Drivers' reactions to real-world forward collision warnings at both macroscopic and microscopic longitudinal levels: A functional approach.

Understanding drivers' reactions to in-vehicle forward collision warnings (FCWs) is vital for advancing FCW design and improving road safety. However, past studies often used aggregated safety measures to analyze the drivers' reactions to FCWs, thereby at the microscopic level, limiting our ability to understand drivers' reactions to FCWs at particular timestamps immediately after FCWs are issued. Additionally, there has been a notable absence of studies at the macroscopic perspective focusing on analyzing how drivers' reactions to FCWs evolve over an extended period of time. To overcome these two limitations, this study proposes a new research framework using Functional data analysis (FDA) approach to model driver behavior profile in response to FCWs at both microscopic and macroscopic longitudinal levels. Real-world FCW data collected from the New York City Connected Vehicle Pilot Deployment project is used for the case study. At the microscopic level, a sparse functional design is adopted to model driver behavior profiles, accounting for irregularly spaced functional measurements. Nonparametric functional linear regression is then used to estimate the drivers' reactions to FCWs at a particular timestamp immediately after FCWs are issued. At the macroscopic level, the functional two-sample test and a functional distance metric are used to examine changes in drivers' reactions to FCWs over the study period and quantify the magnitude of these changes. Time to collision (TTC) and modified time to collision (MTTC) measures are used to represent driver behavior profiles, and both TTC and MTTC after FCWs are issued are modeled as functions with respect to time based on the proposed FDA approach. Compared to using aggregated safety measures including minimum TTC and MTTC as well as mean TTC and MTTC, new patterns of drivers' reactions to FCWs are unveiled at both microscopic and macroscopic longitudinal levels. Study outputs reveal several key insights, including driver compensation behavior that escalates safety risk after an initial safety improvement and the diminishing safety benefits of FCWs from the beginning to the end of the after period. The proposed research framework can be generalized to analyze various types of in-vehicle driver warnings at both microscopic and macroscopic longitudinal levels. The findings of this study can support the calibration of detailed driver response behavior to in-vehicle warnings and facilitate the design of driver warning applications and further investigation of their safety benefits.