Two-dimensional continuous wavelet transform of simulated spatial images of waves on a slowly varying topography

The wavelet transform (WT) is now recognized as a useful, flexible, and efficient technique to analyze intermittent, non-stationary and inhomogeneous signals as well as images which are obtained from experimental or in situ measurements. In this study, the two-dimensional continuous wavelet transform (2-D CWT) was introduced to analyze the spatial image of waves. The numerical algorithm of 2-D CWT was developed and testified in simulated wave field of regular and random waves. Some more simulated wave fields of various wave conditions and sea bed slopes were then assumed to verify the analytical accuracy of this new technique. The comparisons of estimations to theoretical values for several wave parameters show that the 2-D CWT is capable of identifying the directional spectra and wave properties in shallow water.     

Using wavelet transforms to analyze nonlinear ship rolling and heave-roll coupling

The use of wavelet transforms is explored to investigate the nonlinear dynamical characteristics of ship roll and coupled heave-roll motion. The harmonic character, double period character and chaotic character are observed via a time–frequency window of the wavelet transform. Typical wave parameters in different stability regions are considered. Features such as restoring rolling, divergence rolling, steady state and chaotic responses of ship roll are obtained as well. The investigation in this paper not only highlights the feasibility of using wavelet transforms in the analysis of nonlinear dynamic characteristics of ship rolling in waves, but also shows how it could enhance the analysis abilities.     

Wavelet transform based coherence analysis of freak wave and its impact

The present paper presents the results of a wavelet transform-based coherence analysis of freak wave and its impact. Wavelet transform has been used as a tool in analyzing signals in the time domain as well as in the frequency domain. The analysis was applied to laboratory-generated freak waves. The wavelet transform of the time history of the freak wave and its impact force revealed that a wide range of frequency components were contained in them. The coherence analysis was conducted on the wave and its impact force time histories. The coherence analysis revealed that some high-frequency components were highly correlated with the impact forces. The present study demonstrates that the wavelet transform can be an alternative tool in the analysis of strongly nonlinear freak wave and its impact.     

Wave parameters and functions in wavelet analysis

A preliminary study of wave parameters and functions in wavelet analysis is conducted in this paper. The Morlet wavelet transform is used to calculate the time–frequency wavelet energy density function, its volume (i.e. the total energy), its frequency-integral (i.e. the wavelet smoothed instantaneous wave energy history), its time-integral (i.e. the wavelet spectral density function), and two non-dimensional wave indices (NIF, NIT). The processing of the measured wave data obtained from the Chi-Gu coastal observation tower during the period August 2000 to July 2001 indicates that the inter-comparison of wavelet smoothed instantaneous wave energy history and smoothed instantaneous wave energy history (SIWEH) as defined by Funke and Mansard (Proc 17th Int Conf on Ocean Eng, 1980) can reveal the noise structure of the wave signal. The wave data with index NIF greater than 2 is always accompanied with noise, therefore NIF can be used as one of the data quality criteria. The index NIT is linearly correlated with the significant wave period and with the significant wave height, therefore NIT can be used to study the wave growth and decaying phenomena.     

Characterization of bedform morphology generated under combined flows and currents using wavelet analysis

The wavelet transform (WT) has been successfully implemented in many fields such as signal and image processing, communication theory, optics, numerical analysis, and fluid mechanics. However, the application of WT to describe bedform morphology in coastal areas, oceans, and rivers is rare. The present study demonstrates the capability of WT analysis to fully represent the space–frequency characteristics of signals describing bed topography generated in marine and river environments. In this study WT is used to examine the morphological characteristics of bedforms generated in two separate laboratory facilities: a wave tank and a meandering channel. In the wave tank a set of ripples superimposed upon large wave ripples were generated; while in the meandering channel, 2D and 3D migrating ripples and dunes were observed. The WT proved to be a useful tool in detecting the complex variability of the generated bedform structures. The size distribution of the bottom features such as ripples, large wave ripples and sandbars were first examined along a 2D bed profile. Later analysis studied the variability of features in the transverse direction by using the power Hovmöller. Experiments in the wave tank were conducted for a mobility number of ψ=(10, 28), and a Reynolds wave number of R_ew=(17,500, 83,500) which correspond to waves alone (WA) and to combined flow (CF) scenarios, respectively. Experiments in the meandering channel were conducted under a morphological regime that produced mainly migrating sandbars.     

论风浪的局域结构──Ⅰ.风浪的局域结构与局域小波能谱

基于小波变换,引入了能刻画风浪局域结构的局域小波能谱。论述了风浪的整体结构与局域结构。指出了在不同时间尺度上,风浪具有不同的局域化特征。提出了风场演化过程中整体的共振在线性相互作用是否存在的质疑。     

Wave grouping characteristics in nearshore Great Lakes

The recently advanced approach of wavelet transform is applied to the analysis of wave data measured in the nearshore areas of the Great Lakes. The conventional spectrum analysis of wave time series in the frequency domain can be readily generalized to the frequency and time domain using the wavelet transform. The traditional Fourier transform approach has not been able to directly assess the time localized nature of wave groups. With the application of wavelet transformation, the relatively unexplored wave grouping characteristics come to light as the predominant feature of wave processes.     

Wavelet bicoherence analysis of wind–wave interaction

A new technique in the analysis of wind–wave interaction, wavelet bicoherence, will be applied in this article. Wavelet bicohence has the ability to detect phase coupling and nonlinear interactions of the quadratic order with time resolution. It is used in this study to analyze wind–wave interaction during wave growth in a Mistral event. A selected record of simultaneously measured wind and wave data during Mistral is divided into five segments and the computations of the wavelet bicoherence are conducted for the whole record and for all divided segments. The results show that the phase coupling occurs between wind speed and wave height over a certain range of frequencies and that the range is different from one segment to another due to the non-stationary feature of the time series.     

小波变换在水下目标回波奇异性检测中的应用

小波变换突破了传统Fourier变换等信号处理方法均限制,具有表征信号局部特征的能力,信号的局部奇异性包含了信号的许多重要信息,论文研究了信号的奇异性检测问题。给出小波变换和信号奇异性的关系,实现小波分析对信号各类奇异间断点的有效检测,最后进行实例分析,说明此理论与方法适用于对边缘信号与突变信号的处理和提取,为海底底质识别提供理论依据。     

Analysis of Energy Overshoot of High Frequency Waves with Wavelet Transform

—A study is made on the overshoot phenomena in wind-generated waves.The surface displace-ments of time-growing waves are measured at four fetches in a wind wave channel.The evolution of highfrequency waves is displayed with wavelet transform.The results are compared with Sutherland's. It isfound that high frequency wave components experience much stronger energy overshoot in the evolution.The energy of high frequency waves decreases greatly after overshoot.     

Wave profile measurement by wavelet transform

A new technique for measuring wave profiles by wavelet transform using the Mexican Hat wavelet as the mother wavelet is introduced. This technique has the potential to provide low cost, high resolution field measurements of wave profiles in the laboratory. The experiments to capture the video image of the wave profile were carried out in a wave flume. Then, the Mexican Hat wavelet was adopted to trace out the exact profiles of the waves from the captured video images. The series of tests on numerical data and video images show promise as means of detecting two-dimensional profiles of waves.     

A new method for separation of 2D incident and reflected waves by the Morlet wavelet transform

A new method based on the Morlet wavelet transform for separating a 2D wave field into incident and reflected waves is proposed in this paper. The principle of this method, first, is derived for constant depths. Then, using the linear shoaling theory, the method is extended to an arbitrary sloping bathymetry. Owing to the time-frequency characteristic of wavelet transform, the present method can separate waves in the real time domain and is not confined by the stationary assumption of waves. The efficiency and accuracy of this method are demonstrated using numerical simulated data.     

Pressure transfer function in time and time-frequency domains

In this paper, we define a time-domain pressure transfer function calculated from SIWEH (smoothed instantaneous wave energy history) transforms, and a time-frequency domain pressure transfer function calculated from wavelet transforms, of synchronized wave and pressure data. It is our objective to study whether the time-domain pressure transfer function and the time-frequency domain pressure transfer function can provide new interpretation of wind wave behaviors. The detail structure of local time-frequency pressure transfer function in three-dimensional plot from wavelet transform is not employed due to its large variations, instead the time-integral wavelet spectral pressure transfer function and frequency-integral wavelet SIWEH pressure transfer function are used. These two averaged pressure transfer functions are smooth approximations of frequency-domain Fourier and time-domain SIWEH pressure transfer functions, respectively.Application to real ocean waves reveals that in frequency-domain the measured Fourier and wavelet spectral pressure transfer functions can be approximated by the linear pressure transfer function in the dominant wave range. In time-domain, the wavelet SIWEH pressure transfer function is a better indicator of wind wave behaviors than the SIWEH pressure transfer function. A value higher than 0.5 for the wavelet SIWEH pressure transfer function is a good discriminator of relative shallow-water long waves and wave groups are mostly composed of relative low frequency long waves.     

浅谈数学变换在海洋技术中的应用

根据以往的工作积累,作者在文中介绍了在海洋技术中得到应用的几种数学变换,包括基于Fourier变换的频谱分析、波浪分离、相关分析及定义的H artley实现,连续M orlet小波变换在波浪信号分析中的应用,以及离散正交小波变换的降噪作用与悬沙图像的特征提取。文中通过公式推导和数据比较,展示了数学变换在海洋技术应用中的科学魅力。     

数字滤波技术在潮汐观测中的应用研究

潮汐是重要的海洋物理要素。瞬时变化的海面高度信息除了包含潮汐信息外,还包括波浪等高频干扰信息,因此需要对干扰信息进行滤除。如何从获取到的海面瞬时高度变化中提取出潮汐信息就成为一个关键问题。海洋学中通常是通过低通滤波来获取低频的潮汐信息。通过分析常用的3种低通数字滤波的方法,即滑动平均法、快速傅里叶变换法和小波变换法,对3种低通滤波方法应用于潮汐数据处理的效果进行了比较分析,得出滑动平均法在潮汐信息提取中具有较高应用价值的结论。     

Application of Wavelet Algorithm to Spectral Analysis of Oceanic Waves and Offshore Structure Responses

Fourier transform (FT) is a commonly used method in spectral analysis of ocean wave and offshore structure responses,but it is not suitable for records of short length.In this paper another method,wavelet transform (WT),is applied to analyze the data of short length.The Morlet wavelet is employed to calculate the spectral density functions for wave records and simulated Floating Production Storage and Offloading (FPSO) vessels' responses.Computed wave data include simulated wave data based on JONSWAP spectr...     

风浪超射现象的研究 Ⅰ.实验分析

对风浪超射现象进行实验研究,由于峰频率谱值不易精确定,因此通过谱分析不易获得精确的风浪超射曲线。在风浪槽中４个风区处观测随风时成长风浪,以子波变换分析风浪资料,结果表明,风浪高频组成波在成长中姓能量超射,与Ｓｕｔｈｅｒｌａｎｄ等结果相比,该能量超射幅度更大。     

基于小波变换法定义的波群参数

通过小波变换分析的波能过程定义了两个描述波浪群性的参数,由数值模拟波浪和实测波浪资料对其与常用的波群参数进行对比分析,结果表明基于小波波能过程定义的群性参数是有效的,从而展示了小波变换用于在时频域上分析波群的能力。详细探讨了波浪记录长度对群性参数稳定性的影响,分析结果表明,波浪观测长度对于波群参数的影响较大,在考虑波浪群性的波浪模拟及分析时,建议模拟时间长度应在400~500个波以上。     

希尔伯特—黄变换在遥感图像中的实例研究与应用展望

希尔伯特-黄变换是一种处理非线性、非平稳数据的方法,目前该方法已在遥感图像处理中得到高度重视。文中在介绍希尔伯特-黄变换的基础上,首先通过对时间序列数据的不同频率信息进行分离,揭示了希尔伯特-黄变换方法对局部时间尺度的物理含义。通过希尔伯特-黄变换方法对不同空间尺度信息的分离,对SAR遥感图像滤波和SAR遥感图像信息提取开展了实例应用研究,展示了希尔伯特-黄变换方法可以通过遥感图像提供各种尺度信息现象的有效数据。最后讨论与分析了希尔伯特-黄变换方法的局限性与优势,并对其在遥感图像处理中的应用进行了总结和展望。