Robust Identification of 1 DOF Hydrodynamics From Free Decay Tests

Potential flow models are indispensable tools for rapid evaluation and early stage design, yet they routinely misrepresent hydrodynamic damping, especially when viscous effects are significant. Inaccurate damping propagates into biased predictions of decay rates, response amplitudes, fatigue loads, and control/stability margins, ultimately affecting design choices and risk assessments. This motivates a data driven approach to recover effective damping with quantified credibility. We propose a two stage grey box identification workflow for a 1 DoF (degree of freedom) system, in which free-decay records are used to estimate added mass and combined linear and quadratic damping. First, a bounded optimization routine fits the nonlinear ODE to the measured displacement. Second, local uncertainty and identifiability are quantified at the optimum using the Fisher information matrix, and its singular value decomposition is used to assess conditioning and diagnose when linear and quadratic damping are practically separable. Application to multiple free decay records shows that added mass is robustly identified through its influence on the oscillation period, whereas damping coefficients are local and data dependent, and their separability depends strongly on the selected decay segment.