A Characterization Method for Pavement Structural Condition Assessment based on the Distribution Parameter of the Vehicle Vibration Signal

A pavement structural survey plays a vital role in road maintenance and management. This study was intended to explore the feasibility of a non-stop pavement structure assessment method by analyzing the vibration data from a vehicle sensor. In this study, three falling weight deflectometer (FWD) tests and four vehicle vibration tests were conducted on five pavement structures. The FWD test results show that the continuously reinforced composite pavement has a higher structural stiffness than the semi-rigid base asphalt pavement. According to the statistical distribution of vehicle acceleration, a distribution parameter, the peak probability density (PPD), was proposed. The correlation coefficient (−0.722) of the center deflection (D1) and PPD indicates a strong correlation between the two variables. Therefore, PPD is strongly correlated with pavement structural stiffness. This study proposed a novel characterization method for pavement structural conditions based on the distribution parameter of the vehicle vibration signal.

Sufficient statistics for the Pareto distribution parameter

The task of estimating the parameters of the Pareto distribution, first of all, of an indicator of this distribution for a given sample, is relevant. This article establishes that for this estimate, it is sufficient to know the product of the sample elements. It is proved that this product is a sufficient statistic for the Pareto distribution parameter. On the basis of the maximum likelihood method the distribution degree indicator is estimated. It is proved that this estimate is biased, and a formula eliminating the bias is justified. For the product of the sample elements considered as a random variable the distribution function and probability density are found; mathematical expectation, higher moments, and differential entropy are calculated. The corresponding graphs are built. In addition, it is noted that any function of this product is a sufficient statistic, in particular, the geometric mean. For the geometric mean also considered as a random variable, the distribution function, probability density, and the mathematical expectation are found; the higher moments, and the differential entropy are also calculated, and the corresponding graphs are plotted. In addition, it is proved that the geometric mean of the sample is a more convenient sufficient statistic from a practical point of view than the product of the sample elements. Also, on the basis of the Rao–Blackwell–Kolmogorov theorem, effective estimates of the Pareto distribution parameter are constructed. In conclusion, as an example, the technique developed here is applied to the exponential distribution. In this case, both the sum and the arithmetic mean of the sample can be used as sufficient statistics.