混沌时间序列Volterra建模及其在语音信号处理中的应用

项目名称： 混沌时间序列Volterra建模及其在语音信号处理中的应用

项目编号： No.11502133

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 张玉梅

作者单位： 陕西师范大学

项目金额： 22万元

中文摘要： 在非线性动力系统的研究中，混沌时间序列的建模是进行分析问题和解决问题的关键。本项目拟将信息准则理论应用于混沌时间序列Volterra建模时模型阶数和记忆长度的综合选择问题，解决传统方法的指定模型阶数和记忆长度过大引起的计算复杂度和过拟合问题，并通过Bayesian准则确定Volterra模型中模型参数对于模型的贡献大小；考虑LMS和RLS算法存在的合理选择参数问题，拟研究一种基于后验误差假设的具有可变收敛因子和良好抗干扰性的自适应优化算法，并应用于模型系数的更新；设计具有非线性反馈结构的Volterra模型，增加算法的动态特性，从而将提高模型的预测能力；最后将所建模型应用于语音信号的预测中，研究语音信号的混沌特性与声学特性之间的关系，建立以混沌特性为基础的非线性分类模型，并构建不同类别的语音时间序列非线性预测模型。本项目研究将为混沌时间序列建模和预测理论提供新思想、探索新途径。

中文关键词： 非线性动力学；混沌时间序列；Volterra建模；语音信号处理

英文摘要： In the study of nonlinear dynamic systems, modeling for chaotic time series is the key to analysis and solving issues. This project intends to apply information criterion theory to selection of model order and memory length of Volterra modeling for chaotic time series so as to solve computational complexity and over-fitting problems caused by using traditional method through specifying model order and choosing larger memory length. Meanwhile, Bayesian learning principle is employed to determine contributions of the model parameters in the proposed Volterra model. Considering reasonable parameters choice of LMS and RLS algorithms, an adaptive optimization algorithm, which is with a variable convergence factor based on a posteriori error assumption and being characteristic of better anti-jamming, is proposed and is applied to the update of the Volterra model coefficients. Volterra prediction model with nonlinear feedback structure is also devised to increase dynamic characteristics so as to improve prediction property. Finally, through applying the proposed model to prediction of speech signal, the relationship between chaos and characteristics of the acoustic characteristics of the speech signal is studied. A nonlinear classification model based on chaotic characteristics and a nonlinear prediction model for different types of speech time series are constructed. This research project will provide new ideas and explore new avenues for chaotic time series modeling and prediction theory.

英文关键词： nonlinear dynamics;chaos time series;Volterra modeling;speech signal processing