Modelling displacement fields of wood in compression loading using stochastic neural networks

Abstract

Most environmental and biological phenomena, such as underground water flow and pollution and properties of wood, exhibit variability which can not be successfully simulated using deterministic approaches because many components of these systems could be inherently stochastic. However, these systems can be considered as a class of stochastic processes with arbitrarily inherent nature for modelling the system behaviour in space and time. Therefore, mathematical models based on stochastic calculus along with stochastic differential equations have been established to simulate these particular cases of environmental and natural systems. Artificial neural networks (ANNs) are another approach used to model natural and biological systems on the basis of mimicking the information processing methods in the human brain. However, very limited work has been done on investigating the capability of current neural networks to learn and approximate stochastic processes in nature although most neural networks operate in a stochastic environment. As a result, it is necessary to develop a new class of neural network named Stochastic Neural Networks for simulating stochastic processes or stochastic systems. The aim of this research is to create a suitable mathematical model for developing stochastic neural networks and implementing the proposed stochastic neural networks for simulating displacement fields of wood in compression. A stochastic neural network is based on the canonical representation of a class of nonstationary stochastic processes by means of Brownian motion or white noise. The reason is that Brownian motion and white noise, which are two basic stochastic processes, can enable a network to numerically estimate the stochastic integrals of the canonical representation. Depending on whether a stochastic process is represented by a random function or a set of realisations (data) of a stochastic system, different approaches are used to develop stochastic neural networks. This paper just focuses on how to develop a stochastic neural network based on a set of realisations of a stochastic system because this approach is suitable for real stochastic systems as the governing stochastic function is unknown.