Compressive sampling - based extrapolation of free surface displacement data from pressure measurements

This article deals with the problem of extrapolating the time history of the free surface displacement at a given point from wave pressure head records. This problem is relevant to marine engineering applications, where, for instance, the monitoring of marine structures must be arranged without resorting to expensive measurement techniques, or sensor failures must be circumvented through adequate signal processing techniques. Specifically, a Compressive Sensing (CS) based technique is developed by resorting to the concept of sparsity, which is implemented through formulating and solving a L1 – norm minimization problem. Relevant numerical examples show that the proposed CS approach allows extrapolating reliable free surface displacement time histories. Further, the data extrapolated via CS are in better agreement with target free surface data than standard Fourier - based approaches, while possessing the desirable feature of removing the subjective choice of a cut-off frequency requested by the standard techniques. CS limits are highlighted in terms of required optimal pressure sensor position below the mean water level, and of reliability in extrapolating the profiles of steep waves.