The Statistical Inference-based Research On Sample Time Of The Vehicle Driving Cycle Experiment

Because of lacking corresponding theory, it is hard for engineers to determine when the vehicle driving cycle experiments should be stopped. In order to obtain sufficient experimental data, engineers always choose to prolong the time of experiments. However, it costs more money and time, which also prolongs the vehicle design cycle. Aiming at solving this problem, this paper proposed two methods that viewed the problem from two different perspectives, i.e., in road scale and zone scale, to obtain reasonable sample time. All these methods were based on the statistical inference theory.First, analyzing from road scale relies on city digital maps. This paper proposed a grid-based digital map generation method from massive vehicle GPS trajectories to obtain basic maps. It employed the intersection points between grid lines and trajectories to record the location information of trajectories instead of processing all the data points. Furthermore, these intersection points were used to find the position of each road by computing the corresponding trajectories’ centerline. Finally, the method was evaluated by contrasting with a commercial map.The key of vehicle driving cycle experiment is to guarantee the road driving times distribution obtained by experiments to be consistent with the road traffic flow distribution. Thus, a fast map matching method is also needed. Based on the generated map, a grid-based map matching strategy was presented. It focused on pinpointing the road that the trace point located rather than finding its exact location which traditional methods often emphasized. At last, the times of the vehicle driving on each road and the traffic network were obtained after matching all trajectories points. Finally, the sampling distribution of road traffic flow was obtained.City traffic networks are complex networks, which has been proved experimentally and theoretically. In other words, the road traffic flow should obey the power law. That means, if the sampling distribution of road traffic flow can reflect the power law characteristic of the city road traffic flow distribution, the experiment can be stopped. But, before estimating the city road traffic flow distribution, the accuracy of per car per day driving times of each road should be guaranteed. In this paper, the central limit theorem was used to quantify the driving times accuracy. When preset accuracy value was satisfied, we can use these data to estimate the city road traffic flow distribution. Since the power distribution exhibits as a straight line under logarithmic coordinates, the ordinary least square method was employed to estimate the parameters of power distribution. However, after analyzing the experimental data, we found the fluctuation of parameters’ confidence intervals was big which limited the implication of it. Thus, this paper used the stability of parameters to decide when the experiment should be stopped. Based on two simulations, we found that the sample time of the Changchun City was about 50 days.Apparently, analyzing from road scale perspective is complicated. Digital maps and map matching algorithms are needed during the process, which has an influence on the estimation accuracy of the sample time. Aiming at the aforementioned problem, this paper also proposed a method from zone scale perspective. Whether the sample time analysis in zone scale is feasible should be considered first. By using K core algorithm and optimum partition theory, Changchun road hierarchy was obtained. After comparing roads’ VA distributions that were from the same hierarchy, we found they were similar with each other. Besides, roads in same hierarchy also gathered geographically. Thus, these roads can be analyzed in together, i.e. in zone scale. In other words, it is reasonable to analyze the vehicle driving cycle sample time in zone scale.Based on the one month driving data of 100 taxis of Changchun and one week driving data of 2340 taxis of Beijing, the per car per day per square kilometers driving times of each zone was obtained. We also got the zone driving times distribution of Changchun and Beijing. These two distributions were worked as standard distributions to test the quality of sampling distributions generated by experiments. By applying K-S test, this paper found Nakagami distribution and exponential distribution can describe the city zone driving times distribution. Similarly, the statistical inference was also employed to estimate the sample time of Beijing and Changchun. During this process, the maximum likelihood estimation was used to estimate distribution parameters. After the calculation, we got the sample time of Changchun which was 26 days and Beijing was 95 days.In the analysis, we found the key factor of affecting the quality of the sampling distribution is accuracy of each zone’s per car per day per square kilometers driving times. We proved the expectation of zone driving time variable coefficient, which was computed from the sample data, was linear with the parameter that was used to evaluate the similarity between sampling distribution and population distribution theoretically and experimentally. That means, in the vehicle driving cycle experiment, engineers can estimate the sample time by computing the expectation of variable coefficient in real time.