Directional Analysis Based On Wavelet Transform

Understanding and exploring the essence and characteristics of water waves is a process that has proceeded from simplicity to complexity, from ideality to reality, and from superficiality to profoundness. In other words, this process has been implemented step by step, from regular waves to irregular waves, from monodirectional to multidirectional. Natural ocean is a complex non-stationary wave field, which is made up of the superposition of multi-directional irregular waves. Directional spectrum is not only the basic method of describing the wave field, but also important factor that influencing the design of marine structures, the generation mechanism of wind waves, the movement of nearshore and other issues. Therefore, studying the frequency-directional spectrum of the waves makes great sense. As the traditional estimation methods of directional spectrum are based on Fourier transform, the directional distribution of non-stationary wave field cannot be estimated accurately. Yet wavelet transform is a powerful tool for analyzing non-stationary waves. Consequently, directional spectrum study based on wavelet transform is an effective method to address non-stationary waves and to estimate the directional spectrum accurately.In this dissertation, wavelet transform is introduced first. Then directional spectrum estimation method based on wavelet is stated emphatically. Numerical simulation is performed to generate wave elevation time series of multidirectional irregular wave field with known directional distribution. And based on these data, factors such as array types, propagation direction, direction concentration, sampling length, sampling interval were discussed to find out how they impact the results of wavelet spectral analysis. Research indicates that the Wavelet Direction Method (WDM) is suitable for arrays with three or more evenly distributed wave stuffs, also for waves propagating towards any direction, and for waves with directional concentration index greater than20. Compared with traditional methods, the sample length required in WDM is shorter, and the applicable condition is relatively broad, which makes the practicability of this method stronger.Furthermore, wavenumber vectors, wavenumber-directional spectrum and significant wave height of wave field can also be obtained by this method. It turns out that the directions and the magnitudes of wavenumbers fully reflect the energy distribution of waves, and the wavenumber-directional spectrum is completely corresponds to the frequency-directional spectrum. In addition, MIKE21-BW numerical wave model is also used for simulating wave fields. The results indicate that the method based on wavelet has high resolution and it can identify energy distribution of the incident waves and reflected waves. Finally, reflection coefficients of monodirectional and multidirectional waves are calculated with wavelet directional analysis. Research shows that the obtained overall reflection coefficients are consistent with the input values, and this method can separate the frequency spectrums of incident and reflected waves. However, the differences between the directional distribution of the reflection coefficient of multidirectional waves and the target value are significant.