Mass-Stiffness Combined Perturbation Method for Mode Shape Monitoring of Bridge Structures

Table 4

MAC factors obtained by the MSCP method for different damaged scenarios in the FEM analysis and the laboratory tests.

Damage scenarios		MSCP method
		Mode no.	First	Second	Third	Fourth
FEM analysis	D-1	First	1.0000	0.0003	0.0008	0.0019
		Second	0.0003	1.0000	0.0034	0.0080
		Third	0.0007	0.0033	1.0000	0.0234
		Fourth	0.0019	0.0080	0.0232	1.0000
	D-2	First	1.0000	0.0003	0.0008	0.0019
		Second	0.0003	1.0000	0.0034	0.0080
		Third	0.0007	0.0033	1.0000	0.0235
		Fourth	0.0018	0.0080	0.0230	1.0000
	D-3	First	1.0000	0.0002	0.0009	0.0018
		Second	0.0003	1.0000	0.0035	0.0080
		Third	0.0007	0.0032	0.9999	0.0236
		Fourth	0.0018	0.0079	0.0228	1.0000
	D-4	First	1.0000	0.0002	0.0009	0.0018
		Second	0.0003	1.0000	0.0035	0.0080
		Third	0.0006	0.0031	0.9998	0.0237
		Fourth	0.0018	0.0079	0.0226	1.0000
Laboratory test	D1	First	1.0000	0.0032	0.0029	0.0011
		Second	0.0045	0.9994	0.0830	0.0214
		Third	0.0113	0.0568	0.9909	0.0065
		Fourth	0.0090	0.0269	0.0246	0.9679
	D2	First	1.0000	0.0046	0.0066	0.0055
		Second	0.0045	0.9995	0.0253	0.0225
		Third	0.0114	0.0571	0.9907	0.0166
		Fourth	0.0091	0.0258	0.0539	0.9968
	D3	First	1.0000	0.0082	0.0047	0.0044
		Second	0.0043	0.9995	0.0376	0.0284
		Third	0.0115	0.0503	0.9950	0.0094
		Fourth	0.0091	0.0252	0.0451	0.9939
	D4	First	0.9999	0.0055	0.0047	0.0068
		Second	0.0038	0.9999	0.0292	0.0248
		Third	0.0118	0.0509	0.9940	0.0151
		Fourth	0.0098	0.0260	0.0409	0.9976