基于Napofics多维泰勒网的非线性时间序列建模及预测研究

发布时间：2017-12-31 02:39

本文关键词：基于Napofics多维泰勒网的非线性时间序列建模及预测研究　出处：《东南大学》2016年博士论文　论文类型：学位论文

【摘要】：时间序列的相邻数据之间存在着内在联系,这种内在联系是时间序列的一个本质特征。时间序列建模及预测就是根据系统的观测值,建立能反映时间序列中所包含的动态关系的数学模型,揭示系统的运动规律,预测其未来的变化发展规律和走势,是预测方法体系中的重要组成部分。通过综合运用系统的输入输出数据,而非机理,建立非线性时间序列的解析模型,特别是建立具有量变到质变现象的系统的解析模型尤为重要。因此,对时间序列建模及预测方法的研究,无论是在揭示系统运动规律或某一现象与其它现象之间的内在关系及运动规律,进一步发展现有理论,提升对系统运动规律探索与认知这样的科学研究层面,还是在重大工程结构和重要基础设施的垮塌等破坏性灾害预报、环境污染监测这样的科学应用层面,都具有重大意义。为此,本文针对非线性时间序列建模和预测问题,特别是针对物质系统由量变到质变而呈现“平稳→剧变→再平稳→再剧变”这一变化规律的时间序列展开对其建模以及预测的研究。首先,针对非线性时间序列,提出一种新型的、可用于时间序列预测的网络模型——多维泰勒网,并结合该模型,提出了一种新型的非线性时间序列预测方法：其次,在多维泰勒网单步预测的基础上,将该多维泰勒网应用于混沌系统的多步预测,建立多步自适应模型,通过数据窗口的滑动自适应建模,实现对具有混沌特性的非线性时间序列的多步预测；再次,针对实际物质系统中,一些系统的状态变化往往存在由量变到质变,由一个稳定阶段过渡到另一个稳定阶段的现象,从而不断呈现出“平稳→剧变→再平稳→再剧变”的演变规律,在本文导师严洪森教授经过多年方法论研究而提出的正负反馈交替论(Alternate positive negative feedbackics,简称Napofic s)的基础上,提出了一种新颖的、对该变化规律进行动态数学描述的正负反馈交替论模型,并结合多维泰勒网模型,提出了基于该正负反馈交替论的非线性时间序列预测方法；最后,结合物质系统由量变到质变而呈现“平稳→剧变→再平稳→再剧变”这一变化规律,将等效正、负反馈作用的判定尺度拓展为多尺度,即以状态变化速度作为第一尺度、状态变化加速度作为第二尺度,根据状态变化剧烈程度以及剧烈变化趋势,将状态稳定性分离,提出了基于多维泰勒网的多尺度正负反馈交替论模型并应用于预报仿真。具体说来,主要在以下几个方面进行了研究：1.针对非线性时间序列,提出了一种新型的、不同于以往常用研究方法的网络模型——多维泰勒网。该网络是一种新型的、在建立系统解析模型方面具有突出优势的新型网络模型。首先详细介绍了该模型的结构和工作原理。证明了多维泰勒网模型构建形式的可行性,并确定了模型中各加权项的具体表达形式。在此基础上,提出了一种新型的基于多维泰勒网的时间序列预测方法。该新型预测方法的特点是仅利用非线性时间序列的观测数据,通过多维泰勒网得到n元一阶多项式差分方程组,在无需待预测系统的任何先验知识和机理的情况下获得动力学特性描述,实现对非线性时间序列的预测。最后通过典型Lorenz混沌时间序列以及某大型建筑的工程监测数据算例验证了方法的有效性和可行性。2.针对在实际系统中广泛存在的混沌现象,提出了一种新的基于多维泰勒网的多步自适应预测方法,对混沌时间序列这一典型非线性时间序列进行多步预测。定义了多维泰勒多项式,并证明了该多项式可以对定义在有界闭集上的多元函数进行逼近。证明了多维泰勒网n阶差分输入形式的正确性。在此基础上提出的自适应多步预测方法不同于一般进行相空间重构的混沌时间序列预测方法,它不以嵌入维数和时间延迟这两个相空间重构方法中的关键参数的选取为前提。无需系统的先验知识和机理,基于具有混沌特性的时间序列数据,建立多维泰勒网模型,通过数据窗口的滑动自适应建模,从而实现对混沌时间序列的多步预测。最后,通过应用实例验证了该基于多维泰勒网的混沌时间序列多步自适应预测方法的可行性和实用性。3.针对实际物质系统中,一些系统的状态变化往往存在由量变到质变,从一个稳定阶段过渡到另一个稳定阶段的现象,从而不断呈现出“平稳→剧变→再平稳→再剧变”的演变规律,引入等效正负反馈的思想,并将该思想与系统状态这一演变过程相结合,提出了一种新颖的、对该变化规律进行动态数学描述的正负反馈交替论模型,以及基于该正负反馈交替论模型的非线性时间序列预测方法。证明了用正负反馈交替论模型描述系统呈现出的“平稳→剧变→再平稳→再剧变”的演变规律的可行性。根据数据的变化剧烈程度,将状态稳定性分离,用叠加多个死区函数反映系统状态不同剧变期由于能量爆发造成的正反馈作用,将系统状态稳定性分离,不从系统内在的机理出发,而是通过系统内在机理的外部表征数据,建立系统的动力学模型,以从动态数学模型的角度描述系统状态由量变到质变而呈现出“平稳→剧变→再平稳→再剧变”的这一变化规律。最后通过算例实例仿真,验证了该正负反馈交替论模型在非线性时间序列建模及预测中的有效性。4.结合物质系统由量变到质变而呈现“平稳→剧变→再平稳→再剧变”这一变化规律,以及多维泰勒网,引入多尺度概念,提出了一种基于多维泰勒网的多尺度正负反馈交替论模型。证明了用多个尺度描述系统的上述演变规律和建立其多尺度模型的正确性。将状态的变化速度和变化加速度分别作为等效正、负反馈的第一和第二界定尺度,根据状态变化剧烈程度以及剧烈变化趋势,将状态稳定性分离。以动力学方程形式表述物质系统的上述变化规律。该模型是一种能够将“平稳→剧变→再平稳→再剧变”这一变化过程中的剧烈变化阶段系统状态变化量和变化趋势以显性函数的形式表达的、基于观测数据的通用模型。最后,将该模型应用于非线性时间序列预测,以具有典型量变积累到质变的实际系统实测数据为基础,进行系统建模及预报的仿真研究。结果表明,该模型能较准确反映系统的变化规律,能有效进行预报、且精度高,为具有此类演变规律的复杂系统建模及预测提供了一种新颖而有效的手段。
[Abstract]:There is a connection between adjacent data time series, this relation is an essential feature of time series. The modeling and forecasting of time series is based on the observation value, establish mathematical model can reflect the dynamic relationship contained in the time series, reveals the movement of the system, forecast its future development law and the trend is an important part of prediction system. Through the input and output data of the integrated use of the system, rather than a mechanism, an analytical model of nonlinear time series, especially to establish a quantitative change to qualitative change phenomenon of the analytical model of system is particularly important. Therefore, the research on time series modeling and forecasting methods, either the intrinsic relationship between the motion rules and reveal the law of motion of the system or a phenomenon and other phenomena, the further development of existing theories, to enhance the system movement rules The law of exploration and cognition such scientific research level, or in the important project and the important infrastructure collapse and destructive disaster forecasting, environmental pollution monitoring such scientific level, are of great significance. Therefore, based on the nonlinear time series modeling and forecasting of time series, especially for the material system from quantitative to qualitative change show "smooth, smooth, and then again to change the variation of the upheaval of the research on Modeling and prediction. Firstly, aiming at the nonlinear time series, puts forward a new type, can be used, the multi-dimensional Taylor network model for time series prediction network, combined with the model, a method is proposed for predicting the model of nonlinear time series. Secondly, based on the multi-dimensional Taylor network and single step prediction, the multi-dimensional Taylor network applied to chaotic systems with multi step prediction, establish Adaptive model, adaptive modeling by sliding data window, realize multi-step prediction for nonlinear time series have chaotic characteristics; thirdly, according to the actual state of material system, some system changes are from quantitative to qualitative change, from a stable phase transition to another stable stage of the phenomenon, so as to continuously present "the evolution of smooth, smooth, and then again to upheaval upheaval", in the positive and negative mentor Yan Hongsen professor after many years of research methodology of feedback theory (Alternate positive negative feedbackics alternate, referred to as Napofic s) on the basis of a novel, the variation of positive and negative dynamic mathematical description the alternate feedback theory model, and combined with the multi-dimensional Taylor network model, proposed the alternating positive and negative feedback nonlinear time series method based on prediction theory; finally, combined with the The material system from quantitative to qualitative change and showed a "smooth, smooth, and then again, drastic upheaval" the regularity is equivalent, expand the criteria the negative feedback function for multi scale, i.e. to state change rate as the first scale, state change of acceleration as second scale, according to the state of the degree of change and drastic change trend the state, stability of separation, the multi-level network feedback on alternating positive and negative Dovi Taylor model and its application in prediction based on simulation. Specifically, research mainly in the following aspects: 1. according to the non linear time series, we put forward a new network, the model is different from the commonly used research methods -- Dovi Taylor network. The network is a new type of model, network model has advantages in establishing the analytic model of system. First introduces the model and structure of The working principle has been proved. The feasibility of constructing form multi-dimensional Taylor network model, and to determine the specific forms of expression of the weighted model. On this basis, we put forward a new time series prediction method based on multi-dimensional Taylor network. The characteristics of this new prediction method is only using the observation data of nonlinear time series through the multi-dimensional Taylor network N first order polynomial difference equations to describe the dynamic characteristics, without any prior knowledge and mechanism to predict the system's situation, realize the prediction of the nonlinear time series. Finally, through the typical Lorenz chaotic time series and the engineering monitoring data of a large building of the method was verified the effectiveness and feasibility of.2. in chaotic phenomenon widely exists in the actual system, proposes a new adaptive multi step prediction method based on multi-dimensional Taylor network, the The chaotic time series which is a typical nonlinear time series multi-step prediction. The definition of multidimensional Taylor polynomials, and proves that the polynomials can be defined in the bounded closed set of multivariate function approximation. It is proved that the multi-dimensional Taylor network and the difference of n order correct input form. Different adaptive prediction method of chaotic time series is presented in this on the basis of multi step prediction method to reconstruct the phase space, it is not to select the embedding dimension and time delay of the two key parameters of phase space reconstruction method in the premise. Without a priori knowledge of the system and mechanism, time series data are based on chaotic characteristics, establish multi-dimensional Taylor network model. By sliding window adaptive modeling data, so as to realize the multi step prediction of chaotic time series. Finally, the application example of the multi-dimensional Taylor network based on chaotic time sequence Column.3. adaptive multi step prediction of the feasibility and practicability of the method according to the actual state of material system, some system changes are from quantitative to qualitative change, from a stable phase transition to another steady stage phenomenon, and constantly showing smooth evolution, smooth, and then to upheaval upheaval. "The introduction of the equivalent positive and negative feedback of thought, and the thought and system state of the evolution process of the combination, this paper presents a novel, on the variation of positive and negative feedback on alternating dynamic mathematical description model, and based on the alternating positive and negative feedback nonlinear time series theory model forecasting method. Proved by positive and negative feedback replace the theory model to describe the system showing a" smooth, smooth, and then again, change the evolution of upheaval is feasible. According to the data of the degree of change, the stability of state separation And with the superposition of a plurality of dead zone function reflect different system state upheaval period due to a positive feedback effect caused by a burst of energy, the stability of system state separation, not starting from the mechanism inherent in the system, but through the external data representation of the internal mechanism of the system, the dynamic model of system is set up by a quantitative change to qualitative change from the dynamic mathematical model of the angle of system state description shows the variation of stable, smooth, and then again to drastic upheaval ". Finally through the example simulation, verified the positive and negative feedback on alternating combination of material system from quantitative change to qualitative model.4. is effective in modeling and prediction of nonlinear time series in the present", and then change smoothly smooth, then shift "the regularity and multi-dimensional Taylor network, introduced the concept of multi-scale, presents a multi-scale and multi-dimensional Taylor network based on alternating feedback The model is proved by the evolution. Describe the system with multiple scales and establish the multiscale model is correct. The state change rate and the change of acceleration as the equivalent is, first and second negative feedback definition scale, according to the state of the degree of change and drastic change trend, the state of separation. The variation law of stability expression of substance system in the form of dynamic equation. The model is a "smooth, smooth, and then again to upheaval upheaval in the course of this change change stage system state variation and change trend of expression by dominant function in the form of the general model, based on observation data. Finally, the application of the model in the nonlinear time series prediction, which has typical accumulated to the actual system data qualitative basis for simulation modeling and forecasting system. Results It shows that the model can accurately reflect the change rule of the system, and it can predict effectively, and it has high accuracy. It provides a new and effective means for modeling and forecasting complex systems with such evolution rules.

【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.61

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