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.     

A maximum-entropy compound distribution model for extreme wave heights of typhoon-affected sea areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle.The new model is formed by nesting a discrete distribution in a continuous one,having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper.The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea,and the predicted results are compared with those predicted by use of some other compound distribution models.Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.     

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.     

Response based design metocean conditions for a permanently moored FPSO during tropical cyclones: Estimation of greenwater risk

Response based analysis (RBA) is used to establish the design metocean conditions (DMCs) of a generic weather-vaning FPSO off the North West Shelf (NWS) of Australia for determining greenwater severity. A vessel heading prediction tool, an essential component of the RBA analysis for weather-vaning vessels, is developed and evaluated by comparing with full-scale measurements from an operating FPSO. Locations at the bow, amidships and the stern of the vessel are found to be susceptible to greenwater risks and the vessel is often exposed to oblique waves during tropical cyclones. Long-term extrapolation is performed to estimate 1 in. N-year return relative wave-vessel motions represented by both the most probable maximum relative wave-vessel motion within a storm r_mp, and the maximum individual relative wave-vessel motion r_Max. It is observed that r_Max ˜ (1.1–1.2) r_mp. The use of r_Max allows for the variability of the short term maxima per storm and also the fact that the peak in response might not come in the most severe sea-state. Given the focus on greenwater rather than wave severity, the slightly larger value of r_Max at a given return period is used for assessment of greenwater risk. The sea-states that lead to r_Max at a 1 in 100 year level are identified and subsequently used for characterising the wave groups causing maximum relative wave-vessel motion at various locations around the vessel. For a given location, the shapes of the wave time histories which give rise to extreme relative wave-vessel motions in a set of design metocean conditions are similar, indicating that a ‘design wave’, derived within the framework of linear wave theory, may be a useful approach to tackle highly nonlinear and complex greenwater overtopping problems.     

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.