A Takeover Failure Prediction Model Based on Extreme Value Theory and Copula Function

Because of the rarity and randomness of takeover failure events, safety research based on takeover failures often faces issues such as small sample size, aggregation, and lag. Nonfailed takeover data are difficult to describe the risk of takeover failure. This study uses nonfailed takeover data to construct a takeover failure prediction model based on extreme value theory and the Copula function. First, this study conducted a driving simulation takeover experiment, and 756 takeover data were obtained, including 43 takeover failure events. This paper selects the takeover time and minimum takeover collision time (MTCT) indicators based on the takeover behavior mode to describe the safety of takeovers. Second, based on extreme value theory, this study develops the unary extreme value models for each safety indicator: one for takeover time and another for MTCT. Third, the binary Copula extreme value model was constructed with takeover time and MTCT as indexes. Classical Copula functions include six types: logistic, double Logistic, asymmetric Logistic, negative Logistic, Husler-Relss, and asymmetric mixed model. The results showed that the Logistic function was more suitable for describing the correlation between takeover time and MTCT. Fourth, the predicted number of takeover failures and model accuracy indicators are used to evaluate the performance of the three models. The results show that the binary Copula extreme value model outperforms two unary extreme value models in predicting takeover failure events. The contribution of this study is to construct a takeover failure prediction model based on nonfailed takeover data, which provides a methodological reference for preventing takeover failures. In addition, this study applies the extreme value theory to the field of takeover safety analysis, which is valuable for expanding the takeover failure analysis method.