Стохастическое моделирование каскадных сценариев возникновения и развития чрезвычайных ситуаций

Abstract

Introduction. The development of methods for modeling the flows of events in the occurrence and development of emergency and critical states, designed to solve the problems of supporting the management of rapid response to incidents in conditions of incomplete information, as well as the generation of preventive algorithms for rapid response in emergency situations, seems to be a promising direction for improving information and analytical support of management in security systems. The purpose of the research is to create mathematical tools for predicting emergency and critical conditions in local incidents based on discrete-event modeling of the dynamics of emergency situations. Methods of stochastic modeling are based on the representation of a cascade scenario of the dynamics of the development of accidents and catastrophes by a Markov process using a three-parameter Weibull distribution to set the intensities of transitions between emergency and critical states of adjacent levels. Results and discussion. A general stochastic model is constructed that describes the dynamics of the occurrence and development of accidents and catastrophes of technogenic and natural origin initiated by local incidents according to a cascade scenario with a branching structure with a set of possible elementary states represented in the form of a stratified graph. The main stages of the emergence and development of emergency situations are considered within the framework of the proposed representation of the cascade model by a Markov process with discrete states and continuous time. The expediency of local modeling of individual stages is substantiated based on the description of transitions between states of adjacent levels. Local systems of differential equations corresponding to some of the most probable scenarios for the development of events in the event of incidents are given. Non-stationary solutions of differential equations of Kolmogorov-Chapman are obtained, with assignment of intensities of transitions by three-parameter Weibull distributions. Conclusions. The proposed stochastic model makes it possible to predict the dynamics of the development of emergency and critical states according to a cascade scenario, and also reflects the probability characteristics of the timeliness and effectiveness of possible impacts in a prompt response to incidents. Keywords: stochastic modeling of technogenic accidents, cascade development of accidents and catastrophes, Weibull distribution.