Bimodal Distribution Function with Fuzzy Regression in Predicting Random Truckload Patterns

Abstract

A bimodal distribution function with statistical parameters obtained using fuzzy regression is presented for predicting random truckload patterns that include all load ranges including overloads. Overload trucks often appear as a sizable portion of truck populations on highways. In applications when damage estimation of transportation facilities such as pavements and bridges is desired, theoretical models providing a reasonable representation of truckload populations including overloads will be useful. Load populations mostly exhibit inconsistent patterns, often with two or more distinct peaks. This is because of a combination of loaded and empty trucks as well as overloads in the population. As such, a mixed distribution model instead of a simple statistical distribution is used to portray a realistic representation of truckload populations. In this paper, using the bimodal model, theoretical distributions are developed to (1) represent the entire truckload population with weigh-in-motion (WIM) data, and (2) predict the population with limited data. If no truckload population is available, the bimodal distribution model can still be used, with certain assumptions, based on fuzzy regression using certain parameters pertaining to the traffic data such as the average daily truck traffic and an overall estimate of the percentage of overload data in the population. This paper represents new directions in modeling truckload patterns with capabilities to offer the continuity as well as the bimodal feature of the limited load data.