An initial attempt to develop an empirical relation between textureand pavement friction using the HHT approach

Zoltan Rado a, Malal Kane b,n

a LTI – Thomas D. Larson Pennsylvania Transportation Institute, Pennsylvania State University, PA, USAb IFSTTAR – French Institute of Science and Technology for Transport, Development and Networks, Marne la Vallée, France

a r t i c l e i n f o

Article history:Received 29 August 2013Received in revised form30 October 2013Accepted 15 November 2013Available online 3 December 2013

Keywords:Pavement frictionTextureCircular Texture MeterDynamic Friction TesterHuang–Hilbert transformation.

a b s t r a c t

Pavement friction, one of the main factors contributing to road safety, depends mainly on surface texture.However, despite its importance having been well corroborated by the numerous investigationsattempting to predict it, the manner in which texture is related to friction remains widely unknown.The current paper will explore the friction-texture relationship based on a new signal processing methodcalled Huang–Hilbert Transformation, or HHT. This method allows empirical decomposition of a textureprofile to a set of basic profiles in a limited number, called Intrinsic Mode Functions, or IMFs. Each IMFcontains a given interval of amplitudes and frequencies. From the obtained IMFs, a set of four newfunctions called Base Intrinsic Mode Functions, or BIMF are computed based on the frequency and powercontent of the underlying IMFs and are characterized using the Hilbert Transformation technique toobtain the scale-dependent norm frequency and amplitude profiles. Then these two parameters arecorrelated with the pavement friction from a multiple regression analysis. This analysis is applied to a setof texture and friction data measured through test track surfaces in France and lab samples of concrete inthe United States. The textures and frictions are measured with the Circular Texture Meter (CTMeter) andthe Dynamic Friction Tester (DFTester), respectively. The obtained results show a good correlationbetween the BIMF's parameters to friction, thus opening a promising new means for characterizingtexture in relation to friction.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Friction is one of the main factors contributing to road safety.Indeed, it allows drivers the ability to control the direction of theirvehicles and the stopping distance. The developed frictionalcharacteristics of the tire–road interface are certainly not exclusivelya pavement property, but they also depend on tire characteristics(rubber type, wearing course wear level, inflation pressure…),operating conditions (velocities, slip rate, load…), and pavementconditions (dry, wet, snow…) [1]. Considering contributions to thedeveloped friction from the pavement surface, one of the mostimportant parameters is the texture of the surface. Surface textureat different scales contributes to the generation of friction via cyclicdeformations that forces the surface texture in the tire rubber, whichgenerates hysteresis and adhesive contributions to friction [2].

For pavement friction characterization purposes, texture isusually described in two different scales [3]: macrotexture andmicrotexture. The macrotexture describes surface irregularities atwavelengths comprised from 0.5 to 50 mm horizontally and from0.2 to 10 mm vertically and are related to the aggregate size. Thisscale is considered to be the main contributor of the drainage of

water out of the tire-pavement contact patch [4]. The microtexturedescribes the surface irregularities of smaller wavelengths and ispartially related to the aggregates' material properties, particularlyshape and surface roughness [5]. These wavelengths are thosecomprised between 0 and 0.5 mm horizontally and 0 and 0.2 mmvertically. The microtextural properties of the surface allow thesurface to break the residual water film between the tire andpavement and make actual physical contact with the tire materialunder wet conditions [6].

However, this way of characterizing the texture using only tworelatively artificially divided and compiled wavelength regimes fallsshort of yielding satisfactory relationship or description of tire-pavement friction. In fact, two pavements exhibiting the sameaverage macrotexture and microtexture can provide very differentfriction levels. Thus, other alternative descriptors and analysistechniques related to the texture shape have been explored in thepast. Sabey explored the influence of the asperities' shape in thegenerated friction; she showed that asperities with a cone shapegenerate better friction than those with a sphere shape [7]. Forsterpointed out the importance of asperities' sharpness: the smaller theasperities' tip angle, the better the generated friction [8,9]. Dointroduced the indenter concept to characterize texture. He definedthree parameters: the indenter shape related to the asperities' tipangles, the relief related to the difference of the asperities' heights,and the density related to the number of asperities per unit of

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0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.wear.2013.11.015

n Corresponding author. Tel./fax: + 33240845839.E-mail address: malal.kane@ifsttar.fr (M. Kane).

Wear 309 (2014) 233–246

distance [10]. Forster defined a distance separating two valleyscorresponding to consecutive local minima points. He then definedthe indenter shape as the simple angle of the asperities' height onthe distance between the valleys [8]. McGhee et al. divided thetexture profiles into a set of segments and calculated the asperities'average separation from the average height from all segments [11].Other authors, such as Yandell characterized the texture shape fromthe average slope of two consecutive points in the profile [12,13].

Despite all these efforts, no parameter calculated from thesedescribed different approaches achieved a satisfactory correlationwith friction. Attempts based on Fourier, Wavelet, or Fractalanalysis have been made to correlate friction to texture. Amongthese studies, Rado developed a fractal texture model for pave-ment surfaces after showing the achievability of its scale-independent description [14]. From a contact model, he exploredthe relationship of the real area of contact and the frictioncoefficient-slip speed curve. Persson proposed a formula to deter-mine the hysteretic friction of rubber sliding over asperities froma fractal description [15]. Heinrich presented a model of hystereticfriction of a sliding rubber sample over a fractal surface. Hedemonstrated how the fractal descriptor parameters of differenttest pavements can be used to compare tire traction measure-ments obtained on wet test roads [16]. Villani et al., inspired byHeinrich's work, calculated the hysteresis contribution by meansof an analytical model. She described the texture with its fractaldimension and the upper cut-off scale length [17].

The approaches above, constructed from solid physical bases,are very complex for road engineers, as the coefficients accom-panying the proposed models remain difficult, impractical, or evenimpossible to determine. To handle this complexity, new, morestraightforward and easier approaches based on new signalprocessing tools started emerging. Among the new techniques,one of the most promising is the Huang–Hilbert Transform (HHT)[18]. This method provides a way to decompose a signal into a setof functions and obtain amplitude and frequency data. Contrary toother methods, such as the Fourier Transform, HHT is an empiricalapproach rather than a theoretical tool. Cho and Rado explored thepossibility of using this method to analyze the texture–frictionrelationship [19]. After determining a set of parameters calculatedfrom the basic functions of the texture profiles, some parameterswere found to have a significant correlation to friction. Theyconcluded that the HHT method might be a suitable alternativeto conventional techniques such as Fourier and Wavelet transforms.

This paper is a continuation of the earlier study on HHT fortexture description. It explores and extends the use and utility ofHHT analysis to explore the texture–friction relationship. The paperis divided into two distinct sections. The first section describes theexperimental program to measure friction and texture used in thestudy, including the devices and test sites utilized in the datacollection. The second section is divided into two subsections. Thefirst covers the basics of the HHT technique. The second explains itsapplication to the measured texture data and explains in detail thestatistical processing and relationship building between theobtained texture descriptors and the measured friction.

2. Experimental program

To explore the Huang–Hilbert Transformation possibilities topredict pavement friction, one needs a set of pavement texturesand corresponding friction coefficients measured on them. Thispart of the paper is dedicated to the description of the experi-mental program in which DFTester and CTMeter and a substantialnumber of independent test sites in France and lab samples in theUnited States have been utilized for that purpose.

2.1. Description of the texture and friction measuring devices

2.1.1. DFTesterTo collect the data used in this study for all friction measure-

ments, both in the United States and in France, the DynamicFriction Tester (DFTester) was used. This device, designed andmanufactured in Japan, allows friction measurements both in thelab and in the field. It is commonly used in the United States, andin several countries in Asia, and is starting to be in use in Europe.The first equipment in Europe was acquired by IFSTTAR at Francein 2009 [6] and in England, Turkey, Spain, Poland, and Italy.

The device is composed of separate control and measurementunits (Fig. 1). The standard test procedure used in the United Statescan be found in the ASTM E1911 standard [20]. The measuring unithas three rubber pads attached to a disc. During the measurement,the disc, driven by a DC electric motor, is accelerated to reach thetarget circumferential speed set by the operator in the control unit.Prior to reaching the pre-set speed, water is applied and maintainedduring the whole measurement process by the device wateringsystem onto the test surface in a complete 360-degree circle aroundthe rotating measurement pads. Once the set speed of the rubberpads is reached, the electric motor is switched off and the disc withthe measurement pads is lowered into contact with the surfacewith a constant vertical load. Each pad is loaded at 11.8 N. The speedof the pads decreases to a full stop due to the friction generatedfrom the pad/surface contact. The friction is recorded during thedeceleration phase from the set original speed to 0 km/h.

2.1.2. CTMeterThe Circular Texture Meter (CTMeter) was used for all texture

measurements in this study, both in the United States and in France(Fig. 2). This device can also be used both in the laboratory and in thefield. It is a complementary measurement device to the DFTester astexture measurements can be done on the exact same physicalsurface tracks where the DFTester pads have been in contact with thetest surface [21]. It measures texture profiles along a circle of 142 mmradius with a measuring laser mounted on a rotating arm. Theobtained profile is composed of 1.024 points scaled at 0.87 mm,meaning a total profile length of 892 mm. The CTMeter is commonlyused in the United States and in Asia, and is starting to be used inEurope. The first equipment was acquired by IFSTTAR at France in2009 [6] and then later in England, Turkey, Spain, Poland, and Italy.

2.2. Description of the tested sites

2.2.1. IFSTTAR Test Track sitesThe IFSTTAR Test Track is located in Nantes, France, and has a

dozen test surfaces differentiated by their texture and design. Thetest surfaces cover a wide range of textures, from smooth to macroand micro to rough. Fig. 3 displays two of the surfaces and theircorresponding names. Table 3 (Appendix) displays the othersurfaces and their corresponding names. Fig. 4 shows their locationon the test track.

2.2.2. PennDOT sitesThe American surfaces used in this study had been manufactured

and used in a sponsored research project for the PennsylvaniaDepartment of Transportation (PennDOT). For further information,please see the research report by Rado [22]. These surfaces wereconstructed for laboratory testing and evaluation. The purpose of theoriginal research project [22] was to evaluate different Portlandcement concrete surfaces under accelerated polishing for frictionaland textural properties. The present study utilized all the constructedsurfaces and the measured data from these surfaces throughout theaccelerated polishing, treating each surface when new and during

Z. Rado, M. Kane / Wear 309 (2014) 233–246234

Fig. 2. CTMeter (left: side view and right: bottom view).

Fig. 3. Two of the test surfaces at the IFSTTAR Test Track.

Fig. 1. DFTester (left: side view and right: bottom view).

Fig. 4. Test surface location in the IFSTTAR Test Track.

Z. Rado, M. Kane / Wear 309 (2014) 233–246 235

polishing at intervals as independent data points for this study.Polishing of the test surfaces was achieved using a one third scaleaccelerated wear polishing device, the Model Mobile Load Simulator(MMLS3) machine. For further information, please see Rado [22].Each of the surfaces were measured seven times over the course of

the full polishing study, thus yielding different surface characteristicspoints for the present research. A total of 10 different PCC surfaceswere used in the study yielding 70 sets of data.

Each of the different PCC mixtures was worked into preparedforms to produce identically sized laboratory pavement sections foreach mix. The forms consisted of a 1.880 mm X 760 mm X 6mmsteel base plate with bolts welded to the base to mount woodensides. The sides of the wooden frame measured 1.230 mm X610 mm X 127 mm with a 10 mm spacer inserted at the midpointof the frame to create two 610 mm X 610 mm X 127 mm samplesper frame (please see Fig. 5 for details).

The samples prepared in this way created two separate andindependent squares, which were combined into a rectangular-shaped specimen, allowing the surfaces to be worn by the MMLS3machine simultaneously, thus introducing exactly the same wear-ing load on both surfaces. The picture in Fig. 5 shows the wearingtire, and the area of wearing can also be observed as it isdistinguished by a different shade of the surface. The concretesamples were never removed from the forms; they were cured andthen tested in the original forms used to produce the samples.Fig. 5. Laboratory surface samples with frame.

Table 1As-constructed mix parameters.

Abbreviated Sample Name Coarse aggregate content (lb) Gravel Fine aggregate (lb) Water (lb) AE (ml) WR(ml)Vanport Limestone #57

Control 302.34 0.00 184.15 29.44 60.00 80.00AST-G-30 211.50 93.69 189.25 21.49 60.00 80.00AST-G-70 90.65 212.26 185.76 27.26 60.00 80.00AST-G-50 151.04 149.87 184.01 31.00 40.00 50.00

Vanport Limestone #57 Sand stoneAST-S-30 211.78 90.56 183.64 29.95 60.00 100.00AST-S-70 90.78 212.81 183.68 28.65 60.00 100.00

Vanport Limestone #57MFT-70-30 335.54 148.31 32.08 80.00 80.00MFT-30-70 143.81 342.68 29.44 80.00 100.00

Vanport Limestone #57 Vanport limestone #1þ#8MAS-1-57 121.03 181.42 184.99 28.49 80.00 80.00MAS-8-57 120.90 181.21 183.42 30.40 60.00 80.00MAS-8 302.40 184.65 28.88 80.00 92.00

Mix Design (0.157 cu yd batch Size) W/C¼0.4.1 lb¼0.45359237 kg

Table 2Naming conventions and material compositions.

Variation in sample material Abbreviation Concrete aggregate composition Abbreviated sample name

No variation CONTROL 100% Vanport Limestone Coarse Aggregate with AASHTO #57 Gradation and 37%Fine Aggregate Fraction

AST-V-1, AST-V-2

Aggregate substitution AST 30% Gravel/70% Vanport with AASHTO #57 Coarse Aggregate Gradation and 37%Fine Aggregate Fraction

AST-G-30-1, AST-G-30-2

70% Gravel/30% Vanport with AASHTO #57 Coarse Aggregate Gradation and 37%Fine Aggregate Fraction

AST-G-70-1, AST-G-70-2

30% Sandstone/70% Vanport with AASHTO #57 Coarse Aggregate Gradation and37% Fine Aggregate Fraction

AST-S-30-1, AST-S-30-2

70% Sandstone/30% Vanport with AASHTO #57 Coarse Aggregate Gradation and37% Fine Aggregate Fraction

AST-S-70-1, AST-S-70-2

Mortar fraction MFT 70% Coarse/30% Fine with AASHTO #57 Vanport Limestone Coarse AggregateGradation

MFT-70/30-1, MFT-70/30-2

30% Coarse/70% fine with AASHTO #57 Vanport Limestone Coarse AggregateGradation

MFT-30/70-1, MFT-30/70-2

Maximum aggregate size MAS AASHTO #1 and #57 Gradation with Vanport Limestone CoarseAggregate

MAS-1/57-1a, MAS-1/57-2a

AASHTO #8 and #57 Gradation with Vanport Limestone CoarseAggregate

MAS-8/57-1, MAS-8/57-2

AASHTO #8 Gradation with Vanport Limestone Coarse Aggregate MAS-8-1, MAS-8-2

a Screened to max nominal sizer50 mm.

Z. Rado, M. Kane / Wear 309 (2014) 233–246236

One mix design was used for each pair of samples. The concretewas batched and mixed in the lab, placed into the form cavity, andvibrated using a concrete pencil vibrator. Percent air was deter-mined with each mix design and 102 mm�203 mm compressivestrength samples were cast for each mix.

After placing the concrete mix into the forms and consolidatingby using the vibrator, the concrete surface was finished by handtrowel. A moist burlap and plastic sheeting were used to maintaina moist cure. After 2 days of moist cure, each sample wassandblasted in the area of the anticipated MMLS3 wheel path to

remove the top layer of mortar and expose the aggregate near thesurface; the sand blasting also introduced a very uniform, isotropicand homogeneous texture over all the different samples.

Both the surface samples in the forms and the small compres-sive strength samples were then aged for 28 days and theircompressive strength determined. Following achievements ofacceptable compressive strength, the surface samples in the formswere subjected to trafficking using the MMLS3 apparatus.

The concrete mix abbreviations used in Table 1 constitute thenaming conventions and indicators described in Table 2.

The actual mixed concrete parameters were measured andrecorded during the casting process and the data are given inTable 1 (For metric units, the conversion factor of lb to kg is providedin the table footnote).

Due to the large number of surface samples used, it was notpossible to include in the present paper pictures of all utilized surfaces.For full reference please see Rado [22]. A sample surface together withthe polishing machine, MMLS3, in its testing setup is shown in Fig. 6.

The sample concrete slabs were exposed to traffic wearing andaccelerated polishing using the MMLS3. This load simulator iscommonly used to apply longitudinal pneumatic rubber wheelwearing cycles to pavement markings, asphalt cement concretepavements, and other highway materials to determine degradationphenomena. The MMLS3 can apply up to 7200 cycles per hour overa 1.260 mm distance, as shown in the longitudinal section of Fig. 7.As it was anticipated that approximately 400,000 cycles would haveto be applied to observe significant skid resistance reduction, theFig. 6. MMLS-3 machine setup with test surface.

Fig. 7. Model Mobile Load Simulator.

Fig. 8. Abrasive Tire.

Z. Rado, M. Kane / Wear 309 (2014) 233–246 237

device was modified to conform to accelerated polishing and wearas well as to reduce the number of cycles necessary for full testingof the surfaces.

A modification to the machine was initiated to introducesignificant polishing power to the wearing cycles while closelysimulating actual traffic conditions. The traffic conditions weresimulated through the machine's capability to deliver straightlongitudinal roll cycles of a pneumatic tire under load while at thesame time move sideways, successfully introducing distributedtraffic loads. The MMLS3 machine has the capability to introducerandom and periodic sideways movement called wandering. Themachine was modified to extend the sideways movement range tocover a total of 400 mm; thus, the rolling wheels were passingover different sections of the test surfaces at each run covering a400 mm lateral width of the surface. This allowed the measure-ment equipment used to measure the frictional and texturalcharacteristics to measure exclusively in the worn surface area.

The MMLS3 machine uses four 300 mm diameter 80 mm-widthspecial pneumatic rubber tires pressurized to 240 kPa. Two of thepneumatic tires were modified in order to introduce significantpolish and wear to the surface. The tires were coated using a high-strength and flexible polyurethane bonding agent into which ultra-high hardness silica carbide particles were embedded. Fig. 8 showsa coated rubber tire before testing and when testing was finishedwith the particular tire.

The resultant tire surface gave a pneumatic wheel with highabrasive capability on a very fine scale. This combined with theunmodified two pneumatic wheels gave a capacity to the MMLS3machine to rapidly introduce heavy polishing and surface wearthat is relevant to the surface characteristics of PCC pavementsdetermining frictional performance.

For each separate sample surface a completely new set of fourtires, two uncoated and two coated, were installed. The full wearingof the sample surface was completed with the same set of tires.

2.3. Measurements procedure

On each test surface, the spots to be measured were marked bychalk on the surface to ensure correct placement of the DFTesterFig. 9. Algorithm of the EMD procedure.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5Original Texture Profile Measured by the CTMeter Device

Distance [m]

Text

ure

Dep

th [m

m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

Distance [m]

Ele

vatio

n [m

m]

HHT Ananlysis: IMF1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

Distance [m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Distance [m]

Ele

vatio

n [m

m]

-0.5

0

0.5

Ele

vatio

n [m

m]

HHT Ananlysis: IMF5

HHT Ananlysis: IMF10

Fig. 10. An example from the IFSTAR Test Track of an original texture profile and some of its decomposed IMFs.

Z. Rado, M. Kane / Wear 309 (2014) 233–246238

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5Original Texture Profile Measured by the CTMeter Device

Distance [m]

Text

ure

Dep

th [m

m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

Distance [m]

Ele

vatio

n [m

m]

Calculated BASE IMF1

Calculated BASE IMF2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-2

-1

0

1

2

Distance [m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Distance [m]

Ele

vatio

n [m

m]

-2

-1

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1

2

Ele

vatio

n [m

m]

Calculated BASE IMF3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.5

0

0.5

Distance [m]

Ele

vatio

n [m

m]

Calculated BASE IMF4

Fig. 11. An example from the IFSTAR Test Track of an original texture profile and its decomposed BIMFs.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.8

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0

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Distance [m]

00

100

200

300

400

500

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Distance [m]

Ele

vatio

n [m

m]

Hilbert Analysis of BASE IMF1

Freq

uenc

y [1

/m]

BASE IMF ProfileHilbert Instantaneous Amplitude

Hilbert Instantaneous Frequency

Fig. 12. Hilbert Analysis of Base IMF.

Z. Rado, M. Kane / Wear 309 (2014) 233–246 239

and CTMeter devices. At each spot, the texture was measuredusing the CTMeter. Friction was then measured using the DFTesterdevice. Extreme care was exercised to ensure that the DFTesterdevice was placed on the exact location where the CTMeter devicemeasured the surface texture. This ensured that the frictioncoefficient was measured at the same physical track as the textureprofile obtained from the CTMeter device. On the IFSTTAR TestTrack, eighteen different surfaces were measured and 70 surfacesmeasured using the PennDOT surface samples.

3. Analysis of the results

3.1. Application of the HHT to the texture analysis

3.1.1. HHT basisThe Huang–Hilbert Transform, created by Huang [18], is an

empirical data-analysis method. It decomposes measured textureprofiles to a finite set of Intrinsic Mode Functions (See Eq. (1))It is possible to obtain frequency and amplitude data from the

Huang–Hilbert Transform for each IMF.

ZðxÞ ¼ rnðxÞþ ∑n

j ¼ 1CjðxÞ ð1Þ

where:x represents the distance in the texture profile, Z(x) is the

height of a point located at distance x in the profile, Cj(x) is the jthIMF, n is the total number of IMF and rn(x) is the residue obtainedafter the decomposition.

The profile decomposition procedure to fundamental IMFsfollows a method called Empirical Mode Decomposition (EMD).The details of that decomposition can be found in Huang's publica-tion cited at [18]. The algorithm developed in this study summarizesthat EMD procedure is shown in Fig. 9.

Where

� x represents the distance in the texture profile.� Z(x) is the original height of a point located at distance x in the

profile.� Cj(x) is the jth IMF. Each IMF has a number of extrema and a

number of zero crossings either equal or differing at most by

Fig. 13. Linear Stepwise Model Fit data for PennDOT test samples.

Z. Rado, M. Kane / Wear 309 (2014) 233–246240

one, and in which the mean value of the envelopes defined bythe local maxima and local minima has to be zero at all points.

� rj(x) is the residue obtained after the decomposition.� hj

k(x), called “proto-IMF” is obtained at the kth loop during the“sifting process”.

� mjk(x) represents the mean function of upper and lower

envelope functions of hjk(x). The upper (also the lower envel-ope) functions are made by connecting the proto-IMF localmaxima points (similarly the proto-IMF local minima points)by cubic spline lines.

� The SDk are the stopping criterion of the sifting process(Eq. (2)). The sifting process stops when the calculated SDnumber is smaller than a pre-defined value. In this study, thecriterion proposed by Huang is used [18].

SDk ¼R jhk�1

j ðxÞ�hkj ðxÞj2dx

Rhk�1j ðxÞ2dx

ð2Þ

Fig. 10 shows an example of an original texture profile and itsdecomposed IMFs.

3.1.2. From IMFs to BIMFsThe derived IMF functions are then combined into four Base

Intrinsic Mode Functions, BIMF, for all of the measured textureprofiles. This is to have the same number of functions regardless ofthe profile and thus facilitate comparison between profiles.Indeed, the number of IMFs that can be derived from the decom-position of a given texture profile cannot be predicted in advance.Thus only the first 15 IMFs were taken into consideration andseparated into four BIMFs as follows: BIMF1, BIMF2, BIMF3, andBIMF4, consisting respectively of the sum of the first group of fourIMFs, the second group of four following IMFs, the third group offour following IMFs, and the remaining group of three IMFs. Fig. 11shows an example of the BIMFs from the profile texture of Fig. 10.

3.2. BIMF amplitudes and frequencies – friction relationship

The BIMFs deliver the real wave function embedded in thetexture profile on a distinct and separate scale in both frequencyand amplitude characteristics; they are extremely useful in depict-ing real contact between surface and rubber sliders in a way that isrelevant to the physical characteristics of friction [19]. The obtainedBIMFs will represent actual sharpness, power, and curvature of thetexture asperities separated into different scale classes and willpresent a substantial possibility of relating strongly to the frictionalcharacteristics of the surface [14].

Contrary to the classic HHT approach where the Hilberttransformation is applied directly to the IMFs; here, we appliedthat transformation to the BIMFs to obtain the Hilbert instanta-neous frequencies and amplitudes (See Fig. 12). For each BIMF, theinstantaneous frequencies and amplitudes are averaged and thenthe relation between them and the corresponding measuredfriction on that surface is analyzed. The correlation is set up usingthe multiple regression model for BIMF parameters (independentvariables) and DFT friction (dependent variable) at speeds of60 km/h, 40 km/h, and 20 km/h.

4. Results and discussion

A multiple regression model for BIMF parameters (independentvariables) and DFT friction (dependent variable) at each speed(60 km/h, 40 km/h, and 20 km/h) was used.

A linear stepwise model analysis with complete ANOVA wasperformed on the PennDOT data set to determine what BIMFparameters were statistically relevant in explaining variation in

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Measured Friction Values

Pre

dict

ed F

rictio

n V

alue

s

Predicted DFTester measurements at 20km/h

Fig. 14. Predicted friction values against measured friction for the PennDOT testsamples.

Table 3Predicted coefficient of friction of the DFtester device for the PennDot test samplesand IFSTTAR sites at all speeds.

20 km/h 40 km/h 60 km/h

PennDOT R²¼0.74 R²¼0.77 R²¼0.77Coeff of Correl: 0.83 Coeff of Correl: 0.84 Coeff of Correl: 0.85RMSE: 0.055 RMSE: 0.052 RMSE: 0.051MAE: 0.044 MAE: 0.042 MAE: 0.041MARE: 0.075 MARE: 0.084 MARE: 0.091

IFSTTAR R2¼0.87 R2¼0.83 R2¼0.71Coeff of Correl: 0.75 Coeff of Correl: 0.81 Coeff of Correl: 0.84RMSE: 0.098 RMSE: 0.086 RMSE: 0.0770MAE: 0.080 MAE: 0.070 MAE: 0.062MARE: 0.118 MARE: 0.110 MARE: 0.099

MAE: Mean Absolute Error, RMSE: Root Mean Squared Error, and MARE: MeanAbsolute Relative Error.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

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0.7

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Measured Friction Values

Pre

dict

ed F

rictio

n V

alue

s

Predicted DFTester measurements at 20km/h

Fig. 15. Predicted friction values against measured friction in the IFSTTAR TestTrack sites in France.

Z. Rado, M. Kane / Wear 309 (2014) 233–246 241

the measured friction. A systematic analysis adding and removingterms from a multi-linear model based on their statistical sig-nificance in a regression was used. The p value of an F-statistic wascomputed to test models with and without a potential term. If aterm is not currently in the model, the null hypothesis is that thetermwould have a zero coefficient if added to the model. If there issufficient evidence to reject the null hypothesis, the term is addedto the model. Conversely, if a term is currently in the model, thenull hypothesis is that the term has a zero coefficient. If there isinsufficient evidence to reject the null hypothesis, the term isremoved from the model.

The independent variables in this multi-linear analysis werethe

1. Mean amplitudes of the determined Huang–Hilbert Transformsof each of the four BIMF functions.

2. Mean of the instantaneous frequencies of the determinedHuang–Hilbert Transforms of each of the four BIMF functions(see the texture “Frequency [1/m]” section of Fig. 12).

Only the linear model considering these eight independentparameters has been considered. No interactions between the

parameters or other physically relevant geometrical modes (i.e., tipsharpness or summit curvature) that could be calculated usingstatistical methods were considered even though they might berelevant and can serve as a basis for further research.

Thus the considered eight parameters were the following:

X1: Mean Amplitude Height of BIMF1X2: Mean Amplitude Height of BIMF2X3: Mean Amplitude Height of BIMF3X4: Mean Amplitude Height of BIMF4X5: Mean Instantaneous Frequency of BIMF1X6: Mean Instantaneous Frequency of BIMF2X7: Mean Instantaneous Frequency of BIMF3X8: Mean Instantaneous Frequency of BIMF4

The stepwise multi-linear statistical analysis had determined asimple statistical model including the X1, X2, X5, and X6 para-meters, thus the mean amplitudes and mean frequencies of thefirst two BIMF functions are the only statistically significantparameters to satisfactorily explain variations in the measuredfrictional coefficients. The same linear stepwise multi-linear modelfitting process was followed to determine the best statistical

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Fig. 16. Predicted friction values against measured friction in the PennDOT test sites in the United.

Z. Rado, M. Kane / Wear 309 (2014) 233–246242

model to use the texture parameters to explain the variations inthe measured coefficient of friction at three different speeds. Thusa separate full model fitting exercise was performed to relate thedetermined texture parameters to the measured coefficient offriction at 20 km/h speed of the DFTester machine, at 40 km/hspeed and at 60 km/h speed. The results of the model fit withcorresponding t-statistics and p-values are given in Fig. 13 (onlythe two first decimals of these values are significant and reflect theplots on the right side).

It is interesting and important to note in Fig. 13 that the samesignificant linear model was found for the coefficient of friction forall speeds investigated. The model parameter coefficients are, ofcourse, different, but the BIMF amplitudes and frequencies werefound to be the only relevant parameters to contributing to theexplanation of friction variations at all speeds. This could in alllikelihood be an indicator that the shape, asperity height, density,sharpness, summit curvature, and other parameters of the texturalfeatures from these basic HHT functions could be better descrip-tors of texture–friction relationship.

After the multi-linear models for the three speeds weredetermined, the obtained models were fitted to the data of thePennDOT study. The results of the model fittings are given in

Fig. 14. The data in Fig. 14 show the results of the fitted data of themodels given in Fig. 13 at 20 km/h (For 40 km/h and 60 km/h, seethe appendix – Figs. 16 and 17). The corresponding goodness-of-fitand ANOVA parameters are given in Table 3.

Despite the relative simplicity of the model, the relationshipbetween the newly determined texture descriptors and themeasured coefficient of friction is very strong and statisticallysignificant, and the models (notwithstanding the parametervalues) are identical for all measurement speeds.

The CTMeter data from the IFSTTAR test track surfaces wassubjected to the same EMD analysis to produce the four BIMFfunctions and to calculate through the application of the Huang–Hilbert Analysis the same eight amplitude and frequency para-meters as it was calculated for the PennDOT data. A predictedDFTester friction coefficient was calculated for 20 km/h, 40 km/hand 60 km/h DFTester speeds and the data compared and fitted tothe actual measured friction data. The results at 20 km/h aredepicted in Fig. 15 (For 40 km/h and 60 km/h see the appendix –

Figs. 16 and 17).The IFSTTAR models are given in Table 2. The IFSTTAR data are

somewhat better than the PennDOT data used to develop themodel. It is possible that the limited number of tests used in the

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Fig. 17. Predicted friction values against measured friction in the IFSTTAR Test Track sites in France.

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Table 4Some of the test surface at the IFSTTAR Test Track.

Section Pavement Pictures Generic name

A Porous asphalt concrete 0/6 PAC 0/6

E1 Dense asphalt concrete 0/10 (new) DAC 0/10 (new)

F

Colgrip (high skidding resistance)

ColgripCalcined bauxite (1.5/3) on epoxy

C Surface dressing 0.8/1.5 Fine SD

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IFSTTAR measurements provided a better goodness of fit, as alarger and more diverse dataset would most likely result in similarR-square values to those obtained during the PennDOT dataanalysis.

5. Conclusion

This work explored the use of HHT analysis to investigate thetexture–friction relationship. The first part of the paper wasdedicated to the description of the experimental program in whichDFTester and CTMeter and a substantial number of independenttest sites in France and lab samples in the United States have beenutilized. The second part was dedicated to the description of themethodology the analysis, and presentation of the results. TheHHT analysis decomposed the texture profile to a set of IMFs. Fromthe IMFs, a set of four BIMFs were created and characterized usingthe Huang–Hilbert Transformation to obtain averaged frequenciesand amplitudes. These two parameters per BIMF, or a total of eightparameters for the four BIMF functions, were statistically analyzedusing multi-linear, model-fitting algorithms using the data mea-sured only in the United States as the development database. Thedeveloped multi-linear model was then fitted using a correlationalgorithm to the measured pavement friction data using multipleregressions. The obtained results show good correlation betweenthese BIMF parameters to the pavement friction. This resulted in afixed linear model.

The fixed linear model was applied to the data obtained in theFrench measurement study. The calculated correlation betweenthe predicted DFTester friction obtained from the application ofthe final model and the actual DFTester data measured in Franceshowed similar characteristics and good fit.

Appendix

See Figs. 16 and 17, and Table 4 here.

References

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Table 4 (continued )

Section Pavement Pictures Generic name

A′ Surface Dressing 8/10 Rough SD

L2 Sand asphalt 0/4 SA 0/4

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