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Federal Highway Administration Research and Technology
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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
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:
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.
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)
1 m = 3.28 ft.
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.
1 m/km = 5.28 ft/mi
Figure 10. IRI obtained from two repeat runs.
1 m = 3.28 ft
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.
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.
1 cycle/m = 0.3 cycle/ft
Figure 12. Example of a PSD plot.
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).
25.4 mm = 1 inch
Figure 13. Profile recorded by a profiler.
25.4 mm = 1 inch
Figure 14. Profile after being subjected to a 5-m (16-ft) high-pass filter.
25.4 mm = 1 inch
Figure 15. Profile after being subjected to a 10-m (33-ft) low-pass filter.
25.4 mm = 1 inch
Figure 16. Profile after being subjected to a band-pass filter.
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.
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.
1 m = 3.28 ft
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 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.
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:
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:
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: