Identification of recurring patterns and repetitions in time-series, with application to pseudo-stochastic ship rolling

Abstract

A scheme for capturing repeating portions in time-series is proposed. Such repetitions may be temporal or permanent. The scheme is applied for investigating repetitions in ship roll time simulation data, incurred by the use of discretized wave spectra. The presence of repetitions in the forcing can slant the ship motion response data collected via Monte Carlo simulations unless certain precautions are applied. The conventional check for repetitions in data series is based on the observation of high peaks in the autocorrelation function. However, as the autocorrelation reflects averaged resemblance between sets of successive data separated by a time interval, these peaks may not imply repetition in exact sense. By the proposed computational scheme can be elicited whether any given portion of the time-series reappears. The basic idea is the construction of low-dimensional vectorial representatives of short-time portions of the series and the check for similarity (to a level of tolerance) through application of a Euclidian distance metric to these vectors. The scheme is also useful for locating the end of the transient part in simulated ship roll motion data deriving from repeating pseudo-stochastic excitation.