Comparative studies on structural damage detection using Lp norm regularisation. (25th June 2019) - Yue, Zhenguang; Chen, Zepeng; Yu, Ling
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 L p (0 < p < 1) norm regularisation. Compared with the classical Tikhonov regularisation, the L p 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 L 1 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 L p 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 L p norm regularisation.