Estimation method of operational safety risk for mixed traffic flow on expressway

Based on toll collection data, this study identified two key parameters affecting accident rates by considering traffic flow composition and the causes of safety risks: traffic flow saturation and the mixing rate of heavy-duty trucks. The algorithm, threshold values, and generation process for each parameter were proposed. The Pearson correlation coefficient method was employed to analyze the independence between the two parameters, and the coefficient of variation was introduced to examine their dispersion relative to the accident rate. By simulating insect feeding characteristics under varying food densities and incorporating polynomial fitting, a safety risk assessment model for mixed traffic flow on expressways was developed. The model was solved using the Taylor series expansion method and iteratively optimized with the Levenberg-Marquardt algorithm. The model's parameters were calibrated using data from 684 expressway sections in Sichuan Province, and its feasibility was verified. The research results indicate that the proposed safety risk assessment model effectively captures the accident rate characteristics of different sections. After 523 iterations, the model achieves a discrete statistical error of 1%, requiring only 1.42 s. The influence of traffic flow saturation and the mixing rate of heavy-duty trucks on the accident rate aligns with the Peal-Reed model and a cubic polynomial model, respectively. The safety risk of mixed traffic flow peaks when traffic flow saturation reaches 33% and the mixing rate of heavy-duty trucks reaches 71%. By incrementally increasing the accident rate by 10.20% within [0.01, 1.03] and subsequently merging groups, it is found that dividing the accident rate into five levels, each represented by a distinct color scheme, can clearly illustrate the safety risk status of the expressway network. Using the 85th and 15th percentiles to define the mixing rate of heavy-duty trucks and traffic flow saturation, respectively, ensures comprehensive coverage of the parameter ranges. The proposed safety risk assessment method holds significant value for dynamically monitoring expressway traffic safety, guiding the allocation of emergency resources, optimizing the deployment of police and road administration personnel, and facilitating evacuation strategies.