Developing Artificial Intelligence-Based Car-Following Models Using Improved Permutation Entropy Analysis Results - Shahatha, Ali Muhssin; Sahin, Ismail (MDPI, 2026)
Vehicle trajectories are time series, and entropy is a powerful tool for testing or quantifying the complexity of a given series. Entropy tools are often applied to variables such as velocity, acceleration, space headway, and time headway, but the local position data have not been addressed previously. The novelty of this study is that it uses the Improved Permutation Entropy (IPE) for the first time to analyze vehicle position data and convert those data into a limited range (0-0.3317), aiming to understand individual vehicle behavior during car-following and introduce a new prediction method for developing artificial intelligence-based car-following models. The study uses the IPE analysis results as a new input variable, in addition to existing input variables, to improve the prediction accuracy of these models. Three types of neural networks were adopted according to the development of artificial intelligence models: artificial neural networks (ANNs), long short-term memory networks (LSTMs), and Transformer models. The results indicate that all models using the proposed prediction method, which includes the IPE analysis result, outperformed those using the traditional prediction method. The Transformer & IPE model shows the best performance in prediction accuracy of the follower acceleration output; the statistically significant percentage improvements were 2.04%, 1.42%, 1.22%, and 2.62% for RMSE, MAE, MASE, and R-2, in that order. Furthermore, the results indicate that all models using the proposed prediction method outperformed the benchmarking Intelligent Driver Model (IDM) for the follower acceleration output.
Keywords: vehicle trajectory; improved permutation entropy; AI-based car-following models; Chemistry; Engineering; Materials Science; Physics