A versatile algorithm for estimating natural frequencies with high accuracy

Abstract

Detection of damage requires an accurate estimation of the natural frequencies of the monitored structure. This paper introduces an algorithm implemented in Python which improves the frequency readability by increasing the number of spectral lines without requiring a signal extension in the time domain. We achieve this by overlapping several spectra calculated from the acquired signal repeatedly shortened. In this way, the overlapped spectrum gets an increased number of spectral lines. The dense mesh of spectral lines permits us to obtain a fine frequency resolution without being necessary an extension of the signal in the time domain. The high density of the spectral lines ensures a sufficient number of points on the main lobes that permits performing an efficient quadratic polynomial interpolation to find the maximizer. It represents the amplitude of the real frequency and is typically located on an inter-line position, thus cannot be found by standard frequency estimation. We implemented the algorithm in Python and tested it successfully for generated signals, containing one or more harmonics, with known frequencies.