their simplicity, precision and robustness, manual trolleys are the most widely-used apparatus37 for the inspection of the track in the railway industry. Their use can be considered to provide a direct38 measurement since the trolley is equipped with sensors such as a distance transducer and an inclinome-39 ter for the measurement of track gauge and cross-level, respectively, both also known as relative track40 irregularities. It also includes a total station and/or a GPS receiver for the measurement of the absolute41 position of the track centreline. An example of one of the commercial track measuring trolleys that can42 be found in the market is the Amber Survey GRP 1000 by Amberg Technologies [20]. There are also43 other versions of manual trolleys focus on the measurement of rail corrugation. The latter are based on44 the use of several high-precision laser sensors for the survey of the rail heads [21]. It can be also found in45 the literature some prototype trolleys that, on the basis of the convectional models, try to overcome their46 slow performance. An example is the work presented by Chen et al. in [22, 23]. The authors propose47 a sensors fusion algorithm between the GPS and an Inertial Measuring Unit (IMU) that allows a faster48 survey of the track using this trolley without leaving behind the accuracy requirements for a high speed49 line. A similar experimental trolley called REGEOS is presented in the work of Akpinar et al. [24, 25]. In50 this case, a Kalman filter algorithm is proposed to determine track centre line geometry, track gauge and51 super-elevation, that shows an excellent performance according to the International Union of Railway52 (UIC) standards. Jiang et al. present in [26] an algorithm that tries to overcome the low acquisition53 frequency of a total station combining its measurement with a high precision inertial sensor installed on54 2 the trolley and the measurement of some known landmarks along the track under analysis. Despite of55 their precision and good performance, the use of these devices have the handicap of being very slow when56 measuring the track, that used to be around one kilometre per hour. They are a valid solution for the57 inspection of short track segments or occasional measurement but not for a full track measurement or58 continuous track monitoring.59 As an alternative to the manual survey of a track, automated or dynamic methods are presented. In60 this case, the track irregularities are obtained in an indirect manner using the measurement of several61 sensors of different types that are installed on a laboratory vehicle. The key of these methods lies in62 a computational model of the vehicle and the track [27] that uses as inputs the measurement of the63 installed sensors and it is able to determine the track irregularities based on the dynamic response of the64 vehicle. Certainly, the sophistication of the model affects the final results of the estimation model. In the65 work of Sagadeghi et al. [28] the authors demonstrate that in a slab track a 3D model of the wheel-rail66 interaction is required for a correct estimation of the contact forces. An example of an automated method67 is the work of Tsunashima et al. [29] where the vertical irregularity of the track is estimated from the68 car-body vibration using a Kalman filter and a simplified model of the vehicle. Westeon et al. in [30]69 present an alternative way to measure the vertical track irregularity using the pitch angle measured by70 a gyro sensor and accelerometers installed on the bearing boxes from an in-service railway vehicle. The71 estimation of track irregularities from the dynamic response of a vehicle is not an easy task as shown in72 the work of Karis et al. [31]. In this work, the authors try to find a correlation between the dynamic73 response of the vehicle and the excitation generated by the track irregularities using a simple model of74 the vehicle. They conclude that they do not always coincide in absolute values and standard deviations.75 The work of A. De Rosa et al. [32] is focused on the indirect measurement of lateral track irregularities.76 In this work the authors use a modern machine learning algorithm to identify the lateral defects of the77 track. Another interesting work is the one presented by Wei et al. [33] where the alignment of the78 track is determined through a double integration of the acceleration measured by several accelerometers79 placed on the vehicle. Introducing the measurement of the sensors in a computational simulation model80 of the vehicle they are able to determine different ranges of alignment on the measured track. In the81 work of Escalona et al. [34], a track measurement system that can be installed on in-service vehicles82 and combines a kinematic model, a computational vision system and inertial measurement is presented.83 The mentioned system show a strong potential to the automated inspecion of tracks. In conclusion,84 dynamic methods have the clear advantage of being much faster compared with the manual trolleys85 due to the fact that they are based on the use of in-service vehicles. However, the track measurement86 obtained from an in-service vehicle is not as accurate as using a manual trolley since the dynamics of87 the vehicle is included in the measurement. This is explained in [35], where a very interesting analysis88 of the measuring precisions obtained with manual trolleys and laboratory vehicles is presented. As a89 summary, it can be said that the railway industry is tending toward automated track survey systems90 installed on in-service vehicles combining conventional sensorization (inertial or distance sensors) with91 modern computational vision techniques [36] and artificial intelligence algorithms [37]. This could allow92 a daily monitoring of the track resulting on a reduction of the maintenance cost of the infrastructure93 3 thanks to an anticipated intervention. There are also intermediate solutions that are neither a manual94 method nor an automated one. An example is the track inspection wagon presented by Chang et al. in95 [38]. An innovative self-propelled measuring trolley instrumented with a wide variety of sensors such as96 accelerometers and computational vision cameras, that allows a fast and accurate measurement of the97 track. The mentioned vehicle is tested on a laboratory track in which irregularities have been artificially98 introduced. Finally it should be noted that computational vision techniques are gaining ground on the99 track surveying business. An example is the ballast track inspection system presented by Sadegui et al.100 in [39]. This system provides an index that is a function of deficits and excess of ballast in the track.101 As a response to the needs posed by the railways industry in terms of track measurement based on the102 dynamic response of the vehicle, the Mechanical Engineering research group of the University of Seville103 have been working for over two decades on the development of new computational multibody model104 formulations [40, 41] for the state observation from in-service railway vehicles. To guarantee the accuracy105 and good performance of any computational model, the scientific method requires to be experimentally106 validated. However, getting the access to a real railway vehicle and track is not always inexpensive107 neither possible. As an alternative, this research group has been recently using scaled vehicles and tracks108 for its investigations on railway dynamics [42, 43]. Although the dynamic response of an scaled vehicle109 cannot be directly extended to full-scaled vehicles, the utilisation of scaled systems represent an easy110 and relatively inexpensive way to experimentally validate new computational multibody models and new111 theoretical approaches without compromising the safety of the passengers or the integrity of the track.112 In this sense, the proposed method applied to a scaled vehicle and track, is not affected by the vehicle113 dynamics, and can serve as a design strategy to the application of the measurement of track irregularities114 at real tracks. In these tracks, geometry is continuously changing due to temperature effects, movements115 of the foundation and the most important, due to the effect of the wheel-rail contact forces exerted by the116 vehicles. Considering the fact that the vehicle dynamics is highly influenced by the track irregularities,117 it is fundamental to know the geometry of the track under analysis with the greatest possible accuracy,118 reducing this way uncertainties during the validation process of new computational models or a running119 vehicle safety analysis. Indeed, in an ideal scenario, the track should be measured just immediately before120 an experiment and in that case a fast an reliable measuring method is required. In the work of Aceituno121 et al. [44] a possible measuring method is presented but despite its precision, its slowness does not make122 it very operational. That is reason why the goal of this manuscript is to present a novel scaled railway123 vehicle for the automated track survey and calculation of track irregularities. The vehicle is not based on124 the traditional ”chord-method”, that would requires a large system to account for high wavelengths. The125 vehicle is powered by a DC motor and equipped with a LVDT, an inclinometer, a precision encoder and a126 reflector (target prism for the total station). Using the vehicle with the support of the total station, the127 scaled track geometry can be easily obtained within minutes. The track measurement and irregularities128 obtained with the proposed automated inspection method are compared with a very accurate but slow129 manual measuring method, resulting on an great agreement between both approaches.130 The paper is organised as follows: Section 2 is devoted to the design and instrumentation of the131 ARV and the measuring procedure. In Section 3 the MMM is explained in detail. Section 4 deals with132 4 the track centre line optimization process and the calculation of track irregularities. The experimental133 validation of the ARV and the results comparison with the MMM are described in Section 5. Summary134 and conclusions are presented in Section 6.135 2. Automated recording vehicle (ARV) and measuring procedure136 Track irregularities have a great importance for railway operation. Depending on their magnitude,137 they might be only a matter of ride comfort or even compromise the ride safety leading to a derailment138 scenario. Thus, a correct identification and characterization of track irregularities results fundamental in139 railway simulation. In the railways industry, track irregularities are divided in two groups, relative and140 absolute track irregularities. Relative irregularities are the gauge variation and the cross-level. While141 absolute track irregularities are the alignment and the vertical profile. An extended description of track142 irregularities can be found in [45].143 The original idea of this work was the development of a scaled Automated Recording Vehicle (ARV)144 such that, in a short time period, the track geometry could be measured and later on, track irregularities145 calculated. In the case of the scaled track subject of study in this research, having a fast procedure146 for measuring the track is even more important since the geometry can be manually modified if needed.147 Figure 1 (a) shows the mechanisms that are used as the sleepers of the scaled track. Each of them allows148 the variation of track gauge, cant angle and the relative height between both rails. The full track includes149 900 mechanism distributed along its 90 meters of length (see Fig. 1 (b)). With the automated recording150 vehicle presented in this paper, the scaled track can be easily measured before any experimental campaign151 with a scaled railway vehicle [46, 43], minimizing that way possible uncertainties in the computational152 simulation due to errors in the definition of track irregularities.153 (a) (b) Magnetic beacon Figure 1: (a) Track sleepers. (b) Track overall view 2.1. Mechanical design of the ARV154 The automated recording vehicle CAD design is illustrated in Fig. 2 (a). It has two different parts:155 the drive system, consisting on the vehicle’s body and traction wheels, and the measuring axle (see Fig.156 5 2 (b)). Both parts are connected through a spherical joint as sketched in the figure. This mechanical157 joint isolates the rotations of the vehicle’s body and the measuring axle.158 (a) (b) Spherical joint Spherical joint Guide rail Traction wheel Left carriage Right carriage Guide wheels Vehicle’s body Traction spring Figure 2: (a) Automated recording vehicle CAD. (b) Isolated measuring axis CAD The fundamental element of the inspection vehicle is its measuring axle represented on Fig. 2 (b). It159 includes two carriages that slide along a guide rail. Two pairs of guide wheels keep the carriages attached160 to the rails, which ensures that vertical wheels lie in the same relative location with respect to the rail161 cross-section thus avoiding lateral wheel-rail displacement that may occur in other measuring vehicles. A162 traction spring guarantees the contact between the lateral guide wheels and the outer side of both rails.163 The stiffness of the traction spring has been calculated according with the maximum vehicle’s velocity164 in order to guarantee a permanent contact between both lateral wheels and the rails. A third vertical165 wheel installed on the left carriage (see Fig. 3 (b)) avoids the measuring axis to pitch-over when moving166 forward. This mechanical assembly allows the measuring axis to follow the track geometry perfectly while167 it is pushed by the vehicle’s drive system.168 The drive system is shown with further details on Fig. 3. As it can be observed, the belt drive is169 actuated by a brushless DC motor. The output shaft is connected to a differential that drives the traction170 wheels, which are cylindrical, not conical, to minimize the influence that the roll of the traction axle may171 have in the measuring axle. In addition, because the guidance of the vehicle is achieved due to the lateral172 wheels and traction spring of the measuring axle, the traction wheels are wide enough to negotiate the173 curves properly. The differential guarantees the correct performance of the vehicle while it negotiates the174 curve sections of the track.175 6 (a) (b) Traction wheel Brushless DC motor Gearbox Belt drive Differential Vertical wheel 430 mm 245 mm 102 mm Figure 3: (a) Side view of the recording vehicle. (b) Bottom view of the recording vehicle The vehicle has been manufactured in aluminium and 3D printed PolyLactic Acid (PLA). It is 430176 mm long and 245 mm wide with a total mass of 6.5 kg. The measurable track gauge range is 107 mm to177 157 mm and the maximum yaw rotation of the measuring axis is ±35◦. The vehicle is powered with an178 industrial quality brushless electric motor Maxon-ECi30-GP32C-ENC16EASY-MK2. The drive wheels179 can reach a maximum angular velocity of 20πrad/s that corresponds to a forward velocity of 5 m/s. It180 should be noted that, such velocity does not correspond with the maximum velocity recommended for181 the measurement of the track as it will be explained later in this manuscript.182 2.2. Instrumentation of the ARV and data acquisition system183 Figures 4 and 5 show the final assembly of the automated recording vehicle. It is instrumented with184 an LVDT, an inclinometer, a precision encoder and a reflector. These sensors allow the measurement of185 track geometry and irregularities. As explained before in this section, relative track irregularities are the186 gauge variation and cross-level. They are the easiest to determine since they are directly obtained from187 the measurement of the LVDT and the inclinometer. In this case, the vehicle uses a 5mm-range high188 precision LVDT SCHREIBER SM347.10.1.S with a maximum accuracy of ±12.5 microns. The sensor189 body is attached to the right carriage while the rod is in permanent contact with the left carriage thanks190 to an internal spring. The inclinometer has a range of ±10◦and it is installed on the left carriage.191 The traction spring, which is expanded when the vehicle is on the track, tends both carriages towards192 a minimum separation between both guide wheels, being in that way the measuring axle perpendicular193 to both rails. Thus, it can be assumed that the measuring axle follows the track irregularity. While194 measuring, the movement of the left carriage is locked to the guide rail and it is the right carriage the195 one that slides along the guide rail (see Fig. 5 (a)).196 7 (a) (b) Drive wheels Power source DAQ computer Encoder Inclinometer Right carriage Reflector Guide wheels LVDT Left carriage Figure 4: (a) Front view of the recording vehicle. (b) Lateral view of the recording vehicle (a) (b) Inductive sensor Locking screw Front wheels Encoder Inclinometer Guide rail Figure 5: (a) Front view of the instrumented axle. (b) Top view of instrumented axle For the measurement of absolute track irregularities (alignment and vertical profile), the sensors197 installed on the vehicle are complemented with the measurement of a robotic high precision total station198 (see Fig. 6) that follows the trajectory of a reflector rigidly installed on the vehicle’s measuring axis (see199 Fig. 4 (a)). This method allows to capture the trajectory of a fixed point on the measuring axis that200 will be used to determine the absolute track irregularities, as will be shown in the next section. The201 operation speed of the vehicle depends on the total station capabilities and required frequency content202 of the measured irregularities. In this context, according to the limits of track irregularities in full-scale203 tracks given by EN-13848 [47], the smallest wavelength at D1 band (3 m) results in 0.3 m in the scaled204 track. Note that the scaled track is ten times smaller than a full-scale one. This minimum wavelength205 combined with the capabilities of the total station results in a maximum ARV operation speed of 0.9 m/s206 which guarantees the desired frequency content of the measured irregularities. The process to calculate207 the absolute track irregularities is explained later in this manuscript. Finally, the vehicle includes a208 precision encoder that measures the distance travelled by the instrumented axis. The encoder is rigidly209 attached to the rotation axis of one of the wheels of the measuring axle. In order to avoid possible errors210 in the measurement of the distance travelled by the vehicle, due to eventual slides of the measuring wheel,211 8 Table 3: Horizontal projection of the ideal track geometry, optimized Section Type Length (m) A Tangent 21.235 B Transition 1.358 C Constant radius (24m) 25.139 D Transition 7.258 E Tangent 4.483 F Transition 2.766 G Constant radius (6m) 10.989 H Transition 2.169 I Tangent 12.603 Table 4: Vertical projection of the ideal track geometry, optimized Section Type Length (m) A Tangent 20.9 B Constant slope (+0.035%) 15.2 C Tangent 40.9 D Constant slope (+3.2%) 4.7 E Tangent 2 F Constant slope (-4.7%) 3.2 G Tangent 0.6 Position x (m) 0 10 20 30 40 50 60 Position y (m) -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 Measured Designed Optimized Distance s (m) 0 10 20 30 40 50 60 70 80 90 Height z (m) -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Measured Designed Optimized (a) (b) Figure 13: (a) Horizontal projection, measured vs designed geometry vs optimized. (b) Vertical projection, measured vs designed geometry vs optimized 4.2. Calculation of the irregularity325 Once the ideal track geometry is optimized, track irregularities can be calculated as the difference326 between the ideal position of the rails with respect to their actual positions. Figure 14 sketches the327 track irregularity definition. In the figure, rail sections coloured in pale blue represent the ideal positions328 while the dark green ones are the measured positions of the rails. Irregularity vectors are defined as329 ~r lir =h0ylir zliriT and ~r rir =h0yrir zririT respectively. These vectors are expressed in a frame330 15 called track frame (TF), that is attached to the track centre line being its Xtaxis tangent to it, and the331 Ytaxis contained in the line that joins the left and right railheads, as shown in Fig. 14. The alignment332 ξa, gauge ξg, cross-level ξcand vertical profile ξvare defined as a function of the components of the333 irregularity vectors using the following expressions:334 ξa= (ylir +yrir)/2 ξg= (ylir −yrir) ξc= (zlir −zrir) ξv= (zlir −zrir)/2 (2) rlir 2L β δ r t Y t Z β rrir zrrp yrrp ylrp zlrp P urrp Q ulrp Figure 14: Definition of the track irregularities Experimentally, gauge and cross-level are obtained directly from the measurement of the LVDT and335 the inclinometer. The gauge irregularity is defined as the difference between the measured gauge and the336 nominal value of the track. The cross-level is the difference of height between both rails and it can be337 easily obtained as:338 ξc=sin(αinc)·dLV DT (3) where αinc is the angle measured by the inclinometer and dLVDT is the track gauge measured by the339 LVDT.340 Alignment and vertical profile cannot be obtained in such a direct way. It is first required to obtain341 the distance between the optimized track centre line points and the measured ones. To do that, a system342 of non-linear algebraic equations should be solved, which calculates the distance between every single343 measured point and the closest point at the optimised track centre line. Point Piin Fig. 15 represents a344 measured point on the track while point Qiis an arbitrary point at the optimized track centre line. The345 distance between both points is the norm of vector ~ dithat can be calculated using the expression:346 ~ di=~ RQi−~ RPi(4) where ~ RQiis the absolute position of one point of the optimized track centre line and ~ RPiis the absolute347 position of the measured point.348 16 In Fig. 15, ~ tQidenotes the tangent vector to the scaled track ideal centre line at point Qi. Vector ~ di 349 has to be perpendicular to ~ tQi. Thus, the following equation has to be fulfilled:350 ~ di·~ tQi= 0 (5) The process concludes after projecting vector ~ dion the track reference frame according to the next351 expression:352 ¯rirr = (At)Tdi(6) being Atthe transformation matrix of the Track Frame (TF) to the Global Frame (GF). As usual in353 railways kinematics, the GF is a fixed reference frame, while the TF follows the vehicle on its movement354 along the track. In this research, the GF is assumed to be located in the first location where the355 total station was installed. Due to the orientation of the TF with respect to the track centre line, the356 longitudinal coordinate X is equal to zero. Thus, second and third components of vector ~r irr are the357 irregularities of alignment and vertical profile, respectively. Once the alignment, cross-level, gauge and358 vertical profile are determined, system of equations (2) can now be solved to obtain the irregularity vector359 components ylir,zlir,yrir and zrir.360 P(x ,y,z) iPi Pi Pi RPi RQi d Q (x ,y,z) iQi Qi Qi tQi s YX Z Reference geometry Real geometry t X t Z t Y Figure 15: Alignment and vertical profile calculation procedure 4.3. Determination of the rails positions using the ARV361 For a correct performance and accurate measurement of the total station, the reflector is located on362 the ARV in a position such that, it is always visible to the total station during the measurement of the363 track. This requires the reflector to be installed on the top of the ARV as shown in Fig. 5 (b). That364 means, the total station is not directly measuring the track centre line, but a line parallel and close to365 the latter. Considering that, the left carriage (where the sensors are installed) is locked to the guide rail366 and the relative position of the reflector with respect to the left rail is known. As it is explained next,367 using the position of the reflector measured by the total station, the measurement of the inclinometer, the368 17 LVDT, the encoder and the final help of the track pre-processor, the absolute coordinates of the actual369 track centre line can be determined.370 Left rail axis Right rail axis Track centre line Reflector Prism u rr u lr z lr y Gauge inc φ Figure 16: Kinematics of the reflector and the rails Figure 16 shows a kinematics sketch of the rails and the reflector, in witch the latter is assumed to371 be rigidly attached to a reference frame ylr, zlrthat moves together with the left-front wheel that lies372 over the left rail. Let define Alr as the semi-experimental rotation matrix that transforms a vector from373 the left rail reference frame to the global frame,374 Alr =      cos(ψ)−sin(ψ)ϕincsin(ψ) + θinccos(ψ) sin(ψ)cos(ψ)−ϕinccos(ψ) + θincsin(ψ) −θinc ϕinc 1      (7) where ϕinc and θinc are the angles experimentally measured by the dual-axis inclinometer and ψis the375 yaw angle provided by the track pre-processor. Matrix Alr is linearised assuming that the angles of the376 inclinometer are small values. Taking into account that the local position of the reflector with respect377 to the left rail reference frame ¯uP rism is known from the mechanical design of the vehicle, the following378 expression can be established:379 Rlr =RP rism −Alr ¯uP rism (8) where Rlr denotes the position of the left rail axis in the global reference frame and RP rism is the absolute380 position of the reflector measured by the total station, also expressed in the global reference frame. Then,381 the absolute position of the right rail Rrr and the track centre line RT CL can be easily obtained using382 the following expressions:383 Rrr =Rlr +Alr ¯urr (9) RT CL =Rlr +Alr ¯uT CL (10) being ¯urr =h0−gauge 0iT and ¯uT CL =h0−gauge/2 0iT , respectively. Note that, the gauge is384 obtained throughout the measurement of the LVDT.385 18 5. Experimental validation and comparison of results386 In order to validate the performance and accuracy on the measurement using the automated recording387 vehicle, this section presents an experimental comparison between the track irregularities obtained with388 the vehicle and the irregularities drawn from the manual measurement of the track. The manual mea-389 surement is considered as the reference since it has been accomplished in totally controlled conditions.390 However, the measurements of the vehicle, taking into account that they are obtained while the vehicle391 moves at a certain speed along the track, might be affected by the vehicle-track dynamics.392 Figures 17, 18 and 19 show the comparison between the relative track irregularities obtained using393 the automated recording vehicle and the manual method. In this experiment the vehicle moves at a394 constant velocity of 0.5 m/s along the track. It can be observed in Fig. 17 how the gauge variation drawn395 from the measurement of the LVDT almost coincides in both experiments. These results have been396 obtained considering a nominal track gauge of 127.8 mm. In view of the results, it can be said that the397 measurement of the LVDT is not affected by the dynamics of the vehicle at the speed of 0.5 m/s. In Fig.398 19 it is observed that the inclinometer installed in the ARV follows the trend of the manual measurement399 but experiencing larger oscillations. This is something expected due to the fact that, the cross-level is400 obtained using the combined measurement of the LVDT and the inclinometer, and the latter is a type401 of sensor that normally presents a bad dynamic performance. However, the observed differences at the402 speed of 0.5 m/s can be assumed to be sufficiently accurate because the trend of the manual measurement403 is well identified. A possible alternative to the utilisation of an inclinometer to measure the cant angle of404 the track is the use of an Inertial Measurement Unit (IMU) and a sensor fusion algorithm. Two examples405 are the algorithms proposed by Madwick et al. in [51] or Sabatini in [52, 53]. These algorithms are a406 priori suitable for dynamic measurements. They combine the measurement of the acceleration and the407 angular velocities of the IMU to estimate the absolute orientation of the sensor.408 0 10 20 30 40 50 60 70 80 s (m) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Gauge Variation (mm) Manual Vehicle Figure 17: Gauge variation methods comparison 19 31 32 33 34 35 36 37 38 s(m) -1 -0.5 0 0.5 1 Gauge Variation(mm) Manual Vehicle Figure 18: Magnification of gauge variation methods comparison 0 10 20 30 40 50 60 70 80 s (m) -6 -5 -4 -3 -2 -1 0 1 2 3 Cross Level (mm) Manual Vehicle Figure 19: Cross-level methods comparison The repeatability of the sensors measurement when the vehicles moves at different forward velocities409 is also analysed. Figure 20 shows the measurement of the track gauge obtained with the LVDT in three410 different experiments accomplished at 0.5, 0.7 and 0.9 m/s. It is clearly observed how the measurement411 of the LVDT remains stable in the three scenarios. However, the inclinometer measurement shown in Fig.412 21 varies significantly at different velocities. This is observed when the vehicle negotiates the second curve413 of the scaled track located between s= 60 m and s= 75 m, approximately. In this case, the centrifugal414 force experienced by the sensor installed in the vehicle strongly affects its measurement when it moves415 faster than 0.5 m/s. This can be explained given the fact that the inclinometer bases its measurement416 on the capacitive micro pendulum principle and the Earth gravity principle sketches in Fig. 22. Since417 the inclinometer is an inertial sensor, the angle αrepresented in the figure is highly affected by the418 vehicle’s dynamics. In view of these results, it is concluded that the measurement of the track using the419 vehicle must be done at a maximum speed of 0.5 m/s (which is in range of admissible operational speeds420 described in Section 2) in order to guarantee the correct performance of the tilt sensor.421 20 0 10 20 30 40 50 60 70 80 Distance s(m) 126 126.5 127 127.5 128 128.5 129 129.5 130 Track Gauge (mm) VhA 0.5m/s VhA 0.7m/s VhA 0.9m/s Figure 20: Repeatability of LVDT measurement 0 10 20 30 40 50 60 70 80 Distance s(m) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Cant angle (deg) VhA 0.5m/s VhA 0.7m/s VhA 0.9m/s Figure 21: Repeatability of inclinometer measurement - - - - - - + + + + + + - - - - - - + + + + + + α α g Figure 22: Functioning principle of the inclinometer sensor Moreover, the absolute track irregularities have been calculated according the procedure explained in422 the previous section. Figures 23 and 24 show the obtained alignment and vertical profile of the scaled track423 using the measurement of the ARV and the MMM. The signals are filtered according to the European424 standard [47] using a band-pass filter applied in the length domain with a cut-off frequencies between 1/7425 m-1 and 1/0.3 m-1, which correspond with 1/70 m-1 and 1/3 m-1 in a full-scale track. These frequencies426 are determined taking into account the scale reduction of 1:10, and they correspond with the D1 to D2427 range given in the European standard. In what follows, all figures concerning measurements both with428 the manual and vehicle methods, are filtered equally. In the Fig. 23 it is observed a good agreement in429 21 the magnitude of the alignment between both signals. The resultant Root Mean Squared (RMS) level of430 the difference between both signals is summarized in Table 5. In this analysis the track has been divided431 in three sections which correspond with the tangent section located at the beginning of the track, the432 large radius curved section (R = 24 m) and the sharp radius curved section (R = 6 m).433 Table 5: RMS analysis in different track sections Irregularity Tangent (s=0-21m) Curve (s=21-47m) Curve (s=60-73m) Gauge 2.02 ·10−4m 1.26 ·10−4m 1.24 ·10−4m Cross-level 1.79 ·10−4m 2.08 ·10−4m 4.71 ·10−4m Alignment 4.21 ·10−4m 4.99 ·10−4m 6.31 ·10−4m Vertical profile 4.58 ·10−4m 4.29 ·10−4m 4.31 ·10−4m 0 10 20 30 40 50 60 70 80 s (m) -8 -6 -4 -2 0 2 4 6 8 Aligment (mm) Manual Vehicle Figure 23: Alignment of the scaled track 0 10 20 30 40 50 60 70 80 s (m) -5 0 5 Vertical Profile (mm) Manual Vehicle Figure 24: Vertical profile of the scaled track Finally once the four irregularities of track gauge, cross-level, alignment and vertical profile are calcu-434 lated, the real position of the rail’s head (see Fig. 9) given by ylir,yrir,zlir and zrir can be determined435 using Eq. 2. Figure 25 shows the obtained results. Looking at the Figs. 25 (c) and 25 (d) it can be436 observed the difference of height between both rails in the curved sections located at s = [21 - 47] m and s437 22 = [60 - 73] m. This difference of height corresponds with the cant angle manually introduced in the scaled438 track. In view of these results it can be concluded that the ARV demonstrates a quite good performance439 when measuring the scaled track geometry, being the obtained irregularity results analogous to the ones440 drawn from the MMM. In addition, the use of the ARV reduces the measurement time twenty times441 compared with the MMM. The ARV allows a fast and accurate measurement of the track just before an442 experimental campaign with a scaled vehicle.443 23 0 10 20 30 40 50 60 70 80 s (m) -8 -6 -4 -2 0 2 4 6 8 yL (mm) Manual Vehicle 0 10 20 30 40 50 60 70 80 s (m) -8 -6 -4 -2 0 2 4 6 8 yR (mm) Manual Vehicle 0 10 20 30 40 50 60 70 80 s (m) -6 -4 -2 0 2 4 6 zL (mm) Manual Vehicle 0 10 20 30 40 50 60 70 80 s (m) -6 -4 -2 0 2 4 6 zR (mm) Manual Vehicle (a) (b) ( c ) (d) Figure 25: (a) yL, (b) yR, (c) zL, (d) zR displacements 24