Experimental Study of an Adaptive Sequential Nonlinear LSE with Unknown Inputs for Structural Damage Tracking

Table 1

Identified results for all cases.

Case	Parameter	𝑐1	𝑐2	𝑐3	𝑐4	𝑘1	𝑘2	𝑘3	𝑘4	𝛽	𝛾
	Ref. values	—	—	—	—	50.9	53.4→45.9	50.6→46.1	55.4	0.5	0.5
Case  1	Identified	0.37	0.14	0.13	0.42	47.79	55.16→46.82	47.85	56.87	0.57	0.44
	Deviation (%)	—	—	—	—	6.11	3.30, 2.00	3.80	2.65	13.20	11.40
Case  2	Identified	0.24	0.23	0.10	0.46	46.32	48.65	51.03→44.78	54.28	0.64	0.34
	Deviation (%)	—	—	—	—	9.00	5.99	0.85, 2.86	2.02	27.80	32.80
Case  3	Identified	0.26	0.16	0.12	0.41	49.53	55.11→49.70	53.49→47.77	58.44	0.55	0.44
	Deviation (%)	—	—	—	—	2.69	3.20, 8.28	5.71, 3.62	5.49	9.00	12.00
Case  4	Identified	0.17	0.12	0.17	0.61	47.69	53.94→46.99	51.17→49.88	55.41	0.35	0.37
	Deviation (%)	—	—	—	—	6.31	1.00, 2.37	1.13, 8.20	0.02	31.00	26.20

𝑐_𝑖 unit: kNs/m; 𝑘_𝑖 unit: kN/m (𝑖=1,2,3,4).