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research/tfhrc/programs/

infrastructure/pavements/ltpp/

The Long-Term Pavement Performance 

(LTPP) program is a study of in-service 

pavements across North America. Its 

goal is to extend the life of highway 

pavements through various designs of 

new and rehabilitated pavement structures, using different materials and under

different loads, environments, subgrade

 soil, and maintenance practices. LTPP was 

established under the Strategic Highway 

Research Program and is now managed 

by the Federal Highway Administration.

Classification of 

Features of Pavement 

Profiles Using Empirical 

Mode Decomposition

FHWA Publication No.: FHWA-HRT-13-093

FHWA Contact: Deborah Walker, HRDI-30,

(202) 493-3068, deborah.walker@dot.gov

This document was the winning paper submitted to the 

2012 International Contest on LTPP Data Analysis, which 

was cosponsored by the Federal Highway Administration 

(FHWA) and the American Society of Civil Engineers 

(ASCE). The paper was based on author Daniel P. Franta’s 

master’s degree research project at the University of 

Minnesota, Twin Cities.(1)

Abstract

The Long-Term Pavement Performance (LTPP) database 

contains surface profile data for numerous pavements 

that are used mainly for computing International 

Roughness Index (IRI).(2) In order to obtain more information from these surface profiles, a Hilbert-Huang 

Transform (HHT) based surface profile algorithm was 

developed to analyze LTPP field road profile data in 

order to extract smoothed, consistent profiles from 

noise-filled data sets using empirical mode decomposition (EMD). The application of this algorithm to 

concrete surface profiles resulted in the successful 

separation of the intrinsic mode functions contained 

within the profile data for several LTPP pavement test 

sections from Wisconsin, Arizona, and Utah. Arizona 

was the only test section where the profiles showed 

consistent “curl” deflections for the same slab over a 

20-month timespan and during both winter and early fall 

seasons. The consistent slab shape is likely due to built-in 

curl. Built-in curl is defined as permanent concrete slab 

deformation that occurs early in the life of the pavement.
2

By categorizing and separating intrinsic 

mode functions contained within LTPP 

profile data, the results can be used to 

analyze specific portions of LTPP surface 

profile data in order to improve concrete 

pavement models in the future. Currently, 

no comprehensive procedure exists to 

model or estimate long-term, effective 

built-in curling. The developed surface profile algorithm that has proven to be universal can be applied to any LTPP profile data 

for analysis.

Introduction

The LTPP database contains surface profile 

data for pavement sections throughout the 

United States that is used to compute IRI. 

Byrum previously used Wisconsin LTPP 

section profiles to analyze curvature in 

concrete pavement slabs.(3) However, the 

difficulty with analyzing raw field profiles 

is the level of noise and frequency of 

inconsistencies within these data sets. To 

remedy this problem, an automated pavement analysis method was developed to 

smooth the real-field profiles and allow for 

more accurate and consistent analysis of 

pavement sections or slabs. This method 

is based on the EMD process contained 

within the HHT. Past analysis of road 

surface profiles using the HHT is limited. 

Adu-Gyamfi et al. used the empirical mode 

decomposition for pavement surface 

analysis, and Attoh-Okine et al. also used 

it to analyze two flexible pavement 

profiles.(4,5)

The application in this paper focuses on 

grouping intrinsic mode functions (IMF) to 

analyze built-in curl features of rigid pavement profiles. Extraction of noise in real-life 

and artificial profile data can be performed 

by applying a sifting process to filter and 

identify the IMFs that are contained in raw 

surface profiles. The idea behind the HilbertHuang-based sifting process is to identify 

the intrinsic functions contained within the 

data and to subsequently remove and categorize them in order to analyze specific 

portions of the original profile. Figure 1 

shows the basic decomposition of any 

profile.(6)

Where y(x) is the original profile, cj(x)

represents IMFs within the data set, and 

rn(x) is the residue after the first n IMFs have 

been removed.

In the case of pavement profiles, some of 

the IMFs are due to “noise/surface texture,” 

“curling,” and/or “base trends” within 

the pavement. Removing the IMFs due to 

“noise/surface texture” from the distorted, 

non-linear profiles, will reveal the smoother 

functions of the original data set that can 

be attributed to “curl” and/or “base trends.” 

Quotations are used around “noise/surface 

texture,” “curl,” and “base trends” to 

emphasize that these terms are used only 

to group functions of similar characteristics 

contained in surface profiles. Surface 

profiles contain IMFs attributed to many 

different variables. The goal of this paper is 

not to explain what causes trends in pavement profiles but to develop a method to 

analyze them.

After the automated profile analysis is performed, the resulting IMFs can be grouped 

to represent different portions of the 

© Dan Franta

y(x) = n

=1 cj

(x) + r

n(x)

Figure 1. y of x is equal to the summation of c subscript j 

of x plus r subscript n of x. 

j
3

original data set. Based on frequencies 

and wavelengths of the extracted functions, IMFs will be categorized into three 

separate groups. Frequencies of the 

intrinsic mode functions decrease as the 

number of calculated IMFs increase. 

Therefore, the first IMF extracted will 

have the highest frequencies and shortest 

wavelengths of any function within the 

profile. The opposite will be the case for 

the final IMF.

IMF Grouping

The first group, “noise/surface texture” 

functions (NFUN), are high frequency IMFs 

resulting partially from surface texture 

or noise contained within the pavement 

profile. The wavelengths are short and the 

amplitudes small. The peaks of the waves 

tend to appear sharp and pointed.

“Curl” functions (CFUN) compose the second group. Compared to the NFUNs, these 

IMFs are characterized by lower frequencies, higher amplitudes, and longer wavelengths. Before CFUNs are extracted, much 

of the “noise/surface texture” will have 

already been removed from the profile by 

the NFUNs. This will cause the CFUNs to 

appear smoother than the NFUN group. The 

hypothesis used here is that these IMFs are 

partially caused by temperature curling or 

built-in curling within the pavement slabs.

The last group, “base” functions (BFUN), 

display the lowest frequencies, and the 

wavelengths will be longer than the CFUNs. 

The BFUNs are due to overall “base trends” 

within the profile. In ISLAB2005 concrete 

slab models, the curling magnitude is 

always calculated assuming the original 

surface is horizontally flat. This is not the 

case for a real pavement section. If the 

underlying “base trends” of pavement are 

not taken into account, there will likely be 

deflections and curvatures that are incorrectly assumed to be caused by “curling.” 

The BFUNs are the smooth, low frequency 

IMFs. The final residue is always grouped 

with the BFUNs.

Grouping IMFs allows for evaluation of any 

portion of the profile, both individually and 

as a group. For instance, the overall “base 

trend” of a profile can be obtained by summing all the members of the BFUN group. In 

most cases, the portion of greatest interest 

is the removal of the NFUN group to reveal 

the smoother characteristics of the slab profiles in absence of distortions from “noise/

surface texture,” leaving just the combination of the CFUN and BFUN groups representing a smoothed version of the profile.

Grouping IMFs can be difficult because 

there is no clear or concise method by which 

to do it, and profiles contain varying numbers of IMFs. Steps for the classification of 

the IMFs and their grouping into NFUNs, 

CFUNs or BFUNs, previously defined, is 

described below using an LTPP pavement 

section from Wisconsin.

Wisconsin Section 553009

The LTPP database contains a profile for 

Wisconsin pavement section 553009 (see 

figure 2). This profile was collected on 

June 9, 2008, during run 6, at 4:07 p.m. 

from the left wheel path. The 11-slab 

section contains concrete that is 8 inches 

thick. The profile was chosen because the 

slab profiles are easily identified by their 

surface data and provide a good example of 

classifying IMFs.

The developed automated Hilbert-Huangbased algorithm was applied to the entire 

profile shown in figure 2, and the IMF 
4

results for the middle slab (centered on 

x ≈ 800 inches) were extracted for analysis. 

When using this automated profile analysis 

algorithm with field data, spiking effects 

during the empirical mode decomposition 

process tend to cause distortions near the 

edges of the analyzed profiles. The middle 

slab is extracted for analysis to avoid these 

distortions.

The first IMF, and member of the NFUN 

group, is composed of “noise/surface texture” from the original profile. Figure 3 

shows a function with the characteristic 

high frequencies and short wavelengths of 

members of the NFUNs. Spiking and distortion did take place near the edges of the 

11-slab profile during the decomposition 

process, but the profile was long enough 

that the middle slab was unaffected.

Removing the first IMF from the original 

profile leads to the smoother profile 

(referred to as the first residue) as shown 

in figure 4. It is clear that the first IMF 

is indeed a function of the NFUN group. 

There is some noticeable smoothing near 

the bottom of the slabs, meaning the empirical mode decomposition sifting is performing as expected. The amount of data, still 

present within the first residue which 

shows characteristics of “noise/surface texture,” will determine whether the second 

IMF is grouped as an NFUN or a CFUN. 

There appears to still be “noise/surface 

texture” contained within the first residue 

as shown in figure 4. Therefore, the second 

IMF will likely be another member of the 

NFUN group.

Figure 2. Original 11-slab profile from Wisconsin LTPP test section 553009.

© Dan Franta
5

Figure 3. First IMF from the middle Wisconsin LTPP 553009 slab profile.

© Dan Franta

Figure 4. First residue with the original profile from Wisconsin LTPP test section 553009.

© Dan Franta
6

© Dan Franta

Figure 5. Second IMF and second member of the NFUN group.

The second IMF, shown in figure 5, still 

displays the short wavelength and high 

frequency characteristics of “noise/surface 

texture.” Although the second IMF has longer wavelengths and lower frequencies 

than the first IMF, the frequencies and wavelengths displayed are not characteristic of 

“curling.” Therefore, the second IMF will be 

classified as another NFUN. 

Removing the second IMF from the first 

residue gives the resulting second residue 

shown in figure 6. The remaining “noise/

surface texture” portions of the original 

profile have been significantly removed 

by the second IMF, as displayed by the 

smoothness of the second residue. Now 

that the “noise/surface texture” has been 

extracted, the next IMF will likely be composed of “curl.”

Figure 7 shows the portion of the original 

profile resulting from “curl” and classified as 

a member of the CFUNs. It is clear that this 

IMF has lower frequency, smoother waves, 

and larger amplitudes than what was typical 

of the NFUNs. Notice that the “curl” data 

is zeroed on the x-axis. This is because the 

“curl” data is free of nearly all “base trends.” 

Also, notice that “curl” is driven by joint 

spacing. The lengths of the slab correspond 

to the resulting “curl” wavelength. The 

third IMF appears to contain most of the 

“curl” data from the original profile; consequently, after it is removed, the original 

profile is reduced to its “base trends.”

As previously mentioned, the third IMF 

(shown in figure 7) removed the “curl” data 

from the second residue (shown in figure 6). 

Removal of the third IMF from the second residue results in the third residue 

as shown in figure 8. The third residue 

displays the underlying “base trend” of 

the data set for the middle slab. Therefore, 

any remaining IMFs, along with the final 
7

Figure 7. Third IMF and first and only member of the CFUN group.

Figure 6. Second residue with the original shifted profile.

© Dan Franta

© Dan Franta
8

Figure 8. Third residue with original shifted profile. 

residue, will be classified as BFUNs. 

IMFs four, five, and six, along with the 

final residue, compose the BFUN group 

for this Wisconsin slab as shown in 

figure 8. It is clear that the BFUN group 

is free of “noise/surface texture” and “curl.”

Physical grouping of the IMFs can now be 

completed. The summation of the NFUNs 

is shown in figure 9. The CFUNs group is 

composed of the third IMF already displayed in figure 7. The BFUNs with the original slab profile are displayed in figure 8. 

Finally, the combination of CFUNs+BFUNs 

with the original profile is shown in 

figure 10. This final combination of the 

CFUNs+BFUNs constitutes a smoother 

version of the original slab profile.

The sum of the two IMFs comprising the 

NFUN group for this profile is shown in 

figure 9. The high frequency and low 

amplitude wavelengths, along with lack 

of smoothness, are consistent with trends 

associated with “noise/surface texture” and 

thus confirm these IMFs do indeed belong 

in the NFUN group.

Finally, as shown in figure 10, the BFUNs 

and CFUNs comprise the majority of a 

profile data set. The original profile was 

shifted downward over the top of the 

CFUNs+BFUNs result, using a minimization of least squares, in order for easier 

comparison of the two profiles. The 

CFUNs+BFUNs had a significant portion 

of the “noise/surface texture” removed, 

resulting in a smoother profile. NFUNs 

distort original profiles, therefore suggesting that the combination of the 

CFUNs+BFUNs is a more accurate representation of the profile the LTPP data were 

collected to explore.

© Dan Franta
9

Figure 9. NFUN group for the Wisconsin LTPP 553009 slab profile.

Figure 10. CFUNs+BFUNs with the original slab profile (shifted by least squares minimization for comparison). 

© Dan Franta

© Dan Franta
10

Results

Using the grouping of IMFs procedure 

from the Hilbert-Huang-based profile analysis algorithm as described, the results 

from its application to profiles from the 

Arizona and Utah LTPP test sections are 

provided. CFUNs+BFUNs results from 

surface profiles collected at different times 

from the Arizona test section are compared. A condensed version of the automated profile analysis results will be 

provided in this section.

Arizona Section 040215

The surface profile data from Arizona test 

site 040215 was used for the analysis. This 

test section contains profile data (from 

run 1) for eleven 15-ft-long slabs of 

11-inch-thick concrete, collected January 25, 

2010, at 5:37 p.m. The left wheel path data 

were used for analysis. The automated 

Hilbert-Huang-based profile analysis algorithm was applied to the entire profile 

shown in figure 11. 

CFUNs+BFUNs analysis is used in the middle slab to avoid edge spiking effects from 

the sifting process.

The CFUNs+BFUNs group is nearly free of 

all “noise/surface texture” distortions as 

shown in figure 12.

The same test section was analyzed in a 

similar manner using profile data collected 

from run 2 on September 20, 2008, at 2:26 

a.m. from the left wheel path.

The surface profile section displayed in 

figure 13 shares some similarities with the 

profile shown in figure 11.

Figure 11. Original Arizona LTPP 040215 profile collected January 25, 2010.

© Dan Franta
11

Figure 13. The Arizona LTPP 040215 section collected September 20, 2008.

Figure 12. CFUNs+BFUNs with the original middle slab profile from Arizona.

© Dan Franta

© Dan Franta
12

A closer look at the middle slabs from the 

two raw profiles is displayed in figure 14. 

The middle slab shown in figure 14 is 

the profile of interest. Notice the differences between the two raw profiles. 

The CFUNs+BFUNs, as computed by the 

developed Hilbert-Huang-based algorithm, 

for the two different profiles are compared 

in figure 15. The two raw profiles displayed 

in figure 14 are not nearly as similar as 

the two CFUNs+BFUNs profiles shown in 

figure 15. Once the NFUNs were removed, 

the CFUNs+BFUNs for the two slab profiles 

closely resemble one another. These slabs 

were collected approximately 20 months 

apart, during different seasons, and the 

CFUNs+BFUNs profiles remain basically 

the same. This is likely due to the early-age 

built-in curl within the slabs. The developed 

algorithm allows for this determination.

Utah Section 493011

An 11-slab section using the surface profile data from the Utah test section was 

also analyzed using the automated HilbertHuang-based profile analysis algorithm. 

This data is from section 493011, collected 

on October 9, 2007, at 3:01 p.m., during 

run 1, from the left wheel path. The section 

contains 10-inch-thick concrete of varying 

slab lengths.

The same procedure used for the Wisconsin 

and Arizona LTPP test sections is applied 

to the Utah profile shown in figure 16. The 

slab profile used for analysis is centered on 

x ≈ 828 inches.

Again, the developed Hilbert-Huang based 

profile analysis algorithm successfully 

extracted the CFUNs+BFUNs from the middle slab profile as shown in figure 17.

Figure 14. Raw middle three Arizona LTPP 040215 slab profiles from 2010 and 2008.

© Dan Franta
13

Figure 15. CFUNs+BFUNs for the middle slabs collected in 2010 and 2008.

© Dan Franta

Figure 16. Eleven-slab LTPP 493011 profile from Utah.

© Dan Franta
14

Figure 17. Original slab profile with the CFUNs+BFUNs from the middle Utah LTPP 493011 slab profile.

Conclusions

The LTPP database contains vast amounts 

of surface profile data mainly used for computing IRI. The developed Hilbert-Huangbased pavement profile analysis algorithm 

can be used to successfully separate LTPP 

surface profiles into “noise/surface texture,” 

“curl,” and “base trend” sources. Trends 

from surface profiles were identified in 

Wisconsin, Arizona, and Utah LTPP profiles.

Due to spiking during sifting, it is best to 

discard the slabs near the edges for the 

multi-slab scenarios and also to neglect 

them during IMF grouping classifications. 

The length and number of slabs required for 

a multi-slab profile to be effectively decomposed and grouped varies with the unique 

characteristics of each profile. Multiple slab 

configurations tend to provide better separation of NFUNs, CFUNs, and BFUNs than 

single slab configurations and should be 

used with this developed profile analysis 

algorithm whenever possible.

The separation of the profiles allows for 

built-in curl analysis from LTPP surface profile data. An Arizona LTPP slab profile was 

shown to contain consistent “curl” deflections for the same slab over a 20-month 

timespan and during both winter and 

early fall seasons. The raw profiles were 

smoothed using the developed algorithm, 

which allowed for the analysis. The consistent slab shape is likely due to early age 

built-in curl.

© Dan Franta
15

The LTPP database is composed of multiple types of road profile sections with 

various slab lengths, thicknesses, and load 

transfer mechanisms, among other things. 

The developed Hilbert-Huang-based profile 

analysis algorithm has been proven to be 

universal and can be applied to any of these 

various road surface profiles.

Acknowledegments

A special thank you goes out to those 

who assisted in the funding and development of this project. I would like to 

acknowledge the financial support provided through the FHWA/Minnesota 

Department of Transportation (MnDOT) 

project, Determination of the Effective 

Built-In Curling of Concrete Pavements. 

From the Federal Highway Administration, 

I would like to thank Tom Yu. From MnDOT, 

I would like to thank a host of people, 

including Maureen Jensen, Bernard 

Izevbekhai, Steve Olson, Bob Strommen, 

Tom Burnham, Ally Akkari, and Tim Nelson.

References

1. Franta, D.P. (2012) Computational 

Analysis of Rigid Pavement Profiles, 

Master’s Thesis, University Of Minnesota, Twin Cities, Minneapolis/St. 

Paul, MN.

2. “Long-Term Pavement Performance” 

(2011). Standard Data Release 25.0 

(DVD Version), U.S. Department of 

Transportation, Federal Highway 

Administration, Washington, DC

3. Byrum, C. (2000). “Analysis by HighSpeed Profile of Jointed Concrete 

Pavement Slab Curvatures.” Transpor

tation Research Record 1730, pp. 1–9, 

Transportation Research Board, 

Washington, DC.

4. Adu-Gyamfi, Y.O., Attoh-Okine, N.O., and 

Ayenu-Prah, A.Y. (2010). “Critical Analysis 

of Different Hilbert-Huang Algorithms for 

Pavement Profile Evaluation.” Journal of 

Computing in Civil Engineering, Vol. 24, 

No. 6.

5. Attoh-Okine, N.O., Ayenu-Prah, A.Y. Jr., 

and Mensah, S.A. (2006). “Application 

of the Empirical Mode Decomposition to 

Pavement Profile Analysis.” Department 

of Civil and Environmental Engineering, 

University of Delaware, Newark, DE.

6. Huang, N.E. (2005). “Introduction to 

the Hilbert-Huang Transform and its 

Related Mathematical Problems.” World 

Scientific Publishing Co. Pte. Ltd., 

Hackensack, NJ.
16

DECEMBER 2014 FHWA-HRT-13-093

HRDI-30/12-14(250)E

Researchers—Franta, Daniel P., Wojtkiewicz, Steven F., Khazanovich, Lev.

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report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at 

http://www.fhwa.dot.gov/research/.

Key Words—Built-in curl, LTPP, Hilbert-Huang, empirical mode decomposition, intrinsic mode function.

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