Direct Index Method of Beam Damage Location Detection Based on Difference Theory of Strain Modal Shapes and the Genetic Algorithms Application

Table 1

Damage location indices.

Damage location	Order	Damage degree
		6.25%	12.5%	25%	31.25%
Quarter span	First order
	𝐼SMSD(1)	0.0018	0.0049	0.0111	0.0159
	𝐈𝐒𝐌𝐒𝐃(𝟐)	0.0048	0.0092	0.0197	0.0238
	𝐼SMSD(3)	0.0011	0.0013	0.0114	0.0167
	𝐼SMSD(4)			0.0016	0.0022
	𝐼SMSD(5)			0.0010
	Second order
	𝐼SMSD(1)	0.0162	0.0205	0.0673	0.1003
	𝐈𝐒𝐌𝐒𝐃(𝟐)	0.0202	0.0497	0.1054	0.1647
	𝐼SMSD(3)	0.0137	0.0162	0.0655	0.0997
	𝐼SMSD(4)		0.0127	0.0000078	0.0035
	𝐼SMSD(5)			0.0122	0.0105
	𝐼SMSD(6)				0.0154
	Third order
	𝐼SMSD(1)	0.0787	0.0877	0.1005	0.1335
	𝐼SMSD(2)	0.0110	0.0661	0.1699	0.2660
	𝐼SMSD(3)	0.0457	0.0754	0.0885	0.1821
	𝐼SMSD(4)	0.0544	0.0539	0.0649	0.0644
	𝐼SMSD(5)		0.0701	0.0707	0.0753

Note: overstriking index and overstriking data correspond to damage location.