Hybrid non-intrusive MOR of a boat seat multibody model

High-speed planing craft (HSPC) are known to experience complex vibrational phenomena that stem from an interplay of hydrodynamic pressure loads, the dynamics of the propulsion systems and inherent structural properties of the boat subsystems [1]. HSPC frequently encounter high magnitude impacts under varying sea and operational conditions [2] that far exceed permitted levels for the human body [3]. The effects of these whole-body vibrations are strongly influenced by magnitude, waveform, and duration of exposure and prolonged exposure to these repeated shocks significantly impacts crew health and performance [4]. Considerable research has been directed at mitigating these vibrations using suspension seats as it is imperative for crew health and safety. This work focuses on a HSPC seat designed for such shock reduction. The system features a spring-damper suspension system linking the base plate and lower body to the upper body, seat frame and cushion. The system functions like a four-bar linkage mechanism with links connecting and constraining the upper body and seat frame relative to the lower body. A preliminary multibody model of the boat seat was developed using ADAMS View (Hexagon AB, Stockholm, Sweden) using nominal dimensions of an actual seat. To simplify the digital model, the spring forces were applied directly instead of explicitly modelling the spring and damper elements. The links are modelled as flexible elements which were included in the model through a Component Mode Synthesis (CMS) approach. The model takes the accelerations of the base plate in the X, Y, and Z directions as inputs and predicts the seat accelerations in the same directions as outputs. A first validation of the model has been achieved using data from sea trials. Although lateral acceleration plays a key role in overall vibrational response [2], recorded data showed higher magnitudes of acceleration in the vertical direction. The computational costs of the preliminary multibody model were quite large. In the context of digital twins, high-fidelity real time simulations are essential [5], reiterating the need for the creation of a reduced order model of the boat seat that can deliver accurate outputs at lower computational times. A range of different MOR methods (physics based, data-driven and hybrids) have been explored for multibody systems [6]. Recently, data-driven methods have gained traction as they can learn using only input-output sensor data, have provisions of capturing strong non-linearities and can scale with data availability [7]. Hybrid MOR strategies combine physics‐based projections that embed conservation laws or stability constraints into data-driven models to ensure robustness [8]. This study adopts an Operator Inference (OpInf) with Projection modelling approach [9]. High-fidelity simulations “snapshots” were used to compute a reduced Proper Orthogonal Decomposition (POD) basis. The full system states were projected onto this reduced basis and reduced coordinates were defined. Solving a Least Squares objective, the reduced operators representing the key dynamics of the system were learned non-intrusively. Linear Matrix Inequality (LMI) constraints were enforced to the reduced operators to preserve their structural integrity, like previous approaches. [7-9]. Finally, a Newmark-Beta scheme was used to integrate the second order dynamics. The model simulations results showed strong fidelity to the actual system in the vertical direction although high-frequency chatter was observed in the seat lateral acceleration. The damping parameters need further tuning for resolving this issue. The hybrid non-intrusive ROM predicted vertical acceleration with a fair accuracy while significantly reducing computational time—from 15 minutes in the full-order model to just 3 seconds for 60 seconds of output. Future work will focus on refining the multibody model to enhance simulation accuracy and consequently minimizing bias in the ROM. Attention will be directed to capture nonlinear effects to improve predictive accuracy and ensure more representative system dynamics.