commit b6addfea6e06a8979fd11ee07847514ac9e8fe74
parent a6d4c4f2d81aa3969088c0da56911a54684f2c4e
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Sat, 29 Oct 2016 16:24:32 +0300
Include notes taken throughout the last year.
Diffstat:
1 file changed, 30 insertions(+), 0 deletions(-)
diff --git a/phd-diss.org b/phd-diss.org
@@ -29,6 +29,26 @@
* Related work
* ARMA model for ocean wave simulation
** The reasons for the creation of a new ocean simulation model
+ARMA model emerged in response to difficulties encountered by practitioners who
+used wave simulation models developed in the framework of linear wave theory.
+The problems they have encountered in their work can be summarised as the
+following.
+1. /Periodicity/. Linear wave theory approximates waves by a sum of harmonics,
+ so period of the whole wavy surface realisation depends on the number of
+ harmonics in the model. So, reasonably large realisations require large
+ number of coefficients. This in turn results in overall bad performance of
+ the model, no matter how optimised the software implementation is.
+2. /Linearity/. Linear wave theory gives mathematical definition for ocean waves
+ which have small amplitudes compared to their lengths. Waves of this type
+ occur in the ocean, so waves in shallow water as well as storm waves, for
+ which this assumption does not hold, are not perfectly captured by linear
+ theory.
+3. /Probabilistic convergence/. Wave phase, which is often generated by pseudo
+ random number generator (PRNG), has uniform distribution, and this makes wavy
+ surface characteristics (average wave height, wave period, wave length etc.)
+ sometimes converge slowly to the desired values. Convergence rate depends on
+ the values generated by PRNG, which makes it probabilistic.
+
** The shape of ACF for different types of waves
*** Two methods to find ocean wave's ACF
**** Analytic method of finding the ACF.
@@ -46,6 +66,16 @@
** Verification of wavy surface integral characteristics
** Modeling non-linearity of ocean waves
** Non-physical nature of ARMA model
+ARMA model, owing to its non-physical nature, does not have the notion of ocean
+wave; it simulates wavy surface as a whole instead. Motions of individual waves
+and their shape are often rough, and the total number of waves can not be
+predicted precisely. However, integral characteristics of wavy surface match the
+ones of real ocean waves.
+
+In theory, ocean waves themselves can be chosen as ACFs, the only pre-processing
+step is to make them decay exponentially. This is required to make AR model
+stationary and MA model parameters finding algorithm to converge.
+
* Determining wave pressures for discretely given wavy surface
* High-performance software implementation of ocean wave simulation
* Conclusion
