摘要
海洋环境条件设计参数推算模型在海洋工程及海岸防灾等方面有着重要的应用。海洋工程设计需要计算多年一遇重现期水平,海岸防灾等部门需要考虑对海洋灾害建立有效预警,这些都涉及到海洋环境条件设计参数推算模型。国际金融危机使我国外向型经济的发展严重受挫,又恰逢国家转变经济增长方式,强调可持续发展战略,因此从国家经济长远发展的高度考虑,未来可持续发展的、蓝色的海洋经济必定会成为我国经济新的增长点,而提供这一切的基础正是大量海洋工程和海岸工程的建设。基于海洋环境下不确定度及精确地选择适用设计参数推算模型为这些海洋、海岸工程和防灾部门提供了依据。
以往海洋环境条件下设计参数推算模型的选择大部分是人工的,常用的做法有概率纸、适线法等,这样做不但没有减少模型的不确定度,恰恰相反,人为因素的干扰在一定程度上反而增加了模型的不确定度。而且有时候对于同一组海洋环境下的实测数据,不同的模型均能通过假设检验,但是计算出来的结果却相差较大,在这种情况下,选择哪一组计算结果作为设计标准也成了难题。
现阶段设计参数推算模型不确定度的研究主要集中在对具体分布模型的形式分析及其自身信息的不确定度上,然而实际上的整体不确定度通常包含两类信息量,第一类信息量包含着如何选定模型时带来的不确定度,这部分的不确定性往往会被忽略；第二类信息量是当已经假定某个分布模型时该模型自身的不确定度。因此本文利用信息熵反映随机事件不确定度这一性质,通过信息熵作为模型整体不确定度分析的桥梁,综合考虑两类信息量,在样本数据的数量、离散程度,模型的分布形式以及模型参数估计量带来的抽样误差这几个方面对设计参数推算模型的信息熵进行了分析,提出了一种更加全面的计算整体不确定度的方法,并以此方法计算了同一实测数据下不同模型的整体不确定度,为模型的选择和评价提供了新的标准和依据,这方面的研究成果主要有以下几个方面：
(1)针对第一类信息包含的不确定度,主要从数据样本的数量和离散程度进行了分析；对于第二类信息包含的不确定度,主要从模型分布形式及其参数估计量两个方面进行了分析。通过定理分别证明了样本数据的数量和离散程度对信息熵的影响,结果表明样本数据数量和离散程度与信息熵成正比；总结归纳了常见设计参数推算模型自身不确定度的计算公式,这些公式只和模型自身分布参数有关；运用蒙特卡洛方法对参数估计量的进行了抽样,并将误差结果用信息熵表示出来。
(2)将两类信息所包含不确定度的各个方面均通过信息熵表示,给出了一种更加全面的信息熵计算公式,为模型的选择标准和评价指标提供了一种新的建议和依据。应用该公式对实测数据进行了分析,结果表明在该组数据下最大熵分布模型的整体不确定度最小,反映了最大熵模型相比其他模型具有更小的不确定度。
(3)针对以往最大熵模型参数估计困难和计算量大的缺点,本文在矩估计的基础上提出一种改进形式,推导出了基于均值、方差、偏度和峰度等统计特征的参数求解的非线性方程组,有效地减小了参数求解的计算量,求解更加方便、迅速。
The design parameters calculating model under marine environment is very important in ocean engineering and seacoast disaster prevention. Ocean engineering designation will calculate return period, seacoast disaster prevention department will establish effective early warning system, both of them need design parameters calculating model. Under International Financial Crisis, export-oriented economy suffering a serious influence, while national changing economic growth mode and emphasizing sustainable development, in view of national long-term development, ocean will be the new growth pole, while ocean engineering and seacoast engineering provide powerfully support. Selecting appropriate model is the basis of all.
Usually, people select design parameters calculating models under marine environment by probability paper or curve fitting method and so on. It doesn't reduce the uncertainty of data and models, conversely, human interference add uncertainty in some degree. Especially, models, all of which have being tested by hypothesis, will get different results under the same marine measured values. It is hard to choose which one to be as the design criterion in this condition.
Recently, the research of design parameters calculating model's uncertainty is mainly concentrate on distribution formal analysis and its'self-uncertainty. In fact, the whole uncertainty contains both information amount, the first kind information contains the uncertainty of how to choose the model, while this kind of uncertainty usually be neglected; the second kind information is the model's own uncertainty while fix the model. In the paper, for information entropy reflects random event uncertainty, through it as the bridge to analyze whole uncertainty, considering two kind information, analyzing model information entropy in sample data's number, degree of dispersion, model distribution forms and its parameter estimator, giving a new methods which can calculate the whole uncertainty, the research contain:
(1) For the uncertainty involved in the first kind information, it mostly analyzes in sample data's quantity and its'degree of dispersion; for the uncertainty involved in the second kind information, it considers the distribution forms and its parameters estimation. A result that sample data's quantity and its'degree of dispersion are in direct proportion to information entropy is proved by theory. Some common models' self-uncertainties are calculated just by their parameters, and sampling the parameters' estimation by Monte Carlo method.
(2) A new information entropy calculating formula is given to consider the double uncertainty involved in the differ information, which provides a new standard and basis for the choice between differ models and evaluation criterion. Compared with the other models, the analysis based on the series of annual maximum wave heights shows that the Max-Entropy model has the minimum uncertainty.
(3) To improve the difficulty in parameter estimate of the maximum entropy model, this text proposing an improving format on the basic of moment estimation, deviating a nonlinear equations which contain mean, variance, kurtosis and skewness, making the calculation more convenient and fast.
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