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Publication Number: FHWA-HRT-05-054
Date: September 2005

Quantification of Smoothness Index Differences Related To Long-Term Pavement Performance Equipment Type

Chapter 4: Analytical Procedures

INTRODUCTION

This section describes the analytical techniques and software that were used in this research project, and the overall approach that was used to analyze data collected for the various LTPP profiler comparison and verification studies. The following analytical techniques/software were used for data analysis:

  • Roughness profiles.
  • Power spectral density (PSD) plots.
  • Data filtering.
  • Cross correlation.
  • Road Profile Analysis Software (RoadRuf).1

ANALYTICAL TECHNIQUES AND SOFTWARE

Roughness Profiles

The roughness of a section of roadway can be expressed by the IRI, which indicates the average roughness for that road section. However, the roughness within this section of roadway can vary. For example, consider a 100-m- (328-ft-) long section of roadway that has a roughness of 1.23 m/km (6.5 ft/mi). This road section can be divided into 10 equidistant segments, where the length of each segment is 10 m (33 ft). Figure 8 shows the roughness of each of these 10-m (33-ft) segments.

This figure shows a bar chart with the X-axis showing the segment number and the Y-axis showing the International Roughness Index (IRI). The IRI of 10 segments, with each segment represented by a bar is shown in the figure. The IRI of segments 1 through 10 are 1.42, 1.16, 1.07, 1.29, 1.18, 1.32, 1.33, 1.18, 1.01 and 1.34 meters per kilometer (90, 74, 68, 82, 75, 84, 84, 75, 64, and 85 inches per mile) respectively.

1 m/km = 5.28 ft/mi

Figure 8. Roughness of a roadway expressed in 10-m (33-ft) segments.

1Initially funded by FHWA, this software was developed by the University of Michigan‘s Transportation Research Institute.

As shown in this figure, the roughness values for the 10-m (33-ft) segments are variable, with segment 1, which has an IRI of 1.42 m/km (7.5 ft/mi), having the highest roughness, and segment 9, which has an IRI of 1.01 m/km (5.3 ft/mi), having the lowest roughness.

Instead of using a single value to characterize the roughness of a roadway, a roughness profile can be used to show how roughness varies with distance along the roadway. Figure 9 shows a roughness profile based on a 10-m (33-ft) base length for the same section of roadway whose roughness distribution was shown in figure 8. In figure 9, the roughness value for a specific location is the average roughness over a 10-m (33-ft) length (i.e., the base length of the roughness profile) that is centered at that location. For example, the roughness shown at a distance of 25 m (82 ft) is the average roughness from 20 to 30 m (66 to 98 ft). The highest roughness value in the roughness profile occurs at a distance of 50 m (164 ft), and, therefore, the 10-m (33-ft) stretch of the road that has the highest roughness is between 45 and 55 m (148 and 181 ft). A roughness profile can be constructed for any base length. A detailed description of roughness profiles is presented by Sayers.(20)

This figure shows a graph with distance as the X-axis and the IRI as the Y-axis. The distance shown on the graph ranges from 0 to 100 meters (0 to 328 feet). The graph, which is the roughness profile, shows roughness variations between 5 and 95 meters (16 and 312 feet). The roughness between these limits ranges from a low of 0.78 meters per kilometer (49 inches per mile) occurring at 42 meters (138 feet), to a high of 1.63 meters per kilometer (103 inches per mile) occurring at 50 meters (164 feet).

1 m = 3.28 ft.
1 m/km = 5.28 ft/mi

Figure 9. Example of a roughness profile.

When evaluating the IRI repeatability of a profiler, or when comparing IRI values obtained by different profilers, an evaluation of roughness profiles provides much more information than just evaluating the IRI value that is obtained for the entire road section. For example, consider the following case where two repeat runs were conducted by a profiler (not LTPP‘s profiler) on a test section that was 180 m (590 ft) long. The left-wheelpath IRI values for the two runs were 1.66 and 1.63 m/km (105 and 103 inches/mi). The IRI values obtained for the two repeat runs were very similar, which seems to indicate that the profiler is capable of collecting repeatable data. Figure 10 shows the IRI values for the two runs reported at 10-m (33-ft) intervals.

This figure shows that at some segments, there was a considerable difference between the IRI values obtained for the two runs. However, averaging IRI over the 152.4-m- (500-ft-) long section caused these variations to smooth out and gave an overall IRI value for the two repeat runs that was very similar to the individual value for each run.

Figure 11 shows the roughness profiles for a 10-m (33-ft) base length for the two runs whose IRI values are shown in figure 10. As described previously, for the 180-m- (590-ft-) long section, the two runs have IRI values of 1.66 and 1.63 m/km (105 and 103 inches/mi). Although the IRI over the entire section is very similar for the two runs, figure 11 shows there are differences in the spatial distribution of the roughness for the two runs. The roughness profiles present much more information than what is presented in the bar charts shown in figure 10 because the roughness profiles show how the roughness captured by the two runs varies throughout the roadway.

This figure is a bar chart with the X-axis showing the segment number and the Y-axis showing the IRI. The IRI obtained from two repeat runs for 18 segments are shown in this graph. The IRI values obtained from the first run for segments 1 through 18 are 2.16, 1.61, 1.54, 2.04, 2.04, 1.97, 1.37, 2.12, 2.00, 1.53, 1.95, 2.05, 1.10, 1.40, 1.47, 1.20, 1.24, and 1.08 meters per kilometer (137, 102, 98, 129, 129, 125, 87, 134, 127, 97, 124, 130, 70, 89, 93, 76, 79, and 68 inches per mile), respectively. The IRI values obtained from the second run for segments 1 through 18 are 1.52, 1.35, 1.43, 2.10, 1.92, 1.91, 1.44, 1.82, 2.13, 1.51, 2.07, 1.42, 1.30, 1.62, 1.62, 1.74, 1.33, and 1.14 meters per kilometer (96, 86, 91, 133, 122, 121, 91, 115, 135, 96, 131, 90, 82, 103, 103, 110, 84, and 72 inches per mile), respectively.

1 m/km = 5.28 ft/mi

Figure 10. IRI obtained from two repeat runs.

This figure shows the 10-meter (33-foot) base length roughness profile of two profiler runs along the same roadway section. The X-axis of the plot shows the distance, while the Y-axis shows the roughness. The roughness profiles for the two runs over a distance of 180 meters (590 feet) are shown in this figure. Although the two roughness profiles coincide at a few locations, at the majority of the locations there are differences between the two roughness profiles.

1 m = 3.28 ft
1 m/km = 5.28 ft/mi

Figure 11. Roughness profiles at 10-m (33-ft) base length for two runs.

As illustrated in this example, it is important to recognize that, just because the IRI from repeat runs agree well, or the IRI from two devices agree well at a pavement section, it does not necessarily mean that the two devices are collecting similar profile data. Roughness profiles can be used to determine whether repeat runs from a profiler or profile runs from different devices are giving a similar spatial distribution of IRI along the section.

Power Spectral Density Plots

A road profile encompasses a spectrum of sinusoidal wavelengths. A PSD function is a statistical representation of the importance of the various wavelengths contained in the profile.(2) The PSD function of the profile slope best shows the differences in the roughness properties because the basic spectrum of roughness over the wave numbers is more uniform.(2) In this research project, PSD plots that use the profile slope were used in the analyses. Figure 12 shows an example of a PSD plot of a road profile. This plot presents a view of the distribution of the wavelengths that are contained within the road profile. The x-axis of the PSD plot represents the wave number. The wave number is the inverse of the wavelength. If prominent wavelengths are present in a profile, such wavelengths will show up as dominant spikes in the PSD plot.

A power spectral density (PSD) plot shows the distribution of wavelengths that are contained in a road profile. This figure shows an example of a PSD plot. In this plot, the x-axis shows the wavenumber (which is the inverse of wavelength), and the y-axis shows the power spectral desnsity of the left slope. If prominent wavelengths are present in the profile, such wavelengths will show up as spikes in the PSD plot.

1 cycle/m = 0.3 cycle/ft
1 m/cycle = 3 ft/cycle

Figure 12. Example of a PSD plot.

Data Filtering

The profiles obtained by the T-6600 and ICC profilers have been filtered with a 100-m (328-ft) upper-wavelength cutoff filter, while the data obtained by the DNC 690 profilers have been filtered with a 91-m (300-ft) upper-wavelength cutoff filter. The profile data can be further filtered during data analysis to look at details within the profile. The types of filters that are commonly used in analyses are high-pass filters, low-pass filters, and band-pass filters. A high-pass filter removes wavelengths greater than a specified value. A low-pass filter removes wavelengths less than a specified value. A band-pass filter keeps the wavelengths within a specified waveband and removes all other wavelengths.

The following example illustrates the application of filtering techniques to profile data. Figure 13 shows a plot of a typical profile that was obtained from LTPP‘s T-6600 profiler. Figures 14, 15, and 16, respectively, show this profile after it has been subjected to a 5-m (16-ft) high-pass filter, a 10-m (33-ft) low-pass filter, and a band-pass filter that has a lower wavelength of 5 m (16 ft) and an upper wavelength of 10 m (33 ft).

The profile plot shown in figure 14 has all wavelengths that are greater than 5 m (16 ft) removed. The profile plot shown in figure 15 has all wavelengths less than 10 m (33 ft) removed. The plot shown in figure 16 contains only the wavelengths between 5 and 10 m (16 and 33 ft).

This figure shows a plot of a profile recorded by a profiler. The X-axis shows the distance, while the Y-axis shows the elevation. The profile recorded over a distance of 152 meters (500 feet) is shown in this figure. The elevation values between these limits range from negative 10 to positive 8 millimeters (negative 0.39 to positive 0.31 inches).

25.4 mm = 1 inch
1 m = 3.28 ft

Figure 13. Profile recorded by a profiler.

This figure shows the profile in figure 13 after it has been subjected to a 5-meter (16-foot) high-pass filter. The X-axis in the figure shows distance, while the Y-axis shows the elevation. The long wavelengths have been taken out of the profile by the high pass filter, and more shirt wavelength details of the profile are seen in this figure. The profile elevations range from negative 8 to positive 2.2 millimeters (negative 0.31 to positive 0.09 inches).

25.4 mm = 1 inch
1 m = 3.28 ft

Figure 14. Profile after being subjected to a 5-m (16-ft) high-pass filter.

This figure shows the profile in figure 13 after it has been subjected to a 10-meter (33-foot) low-pass filter. The X-axis in the figure shows distance, while the Y-axis shows the elevation. The wavelengths less than 10 meters (33 feet) have been taken out of the profile shown in figure 13. Short interval profile features that are seen in figure 13 are not shown in this figure, because they have been removed by the application of the low-pass filter. The profile elevations range from negative 1.2 to positive 3.8 millimeters (negative 0.05 to positive 0.15 inches).

25.4 mm = 1 inch
1 m = 3.28 ft

Figure 15. Profile after being subjected to a 10-m (33-ft) low-pass filter.

This figure shows the profile in figure 13 after it has been subjected to a band-pass filter that only kept wavelengths between 5 and 10 meters (16 and 33 feet). The X-axis in the figure shows distance, while the Y-axis shows the elevation. The profile elevations range from negative 2.9 to positive 0.23 millimeters (negative 0.11 to positive 0.01 inches).

25.4 mm = 1 inch
1 m = 3.28 ft

Figure 16. Profile after being subjected to a band-pass filter.

Cross Correlation

The cross-correlation method for analyzing road profiles, which is an objective procedure for rating the agreement between profile measurements, was developed by Karamihas.(21) This procedure is based on the cross-correlation function described by Bendant and Piersol.(22) The description of the cross-correlation procedure presented in this section was obtained from University of Michigan Transportation Research Institute (UMTRI) report 2002-36.(21)

The cross-correlation method can be used to rate agreement between profiles in a given waveband. It can also be applied to rate agreement between the devices for any given roughness index, including IRI. This procedure provides a single, unitless rating agreement (ranging from 0 to 1) that describes how well two profiles correlate with each other.

Consider the example presented previously during the discussion on roughness profiles, where two repeat runs from a profiler provided very good agreement in overall IRI; however, there were significant differences in the distribution of roughness within the section. The cross-correlation method can be applied to this situation to obtain a value between 0 and 1 that will indicate how well the profiles agreed with each other in their ability to measure IRI over the section. This method compares the magnitude as well as the spatial distribution of the roughness within the section when computing the value of the correlation. When the cross-correlation method is used to compare the IRI for two profiles, both profiles are first filtered with the IRI filter that is contained in the IRI algorithm. Afterwards, the cross-correlation method is used on these filtered profiles to obtain a cross-correlation rating. To have a high rating between the two filtered profiles, the same level of roughness should be present in the two filtered profiles and, in addition, the rough features in both profiles must appear at the same location and have the same shape.

Cross correlation is superior to direct comparison of IRI values because it compares the overall roughness, as well as the spatial distribution of the roughness. Figure 17 shows an example of three repeat measurements made by a profiler after they have passed through the filters in the IRI algorithm. The filtered signals compare well with each other and have an average cross correlation that is higher than 0.995. The average cross correlation was computed by comparing two profiles at a time for all possible combinations and then computing the average of the cross-correlation values. The traces shown in figure 17 overlay so well that they are barely distinguishable from each other.

This figure shows a plot of three repeat profile measurements taken by a profiler at a section after the measurements have passed through the filters in the IRI algorithm. The X-axis of the plot shows distance, while the Y-axis shows the IRI filter output. The figure shows the profiles over a distance of 90 meters (295 feet). The three filtered profile plots overlay extremely well with each other. At the majority of the locations the three profiles coincide with each other, while at a few locations a very slight difference between the profiles can be seen. Overall, when looking at the profile plot, differences between the profiles are barely distinguishable.

Figure 17. Three IRI filtered profiles with an average correlation greater than 0.995.(21)

Figure 18 provides an example of a moderate correlation. It shows the repeat measurements from the same device on a different pavement section after they have passed through the filters of the IRI algorithm. The profiles compare fairly well, with an average correlation of 0.84. The traces do not overlay nearly as well as the traces shown in figure 17, and significant differences in the IRI filtered profiles are noted at some locations.

This figure shows a plot of the three repeat profile measurements taken by a profiler at a section after the measurements have passed through the filters in the IRI algorithm. The X-axis of the plot shows distance, while the Y-axis shows the IRI filter output. The figure shows the profiles over a distance of 90 meters (295 feet). Differences between the profiles are noticeable over the entire length of the section.

1 m = 3.28 ft
1 m/km = 5.28 ft/mi

Figure 18. Three IRI filtered profiles with an average correlation of 0.84.(21)

The cross-correlation method can also be used to compare two profiles over different wavebands. For example, the agreement between two profiles can be evaluated for short wavelengths, medium wavelengths, and long wavelengths.

The rating agreement provided by this procedure represents repeatability when it is applied to two measurements of the same profile by the same device, reproducibility when it is applied to two measurements of the same profile by different devices, and accuracy when a measurement from one of the devices is deemed to be correct.

An important step before applying the cross-correlation method is to ensure that the two profiles are properly synchronized so that the start location for both profilers is the same. Any error in the DMI of a profiler could have an impact on the results obtained from this method when it is applied to evaluate the reproducibility or accuracy of a profiler.

Another important assumption made when evaluating repeatability or reproducibility is that the profiles were obtained along the same path. Lateral variability during profiling can cause differences in the profile features that are measured, and these will be interpreted as an equipment factor during cross-correlation analysis. When this method is used to compare a profiler with a reference device, it is assumed that the measurements obtained by the reference device are error free.

RoadRuf Software

RoadRuf is an integrated set of computer tools for interpreting longitudinal road profiles.(23) RoadRuf was developed at UMTRI and was funded by FHWA. It is free software and can be downloaded from the Internet. RoadRuf contains a variety of tools for analyzing road profiles. The tools available in RoadRuf that were used in this research project are: (1) computing IRI and Ride Number (RN) values, (2) plotting profile data, (3) evaluating roughness profiles, and (4) plotting PSD.

ANALYTICAL APPROACH

This section describes the analytical approach that was used in this research project to analyze data obtained from LTPP profiler comparison and verification studies. When analyzing profile data obtained from the T-6600 and ICC profilers, the 25-mm (1-inch) data were used. For the DNC 690 profiler, only the data recorded at 152.4-mm (6-inch) intervals are available.

During LTPP profiler comparison studies, each profiler performs replicate profile runs on a test section. Initially, the following analyses were performed for each profiler, at each test section, separately for the left- and right-wheelpath profile data:

  1. Overlay the repeat runs of the profiler and perform a visual evaluation of the profiles. Distinct features observed in the profile were noted.
  2. Filter the profile data using a 1-m (0.3-ft) high-pass filter, a 10-m (33-ft) high-pass filter, and a band-pass filter having a wavelength cutoff between 1 and 30 m (3 and 100 ft), and evaluate the distinct features in the profile. Also look at the differences in the profile features among the repeat runs.
  3. Evaluate the repeatability of the roughness profiles computed for a 10-m (33-ft) base length by overlaying the roughness profiles obtained for the repeat runs. If differences in the roughness profiles are noted, evaluate the profile data to identify the profile features that cause the roughness profiles to be different.
  4. Compare PSD plots of the repeat runs. If differences in the PSD plots are noted, evaluate the profile data to identify the profile features that cause the PSD plots to be different.

After performing this evaluation, a representative profile run was selected for each profiler at each test section. Thereafter, for each LTPP comparison, the following analyses were performed separately for the left and right wheelpaths:

  1. Overlay the profile runs obtained from four of LTPP‘s profilers and perform a visual evaluation of the profile data. Note any distinct features that are different among the profiles.
  2. Filter the profile data using a 1-m (0.3-ft) high-pass filter, a 10-m (33-ft) high-pass filter, and a band-pass filter having a wavelength cutoff between 1 and 30 m (3 and 100 ft), and compare the profile features recorded by the four profilers. Note any distinct features that are different among the profiles.
  3. Overlay the 10-m (33-ft) base-length roughness profiles for the four profilers and Dipstick, and evaluate the repeatability of the roughness profiles. If major differences among the roughness profiles are noted, look at the profile data to identify features that cause the roughness profiles to be different.
  4. Overlay the PSD plots for the four profilers and determine whether there are differences in the PSD plots. If major differences are noted, analyze the profile data for the profiler that is different to identify the features in the profile that cause the difference.
  5. Perform a cross-correlation analysis between the profiler and Dipstick data.

Changes in LTPP‘s profiling equipment occurred in 1996 and 2002. On both of these occasions, before using the new profiler, each region performed a verification study between their old profiler and the new profiler. Data obtained from these two studies were used to evaluate the profile data collected by the two profilers. When comparing the data from the DNC 690 and T 6600 profilers, the ProQual-processed data, which is averaged profile data, were used. When comparing the profile data between the T-6600 and ICC profilers, profile data at 25-mm (1-inch) intervals were used. The following analyses were conducted at each test section and were performed separately for the left and right wheelpaths:

  1. Overlay the profile data from the two profilers and perform a visual evaluation of the profiles. Determine whether there are differences in the features contained in the profile data.
  2. Filter the profile data using a 1-m (3-ft) high-pass filter, a 10-m (33-ft) high-pass filter, and a band-pass filter having a wavelength cutoff between 1 and 30 m (3 and 100 ft), and evaluate the distinct features in the profile. Also look at the differences in the profile features among the repeat runs.
  3. Overlay the 10-m (33-ft) base-length roughness profiles for the two profilers to evaluate the agreement of the roughness distribution within a section. If major differences among the roughness profiles are noted, look at the profile data to identify the features that cause the roughness profiles to be different.
  4. Compare the PSD plots for the two profilers to determine whether the wavelength distribution for the two profilers is similar.
  5. Perform a cross-correlation analysis on a subset of the profiles to evaluate the agreement among the profiles collected by the two profilers.
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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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