Volterra级数建模预报方法研究及在船舶运动预报中应用
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摘要
在实际工程应用中存在着大量的非线性系统,因此研究非线性系统的建模预报方法具有十分重要的意义。非线性系统的Volterra级数核是系统的本质特征,在基于混沌时间序列的非线性函数变换的自适应滤波预报方法中,Volterra级数能够描述具有响应和记忆功能的非线性行为,已经得到了广泛的应用。所以,本文重点研究Volterra级数核的辨识方法,并将其应用于构建船舶运动混沌时间序列的非线性预测模型,从而实现船舶运动预报。主要研究内容如下：
1.根据时间序列混沌特征分析和混沌时间序列的相空间重构理论,对船舶运动序列的混沌特性进行分析研究,证明了船舶横摇运动时间序列具有混沌特性。同时系统分析研究了Volterra级数自适应预报模型,为混沌时间序列的船舶运动预报研究奠定了理论基础。
2.深入分析了LMS算法的理论和LMS的相关算法,对LMS相关算法辨识Volterra级数核的估计算法进行了深入研究,提出NLMS和VSS-LMS辨识Volterra级数核的估计算法,通过对船舶运动的多步预报,表明VSS-LMS比NLMS的预报精度相对较高,验证了方法的实用性和良好效果。
3.系统介绍了ANN的模型以及BP神经网络模型,分析研究了Volterra级数和BP神经网络模型的原理关系,提出利用单输出三层BP神经网络辨识Volterra级数核的估计算法,实现了对船舶运动的多步预报,证明该方法在预报精度上优于LMS相关算法辨识Volterra级数核的估计算法。
4.将GA全局搜索最优和BP神经网络模型局部寻优结合起来,解决BP神经网络在训练过程中陷入局部极小值的问题,提出GA优化BP神经网络的初始权值和阈值进行单输出三层BP神经网络辨识Volterra级数核的估计算法,GA优化BP神经网络获得最优的初始权值和阈值,在此基础上进行Taylor级数分解,从而得到Volterra级数各阶核,实现对船舶运动多步预报。
5.在Kalman辨识Volterra级数核的船舶运动预报方法部分,分析了Kalman滤波原理及状态估计,在此基础上重点研究了Kalman辨识Volterra级数核的估计算法,提出Kalman辨识Volterra级数核的船舶运动预报方法,实现对船舶运动的多步预报。
本文提出的自适应算法辨识Volterra级数核的方法,通过对船舶运动预报的建模仿真,在理论验证了它们是可行的和有效的,为实时在线预报提供了理论依据。
Research on model forecast method of nonlinear system is vitally significant, because there are plenty of nonlinear systems in the application of practical engineering. Volterra series nucleus is the essential characteristics of nonlinear system. Based on chaotic time series in the adaptive filter forecast method of nonlinear functional transform, Volterra series can describe nonlinear behavior that possesses the function of response and memory, which has been widely used. Therefore, this paper focuses on the identification method of Volterra series nucleus and applying it into the nonlinear prediction model constructing ship motion chaos time series so as to realize the prediction of ship motion. The main research contents are as follows:
First of all, According to the time sequence analysis of characteristics of chaos as well as chaotic time series of phase space reconstruction theory, the paper analyzes the chaotic characteristic of ship motion sequence and proves that the ship roll motion time series have chaos characteristics. Meanwhile, it also systematically analyzes and researches the Volterra series adaptive prediction models laying a theoretical basis on the chaos time series prediction of the ship motion research.
Secondly, the paper deeps in the analysis of the LMS (Least Mean Square, LMS) algorithm theory and the related LMS algorithm, studies the LMS algorithm to identify the Volterra series nucleus estimation algorithm profoundly, and puts forward NLMS (Normalization Least Mean Square, NLMS) and VSS-LMS (Variable Step Size Least Mean Square, VSS-LMS) to identify the Volterra series of nucleus estimate algorithm. Based on the forecast of ship motion, the paper shows that the forecast accuracy of VSS-LMS is higher than NLMS, and validates the practicability and good effects of this method.
Thirdly, The system introduces ANN model and the BP neural network model, and studies principle relationship between Volterra series and the BP neural network model. This paper proposes to apply a single output of three layers of BP neural network to identify the estimation algorithm of Volterra series nucleus in order to realize the multistep forecast of ship movements, and proves that the forecast accuracy of this method excels the estimation of the related algorithm of LMS to identify Volterra series nucleus.
Fourthly, through combining GA whole-searching optimization and the BP neural network local-searching optimization, the paper solves the problem of BP neural network in the training process into the local minimum value, and puts forward the threshold value and single figure of GA optimizing BP weights of the neural network to output three layers of BP neural network to identify Volterra series nucleus estimation algorithm. The GA optimizing BP neural network gains the best weights of the threshold value and single figure, based on Taylor progression to decompose to obtain Volterra series nucleus in all levels, and realizes the multi-step ship motions prediction.
Finally, with the part of forecast method of ship motions of Kalman Volterra series nucleus identification, the paper analyzes the Kalman filter principle and state estimation, then it focuses on the study of the Kalman identifying the estimation algorithm of Volterra series nucleus, lodges ship motion forecast method of the Kalman identifying Volterra series nucleus, and realizes multi-step ship motion prediction.
This paper raises the adaptive algorithm to identify Volterra series nucleus, through the modeling simulation of ship motion prediction, theoretically proves the feasibility and validity of methods, and provides the theory basis of real-time online prediction.
1.根据时间序列混沌特征分析和混沌时间序列的相空间重构理论,对船舶运动序列的混沌特性进行分析研究,证明了船舶横摇运动时间序列具有混沌特性。同时系统分析研究了Volterra级数自适应预报模型,为混沌时间序列的船舶运动预报研究奠定了理论基础。
2.深入分析了LMS算法的理论和LMS的相关算法,对LMS相关算法辨识Volterra级数核的估计算法进行了深入研究,提出NLMS和VSS-LMS辨识Volterra级数核的估计算法,通过对船舶运动的多步预报,表明VSS-LMS比NLMS的预报精度相对较高,验证了方法的实用性和良好效果。
3.系统介绍了ANN的模型以及BP神经网络模型,分析研究了Volterra级数和BP神经网络模型的原理关系,提出利用单输出三层BP神经网络辨识Volterra级数核的估计算法,实现了对船舶运动的多步预报,证明该方法在预报精度上优于LMS相关算法辨识Volterra级数核的估计算法。
4.将GA全局搜索最优和BP神经网络模型局部寻优结合起来,解决BP神经网络在训练过程中陷入局部极小值的问题,提出GA优化BP神经网络的初始权值和阈值进行单输出三层BP神经网络辨识Volterra级数核的估计算法,GA优化BP神经网络获得最优的初始权值和阈值,在此基础上进行Taylor级数分解,从而得到Volterra级数各阶核,实现对船舶运动多步预报。
5.在Kalman辨识Volterra级数核的船舶运动预报方法部分,分析了Kalman滤波原理及状态估计,在此基础上重点研究了Kalman辨识Volterra级数核的估计算法,提出Kalman辨识Volterra级数核的船舶运动预报方法,实现对船舶运动的多步预报。
本文提出的自适应算法辨识Volterra级数核的方法,通过对船舶运动预报的建模仿真,在理论验证了它们是可行的和有效的,为实时在线预报提供了理论依据。
Research on model forecast method of nonlinear system is vitally significant, because there are plenty of nonlinear systems in the application of practical engineering. Volterra series nucleus is the essential characteristics of nonlinear system. Based on chaotic time series in the adaptive filter forecast method of nonlinear functional transform, Volterra series can describe nonlinear behavior that possesses the function of response and memory, which has been widely used. Therefore, this paper focuses on the identification method of Volterra series nucleus and applying it into the nonlinear prediction model constructing ship motion chaos time series so as to realize the prediction of ship motion. The main research contents are as follows:
First of all, According to the time sequence analysis of characteristics of chaos as well as chaotic time series of phase space reconstruction theory, the paper analyzes the chaotic characteristic of ship motion sequence and proves that the ship roll motion time series have chaos characteristics. Meanwhile, it also systematically analyzes and researches the Volterra series adaptive prediction models laying a theoretical basis on the chaos time series prediction of the ship motion research.
Secondly, the paper deeps in the analysis of the LMS (Least Mean Square, LMS) algorithm theory and the related LMS algorithm, studies the LMS algorithm to identify the Volterra series nucleus estimation algorithm profoundly, and puts forward NLMS (Normalization Least Mean Square, NLMS) and VSS-LMS (Variable Step Size Least Mean Square, VSS-LMS) to identify the Volterra series of nucleus estimate algorithm. Based on the forecast of ship motion, the paper shows that the forecast accuracy of VSS-LMS is higher than NLMS, and validates the practicability and good effects of this method.
Thirdly, The system introduces ANN model and the BP neural network model, and studies principle relationship between Volterra series and the BP neural network model. This paper proposes to apply a single output of three layers of BP neural network to identify the estimation algorithm of Volterra series nucleus in order to realize the multistep forecast of ship movements, and proves that the forecast accuracy of this method excels the estimation of the related algorithm of LMS to identify Volterra series nucleus.
Fourthly, through combining GA whole-searching optimization and the BP neural network local-searching optimization, the paper solves the problem of BP neural network in the training process into the local minimum value, and puts forward the threshold value and single figure of GA optimizing BP weights of the neural network to output three layers of BP neural network to identify Volterra series nucleus estimation algorithm. The GA optimizing BP neural network gains the best weights of the threshold value and single figure, based on Taylor progression to decompose to obtain Volterra series nucleus in all levels, and realizes the multi-step ship motions prediction.
Finally, with the part of forecast method of ship motions of Kalman Volterra series nucleus identification, the paper analyzes the Kalman filter principle and state estimation, then it focuses on the study of the Kalman identifying the estimation algorithm of Volterra series nucleus, lodges ship motion forecast method of the Kalman identifying Volterra series nucleus, and realizes multi-step ship motion prediction.
This paper raises the adaptive algorithm to identify Volterra series nucleus, through the modeling simulation of ship motion prediction, theoretically proves the feasibility and validity of methods, and provides the theory basis of real-time online prediction.
引文
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