Semi-empirical Neural Network Model of Real Thread Sagging

Abstract

We propose a new approach to building multilayer neural network models of real objects. It is based on the method of constructing approximate layered solutions for ordinary differential equations (ODEs), which has been successfully applied by the authors earlier. The essence of this method lies in the modification of known numerical methods for solving ODEs and their application to an interval of variable length. Classical methods give as a result a table of numbers; our methods provide approximate solutions as functions. This allows refining the model as new information becomes available. In accordance with the proposed concept of building models of complex objects or processes, this method is used by the authors to build a neural network model of a freely sagging real thread. We obtained measurements by conducting experiments with a real hemp rope. Initially, we constructed a rough rope model as a system of ODEs. It turned out that the selection of unknown parameters of this model does not allow capturing the experimental data with acceptable accuracy. Then three approximate functional solutions were built with the use of the authors’ method. The selection of the same parameters for two solutions allowed us obtaining the approximations, corresponding to experimental data with accuracy close to the measurement error. Our approach illustrates a new paradigm for mathematical modeling. From our point of view, boundary value problems, experimental data, etc. are considered as raw material for the construction of a mathematical model which accuracy and complexity are adequate to baseline data.