Application of Linear Mean-Square Estimation in Ocean Engineering

The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method’s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations (adjacent to the concerning sea area) and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.     

Maximum Entropy Estimation of n-Year Extreme Waveheights

A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamihonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)= aH^γe-^βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α,β, and γ in the function me expressed in terms of the mean H, variance V=(H-H^-)^2—— and bias B = (H - H^-)^3——; and (3) with H^-, V and B estimated from observed data, the n-year return-period wave height Hn is computed in accordance with the formula 1/1-F(Hn)=n, where F( Hn ) is defined as F( Hn ) = ∫0^Hnf(H)dH .Examples of estimating the 50 and 100-year return period waveheighls by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.     

On the annual maximum distribution in dependent partial duration series

As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.     

An improved ‘Battjes’ method for predicting the probability of extreme waves

The Battjes method for predicting the 50 or 100-year design wave was developed to allow for the possibility that the highest wave in a 50 or 100 year period may occur during the second highest storm or even in lower storms. It uses the probability distribution of individual waves. It is first shown that a slightly different logical approach removes some of the problems encountered with the use of the method. It is then shown that it actually uses a different definition of return period to that used by the classic method because if two or more waves in a severe storm exceed H₅₀, then these are counted as separate events. A formula is developed which considers each storm as one event, but still takes account of the possibility of the highest wave in 50 years not coming from the most severe storm. Computation using this formula shows that it reduces H₅₀ by about 3% relative to the Battjes method.     

A new approach to estimating the T-year return-period wave height

The paper introduces a new approach to estimating the T-year return-period wave height (TRPW), i.e. the wave height expected to occur in T-year, from two sets of observed extreme data and on the basis of the maximum entropy principle. The main points of the approach are as follows. 1) A maximum entropy probability density function (PDF) for the extreme wave height H is derived from a Euler equation subject to some necessary and rational constraints. 2) The parameters in the function are expressed in terms of the mth moment of H. 3) This PDF is convenient to theoretical and practical applications as it is simple and its four parameters are easy to be determined from observed extreme data. An example is given for estimating the TRPW in 50 and 100 years by the present approach and by some currently used methods using observed data at two hydrographic stations.The comparison of the estimated results shows that the present approach is quite similar to the Pearson-Ⅲ and Gumbel methods.     

T年重现期波高的最大熵估计

本文在最大熵原则的基础上,通过解一条件变分问题,导出一种由观测数据估计T年（常用的有50a或100a）重现期波高的新方法.本文导出的概率密度函数为f4（H）=αH^γe^-βH4,式中参量α、β、γ可以由年极值波高H的1～4阶分布矩（Hm^-,m=1,2,3,4）显式地表示出来.其具有如下的优越性：（1）参量中包含了H的3阶和4阶分布矩,适用于描述不确定性很大的海浪的重现期波高;（2）符合最大熵原则,即其信息熵最大,从而特别适用于重现期波高的估计;（3）形式简单且其参量容易由已知观测数据确定,便于理论和实际应用.作者对两个水文观测站的实测数据,分别使用该方法,及一些现有常用的方法计算其50、100a重现期波高.比较计算结果表明该方法非常接近于皮尔逊-Ⅲ方法和龚贝尔方法的结果.