| Summary: | 博士 === 國立臺灣海洋大學 === 河海工程學系 === 105 === The signals on sea area appear random phenomena, and only through statistical methods to recoginize the characterisitic of the signals, and to decide the appropriative design conditions for related structure construction. Especially, in the eastern part of Taiwan, where is directly impacted by wave from the Pacific Ocean. These include general season waves and extremely typhoon waves. For the purpose of coastal protection and port development, it primary needs enough time seris of wave measurement data and stastic analysis consequently.
In traditionally, the wave statistical methods can be divided into two categories: the frequency domain and the time domain analysis. The analysis of the frequency domain mainly refers to the use of Fast Fourier transform (FFT) to analyze the energy density of each hypothetical component wave, and to discuss the energy concentration in a group of fluctuations of waves. However, because of the analysis of FFT may loss the true phase of each component wave during transform process. The relationship of parameters and recovery of waveform as wave height and the wave period parameters can only be established by the spectral moments or inverse of FFT. The analysis of the time domain is usually driven by Zero Up Crossing Analysis (ZRU), or the Empirical Mode Decomposition (EMD) method to analyze the fluctuation of water surface and the wave height or period in statistics. Although the ZRU method can analyze the wave height and period, but somtimes it is difficult to identify the component waves from these time series observation data, such as the riding wave, short period with large wave height induces wave height becoming larger or smaller.
In this paper, we firstly study the phase problem of FFT in frequency domain by employing of numerical experiments to find out how effectively applying the spectral analysis in the random sea states and recovery to orginal waveform in time series. Secondly, the research implements a new analytical method, the combination of EMD and ZRU. After the IMF simple waveforms driven from EMD, the ZRU is employed subsequently to identify the wave heights and related wave periods and try to solve the riding wave problem.
For the frequency phase problem, the research not only includes single component wave, linear wave nonlinear wave (including the second order and third order of Stokes wave), but also (1) an integer crossover frequency - linear regular wave; (2) noninteger crossover frequency - linear regular wave; (3) an integer crossover frequency - nonlinear regular wave; (4) noninteger crossover frequency - nonlinear nonlinear regular wave; (5) testing of irregular wave; and (6) solitary wave conditions. Whether wave belongs to the FFT analysis can resolved directly or not. After comprising different initial phases test results of the FFT analysis the study finds that the initial frequency phase ε can be obtained from the principle frequency phase ε_F to eliminate the basic phase ε_OF, (ε=ε_F-ε_OF). Although the initial phase of the principle frequency phase is not equal, but the principle frequency phases appear linearly at each crossover frequency, and parallel for all different principle frequencies. The difference between two adjacent principle frequency equal to initial phase frequency. And the difference of highest principle frequency and lowest principle frequency just as 180 (π).
A new time series signal analysis method, the combination EMD and ZRU is implemented in this study. For testing the new analysis method, the wave observation data at both north and south sides of GueiSan Island from the end of 1999 to the end 2001 are applied. Comapring the result of EMD +ZRU method and only ZRU method on the characteristic of wave height and period, the research found the wave height obtained by EMD + ZRU is smaller than that of ZRU in general. These results can explain the distorted phenomenon induced by riding wave during the ZRU analysis process. For the characteristic of wave period, the result between EMD + ZRU results and ZRU analysis results are quite close, but slightly larger. Apart from above result, the study also carry out the dimensionless analysis for all wave height divided by H_(1/3), H_mean, √(m_0 ) and for wave period divided by T_(1/3), T_mean, T_peak. In all case, both EMD + ZRU and ZRU, the wave height of each dimensionless vaule decreases with the increase of the probability of excess, but for the wave period of dimensionless, the EMD + ZRU is increasing where ZRU is decreasing. However, the comparison the parameters of the mean value, standard deviation and the confidence of the wave height and the wave period in the five groups at both north and south side of GueiSan Island performing similar statistic property. It also emphasizes the methodology of combination of EMD and ZRU presenting highly stability in statistic, and may apply to Ocean Engineering, prospectively.
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