Simulation of active movement of people during evacuation from buildings

Abstract

The following categories of movement are considered: comfortable, calm, active, with high activity. When the category of human movement becomes active with possible forceful actions, the task of modeling their active movement taking into account the natural deformations of human bodies arises. The anthropological characteristics of the person from the point of view of physical restrictions on mutual position of parts of a body at their active movement with force actions are analyzed. Taking into account the properties of physical limitations of the human body, a three-component mathematical model of horizontal projection of a person is proposed, which takes into account the conditions of gluing model components into a single complex object and restrictions on the angles of rotation of components. The model of the human body is represented by union of three ellipses: the main and two auxiliary. The main one can rotate continuously within the framework of maneuverability, and the auxiliary ones - within the angles arising from the anthropological properties of man. A meaningful formulation of the problem of modeling the active movement of people taking into account the natural deformations of bodies is proposed and the modeling algorithm is modified. Modification is to take into account the natural deformations of the human body by modeling the change in the spatial shape of the three-component model of the human body. Analytical expressions of the conditions of their non-intersection and placement in areas are obtained for the considered complex objects, which will allow to present the problem as a classical nonlinear programming problem and to use the existing optimization packages. The ability of the proposed algorithm to model the movement of people and the constraints of the problem, for which are obtained analytical expressions in the work, is shown by computer modeling. It should be noted that the restrictions considered in the paper on both the number of components of the object of movement and its shape are not fundamental. Models and algorithms allow you to make changes in both the number of components of the object and their spatial forms, which will only increase the complexity of the algorithms for solving the problem.