Enhanced American Association of State Highway and Transportation Officials Cumulative Difference Approach for Pavement Data Segmentation

Abstract

This paper proposes improving the American Association of State Highway and Transportation Officials cumulative difference approach to pavement data segmentation. Although this approach is popular in pavement management applications, it is heuristic, based on visual inspection of plots of data, and has well-documented limitations. One main limitation is reliance on a change in sign of the slope of the cumulative sum of the data to identify segment breakpoints. This makes it very sensitive to small data variations (such as noise), and researchers have shown that segment breakpoints can occur without a change in the sign of the slope. Our proposed approach uses the maximum (in absolute value) of the cumulative sum to identify a potential breakpoint. Whether that maximum is because of random variation or the presence of a true breakpoint is rigorously tested at a user-specified significance level using the known statistical distribution of that maximum. The approach also allows specifying a minimum segment length and minimum difference between adjacent segments. Simulation studies show that when the process that generated the data consists of piecewise constant segments, the Type I error of erroneously identifying breakpoints is controlled at the chosen statistical significance level, both for normally distributed random variation in the data and any distribution with well-defined variance. When the process that generated the data does not consist of piecewise constant segments, the approach results in a segmentation with a very low mean square error or mean absolute error with respect to the data generating process. We show an application to traffic speed deflectometer deflection data.