High Order Dynamic Mode Decomposition for Mechanical Vibrations and Modal Analysis

Abstract: In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important role. They allow an extraction of required information content from signals in another base by decomposing it in its spectral components for further processing.In theory this approach is very powerful, even in some 'simple' or 'not too complicated' practical cases it has proven its utility and efficiency. However, for real-world applications such as mechanical modal analysis of large dimension systems including damping, noise and unpredictable excitation those signals are often so complex that it can be almost impossible to obtain a high-resolution spectral decomposition with these methods due to the time-bandwidth limitation. In this paper we describe an alternative approach for spectral analysis based on the High Order Dynamical Mode Decomposition (HODMD) and Kernel Density Spectrum (KDS). We will show that this method allows overcoming some limitations of the FFT and may be a promising approach to for a much more precisely the spectral decomposition.