PSI - Issue 77

2

Francisco Castro/ Structural Integrity Procedia 00 (2026) 000 – 000

612 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ICSI organizers Keywords: Vehicle’s CoG height; Vehicle dynamics; Vehicle active safety; Rollover accidents. Francisco Castro et al. / Procedia Structural Integrity 77 (2026) 611–630

1. Introduction Rollover accidents are characterized as a dangerous type of vehicle crash, with significant impact on road safety. These type of accidents can be classified as either tripped, typically caused by external impacts, or untripped, as a consequence of excessive lateral forces during cornering. Regarding untripped rollovers, a rollover occurs when destabilizing forces – affected by speed, turn radius, lateral acceleration, track width and CoG height – exceeds stabilized forces. Thus, this phenomenon is more prone to occur in vehicles with a higher center of gravity, such as sport utility vehicles (SUV’s), emergency, military and heavy vehicles. In situation of an emergency, it is difficult for drivers to detect unstable states, thus it is important to develop methods to predict and detect the risk of rollover. The criterion used to assess and quantify the rollover risk is the rollover index (RI). The RI provides a numerical measure for the rollover propensity, and when a predefined threshold is exceeded, active safety systems such as electronic stability control (ESC), roll stability control (RSC) or differential braking may be triggered to prevent a rollover (Park & Choi, 2021), e.g. by reducing the yaw rate or decreasing the vehicle velocity. RI approaches can be categorized into static and dynamic. Static RIs, such as the ratio between track width and CoG height, provide a basic estimation based on equilibrium conditions. On the other hand, dynamic RIs can incorporate real-time vehicle states such as lateral acceleration, roll angle, roll rate and time to wheel lift-off (Yang et al., 2022), providing a more accurate and responsive assessment of rollover risk under transient conditions. The effectiveness of RI-based safety system is related to the precision of the input parameters. Among all vehicle parameters, the position of the CoG height has an essential role in determining vehicle dynamic behavior, especially during aggressive maneuvers or emergency situations. Inaccuracies in CoG height estimation may result in unreliable RI values, compromising the performance of safety systems and potentially increasing the likelihood of rollover. The CoG position is not often provided by the manufacturers and when provided, only the nominal values for inertial properties and CoG position for unloaded conditions are given. However, it doesn’t reflect the real -world operational variations, since it can vary considerably with passenger and cargo loading. The horizontal and lateral components of the center of gravity can be estimated via axle load measurements or by placing an individual scale at each wheel (Mango, 2004; Patel Jainish J Topiwala & Gopalbhai Patel, 2017); although determining the vertical component is more complex. While static procedure measurements such as the lifting method or the swing method provide relatively accurate CoG height values, they are not practical for real-time application due to operational complexity and long measurement times. As a result, dynamic estimation techniques based on vehicle dynamics and sensor data, which estimate the CoG height position from measurable states during motion, have been developed as an alternative. Methods to estimate vehicle’s CoG height: state of art The estimation of a vehicle’s CoG height position cannot be directly measured with standard onboard sensors. Therefore, the estimation of the vehicle’s CoG height has been a research topic in the context of rollover prevention and vehicle dynamics control. The methods proposed in the literature are extended from dynamic models variations and according to different estimation theory approaches. Model-based methods are a significant percentage of the literature, since these methods rely on assumed linear behavior and predefined model parameters. The more common vehicle model-based used is the roll model, as in (Wittmer et al., 2023), (Yang et al., 2022), (Cairano et al., 2021), (Park & Choi, 2021), (Boada et al., 2016; X. Huang & Wang, 2013; Rajamani et al., 2011; Wang et al., 2021), (J. Huang & Lin, 2009) (Solmaz et al., n.d.). The vehicle