A topologically based neural network algorithm is used to conduct an in-depth study and analysis of domino accident risk data in chemical parks, and this is used to construct a prevention and control system applied to the safety prediction of chemical parks. Firstly, the operating model of the flue gas turbine is expanded and analyzed according to the basic theory of topology, and the object element model is constructed to determine the feature vector and potential risk level. Then, the idea of differential evolution is introduced into the topological neural network to solve the problem that the learning rate and weighting coefficients are difficult to determine, and then the complete DE-ENN algorithm is proposed and tested with the UCI standard data set to verify the effectiveness of the algorithm. Finally, the algorithm is applied to the potential risk identification of the smoke machine operation model, and the experimental results show that the method not only has a simple structure, short running time, and high prediction accuracy but also has excellent generalization ability. For the inherent risk and domino effect risk of chemical equipment in chemical fiber enterprises, the accident risk assessment method based on the protection layer analysis method is proposed; combined with the probability of domino accident and personnel vulnerability model based on the comprehensive analysis of the research results of the allowable risk standard, the allowable risk standard applicable to chemical fiber production enterprises in China is proposed. Given the potential accident risk characteristics of chemical fiber production enterprises, the calculation method of firefighting demand and firefighting capacity of firefighting system is given; the index system of firefighting system emergency response capacity assessment is constructed from three aspects of firefighting system integrity, reliability, and effectiveness, and the assessment model and grade classification standard of firefighting emergency response capacity of chemical fiber production enterprises are determined.