基于Volterra级数预测的音频频带扩展

 本文采用非线性分析方法,基于Volterra级数提出了一种宽带音频信号的频带扩展方法,并利用高斯混合模型(Gaussian Mixture Model,GMM)和码本映射技术对扩展后的音频信号进行了谱包络和能量增益调整.实验表明,所提算法的性能要好于已有的非线性频带扩展算法,当用本文的方法替代ITU-T G.722.1C编码器中的噪声填充技术时,在24kbps得到了提升的超宽带音频质量.     

非线性系统构成哈默斯坦模型的必要条件

借助相关分析方法导出了黑箱非线性系统构成哈默斯坦模型的必要条件,为辨识一大类可以表示成这种模型的非线性系统提供了一种实用的判别依据,借助于渥尔特拉级数和维纳理论,还给出了这种判别依据用表征非线性系统固有属性的渥尔特拉核和维纳核来表示的形式.数值模拟算例表明:所导出的表达式正确有效.     

基于Volterra泛函级数的涡轮建模研究

给出了对非线性动态系统做任意精度逼近的Volterra级数高阶核的全新估算方法并将其应用在涡喷发动机的转速控制上。该方法在核函数理论基础上,构造线性空间,将求解Volterra级数各阶核的问题转化为求输出观测向量在希尔伯特空间中某一子空间上的投影的问题,使原本复杂的非线性系统的Volterra级数的逼近问题在线性空间中以向量内积的方式得到解决。与其他时域或频域估算Volterra核的方法相比较,该算法的优点在于理论体系严密、计算量不随阶数增高而成几何级数增加、辨识精度高。该方法理论上能够估算任意阶核,弥补了现有方法难以估算四阶以上核的缺点,可应用于动态系统和强非线性系统的建模。将发动机动态过程描述为四阶的Volterra级数模型。     

High-order Volterra Model Predictive Control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

基于混沌的交通流量Volterra自适应预测模型*

采用基于混沌动力系统的相空间重构和非线性系统的Volterra级数展开式,构建了交通流量的Volterra自适应预测模型。其基本思想是首先采用Lyapunov指数判定交通流时间序列存在混沌的前提下,对该时间序列进行相空间重构;然后选择Volterra级数构造非线性预测模型,并采用LMS类型的自适应算法来实时调整模型的系数。应用该模型对Lorenz、Rossler和交通流时间序列进行仿真研究。结果表明,提出的Volterra自适应预测模型能有效地预测低维混沌时间序列和交通流时间序列。     

基于Volterra核的MIMO非线性电路建模及智能特征提取

为了解决模拟乘法器等多输入测量电路的智能故障诊断准确率低的问题,文中研究了多输入多输出(MIMO)电路的基于Volterra级数的建模方法,为电路的故障诊断提供模型,提出了整体退火遗传特征提取方法,利用整体退火遗传算法的全局寻优能力优化故障诊断特征参数的提取,以选出各种故障状态之间特征差异最大的特征,以提高故障诊断的准确率,以模拟乘法器电路为例进行了建模及故障特征智能优化提取实验.实验表明,文中方法可以有效建模并提高智能故障诊断的准确率.     

The early days of geometric nonlinear control

Around 1970 the study of nonlinear control systems took a sharp turn. In part, this was driven by the hope for a more inclusive theory which would be applicable to various newly emerging aerospace problems lying outside the scope of linear theory, and also by the gradual realization that tools from differential geometry, and Lie theory in particular, could be seen as providing a remarkably nice fit with what seemed to be needed for the wholesale extension of linear control theory into a nonlinear setting. This paper discusses an initial phase of the development of geometric nonlinear control, including material on the broader context from which it emerged. We limit our account to developments occurring up to the early 1980s, not because the field stopped developing at that point but rather to limit the scope of the project to something manageable. Even so, because of the volume and diversity of the literature we have had to be selective, even within the given time frame.     

非线性系统二阶Volterra核的推导

本文所研究的非线性系统是指其特性能够完全用Ｖｏｌｔｅｒｒａ级数描述的系统。作者在详细推导出单节点－单非线性元件系统的二阶Ｖｏｌｔｅｒｒａ核的函数表达式的基础上，简洁导出了具有任意节点数和非线性元件数的一般非线性系统的二阶Ｖｏｌｔｅｒｒａ核函数表达式。     

Filtering of absorbing and reflecting Brownian motions

Two filtering problems for Brownian motions with absorbing and reflecting barriers are examined and shown to reduce to two classical boundary value problems (BVPs). It turns out that the solution of the first one is basically the same as those obtained by Bene [2] for the ‘3-dimensional’ Bessel process. The presence,of a reflecting barrier manifests itself via an appropriate boundary. condition and some additional term in the PDE. Two different formulas solving the second BVP are obtained.     

基于Volterra 模型的非线性系统预测控制

基于系统的正、负和双阶跃响应,提出一种新的非线性预测控制模型的建立方法,同时给出了相应的非线性控制算法,并证明了控制算法解的存在性和唯一性,针对 化工过程蒸馏塔控制系统,通过仿真计算验证了该方法的有效性。