Empirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems

Abstract

A relationship between Intrinsic Mode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identification of a planar rigid airfoil

Non-linear system identification of the dynamics of aeroelastic instability suppression based on targeted energy transfers

“…Empirical mode decomposition (EMD) combined with Hilbert spectral analysis (33) has been utilised for nonlinear system identification and damage detection of structures (34,35,36,37,38,39) . In particular, Lee et al (40) applied the EMD method for reduced-order modeling of aeroelastic systems extracted from computational transonic aeroelastic responses with strong nonlinearities. Recently, the slowflow model identification method for strongly nonlinear systems studied in Kerschen et al (39) was expanded to establish an analytical equivalence between analytical and empirical slow-flow analyses (41) ; the basic elements of the nonlinear system identification method based on multiscale dynamic partitions were developed in Lee et al (42) .…”