Modeling of materials with fading memory using neural networks
Modeling of materials with fading memory using neural networks
复制标题
使用神经网络对具有褪色记忆的材料进行建模
DOI：
10.1002/nme.2518
复制
发表时间：
2009
影响因子：
2.9
通讯作者：
S. Freitag
中科院分区：
文献类型：
--
作者：
M. Oeser;S. Freitag
本文提出了一种基于神经网络的分数阶微分方程求解方法。分数阶微分方程用于模拟流变材料的行为，表现出特殊的负载（应力）历史特性（例如衰减记忆）。新概念的重点是流变材料，表现出牛顿般的位移行为时，经历（时变）蠕变载荷。为此，开发了一种部分递归人工神经网络。与分数阶微分方程的精确解相比，该网络取代了整个载荷（应力）历史的存储，在分数阶微分方程中，需要访问所有先前的载荷（应力）增量以确定新的位移（应变）增量。该网络使用从六个不同的蠕变模拟获得的数据进行训练。这些蠕变模拟已进行的分数阶微分方程的精确解，这也包括在文件中。此外，网络结构以及一套完整的网络参数。该网络的验证已经进行，其结果进行了讨论的文件。为了说明网络工作的特定方式，所有相关算法（例如，输入数据的缩放、数据处理、输出信号的变换等）都将被描述。在本文中提供给读者。版权所有© 2008约翰威利父子有限公司。
A neural network‐based concept for the solution of a fractional differential equation is presented in this paper. Fractional differential equations are used to model the behavior of rheological materials that exhibit special load (stress) history characteristics (e.g. fading memory). The new concept focuses on rheological materials that exhibit Newtonian‐like displacement behavior when undergoing (time varying) creep loads. For this purpose, a partial recurrent artificial neural network is developed. The network supersedes the storage of the entire load (stress) history in contrast to the exact solution of the fractional differential equation, where access to all previous load (stress) increments is required to determine the new displacement (strain) increment. The network is trained using data obtained from six different creep simulations. These creep simulations have been conducted by means of the exact solution of the fractional differential equation, which is also included in the paper. Furthermore, the network architecture as well as a complete set of network parameters is given. A validation of the network has been carried out and its outcome is discussed in the paper. To illustrate the particular way the network works, all relevant algorithms (e.g. scaling of the input data, data processing, transformation of the output signal, etc.) are provided to the reader in this paper. Copyright © 2008 John Wiley & Sons, Ltd.