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。     

The initial stage of dam-break flow of two immiscible fluids. Linear analysis of global flow

Two-dimensional impulsive flow of two immiscible fluids is studied within the potential flow theory. Initially the fluids of different depths and different densities are at rest and separated with a thin vertical plate. The plate is withdrawn suddenly and gravity-driven flow of the fluids starts. During the early stage the flow is described by the linear potential theory. Attention is paid to the motion of the interface between the fluids and the singular behaviour of the velocity field at the triple point, where the free surfaces of the fluids and the interface meet each other. The linear problem is solved by the Fourier series method. Local analysis of the flow field close to the triple point reveals that the singularity of the flow depends on the ratio of the fluid densities with a coefficient dependent on both the density ratio and the shape of the flow region. The flow velocity is also log-singular at the point where the interface meets the bottom. The intensity of this singularity depends on the density ratio. The latter singularity disappears when the densities of the fluids are equal. The Fourier series solution supplemented by the singularity analysis at the corner points resolves these initial singularities. Comparisons with solutions obtained through the boundary element method are established for validation purposes. The numerical analysis of the problem by the boundary element method is carried out and it compares quite well with the Fourier series solution. The singular flow field which leads to the jet formation at the initial instant has been observed by both methods. The problem of dam-break flow for the wet-bed case corresponds to the present problem with equal densities of the fluids. Comparisons with data available in literature are established in the case of fluids with the same density.     

纬度正反解问题的傅里叶级数解算方法

讨论了一种在一般闭区间上连续的无穷级数展开方法,针对测量和地图学中常用纬度间正反解等一类问题,给出了一种傅里叶级数解算方法,并进行了相应的理论分析和计算。基于Mathematica计算机代数系统,推导出常用纬度与大地纬度间正反解的级数展开式,表明运用傅里叶级数解法可以简单表示和计算一类复杂奇函数的正反解无穷展开式。算例分析验证表明,该方法推导出的纬度正反解展开式是正确的。傅里叶级数方法为分析一类正反解问题无穷展开式的一般系数和形式提供了理论分析依据,具有通用性,丰富了纬度正反解变换的相关理论。     

Analysis of orthogonal wave reflection by a caisson with open front chamber filled with sloping rubble mound

A new combined caisson, including an open window on the front wall and an internal rubble mound with a slope, has been proposed and used in Italy. This study presents a semi-analytical solution to estimate the wave absorbing performance of the new combined caisson with regard to orthogonal wave attack. The internal slope of the rubble mound is assumed to be a series of horizontal steps. Then the matched eigenfunction expansions are used to develop the semi-analytical solution. The square-root singularity of fluid velocity at the upper tip of the front submerged wall is incorporated into the solution to enhance the convergence of calculated results. The new semi-analytical solution is confirmed by an independently developed multi-domain boundary element method solution. Also the predictions of the semi-analytical solution agree reasonably well with experimental data. Based on both the calculations and the experimental data, some useful results are presented for practical engineering.     

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability, the convective derivatives in the free-surface boundary conditions are treated using an upwind-biased stencil. Instead of solving for the radiation impulse response functions, a pseudo-impulsive Gaussian type displacement is employed in order to tailor the frequency-content to the discrete spatial resolution. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth-order convergence of the calculations on simple geometries is demonstrated, along with a nearly linear scaling of the solution effort with increasing grid resolution. The code is validated by comparison with analytical and semi-analytical solutions using submerged and floating closed-form geometries. Calculations are also made for a modern bulk carrier, and good agreement is found with experimental measurements.     

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

In this paper, the generalised two-dimensional differential transform method (DTM) of solving the time-fractional coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the generalised two-dimensional DTM is effective for the coupled equations.     

Analysis and simulation of wave records through fast Hartley transform

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and synthesis of ocean surface wave records. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms, as well as computational benefits and disadvantages between numerical algorithms used to evaluate their discrete versions, are presented. The fast Hartley transform algorithm is used to simulate stationary Gaussian time series of the sea surface elevation and to estimate the spectral density function, the Hilbert transform and the envelope function of wave records.     

利用EMD方法和小波变换进行信号奇异性检测

本文采用经验模式分解 (EMD)与小波变换相结合的方法分析非平稳机械故障信号的奇异性 ,进行机械故障诊断。与直接对原信号进行小波分析相比较 ,该方法提取的奇异性特征明显。数值模拟和对故障轴承的振动信号分析表明了该方法的有效性。     

High-Resolution Signal and Noise Field Estimation Using theL1 (Least Absolute Values) Norm

In this paper a new method for obtaining a quantitative estimate of an acoustic field consisting of a set of discrete sources and background noise is described. The method is based on theL1 (least absolute values) norm solution to an underdetermined system of linear equations defining the Fourier transform of the signal series. Implementations of the method with either equality or inequality constraints are presented and discussed. The much faster and more compact equality constraint version with a provision for modeling the noise field is recommended in practice. Experience with real data has shown the necessity of correcting for an observed Gaussian decay on the covariances. A simple means of estimating this effect and taking it into account in the signal estimation procedure is discussed, and the implications of this effect in high-resolution beamforming are considered. The effectiveness and versatility of theL1 method indicate that it has a useful role in high-resolution signal estimation.     

Analysis of correlations between time series with the use of the phase spectrum

In connection with the problem of revealing cause-effect relations among different climatic characteristics, methods for determining the dependence between time series on the basis of selected auto-and cross-covariance functions and periodograms expressed in terms of the Fourier coefficients of the initial series are discussed. Real time series do not always satisfy the conditions of statistical stationarity, so that their analysis requires a combination of statistical and deterministic approaches. The possibility of using the above numerical characteristics in relation to such series is considered. Characteristic features of describing finite segments of time series with the use of their Fourier coefficients is studied in detail. The main emphasis is on the determination of the time shifts (delays) at which the covariance between the series is maximal. The problems that appear during a practical implementation of the periodogram method for shift estimation are discussed. A previously unknown formula that is necessary for further studies and relates the Fourier transform of a selected correlation function to the periodogram of the series is derived.     

Identification of resonances of an acoustically rigid sphere

Identification of resonances of an acoustically rigid sphere from simulated input-output data is presented. Scattering from the sphere is formulated using the classic Mie series and the singularity expansion method (SEM). A parametric inverse based on the SEM is discussed. The scattered velocity potential is divided into reflection, first creeping-wave, and second creeping-wave components. The effects on the identification of removing various components of the scattered potential are shown, along with the effects of adding small amounts of noise.     

Use of advanced directional wave spectra analysis methods

Frequency-dependent cross-spectral parameters for pitch-roll buoy data and parameters that describe directional wave spectra based on a directional Fourier series are developed by the National Data Buoy Center (NDBC) and other organizations that collect wave data. The World Meteorological Organization (WMO) specifies wave data product formats in its Wave Observation (FM 65 WAVEOB) code. Other organizations, such as the US Army Corps of Engineers Field Wave Gaging Program (FWGP), have similar specifications. A directional Fourier series has poor directional resolution compared with advanced methods such as those based on maximum likelihood and maximum entropy. Transformations are developed for applying the advanced methods and working with directional wave information stored in the WMO's FM 65 WAVEOB code, the FWGP's Wave Data Analysis Standard (WDAS) format, and similar codes and formats. Using the transformations, a directional Fourier series expansion method, a Maximum Likelihood Method (MLM), and a Maximum Entropy Method (MEM) are each applied to 115 sets of NDBC directional wave data. The MEM and MLM provide better directional resolution, but the MEM produces artificial double peaks. There are considerable differences for the three used methods. The developed transformation equations enable wave data users to apply the method that best suits their applications.     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

Energy dissipation in sloshing waves in a rolling rectangular tank—II. Solution method and analysis of numerical technique

In Part I of these series of papers, the complete problem formulation in a linearized form was presented. In order to provide the engineer with an in-depth knowledge about the exact solution of the problem, it is natural and essential to start with a linear solution. This will be the objective of Part II, together with an exposition to the analysis of numerical technique utilized.A truncated infinite Fourier series-type solution is adopted for the linearized boundary value problem. It is shown that such a solution is mathematically consistent and represents the phenomenon properly by satisfying all of the field equations and the imposed boundary conditions. The dependence of the Fourier coefficients on the truncation limit has been investigated. The best lower and upper “cutoff limits” for the truncation of an infinite series are determined. An error analysis of the solution technique is performed.     

时间不连续压力序列的傅立叶分析方法

提出了一种用于对不连续压力采样序列的傅立叶分析方法.此方法将周期函数展开成傅立叶级数,但在数值积分时取函数周期内有采样值的区间作为积分域,然后求解线性方程组得到傅立叶级数的系数值.为了检验本方法的有效性,利用此方法对解析函数进行了拟合,当一个周期内的取样时间大于1/2周期时,利用此方法能够得到满意的结果.利用实验方法研究了波浪作用下截断圆柱表面的压力分布.在波浪作用下静水面附近的测点在露出水面时没有压力值.利用所提出的傅立叶分析方法对略低于静水面位置的实测压力进行了分析,拟合结果与实测结果吻合很好,说明此方法在处理物理模型实验中间断采样得到的数据是有效的.利用数值方法对波浪压力进行了计算,并将一阶和二阶波压力的数值结果与实测值进行了比较.     

High-resolution beamforming by the Wigner-Ville distribution method

The Wigner-Ville distribution (WVD) function was originally proposed by Wigner in quantum mechanics and Ville applied it for signal analysis. This method has made it possible to represent a signal's power density spectrum in the time-frequency domain as a natural extension of the Fourier transform method (FTM). Recently, it has attracted great interest for its validity to analyze time-varying signals accomplished by the development of high-speed digital signal processing, and it is used for analyzing nonstationary signals. Conventionally, a sonar beamformer is constructed using delay lines, but the development of the high-speed processor has made it possible to apply the FTM for sonar beamforming. However, the bearing resolution of the beamformer is not enough for discriminating small underwater objects on the sea bottom by this method. To solve this problem, we aim to apply the WVD method, which can represent finer structure of signals as a natural extension of the FTM, for sonar beamforming to obtain sharper beam patterns than those of the beamforming method by FTM. Simulation results by computational calculations to clarify the resolution by the WVD method, which is presented in this paper, becomes approximately twice as high as by conventional FTM. The results of an experiment at sea also show the performance of this method     

RhoVe method: A new empirical pore pressure transform

A new empirical pore pressure transform has been developed that includes many of the advanced, state-of-the-art concepts that are useful in today’s pore pressure estimation and theory. The rhob-velocity-effective stress (Rho-V-e) method produces a model-driven, stand-alone set of “virtual” rock property relationships, which at intermediate positions are consistent with Bowers method default values for the Gulf of Mexico. The RhoVe method uses a single transform to convert both compressional sonic and bulk density to common estimates of effective stress and pore pressure where convergence of the two transformed properties offers a robust solution.Velocity-density conversion functions are mathematically linked to a continuous series of velocity-depth normal compaction trend functions. The calculations are limited by bounding end-member curves that provide a basis for intermediate (fractional) solutions of velocity-effective stress and density-effective stress relationships that are applied to a well of interest.Paired “virtual” velocity-depth compaction trends were iteratively solved by using published theoretical smectite and illite porosity trends and velocity-depth normal compaction trends. By using the RhoVe-derived velocity-density functions that match the well of interest in cross-plot, normal effective stress for each end-member and intermediate solution can be calculated. Effective stress is calculated by taking the difference between the integrated density-depth virtual overburden profile, converted from velocity-depth, and the inclusion of hydrostatic pressure. The method produces robust solutions as tested on multiple deep water Gulf of Mexico wells, and extends the predictability of high-velocity, low-effective stress rock types such as those found in the Deepwater Gulf of Mexico Wilcox-equivalent Paleogene and older section. The velocity-effective stress trend curves can also improve pore pressure characterization of the overlying overburden section extending to the mud line. Advantages of the RhoVe method are that it can be made interactive and fast, relative to the application of other acoustic transform methods.This paper attempts to build on previous efforts by other workers to include the role of clay type, clay volume and diagenesis on altering velocity-effective stress relationships and presents a technique in which the effects of clay diagenesis and other factors may be captured and utilized empirically for pore pressure analysis and prediction.     

基于小波变换的海洋地磁日变改正研究

基于现有地磁日变理论和改正方法,对国际公开地磁静日变数据进行傅里叶变换和一维连续小波变换综合分析,判断大于0.2 Hz频段为磁扰变化场在频域的体现,并利用一维离散小波变换将数据分离,完善了已有的地磁静日变改正方法。根据日变数据特征和一维离散小波分解特性,选定sym8小波作为基本小波对数据进行7尺度分解,将日变数据中长期变化和短期变化与磁扰部分在保证保真度条件下有效分离,并与傅里叶级数分解和低通滤波处理效果作对比验证,结果显示一维离散小波变换处理效果更佳。日变数据中短、长期变化与磁扰两部分数据的有效分离并分别改正可提高海洋地磁测量日变改正质量,降低海洋地磁数据处理过程中误差累积程度,提高了现行日变改正方法的科学性、准确性。     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.