摘要
论文全面地介绍了神经网络研究的发展历史及其意义、神经网络研究内容、神经网络应用前景、神经网络基本概念等,重点阐述了BP神经网络还存在的各种局限性及其改进方法。
针对线性方程组求解问题,论文提出了基于矩阵元素的神经网络模型算法、基于向量空间的神经网络模型算法以及基于LDU分解的神经网络模型算法,证明了三种模型算法的收敛性,为神经网络学习率大小的确定建立了理论依据。在权值调整中采用龙贝格(Romberg)修正法,有效避免了BP算法存在局部极小的问题。仿真研究结果表明,所提出的基于神经网络算法的线性方程组求解方法不仅具有高的计算精度,而且不涉及逆矩阵运算,因而是有效的计算方法。
针对非线性方程和非线性方程组的求解问题,论文分别对神经网络模型和算法作了探索性研究,证明了算法的收敛性,为神经网络学习率大小的确定建立了理论依据。在权值调整中引入了动量项,有效加快了网络收敛速度。仿真研究结果表明,本文研究的求解非线性方程和非线性方程组的神经网络算法具有收敛速度快、计算精度高、收敛性不依赖初始值等特点。
针对数值积分问题背景,论文对神经网络模型和算法作了一系列探索性研究,分析了神经网络算法的收敛性,为神经网络学习率大小的选择建立了理论依据,创造性地建立了数值积分与神经网络权值之间的关系。仿真研究结果表明,所提出的数值积分方法具有计算精度高,计算速度快的特点。
针对微分方程初值问题的求解,论文探索性研究了求解微分方程初值问题的神经网络模型算法,并分析了算法的收敛性,为神经网络学习率大小的确定建立了理论依据。仿真结果表明,解微分方程初值问题的神经网络算法可以对微分方程初值问题的解建立数学模型,因而可以计算出任意给定点处的函数值,这是任何差分方法无法做到的。
针对FIR(Finite Impulse Response)线性相位数字滤波器优化设计问题,提出了以余弦基函数cos( nω)为隐层神经元激励函数的神经网络模型算法,证明了神经网络算法的收敛性,为神经网络学习率大小的确定建立了理论依据。此外,本文将四种情况下的FIR线性相位数字滤波器的优化设计进行了有效统一,算法的通用性强。仿真实验结果表明,所提出的FIR线性相位数字滤波器优化设计方法有效避免了求逆矩阵的问题,因而有效克服了高阶FIR线性相位数字滤波器的优化设计瓶颈。
针对信号的频谱分析问题背景,本文探索性研究了基于傅立叶基函数的神经网络模型算法,研究了算法的收敛性,为神经网络学习率大小的确定给出了理论依据。所提出的基于神经网络算法的信号处理方法(频谱分析、随机噪声滤波)不涉及复数的乘法运算和复数的加法运算,计算精度高,特别适合基于DSP芯片的软、硬件实现。
最后,本文介绍了神经网络算法在传感器中的应用实例。使用傅立叶基函数神经网络算法拟合曲线的方法,对传感器灵敏度-温度特性曲线进行了拟合。研究结果表明,用傅立叶正交基函数神经网络算法拟合的曲线十分光滑,拟合精度高。
基于正交基神经网络算法的传感器误差补偿方法具有高的补偿精度,计算量小,收敛速度快,与最佳直线拟合法、最小二乘法多项式曲线拟合法、非线性反函数补偿法以及其它神经网络的非线性补偿等方法相比具有明显的优势,因而是一种有效的传感器误差补偿方法。
利用正交基神经网络与最小二乘递推算法相结合的多传感器信息融合方法对参数进行检测时,不需要知道传感器量测数据的任何先验知识,就可以通过神经网络训练估计出分布式参数的值。该方法既可以提高参数的检测精度,同时也具有很好的稳定性,计算量小,便于计算机实时处理,因而是一种有效的多传感器信息融合方法。
This dissertation introduces a more comprehensive of the neural network research on the history, significance, research contents, application prospects, and other basic concepts etc. Focus on BP neural network, its limitations and improved methods were introduced.
According to Linear systems, the article put respectively forward neural network model and algorithm based on the matrix elements, vector space and the LDU decomposition. The convergence of three kinds of neural network algorithms was proved. The theory gist selecting the neural network learning rate was given. As the Romberg method was used to the weights adjustment of neural network, the local minimum problems of the BP algorithm were effectively prevented. The results showed that the numerical method to solve linear systems based on the neural network algorithm not only has high precision, but also do not involve inverse matrix operation. Therefore it is an effective method of calculation.
For the problems to solve nonlinear equation and nonlinear systems, the neural network models and algorithms were explored and studied in the paper. The convergence of neural network algorithms was proved. The theory gist was determined on selecting the neural network learning rate. Weight adjustment with the momentum term speeds effectively up the convergence speed of the neural network. The simulation results showed that the neural network algorithm, which is used to solve nonlinear equation and nonlinear systems, is of fast convergence speed and high accuracy, and the convergence is not dependent on the characteristics of the initial value.
The dissertation introduced the neural network model and algorithm for solving numerical integration problem. The convergence of neural network algorithms was presented and proved. The theory gist was determined on selecting the neural network learning rate. The relations between a numerical integration and neural network weights were creatively built. The simulation results showed that the numerical integration method has high accuracy, fast computing speed characteristics.
This dissertation discussed and studied the neural network algorithm solving differential equations with initial value problems. The convergence of neural network algorithms was proved. The theory gist was determined on selecting the neural network learning rate. The results of experiments show that the neural network algorithm solving differential equations with the initial value problem can establish mathematical model, which can be calculated any given point of function, which is any difference method can not do.
According to linear phase FIR digital filter optimization design, the neural network model algorithm was put forward using a cosine basis functions cos( nω) as hidden layer neuron activation functions. The neural network algorithm convergence was proved. The theory gist selecting the neural network learning rate was determined. In addition, optimization design approaches of four kinds of the linear phase FIR digital filters were effectively reunified. Algorithm has strong generality. The results showed that the optimization design methods of the linear phase FIR digital filters presented in this paper can effectively prevent the inverse matrix problems. Therefore, it effectively overcomes the optimization design bottleneck of the higher-order linear phase FIR digital filters.
Spectrum analysis method based on neural network algorithm with Fourier basic functions was explored and studied. The convergence of neural network algorithms was presented and proved. The theory gist was determined on selecting the neural network learning rate. Signal processing approach presented in this paper based on neural network algorithm (spectral analysis, Random noise filtering) does not involve the complex multiplication and addition operations. Its computing accuracy is high. It is particularly suitable for the implementation of software and hardware based on DSP chip.
Finally, this paper introduces application examples of sensor based on the neural network algorithm. The model fitting the sensor sensitivity - temperature characteristic curve based on the neural network algorithm with Fourier basis functions was used. The results show that the fitting curve is very smooth using neural network algorithm with Fourier orthogonal basis function, and its fitting precision is very high.
The sensor error compensation method based on orthogonal basis neural network algorithm has high accuracy of compensation, small calculated amount and fast convergence rate. It has significant advantages compared with the best linear fit, the least-squares polynomial curve fitting, nonlinear inverse function compensation, and other nonlinear neural network compensation methods. Therefore it is an effective method of sensor error compensation.
The method can estimate the value of distributed parameter by orthogonal basis neural network training based on recursive least squares algorithm in the field of parameters detection of the multi-sensor information fusion, which does not need to know the measurement data of any a priori knowledge of sensor. The approach can improve the accuracy of measurement parameters, but also has good stability, a small amount of calculation and to facilitate real-time processing, which is an effective multi-sensor data fusion method.
引文
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