Comparative Analysis of New Semi-empirical Methods of Modeling the Sag of the Thread

Abstract

We propose a new approach to the construction of multilayer neural network models of real objects. It is based on the method of constructing approximate multilayer solutions of ordinary differential equations (ODEs), which was successfully used by the authors earlier. The essence of this method is to modify known numerical methods for solving ODEs and applying them to a variable-length interval. Classical methods produce a table of numbers as a result; our methods provide approximate solutions in the form of functions. This approach allows refining the model when new information is received. In accordance with the proposed concept of constructing models of complex objects or processes, this method is used by the authors to construct a neural network model of a freely sagging real thread. Measurements were made using experiments with a real hemp rope. Originally, a rough rope model was constructed in the form of an ODE system. It turned out that the selection of unknown parameters of this model does not allow satisfying the experimental data with acceptable accuracy. Then, using the author's method, three approximate functional solutions were constructed and analyzed. The selection of the same parameters allowed us to obtain the approximations, corresponding to experimental data with accuracy close to the measurement error. Our approach illustrates a new paradigm of mathematical modeling. From our point of view, it is natural to regard conditions, such as boundary value problems, experimental data, as raw materials for constructing a mathematical model, the accuracy and the complexity of which must correspond to the initial data.