Application Of Multifractal Analysis In Marine Wave Height Data Analysis

The change of the marine environment is very complex, marine engineering must be able to withstand the impact of the typhoon, waves, currents, tides and other strongly natural factors, the external force analysis and design of the coastwise building must take into account the random nature of the various dynamic factors. To fully explore the oceanographic changing characteristics of the phenomenon in time and space, we must take a large number of observations, but due to the limited observations, we can only grasp the general statistical characteristics of the design elements of the marine environment at a certain scale. The problem is, how to infer and discover another larger scale hydrological statistical characteristic from a certain scale. The statistical self-similarity of the fluctuation of sea waves provides a research topic for fractal theory. The focus study of this paper is to analyze and explore the statistical characteristic of marine wave height data from the perspective of multifractal.In this paper, the multi-fractal analysis is applied into the analysis of the ocean wave heights sequence observed from marine hydrological station, such analysis is meaningful. The traditional method of calculating significant wave heights that occur once in many years was to choose a probability distribution model as the probability distribution for annual extremes of wave heights. Observed annual extreme wave heights were used to determine the parameters of the probability distribution, after which a cumulative rate determined the wave height that only occurs once in many years. Such a method has some shortcomings and areas for improvement. In fact, the long-term evolution of wave heights at an observation point is very complex system, and only by conducting multifractal analysis to reveal the relationship between the short-term observational wave height sequence (parts) and the long-term observational wave height sequence (overall) can the latter be inferred by the former, thus providing a good empirical support for more reasonable estimations of wave heights that only occur once in many years.Currently, two main multiple analysis methods have been proposed:the partition function method and the multifractal detrended fluctuation analysis (MF-DFA) method. Detrending the fluctuation is an important part of MF-DFA method, but this step of the calculation has following shortcomings:First, the fitting polynomial is not continuous at the adjacent interval connection point, which will produce a new pseudo fluctuation error; Second, the selection of the fitting polynomial order is highly subjective, the lower-order cannot reflect the fluctuation trend well, while the higher-order will produce over-fitting problem.In this paper, signal mode decomposition method is used to identify the fluctuation function, which is an improvement to address the existing problems of the MF-DFA method, the fractal theory is introduced to analyze the fluctuation characteristics of the sea wave, the multifractal methods of partition function, MF-DFA and its improvement is applied into the analysis of tidal wave height data recorded along the coast of Chaolian Island, the results show that:Fluctuations in tidal waves have weak multifractal characteristics; the improved MF-DFA method can not only better meet the requirements of the original method based on the elimination of the trend, but also avoid the shortcomings of the original one, has certain advantages.