A Bayesian inverse dynamic approach for impulsive wave loading reconstruction

Abstract

The measurement of wave forces acting on marine structures is a complicated task, both during physical experiments and, even more so, in the field. Force transducers adopted in laboratory experiments require a minimum level of structural movement, thus violating the main assumption of fully rigid structure and introducing a dynamic response of the system. Sometimes the induced vibrations are so intense that they completely nullify the reliability of the experiments. On-site, it is even more complex, since there are no force transducers of the size and capacity able to measure such massive force intensity acting over the very large domain of a marine structure. To this end, this investigation proposes a Bayesian methodology aimed to remove the undesired effects from the directly (laboratory applications) or indirectly (field applications) measured wave forces. The paper presents three applications of the method: i) a theoretical application on a synthetic signal for which MATLAB® procedures are provided, ii) an experimental application on laboratory data collected during experiments aimed to model broken wave loading on a cylinder upon a shoal and iii) a field application designed to reconstruct the wave force that generated recorded vibrations on the Wolf Rock lighthouse during Hurricane Ophelia. The proposed methodology allows the inclusion of existing information on breaking and broken wave forces through the process-based informative prior distributions, while it also provides the formal framework for uncertainty quantification of the results through the posterior distribution. Notable findings are that the broken wave loading shows similar features for both laboratory and field data. The load time series is characterised by an initial impulsive component constituted by two peaks and followed by a delayed smoother one. The first two peaks are due to the initial impact of the aerated front and to the sudden deceleration of the falling water mass previously upward accelerated by the initial impact. The third, less intense peak, is due to the interaction between the cylinder and remaining water mass carried by the individual wave. Finally, the method allows to properly identify the length of the impulsive loading component. The implications of this length on the use of the impulse theory for the assessment or design of marine structures are discussed.