非平稳信号的MFDCCA大偏差研究

Multifractal cross-correlation analysis (MFDCCA) technique based on detrended fluctuation analysis has gradually become one of the most popular tools to study information extraction, information processing and information representation with the expansion and deep-going of its applications. There are urgent needs of further research of the basic theory, model algorithms and parametric estimation related to this technique. To solve this key scientific issue, based on nonlinear time series theory, optimization theory, and approximation theory, this project will introduce multifractal large deviation theory into the MFDCCA technique, which aims to reveal the generation mechanisms of multifractal cross-correlations between non-stationary signals from the perspective of large deviation spectra, explore the effect on multifractal large deviation spectra of non-stationarity of signals and nonlinear filtering etc., propose and develop effective methods to quantify the presence/absence of scale invariance of cross-correlations of complex signals, and finally construct systematic models and optimal algorithms to accurately calculate the multifractal large deviation spectra of cross-correlations of signals. We strive to have new breakthroughs in both theories and methodologies, focus on finding solutions to bottleneck issues of multifractal cross-correlation analysis, and provide theoretical and methodological support to the applications of MFDCCA large deviation theory.

随着应用的深入和拓展，以趋势消除波动分析为基础的重分形交叉相关分析（MFDCCA）技术已逐渐成为人们进行信息提取、信息处理、信息表现研究中最常用的工具之一。对此技术涉及的基础理论、模型算法、参数估计的更加深入的研究已刻不容缓。针对其迫切需要解决的关键科学问题，本项目将重分形大偏差理论引入到MFDCCA技术，以非线性时间序列理论、最优化理论、函数逼近论为基础，旨在从大偏差谱的视角揭示非平稳信号间重分形交叉相关性的生成机理，探究信号的非平稳性、非线性滤波等对其重分形大偏差谱的影响，提出和发展能够量化复杂信号交叉相关(非)标度不变性的有效方法，构建系统化的模型和优化算法以准确计算信号交叉相关的重分形大偏差谱。力求在理论与方法上有新的突破，着重解决重分形交叉相关分析技术中的瓶颈问题，为MFDCCA大偏差理论的实际应用提供理论与方法支撑。

随着应用的深入和拓展，以趋势消除波动分析为基础的重分形交叉相关分析（MFDCCA）技术已逐渐成为人们进行信息提取、信息处理、信息表现研究中最常用的工具之一。对此技术涉及的基础理论、模型算法、参数估计的更加深入的研究已刻不容缓。针对其迫切需要解决的关键科学问题，本项目将重分形大偏差理论引入到MFDCCA技术，以非线性时间序列理论、最优化理论、函数逼近论为基础，我们从大偏差谱的视角揭示了非平稳信号间重分形交叉相关性的生成机理，探究了信号的非平稳性、非线性滤波等对其重分形大偏差谱的影响，提出和发展了能够量化复杂信号交叉相关(非)标度不变性的有效方法，构建了系统化的模型和优化算法以准确计算信号交叉相关的重分形大偏差谱。我们在理论与方法上有新的突破，着重解决了重分形交叉相关分析技术中的瓶颈问题，为MFDCCA大偏差理论的实际应用提供了理论与方法支撑。.2014 年以来，项目组成员在国内外有影响的学术刊物上发表了SCI检索论文59篇（标注项目批准号）。邀请该领域顶尖科学家来华进行了学术交流，并参加了多次高水平的国际学术会议。依托本项目培养博士生8名，硕士生20余名。