On the limitations of inverse force estimation with strain-based sensing and reduced modal models in hydroelastic systems

Abstract

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.