Comparative studies on structural damage detection using <i>L</i><SUB align="right"><i>p</i> norm regularisation

Abstract

In order to get sparse solution to the structural damage detection (SDD) problem, a new SDD method is proposed based on the finite element model updating technique through combining sensitivity analysis with the Lp (0 < p < 1) norm regularisation. Compared with the classical Tikhonov regularisation, the Lp norm regularisation method can avoid over-smoothness, which is a main difficulty for the Tikhonov regularisation, and its solutions are also more accurate than that by the L1 norm regularisation, another widely used sparse regularisation method. Moreover, the effects of different p-values on SDD results are also studied and discussed. Numerical simulations on a cantilever beam and a simple supported beam, and all the laboratory experiments on a cantilever beam under different assumed damage cases verify the effectiveness of the proposed method. The SDD results show that a good sparse solution is assured via the Lp norm regularisation especially when the value of p ranges from 0.1 to 0.5. In contrast, its accuracy shows a slightly decline when the value of p changes from 0.5 to 1.0. Finally, the results also show that p = 1/2 is the best choice for SDD when using Lp norm regularisation.