理性神经网络方法及其在粘弹性谱分析中的应用

项目名称： 理性神经网络方法及其在粘弹性谱分析中的应用

项目编号： No.11262014

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李海滨

作者单位： 内蒙古工业大学

项目金额： 60万元

中文摘要： 神经网络计算有望成为一种高效乃至实时的结构分析方法，但是由于网络泛化能力差的原因，其在计算精度、结果的可靠性等方面仍存在诸多亟待解决的问题。其中，不适定性是泛化能力差的根本原因。本课题拟将力学问题归结为数理方程的边值问题，并以此为先导建立一种结构分析的理性神经网络计算方法。首先在网络误差能量函数上，将数理方程与神经网络融合，由Tikhonov泛函取极值的必要条件导出网络拓扑与神经元激活函数；其次以网络建模精度为依据，确定样本数量、分布及隐层神经元个数；然后以边界条件作为网络学习样本，通过研究针对混合边界条件的全局收敛训练算法，实现结构分析的神经网络建模；最后以固体火箭发动机随机振动问题为研究对象，建立药柱粘弹性分数阶导数模型，将所提出的理性神经网络方法与对应原理、动态子结构法相结合得到谱分析结果。与有限元法及试验结果进行对比，以验证所提方法的有效性。

中文关键词： 理性神经网络；对偶神经网络；结构分析；训练算法；谱分析

英文摘要： The neural network computing can become an efficient and real-time structural analysis method. However, due to the bad generalized ability of networks there still exist some problems such as the computational precision,the reliability of results, and so on. The ill-posedness of the above problems is the most fundamental reason for the bad generalized ability. In this project, the mechanical problem is turned into the boundary value problem of mathematical and physical equations. Then, a rational neural network computing method for the structural analysis is proposed. a neural network computing model is constructed. Firstly, the error energy function of the neural network is determined according to the mathematical and physical equations. Furthermore, the functions of the network topology and neurons activations are derived by the essential condition of the extreme value of Tikhonov functional analysis. Secondly, the number and distribution of the training samples and the number of neurons in the hidden layers are determined according to the computational accuracy of the neural network.Thirdly, the improved error back propagation algorithm is adopted to train the samples which are the mixed boundary conditions. In view of the above, a rational neural network computing method based on the structural analysis is de

英文关键词： Rational neural network；Dual neural network；structural analysis；Training Algorithm；spectrum analysis