A novel Tikhonov regularization-based iterative method for structural damage identification of offshore platforms

The structural damage identification, which entails finding a best approximate solution to an over-determined system of linear equations, is actually one of the practical problems encountered in structural health monitoring. A major challenge to structural damage identification is the ill-conditioned problem caused by noise contamination and spatially incomplete measurements. A novel Tikhonov regularization iterative method (TRIM) is proposed to solve the ill-conditioned system of linear equations. This method iteratively reconstructs the regularization matrix by gradually updating the regularized solution. A merit is that the false-positive indicators of damage are greatly reduced; and as a result this approach would be able to detect smaller damages that could not be detected by using traditional approaches. Another development embedded in TRIM is that a procedure, called singular value dichotomy, is developed to determine the regularization parameters. Several problems, such as the tremendous prior trials, due to the application of L-curve, are avoided. A numerical study is conducted on an offshore platform structure to demonstrate the effectiveness of the proposed method. The result shows that the new method outperforms the traditional Tikhonov regularization method in damage identification.