Early Structural Damage Assessment by Using an Improved Frequency Evaluation Algorithm

Abstract

This paper introduces a method to identify damages in beam-like structures by analyzing the natural frequency changes of the first six transversal vibration modes. A correlation between the damage location and frequency change is established for each mode separately, by considering the modal strain energy stored in that location. The mathematical relation describing this correlation is used to characterize the dynamic behavior of a beam with a damage of known position and to derive its Damage Location Indicator (DLI) as a six-term vector. The method consists in comparing the vectors describing the damage at any possible location along the beam with the Damage Signature (DS), which is achieved from the measurements that compare the beam's frequencies in healthy and damaged state. A modified Kullback-Leibler Divergence is used to assess the damage location. In order to permit early damage assessment, an improved frequency evaluation algorithm was developed. It is based on signal truncation and consequent spectral lines rearrangement, in order to accurately find the strongest spectral components. The effectiveness of the proposed method is demonstrated by simulations and experiments.

Interdependencies between Dynamic Response and Crack Growth in a 3D-Printed Acrylonitrile Butadiene Styrene (ABS) Cantilever Beam under Thermo-Mechanical Loads

“…These dynamic responses contain information regarding the locations and sizes of the crack(s). Many researchers have focused on the vibration characteristics of cracked beams [ 1 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. Ostachowicz and Krawczuk (1991) modelled the crack as a torsional spring model and calculated the natural frequencies of single-sided and double-sided crack cantilever beams [ 46 ].…”

“…However, the torsional spring model can only represent the shallow cracks. Moreover, certain researchers investigated the relationship between the natural frequency and crack propagation [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 19 , 25 , 26 , 34 , 44 ]. Mode shapes were applied to estimate the location and size of damage [ 18 , 22 , 33 , 43 ].…”

A versatile algorithm for estimating natural frequencies with high accuracy

“…The mathematical relationship between the damage dimensions and the frequency drop is proposed in [9]. 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. The simplest way to achieve this target is using an interpolation method based on two spectral lines [11][12][13] or three spectral lines [14][15][16], but the results have been proved to be unsatisfactory for detecting damage in the early stage [17].…”

Assessing multiple cracks in beams by a method based on the damage location coefficients

“…If more vibration modes are involved, the comparison is made by using dissimilarity estimators that perform a bin-by-bin evaluation [10][11][12]. It is possible to separate the problem of finding the crack location and severity by applying two consecutive normalizations [13]. Initially, the location is determined involving the Damage Location Coefficients (DLC).…”