Extraction of Single-Mode Free Responses by the Constrained Mode Decomposition Method

This contribution presents, discusses and illustrates the constrained mode decomposition (CMD) method. The CMD is a recently proposed method that extracts single mode components from measured multimodal free structural responses. These components can be then processed, in time domain or in frequency domain, for identification of modal parameters, and ultimately, for structural health monitoring. The aim of the CMD is thus similar to the aims of other well-known mode decomposition approaches, such as the empirical mode decomposition (EMD) or the variational mode decomposition (VMD). However, in contrast to the EMD, the CMD-processed responses retain the characteristics of the free response (satisfy the equation of motion of the same structure) and they have thus a clear, well-defined physical meaning. In comparison to the VMD, the formulation of the CMD is much simpler: the CMD combines linearly recorded structural responses in a way that simultaneously (1) amplifies the selected modal component and (2) constrains/suppresses other components. The amplification/suppression process is quantified in terms of the FRF peaks or, in case of closely spaced modes, in terms of FRF derivatives.