NIXO-Based Identification of the Dominant Terms in a Nonlinear Equation of Motion

Abstract

While many algorithms have been proposed to identify nonlinear dynamic systems, nearly all methods require that the form of equation of motion is known a priori. Examples of very effective methods of this kind are NIFO, CRP, and NARMAX. Several works have sought to extend NARX or NARMAX to a black-box modeling technique. They have proven to be successful in finding accurate mathematical models for certain types of nonlinear systems, yet no method has proved universally successful. This work presents and evaluates a new black-box identification approach based on a new NIFO/CRP type algorithm called Nonlinear Identification through eXtended Outputs (NIXO). The proposed algorithm expresses the nonlinear part of equation of motion as a polynomial of high order and then removes the terms that are classified (with high probability) as irrelevant in the mechanical system’s response. This division into dominant and irrelevant nonlinear terms relies on the values of two novel indicators that are particular to NIXO. This technique is demonstrated on a numerical case study employing a curved beam. Then, the method will be used to estimate the NLEOM of flat and curved beams that were manufactured using a 3D printer. The experimental results will be validated against those obtained using phase resonance testing, which identifies a nonlinear normal mode (NNM) of the system using a vastly different approach.