Adaptive Tikhonov regularization for damage detection based on nonlinear model updating

This paper presents an adaptive regularization approach for solving the nonlinear model updating inverse problem. The discrimination of possible damaged elements and undamaged elements is done from results obtained in previous iterations via a new side condition which aims at (a) to limit the local change in damaged structural elements in each iteration; and (b) to force the variation of other undamaged elements close to zero. A thirty-one bar plane truss structure with multiple damages is studied. Results obtained from the proposed method are greatly improved over those obtained from the traditional Tikhonov regularization even with large noise contamination in the measurements.