Modeling And Application For Pedestrian Flow Based On Cost Potential Field

Pedestrian traffic is an important part of urban traffic,and the congestion of pedestrian traffic will seriously affect social economy and security.The dissertation focuses on the theoretical modeling and numerical simulation of pedestrian crowds.The Fermat's principle for light propagation is extended to establish the cost potential field,by which we assume that a pedestrian intends to minimize his/her total cost to the destination.The path choice strategy is based on the instantaneous information in walking facilities,which is known as the“reactive dynamic user optimization”principle.Accordingly,we propose three types of models,i.e.,the continuum,many-particle and cellular automaton models.All these models are more suited for a walking domain with complex geometries and multiple exits.By simulation,the flow-density fundamental diagram,the evacuation from a room with exit(s)and the formation of lanes in counter flow are reproduced with detailed analysis.The main contents of the dissertation are briefed in the following.?.By repairing the continuum model for bi-directional pedestrian flows,the mirror symmetry of lane formation in counter flow is thoroughly investigated.The formation of lanes is reproduced by designing a relaxation scheme for solving the convection equations of pedestrian flow.This self-organization phenomenon is explained as pedestrians'avoidance of higher costs for mingling with the other pedestrian group,because their costs are supposed to be minimized.The phenomenon can also be explained as symmetry-breaking which is triggered by noises or numerical viscosities,and all pairs of these solutions can be predicted corresponding to biased sweeping orders in solving the Eikonal equation,which is verified by numerical simulations.?.A many-particle model is proposed based on the cost potential field.In the modeling,we assume that a pedestrian is navigated by the potential field,and his/her moving speed depends on the density in the surroundings,where the density is reconstructed by mainly taking into account the visible fan sector in front of a pedestrian.The proposed model is applied to simulate the evacuation from a room respectively with one and two exits,where the typical arching effect is observed in the middle of evacuation process.For the case with two exits,the simulation indicates a typical self-organization phenomenon,i.e.,the ending of evacuation at one exit approximately coincides with that at the other exit;moreover,the optimal layout of two exits is studied through numerical simulation.The model is suitable to deal with multi-exits evacuation,and each exit can be fully utilized in our model.?.A potential field cellular automaton model is proposed for overcrowded pedestrian flow by adopting refined grids and similar optimal choice strategy.The basic rules for occupation of cells reasonably takes into account the compressibility among pedestrians and the compressibility between pedestrians and walls,thus it allows a maximal density over 14 ped/m~2,which had been observed before the occurrence of some pedestrian disasters.The simulated fundamental diagram and evacuation process agree with the observed results in the literature.The formation of lanes in counter flow is reproduced in high density situations,by adopting an optimal path choice strategy for two pedestrian groups,which similarly suggests that pedestrians intend to avoid mingling with the other pedestrian group.In summary,the dissertation proposes and enriches the theoretical model for pedestrian flow which are based on the cost potential field.The typical self-organization phenomena such as exits evacuation and lanes formation in counterflow are studied.