# SIST EN 13036-5:2019

(Main)## Road and airfield surface characteristics - Test methods - Part 5: Determination of longitudinal unevenness indices

## Road and airfield surface characteristics - Test methods - Part 5: Determination of longitudinal unevenness indices

This European Standard specifies the mathematical processing of digitized longitudinal profile measurements to produce evenness indices. The document describes the calculation procedure for the International Roughness Index (IRI), Root Mean Square (RMS) and Longitudinal Profile Variance (LPV) from three separate wavelength bands and the σWLP and ΔWLP from the Weighted Longitudinal Profile (WLP).

The purpose of this document is to provide a standard practice for calculating and reporting estimates of road evenness from digitized longitudinal profiles. Other aims with the standard are to facilitate the comparison of evenness measurement results carried out with different profiling instruments in European countries.

The evenness range covered in this standard is defined as the wavelength range 0.5 m to 50 m. It should be noted that both shorter and longer wavelengths can also influence the driving comfort but those are not covered in this standard.

The quantified evenness indices derived from the standard are useful support for pavement management systems. The output can also be used for type approval and performance control of new and old pavements. The indices can be used on rigid, flexible and gravel road surfaces.

The standard doesn´t define from what position on the road the longitudinal profile should be obtained.

The derived indices are portable in the sense that they can be obtained from longitudinal profiles measured with a variety of instruments.

## Oberflächeneigenschaften von Straßen und Flugplätzen - Prüfverfahren - Teil 5: Bestimmung der Längsunebenheitindizes

Diese Europäische Norm legt die mathematische Verarbeitung von digitalisierten Längsprofilmessungen fest, um Ebenheitsindizes zu erstellen. Das Dokument beschreibt das Berechnungsverfahren für den Internationalen Rauigkeitsindex (IRI, en: International Roughness Index), quadratischer Mittelwert (RMS, en: Root Mean Square) und Varianz des Längsprofils (LPV, en: Longitudinal Profile Variance) von drei separaten Wellenbändern und σWLP und ΔWLP des Bewerteten Längsprofils (WLP, en: Weighted Longitudinal Profile).

Der Zweck des vorliegenden Dokuments besteht darin, ein Standardverfahren für die Berechnung und Berichterstattung von Schätzwerten der Straßenebenheit von digitalisierten Längsprofilen zu liefern. Weitere Ziele dieser Norm bestehen darin, den Vergleich der Ergebnisse von Ebenheitsmessungen, die mit verschiedenen Profilometern in europäischen Ländern durchgeführt wurden, zu ermöglichen.

Der in dieser Norm abgedeckte Ebenheitsbereich umfasst den festgelegten Wellenlängenbereich von 0,5 m bis 50 m. Es sollte beachtet werden, dass kürzere und längere Wellenlängen den Fahrkomfort beeinflussen können, jedoch in dieser Norm nicht abgedeckt sind.

Die nach dieser Norm abgeleiteten quantifizierten Ebenheitsindizes sind eine nützliche Unterstützung für Fahrbahnmanagementsysteme. Das Ergebnis kann auch für die Typprüfung und Leistungskontrolle von neuen und alten Fahrbahnbelägen genutzt werden. Die Indizes können auf starre, flexible und Schotterstraßenoberflächen angewendet werden.

Die Norm legt nicht fest, von welcher Stelle auf der Straße das Längsprofil erhalten werden sollte.

Die abgeleiteten Indizes sind in dem Sinne übertragbar, dass sie von Längsprofilen erhalten werden können, die mit verschiedenen Messgeräten gemessen wurden.

## Caractéristiques de surface des routes et aérodromes - Méthodes d’essais - Partie 5 : Détermination des indices d’uni longitudinal

Le présent document spécifie le traitement mathématique du mesurage des profils longitudinaux numérisés en vue de produire des indicateurs d’uni. Il décrit la procédure de calcul de l’indicateur d’uni international (IRI), de la moyenne quadratique (RMS) et de la variance du profil longitudinal (LPV) à partir de trois bandes de longueurs d’onde distinctes ainsi que le σWLP et le ΔWLP issus du profil longitudinal pondéré (WLP).

Le but du présent document est de normaliser la procédure de calcul et de consignation des évaluations de l’uni de la chaussée à partir des profils longitudinaux numérisés. Ce document vise également à faciliter la comparaison des résultats des mesurages d’uni réalisés avec des profilomètres différents dans les pays européens.

La plage d’uni couverte par le présent document est définie comme la plage de longueurs d’onde de 0,5 m à 50 m. Il est à noter que des longueurs d’onde plus courtes et plus longues peuvent également influencer le confort de conduite, mais celles-ci ne sont pas abordées par le présent document.

Les indicateurs d’uni quantifiés dérivés du présent document constituent une base utile pour les systèmes de gestion de la chaussée. Les produits peuvent également être utilisés pour l’homologation de type et le contrôle des performances des chaussées neuves et anciennes. Les indicateurs peuvent être utilisés sur des chaussées rigides, flexibles et gravillonneuses.

Le présent document ne définit pas la position sur la chaussée à partir de laquelle il convient d’obtenir le profil longitudinal.

Les indicateurs dérivés sont transférables dans le sens où ils peuvent être obtenus à partir de profils longitudinaux mesurés en utilisant une variété d’instruments.

## Značilnosti cestnih in letaliških površin - Preskusne metode - 5. del: Določanje indeksov vzdolžnih neravnin

Ta evropski standard določa matematično obdelavo digitaliziranih meritev vzdolžnega profila za izdelavo indeksov neravnin. Dokument opisuje postopek izračuna za mednarodni indeks hrapavosti (IRI), geometrično povprečje (RMS) in odstopanje vzdolžnega profila (LPV) iz treh ločenih pasov valovne dolžine ter σWLP in ΔWLP iz tehtanega vzdolžnega profila (WLP).

Namen tega dokumenta je zagotoviti standardno prakso za izračun in poročanje o neravninah cest iz digitaliziranih vzdolžnih profilov. Drugi cilji standarda so olajšanje primerjave rezultatov meritev neravnin, izvedenih z različnimi instrumenti za profiliranje v evropskih državah.

Obseg neravnine, zajet v tem standardu, je opredeljen kot območje valovne dolžine od 0,5 m do 50 m. Upoštevati je treba, da lahko na udobje vožnje vplivajo tako krajše kot daljše valovne dolžine, ki pa v tem standardu niso zajete.

Količinsko opredeljeni indeksi neravnin, izpeljani iz standarda, so koristna podpora za sisteme upravljanja pločnikov. Rezultat je mogoče uporabiti tudi za homologacijo in nadzor učinkovitosti novih ter starih pločnikov. Indekse je mogoče uporabiti na togih, prožnih in gramoznih cestnih površinah.

Standard ne določa, iz katerega položaja na cesti naj bi pridobili vzdolžni profil.

Izpeljani indeksi so prenosljivi, tako da jih je mogoče pridobiti iz vzdolžnih profilov, merjenih z različnimi instrumenti.

### General Information

### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN 13036-5:2019

01-november-2019

Značilnosti cestnih in letaliških površin - Preskusne metode - 5. del: Določanje

indeksov vzdolžnih neravnin

Road and airfield surface characteristics - Test methods - Part 5: Determination of

longitudinal unevenness indices

Oberflächeneigenschaften von Straßen und Flugplätzen - Prüfverfahren - Teil 5:

Bestimmung der Längsunebenheitindizes

Caractéristiques de surface des routes et aérodromes - Méthodes d’essais - Partie 5 :

Détermination des indices d’uni longitudinal

Ta slovenski standard je istoveten z: EN 13036-5:2019

ICS:

17.040.20 Lastnosti površin Properties of surfaces

93.080.10 Gradnja cest Road construction

93.120 Gradnja letališč Construction of airports

SIST EN 13036-5:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 13036-5:2019

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SIST EN 13036-5:2019

EN 13036-5

EUROPEAN STANDARD

NORME EUROPÉENNE

September 2019

EUROPÄISCHE NORM

ICS 17.040.20; 93.080.10

English Version

Road and airfield surface characteristics - Test methods -

Part 5: Determination of longitudinal unevenness indices

Caractéristiques de surface des routes et aérodromes - Oberflächeneigenschaften von Straßen und

Méthodes d'essais - Partie 5 : Détermination des Flugplätzen - Prüfverfahren - Teil 5: Bestimmung der

indices d'uni longitudinal Längsunebenheitindizes

This European Standard was approved by CEN on 21 July 2019.

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. Up-to-date lists and bibliographical references

concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN

member.

This European Standard exists 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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

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

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13036-5:2019 E

worldwide for CEN national Members.

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Contents Page

European foreword . 3

Introduction . 3

1 Scope . 5

2 Normative references . 5

3 Terms and definitions . 5

4 Symbols and abbreviations . 8

5 Calculation of evenness indices . 8

6 International Roughness Index (IRI) . 10

6.1 General . 10

6.2 Representation of the obtained results . 11

7 Wave band analysis . 11

7.1 General . 11

7.2 Wave band indices . 12

8 Weighted Longitudinal Profile (WLP) analysis . 12

8.1 General . 12

8.2 Prerequisites . 12

9 Reporting . 13

Annex A (normative) Calculation of the IRI . 14

Annex B (informative) Example code for IRI calculation . 18

Annex C (informative) Wave band analysis using bi-octave bands and RMS . 20

Annex D (informative) Wave band analysis using LPV over selected wavelengths . 42

Annex E (informative) Calculation of the WLP . 45

Annex F (informative) Indicator implementation check . 52

Bibliography . 53

2

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European foreword

This document (EN 13036-5:2019) has been prepared by Technical Committee CEN/TC 227 “Road

materials”, the secretariat of which is held by DIN.

This European Standard shall be given the status of a national standard, either by publication of an

identical text or by endorsement, at the latest by March 2020, and conflicting national standards shall

be withdrawn at the latest by March 2020.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

According to the CEN-CENELEC Internal Regulations, the national standards organisations of the

following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.

3

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Introduction

Through road/vehicle dynamic interaction and vehicle vibration, the road profile evenness affects

safety (tyre contact forces), ride quality, energy consumption, vehicle wear as well as pavement and

road durability. The road profile evenness is consequently key information for road maintenance-

management-systems and performance control.

The purpose of this document is to provide a standard practice for calculating and reporting estimates

of road evenness from digitized longitudinal profiles.

This practice covers the mathematical processing of longitudinal profile measurements to produce

evenness statistics (indices) covering the wavelength range 0,5 m to 50 m. These wavelengths cover

1)

most situations for cars . The practice describes the calculation procedure for the International

Roughness Index (IRI), wave band analysis (Root Mean Square (RMS) and Longitudinal Profile Variance

(LPV)) and the Weighted Longitudinal Profile (WLP).

The purpose of the practice is to ensure that when applying one of the possible procedures, exactly the

same steps are carried out, with the aim of facilitating the comparison of evenness measurements

carried out with different profiling instruments in European countries. The Wave band analysis

procedures are informative and therefore IRI is preferred as benchmarking parameter.

NOTE As a control of the implementation of calculation of the evenness indices, three longitudinal profiles

are available including the “true values”. They can be found at www.erpug.org in the directory reference profiles.

More on this can be found in Annex F.

1) For higher speed, e.g. on airport runways or highways, longer wavelengths could also be important.

4

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1 Scope

This document specifies the mathematical processing of digitized longitudinal profile measurements to

produce evenness indices. The document describes the calculation procedure for the International

Roughness Index (IRI), Root Mean Square (RMS) and Longitudinal Profile Variance (LPV) from three

separate wavelength bands and the σWLP and ΔWLP from the Weighted Longitudinal Profile (WLP).

The purpose of this document is to provide a standard practice for calculating and reporting estimates

of road evenness from digitized longitudinal profiles. Other aims with this document are to facilitate the

comparison of evenness measurement results carried out with different profiling instruments in

European countries.

The evenness range covered in this document is defined as the wavelength range 0,5 m to 50 m. It is

noted that both shorter and longer wavelengths can also influence the driving comfort but those are not

covered in this document.

The quantified evenness indices derived from this document are useful support for pavement

management systems. The output can also be used for type approval and performance control of new

and old pavements. The indices can be used on rigid, flexible and gravel road surfaces.

This document doesn’t define from what position on the road the longitudinal profile should be

obtained.

The derived indices are portable in the sense that they can be obtained from longitudinal profiles

measured with a variety of instruments.

2 Normative references

There are no normative references in this document.

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 https://www.iso.org/obp

3.1

reporting repetition interval

measurements made over the road surface which are often analysed using shorter parts or samples to

allow for a more precise description of the measured profile and which is the length of such a sample

Note 1 to entry: For more information on samples see key 4, l to l in Figure 1

0 n

5

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Key

1 longitudinal profile

2 B to C profile measurement length

3 A to D overall profilometer route

4 l …l reporting repetition interval

0 n

Figure 1 — Profile lengths definitions

3.2

longitudinal evenness

deviation of the longitudinal profile from a straight line in a defined wavelength range, e.g. 0,5 m to 50

m

3.3

longitudinal profile

intersection between the pavement surface and a conventional reference plane perpendicular to the

pavement surface and parallel to the lane direction

Note 1 to entry: Usually one of the profiles measured in the wheel paths is used.

Note 2 to entry: The longitudinal road profile is typically saved every 50 mm or 100 mm (acquisition repetition

interval).

3.4

measuring path

selected intersection path, of all possible profiles along the transverse direction

3.5

pre-processed profile

profile obtained by applying resampling and filtering procedures

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3.6

profile

profile of the surface that is described by two coordinates: one in the surface plane following the line of

travel of the profilometer called distance (the abscissa), and the other in a direction normal to the

surface plane, called vertical displacement (the ordinate)

3.7

profilometer

instrument to measure and collect profiles covering the evenness from, e.g., roads and airfields

3.8

profile measurement length

length of an uninterrupted profile measurement and which expresses the length over which the

profilometer continuously and accurately digitises and records the profile (from point B to C in

Figure 1)

Note 1 to entry: Most profilometers need to run for some minimum distance before and after the

profile they are to measure; these starting (from point A to B in Figure 1) and ending phases (from point

C to D, in Figure 1) should not be included in the profile measurement length.

3.9

longitudinal raw profile

profile given by a profilometer when measuring a longitudinal road profile, the characteristics of which

depend on the profilometer used

3.10

resampling

procedure applied on the original measured profile (longitudinal raw profile) to create a new profile

with an alternative sampling distance

3.11

spatial frequency

N

reciprocal of a wavelength in cycles per metre that defines the number of waves N, of wavelength λ, per

metre:

1

N= (1)

λ

3.12

acquisition repetition interval

absolute value of the difference of abscissa between two adjacent points of the digitised longitudinal

profile line

Note 1 to entry: This definition assumes that the distance measured by the profilometer, which is

usually related to the curvilinear abscissa, is close enough to the abscissa in the mathematical sense

3.13

wavelength

quantity describing the horizontal dimension of the irregularities of a longitudinal profile

Note 1 to entry: Longitudinal wavelength is normally expressed in metres (m) or millimetres (mm) and

is a descriptor of the wavelength components of the profile and is related to the concept of the Fourier

Transform of a series regularly sampled measurement points along a spatial axis.

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3.14

wheel paths

area of a pavement surface where the large majority of vehicle wheel passages are concentrated

4 Symbols and abbreviations

B is the base used for IRI calculation in metres (m). It is the length over which the IRI

calculation is performed (or reporting length using the terminology of this document)

L denotes the measurement length

N

1

is the spatial frequency, in cycles per metre: N= ; N is usually called a wave number

λ

x is the abscissa of the sampled point i, in metres (m)

i

z is the elevation of the profile determined at the sampling point i, in metres or millimetres

i

δ is the acquisition repetition interval for the digitization of the profile, in metres or millimetres

x

λ

is the wavelength, in metres (m)

Δ sample interval

IRI is the International Roughness Index

WB is the wave band index calculated by using root mean square analysis applied to the pre-

processed profile elevations for the wave band W, in metres

RMS root means square

SW is the Root Mean Square value for the short wavelength band

LPV longitudinal profile variance

MW is the Root Mean Square value for the medium wavelength band

LW is the Root Mean Square value for the long wavelength band

w is the waviness of the reference spectrum used for the WLP

WLP is the Weighted Longitudinal Profile

σWLP is the standard deviation of the WLP

ΔWLP is the range of variation of the WLP

5 Calculation of evenness indices

A profile can be obtained starting from any lateral position in the lane. This document doesn’t specify

which of those profiles that should be used, only how to calculate any of the four evenness indices

specified.

The calculation of evenness indices, involves the following steps:

— the measurement of the profile, which includes identification of the start and end points of the

profile measurement length and possible events (e.g. roundabouts, speed bumps, milestones, etc.);

— if the purpose is benchmarking it is preferred that the profile are sampled with a 0,1 m step. It is

essential to consider the method of resampling to avoid erroneous energy in the signal;

— the calculation of one or more indices;

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Pre-processing including resampling and filtering is essential in the case of wave band analysis and is

recommended to homogenize the profiles and facilitate comparisons. For benchmark purposes a

2)

resampling procedure according to the resample function in Matlab® is needed. For other use a linear

model could be used. Depending on purpose there are four possible evenness indices groups to choose

from. The first is the calculation of the International Roughness Index, IRI, described in Annex A

(normative) that should be used in international comparison and benchmark tests, second is calculating

evenness-energy in three different wavelength bands using the bi-octave processing (RMS) described in

Annex C (informative). The third is an alternative method to calculate evenness-energy in three wave

band bands using profile variance (LPV) in Annex D (informative). Finally, the fourth method is to

calculate the range of evenness-variation and deviation using the weighted longitudinal profile (WLP)

described in Annex E (informative). In Annex B, an example code to calculate IRI is presented. The

general process on calculation of evenness indices is illustrated in Figure 2.

Figure 2 — Overview of the calculation process of indices (references to chapter in paranthesis)

2) Matlab® is an example of a suitable product available commercially. This information is given for the

convenience of users of this European Standard and does not constitute an endorsement by CEN of this product.

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6 International Roughness Index (IRI)

6.1 General

The IRI is an index computed from a longitudinal road profile measurement using a virtual response

type system, quarter-car simulation, running at a speed of 80 km/h, see Figure 3. The quarter-car

simulation applied on the digitized road profile calculates the accumulated suspension motions Z and

s

Z in Figure 3 divided by the distance travelled. The description of the IRI calculation is based on [7]:

u

— IRI is computed from a single longitudinal road profile. The acquisition repetition interval should

be no larger than 125 mm for accurate calculations. The required vertical sensor resolution

depends on the evenness level, with finer resolution being needed for smooth roads. A vertical

sensor resolution of 0,5 mm is suitable for all conditions;

— the profile is assumed to have a constant slope between sampled elevation points;

— the profile is smoothed with a moving average whose base length is 250 mm;

— the smoothed profile is filtered using a quarter-car simulation, with specific parameter values, at a

simulated speed of 80 km/h;

— the simulated suspension motion is linearly accumulated and divided by the length of the profile to

yield IRI. Thus, IRI has units of slope, such as millimetres per meter or metres per kilometre.

Key

1 sprung mass m 4 unsprung mass m

s u

2 suspension damping rate c 5 tyre spring rate k

s t

3 suspension spring rate k 6 longitudinal profile Z(x)

s

Z and Z accumulated suspension motions

s u

Figure 3 — Quarter car (virtual response type system)

More details on the method of IRI calculation and sample code are given in Annex A and Annex B.

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6.2 Representation of the obtained results

The IRI can be calculated with a different evaluation length L. For a more detailed analysis of the road

profile data, one can vary the evaluation length L. Therefore, this should be indicated as the first sub

index, e.g. IRI if the length L = 20 m. For the purpose of European benchmarking 100 m evaluation

20

length is recommended and should be denoted IRI .

100

Variations in IRI parameters as shown in Figure 3 or in the simulation speed are beyond the scope of

this document. If, however, for whatever reason the Quarter-car simulation is calculated with other

parameters than those mentioned, it should not be denoted as IRI.

7 Wave band analysis

7.1 General

In order to perform wave band analysis, the pre-processed profile is split into different wave band

limited profiles using filters, see Figure 4. The wave bands are generally selected to represent different

features of ride quality. For example, applying a short wavelength filter can result in an index that

reflects the presence of small undulations in the road surface, which could be more significant at lower

speeds. In contrast, applying a longer wavelength filter can result in an index that reflects the presence

of long wavelength undulations that would be most likely to affect ride quality at higher speeds.

The definition of the wave bands used as well as the characteristics of the filters used to obtain band

limited signals, from the original longitudinal profile shall be reported. How indices are derived from

the band limited signals shall also be defined.

Key

1 pre-processed profile

2 short wavelength filtered profile

3 medium wavelength filtered profile

4 long wavelength filtered profile

Figure 4 — Wave band splitting

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The filters applied to the longitudinal profile are generally either:

— band-pass filters, where wavelengths outside of a defined range are attenuated; or

— high-pass filters, where wavelengths greater than a defined wavelength are attenuated.

The filters used to break the original longitudinal profile into the previously defined bands, should be

carefully chosen in order to introduce as little distortion as possible in the filtered signals, a common

technique in that view is to use digital forward and reverse filtering associated with measured section

extending beyond the profile which is to be assessed.

7.2 Wave band indices

In order to characterize the different wave band filtered profiles two methods including indices are

specified:

— Root Mean Square (RMS) over bi-octave bands (see Annex C);

— Longitudinal profile variance (LPV) over selected wavelengths (see Annex D).

8 Weighted Longitudinal Profile (WLP) analysis

8.1 General

The Weighted Longitudinal Profile (WLP) is the longitudinal profile which has been weighted by a

weighting function in the frequency domain. The weighting function enhances small wavelengths and

decreases large wavelengths in such a way that their respective power contents become measurable

later by the same scale in the spatial domain. Following the weighting of the spectrum, the WLP is

calculated by carrying out the following steps:

— filtering the weighted signal in octave bands,

— multiplying the octave band-filtered signals by pre-factors (which take into account their respective

power distributions to the total power content), and

— adding up the signals to give the WLP.

The WLP is characterized by the standard deviation, σWLP, and the range of variation, ΔWLP.

8.2 Prerequisites

The WLP calculation is based on the pre-processed profile. The pre-processing involves:

— De-trending the raw profile using a linear regression to remove the offset and trend of the signal.

— Resampling by applying a constant interval of 0,1 m, using a linear interpolation algorithm.

— Pre-filtering by applying a high pass filter to attenuate wavelengths in excess of 100 m. The filter

shall be such that the amplitude of wavelengths greater than 150 m are attenuated by at least 50 %.

The filter should not distort the phase of any profile features with wavelengths shorter than 100 m.

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9 Reporting

The calculated evenness index should be reported per an agreed presentation length. In the case of

international benchmarking this should be 100 meter. This should be indicated as a sub-index as

described in Figure 1 and explained in IRI in 6.2. It is recommended to include the following

administrative information:

— geographic position and information about the measured object;

— the lateral position of longitudinal profile, e.g. right or left wheel path. For benchmark purposes this

should be the outermost wheel path;

— distance measured;

— date and time;

— conditions that could affect the result.

More mandatory information can be found in EN 13036-6 and should be included in the reporting.

Finally any deviation from this document, EN 13036-5, should be documented and reported.

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Annex A

(normative)

Calculation of the IRI

A.1 The IRI calculation

The IRI calculation includes two distinct filters: a moving average and a quarter-car model.

A.2 Moving Average Filter

The moving average filter was included for two reasons; to simulate the enveloping behaviour of

pneumatic tyres on motor vehicles and to reduce the sensitivity of the IRI algorithm to the sample

interval, Δ. For a profile that has been sampled at Δ, a moving average smoothing filter is defined by the

summation in (Formula A.1):

ik+−1

1

h i = hj

() ( )

ps p

∑

k

ji=

(A.1)

L

B

k= max1, nint

∆

where

h profile height;

p

h smoothed profile height;

ps

max maximum of two arguments;

nint nearest integer, and

L moving average base length, 250 mm.

B

A.3 The quarter-car simulation parameters defining IRI

The IRI is calculated using the quarter-car simulation. It includes the major dynamic effects that

determine how unevenness causes vibrations in a road vehicle. The masses, springs, and dampers are

defined by the following parameters:

c = suspension damping rate

s

k = suspension spring rate

s

k = tyre spring rate

t

m = sprung mass (portion of vehicle body mass supported by one wheel)

s

14

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SIST EN 13036-5:2019

EN 13036-5:2019 (E)

m = unsprung mass (mass of wheel, tyre, and half of axle/suspension)

u

To simplify the equations, the parameters are normalized by the sprung mass, m . The following values

s

for the normalized parameters define the IRI set:

c = c /m = 6,0 k = k /m = 653

s s 1 t s

(A.2)

k = k /m = 63,3 µ = m /m = 0,15

2 s s u s

The quarter-car simulation is described by four first-order ordinary differential equations that can be

written in matrix form (Formula A.3).

(A.3)

x Ax+ Bh

ps

where the x, A, and B arrays are defined as follows:

T

x= z z z z

s s u u

01 0 0

−−kc k c

22

0 0 0 1

A= (A.4)

k kk+

cc

2 12

− −

µµ µ µ

T

k

1

B= 000

µ

where

h = smoothed profile elevation;

ps

z = height (vertical position) of the sprung mass;

s

z = height (vertical position) of the unsprung mass; and

u

x = array of state variables (i.e. the variable that completely describe the stat of the simulated

system).

Time derivatives are indicated with a dot (e.g. z ). Time is calculated from the longitudinal distance and

s

the simulated speed V, which is defined as 80 km/h.

The IRI is an accumulation of the simulated motion between the sprung and the unsprung masses in the

quarter-car simulation, normalized by the length L of the profile:

LV/

1

IRI z− z dt (A.5)

su

∫

L

0

A.4 Solving the differential equation

To solve differential equation such as Formula A.3, one should know the initial values of the state

variables at the starting time. In the standard IRI simulation, the initial values influence the quarter car

response for about 20 m. In order to estimate the initial values, z and z should be set to match the

s u

height of the first profile point and z and z should be set to match the average change in profile

s u

15

=

=

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SIST EN 13036-5:2019

EN 13036-5:2019 (E)

height per secon

**...**

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