Stationary Intervals for Random Waves by Functional Clustering of Spectral Densities

2021 ◽  
Author(s):  
Diego Rivera Garc\xeda ◽  
Luis Angel Garc\xeda Escudero ◽  
Agustin Mayo Iscar ◽  
Joaquin Ortega
Keyword(s):  
Random Waves ◽  
Spectral Densities ◽  
Functional Clustering

Stationary Intervals for Random Waves by Functional Clustering of Spectral Densities

2020 ◽  
Author(s):  
Diego Rivera-García ◽  
Luis Angel García-Escudero ◽  
Agustín Mayo-Iscar ◽  
Joaquin Ortega
Keyword(s):  
Time Series ◽  
Functional Data ◽  
Random Waves ◽  
Spectral Densities ◽  
Time Intervals ◽  
Functional Clustering ◽  
Wave Data ◽  
Model Method ◽  
Spline Basis ◽  
Consecutive Time

Abstract 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.

Time Series, Spectral Densities and Robust Functional Clustering

2018 ◽  
Vol 52 (1) ◽  
pp. 135-152
Author(s):  
D. Rivera-García ◽  
L. A. García-Escudero ◽  
A. Mayo-Iscar ◽  
J. Ortega
Keyword(s):  
Time Series ◽  
Spectral Densities ◽  
Functional Clustering

Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

2018 ◽  
Vol 15 (1) ◽  
pp. 84-93
Author(s):  
V. I. Volovach ◽  
V. M. Artyushenko
Keyword(s):  
Spectral Characteristics ◽  
Random Processes ◽  
Spectral Densities ◽  
Differential Systems ◽  
Non Gaussian ◽  
Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

scholarly journals Gaussian processes with skewed Laplace spectral mixture kernels for long-term forecasting

2021 ◽  
Author(s):  
Kai Chen ◽  
Twan van Laarhoven ◽  
Elena Marchiori
Keyword(s):  
Gaussian Processes ◽  
Multivariate Time Series ◽  
Heavy Tail ◽  
Lottery Ticket ◽  
Spectral Densities ◽  
Heavy Tailed ◽  
Long Term Forecasting ◽  
The Time Domain ◽  
Spectral Mixture

AbstractLong-term forecasting involves predicting a horizon that is far ahead of the last observation. It is a problem of high practical relevance, for instance for companies in order to decide upon expensive long-term investments. Despite the recent progress and success of Gaussian processes (GPs) based on spectral mixture kernels, long-term forecasting remains a challenging problem for these kernels because they decay exponentially at large horizons. This is mainly due to their use of a mixture of Gaussians to model spectral densities. Characteristics of the signal important for long-term forecasting can be unravelled by investigating the distribution of the Fourier coefficients of (the training part of) the signal, which is non-smooth, heavy-tailed, sparse, and skewed. The heavy tail and skewness characteristics of such distributions in the spectral domain allow to capture long-range covariance of the signal in the time domain. Motivated by these observations, we propose to model spectral densities using a skewed Laplace spectral mixture (SLSM) due to the skewness of its peaks, sparsity, non-smoothness, and heavy tail characteristics. By applying the inverse Fourier Transform to this spectral density we obtain a new GP kernel for long-term forecasting. In addition, we adapt the lottery ticket method, originally developed to prune weights of a neural network, to GPs in order to automatically select the number of kernel components. Results of extensive experiments, including a multivariate time series, show the beneficial effect of the proposed SLSM kernel for long-term extrapolation and robustness to the choice of the number of mixture components.

Probabilistic Calculation Model of Directional Random Waves

1993 ◽  
Author(s):  
Wi-Gwang Pae ◽  
Hajime Mase ◽  
Tetsuo Sakai
Keyword(s):  
Calculation Model ◽  
Random Waves

scholarly journals Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method

2021 ◽  
Vol 9 (1) ◽  
pp. 76
Author(s):  
Duoc Nguyen ◽  
Niels Jacobsen ◽  
Dano Roelvink
Keyword(s):  
Surface Waves ◽  
Deep Water ◽  
Surf Zone ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Successful Implementation ◽  
Random Waves ◽  
Mean Motion ◽  
Generalized Lagrangian

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

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