Data-Driven System Identification of High-Speed Craft Dynamics Uncovering Governing Equations with Machine Learning

Abstract The dynamics of high-speed craft operating in the marine environment are characterized by interactions between hydrodynamic, aerodynamic and inertia forces. This results in a highly nonlinear coupled dynamic motion in head seas heave and pitch. The traditional approach for system identification often relies on first principles approximate hydrodynamic methods or high-fidelity Computational Fluid Dynamics (CFD). Although CFD methods are effective, however computationally expensive, particularly during the iterative design process, or real time applications. To overcome such limitations, in this study we are investigating the feasibility of system identification methods, using Sparse Identification of Non-Linear Dynamics (SINDy) algorithm for the system identification of the dynamics of high-speed crafts. SINDy is a data-driven approach that identifies sparse governing equations directly from motion data, which offers a computationally efficient framework for reduced order modeling of a complex system. The goal is to identify explicit governing equations of the system, represented as a sparse set of basis functions. This work mainly focuses on the planar motion of high-speed craft, i.e., coupled heave and pitch motion. The training data is generated using CFD analysis which is used as a black box function that calculates the hull response in vertical planar motion when subjected to an external forcing term, i.e., external heave force and pitch moment time history. External forcing terms are modeled as multi-sine excitations, applied to the hull free to move in vertical plane. The external forcing terms are applied after 5 seconds of free run in calm water to capture the initial steady state dynamics, after 5 seconds the data captures the highly non-linear dynamics due to external forcing. These simulations are run for multiple combinations of amplitudes and frequencies of forcing terms to create the design space which corelates to the operating scenario of a high-speed craft. SINDy algorithm is applied to the training datasets, with the modified custom library functions such as polynomials, trigonometric terms, and interaction terms to represent the nonlinear, coupled dynamics. Sparse regression techniques such as STLSQ, are used to promote sparsity and avoid overfitting, which ensures that the identified models are parsimonious. The identified models were validated using test data, which are not included in the training phase. The model accuracy is calculated using root mean square error (RMS) and the final model is selected based on minimizing RMS error. The impact of data time span and moving time window is analyzed to determine the balance between temporal coverage and data diversity needed to minimize the error. This study focuses on integrating SINDy with CFD-generated motion data, and its application as a reduced order modelling tool for system identification. Although other methods such as Neural Networks, Gaussian Processes could be used which provide approximate functions, but without explicit governing equations. On the contrary, SINDy identifies explicit governing equations of the system and excels at extrapolating when the governing rules are well captured.