ニューラルネットワークによる非線形振動系の同定の基礎検討

抄録

In this study, we investigate a time-domain method to identify linear parameters such as mass, damping coefficient, and stiffness, and nonlinear force of a nonlinear vibration system using a neural network (NN). In this method, excitation forces, accelerations, velocities, and displacements measured from experiments are input to the NN, and the NN learns the equilibrium of forces between the external force, inertial force, damping force, and restoring force to identify the characteristics of the vibration system. The proposed NN consists of a global NN that computes equilibrium of forces by linear and nonlinear sub-networks, and a local NN that extracts linear parameters from the nonlinear sub-networks. This study targets vibration systems with smooth nonlinear characteristics governed by Duffing's equation or Van der Pol's equation. Furthermore, as an example of a vibration system in which the slope of the nonlinear force, the dependent variable, increases when the displacement, the dependent variable, takes a value close to zero, we also target vibration systems in which the nonlinear force is expressed as a sinusoidal function. Then, the data obtained by numerically solving the equation of motion is regarded as the data obtained experimentally, and the validity is confirmed by identifying the linear parameters and nonlinear forces.