Modified Voronoi Method For Measuring Pedestrian Density And Its Model Based On Occupy Area

Pedestrian dynamics research has been a very important content of pedestrian evacuation.Pedestrian evacuation experiment and modeling are the most important methods of pedestrian dynamics research.Through a large number of observations and controlled experiments,researchers got some characteristics of pedestrian movement,and revealed the motion law of human.But the empirical databases for quantitative calibration are still insufficient.After summarizing the predecessors' global and local density,based on Voronoi method and combined with personal distance and field of vision,this paper proposes a pedestrian-occupy-polygon method to calculate the density and velocity of pedestrian.By comparing the three different methods' results(average density and average velocity),we find that the results in this paper change continuously,have smaller fluctuations than classical method and are more reasonable than Voronoi method at low density.For the individual velocity-density scatter plot,the results with new method are more concentrated than Voronoi method,especially to remove the unreasonable data(low density with small velocity).It seems that using pedestrians' forward 120° view area to calculate the local density is more reasonable than using pedestrians occupy polygon's area.Because prior to 120° method' density conform to the basic relationship between pedestrian speed and density better.And based on this,we get the velocity distribution with different local density and the relationship between the local density and velocity.By learning from the traffic flow model and the pedestrian movement direction mechanism,using the characteristics of pedestrian-occupy-polygon,the pedestrian occupy polygon' movement model is put forward.We simulated the single channel scene with bottleneck and without bottleneck by using this model.The prior to 120°view range is divided into three parts-front,left front and right front.There are two ways to get the direction of pedestrian,one is selecting the largest area of the three parts,and the other is choosing the direction probability according to the size of the three parts.Also,there are two ways to determine the velocity:A)according to the prior to 120° area of visual field to get the local density and speed,B)according to the selected direction and its area to calculate the local density and get the speed.There are four solutions of two combinations.Through the simulation of single channel scene,we found that the result with 1)and B)is the most accord with the experiment results.It shows that most of pedestrian determine their direction and speed by using 1)and B)method.We added some virtual points to take the place of boundary and bottleneck,and the single channel scene with bottleneck was simulated.The congestion and arch distribution phenomena can be found in the process of simulation.Considering that the introduction of virtual point will decrease the effective width of bottleneck,we changed the place of virtual points to make sure that the effective width of bottleneck was as same as the experiment scene.After that,the scene of single channel with bottleneck was simulated again.The whole time of all the pedestrians getting through the passage is similar to the time of experiment by the difference of 5.25%.