Stationary intervals for random waves by functional clustering of spectral densities

Diego Rivera-García, Luis Angel García-Escudero, Agustín Mayo-Iscar, Joaquin Ortega

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A new time series clustering procedure, based on Functional Data Analysis techniques applied to spectral densities, is employed in this work for the detection of stationary intervals in random waves. Long records of wave data are divided into 30- minute or one-hour segments and the spectral density of each interval is estimated by one of the standard methods available. These spectra are regarded as the main characteristic of each 30-minute time series for clustering purposes. The spectra are considered as functional data and, after representation on a spline basis, they are clustered by a mixtures model method based on a truncated Karhunen-Loéve expansion as an approximation to the density function for functional data. The clustering method uses trimming techniques and restrictions on the scatter within groups to reduce the effect of outliers and to prevent the detection of spurious clusters. Simulation examples show that the procedure works well in the presence of noise and the restrictions on the scatter are effective in avoiding the detection of false clusters. Consecutive time intervals clustered together are considered as a single stationary segment of the time series. An application to real wave data is presented.
Original languageEnglish (US)
Title of host publicationVolume 6B: Ocean Engineering
PublisherAmerican Society of Mechanical Engineers
ISBN (Print)9780791884386
StatePublished - Dec 18 2020

Bibliographical note

KAUST Repository Item: Exported on 2021-02-04
Acknowledgements: This work was supported by the Spanish Ministerio de Economía y Competitividad, grant MTM2017-86061-C2-1-P, and by Consejería de Educación de la Junta de Castilla y León and FEDER, grant VA005P17 and VA002G18.


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