大规模非平稳多元混沌时间序列分析与建模研究

Researches on the chaotic feature of realistic complex systems, such as meteorological systems,ecosystems are being widely conducted. As the development of imformation acquistion technology, the quantity and quality of observed data inccreases rapidly.The multivariate chaotic time series from complex systems shows the new feature of large-scale and nonstationary. To solve the problems of the curse of dimensionality and time varying statistical features brought by the data characteristics of large-scale and nonstationary, we do researches on the dynamic feature extraction methods and build novel prediction models. Moreover, we apply the real data from systems like meteorological systems to substantiate the effectiveness of the models, and then extend the models to the general complex systems. Hence it can provide support for the representation and management of complex systems, and it has great scientific significance and application values.The major research contents are as follows: 1) Analyze the chaotic and high dimensional characteristics of multivariate time series, and conbine the above analysis with fast feature extraction methods to propose dynamic feature extraction methods applicable for high dimensional variables. 2) To handle the data in large scale, nonlinear dimension reduction methods and novel regularized methods are used to construct the sparse prediction models. 3) To deal with the nonstationary time series, the model parameters are updated adaptively. As a result,the online prediction models can be built. 4) Evaluate the prediction performance of the models and modify the models in return. Above all, this project proposes a group of plans for analyzing and modeling large-scale nonstantionary multivariate chaotic time series. It provides theoretic and methodological support for the mathematical description of complex systems as well.

气象、生态等实际复杂系统的混沌特性已被广泛研究。随着信息采录技术的进步，观测数据的数量和质量迅速提高，从复杂系统中获得的多元混沌时间序列呈现出大规模非平稳的新特点。针对大规模和非平稳特性带来的维数灾难问题及统计特征时变问题，本项目研究动态特征提取方法，建立新型预测模型，并使用气象等实测数据进行验证，将模型推广到一般复杂系统中，为复杂系统的表达和管理提供支持，具有重要的科学意义与应用价值。研究内容如下：1）分析多元时间序列的混沌特性和高维相关性，结合快速特征提取方法，提出适用于高维变量的动态特征提取方法；2）针对大规模特性，使用非线性降维方法及新型正则化方法，建立稀疏预测模型；3）针对非平稳特性，自适应更新模型参数，建立在线预测模型；4）对模型的预测性能进行评估，反馈修正模型。综上，本项目提出一套完整的大规模非平稳多元混沌时间序列分析与建模方案，为复杂系统的数学化描述提供理论和方法依据。

气象、生态等复杂系统大多具有混沌特性。随着传感技术的发展，从复杂系统中获得的多元混沌时间序列呈现出大规模特点。针对大规模非平稳多元混沌时间序列的建模问题，本项目从以下四个方面展开研究：1）研究基于互信息及改进灰色关联分析方法，构造大规模时间序列在相互关联关系下的特征提取方法；2）建立基于非线性流形学习及范数正则化的稀疏预测模型，约简模型状态变量，提高模型泛化性能；3）构造基于核方法和自适应滤波器的新型在线预测模型，拟合时间序列的非平稳趋势，跟踪系统的动态特性；4）对所建模型通过局部邻域线性化，使用线性系统理论验证、分析模型的稳定性、可控性及可观性。在基金资助下，共发表论文76篇，并于2015年12月出版专著1部。主要研究成果发表在国际著名期刊《IEEE Transactions on Neural Network and Learning Systems》、《IEEE Transactions on Cybernetics》、《Engineering Applications of Artificial Intelligence》等和国内重要期刊《自动化学报》、《控制与决策》、《物理学报》等上。在基金支持下，研究小组共培养博士、硕士研究生13人。本项目对大规模非平稳多元混沌时间序列的特征提取、在线建模、稀疏建模和性能分析进行了积极探索，取得了一批有价值的研究成果，所提出的方案为大规模非平稳多元混沌时间序列的建模提供了重要理论依据。