Stability and capsizing analysis of nonlinear ship rolling in wind and stochastic beam seas

Considering the actual seaway condition, stability and capsizing of nonlinear ship rolling system in stochastic beam seas is of significant importance for voyage safety. Safe zone are defined in the phase space plan of the unperturbed Hamilton system to qualitatively distinguish ship motions as capsize and noncapsize. Capsize events are defined by solutions passing out of the safe zone. The probability of such an occurrence is studied by virtue of the random Melnikov function and the concept of phase space flux. In this paper, besides conventional wave excitation, the effect of wind load is also taken into account. The introduction of wind load will lead to asymmetry, in other words, it transforms the symmetric heteroclinic orbits into asymmetric homoclinic orbits. For asymmetric dynamical system, the orbital analytic solutions and its power spectrum are not readily available, and the technique of discrete time Fourier transformation (DTFT) is used. In the end, as verification of theoretical critical significant wave height, capsizing probability contour diagram is generated by means of numerical simulation. The contour diagram shows that these analytical methods provide reliable and predictive results about the likelihood of a vessel capsizing in a given seaway condition.     

GRAPES全球集合预报系统模式扰动随机动能补偿方案初步探究

为了体现次网格尺度能量升尺度转换过程中存在的不确定性, 文中将随机动能补偿(Stochastic Kinetic Energy Backscatter, SKEB)方案应用于GRAPES(Global/Regional Assimilation and Prediction System)全球集合预报系统(GRAPES-GEPS), 以更好地表征模式误差并且增大集合离散度。使用的SKEB方案基于具有一定时、空相关特征的随机型以及由数值扩散导致的局地动能耗散率来构造随机流函数强迫。并根据流函数与水平风速旋转分量的关系, 将SKEB方案中的流函数强迫转化为适用于GRAPES全球模式的水平风速扰动。结果表明, SKEB方案的使用一方面能够提高GRAPES对大气动能谱的模拟能力; 另一方面能够改善GRAPES-GEPS的集合离散度与集合平均误差的关系, 增加了集合离散度, 并在一定程度上减小了集合平均误差, 尤其是在热带地区这种改进更为显著。而且该方案使得热带地区连续分级概率评分(CRPS评分)显著减小。就降水预报而言, 从Brier评分与相对作用特征面积(AROC, Area under the Relative Operating Characteristics)的结果来看, SKEB方案有助于改善中国地区小雨[0.1 mm, 10 mm)、中雨[10 mm, 25 mm)与大雨[25 mm, 50 mm)量级降水的概率预报技巧, 而对暴雨[50 mm, ∞)量级降水预报技巧影响很小(24 h降水量)。总体上, 模式扰动随机动能补偿方案提高了GRAPES-GEPS的概率预报技巧。      

Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (H_s) and spectral peak period (T_p), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.     

Nonlinear random wave-induced drag force on a vegetation field

This paper provides a practical method by which the drag force on a vegetation field beneath nonlinear random waves can be estimated. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (Mendez, F.J., Losada, I.J., Losada, M.A., 1999. Hydrodynamics induced by wind waves in a vegetation field. J. Geophys. Res. 104 (C8), 18383–18396). Effects of nonlinear waves are included by using Stokes second order wave theory where the basic harmonic motion is assumed to be a stationary Gaussian narrow–band random process. An example of calculation is also presented.     

An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization

Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.     

A survey of numerical methods for stochastic differential equations

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.     

Evaluation of rainfall-runoff performance using the stochastic integral equation method

The stochastic integral equation method (S.I.E.M.) is used to evaluate the relative performance of a set of both calibrated and uncalibrated rainfall-runoff models with respect to prediction errors. The S.I.E.M. is also used to estimate confidence (prediction) interval values of a runoff criterion variable, given a prescribed rainfall-runoff model, and a similarity measure used to condition the storms that are utilized for model calibration purposes.Because of the increasing attention given to the issue of uncertainty in rainfall-runoff modeling estimates, the S.I.E.M. provides a promising tool for the hydrologist to consider in both research and design.     

On the modelling of sand bedforms using the semivariogram

This study shows the usefulness of the semivariogram for modelling sand ripples created by water flows of varied flow intensity. A combination of two mathematical functions is fitted to each sample semivariogram, that is an exponential (or stochastic) component and a periodic component. The parameters of each of these components have direct physical meaning. A non-dimensional ratio combining the two parameters of the exponential model is interpreted as a regularity index (which increases with the degree of regularity of bedform arrangement). This regularity index is inversely related to the Froude number of the flow. The non-dimensional wavelength, estimated from the dominant periodic function, is also inversely and closely related to the Froude number. The wave height, accurately estimated from properties of the two fitted components, is a direct function of flow velocity and is also proportional to the standard deviation of bed elevations. The bedform shape introduces a considerable discrepancy between the generally assumed normal frequency distribution and the empirical distributions of bed height. The series of bed elevations are generally characterized by a mixture of normal distributions having the same variance but different means. The calculation of a covariance assuming a constant and single mean (as in spectral analysis) can therefore be misleading and the problem may be avoided by using the semivariogram.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.     

A review on stochastic differential equations for applications in hydrology

Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources.