Singular Value Decomposition of Road Events Into Characteristic Shapes

Road profiles are typically characterized by their spectral content. It has been noted by several researches, however, that road profiles are generally nonstationary signals that contain significant irregularities such as potholes. Such signals are not well described in the spectral domain. The objective of this work is to describe road profiles in the spatial domain by developing a set of characteristic shapes onto which individual events can be cast. A set of analytical functions describing these shapes is also developed. In order to develop a set a characteristic shapes, more than a million events are investigated from a mixture of road types (from highways to gravel roads) and a variety of locations throughout the United States. A set of characteristic shapes is developed for each road type and location. Although the events were drawn from diverse samples, the resulting sets of characteristic shapes are nearly indistinguishable. This similarity allows a single set of characteristic shapes to describe events for a wide class of roads. Variations in these sets are discussed and used in deriving a set of orthogonal analytical functions that describe the characteristic shapes. Individual road events are then mapped onto this set of characteristic shapes. The implications of decomposing road events into these characteristic shapes are discussed.