Sensitivity analysis of chaos in a nonlinear pendulum through artificial neural networks

Abstract

Verifying under what configurations a system will manifest chaotic behavior is a complex task that involves different aspects, ranging from applied mathematics to numerical analysis. Thus, the present work aims at proposing a new method to assess chaos behavior by using Artificial Neural Networks via a Modified Profile Method applied to a significance study in order to determine which constitutive variables of a system most affect the emergence of chaos. A phase portrait was implemented in order to assess the quali-quantitative chaos behavior of a general second-order nonlinear system, applying the Lyapunov exponents and the Poincare map. The results confidently showed that the variations of the damping ratio and natural frequencies were the most important in producing the system to manifest chaos. The second- and third-order interactions did not significantly contribute to the chaotic behavior of the system. The results of all the trained topologies were consistent. In conclusion, the proposed methodology showed a strong agreement with what is presented in the literature.