Damage detection in beams using spatial Fourier analysis and neural networks

This study investigates the effect of damage on beams with fixed boundary conditions using Fourier analysis of mode shapes in the spatial domain. A finite element model is used to obtain the mode shapes of a damaged fixed-fixed beam, and the damaged mode shapes are expanded using a spatial Fourier series and the effect of damage on the harmonics is investigated. This approach contrasts with the typical time domain application of Fourier analysis for vibration problems. It is found that damage causes considerable change in the Fourier coefficients of the mode shapes, which are found to be sensitive to both damage size and location. Therefore, a damage index in the form of a vector of Fourier coefficients is formulated. A neural network is trained to detect the damage location and size using Fourier coefficients as input. Numerical studies show that damage detection using Fourier coefficients and neural networks has the capability to detect the location and damage size accurately. Finally, the performance of the method in the presence of noise is studied and it is found that the method performs satisfactorily in the presence of some noise in the data.