Modeling of materials with fading memory using neural networks

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 (eg. 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 thee 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 (c) 2008 John Wiley & Sons, Ltd.