Identification of state-space coefficients for oscillating water columns using temporal series

• A new method to obtain the state-space that approximates the Cummins equation is proposed.
• The displacement resulting from decay tests is used to obtain matrix coefficients.
• The matrix and the displacement by regular waves are used to identify the vectors.
• The results are in very good agreement with the compared series.

A methodology to identify the state-space matrix and the vectors which solves the Cummins equations directly using free surface temporal series, obtained from laboratory or CFD codes, avoiding the use of potential flow solvers, is presented. The new methodology is applied to the solution of the piston-like movement of an Oscillating Water Column (OWC) moving in heave, assuming that sloshing is negligible, to incorporate flow effects that are not captured with traditional methods using potential flow solvers. The identification of the state-space components is done in two steps. The first step uses the solution of the state-space for decay tests, no forcing terms, obtaining a possible solution. This solution is used in the second step to solve regular waves, nonzero forcing term and no initial condition. The solution obtained in the second step is the component of the state-space that characterizes the movement of the OWC. The numerical series used to compute the solution are obtained using IH2VOF in this study, but they can be obtained by means of other sources, such as different numerical codes or laboratory measurements. Once the solution is found, the resulting state-space is validated against numerical results of IH2VOF for regular and irregular wave trains.