commit 028a90c6e8e30d05fcdc917534a1dfdaff1d914e
parent 53199fcfd1024b62726397f0b2e27499cb5a052b
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Mon, 29 May 2017 17:29:57 +0300
Edit related work.
Diffstat:
| arma.org | | | 70 | +++++++++++++++++++++++++++++++++++----------------------------------- |
1 file changed, 35 insertions(+), 35 deletions(-)
diff --git a/arma.org b/arma.org
@@ -121,41 +121,41 @@ long-term simulation.
* Related work
** Ocean wave modelling
-One of the first application of ARMA model for oceanological processes modelling
-was done in\nbsp{}cite:rozhkov1990. Another approach to modelling wind waves is
-possible in terms of the representation of a stochastic moving surface as a
-linear transformation of white noise with memory. These methods are one of the
-most popular ways of modelling stationary ergodic Gaussian random processes with
-given correlation characteristics\nbsp{}cite:box1976time. However, these methods
-were not used to simulate wind waves for a long time. The first attempts to
-model two-dimensional disturbances were undertaken in the early 70's
-(cf.\nbsp{}cite:kostecki1972stochastic), and the impetus for this was the
-development of the resonance theory of waves in wind. However, the formal
-mathematical framework was developed in\nbsp{}cite:rozhkov1990,gurgenidze1988.
-They built a one-dimensional model of ocean waves, on the basis of an
-autoregressive-moving average (ARMA) model.
-
-In\nbsp{}cite:spanos1982arma ARMA model is used to generate time series spectrum of
-which is compatible with Pierson---Moskowitz (PM) approximation of ocean wave
-spectrum. The authors carry out experiments for one-dimensional AR, MA and ARMA
-models. They mention excellent agreement between target and initial spectra and
-higher performance of ARMA model compared to models based on summing large
-number of harmonic components with random phases. The also mention that in order
-to reach agreement between target and initial spectrum MA model require lesser
-number of coefficients than AR model. In\nbsp{}cite:spanos1996efficient the authors
-generalise ARMA model coefficients determination formulae for multi-variate
-(vector) case.
-
-In\nbsp{}cite:fusco2010short AR model is used to predict swell waves to control
-wave-energy converters (WEC) in real-time. In order to make WEC more efficient
-its internal oscillator frequency should match the one of ocean waves. The
-authors treat wave elevation as time series and compare performance of AR model,
-neural networks and cyclical models in forecasting time series future values. AR
-model gives the most accurate prediction of low-frequency swell waves for up to
-two typical wave periods. It is an example of successful application of AR
-process to ocean wave modelling.
-
-One thing that distinguishes present work with respect to afore-mentioned ones
+Another approach to simulating sea waves involves representing stochastic moving
+surface as a linear transformation of white noise with memory, which allows to
+model stationary ergodic Gaussian random process with given correlation
+characteristics\nbsp{}cite:box1976time. The first attempts to model
+two-dimensional disturbances were undertaken
+in\nbsp{}cite:kostecki1972stochastic, which resulted in the development of the
+resonance theory of wind waves, and the formal mathematical framework was
+developed in\nbsp{}cite:rozhkov1990,gurgenidze1988 --- the authors built a
+one-dimensional model of ocean waves based on autoregressive-moving
+average (ARMA) model.
+
+One-dimensional ARMA model does not have some of the LH model deficiencies: it
+is both computationally efficient and requires less number of coefficients to
+converge. In\nbsp{}cite:spanos1982arma ARMA model is used to generate time
+series spectrum of which is compatible with Pierson---Moskowitz (PM)
+approximation of ocean wave spectrum. The authors carry out experiments for
+one-dimensional AR, MA and ARMA models. They mention excellent agreement between
+target and initial spectra and higher performance of ARMA model compared to
+models based on summing large number of harmonic components with random phases.
+They also mention that in order to reach agreement between target and initial
+spectrum MA model require lesser number of coefficients than AR model.
+In\nbsp{}cite:spanos1996efficient the authors generalise ARMA model coefficients
+determination formulae for multi-variate case.
+
+AR model was successfully applied to predict evolution of propagating wave
+profiles based on instantaneous wave recordings. In\nbsp{}cite:fusco2010short AR
+model is used to predict swell waves to control wave-energy converters (WEC) in
+real-time. In order to make WEC more efficient its internal oscillator frequency
+should match the one of ocean waves. The authors treat wave elevation as time
+series and compare performance of AR model, neural networks and cyclical models
+in forecasting time series future values. AR model gives the most accurate
+prediction of low-frequency swell waves for up to two typical wave periods. It
+is an example of successful application of AR process to ocean wave modelling.
+
+The feature that distinguishes present work with respect to afore-mentioned ones
is the study of three-dimensional (2D in space and 1D in time) ARMA model, which
is mostly a different problem.
1. Yule---Walker system of equations, which are used to determine AR
