非平稳信号高阶矩的多尺度大偏差谱研究

With the deep development and expansion of the multiscale theory of time series, multiscale large deviation technique based on law of large numbers and central limit theorem has been one of the most popular tools for the research on information extraction, information processing and information representation. It is urgent to study the basic theory, model algorithm and parameter estimation for this technique. Aiming at the key scientific problems that need to be solved urgently, this project introduces the large deviation theory of higher moments into the multiscale analysis technique of nonstationary signals and is based on stochastic analysis, time series analysis, functional analysis and so on. The purpose of this project is to reveal the intrinsic dynamic mechanism of nonstationary signals from the perspective of multiscale large deviations of higher moments, and to investigate the influence of nonstationarity, extreme events and higher moments on the large deviation spectrum. It establishes and explores the inner link between the signal extraction technologies such as the multiscale large deviation theory and multiscale information entropy etc., and develop, improve and perfect the effective method to quantify the scaling invariance of complex signals, while a systematic model and optimization algorithm are built to compute the multi-scale large deviation spectrum of higher moments for nonstationary signals. Striving to the new breakthrough in theory and method, this project focuses on solving the bottleneck problem in the multiscale analysis of nonstationary signals, which provides theoretical and methodological support for the practical application of the large deviation theory.

随着时间序列多尺度理论研究的深入和拓展，以大数定律和中心极限定理为基础的多尺度大偏差技术已逐渐成为人们进行信息提取、信息处理、信息表现研究中广泛使用的工具之一。对此技术涉及的基础理论、模型算法、参数估计的深入研究已刻不容缓。针对其迫切需要解决的关键科学问题，本项目将高阶矩大偏差理论引入到非平稳信号多尺度分析技术，以随机分析、时间序列分析、泛函分析等为基础，旨在从高阶矩多尺度大偏差的视角揭示非平稳信号内在动力学机理，探究信号的非平稳性、极端事件、高阶矩等对其大偏差谱的影响，建立和探索多尺度大偏差理论和多尺度信息熵等信号提取技术之间的内在联系，发展和完善能够量化复杂信号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非平稳信号高阶矩多尺度大偏差谱。力求在理论与方法上有新的突破，着重解决非平稳信号多尺度分析技术中的瓶颈问题，为高阶矩大偏差理论的实际应用提供理论与方法支撑。

本项目研究了人们十分关心的非平稳信号高阶矩多尺度大偏差理论的基本问题。随着时间序列多尺度理论研究的深入和拓展，对此技术涉及的基础理论、模型算法、参数估计的深入研究已刻不容缓。针对其迫切需要解决的关键科学问题，本项目将高阶矩大偏差理论引入到非平稳信号多尺度分析技术，以随机分析、时间序列分析、泛函分析等为基础，旨在从高阶矩多尺度大偏差的视角揭示非平稳信号内在动力学机理，探究信号的非平稳性、极端事件、高阶矩等对其大偏差谱的影响，建立和探索多尺度大偏差理论和多尺度信息熵等信号提取技术之间的内在联系，发展和完善能够量化复杂信号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非平稳信号高阶矩多尺度大偏差谱。我们顺利解决了各关键科学问题，圆满完成了各项预定计划和研究任务。.总之，我们在理论与方法上有新的突破，解决了非平稳信号多尺度分析技术中的瓶颈问题，为高阶矩大偏差理论的实际应用提供了理论与方法支撑。2018年以来，项目组成员在国内外有影响的学术刊物上发表与本项目相关的SCI检索论文87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内外学术会议。依托本项目培养博士生11名，硕士生15名。