PSI - Issue 77

Francisco Castro et al. / Procedia Structural Integrity 77 (2026) 611–630 Francisco Castro/ Structural Integrity Procedia 00 (2026) 000 – 000

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longitudinal model is used for the estimation of the CoG height position, with the in the assumption that there is a load shift, through a braking maneuvers as in (Park & Choi, 2021; Yue et al., 2015) or in a pitched road as in (X. Huang & Wang, 2013), (X. Huang & Wang, 2014; Wu et al., 2023). Another different approach is presented in (Yu & Watanabe, 2021), where instead of developing a model-based method, the authors estimate the CoG position through vibration based analysis, by leveraging the natural frequencies of the vehicle oscillations. Different estimation techniques have been investigated to determine the CoG location more accurately, particularly in the presence of signal noise and time-varying. conditions. The most common filtering technique is the Kalman Filters, including the standard Kalman Filter (KF) (X. Huang & Wang, 2013), Extended Kalman Filters (EKF) (J. Huang & Lin, 2009; Wittmer et al., 2023), Dual Extended Kalman Filter (Boada et al., 2016), and hybrid approaches which combines EKF with other variations as Adaptive Kalman Filter (AKF) (X. Huang & Wang, 2014) and with Huber Extended Kalman Filter (Wu et al., 2023). Another estimation algorithm used for the CoG position estimation is the Recursive Least Squares (RLS), including its variants, such as the Linear Recursive Least Squares (LRLS) as described in (Park & Choi, 2021; Solmaz et al., n.d.) and the Fast Fixed Recursive Least Squares (FFRLS) applied in (Wang et al., 2021). Moreover, Least Mean Squares (LMS) were also applied into the estimation process, as in (Yang et al., 2022) where the authors used Normalized Least Mean Squares (NLMS). Nevertheless, despite all the achievements and extensive investigation throughout the last years, challenges remain, especially because the existing methods rely on high quality sensors or onboard sensors and their respective integration in the models developed, which causes high computational burden, limiting their applicability to mass-production vehicles. Moreover, with these problems addressed, there isn’t still a cost-effective method or standard equipment to evaluate the CoG position with the vehicle at motion that ensures accurate and real-time feasibility for a wide range of vehicles and maneuvers. The main objective of this paper is to develop a method to estimate the vehicle’s CoG height in motion. A vehicle longitudinal model was developed for a braking maneuver, and a vehicle roll model was developed for a cornering maneuver. For the in motion measurements, it was necessary to measure the accelerations and the angles that the vehicle body is subjected by an Inertial Measurement Unit (IMU) sensor installed in the vehicle. In comparison with other studies, this paper proposes two simpler methods, which increase the convergence rate, where some characteristics of the vehicles are easily measurable during daily operations, or could be given by the manufacturers, doesn’t require high computational power , doesn’t need any information from onboard sensors and can be applied with low-cost sensors to estimate accelerations and tilt angles. The structure of this paper is organized as follows. Chapter 2 presents the development of the vehicle longitudinal model and roll model formulations used to estimate the vehicle’s CoG height in motion, together with the experimental setup designed to validate the road tests. Chapter 3 reports the results obtained from both the static procedure and the in-motion roads tests under different load case scenarios selected, followed by a discussion of the findings. Lastly, the conclusions are summarized in the last chapter. 2. Materials and methods This chapter presents the development of a dynamic method for estimating the vehicle's center of gravity (CoG) height during motion, based on a longitudinal model – braking action – and based on a roll model – cornering, reflecting the vehicle's actual operational state, including variable loading conditions. The proposed method is later evaluated and validated by comparing its results with those obtained through static measurement techniques, as the traditional lifting method.