Application of Markov chains to rank fires and forecast fire development phases

Introduction. The simulation of fire development and suppression processes must take account of a large number of random factors concerning the fire environment and the resources, available for its putting out. An important feature of the fire development is its step-by-step nature, whereby one phase (stage) is naturally replaced by another as a result of physical combustion processes and decisions made amid certain states of fire. In the practice of modeling multiphase (multistage) processes, such models as decision trees, multistep positional games, random processes, including discrete Markov chains, and others are widely used. Each of these models has its own structure and parameters. The choice of the model structure for a particular application represents a heuristic step. In almost every case, parameters of models are set on the basis of logical inferences, physics, ongoing processes and available statistical data about the simulated phenomenon. This approach is usually referred to as normative. Its alternative is an adaptive approach, whereby model parameters are evaluated using historical data. This approach allows to make models that are sufficiently similar to real objects and capable of adapting to the nonstationary features of the environment and the changeability of the decision maker’s preferences.
The relevance of the study lies in the development of a machine learning technology for the Markov models of the fire development process, which allow predicting the completion time of individual phases and the whole fire. The Markov model can also serve as the basis for determining the optimal fire rank.
Goals and objectives. The aim of the work is to create and test the technology for designing models that allow to make projections of the fire completion time. The tasks of the model machine learning and its use as a tool for making projections and determining the rank of fire are set in line with this goal.
Methods. The authors used methods of the theory of random processes, mathematical statistics, simulation modeling, technical and economic evaluations. The research is based on materials extracted from domestic and foreign publications.
Results and discussion. The proposed method, designated for the machine learning of the Markov chains using statistical data on the response time of firefighting and rescue units, coupled with the use of trained models, technical and economic evaluations for assigning optimal fire ranks allow to apply algorithms built on their basis as part of fire safety decision support systems.
Conclusions. The presented solutions to the problem of designing adequate models designated for projecting fire development phases and assigning fire ranks serve as the basis for effective decision support systems in terms of the short-term fire safety management.

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