Modeling nonlinear relationship between crash frequency by severity and contributing factors by neural networks

•NNs are developed for modeling relationship between crash frequency by severity and factors.•A structure optimization algorithm is proposed to improve generalization performance.•A rule extraction algorithm is proposed to illustrate the effects of the contributing factors.•The optimized NNs outperform the multivariate Poisson-lognormal model.•The results confirm that factors are nonlinearly associated with crash frequency by severity.

This study develops neural network models to explore the nonlinear relationship between crash frequency by severity and risk factors. To eliminate the possibility of over-fitting and to deal with black-box characteristic, a network structure optimization and a rule extraction method are proposed. A case study compares the performance of the modified neural network models with that of the traditional multivariate Poisson-lognormal model for predicting crash frequency by severity on road segments in Hong Kong. The results indicate that the trained and optimized neural networks have better fitting and predictive performance than the multivariate Poisson-lognormal model. Moreover, the smaller differences between training and testing errors in the optimized neural networks with pruned input and hidden nodes demonstrate the ability of the structure optimization algorithm to identify insignificant factors and to improve the model's generalizability. Furthermore, two rule-sets are extracted from the optimized neural networks to explicitly reveal the exact effect of each significant explanatory variable on the crash frequency by severity under different conditions. The rules imply that there is a nonlinear relationship between risk factors and crash frequencies with each injury-severity outcome. With the structure optimization algorithm and rule extraction method, the modified neural network models have great potential for modeling crash frequency by severity, and should be considered a good alternative for road safety analysis.