Improving reliability of safety countermeasure evaluation at highway-rail grade crossings through aleatoric uncertainty modeling with machine learning techniques

Traditional Collision Modification Factor (CMF) calculation methods rely on simplistic statistical models that often fail to account for the complex, non-linear relationships influencing collision rates, leading to uncertain estimates. To address this gap, this study aims to improve the reliability of CMF estimation for safety countermeasures by introducing a novel hybrid model that combines Negative Binomial (NB) regression with a Long Short-Term Memory (LSTM) neural network to estimate aleatoric uncertainty. In other words, the proposed method integrates statistical modelling with machine learning techniques within the Empirical Bayes (EB) framework to compute uncertainty for enhancing CMF accuracy and stability. By increasing the reliability of collision frequency predictions and calculating more precise CMFs, the proposed method enables the selection of appropriate countermeasures, ultimately reducing fatalities and costs. The model is trained using data from Highway-Rail Grade Crossings (HRGC) inventory and collision records from the Federal Railroad Administration (FRA) for 2016–2022. The NB regression model provides a statistical foundation for collision prediction, while the LSTM component models uncertainties, significantly improve CMF calculation. Compared to the traditional NB model, the hybrid NB-LSTM approach reduces root mean squared error (RMSE) by 62.5 % and mean absolute error (MAE) by 61 % in predicting collision frequencies, leading to more reliable CMFs. The model identifies that gates reduce collisions by 61 % in high-traffic HRGCs, bells decrease collisions by 67 % in high-speed areas, and flashing lights achieve a 72 % reduction in low-traffic, high-speed crossings. Additionally, the proposed method achieves lower standard errors (S.E.) across all countermeasures.