大型船舶横摇运动姿态预报技术研究
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摘要
船舶在波浪中六自由度运动的时域预报问题是一项为国际航运界、船舶工程界，尤其是各国海军所关注而至今未能很好解决的课题。目前，在解决船舶运动预报问题时常常采用时间序列分析、灰色系统理论和神经网络等方法，这些方法的最大优点是无需知道海浪的任何先验信息和船舶航行姿态的状态方程，仅仅通过在船舶运动的历史数据中寻求规律，进而进行预报。然而这些数据通常表现出多变量动态演化行为和多层次结构等特点，若想得出十分确切的预报模型比较困难，但是运动序列具有一定的规律性，如某时期的发展变化与以前某时期的发展有着相似或相同的规律等。因此，为进一步提高船舶横向运动预报的有效预报时长及实时性，本文借鉴基于数据驱动的预报思想，从两个方面分别分析了横摇运动姿态时间序列的内在特征及演化特征，同时针对性的结合神经网络方法和支持向量机方法设计了几种预报模型。具体内容包括以下几方面：
首先，针对传统单一的预报方法难以在信息贫乏和不确定条件下做出准确预报的问题，设计了基于经验模式分解的船舶运动姿态混合智能预报模型。对横摇运动姿态时间序列本身的特征进行深入的分析和研究，采用经验模式分解方法把不同的特征信息分解开来；采用游程法将若干个基本模式分量和一个余项重构为高、中、低频三个分量，使得预报对象数目固定；针对每个分量建立不同的信息熵加权Elman神经网络预报模型；采用GRNN神经网络对各个预报分量的结果进行加权求和，并输出最终的预报结果。
其次，由于船舶运动姿态的不确定性与混沌特性是紧密相连的，针对船舶运动姿态的非线性、不确定性。对四种不同海情下的横摇运动姿态时间序列的混沌特性问题进行了具体的分析。在横摇时间序列的相空间重构方面，讨论了延迟时间与嵌入维数的选取方法，采用互信息函数法和假近邻法分别计算了各横摇序列的最佳嵌入维数和时间延迟。在混沌特征分析方面，绘制了船舶横摇时间序列的三维相图，并分析了随机序列、Lorenz映射及横摇时序这三种三维相图的各自特点及区别；同时采用饱和关联维数法和小数据量法对船舶横摇时间序列的关联维数、Kolmogorov熵以及最大Lyapunov指数进行计算，从定性和定量两方面来证明横摇运动姿态具有一定的混沌动力学特性。
接着，针对横摇运动姿态的混沌特性，通过相空间重构来近似恢复原来的多维非线性混沌系统，并结合适用于非线性、小样本、不确定性问题的支持向量机回归方法，建立基于改进支持向量机的混沌智能预报方法，利用吸引子在不同层次间的自相似结构进行预报。在支持向量机回归方法方面，主要研究内容包括：鉴于常用的核函数在理论上不可能逼近平方可积空间上任意曲线的问题，构造满足Mercer条件的Marr小波核函数；调整最优化问题的置信范围，建立参数b与最优化问题的对偶问题最优解之间的关系，获得变异支持向量机，其对偶问题少了一个约束条件，具有更加简洁的形式；设计鲁棒损失函数，建立了满足基于间隔的结构风险最小化原则的分段式支持向量机问题，使算法具有更强的鲁棒性；用单松弛变量代替两个松弛变量来控制误差的大小，设计了改进支持向量机，即单松弛变量鲁棒小波ν支持向量机，减少了对偶问题的优化范围，提高了运算速度；根据基于几何间隔的结构风险最小化原则，对改进支持向量机的若干结论进行了证明。在参数组合优化方面，针对标准粒子群算法局部搜索能力差及早熟收敛等问题，提出了多种群协调进化自适应混沌粒子群算法，通过混沌初始化种群策略和多个子种群相互协调策略的设计，达到了自适应调节各自惯性权重和学习因子从而进行种群进化的效果。
最后，研究了船舶运动时间序列的在线预报方法。针对采用离线训练方式的预报模型在训练时并没有考虑样本的动态特性导致长时间的预报精度下降很快这一问题，研究了支持向量机的在线式学习算法，提出了混沌在线最小二乘支持向量机在线预报模型。此模型使得历史数据的训练结果得到充分利用，完成了在线更新样本集和回归函数，在线预报。针对超参数不能随着样本的变化而进行自动调节的问题，提出了最小二乘支持向量机在线建模策略。采用启发式规则在三个最小二乘支持向量机的交替工作过程中自动更新支持向量机超参数，由此设计了变参数最小二乘支持向量机在线预报方法。预报模型采用变化的参数替代固定的参数，更加确切的解释了存在于样本中的可变性。这种建模方法可在过程的不同变化时段调整预报模型的表达式，具有一定的自适应调节能力。
本文的研究成果具有重要的理论研究意义和潜在的应用前景，其研究成果可推广到船舶纵摇、艏摇运动预报及其它领域的时间序列预报研究中去。
It is a concerned problem that real-time forecast of six degree of freedom for shipmotion in wave by international shipping industry and ship engineering, especially eachcountry navy. At present, time series analysis, gray system theory and neural network areusually used for forecast of ship motion, the largest advantage of which is that the law isjust sought by history data of ship motion for prediction, without knowing any priorinformation and state equation of ship navigation attitude. However, it is difficult toestablish an exact forecast model, because these data typically exhibit multi-variabledynamic evolution behavior and multi-level structure characteristics and so on. But motionseries have some laws, such as development of the period has similar or identical law to thatof the previous period. Therefore, in order to improve real-time and effective length of timeof forecast, intrinsic characteristics and evolution characteristics of ship rolling motion timeseries are analyzed from two aspects based on forecast thought of data-driven,respectively.Meantime, some kinds of forecast models are targeted designed by combiningneural network and support vector machine, which specifically includes the followingaspects:
Firstly, in order to solve accurate forecast problem under poor information anduncertain conditions for traditional single prediction methods, a hybrid intelligent forecastmodel of ship motion is designed based on empirical mode decomposition. Thecharacteristics of ship rolling motion series is studied and analyzed using empirical modedecomposition method to decompose feature information. Several basic mode componentsand a remainder are reconstructed into high, middle and low frequency three componentsusing run-length method, which makes the number of forecast objects fixed. Andinformation entropy weighted Elman neural network forecast model is established for eachcomponent. The result of each component conducts weighted addition by GRNN neuralnetwork, and then forecast result is obtained.
Secondly, uncertain and chaos characteristics of ship motion attitude are closely linked.Considering nonlinear and uncertainty of ship motion, chaos characteristics of ship rollingtime series is specifically analyzed under four different sea conditions. The selectionmethod of delay time and embedded dimension is discussed about phase spacereconstruction of ship rolling time series, and mutual information function method and false nearest neighbor method are used to calculate the best delay time and embedded dimension.Three dimension phase diagram of ship rolling time series is drawn about chaoticcharacteristics analysis, and characteristics and differences of three dimension phasediagram for random sequence, Lorenz mapping and roll time series are also analyzed,respectively. Meantime, saturation correlation dimension method and small datum methodare used to calculate correlation dimension, Kolmogorov entropy and the largest Lyapunovexponent. Ship rolling motion is proved to possess some chaotic dynamic characteristicsfrom two aspects of qualitative and quantitative.
Then, phase space reconstruction is used to approximately recover the originalmulti-dimensional nonlinear chaotic systems aiming at chaotic characteristics of rollingmotion, and combines support vector machine, which is adaptive to solve nonlinear, smallsample and uncertainty question, to establish hybrid intelligent forecast method based onimproved support vector machine, which uses self-similar structure of attractor in differentlevels to predict. About support vector machine regression method, the main researchcontent includes: Marr wavelet nuclear function is constructed to satisfy Mercer conditionfor the problem, which common kernel function can not approach any curve on squareintegrable space in theory. Variant support vector machine is obtained by adjustingconfidence range of optimization problems and establishing relationship between parameterband optimal solution of the dual problem for optimization problem, dual problem ofwhich reduce a constraint and has more concise form. Segmented support vector machine isestablished to meet the interval-based structure risk minimization principle by designingrobust loss function, which has more robust. Improved support vector machine is designedby replace two slack variables with single slack variable to adjust error, namely single slackvariable robust waveletν support vector machine, which reduces optimization range ofdual problem and improves computing speed. A number of conclusions are proved forimprove support vector machine in terms of geometric interval-based structure riskminimization principle. About optimization of parameter combinations, multi-groupcoordination evolution adaptive chaotic particle swarm algorithm is proposed to aim atsolving poor local search ability and premature convergence of the standard particle swarmalgorithm, which can adaptively adjust itself inertia weight and learning factors to completepopulation evolutionary by chaotic initialization population strategy and multiplesubpopulations coordinated strategy.
At last, real-time online forecast method of ship motion time series is studied. Chaos online least squares support vector machine real-time forecast model is proposed to dealwith the problem, which forecast model obtained by training offline without consideringdynamic characteristics of data may result in sharply decline of forecast accuracy as timegoes. The model can make training result of history data obtain good use, and completeonline update sample set, regression function and real-time prediction. Least squaressupport vector machine online modeling strategy is proposed to solve the problem, whichhyper-parameter can not automatically adjust with the change of samples. Varyingparameters least squares support vector machine online forecast method is designed byheuristic rules, which hyper-parameter of support vector machine can automatically adjustby three least squares support vector machine alternating work process. Fixed parameter offorecast model is replaced by varying parameter, which more exactly explain the variabilitypresented in the sample. The method can adjust expression of forecast model in differentvariation periods of the process, which has some adaptive adjustment capability.
The results of the research have important theoretical significance and potentialapplications, some of which can be applied to time series forecast research of other areas.
首先，针对传统单一的预报方法难以在信息贫乏和不确定条件下做出准确预报的问题，设计了基于经验模式分解的船舶运动姿态混合智能预报模型。对横摇运动姿态时间序列本身的特征进行深入的分析和研究，采用经验模式分解方法把不同的特征信息分解开来；采用游程法将若干个基本模式分量和一个余项重构为高、中、低频三个分量，使得预报对象数目固定；针对每个分量建立不同的信息熵加权Elman神经网络预报模型；采用GRNN神经网络对各个预报分量的结果进行加权求和，并输出最终的预报结果。
其次，由于船舶运动姿态的不确定性与混沌特性是紧密相连的，针对船舶运动姿态的非线性、不确定性。对四种不同海情下的横摇运动姿态时间序列的混沌特性问题进行了具体的分析。在横摇时间序列的相空间重构方面，讨论了延迟时间与嵌入维数的选取方法，采用互信息函数法和假近邻法分别计算了各横摇序列的最佳嵌入维数和时间延迟。在混沌特征分析方面，绘制了船舶横摇时间序列的三维相图，并分析了随机序列、Lorenz映射及横摇时序这三种三维相图的各自特点及区别；同时采用饱和关联维数法和小数据量法对船舶横摇时间序列的关联维数、Kolmogorov熵以及最大Lyapunov指数进行计算，从定性和定量两方面来证明横摇运动姿态具有一定的混沌动力学特性。
接着，针对横摇运动姿态的混沌特性，通过相空间重构来近似恢复原来的多维非线性混沌系统，并结合适用于非线性、小样本、不确定性问题的支持向量机回归方法，建立基于改进支持向量机的混沌智能预报方法，利用吸引子在不同层次间的自相似结构进行预报。在支持向量机回归方法方面，主要研究内容包括：鉴于常用的核函数在理论上不可能逼近平方可积空间上任意曲线的问题，构造满足Mercer条件的Marr小波核函数；调整最优化问题的置信范围，建立参数b与最优化问题的对偶问题最优解之间的关系，获得变异支持向量机，其对偶问题少了一个约束条件，具有更加简洁的形式；设计鲁棒损失函数，建立了满足基于间隔的结构风险最小化原则的分段式支持向量机问题，使算法具有更强的鲁棒性；用单松弛变量代替两个松弛变量来控制误差的大小，设计了改进支持向量机，即单松弛变量鲁棒小波ν支持向量机，减少了对偶问题的优化范围，提高了运算速度；根据基于几何间隔的结构风险最小化原则，对改进支持向量机的若干结论进行了证明。在参数组合优化方面，针对标准粒子群算法局部搜索能力差及早熟收敛等问题，提出了多种群协调进化自适应混沌粒子群算法，通过混沌初始化种群策略和多个子种群相互协调策略的设计，达到了自适应调节各自惯性权重和学习因子从而进行种群进化的效果。
最后，研究了船舶运动时间序列的在线预报方法。针对采用离线训练方式的预报模型在训练时并没有考虑样本的动态特性导致长时间的预报精度下降很快这一问题，研究了支持向量机的在线式学习算法，提出了混沌在线最小二乘支持向量机在线预报模型。此模型使得历史数据的训练结果得到充分利用，完成了在线更新样本集和回归函数，在线预报。针对超参数不能随着样本的变化而进行自动调节的问题，提出了最小二乘支持向量机在线建模策略。采用启发式规则在三个最小二乘支持向量机的交替工作过程中自动更新支持向量机超参数，由此设计了变参数最小二乘支持向量机在线预报方法。预报模型采用变化的参数替代固定的参数，更加确切的解释了存在于样本中的可变性。这种建模方法可在过程的不同变化时段调整预报模型的表达式，具有一定的自适应调节能力。
本文的研究成果具有重要的理论研究意义和潜在的应用前景，其研究成果可推广到船舶纵摇、艏摇运动预报及其它领域的时间序列预报研究中去。
It is a concerned problem that real-time forecast of six degree of freedom for shipmotion in wave by international shipping industry and ship engineering, especially eachcountry navy. At present, time series analysis, gray system theory and neural network areusually used for forecast of ship motion, the largest advantage of which is that the law isjust sought by history data of ship motion for prediction, without knowing any priorinformation and state equation of ship navigation attitude. However, it is difficult toestablish an exact forecast model, because these data typically exhibit multi-variabledynamic evolution behavior and multi-level structure characteristics and so on. But motionseries have some laws, such as development of the period has similar or identical law to thatof the previous period. Therefore, in order to improve real-time and effective length of timeof forecast, intrinsic characteristics and evolution characteristics of ship rolling motion timeseries are analyzed from two aspects based on forecast thought of data-driven,respectively.Meantime, some kinds of forecast models are targeted designed by combiningneural network and support vector machine, which specifically includes the followingaspects:
Firstly, in order to solve accurate forecast problem under poor information anduncertain conditions for traditional single prediction methods, a hybrid intelligent forecastmodel of ship motion is designed based on empirical mode decomposition. Thecharacteristics of ship rolling motion series is studied and analyzed using empirical modedecomposition method to decompose feature information. Several basic mode componentsand a remainder are reconstructed into high, middle and low frequency three componentsusing run-length method, which makes the number of forecast objects fixed. Andinformation entropy weighted Elman neural network forecast model is established for eachcomponent. The result of each component conducts weighted addition by GRNN neuralnetwork, and then forecast result is obtained.
Secondly, uncertain and chaos characteristics of ship motion attitude are closely linked.Considering nonlinear and uncertainty of ship motion, chaos characteristics of ship rollingtime series is specifically analyzed under four different sea conditions. The selectionmethod of delay time and embedded dimension is discussed about phase spacereconstruction of ship rolling time series, and mutual information function method and false nearest neighbor method are used to calculate the best delay time and embedded dimension.Three dimension phase diagram of ship rolling time series is drawn about chaoticcharacteristics analysis, and characteristics and differences of three dimension phasediagram for random sequence, Lorenz mapping and roll time series are also analyzed,respectively. Meantime, saturation correlation dimension method and small datum methodare used to calculate correlation dimension, Kolmogorov entropy and the largest Lyapunovexponent. Ship rolling motion is proved to possess some chaotic dynamic characteristicsfrom two aspects of qualitative and quantitative.
Then, phase space reconstruction is used to approximately recover the originalmulti-dimensional nonlinear chaotic systems aiming at chaotic characteristics of rollingmotion, and combines support vector machine, which is adaptive to solve nonlinear, smallsample and uncertainty question, to establish hybrid intelligent forecast method based onimproved support vector machine, which uses self-similar structure of attractor in differentlevels to predict. About support vector machine regression method, the main researchcontent includes: Marr wavelet nuclear function is constructed to satisfy Mercer conditionfor the problem, which common kernel function can not approach any curve on squareintegrable space in theory. Variant support vector machine is obtained by adjustingconfidence range of optimization problems and establishing relationship between parameterband optimal solution of the dual problem for optimization problem, dual problem ofwhich reduce a constraint and has more concise form. Segmented support vector machine isestablished to meet the interval-based structure risk minimization principle by designingrobust loss function, which has more robust. Improved support vector machine is designedby replace two slack variables with single slack variable to adjust error, namely single slackvariable robust waveletν support vector machine, which reduces optimization range ofdual problem and improves computing speed. A number of conclusions are proved forimprove support vector machine in terms of geometric interval-based structure riskminimization principle. About optimization of parameter combinations, multi-groupcoordination evolution adaptive chaotic particle swarm algorithm is proposed to aim atsolving poor local search ability and premature convergence of the standard particle swarmalgorithm, which can adaptively adjust itself inertia weight and learning factors to completepopulation evolutionary by chaotic initialization population strategy and multiplesubpopulations coordinated strategy.
At last, real-time online forecast method of ship motion time series is studied. Chaos online least squares support vector machine real-time forecast model is proposed to dealwith the problem, which forecast model obtained by training offline without consideringdynamic characteristics of data may result in sharply decline of forecast accuracy as timegoes. The model can make training result of history data obtain good use, and completeonline update sample set, regression function and real-time prediction. Least squaressupport vector machine online modeling strategy is proposed to solve the problem, whichhyper-parameter can not automatically adjust with the change of samples. Varyingparameters least squares support vector machine online forecast method is designed byheuristic rules, which hyper-parameter of support vector machine can automatically adjustby three least squares support vector machine alternating work process. Fixed parameter offorecast model is replaced by varying parameter, which more exactly explain the variabilitypresented in the sample. The method can adjust expression of forecast model in differentvariation periods of the process, which has some adaptive adjustment capability.
The results of the research have important theoretical significance and potentialapplications, some of which can be applied to time series forecast research of other areas.
引文
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