Abstract
This paper deals with the spectral estimation of sea wave elevation time series by means of ARMA models. To start, the procedure to estimate the ARMA coefficients, based on the use of the Prony’s method applied to the auto-covariance series, is presented. Afterwards, an analysis on how the parameters involved in the ARMA reconstruction procedure—for example, the signal time length, the number of poles and data used—affect the spectral estimates is carried out, providing evidence on their effect on the accuracy of results. This allowed us to provide guidelines on how to set these parameters in order to make the ARMA model as accurate as possible. The paper focuses on mono-modal sea states. Nevertheless, examples also related to bi-modal sea states are discussed.
Highlights
Knowledge of the weather conditions in the context of marine engineering applications is often a key point for structural safety, and for people’s comfort in the case of ships in navigation
In the estimation process of an Auto-Regressive Moving Average (ARMA) model starting from time series, in addition to the proper choice of the available algorithms and of the procedure to be followed to estimate the parameters among all those available, great attention must be paid on how to properly apply the selected method
In the case considered here, and despite that the selected method—described in Section 3—is based on well-known algorithms, their effectiveness when used together in estimating ARMA models able to accurately describe the sea frequency behaviour strongly depends on the choice of the free parameters
Summary
Knowledge of the weather conditions in the context of marine engineering applications is often a key point for structural safety, and for people’s comfort in the case of ships in navigation. This paper will address some of these points in order to clarify strengths and drawbacks of the considered identification approach, providing guidelines for setting some of the key parameters of the procedure such as the number of samples that can be used, given a certain time series, and the number of the poles of the ARMA model, which are shown to strongly affect the effectiveness of the power spectral density reconstruction To this purpose, the paper is organised into nine sections where Sections 2–4 are related to the methods on which the proposed estimation procedure is based, Section 5 describes the method used to simulate the data for testing this approach, while Sections 6–8 are aimed at presenting the results and at their discussion.
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