非负矩阵分解在潮汐分析和预报中的应用研究

发布时间：2018-07-10 06:02

本文选题：潮汐分析 + 调和分析　；参考：《上海海洋大学》2016年硕士论文

【摘要】：潮汐的调和分析方法是潮汐分析预测的最主要方法之一,其根据最小二乘法原理求出各分潮的调和常数,最后叠加到一起成为实测潮汐表达式。随着计算机的出现和计算性能的提高,调和分析方法的理论研究已经非常成熟,但针对实际问题,依然存在很多问题:在沿海存在浅水口岸地区,由于浅水分潮的存在,潮汐分析和预报仍然不精确;当出现极端天气状况时,风暴潮和天文潮的非线性耦合导致天文潮分潮的调和常数计算错误,如何有效的剔除风暴潮成分亟需解决;对于潮汐调和分析,要想计算出准确的调和常数,至少需要搜集18.6年的潮汐数据,对于很多偏远欠发达的沿海地区,尚未收集到这样的长时间的观测数据。为了解决上述调和分析中存在的问题,本文将非负矩阵分解思想引入到潮汐的分析和预测中。以计算思维为基础,选择基于智能计算的方法,将不同频率(能量)海面波动必有产生此波动的作用力相对应作为理论基础,依据相对有限的观测数据,对海洋环境要素的观测资料进行研究分析,根据各个要素随时空变化呈现出的不同特征,研究海洋环境要素的变化规律,进而通过利用这些要素进行建模来模拟、预测整个海洋环境的状况,为其它海洋运动规律的研究提供一个可借鉴的新途径。主要研究内容和结果如下:1、使用基于最小二乘的潮汐调和分析方法,处理中期水位观测资料,按照中潮汐分析的基本流程,首先对潮位数据进行降噪处理,去除特殊值点,然后对潮汐数据进行潮汐调和常数计算,最后通过计算的调和常数推算潮汐水位值和高低潮潮位值,并结合KM站的潮汐实测数据与计算潮位值比较分析误差存在的原因。2、引入非负矩阵分解方法,非负矩阵分解不允许分解的矩阵中的元素出现负值,但是却不要求分解的两个矩阵的行列必须是标准正交的,这种非负限制抓住了智能数据描述的本质,非负性使得对某些数据的解释更加合理,例如潮汐的天文潮分潮不可能出现负值,无法解释。同时针对传统基于乘性迭代方法非负矩阵分解(NMF)求解盲信号分离过程中出现的运算量大、收敛速度慢等问题,提出了一种基于投影梯度法的NMF分解的盲信号分离算法(PGNMFB)。该算法将最优化问题转化为交替的最小二乘问题,并在此基础上增加了行列式约束使分解结果唯一以及稀疏性和最小相关性约束来提高信号分解的精度,利用投影梯度的迭代方法求解基于约束的NMF分解盲信号分离问题。仿真实验结果表明该算法能够很好的平衡重构误差,在维持源分离信号稀疏性的基础上实现了混合信号的唯一分解,PGNMFB算法的收敛速度和分解时间更短比经典NMF和NMFDSC等算法更快、更短;且分解出的源信号的信噪比(SNR)也高于经典NMF算法和NMFDSC算法。3、将基于非监督的非负矩阵分解方法应用到潮汐分析和预测中,利用“混合像元分解”思想将潮汐信号分离,将观测到的潮汐数据看成是天文潮分潮等成分元素的线性组合,并应用强大的基于非监督的混合像元分解算法来提取这些成分元素数据以及各元素对应的混合系数。这类分解方法是能够立即从实际观测数据中检测,分离,提取成分数据元素,能够将潮汐分析和预测提高到前所未有的性能水平。本文所提出的潮汐混合像元分解的方法,与传统的调和分析有着根本性的区别。1)将观测到的数据作为一个整体,因此不需要对不同类型的潮汐进行不同的预处理;2)该分解方法是无监督的,在这个意义上,它不需要先验知识的源标签。在正常的天气条件下,源标签会很好地与调和分析中使用的七个最重要的天文分潮相匹配;3)与传统的调和分析的最重要的区别在于该方法不需要长期的实际观测数据就能够有助于在线潮汐预报。
[Abstract]:The harmonic analysis of tides is one of the most important methods for tidal analysis and prediction. According to the principle of the least square method, the harmonic constants of the various tides are calculated, and finally superimposed together to become the measured tidal expressions. With the emergence of the computer and the improvement of the calculation performance, the theoretical research of harmonic analysis method has been very mature, but it is aimed at the reality. There are still a lot of problems: in the coastal shallow water ports, the tidal analysis and prediction are still inaccurate due to the existence of shallow water. When extreme weather conditions occur, the nonlinear coupling of storm tide and astronomical tide leads to the calculation error of the harmonic constants of the astronomical tide tide, and how to effectively eliminate the storm tide components needs to be solved. For tidal harmonic analysis, in order to calculate accurate harmonic constants, at least 18.6 years of tidal data need to be collected. For many far less developed coastal areas, such long time observation data have not been collected. In order to solve the problems in the above harmonic analysis, this paper introduces the idea of nonnegative matrix decomposition to tidal points. In the analysis and prediction, based on the calculation thinking, the method based on intelligent calculation is chosen to make the force of the wave of different frequency (energy) sea surface fluctuate as the theoretical basis. According to the relatively limited observation data, the observation data of the marine environmental factors are studied and analyzed, according to the changes of each element with time and space. Different characteristics of the marine environment factors are studied, and then by using these elements to model the modeling to predict the condition of the whole marine environment and provide a new way for the study of other marine motion laws. The main contents and results are as follows: 1, using the least square based tidal harmonic analysis square In accordance with the basic flow of mid tide analysis, the method of processing the observation data of the middle stage water level is to de-noise the tidal data and remove the special value points, then calculate the tidal harmonic constants for the tidal data. Finally, the tidal water level and the high tide tide value are calculated by the calculated harmonic constants, and the tidal measured data of the KM station are combined with the tidal measured data. The reason for the analysis of the relative error of the comparative analysis of the tidal value is.2, and the non negative matrix decomposition method is introduced. The elements in the matrix that are not decomposed by the non negative matrix decomposition are negative, but the ranks of the two matrices that are not required to be decomposed must be standard orthogonal. This non negative restriction holds the essence of the intelligent data description. The interpretation of some data is more reasonable, for example, the tide tide tidal wave can not appear negative, and can not be explained. At the same time, a blind signal of NMF decomposition based on the projection gradient method is proposed for the problem that the traditional multiplicative iterative method based on the non negative matrix decomposition (NMF) solves the problem of large computation and slow convergence in the blind signal separation process. The algorithm (PGNMFB). The algorithm transforms the optimization problem into the alternate least squares problem, and on this basis, the determinant constraints are added to make the decomposition result unique, sparsity and minimal correlation constraints to improve the precision of signal decomposition. The iterative method of projection gradient is used to solve the constraint based NMF decomposition blind signal separation question. The simulation experiment results show that the algorithm can balance the reconstruction error well and realize the unique decomposition of the mixed signal on the basis of maintaining the sparsity of the source separation signal. The convergence speed and the shorter decomposition time of the PGNMFB algorithm are faster and shorter than the classical NMF and NMFDSC algorithms, and the signal to noise ratio (SNR) of the decomposed source signals is also higher than that of the classics. The canonical NMF algorithm and the NMFDSC algorithm.3 are applied to the tidal analysis and prediction based on the unsupervised non negative matrix decomposition method. The tidal signals are separated by the "mixed pixel decomposition" idea, and the observed tidal data are considered as the linear combination of the component elements such as the astronomical tide tide and so on, and the powerful unsupervised hybrid pixels are applied. The decomposition algorithm is used to extract the element data and the corresponding mixing coefficients. This kind of decomposition method is capable of detecting, separating and extracting component data elements from the actual observation data, which can improve the tidal analysis and prediction to the unprecedented level of performance. There is a fundamental difference between the traditional harmonic analysis (.1)) and the observed data as a whole, so it does not need to be pretreated for different types of tides; 2) the decomposition method is unsupervised, and in this sense it does not require a priori knowledge of the source label. In normal weather conditions, the source label will be well adjusted. The seven most important astronomical tides used in the analysis are matched; 3) the most important difference from the traditional harmonic analysis is that the method does not require long-term actual observation data to contribute to the online tidal forecast.
【学位授予单位】：上海海洋大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P731;O151.21

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