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A neural network algorithm for system modeling, global extrapolation, and parameter estimation for acoustical data.

机译：用于系统建模，全局外推和声学数据参数估计的神经网络算法。

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摘要

This thesis presents a coherent set of three neural-network based techniques to solve the related problems of system modeling, global function extrapolation, and parameter estimation for a class of problems that can be described as being of strongly separated type. The coherency derives from a semigroup property which is first developed in the model, is then continued in the extrapolation process, and is finally used as a basis for parameter estimation. It is intended primarily for application to the fields of acoustics and nonlinear vibrations, but can be generalized to other areas such as fluid flow and heat flow. It is assumed throughout that no prior analytical description of the data exists.; The system modeling technique requires that the resulting approximating function lends itself to a particular interpretation involving the product of a coefficient vector which is dependent on one system variable with a basis set of vectors, which are dependent on the remaining system variables, where the coefficient vector possesses a semigroup property. Extrapolation of the model reduces to extrapolation of the coefficient vector and consists of continuing the semigroup property which produced the original coefficient vector. Parameter estimation is based on establishing a linear relationship between a given coefficient vector with an unknown system parameter and a reference coefficient vector with a known system parameter. Under certain circumstances, the elements of the matrix which measure the relationship between coefficient vectors can be put into 1-1 correspondence with the system parameters.; The neural network implementation has several novel features. Concerning the architecture, semigroup theory requires that the neural network realization of the system modeling consists of dual channels, one of which is implementing a finite-dimensional function space and the other of which is selecting a specific function from within the function space. Concerning the operation, semigroup theory requires that the selection channel operates as a semigroup of operators. Concerning the extrapolation, it is based on a two-tier interpretation of training. On the lower tier, the network is trained to replicate a sequence of incrementally longer and longer sections of the overall coefficient trajectory. On the upper tier, the sequence of incremental weight changes is monitored. Under certain circumstances, the sequence of incremental weight changes converges and becomes differential in magnitude. (Abstract shortened by UMI.)
机译：本文提出了一套基于三类神经网络的连贯技术，以解决系统建模，全局函数外推和参数估计等相关问题，这些问题可以描述为强分离类型。相干性源自于模型中首先开发的半群性质，然后在外推过程中继续进行，最后用作参数估计的基础。它主要用于声学和非线性振动领域，但可以推广到其他领域，例如流体流和热流。始终假设不存在数据的先前分析描述。系统建模技术要求所得的逼近函数适合于一种特定的解释，该解释涉及系数矢量的乘积，该系数矢量取决于一个系统变量与矢量的基础集，矢量的基础集取决于其余的系统变量，其中系数矢量拥有半群性质。模型的外推法减少到系数向量的外推法，并且包括继续产生原始系数向量的半群性质。参数估计基于在系统参数未知的给定系数向量与系统参数已知的参考系数向量之间建立线性关系。在某些情况下，可以将测量系数矢量之间关系的矩阵元素与系统参数设置为1-1对应。神经网络实现具有几个新颖的特征。关于体系结构，半群理论要求系统建模的神经网络实现包括双通道，其中一个通道实现有限维功能空间，而另一个通道则从功能空间中选择特定功能。关于运算，半群理论要求选择通道作为运算符的半群进行运算。关于外推，它基于培训的两层解释。在较低的层上，对网络进行训练以复制整个系数轨迹的越来越长的部分序列。在上层，监视体重增加的变化顺序。在某些情况下，重量增加的变化顺序会收敛并在大小上有所差异。 （摘要由UMI缩短。）

著录项

  • 作者

    Velas, John P.;

  • 作者单位

    The Pennsylvania State University.;

  • 授予单位 The Pennsylvania State University.;
  • 学科 Engineering General.; Engineering System Science.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 238 p.
  • 总页数 238
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 工程基础科学;系统科学;
  • 关键词

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