Assessment of cracks in beams using changes in the measured frequencies and Particle Swarm Optimization

This paper presents a method for detecting a crack in simply supported beams by identifying its location and severity (depth). The method is based on the measured natural frequencies for several bending vibration modes of an intact and cracked beam and the Particle Swarm Optimization (PSO). To explain the approach, we calculate the relative frequency shifts (RFS) for eight vibration modes for all possible damage cases. To this aim, we use a mathematical relation deduced in previous research. Next, we monitor the natural frequencies, and in case of arising changes, we calculate the RFSs. We subtract, separately for all modes, the measured RFSs from all calculated RFSs. Considering the absolute values the subtractions achieve, we obtain eight surfaces that achieve elevation zero if the calculated and measured RFSs coincide. The zero-elevation points form curves with different shapes for the different vibration modes. The intersection of these curves, thus the location where all surfaces have zero elevation, indicates the damage location and severity. Adding the elevation values of the eight surfaces point by point, we obtain a new surface that has two points (due to symmetry) with zero elevation. The coordinates of these points indicate the damage parameters. We use the generated surface as an objective function and find the coordinates of the minima involving PSO. Using this method, we accurately identified the damage location and severity.