EUROPEAN STANDARD DRAFT

NORME EUROPÉENNE prEN 13848-2

EUROPÄISCHE NORM
October 2018

ICS 93.100 Will supersede EN 13848-2:2006

English Version

Railway applications - Track - Track geometry quality -

Part 2: Measuring systems - Track recording vehicles
Applications ferroviaires - Voie - Qualité géométrique Bahnanwendungen - Oberbau - Geometrische
de la voie - Partie 2 : Systèmes de mesure - Véhicules Gleislagegüte - Teil 2: Messsysteme -
d'enregistrement de la voie Gleismessfahrzeuge

This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 256.

If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations
which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC
Management Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.

Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.

Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.

EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 13848-2:2018 E
worldwide for CEN national Members.
prEN 13848-2:2018 (E)

Contents Page

European foreword....................................................................................................................................................... 4
1 Scope .................................................................................................................................................................... 5
2 Normative references .................................................................................................................................... 5
3 Terms and definitions ................................................................................................................................... 5
4 Symbols and abbreviations ......................................................................................................................... 7
5 Track geometry recording system ............................................................................................................ 8
5.1 General description ........................................................................................................................................ 8
5.2 Environmental conditions ........................................................................................................................... 9
5.2.1 Introduction ...................................................................................................................................................... 9
5.2.2 Climatic conditions ......................................................................................................................................... 9
5.2.3 Operating conditions ..................................................................................................................................... 9
5.3 Track features input ................................................................................................................................... 10
5.4 Localization device ...................................................................................................................................... 10
5.5 Measuring devices ....................................................................................................................................... 11
5.5.1 General ............................................................................................................................................................. 11
5.5.2 Sensors ............................................................................................................................................................. 11
5.5.3 Signal transmission ..................................................................................................................................... 11
5.6 Resolution ....................................................................................................................................................... 11
5.7 Signal processing .......................................................................................................................................... 11
5.8 Data processing and analysis ................................................................................................................... 12
5.8.1 General requirements ................................................................................................................................ 12
5.8.2 Parameter generation ................................................................................................................................ 12
5.8.3 Data merging.................................................................................................................................................. 12
5.8.4 Parameter analysis ...................................................................................................................................... 12
5.8.5 Preparation for output interfaces .......................................................................................................... 12
5.9 Data presentation and storage ................................................................................................................ 12
5.9.1 Operator- interfaces.................................................................................................................................... 12
5.9.2 User-interfaces .............................................................................................................................................. 13
5.9.3 Output of analysis results.......................................................................................................................... 13
5.9.4 Data transmission ........................................................................................................................................ 13
5.9.5 Data storage ................................................................................................................................................... 13
6 Testing of track geometry recording system ..................................................................................... 13
6.1 Introduction ................................................................................................................................................... 13
6.2 Calibration ...................................................................................................................................................... 14
6.3 Validation ........................................................................................................................................................ 14
6.3.1 Overview ......................................................................................................................................................... 14
6.3.2 Static tests ....................................................................................................................................................... 14
6.3.3 Dynamic tests ................................................................................................................................................ 14
6.3.4 Methodology and frequency of the validation tests ........................................................................ 17
6.3.5 Verification of measuring runs (during operation)......................................................................... 24
Annex A (informative) Frequency analysis...................................................................................................... 25
A.1 General description ..................................................................................................................................... 25

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A.1.1 Transfer function .......................................................................................................................................... 25

A.1.2 Coherence function ...................................................................................................................................... 26
A.1.3 Power Spectral Density (PSD) .................................................................................................................. 26
A.2 Practical calculation .................................................................................................................................... 26
A.3 Applications within this standard .......................................................................................................... 27
A.3.1 Comparison between two runs ................................................................................................................ 27
A.3.1.1 Transfer and coherence functions.......................................................................................................... 27
A.3.1.2 PSD ..................................................................................................................................................................... 28
A.3.2 Cross check...................................................................................................................................................... 28
Annex B (informative) Principles of measurement....................................................................................... 30
B.1 General description ..................................................................................................................................... 30
B.2 Longitudinal level and alignment ........................................................................................................... 30
B.2.1 Chord measuring system ........................................................................................................................... 30
B.2.2 Inertial measuring system......................................................................................................................... 30
B.3 Track gauge..................................................................................................................................................... 30
B.4 Cant .................................................................................................................................................................... 31
B.5 Twist .................................................................................................................................................................. 31
Annex C (normative) Description of field tests: values to be respected ................................................ 32
C.1 General ............................................................................................................................................................. 32
C.2 Repeatability .................................................................................................................................................. 32
C.2.1 Statistical analysis of parameter data ................................................................................................... 32
C.2.2 Frequency analysis....................................................................................................................................... 33
C.3 Reproducibility.............................................................................................................................................. 34
C.3.1 Statistical analysis of parameter data ................................................................................................... 34
C.3.2 Frequency analysis....................................................................................................................................... 34
C.4 Cross check...................................................................................................................................................... 35
C.4.1 General ............................................................................................................................................................. 35
C.4.2 Transfer function .......................................................................................................................................... 35
C.4.3 Coherence function ...................................................................................................................................... 36
Annex D (informative) Track geometry measurement uncertainty ....................................................... 37
D.1 General ............................................................................................................................................................. 37
D.2 Evaluating uncertainty for track geometry measurement systems ........................................... 39
D.3 Measurement uncertainty: limit values ............................................................................................... 41
Annex E (informative) Cross checks in the space domain .......................................................................... 43
Bibliography ................................................................................................................................................................. 44

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European foreword

This document (prEN 13848-2:2018) has been prepared by Technical Committee CEN/TC 256 “Railway
applications”, the secretariat of which is held by DIN.

This document is currently submitted to the CEN Enquiry.

This document will supersede EN 13848-2:2006.

This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association.

This European Standard is one of the series EN 13848 “Railway applications — Track — Track geometry
quality” as listed below:

— Part 1: Characterization of track geometry;

— Part 2: Measuring systems — Track recording vehicles;

— Part 3: Measuring systems — Track construction and maintenance machines;

— Part 4: Measuring systems — Manual and lightweight devices;

— Part 5: Geometric quality levels — Plain line, switches and crossings;

— Part 6: Characterization of track geometry quality.

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1 Scope
This document specifies the minimum requirements for track geometry measuring principles and
systems in order to produce comparable results when measuring the same track. It applies to all
measuring systems, attended or unattended, fitted on any vehicle, except those systems defined in
EN 13848-3 and EN 13848-4. Only systems put into service after the standard comes into force are
concerned.
This document doesn't define the requirements for vehicle acceptance.
This document does not apply to measuring systems dedicated to Urban Rail Systems.

2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
EN 13848-1, Railway applications — Track — Track geometry quality — Part 1: Characterisation of track
geometry

EN 13848-6, Railway applications - Track - Track geometry quality - Part 6: Characterisation of track
geometry quality

JCGM 200:2012 International vocabulary of metrology – Basic and general concepts and associated terms
(VIM)

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/

— ISO Online browsing platform: available at http://www.iso.org/obp

3.1
track geometry recording vehicle
self-propelled or hauled vehicle with fixed, dedicated, measuring equipment and systems, used for the
measurement, assessment and recording of track geometry parameters under loaded conditions, which
measures and produces consistent results to the requirements of EN 13848-1

Note 1 to entry: The measuring system can be attended or not. The track geometry recording vehicle belongs to
the infrastructure inspection vehicles as defined in TSI Loc&Pas 1302/2014/EU.

3.2
sensor
device which detects, measures and translates characteristics of track geometry into quantities that can
be used for further data processing

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3.3
repeatability
degree of agreement between the values of successive measurements of the same parameter made
under the same conditions (speed, direction of measurement), where the individual measurements are
carried out on the same section of track subject to the following controls:

— same measurement method;

— same vehicle orientation;

— same method of interpretation;

— similar environmental conditions;

— short period of time between successive runs

3.4
reproducibility
degree of agreement between the values of successive measurements of the same parameter made
under varying conditions, where the individual measurements are carried out on the same section of
track using the same measurement and interpretation methods, subject to one or more of the following:

— variation of speed;

— different directions of measurement;

— different vehicle orientations;

— different environmental conditions;

— short period of time between successive runs

3.5
comparability
degree of agreement of different track recording vehicles achieved under the same conditions

3.6
validation
set of tests for determining if a track recording vehicle complies with the requirements of this standard

3.7
calibration
set of procedures for adjusting the measuring devices of track measuring systems in order to meet the
requirements of this standard as defined in JCGM 200:2012

3.8
event
record of a track or line-side feature that can be either technical, physical or natural

3.9
localisation
information required to locate events and the measured track geometry

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3.10
reference track
track with known characteristics necessary to allow adequate testing of the track geometry recording
system

3.11
unattended geometry measuring system (UGMS)
track geometry measuring system fitted on a vehicle, without any human interaction during the
measurements

3.12
adjustment of a measuring system
set of operations carried out on a measuring system so that it provides prescribed indications
corresponding to given values of a quantity to be measured (VIM- International vocabulary of
metrology JCGM 200:2012)

3.13
cross check
method for comparing signals of a single run for linked parameters (e.g. longitudinal level of each rail
vs. cross level or alignment of each rail vs. gauge) obtained from different inputs (e.g. devices or signal
processing)

4 Symbols and abbreviations

For the purposes of this document, the following symbols and abbreviations apply.
Table 1 — Symbols and abbreviations

No. Symbol Designation Unit

1 D1 Wavelength range 3 m < λ ≤ 25 m m
2 D2 Wavelength range 25 m < λ ≤ 70 m m
Wavelength range 70 m < λ ≤ 150 m for longitudinal level
3 D3 m
Wavelength range 70 m < λ ≤ 200 m for alignment
4 λ Wavelength m
5 Vmax Maximum possible measuring speed of a recording system km/h
6 Vmin Minimum possible measuring speed of a recording system km/h

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5 Track geometry recording system

5.1 General description

For the purpose of this standard, the track geometry recording system is divided into several units as
represented in Figure 1 below:

Figure 1 — Track geometry recording system

When measuring the same track, track geometry recording systems shall produce results that are
consistent and comparable, irrespective of the measuring speed and direction of travel. These results
can be used for track quality monitoring, maintenance planning and safety assurance as related to track
geometry.
The track geometry recording system represents the totality of the equipment required to:
— measure track geometry parameters;

— take measurement or information to allow the position to be determined during measuring

operations;

— associate these two measurements in order to locate precisely on the track the values exceeding a
prescribed threshold or other elements characterizing the track;

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— record these parameters on computer readable media;

— calculate, based on the direct measured parameters, other parameters of the track geometry (e.g.
twist, curvature);

— process the measured data, in order to analyse the track geometry parameters;

— present and store the results.

The output of the track geometry recording system shall meet the individual parameter requirements of
EN 13848-1. All the data necessary to determine the parameters specified in EN 13848-1 shall be taken
and stored during the run. The determined parameters should be graphically displayed and analysed in
strict relation to the corresponding distance location.
The track geometry recording system shall be monitored and shall allow track geometrical
measurements as specified in EN 13848-1 under loaded conditions of the track.
The computer system shall be of a kind and type suitable for railway vehicle bound applications.
To prevent the interruption of the track geometry measurement and the loss of recorded data in case
the measuring hardware power supply fails, an adequate uninterruptible power supply should be
provided.
5.2 Environmental conditions
5.2.1 Introduction

All the measuring devices and hardware components fitted on a track-recording vehicle shall comply
with the environmental conditions specified below.
5.2.2 Climatic conditions

For outside and inside components the following elements shall be respectively considered:
— Outside components

— ambient temperature;

— condensation, particularly with sudden variation of temperature at the entrance or at the exit
of a tunnel;

— possibility of extreme weather conditions (heavy rain, snow, direct sunlight, …);

— ambient relative humidity.

— Inside components

— ambient temperature for operating and storage conditions;

— ambient relative humidity.

5.2.3 Operating conditions

The following elements shall be considered:

— ballast or iron fragments impacts;

— grease on the rail;

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— reflection condition of the rail;

— characteristic light conditions;

— dust, water and snow in connection with aerodynamic conditions;

— safety requirements (laser beam, for example);

— vibrations and shocks;

— electromagnetic environment;

— compatibility with signalling and communication systems.

5.3 Track features input

The track features input supports the data analysis (see 5.8) and shall include at least:
— set of limit values of track geometry parameters as defined in EN 13848-5;

— line speed.

Other inputs may be beneficial as, for example:

— geo-spatial positioning;

— line side features such as switches, level crossings, bridges, tunnels;

— track components and track alignment design parameters.

All this data should be able to be entered by manual or automatic means.

5.4 Localization device

The reference point for the data localization system may be the kilometre post or other fixed points.
The localization device gives the track recording vehicle’s position along the track and shall fulfil the
following functions:
— synchronises the position with the reference point by various methods, using for example the
satellite based positioning system, active or passive beacons, track layout or other singular points;

— measures the distance covered by the track recording vehicle, compensated for direction “reverse”,
and is generally based on a synchronisation signal, which could be given by a wheel-mounted
encoder or any other equivalent method;

— corrects manually or automatically the inaccuracies caused by:

— wear, sliding, conicity of the track recording vehicle wheels;

— difference of kilometre’s length;

— uncertainty of the distance run transducer.

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5.5 Measuring devices

5.5.1 General

Track geometry measuring system relies on sensors, signal transmission and signal processing
following various measuring principles as described in Annex B.
The speed range shall be from standstill to the maximum permissible measuring speed of the vehicle if a
chord-type measuring system is used; if an inertial-type measurement is used, a minimum speed may
be necessary to measure some parameters. The minimum speed should be specified according to the
characteristics of the used system and the needs defined by the infrastructure manager (e.g. for
conventional inertial-type measurement systems usually 10 km/h is necessary for the wavelength
range D1).
5.5.2 Sensors

The sensors shall measure in real time the track geometry parameters or their components. In order to
measure the parameters under track loaded conditions, the sensors placed under the vehicle’s frame
shall be as close as possible to one of the vehicle’s loaded axles to respect measurement conditions
indicated in EN 13848-1. The sensors can be either contact type or non-contact type sensors.
The sensors’ mechanical and electrical characteristics (frequency response, signal-to-noise ratio, gain,
etc.) shall be adequate to enable the generation of track geometry parameters, independently of the
environmental conditions on the railway network.
5.5.3 Signal transmission

Signal transmission comprises of all components which are necessary for data interchange between the
sensors and the signal processing unit.
It shall at least comply with the following requirements:
— no phase shift;

— no distortion of results data;

— compliance with appropriate industry-accepted data interchange standards.

The transmission characteristics shall be appropriate to the maximum measuring speed of the track
recording vehicle and the data volume.
5.6 Resolution

The resolution shall be ≤ 0,1 mm for every measured principal track geometric parameter, as defined in
EN 13848-1.
5.7 Signal processing

Signal processing provides the data for some of the track geometry parameters compliant with
EN 13848-1 using signals coming from several sensors. The remaining parameters are calculated from
the output of the signal processing e.g. twist.
The signal processing shall respect the following points:
— sampling: all measurements shall be sampled at equally spaced intervals of preferably 0,25 m or
less but not larger than 0,5 m;

— decolouring: in case of chord measurements the signal shall be decoloured according to

EN 13848-1;

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— filtering: the filter characteristics for the wavelength ranges shall be compliant with EN 13848-1
and shall be described. To prevent aliasing of the data the analogue signal shall be filtered in
accordance with the sampling theorem.

5.8 Data processing and analysis

5.8.1 General requirements

The software shall be flexible and modular in order to facilitate modifications, for example filter
implementations or output formats.
An increase in the number of input signals as well as of the number of calculations made shall be
foreseen in the system design.
5.8.2 Parameter generation

The output of signal processing in 5.7 is used to generate all the track parameters as defined in
EN 13848-1.
5.8.3 Data merging

In order to assess the track geometry quality, the track parameters shall be synchronised with track
localization and track features.
5.8.4 Parameter analysis

The track geometry parameters defined in EN 13848-1 are analysed for the quality levels and safety
related limits defined in EN 13848-5.
5.8.5 Preparation for output interfaces

The data processing system shall condition signals and associated information for different outputs:
— data storage;

— parameters visualization;

— track geometry chart;

— threshold exceeding values;

— standard deviation and mean values;

— calibration;

— online plausibility check.

5.9 Data presentation and storage

5.9.1 Operator- interfaces

In order to allow the operator monitoring the track geometry recording system an interface shall be
provided with the following characteristics:
— access to the system configuration parameters e.g. filter coefficients, calibration settings;

— access to all diagnostic information of the measuring system (e.g. laser temperature, raw data,
sensor voltage) in order to detect and analyse malfunctions.

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5.9.2 User-interfaces

The users of the measured data, e.g. permanent way engineers, are more particularly interested in the
track geometry condition.
As a minimum the user interface shall comprise of in graphical and/or text format:
— track geometry parameters;

— threshold values;

— localization data;

— track features.

5.9.3 Output of analysis results

Outputs shall be provided in accordance with requirements stated in EN 13848-1 and 5.8.5 above.
5.9.4 Data transmission

The data shall be transferable using removable storage media, a network or radio link complying with
an industry standard.
5.9.5 Data storage

As a minimum, the following data shall be stored in a prescribed retrievable format:

— measured parameters as described in EN 13848-1;

— results of the parameters analysis described above, including settings, if processing is done on
board;

— localization information linked to measured parameters;

— date and time of the measuring run;

— identification of the measuring vehicle;

— user remarks and actions;

— information of measurement validity.

6 Testing of track geometry recording system

6.1 Introduction

This clause covers actions and procedures, which are necessary to ensure effective operation of both
the measuring devices and the corresponding processing system:
a) Calibration

This ensures an accurate setting of the devices within the track geometry recording system.

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b) Validation and adjustment

This demonstrates that the whole system complies with the requirements needed to operate
correctly. Also this ensures that the system continues to operate correctly during routine
operations.

6.2 Calibration

The measuring device shall be calibrated to ensure the continued accuracy of measurements. The
calibration is performed according to a specified process. It shall be carried out by appointment by the
manufacturer or the user.
NOTE Usually the calibration is made before the delivery of the measuring system.

6.3 Validation
6.3.1 Overview

After the calibration of the track geometry recording system, a method based on comparison between
different measurement runs on the same section of track shall be used to validate the recording system.
Validation procedures shall be applied to the following:
— initial testing of a new or modified track geometry recording system;

— after a maintenance or repair operation on the track geometry recording system;

— on regular basis.

Additionally, simplified validation can be applied during normal operation.

There are three kinds of validation:
— static tests (see 6.3.2);

— dynamic tests (see 6.3.3);

— in operation (see 6.3.5).

6.3.2 Static tests

Static tests concern mainly track gauge and cross level measurements. This consists of comparing the
measured value with a defined reference.
6.3.3 Dynamic tests

6.3.3.1 Overview

Dynamic tests concern all track geometry parameters according to EN 13848-1. This consists of
comparing the measured values of consecutive measurement runs performed under identical or
varying measurement conditions. For linked parameters, cross checks are also applicable.
6.3.3.2 Measurement conditions for validation

The track geometry recording system shall meet the requirements of EN 13848-1 in all the following
test conditions:
— normal operation of the recording vehicle as specified by the manufacturer;

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— various measuring speeds which shall include at least the minimum and maximum possible
measuring speeds;

— both measuring directions;

— both measuring orientations of the vehicle.

NOTE 1 In some networks the use of measurement vehicles is restricted to limited combinations of measuring
direction and orientation. For these networks only these combinations are considered for the validation.

NOTE 2 The maximum measuring speed is limited by the measuring system, the vehicle, the line speed and any
conditions defined by the network.

If possible also the measurement conditions as stated in 5.2 should be tested.

6.3.3.3 Track conditions for validation

For use on conventional lines, the track geometry recording system shall be tested over a wide range of
track design features: curves of various radii and directions, significant cant, frequent alternation of
curves and straight lines etc.
The track geometric quality should preferably include standard deviations ranging from class A to class
C as defined in EN 13848-6 for speed range from 120 to 160 km/h.
Due to the risk of high dynamic track responses, specific track sections may be excluded from the
validation as for example:
— class E quality sections for the same speed range;

— track sections that do not conform to plain line (e.g. sidings, switches and crossings…);

— track sections that include degraded components such as loose fasteners.

The total length of the test sections used for validation should not be less than 5 km (typical length:
10 km). For speeds lower than or equal to 40 km/h a shorter total length of the test sections e.g. 1 km
may be used.
A reference track may be used to ensure a better comparability between systems and over time.
Data defining the characteristics, such as curve radii, and geometric quality of the track used for the test
runs shall be provided with the test report.
6.3.3.4 Comparison of different runs

6.3.3.4.1 Overview

Two types of analysis can be carried out:

— comparison of runs of the same recording system;

— comparison of runs to track geometry data obtained by another recording system.

The statistical analysis of parameter data shall be used to compare recording runs (see 6.3.3.4.3).
The frequency analysis should be used (see 6.3.3.4.4).
Additionally, the uncertainty analysis can be performed (see 6.3.3.4.5).

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6.3.3.4.2 Synchronisation

To get reliable results when comparing parameters, data synchronisation is necessary. Because of the
effects of drift on the measured distance, this drift should be computed and compensated on short
sections of e.g. 200 m length by shifting the signal. All track geometry parameters shall be compensated
by applying the same shift.
Other treatments such as resampling or interpolation may be performed.
6.3.3.4.3 Statistical analysis of parameter data

The calculation shall be made for each parameter to be validated and for each pair of runs used for the
comparison. It consists of the following steps:
— calculation of the differences between the values;

— evaluation of the distribution of the differences for the total length of the test sections;

— calculation of the 95th percentile of the distribution of the absolute differences.

6.3.3.4.4 Frequency analysis of parameter data

Another way to compare two runs is to use frequency analysis such as transfer and coherence functions.
A brief description of these functions is given in Annex A.
With this method it is possible to check the similarity in frequency domain of two measurements of the
same track section. When applying this method a total length of the test sections of at least 5 km should
be used.
The transfer function indicates the distortions existing in frequency domain, and the coherence
function, the degree of reliability for the calculation made on transfer function.
The modulus of the transfer function should be as close as possible to unity and the phase as close as
possible to zero for the wavelength ranges specified in EN 13848-1.
The fixed relationship between the sample size and the wavelength range (D1, D2, D3) in which the
frequency analysis is made should be considered to determine the minimum length of the test section
(see Annex A).
6.3.3.4.5 Uncertainty analysis

The estimation of measurement uncertainty can be used to evaluate the quality of the measurement
system and to determine if the measurement process is fit for its intended use.
A suitable method and limit values for measurement uncertainty are proposed in Annex D.
6.3.3.5 Cross check

Cross checks can be performed in the frequency and in the space domain.
A method for the frequency domain is described in A.3.2 and the results shall comply with the limit
values given in C.4.
A method for the space domain is described in Annex E. Limit values are still an open point due to the
lack of experience.

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6.3.4 Methodology and frequency of the validation tests

6.3.4.1 Overview

Depending on the circumstances different validation tests shall be carried out. They are described in the
following sections.
6.3.4.2 Validation of a new system

6.3.4.2.1 Introduction

This validation is part of the acceptance test of a new measurement system. This also applies to totally
refurbished measuring systems or modifications of the vehicle which have a relevant effect on the
measurement principle e.g. bogie replacement.
The validation of a new measurement system consists of one of the following mandatory tests:
— reference method: full comparison of runs of the same vehicle (see 6.3.4.2.2);

— alternative method: partial comparison of runs of the same vehicle and comparison of runs to track
geometry data obtained by a validated reference measurement system (see 6.3.4.2.3).

Additionally, cross checks shall be applied (see 6.3.3.5).

6.3.4.2.2 Reference method

This method is based on comparisons of runs for the same vehicle. It is the preferred method for track
recording cars.
For each different test configuration (see 6.3.3.2) a run has to be made over a predefined track which
fulfils all the requirements in 6.3.3.3.
For all configurations two types of tests shall be carried out:
— repeatability;

— reproducibility.

Additionally, an uncertainty computation should be carried out (see Annex D).

New system tests shall comply with the requirements of Annex C.
For repeatability and reproducibility, the minimum combination of runs and analyses shown in Tables 2
and 3 shall be carried out. For measuring systems able to measure down to standstill, the runs at
minimum speed Vmin are replaced with runs at low speed (at least 5 km/h) containing stops.
The comparison of the runs stated in Table 3 shall be done by applying the comparison methods stated
in 6.3.3.4.2 to 6.3.3.4.4 for every configuration pair separately. Each individual result is compared with
the limit values given in Annex C.
If the maximum measuring speed is ≤ 160 km/h the speeds V1 and V2 are defined as:
— V1 = Vmin and V2 = Vmax.

If the geometry recording system is capable to measure at speed above 160 km/h the Tables 2 and 3
shall be applied twice:
— case 1: on a line with line speed V ≤ 160 km/h: V1 = Vmin and V2 = Vline;

— case 2: secondly on a line which allows maximum measurement speed: V1 = V2 (case 1) and
V2 = Vmax.

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Table 2 — Required test conditions

Condition number Speed Direction Vehicle orientation

1a V1 A- > B

1b V1 A- > B

2a V2 A- > B

2b V2 A- > B

3a V1 B- > A

3b V1 B- > A

4a V2 B- > A

4b V2 B- > A

5a V1 B- > A

5b V1 B- > A

6a V2 B- > A

6b V2 B- > A

7a V1 A- > B

7b V1 A- > B

8a V2 A- > B

8b V2 A- > B
NOTE 1 For Vmin lower than or equal to 40 km/h shorter test sections e.g. 1 km can be used.
NOTE 2 The run numbers 5a/b to 8a/b are only required if the recording vehicle is capable of
measuring in both orientations.

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Table 3 — Required comparisons

Recording vehicle with

Recording vehicle with 2
Type of analysis 1 measuring
measuring orientations
orientation
Repeatability 1a and 1b 1a and 1b
2a and 2b 2a and 2b
3a and 3b 3a and 3b
4a and 4b 4a and 4b
5a and 5b
6a and 6b
7a and 7b
8a and 8b
Reproducibility 1 and 2 1 and 2
1 and 3 1 and 3
1 and 4 1 and 4
2 and 3 1 and 5
2 and 4 1 and 6
3 and 4 1 and 7
1 and 8
2 and 3
2 and 4
2 and 5
2 and 6
2 and 7
2 and 8
3 and 4
3 and 5
3 and 6
3 and 7
3 and 8
4 and 5
4 and 6
4 and 7
4 and 8
5 and 6
5 and 7
5 and 8
6 and 7
6 and 8
7 and 8
NOTE 1 The run numbers without a letter means either run “a” or run “b”.
NOTE 2 The run numbers 5 to 8 are only required if the recording vehicle is capable of
measuring in both orientations.

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An example for a practical realization of the test runs for a recording vehicle capable of measuring in
both orientations is shown in Figure 2. This procedure should be repeated on different line categories in
order to cover all track conditions for validation (see 6.3.3.3).

a)

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 prEN 13848-2:2018 (E)

b)

c)

Figure 2 — Example for a practical realization of the test runs

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For the determination of the measurement uncertainty according to Annex D additional measuring runs
are necessary.
6.3.4.2.3 Alternative Method

In case where the reference method is not applicable (e.g. for unattended measuring systems mounted
on commercial trains) the following procedure can be used for validation of a track geometry recording
system. This method shall consist of two steps:
— repeatability test; and

— comparison with a reference system (validated according to 6.3.4.2.2).

The repeatability test is carried out by pairwise comparisons of runs within a narrow time span (in
order to avoid the effects of track deterioration). The test shall cover the whole range of operational
conditions according to the intended usage of the track geometry recording system. The track sections
shall meet the requirements described in 6.3.3.3. The comparison of the runs shall be done by applying
the comparison methods stated in 6.3.3.4.2 to 6.3.3.4.4 for every configuration pair separately. Each
individual result shall comply with the limit values for repeatability given in C.2.
In order to replace the reproducibility test of the reference method, the measuring results used in the
repeatability test shall be compared with measuring results of a fully validated reference measuring
system (reference signals). The comparisons shall be carried out for all track sections of the
repeatability test by calculating the mean of pairwise measuring signals of the tested system and
comparing them with the reference signals according to the methods described in 6.3.3.4.2 to 6.3.3.4.4.
Each individual result should comply with the limit values for reproducibility given in C.3. In order to
improve the reliability of the reference signal averaging of multiple runs can be used.
NOTE Due to the lack of experience no limit values for the comparison with the reference system are
provided as requirement.

In order to identify possible offsets due to different measuring conditions an additional analysis shall be
performed. This shall be done by computing the distributions of the differences between the mean
measurement signals and the reference signals according to 6.3.3.4.3. The distributions shall be
compared separately for different running configurations (e.g. low and high speed, forward and reverse
orientations) in order to determinate possible offsets.
Measuring systems validated by this alternative method shall not be used as a reference system for
validation of other track geometry recording systems.
6.3.4.3 Simplified validation

A simplified validation shall be carried out in accordance with the manufacturer’s maintenance manual
in the following circumstances:
— after a maintenance or repair operation which may affect the measuring system, e.g. sensor
replacement;

— at least once a year.

The simplified validation consists of a comparison of runs of the same vehicle.

If possible, a comparison with a validated reference measuring system is recommended.
For repeatability and reproducibility, the minimum combination of runs and analyses shown in Tables 4
and 5 shall be carried out. The comparison of the runs stated in Table 7 shall be done according to
6.3.3.4.

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 prEN 13848-2:2018 (E)

In addition, static tests shall be carried out for example to ensure that there are no offsets in the
measurement of cross level and track gauge.
If the maximum measuring speed is ≤ 160 km/h the speeds V1 and V2 are defined as:
— V1 = Vmin and V2 = Vmax.

If the geometry recording system is capable to measure at speed above 160 km/h the Tables 4 and 5
shall be applied twice:
— case 1: on a line with line speed V ≤ 160 km/h: V1 = Vmin and V2 = Vline;

— case 2: secondly on a line which allows maximum measurement speed: V1 = V2 (case 1) and
V2 = Vmax.

Table 4 — Required test conditions

Condition number Speed Direction Orientation

1a V1 A- > B

1b V1 A- > B

2a V2 A- > B

2b V2 A- > B

3 V1 B- > A

4 V2 B- > A

5 V1 B- > A

6 V2 B- > A

NOTE 1 For Vmin lower than or equal to 40 km/h shorter test sections e.g. 1 km can be used.
NOTE 2 The run numbers 5 and 6 are only required if the recording vehicle is capable of measuring in
both orientations.

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Table 5 — Required comparisons

Type of analysis Recording vehicle with Recording vehicle with 2

1 measuring measuring orientations
orientation
Repeatability 1a and 1b 1a and 1b
2a and 2b 2a and 2b
Reproducibility 1a and 4, 2a and 4, 2a 1a and 4, 2a and 4, 2a and 3, 1b and
and 3, 1b and 4, 2b and 4, 4, 2b and 4, 2b and 3, 1b and 6, 2b
2b and 3 and 6, 2b and 5, 2a and 5
NOTE The run numbers 5 and 6 are only required if the recording vehicle is capable of
measuring in both orientations.
If a validated reference measuring system is used any of the run given in Table 6 can be used for the
comparisons.
6.3.5 Verification of measuring runs (during operation)

6.3.5.1 Introduction

Periodic checking shall be carried out by the operators in accordance with the procedures described by
the manufacturer in the operator manual.
They can consist of cross checks, adjustment operations and/or comparison with historical data.
6.3.5.2 Comparison of different measurement systems on the same vehicle

Some parameters are linked, for example, alignment of each rail and the gauge, or longitudinal level of
each rail and the cross level. When two linked parameters are detected by a separate set of measuring
devices, malfunctioning devices can be found by comparison of the two signals.
6.3.5.3 Adjustment

Adjustment can be applied to some parameters after dynamic or static validation tests. In order to keep
the consistency of the measurements, they should be made before a run. For example, it can consist in
setting a new offset for track gauge before a run when a recent static test has shown this necessity.
In specific cases (e.g. when there is a noticeable variation of a parameter or a sensor), adjustment can
be made during a run. In such a case, the corresponding modification has to be mentioned in the run log
in order to easily identify the data measured before the adjustment from those measured after.
6.3.5.4 Comparison with historical data

Historical data can be used to identify measurement errors, e.g. offsets. For this comparison a track
which is not likely to change over time, e.g. slab track, should be used. Attention should be paid to track
works which affect the track geometry.

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Annex A
(informative)

Frequency analysis

A.1 General description

A.1.1 Transfer function

A track recording vehicle gives a representation of the track geometry parameters modified by the
filters and the filtering effects of the track geometry recording system itself. These modifications are
dependent on the wavelength range of the considered parameter.
A transfer function H(ν) expresses in the frequency domain the distortions existing between an input
signal x and an output signal y of a system. It is defined by the following formula:
Y (ν ) = H (ν ) × X (ν )

or
H (ν ) = Y (ν ) / X (ν )

where:
ν is the spatial frequency (ν = 1/λ)
λ is the wavelength
X the Fourier transform of the input x
Y the Fourier transform of the output y
NOTE 1 In the following, lower case letters will represent the signal expressed as a function of distance ℓ, for
example: x(ℓ), y(ℓ), and capital letters will represent the Fourier transform expressed in spatial frequency domain
as a function of ν, for example: X(ν), Y(ν).

NOTE 2 In order to simplify the formulae, the variables ℓ or ν will be omitted.

The transfer function can also be expressed as follows:

X ×Y S xy
H= =
X×X S xx

where:
X� and‾Y represent the complex conjugates
Sxy is the cross-spectral density between x and y signals: S xy = X × Y
2
Sxx is spectral density of x: Sxx = X × X = X

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prEN 13848-2:2018 (E)

Figure A.1 — Transfer function

The transfer function consists of a real and an imaginary part. In practice, the transfer function is
characterized by its module, and its phase.
— The modulus gives the way in which the amplitude of the input is modified by the system, according
to frequency.

— The phase represents the delay and hence the way in which the shape of the input is modified,
according to frequency.

A.1.2 Coherence function

The coherence function Γ is the Fourier transform of the correlation function in the time domain. It
represents the degree of linearity between input and output, i.e. the degree of confidence in the result
obtained with the transfer function.
It can be represented by the following formula:
2
Sxy
Γ=
Sxx × Syy

where:
Sxy is the cross-spectral density
Sxx and Syy are respectively the spectral densities of x and y
The coherence function is always ≤ 1, and the nearer to unity it is, the more linear is the system.
In practice coherence between 0,85 and 1 could be considered as good. A lower value of coherence can
indicate problems:
— non linearity existence in measuring system;

— multiple inputs, e.g. noise, present in the signals.

A.1.3 Power Spectral Density (PSD)

The PSD gives the energy of the signal in relation to frequency for a given track geometry parameter
measured over a given track section (see EN 13848-6:2014).

A.2 Practical calculation

Considering two signals x and y, representing respectively the input and output of a system, the
practical calculation can be done as follows:
— calculation of spectral densities Sxx,i and Syy,i and cross-spectral densities Sxy,i for each section i;

NOTE The length of the tests sections is chosen according to the required sample size. See example below.

— averaging of the spectral densities Sxx,i and Syy,i giving Sxx and Syy;

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 prEN 13848-2:2018 (E)

— averaging of cross-spectral densities Sxy,i giving Sxy. Cross-spectral density has both real and
imaginary parts;

— calculation of transfer H and coherence functions Γ using the averaged density functions.

X ×Y S xy
H= =
X×X S xx

and
2
Sxy
Γ=
Sxx × Syy

Calculation:
— Splitting the track in at least 5 separate sections of 1000 m;

— Calculation of the Fourier Transform for every section and both test runs;

FFT Settings:

— Window Hanning;

— FFT Length = 4096;

— Normalize to mean square amplitude;

— Calculation of the spectral density for every section:

— Sxx = |X|^2 (Sxx is the spectral density of the first test run);

— Syy = |Y|^2 (Syy is the spectral density of the second test run);

— Sxy = X Y* (Sxy is the cross-spectral density);

— Averaging of the spectral densities Sxx, Syy and Sxy over all sections not including switches and
crossings.

A.3 Applications within this standard

A.3.1 Comparison between two runs

A.3.1.1 Transfer and coherence functions

This comparison can be made for one given parameter in the following cases:
— repeatability test;

— reproducibility test;

— comparison between two track geometry recording systems.

This latter case is more general, because the measuring transfer function can be different for the two
systems. It is described below.

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When a same track is measured twice by two systems the respective transfer functions H1 and H2 of
each system can be expressed as follows:
H 1 = Y1 / X and H 2 = Y2 / X Y1 and Y2 are respectively the output data coming from the 2
systems

The transfer function H between the data obtained with two successive runs is:
H = Y2 / Y1

Replacing Y1 and Y2 by the expression for H1 and H2, H becomes:

H = H 2 / H1

It represents the ratio between the transfer function H1 and H2 of each track geometry recording
system. So when a measurement is made twice on a same section with two different track geometry
recording systems, the transfer function between the outputs of each system (y1 and y2) can be
compared to the ratio of theoretical transfer function of each system.
This can be summarized as follows:

Figure A.2 — Comparison of two track geometry recording systems

For repeatability and reproducibility tests, the same vehicle is used, so H2 = H1 and the transfer function
H between the two runs has to be compared to 1. This allows assessing with the help of coherence the
frequency domain in which the repeatability or reproducibility is fulfilled.
A.3.1.2 PSD

The PSD can be used for a qualitative comparison of different measurements. It allows the identification
of frequencies where the results are different without requiring the precise synchronisation of the
signals.
A.3.2 Cross check

Track gauge and cross level are generally not modified by the track geometry recording system (the
transfer function is equal to 1 for all spatial frequencies). On the other hand, alignment and longitudinal
level are modified by the transfer function of the measuring systems.

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An evaluation of the theoretical transfer function can be made using as input one single signal, for
example track gauge or cross level, and as output a combination of signals representing the difference
of alignment of each rail or the difference of longitudinal level of each rail.
This corresponds, for track gauge and alignment, to the following expression:
H 1 = (YAL1 − YAL 2 ) / YG

where:
YAL1, YAL2: Fourier transform of the alignment of each rail
YG: Fourier transform of the track gauge
A similar calculation for the cross level leads to:
H 2 = (YLL1 − YLL 2 ) / YCL

where
YLL1, YLL2: Fourier transform of the longitudinal level of each rail
YCL: Fourier transform of the cross level
The calculated transfer function can be compared to the theoretical one in order to assess, with the help
of the coherence function, the spatial frequency domain where the measuring system is reliable.
NOTE PSDs can also provide useful information for cross check.

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Annex B
(informative)

Principles of measurement

B.1 General description

The principles of measurement of the parameters, described in EN 13848-1, are discussed below. Up to
now, two main principles can be considered:
— chord measuring system;

— inertial measuring system.

This applies to measurement of longitudinal level and alignment, which is described in B.2.
Measurement of other parameters is briefly described in B.3 to B.5.

B.2 Longitudinal level and alignment

B.2.1 Chord measuring system

The track geometry is taken from the offset measured at an intermediate point from a straight-line
chord.
The offset measurement needs in any case a reference, which can be given by the body of the vehicle, if
it is stiff enough, or, if not, by a compensation of its movement. In the latter case, the compensation can
be obtained by measuring the body behaviour in bending and twist relatively to an external and
absolute reference (e.g. laser beam).
The sensors can be of contact or non-contact type. Normally, contact measurement sensors use the
wheels in vertical direction, and specific sensors, like trolleys or rollers for lateral direction.
Considering the measurement itself, one main characteristic of the chord method is its complicated
transfer function. This can be corrected using analytical methods (see EN 13848-1, Annex A) in order to
comply with the requirements of EN 13848-1 in terms of wavelength ranges. However, this requires an
asymmetrical base to avoid zeros in particular wavelengths.
A chord measuring system does not require any minimum speed to be operated.
B.2.2 Inertial measuring system

The track geometry is taken from the position of the rail in vertical and lateral direction, relative to an
inertial reference, which may be provided by accelerometers and/or gyroscopes.
Depending on where the inertial system is mounted, e.g. vehicle body or bogie, additional sensors are
used to measure the distance between rails and the inertial reference system.
For inertial systems based solely on accelerometers, a minimum speed of measurement is necessary to
give reliable results. Additional methods can be used to reduce the minimum measuring speed and even
enable a temporary stop of the measurement vehicle.

B.3 Track gauge

Track gauge is measured either by use of mechanical sensors (trolleys or rollers) or non-contact
sensors (generally optical sensors) which may be fitted to a bogie or the vehicle body.

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B.4 Cant
Cant is normally measured using an inertial measuring system. Additional sensors may be necessary in
order to compensate for the motion of the inertial system relative to the rails.

B.5 Twist
Twist can be either derived from cant measurement or measured directly with contact or non-contact
type sensors.

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Annex C
(normative)

Description of field tests: values to be respected

C.1 General
In the following tables, values for wavelength ranges which are not used in the network are not
applicable.

C.2 Repeatability
C.2.1 Statistical analysis of parameter data

The distribution of the absolute difference between the parameter data obtained on each run shall be
evaluated for each parameter. The 95th percentile of the distribution shall respect the limit values given
in Tables C.1 to C.3.
Table C.1 — Limit values for repeatability — Longitudinal level and alignment — 95th percentile
Dimensions in millimetres
Wavelength range
Parameter
D1 D2 D3
Longitudinal level 0,5 1 3
Alignment 0,7 2 4

Table C.2 — Limit values for repeatability — Gauge and cross level — 95th percentile
Dimensions in millimetres
Parameter
Gauge 0,5
Cross level 1,5

Table C.3 — Limit values for repeatability — Twist — 95th percentile

Dimensions in millimetres/metre
Parameter ℓ ≤ 5,5 m 5,5 m < ℓ ≤ 20 m
Twist
0,7/ℓ 0,8/ℓ
direct measurement
Twist
1/ℓ 2/ℓ
computed from cross level

ℓ: Twist base-length
EXAMPLE For a base length of 10 m the limit value for a direct twist measurement is 0,08 mm/m giving a
difference of cant of 0,8 mm.

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C.2.2 Frequency analysis

The transfer and coherence functions obtained on two runs made under the same conditions should be
evaluated for each parameter. For the computation of transfer and coherence functions the method
described in Annex A or any other equivalent method should be used. If an equivalent method is used
then it should be described.
The values given in the following Tables (C.4 to C.6) represent the range of variation for the modulus of
the transfer function and for the coherence function (theoretically equal to one).
Table C.4 — Limit values for frequency analysis — Repeatability — Longitudinal level and
alignment

Wavelength range
Parameter Function
D1 D2 D3

Transfer function ±5 % ±7 % ±10 %

Longitudinal level
Coherence function > 0,97 > 0,95 > 0,90
Transfer function ±7 % ±10 % ±15 %
Alignment
Coherence function > 0,95 > 0,90 > 0,85
The choice of the reference signal may lead to slightly different results.
Table C.5 — Limit values for frequency analysis — Repeatability — Gauge and cross level

Parameter Function Tolerance

Transfer function ±5 %
Gauge
Coherence function > 0,95

Transfer function ±10 %

Cross level
Coherence function > 0,90

Table C.6 — Limit values for frequency analysis — Repeatability — Twist

Tolerance
Parameter Function
ℓ ≤ 5,5 m 5,5 m < ℓ ≤ 20 m
Twist Transfer function ±5 % ±5 %
direct measurement Coherence function > 0,97 > 0,97
Twist Transfer function ±5 % ±5 %
computed from cross
level Coherence function > 0,97 > 0,97
ℓ: Twist base-length

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C.3 Reproducibility
C.3.1 Statistical analysis of parameter data

The distribution of the absolute difference between parameter data obtained on each run shall be
evaluated for each parameter. The 95th percentile of the distribution shall respect the values given in
Tables C.7 to C.9.
Table C.7 — Limit values for reproducibility —Longitudinal level and alignment — 95th
percentile
Dimensions in millimetres
Wavelength range
Parameter
D1 D2 D3

Longitudinal level 0,8 2 5

Alignment 1,1 3 7

Table C.8 — Limit values for reproducibility —Gauge and cross level — 95th percentile
Dimensions in millimetres
Parameter
Gauge 1,5
Cross level 2,5
NOTE The reproducibility of the track gauge is especially sensitive to the vehicle track interaction which can
explain the difficulties reaching the above limit value in some cases.

Table C.9 — Limit values for reproducibility —Twist — 95th percentile

Dimensions in millimetres/metre
Parameter ℓ ≤ 5,5 m 5,5 m < ℓ ≤ 20 m
Twist
1/ℓ 1/ℓ
direct measurement
Twist
computed from cross 1,5/ℓ 3/ℓ
level
ℓ: Twist base-length
C.3.2 Frequency analysis

The transfer and coherence functions obtained on two runs made under varying conditions should be
evaluated for each parameter. For the computation of transfer and coherence functions the method
described in Annex A or any other equivalent method should be used. If an equivalent method is used
then it should be described.
The values given in the following Tables (C.10 to C.12) represent the possible range of variation for the
modulus of the transfer function and for the coherence function (theoretically equal to one).

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Table C.10 — Limit values for frequency analysis — Reproducibility — Longitudinal level and
alignment

Wavelength range
Parameter Function
D1 D2 D3
Transfer function ±7 % ±10 % ±15 %
Longitudinal level
Coherence function > 0,95 > 0,90 > 0,85
Transfer function ±10 % ±15 % ±20 %
Alignment
Coherence function > 0,90 > 0,85 > 0,80

Table C.11 — Limit values for frequency analysis — Reproducibility — Gauge and cross level

Parameter Function Tolerance

Transfer function ±10 %

Gauge
Coherence function > 0,90
Transfer function ±15 %
Cross level
Coherence function > 0,85

Table C.12 — Limit values for frequency analysis — Reproducibility — Twist

Tolerance
Parameter Function
ℓ ≤ 5,5 m 5,5 m < ℓ ≤ 20 m
Twist Transfer function ±7 % ±7 %
direct measurement Coherence function > 0,95 > 0,95
Twist Transfer function ±7 % ±7 %
computed from cross
level Coherence function > 0,95 > 0,95

ℓ: Twist base-length

C.4 Cross check

C.4.1 General

Limit values for the frequency domain are given below for the two following groups of parameters:
— difference of alignment and gauge;

— difference of longitudinal level and cross level.

C.4.2 Transfer function

The values given in the following table represent the accepted range of variation in comparison with the
modulus of the theoretical transfer function.

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Table C.13 — Cross check — Transfer function — Tolerances

Wavelength range
Parameter
D1 D2 D3

Gauge and difference

±0,05 ±0,07 ±0,10
of alignment
Cross level and
difference of ±0,05 ±0,07 ±0,10
longitudinal level
C.4.3 Coherence function

The values given in the following table represent the accepted minimum values for the coherence
function.
Table C.14 — Cross check — Coherence function — Tolerances

Wavelength range
Parameter
D1 D2 D3
Gauge and difference
> 0,97 > 0,95 > 0,90
of alignment
Cross level and
difference of > 0,97 > 0,95 > 0,90
longitudinal level

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 prEN 13848-2:2018 (E)

Annex D
(informative)

Track geometry measurement uncertainty

D.1 General
When reporting the result of a measurement, quantitative indication of the quality of the result should
be given to assess its reliability. Without such an indication, measurement results cannot be compared,
either among themselves or with reference values given in a specification or a standard.
According to EN ISO 10012:2003 “Measurement management systems - Requirement for measurement
processes and measuring equipment”, an effective measurement management system ensures that
measuring equipment and measurement processes are fit for their intended use.
An important part of the measurement management system is the metrological confirmation including
estimation of measurement uncertainty. The commonly used method for the estimation of
measurement uncertainty is described in the ISO/IEC Guide 98-3: 2008-09 (JCGM 100:2008):
Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (reissue of
GUM: 1995).
This informative annex gives a short introduction and an example of application to the track geometry
recording systems.
When estimating the uncertainty of a track geometry recording system, all relevant uncertainty sources
have to be included into the analysis.
As shown in Figure D.1 there are a lot of different uncertainty sources which may have an impact on the
measurement result.

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Figure D.1 — Influences to the measurement result

The track geometry measurement is mainly influenced by:

— the measurement system itself (including e.g. the calibration, the resolution, the bias, the
repeatability, system arrangement);

— the operation conditions (e.g. speed, running direction and vehicle orientation);

— the environmental conditions (e.g. weather, light, humidity);

— the measured object (e.g. track layout, track superstructure, track quality).

The uncertainty consists of several independent components (standard uncertainties) which can be
obtained:
— from a series of repeated independent observations and expressed as an experimental standard
deviation (category A); or

— by using available knowledge, e.g. previous measurement data, experience or general knowledge,
data generated during calibration etc. (category B).

The Combined Uncertainty UC is characterized by the numerical value obtained by applying the usual
method for the combination of variances. The Combined Uncertainty and its components are expressed
in the form of standard deviations.
The Expanded Uncertainty U is defined as a “quantity defining an interval about the result of a
measurement that may be expected to encompass a large fraction of the distribution of values that
could reasonably be attributed to the measurand” [JCGM 200:2012]. The Expanded Uncertainty is the
product of the Combined Uncertainty and a coverage factor. The value of the coverage factor is chosen
on the basis of the level of confidence required in the interval y-U to y+U, where y is a measured value.

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The coverage factor depends upon the type of probability distribution and on selected coverage
probability or level of confidence.
In the uncertainty budget the following information has to be documented:
— the method used to determine each standard uncertainty (Category A or B);

— the type of probability density functions of each uncertainty component;

— the combined uncertainty;

— the expanded uncertainty and the coverage factor used.

D.2 Evaluating uncertainty for track geometry measurement systems

The above method can be adapted to track geometry measurement systems. In the uncertainty budget
all known uncertainty components should be used. It is recommended to use reproducibility
component as a minimum.
An example of the uncertainty estimation and the resulting budget for the track gauge measurement is
given in Table D.1.

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Table D.1 — Track gauge measurement uncertainty budget with a coverage factor k = 2
(confidence level of 95 %)

Uncertainty Symbol Cate- Distribution Transfer Standard uncertainty US Gauge

component gory Coefficient [mm]
b and
limit value
a
1 Resolution uRes B Rectangular 1 uS = b * a / 2 0,003
b=
√3
a = 0,01
2 Uncertainty of uAD A Normal 1 n 0,008
∑ ( xi − x )
2
the adjustment =uS
device n − 1 i =1
3 Influence of the uUA A Normal 1 n 0,140
∑ ( xi − x )
2
user on the =uS
adjustment n − 1 i =1
4 Influence of the uTA B Rectangular
b=
1 b * L * α * ( t p − tm ) 0,120
temperature t √3 uS =
on the 2
adjustment a = 10 °C L: initial length, α:
thermal expansion
coefficient, tp: upper
temperature, tm: lower
temperature
5 Uncertainty of uRef A Normal 1 n 0,023
∑ ( xi − x )
2
reference =uS
standard n − 1 i =1
6 Abs. deviation uAbs A Normal 1 n 0,063
∑ ( xi − x )
2
between =uS
measurand and n − 1 i =1
reference
7 Reproducibility uR A Normal 1 n 0,228
∑ ( xi − x )
2
=uS
n − 1 i =1
8 Combined Uc = 2
uRes 2
+ u AD 2
+ uUA 2
+ uTA 2
+ uRef 2
+ u Abs + uR2 0,3
uncertainty
9 Expanded U = k ⋅U c 0,6
uncertainty
NOTE 1 For the values a and b refer to JCGM 200:2012.

NOTE 2 For this example independency of all uncertainty components is assumed.

In this example the Reproducibility (uR) covers different uncertainty sources, which may have an effect
on the measurement result: measured object, operation and environmental conditions.
The uncertainty estimation is based on in-field reproducibility analysis using a substantial number of
measuring runs (at least the number required for the reference method in 6.3.4.2.2 performed with the
same vehicle on the same representative track. The test conditions of the individual measuring runs

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have to be varied according to 6.3.3.2 and 6.3.3.3 in order to cover the whole range of practical
application of the track geometry recording vehicle.
After precise synchronisation of all measurement runs, the standard deviation across all runs is
computed at every sampling point along the track. The standard uncertainty of the reproducibility (uR)
is obtained from the mean value of all calculated standard deviations.
All uncertainty components quantified in Table D.1 are used to compute the Combined Uncertainty Uc.
The expanded uncertainty U is the product of the combined uncertainty uc and the coverage factor k. As
the distribution of the measured result is assumed to be normal, the coverage factor is chosen to be
k = 2 for a level of confidence of approximately 95 %.

D.3 Measurement uncertainty: limit values

The limit values for the expanded uncertainty with a coverage factor of k = 2 are given in Table D.2 for
each track geometry parameter. They are empirical and not correlated with the uncertainty estimation
method described in D.2.
Table D.2 — Limit values for the measurement uncertainty of the track geometry parameters

Measurement uncertainty [mm]

Track geometry Wavelength range

parameter D1 D2 D3
Track gauge ±1
Longitudinal level ±1 ±3 ±5
Cross level ±3
relative value (difference of successive cross level values) to be used for
the twist calculation ± 1
Twist (When twist is
expressed as a ratio this
±1,5
value shall be divided by
the base-length)
Alignment ±1,5 ±4 ±10
The experience shows that the uncertainty of current track recording systems in relation with the IAL
values given in EN 13848-5 is appropriately safe. Therefore, as a minimum recommendation, the
expanded uncertainty of new track geometry recording systems should at least respect the expanded
uncertainties of current systems computed according to the method in D.2.
The measurement uncertainty should be suitable to classify track geometry defects properly according
to the defined thresholds AL, IL and IAL. For example, in order to distinguish between these thresholds
the measurement uncertainty should not exceed 25 % of the minimum differences between AL and IL
as well as between IL and IAL values as shown in Figure D.2.

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Key
1 measured quantity e.g. Y
2 limit values e.g. IL (2a) and IAL (2b)
3 tolerance band (Δ between upper and lower limit value)
4 measured value y ± U
5 acceptable measurement uncertainty U
6 unacceptable measurement uncertainty U

Figure D.2 — Required measurement uncertainty as a function of the thresholds

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Annex E
(informative)

Cross checks in the space domain

For linked parameters (e.g. track gauge vs. alignment and cross level vs. longitudinal level) a cross check
method in space domain is described in the following example illustrated in Figure E.1.
EXAMPLE For track gauge vs. alignment, the cross check is done according to the following steps:

1) Filtering of track gauge with the same filter applied to the alignment;

2) Comparison between the filtered measured track gauge and the difference between the alignment
of the left and the right rail (calculated track gauge);

3) Compute the distribution of the differences between the calculated and the measured track gauge;

4) Compute the 95th percentile of the distribution.

Key
1 left alignment
2 right alignment
3 differences between measured and calculated track gauge
4 zero phase band pass filtering
5 measured track gauge

Figure E.1 — Cross check for track gauge vs. alignment

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Bibliography

[1] TSI Loc&Pas 1302/2014/EU, Locomotives and passenger rolling stock

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