Abstract
Fault detection methods are significant in health monitoring of critical system components, including aerospace applications. Failure in such systems is unacceptable, even though engineers try to achieve very low failure probability in these systems. The ability to accurately model and analyze the characteristics of such systems would reduce the rates of false positives and missed detections in structural health monitoring. Previously, a detection model was developed to investigate the effects of combined impact of geometrical variations of machining errors and crack presence in beams. The model utilized the Leap Frog finite difference method, which had a restrictive condition on stability of the numerical method. This restriction would show to be critical with materials with high modulus and low density values. The proposed work will overcome the drawback of the current detection model by utilizing other finite difference methods to remove or relax the stability condition of the method; namely, the Weighted Average method and Du Fort-Frankel method. The presented result clearly shows that the Theta method could be used to obtain an unconditionally stable finite difference model with high accuracy. It is also observed that the result from the Du Fort-Frankel method is still conditionally stable, but the stability condition is more relaxed compared to the Leap Frog method. The results obtained from the improved model show good agreement with the example in the literature. The improved model is also applied to investigate a cantilevered beam with the presence of cracks and geometrical variations.