A Non-linear Statistical Analysis On The Measurement Data Of Traffic Flow

Traffic flow study is a multi-course subject, involving mechanics, non-linear science, statistics, information science, and traffic engineering, etc. It reveals the basics and laws of traffic flow through studying their common characteristics, thus to better guide the related traffic engineering department in their planning, designing and improving of traffic network and traffic controlling system.Supported by NSFC, a method based on video record to get traffic flow parameters is proposed to get a series of micro car-following data of short-time interval, such as continuous headway, velocity and acceleration. These data are composed to 5 traffic flow time series totalling 90,000. We test their rationality, and find:the headway and velocity data meet the normal distribution, and the relation between the average velocity and average headway correspond to the common rules of traffic flow; as a result of China's traffic crowdedness outnumbering our western fellows, the characteristic of free flow under low density pointed out by Kerner is less obvious along with the increasing of density, and it may show nonlinearity under all levels of density; the distribution of acceleration is a normal one as well. Average acceleration is sensitive to average velocity, yet insensitive to average headway.To find out the nonlinear characteristics of traffic flow, we apply R/S analysis to the above mentioned five samples to calculate their Hurst exponents and average cycle time. Hurst exponent is to measure the statistic relevance, while average cycle time judges how long the initial information will lose its impact. Both are important nonlinear statistic index. To better understand these two indexes and R/S analysis itself, a series of real samples, including cyclic time series and those combined with white noises, are tested and found:in terms of periodic series alone, average cycle time is not equal to their real cycle period, but judges how long the initial information will lose its impact, which is more important to non-periodic series; in condition of periodic series with white noises, Hurst exponent is sensitive to some extent, while average cycle time is non-sensitive to a certain extent.Lastly, the headway time series samples from the above five different cities and different roads are applied with R/S analysis. It is found:the Hurst exponents and the average cycle times are more objective, affected less by the human factors in the data and different roads are applied with R/S analysis. It is found:the Hurst exponents and the average cycle times are more objective, affected less by the human factors in the data collection procedure; the traffic flow demonstrates positively correlated trend, and this trend is increasing with the crowdedness of the road; the time series established can be applied for the short-term or long-term traffic flow prediction and management.