Study On Multivariate Maximum Entropy Models And Their Applications In Coastal And Ocean Engineering

The surrounding environmental conditions of marine and offshore structureswhich are influenced frequently by severe synoptic processes including typhoon andcold wave are very harsh. Sea dikes play an extremely important role in marinedisaster prevention. Once they are damaged by typhoon, the economic losses andcasualties are not overestimated because of high developed economy and populationdensity along the China’s coastline. In addition, disastrous synoptic processes severelyimpact the regular work of offshore platforms with high cost. At worst, these poorconditions would result in platforms overturning and oil spill which cause pollution tothe ocean circumstance and destruction of the ecological environment. Actually, theprimary environmental elements that affect the coastal and ocean structures includewind, wave, tide, current, sea ice, sea fog, and so forth. The establishment of jointdesign criteria of these loads is crucial for the safety and reliability of marinestructures. However, the traditional design standard is too conservative to reflect thereal ocean circumstance, since it regards all the environmental elements asindependent variables. Therefore, it is necessary to study the joint design criteria ofmultivariate environmental elements which demands proper multivariate probabilitydistributions. While, there are several shortages for existing models, such as singletype and large errors in data fitting.In this paper, several bivariate and multivariate maximum entropy modelsdeduced based on maximum entropy theory are applied in the joint design ofmultivariate environmental loads on sea dikes and ocean platforms. Also, thesemodels are introduced into multivariate compound extreme value theory, reliabilityanalysis of structure and risk analysis. The main work of this paper is as follows.One-dimensional maximum entropy distribution (OMED) function covers almostall the distributions adopted in ocean environmental design, so fitting the observationswith it can avoid the choice of fitting curves. This paper proposes or summarizes seven parameter estimation methods for OMED, including method of moment withthree parameters (MMT), method of moment with four parameters (MMF), empiricalcurve-fitting method (ECFM), maximum likelihood method (MLM), probabilityweighted method (PWM), L-moment method (LMM) and particle swarmoptimization method (PSOM). These methods are tested and validated using field dataand corresponding Monte-Carlo simulations. Results indicate that MLM and ECFMare both recommended due to their best fit to data.To avoid large errors of point estimation for design values of marineenvironmental elements, the concept of confidence intervals is introduced in thispaper. It contains five interval estimation methods for design return values, such asWoodruff method, maximum likelihood method, sample quantile asymptotic method,order statistic method and sign test method. According to the results of simulation andcase studies, with respect to OMED, parameter methods, among which maximumlikelihood is recommended firstly, are always better than non-parameter methods.Exactly as OMED, bivariate maximum entropy distribution (BMED) is deducedwith proper constraints for two-dimensional joint Shannon entropy. Meanwhile, themoment method for its parameters estimation is derived. Based on bivariate Copulafunctions, several types of BMED models with OMED as marginal distributions areconstructed. More importantly, they would be consistent with maximum entropytheory. These models are utilized to establish the joint probability design of waveheight and corresponding wind speed, analyze corresponding probability of sea icebetween Yingkou and Huludao. The conclusion is that BMED models can fit bivariatedata well.Presently, most multivariate models are limited in two or three dimensions anddifficult to be generalized to higher dimensions. On the basis of multivariate jointinformation entropy and maximum entropy theory, this paper proposes generalmultivariate maximum entropy models (MMEDs), MMEDs with moment constraints,and trivariate maximum entropy distribution (TMED) function with proper constraintsfor marine environments. Since the calculation for TMED function is very hard, TMED models with OMED margins based on trivariate Copuls are constructed.Similarly it could coincide with maximum entropy theory. As an example, a jointdesign method for the crest level and overtopping rate of sea dikes is proposed usingthe data of25a annual extreme wave height, wave period and storm surge observatedin an island of Huanghai Sea.This paper proposes two new multivariate compound extreme models fordifferent data samples (all extreme values in the same process, and concomitantvalues when the load is the largest in one process) in severe weather processes. Andthen multivariate compound maximum entropy models are easily derived. Applyingthese models, the classification criteria of storm intensity in Qingdao is establishedand the environmental element design values for a jacket platform in severe weatherprocesses are calculated.Combined with direct integration method, MMEDs are introduced into staticstructure reliability analysis. Consequently, total probability method becomes feasible.However, time-varying condition of resistances and loads does not take into accountin this analytical procedure. In order to overcome this difficulty, time-variantreliability analysis is discussed, and several calculation equations of time-variantreliability in the tour of duty are deduced here.In fact, severe synoptic processes could be treated as stochastic point eventsaccording to scale point process theory. Poisson multivariate scale point processmodel for severe synoptic processes could be established if considering the extremevalues of environmental elements in one process as the scale values of the point event.Adopting MMED to fit the joint distribution of multivariate scale values, the syntheticrisk of ocean platforms is derived, which might provide references for safetyprotection.