Inverse Wave Force Estimation Using Frequency- and Time-Domain Hydroelastic Models

Abstract

Accurate knowledge of wave-induced loads is essential for the safe and efficient design and operation of offshore structures, yet direct measurement of hydrodynamic forces remains challenging. This study investigates whether wave excitation forces can be estimated from measured structural responses by treating the structure as a distributed force sensor. A hydroelastic state-space model incorporating frequency-dependent added mass and radiation damping, obtained through rational approximation of radiation forces, is employed. A joint input–state Kalman filter is used to estimate both dynamic states and unknown excitation forces from noisy acceleration measurements. Its performance is evaluated against frequency-domain inverse methods based on least-squares inversion of acceleration frequency response functions, including a Tikhonov-regularised formulation to address ill-conditioning. Results show that accurate force reconstruction is primarily achieved within frequency ranges where the forward operator is well conditioned, particularly near modal resonances and for lower-order modes. While Tikhonov regularisation yields the lowest estimator variance, it introduces bias and underestimates force energy for higher-order modes. The time-domain Kalman filter provides a more balanced trade-off between variance reduction and bias through implicit regularisation introduced by system dynamics. The results demonstrate that regularisation improves estimator stability but may suppress physically relevant force content when applied excessively.