Multiple Analytical Mode Decompositions for Nonlinear System Identification from Forced Vibration


In this study, multiple analytical mode decompositions (M-AMD) are proposed to identify the parameters of nonlinear structures from forced vibration. For the time-varying damping (or stiffness) coefficient of a weakly-to-moderately nonlinear system, the slow-varying part is first estimated from the system responses and their Hilbert transforms, which is corrected with an adaptive low-pass filter referred to as analytical mode decomposition (AMD). The fast-varying part can then be identified from the responses together with the estimated slow-varying part, which is again corrected with the AMD. The computational efficiency and accuracy of the proposed M-AMD are demonstrated with a Duffing oscillator subjected to harmonic loading. The errors in estimation of all model parameters are less than 3% from uncontaminated displacement responses, which is more accurate compared with the results from Hilbert spectral analysis. Changes of the fast-varying stiffness part have been taken into account with high accuracy. The M-AMD algorithm is then validated with a ¼-scale, 3-story building with one piezoelectric friction damper under earthquake excitations. The parameters of such a semi-active damper are identified with less than 1% error on average.


Civil, Architectural and Environmental Engineering


Financial support to complete this study was provided by the U.S.National Science Foundation under Award No. CMMI1538416.

Keywords and Phrases

Adaptive filtering; Adaptive filters; Computational efficiency; Earthquakes; Hilbert spaces; Low pass filters; Mathematical transformations; Nonlinear systems; Religious buildings; Signal processing; Spectrum analysis; Stiffness; Analytical mode decompositions; Displacement response; Earthquake excitation; Forced vibration; Hilbert spectral analysis; Hilbert transform; Piezoelectric friction damper; Semi-active dampers; Vibration analysis; Algorithm; Building; Damping; Decomposition analysis; Earthquake engineering; Error analysis; Identification method; Nonlinearity; Seismic response; Signal processing; Spectral analysis; Transform; Vibration; Analytical mode decomposition; Nonlinear system identification

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