| Summary: | 碩士 === 國立成功大學 === 水利及海洋工程學系 === 86 === Chaos theory is increasingly used both to classify a system
and as an aid tomodeling. Also, on applying chaos theory to
random process analysis has becomea tool for better
understanding of signals. This study is trying to combine the
time-delay embedding method (TDEM) with the correlation
dimension method (CDM) to investigate the chaotic behavior of
simulated wave signals and fieldobserved wave data. The
comparison of chaotic properties between collected field data
and simulated data shows the deficiency in the assumption that
ran-dom wave profiles are the result of linear superposition of
infinite number ofinfinitesimal wavelets with various
frequencies. Some simple signals,
which is composed of linearly regular waves,were chosento
examine the criteria of computation and to realize its physical
meanings onapplying the tools of TDEMand CDM. To investigate
whether the time series is chaotic, a set of m-dimensional
vectors should be reconstructed from the orig-inal time series
and then its trajectory is examined using the correlation
integral method. As expected, it is impossible to define a
straight line of slope in the correlation integral plot. That
is, there is no possibility thatthe time series generated by
linearly regular waves are chaotic. The questionis raised now.
Since the random waves are often represented by some spectral
forms, do these representation still inherit chaotic
characteristics? Unfortu-nately, no matter how many wave
components are considered, which consist of 2,3 or up to 128
components of the JONSWAP form, the simulated wave series are
always not chaotic. A second question may be asked that does
the noise affectthe chaotic properties in the wave data? Many
sets of random noises were thengenerated and to be added to
the simulated wave in order to investigate its chaoticity. It
was shown that the noise itself is not chaotic, in addition,
the simulated waves contaminated with noises are not chaotic,
either. The second aim of the work is to justify
observed wave signal as chaotic andto characterize its dynamics
through the analysis of the correlation dimension.The results
showed a highly chaotic behavior in both wave elevation and
sign-ificant wave heights. Also, the strong dependence of
correlation dimension D2on significant wave height may give us a
rough information on calculating D2. If the relationship could
be more justified, then the tedious estimation of correlation
dimensions will be much simplified.
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