# SPN-Based Dynamic Risk Modeling of Fire Incidents in a Smart City
## 1 Introduction
To tackle the challenges within a Dynamic Probabilistic Risk Assessment (DPRA), References [8; 9] have put forward a multitude of modeling methodologies, such as dynamic fault trees and extended event sequence diagrams. These methods have exerted a substantial impact on enhancing the existing modeling and assessment frameworks, proffering additional alternatives and tools for risk assessment techniques and augmenting the capacity to evaluate dynamic probabilistic risks. In real-world scenarios, the occurrence of a natural fire represents an event process instigated by the activities of actors or preceding events, and there exist sequential, parallel, or even more intricate influence relationships among these actions and events. Reference [10] have markedly enhanced the simulation capabilities of the system model through the introduction of SPN. In recent years, SPN has found extensive application in the analysis of emergency response, system failure, and other processes. Reference [11] utilized SPN to model the emission accident of offshore oil and gas production facilities, reference [12] employed a Colored Hybrid Petri Net (HPN)to simulate the accident emergency response process, and reference [13] analyzed the emergency response process via a Timed Colored Hybrid Petri Net (TCHPN). Nonetheless, given the long incubation period of natural fire accidents and the difficulty in determining the delay time, the traditional Markov process is restricted to the exponential distribution when deducing the probabilities of subsequent events. This constraint might be overly stringent for complex system modeling, as the Markov chain is only applicable to systems with exponentially distributed lifetimes. Moreover, event simulation demands more memory and may take a longer time to execute. It cannot encompass all scenarios and is typically confined to a subset of state trajectories. A Bayesian Network (BN), on the other hand, can circumvent the state space explosion issue and is generally capable of handling diverse types of lifetime distributions and uncertainties. It can also be utilized for robust reasoning under uncertain conditions. With the given prior information, the probabilities of subsequent events in the causal structure can be dynamically updated using the observed data. Bayesian theory is applied in various fields, including system lifetime estimation and risk analysis, to augment the dynamics of SPN systems for discrete event modeling. The Bayesian Stochastic Petri Net (BSPN) model proposed by reference [14] effectively enhances the application of SPN in dynamic safety analysis. Reference [15] demonstrated how to employ Bayesian theory to predict the occurrence frequency of abnormal events from accident precursor data. The aforementioned studies suggest that Bayesian theory can effectively and dynamically update the occurrence frequency of events and plays a vital role in the dynamic update of the SPN model. After multiple accidents occur, through the quantitative risk assessment method [16], the risk can be comprehensively evaluated, all possible events can be estimated, and the accident risk can be accurately estimated. The aforementioned methods have significantly advanced the progress of dynamic risk analysis and accident analysis. Nevertheless, several issues remain to be addressed in the dynamic risk assessment model of urban natural fire accidents. The principal work and novel contributions of this paper are as follows:  
1. In the analysis of urban natural fire accidents, although the accident cause is conventionally the primary focus of research, the accident occurrence process is continuous. The durations of events or actions within the process vary. Research based on the evolution of accident process nodes can enhance the authenticity of studies on urban natural fire accidents. Simulation analysis shows (as shown in Table 1 that the steady-state probabilities of key nodes in fire evolution (such as P2 and P4) are significantly higher than those of other nodes (P(M2) = 0.2261, P(M4) = 0.1522).