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

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. •Features of autocorrelation function of Gaussian process, found according to discretization of frequency interval.•New scheme for identifying recurrence in time-series, based on vectorial representation of time-windows and time-marching.•Scheme demonstrated and verified for ship roll excitation and response simulation data.•Insights into the optimal implementation of the scheme (least number of vector components, time-marching step etc).•Extension for determining the transient part in pseudo-random roll motion time-series.