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.
Highlights
Features extracted from the vibration response are used since decades to characterize structures [1,2,3]
Because the damage has a low influence on the frequency changes, in order to observe the occurrence of damage as soon as possible [10], accurate frequency estimation is requested
We developed an algorithm which performs a quadratic interpolation based on three points that belong to three spectra, each spectrum being obtained for the original signal with a different time length
Summary
Features extracted from the vibration response are used since decades to characterize structures [1,2,3]. There are numerous methods for detecting defects based on vibration measurement [4,5,6,7,8]. We have developed a structure excitation procedure that provides the highest amplitude for the targeted vibration mode [21]. We complete the procedure with an original algorithm based on quadratic polynomial interpolation that helps finding the real frequency at an inter-line position. We managed to estimate both frequencies and amplitudes with high accuracy and found that the application is easy to use and versatile, allowing the user to choose the optimal input parameters during the frequency evaluation process.
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