## 1 Introduction  
Vehicle rollover is a very dangerous type of road accident. With the increasing complexity of the traffic environment and the continuous growth of passenger car ownership, traffic accidents have become commonplace. In 2014, the National Highway Traffic Safety Administration (NHTSA) recorded that 18.9% percent of traffic fatalities were caused by rollovers (7592 of 40,164) [1]. In 2018, these rollovers caused 22.4% of the total traffic fatalities according to the NHTSA statistics (8111 of 32,675) [2]. Although automobile research and design are constantly improving, the fatality rate remains at a very high level. One major reason is that drivers have difficulty predicting the risk of rollover directly. In the event of a rollover, cars are difficult to control due to the great decline of vehicle handling and the fluctuation of the drivers' psychological state. To protect people's lives and to ensure the safety of property, rollovers must be detected as soon as they occur. Moreover, an active anti-rollover control method must be adopted. One research hotspot in the field of the active safety control of vehicles is predicting the vehicle driving state and determining the real-time state parameters transmitted to prevent vehicle rolloveraccidents [3; 4]. In terms of time sequence, two steps can be taken for vehicle rollover prevention: vehicle rollover warning and vehicle rollover prevention action [5]. Many indexes are used to predict a rollover, and they are also used as vehicle rollover warning parameters. The static stability factor (SSF) is the first basic index that shows the inherent tendency of a vehicle to rollover [6]. It was used by [PERSON] et al. to explain the relationship between vehicle geometry and rollover stability and to describe the anti-rollover performance of vehicles [7]. As one of the indexes for New Car Assessment Program in evaluating vehicle rollover performance, SSF is defined as half of the ratio of the wheel distance to the mass gravity center height. It ignores the dynamic performance of suspension, and its control strategy has limitations in practical application. The dynamic stability factor (DFC) was indicated by [PERSON] and [PERSON] to solve the problem in which vehicle dynamic information cannot be reflected in SSF [8]. Energy utilization is another index, which uses vehicle kinetic energy compared with the maximum potential energy [9]. Lateral load transfer ratio (LTR), according to the force between the tire and the road surface, is defined as the ratio of the difference between the vertical loads of the left and right wheels and the sum of these loads [10]. It has been widely used because of its simple expression and good portability [11; 12; 13; 14]. [PERSON] et al. and [PERSON] et al. indicated that the tire vertical acceleration and other information are required for an index based on LTR, which can simultaneously identify tripped rollover and un-tripped rollover [15]. To improve the prediction ability of traditional LTR, [PERSON] et al. put forward predictive LTR (PLTR) through a theoretical derivation of the linear vehicle dynamics model [16]. The rollover index (RI) is an experience index proposed by [PERSON] et al., which uses dynamic simulation and has high precision and certain prediction ability [17]. For RI, a large number of experimental data need to be compared and accumulated. An improved algorithm of RI was formulated by [PERSON] and [PERSON] by using the gray model [18], which adds the prediction function of RI [19]. Moreover, [PERSON] et al. proposed a method for judging the rollover of wheels after leaving the ground by studying the dynamic characteristics of vehicles with wheels off the ground [20]. To improve the prediction effect, [PERSON] and [PERSON] proposed a strong prediction ability index called time to rollover (TTR) [21]. TTR is defined according to the lateral pressure and roll angle, depending on the state estimation of the linear vehicle model; it can be realized by different algorithms [22]. In addition, [PERSON] et al.