Nonlinear output frequency response functions: A new evaluation approach and applications to railway and manufacturing systems’ condition monitoring

The Nonlinear Output Frequency Response Functions (NOFRFs) are an extension of the well-known Frequency Response Function (FRF) of linear systems to the nonlinear case and have recently been applied by many researchers to resolve different engineering problems. However, there exist several issues with current methods that can be used for the evaluation of the NOFRFs of practical systems. These include the difficulty and lack of an effective approach of accurately evaluating the NOFRFs for a general class of nonlinear systems. In the present study, a new concept known as the Generalized Associated Linear Equations (GALEs) is introduced to develop a novel approach to systematically address these problems. By using the GALEs, the NOFRFs of the NARX (Nonlinear Auto Regressive with eXegenous input) model or NDE (Nonlinear Differential Equation) model of nonlinear systems can be accurately evaluated by simply dealing with the solutions to a series of linear difference or differential equations. This can significantly facilitate the NOFRFs based nonlinear system analyses and associated practical applications. Two experimental studies including monitoring fatigue damage of train wheels and inspecting wearing conditions of cutting tools, respectively, demonstrate the significance and potential applications of the new GALEs based NOFRFs evaluation in railway and manufacturing systems’ condition monitoring.