Inverse methods are commonly used to estimate external forces on structures when direct measurements are impractical, such as wave loading on marine structures. However, all inverse estimation approaches implicitly assume that the available measurements contain sufficient information to uniquely identify the force components of interest. The present investigation demonstrates that this assumption can be violated in a commonly adopted hydroelastic modelling framework, in which excitation forces are represented in a dry structural modal basis that includes rigid-body modes. Using a simplified hydroelastic system as a controlled example, it is demonstrated that when strain-based sensing is combined with a modal force representation that includes rigid-body modes, the resulting inverse problem can become non-identifiable. Although rigid-body motion produces negligible strain directly, hydroelastic coupling allows rigid-body forces to induce flexible deformation, causing rigid-body and flexible force components to excite overlapping strain-response subspaces. As a result, distinct force distributions cannot, in general, be uniquely separated from strain measurements alone. The analysis shows that acceleration-based inversion is globally ill-conditioned at low frequencies, while strain-based inversion is affected by a persistent near-null subspace associated with rigid-body modes. Regularization is used here as an illustrative mechanism for probing the inverse problem: it stabilizes the solution by suppressing poorly observable directions, but cannot recover force components aligned with them, leading to bias. Modal truncation removes these directions but yields force estimates that represent equivalent forcing within a reduced subspace rather than physical modal forces. Mixed strain-acceleration sensing improves estimation of flexible components, but rigid-body components remain sensitive to low-frequency ill-conditioning. These results demonstrate that the identifiability of modal force components is governed by the interaction between the chosen force representation, sensing type, and hydroelastic coupling. The findings therefore establish a general limitation of inverse force estimation in coupled fluid-structure systems, independent of the specific estimation method used. ... Read more

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. ... Read more

The growth of offshore wind farms is accelerating to meet the renewable energy target by 2030, driving the development of larger offshore wind turbines (OWTs) to boost energy capacity. To support these OWTs, large monopiles are being installed by using impact hammers, which in turn emit low-frequency underwater noise, posing challenges for traditional noise mitigation systems and increasing risks to marine life. To address this, a metamaterial-based cushion (meta-cushion) was proposed, embedding resonators to filter longitudinal waves associated with high underwater noise levels. While prior work has demonstrated the meta-cushion's noise attenuation potential, design guidelines are required for adaptation to various monopile installations. This paper introduces, for the first time, a design methodology for the meta-cushion, which based on the input parameters of the monopile system, it details the procedure for selecting the resonant elements contributing to the attenuation performance and their spatial arrangement on the cushion for enhancing mechanical performance. Such performance indicators are evaluated via finite element simulations and experimental modal analyses. The methodology concludes with a nondimensional study of the spiral resonator, which showed the best attenuation response in experiments, exploring its behavior under varying material and geometric parameters. This methodology enables the development of meta-cushions adaptable to monopile installations under any environmental conditions. ... Read more