It is essential to identify damage within a structure as early as possible in order to propose corrective measures to prevent mechanical failure - ultimately extending service life. Such damage detection can be effected through non-destructive means that employ the updating of a physics model describing the system of interest. The resulting inverse problem is concerned with locating and characterizing the damage, by considering the structural dynamic response, before and after the onset of damage. Such model-based approaches also afford prognosis potential, as a calibrated physics model is subsequently available for the damaged system. In this work, a partitioned fluid-structure forward modeling capability is developed from combining an open source CFD tool (OpenFOAM) with an open source CSD solver (CU-BEN) in a tightly coupled framework that affords stable solutions. However, such high fidelity, coupled-physics forward modeling is prohibitive for use in solving model-based inverse problems where the forward model must be called repeatedly, necessitating the consideration of reduced-order modeling methods. Within the context of inversion, the high-fidelity FSI forward model is evaluated on a series of physically inspired "damaged" states to create an offline parametrized library of modeled damaged responses. These responses are expressed in compressed form through empirical eigen-functions, obtained via proper orthogonal decomposition, and subsequently represented as points on a certain Riemannian manifold. From this offline library of reduced-order responses from the fluid-structure interaction model, a proxy model is constructed through manifold interpolation on the nonlinear Riemannian manifold to consider variations on our parameter of interest not explicitly contained within the library, but required as a complete part of the inversion. This subsequent online inversion is effected as a non-convex optimization problem, employing a genetic algorithm to arrive at a plausible reduced order model instance that conforms to observations within some prescribed limits. The robustness of this framework is examined on an example problem, with exploration into the effects of management of the sparse database on the accuracy and efficiency of the proxy modeling and subsequent parameter estimation inversion. A study aimed at characterizing common damaged states for the marine propeller 4381 is proposed as a possible application for this system.