【作者】 李加莲；

【导师】 沈继红；

【作者基本信息】 哈尔滨工程大学 ， 应用数学， 2008， 硕士

【摘要】 海浪研究是海洋学的重要领域之一,它为海上的船舶运输、渔业生产、海上石油开发和军事活动等提供环境资料,保障海上活动的安全。由于海浪具有很多的随机特性和不确定因素,因此海浪的预报是海洋科学中的热点和难点问题,预报的难度和准确度依然是目前要解决的关键课题。本论文基于海浪有效波高的实测历史数据,分别研究了平滑GM(1,1)模型,陡型GM(1,1)模型,移动平均模型,指数平滑模型和ARMA模型,用于海浪预报的适用范围,并通过预报的效果分析给出具体的修正改进。首先,建立平滑型GM(1,1)模型对有效波高进行预测,并结合实例分析,发现该模型在预报海浪有效波高时的适用范围——整体单调且比较平滑的数据。其次,建立陡型GM(1,1)模型对海浪有效波高进行预测,并结合实例分析,发现该模型在预报海浪有效波高时的适用范围——“陡”型数据。再次,把海浪有效波高数据列看成时间序列,建立了海浪有效波高的移动平均预测模型,并结合实例分析,发现了它的不足——移动项数的选取及历史时刻数据取平均。针对其不足进行改进,建立了加权移动平均预测模型,并结合实例分析,发现了它的不足——权系数的选取往往依靠经验。针对其不足进行改进,建立了三次指数平滑预测模型。该模型遵循“重近轻远”的原则,预测结果较好。最后,由于海浪有效波高是非平稳的,故本文先对其进行平稳化处理(差分),然后对处理后的、平稳的数据列建立自回归滑动平均模型(ARMA),并结合实例分析,指出用其预报海浪有效波高的可行性和有效性。更多还原

【Abstract】 The investigation of sea wave is one of the important fields in oceanography. It provides environmental information for sea transportation, fishery, oil development and military activities and so on, furthermore guarantees the safety of maritime activities.For a lot of random characters and undetermined factors, the prediction of sea waves is the hot point and difficult point in oceanography, the difficulty and accuracy of the prediction are still key issues to solve.On the basis of real history data of significant wave height, we researched that the suitable range of the models, GM(1,1), steep GM(1,1), moving average model, cubic exponential smoothing model and ARMA, when used to do prediction for sea wave, and the improvements are applied according to prediction condition analysis.Firstly, grey GM(1,1) model is established to predict the significant wave height. Through the simulation experiment and analysis, the grey GM(1,1) model is suitable for the prediction of significant wave height with monotonous smooth data.Secondly, steep GM(1,1) model is established to predict the significant wave height with the oscillation characters.Thirdly, the paper take the significant wave height data as time series, and establish the prediction models of moving average. For the data with the experimental analysis, it is found that the model is disadvanced for the determination of moving coefficients and the averaging of the data. The paper do some improvement to build right moving average prediction model pointing to the disadvantages of the moving average model with the experimental analysis, it is pointed out that its disadvantage is experienced determination of the right coefficients. Thus, the paper build the cubic exponential smoothing model, which follows the rule of "light weight from the past" and the prediction condition is good.Finally, for unstable character of sea wave, the paper do stabilized processing to the significant wave height data, then establish Auto-Regressive Moving Average model(ARMA) for the processed data, it is pointed out that it is suitable for the prediction of significant wave height, and confirmed that through massive simulation experiments.更多还原