Abstract: Modal analysis is used for structural vibration and health monitoring, where it is important to extract the frequencies of vibration and detect problematic changes. Traditional blind source separation, such as the complexity pursuit algorithm, extracts the same number of frequencies as sensor time series and assumes that frequencies are constant over time. We introduce an unsupervised deep learning approach, which uses physics-informed loss functions to separate the nonlinear modes present in time series data. Our approach finds a set of dominant modes, identifies the parameters of the modes (resonant frequencies and damping ratios), and allows those modal parameters to shift in time. We demonstrate the method on several dynamical systems, with and without noise, and on experimental data.
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