HYBRID MODELING METHODOLOGY FOR PREDICTING RISKS IN EMERGENCY MANAGEMENT

Abstract

This research addresses the critical challenge of forecasting natural and man-made emergency situations, with a specific focus on industrial and forest fire dynamics. Traditional emergency management often relies on deterministic models that, while physically accurate, struggle to incorporate the inherent stochasticity of environmental variables. Conversely, purely statistical approaches frequently fail to account for unique, non-linear scenarios where historical data is insufficient. To bridge this gap, this paper proposes a robust hybrid modeling methodology that integrates fundamental physico-mathematical equations with advanced probability theory methods. The core of the deterministic component is based on the parabolic partial differential equation of heat conduction, which describes the thermal evolution of objects under stress. To account for real-world uncertainties, environmental parameters such as wind speed and ambient temperature are treated as random variables, modeled using Weibull and Gaussian distributions respectively. A comprehensive computational experiment was conducted using the Monte Carlo simulation method, executed via Python-based algorithms to perform 10,000 iterations for dynamic fire risk assessment. The Finite Difference Method (FDM) was employed to solve the heat transfer equations iteratively. The results indicate that while a static deterministic model predicts a failure time of 24.5 minutes, the hybrid approach reveals a significant stochastic variance, with failure times ranging from 15 to 45 minutes. Notably, the model identified a "Tail Risk" where 5% of the simulations resulted in failure within less than 18 minutes—a critical safety window that traditional models overlook. Furthermore, a counter-intuitive physical correlation was observed where higher wind speeds occasionally delayed failure due to enhanced convective cooling effects. This methodology provides a more realistic and granular tool for decision-makers in emergency management, offering not just a single risk value but a comprehensive probability interval essential for life-saving evacuation planning.