On the Statistical Distribution of Stationary Segment Lengths of Road Vehicles Vibrations

This paper presents an important outcome of a research programme which focuses on the development of a method for synthesizing, under controlled conditions in the laboratory, the non-stationary random vibrations generated by road transport vehicles. It addresses an important limitation of current methods used for synthesising random vehicle vibrations which assume that vibrations produced by wheeled vehicles can be approximated by a zero-mean, normally-distributed (Gaussian) random process and, therefore, fails to accurately reproduce the fluctuations in vibration levels that occur naturally during road transportation realizations [1]. The paper builds upon the observation that non-stationary random vehicle vibrations are composed of a sequence of zero-mean random Gaussian processes of varying standard deviations [2]. It discusses the important parameters that need to be addressed when dealing with the synthesis of random sequences. The paper presents the development of a change-point detection algorithm that was used to determine the length of stationary segments within a large number of typical non-stationary random vibration records. These include measured vibration records as well as numerically-generated records based on measured pavement profiles. The algorithm, based on the cum-sum / bootstrapping techniques, was developed and applied to the instantaneous magnitude of sample vibration records. The statistical distribution of segment lengths for each vibration record was computed with the aim of identifying similarities and trends for the development of an overall statistical model for segment lengths to be used for synthesis purposes. One outcome of note was that the shape of the segment length distributions computed from a wide range of vibration records are generally comparable and exhibit an asymptotic-like decrease in probability of occurrence as the segment length increases. This behaviour was found to be adequately modelled with a hyperbolic trigonometric function which was found to be useful for characterising the general statistical behaviour of segment length for non-stationary random vibrations produced by road vehicles. Finally, the significance and relevance of this outcome with respect to the synthesis of non-stationary vibrations for package evaluation and validation purposes is highlighted.