Load field reconstruction with a combined POD and integral spline approximation technique

• Distribution of sectional loads along a slender body is obtained from few force data.
• Decomposition of an unsteady load field with POD allows efficient reconstruction.
• Splines with integral constraints convert global into local load estimations.
• Choice of closure conditions for spline approximation is discussed.

In this paper, a new technique for determining a load field (e.g., pressure) on the basis of a few global measurements (e.g., forces) is presented. This technique is based on a combination of proper orthogonal decomposition (POD) and polynomial spline approximation with integral constraints and is here illustrated with respect to the prediction of the wave load distribution along a slender floating body like a ship. The input data are provided by the time-histories of the lumped vertical forces acting on several longitudinal portions (i.e., segments) of a scaled model of a fast ship. To achieve a better understanding of the accuracy of this technique, the segment forces are not experimentally but numerically obtained by integrating the sectional forces over the length of the segments. These forces, calculated with a strip-theory approach precessing experimental data relative to ship motion in waves, provide also the target distribution for validating the present procedure. The set of lumped hydrodynamic forces defines the vector process to which POD is applied. The components of the identified POD modes provide the integral constraints for the spline polynomials approximating the continuous basis functions of the sectional load distribution. The sectional load distribution along the hull is then reconstructed, showing good agreement with the original load data. Finally, the robustness of the proposed technique is investigated by studying the propagation of bias errors and additive white noise from input data to final results.