基于组合预测方法的舰船纵摇运动预报
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摘要
舰船的运动由于受到海浪、海风及其它因素的影响,产生了六自由度的复杂运动,具有很强的随机性和非线性,因此舰船极短期预报对于舰船航行有着重要的意义。舰船运动极短期预报就是根据舰船的运动历史数据对船体运动进行几秒或十几秒的预测。以往曾有时间序列法、周期图法、神经网络法、灰色系统理论等方法进行舰船的预报。本论文立足于舰船的纵摇运动预报,研究了组合预测方法在纵摇运动预报中的应用。组合预测方法需要利用各单项预测模型的有效信息,基于此本文研究了几种单项预测方法在纵摇运动预报中的应用。并针对实际的舰船运动数据进行了数值仿真。对船的纵摇的理论研究可帮助认识船的纵摇的规律,从而掌握和利用它为舰船航行服务。主要完成的工作有：
首先,介绍了灰色系统建模的数据生成方式及建模的理论基础,考虑到灰色拓扑预测方法的趋势预测的特性,结合新陈代谢GM(1,1)模型,对纵摇运动角度建立了拓扑预测模型,根据不同的阈值,建立所对应的时间序列的新陈代谢GM(1,1)模型群。用此模型群对未来可能的运动趋势进行预测,并运用预测的有效点绘制拓扑预测曲线。
其次,在纵摇运动预报过程中,突变点的出现影响到建模及预报的精度,对突变点及附近的数据处理是必要的。第三章将小波变换奇异点检测理论应用到舰船纵摇角度处理中,通过对模极大值的检测来确定突变点发生的时刻,并在第四章介绍了数据处理的方法,最后用处理后的数据建立推广GM(1,1)模型,提高了预报精度。
再次,灰色系统传统的GM(1,1)模型白化方程反映出生成数据仅与本身及其变化有关,而实际上很多时候生成数据还要受到其它因素的影响,这些因素不能完全由灰作用量表示。针对这个问题,本文先给出服从非纯指数函数变化的推广GM(1,1)模型,同时考虑初始点拟合误差的影响,改变初始值,从而构建了优化的时间响应函数,提高了模拟精度。最后针对船的纵摇角度数据的灰色特征应用这种模型进行建模,数值试验表明这种方法是可行的。
最后,以预测值的对数的相关系数为误差标准,提出了基于相关系数的加权几何平均组合预测模型,加权几何平均组合预测为一种非线性的组合预测方法。针对基于相关系数的加权几何平均组合预测模型,定义了优性组合预测模型、预测方法优超、组合预测冗余度等概念,讨论了在一定的条件下,该组合预测存在非劣性及优性组合预测的充分条件,得出了一个判断冗余预测方法的判定定理。从理论上说明基于对数相关系数的非线性组合预测模型的有效性,同时本文用推广GM(1,1)模型及支持向量机回归模型作为单项预测模型,对纵摇角度应用该组合预测模型进行预报,验证了该模型的有效性。
The movement of ship is affected by the influence of ocean waves, wind and other interactions, ships can have complex movements of six free degrees, which have the randomness and the non-linearity. So the prediction of ship motion has an important significance for the ship sailing. Extremely short time prediction of ship motion is on the basis of historical data to predict the ship motion in the future shorter time with some theory and technology. Previously time series method, periodogram, neural network method, the grey system theory and other methods of prediction of ship are applied. This paper aimed at prediction of ship pitch, combination forecasting method is studied on prediction of ship pitch. Combination prediction methods made use of effective information of the individual model prediction, based on this aspect, In this paper, several methods of individual forecasting in the prediction of ship pitch are researched. it was done aiming at some actual ship pitch angle that the prediction and simulation of ship motion. The ship pitching theoretical research can help us to understand the law of ship pitching so as to use it as ship navigation services. The research was done mainly in this paper:
The basic theory of grey system modeling and data generation methods were introduced, taking into account the characteristics of trend prediction of the grey topological prediction method, combination of metabolic GM(1,1) model, a topology prediction model are set up on the ship pitch angle. According to different thresholds, setting up the metabolic GM(1,1) model group by the corresponding time series. Using effective forecasting points to draw topology prediction curve, this model can predict the possible future trends for ship pitch motion.
In the process of ship pitching prediction, the emergence of point mutations affects the accuracy of modeling and forecasting, singularity detection theory of wavelet transform was applied to deal with the singularity of ship pitching angle, through modulus maxima determining the occurrence time of mutation point; a singular point of data processing methods was introduced, finally non-homogeneous GM (1,1) model was set up with the data, the model improves the forecast accuracy.
The whitening equation of the traditional grey system GM (1,1) model reflects only generating data relate with themselves and their changes, in fact generating data are affected by other factors, these factors can't fully expressed by grey number. According to this issue, This article first give the analytic formula of the improved GM(1,1) grey differential equation model which obey non-pure exponential growth law, so time series response type was given; At the same time taking into account the impact of the fitting error of the initial point of the grey sequence, the initial value was changed, thus the optimized time response function was constructed, the model improves the simulation accuracy. Finally the model was applied to model for the data of ship pitching angle, numerical experiments show that this method is feasible.
Take the correlation coefficient of the logarithm of forecasting value for the error standard, Weighted geometric means combination forecasting based on correlation coefficients was put forward, weighted geometric means combination forecasting is a kind of nonlinear combination prediction method. Weighted geometric means combination forecasting is a kind of nonlinear combination forecasting model. Based on correlation coefficients, a weighted geometric means combination forecasting model is proposed. Superior combination forecasting, dominant forecasting method and redundant degree are put forward. Under certain conditions the sufficient condition of existence of non-inferior combination and superior combination forecasting are discussed, redundant information is pointed out in a judging theorem. It shows that this nonlinear model is effective theoretically, at the same time, this paper verifies the validity of the model with ship pitch angle prediction through computer simulation test.
首先,介绍了灰色系统建模的数据生成方式及建模的理论基础,考虑到灰色拓扑预测方法的趋势预测的特性,结合新陈代谢GM(1,1)模型,对纵摇运动角度建立了拓扑预测模型,根据不同的阈值,建立所对应的时间序列的新陈代谢GM(1,1)模型群。用此模型群对未来可能的运动趋势进行预测,并运用预测的有效点绘制拓扑预测曲线。
其次,在纵摇运动预报过程中,突变点的出现影响到建模及预报的精度,对突变点及附近的数据处理是必要的。第三章将小波变换奇异点检测理论应用到舰船纵摇角度处理中,通过对模极大值的检测来确定突变点发生的时刻,并在第四章介绍了数据处理的方法,最后用处理后的数据建立推广GM(1,1)模型,提高了预报精度。
再次,灰色系统传统的GM(1,1)模型白化方程反映出生成数据仅与本身及其变化有关,而实际上很多时候生成数据还要受到其它因素的影响,这些因素不能完全由灰作用量表示。针对这个问题,本文先给出服从非纯指数函数变化的推广GM(1,1)模型,同时考虑初始点拟合误差的影响,改变初始值,从而构建了优化的时间响应函数,提高了模拟精度。最后针对船的纵摇角度数据的灰色特征应用这种模型进行建模,数值试验表明这种方法是可行的。
最后,以预测值的对数的相关系数为误差标准,提出了基于相关系数的加权几何平均组合预测模型,加权几何平均组合预测为一种非线性的组合预测方法。针对基于相关系数的加权几何平均组合预测模型,定义了优性组合预测模型、预测方法优超、组合预测冗余度等概念,讨论了在一定的条件下,该组合预测存在非劣性及优性组合预测的充分条件,得出了一个判断冗余预测方法的判定定理。从理论上说明基于对数相关系数的非线性组合预测模型的有效性,同时本文用推广GM(1,1)模型及支持向量机回归模型作为单项预测模型,对纵摇角度应用该组合预测模型进行预报,验证了该模型的有效性。
The movement of ship is affected by the influence of ocean waves, wind and other interactions, ships can have complex movements of six free degrees, which have the randomness and the non-linearity. So the prediction of ship motion has an important significance for the ship sailing. Extremely short time prediction of ship motion is on the basis of historical data to predict the ship motion in the future shorter time with some theory and technology. Previously time series method, periodogram, neural network method, the grey system theory and other methods of prediction of ship are applied. This paper aimed at prediction of ship pitch, combination forecasting method is studied on prediction of ship pitch. Combination prediction methods made use of effective information of the individual model prediction, based on this aspect, In this paper, several methods of individual forecasting in the prediction of ship pitch are researched. it was done aiming at some actual ship pitch angle that the prediction and simulation of ship motion. The ship pitching theoretical research can help us to understand the law of ship pitching so as to use it as ship navigation services. The research was done mainly in this paper:
The basic theory of grey system modeling and data generation methods were introduced, taking into account the characteristics of trend prediction of the grey topological prediction method, combination of metabolic GM(1,1) model, a topology prediction model are set up on the ship pitch angle. According to different thresholds, setting up the metabolic GM(1,1) model group by the corresponding time series. Using effective forecasting points to draw topology prediction curve, this model can predict the possible future trends for ship pitch motion.
In the process of ship pitching prediction, the emergence of point mutations affects the accuracy of modeling and forecasting, singularity detection theory of wavelet transform was applied to deal with the singularity of ship pitching angle, through modulus maxima determining the occurrence time of mutation point; a singular point of data processing methods was introduced, finally non-homogeneous GM (1,1) model was set up with the data, the model improves the forecast accuracy.
The whitening equation of the traditional grey system GM (1,1) model reflects only generating data relate with themselves and their changes, in fact generating data are affected by other factors, these factors can't fully expressed by grey number. According to this issue, This article first give the analytic formula of the improved GM(1,1) grey differential equation model which obey non-pure exponential growth law, so time series response type was given; At the same time taking into account the impact of the fitting error of the initial point of the grey sequence, the initial value was changed, thus the optimized time response function was constructed, the model improves the simulation accuracy. Finally the model was applied to model for the data of ship pitching angle, numerical experiments show that this method is feasible.
Take the correlation coefficient of the logarithm of forecasting value for the error standard, Weighted geometric means combination forecasting based on correlation coefficients was put forward, weighted geometric means combination forecasting is a kind of nonlinear combination prediction method. Weighted geometric means combination forecasting is a kind of nonlinear combination forecasting model. Based on correlation coefficients, a weighted geometric means combination forecasting model is proposed. Superior combination forecasting, dominant forecasting method and redundant degree are put forward. Under certain conditions the sufficient condition of existence of non-inferior combination and superior combination forecasting are discussed, redundant information is pointed out in a judging theorem. It shows that this nonlinear model is effective theoretically, at the same time, this paper verifies the validity of the model with ship pitch angle prediction through computer simulation test.
引文
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