A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment
An algorithm for detecting cracks on the beams and a statistical process for minimising the measurement errors in experiments are presented in this paper. Natural frequencies are determined by using the theoretical model for different depths and locations of single crack. The ratios of cracked and un-cracked beams natural frequencies constitute the prediction tables scaled in two axes as crack location and crack depth. Frequency contour lines corresponding to measured natural frequency ratios are matched with the interpolated prediction table, called frequency map, and are used for detection of a single crack. However, contour lines do not give any information about the existence of two cracks. The algorithm presented in this paper makes it possible to locate the suitable positions of two cracks searched over the frequency map. The algorithm is tested in the examples employing the frequency map prepared by the theory presented and the input frequency ratios obtained by the commercial finite element program. The algorithm is also verified by using the natural frequencies of cracked and un-cracked cantilever beams employed in several experiments. In measurement, determination of accurate natural frequency ratios is crucial for the success of crack detection. Therefore, this paper also presents a statistical approach called recursively scaled zoomed frequencies (RSZF) for minimising the deviations caused by sensitivity and resolution lack in measured natural frequencies. In this approach, the measured frequencies in spectrum are modified by the mean value of the natural frequencies determined in different frequency scales. Zoomed frequencies are obtained by the cubic spline interpolation method that increases the resolution of frequency spectrum. RSZF comes into further prominence especially when the cracks are needed to be detected by very small sized data. All of the experimental results represent that single crack and double cracks are successfully detected by using the methods presented.
frequency contour lines recursively scaled zoomed frequencies cracked beam vibration crack detection algorithm experimental natural frequencies