Health Assessment of Large Two Dimensional Structures Using Limited Information: Recent Advances

Table 2

Stiffness parameter (EI/L) identification for defect 1 using GILS-EKF-UI.

(a) Stage 1: Identification of substructure

Member	Nominal/Theoretical	Identified (EI/L) values in (kN-m) for the substructure
		𝑘15 reduced by 15%		𝑘15 reduced by 30%		𝑘15 reduced by 50%		𝑘15 reduced by 90%
		Identified	Error (%)	Identified	Error (%)	Identified	Error (%)	Identified	Error (%)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
𝑘1	13476	13479	0.02	13479	0.02	13479	0.02	13479	0.02
𝑘4	14553	14556	0.02	14556	0.02	14556	0.02	14556	0.02
𝑘11	14553	14580	0.19	14594	0.28	14613	0.41	14653	0.69
𝑘15	13476	11476	−14.8	9460	−29.8	6766	−49.7	1357	−89.9
𝑘18	14553	14580	0.19	14594	0.28	14614	0.42	14655	0.70

(b) Stage 2: Identification of whole frame

Member	Nominal/Theoretical	Identified (EI/L) values in (kN-m) for the whole frame
		𝑘15 reduced by 15%		𝑘15 reduced by 30%		𝑘15 reduced by 50%		𝑘15 reduced by 90%
		24 DDOFs		24 DDOFs		24 DDOFs		24 DDOFs
		Identified	Error (%)	Identified	Error (%)	Identified	Error (%)	Identified	Error (%)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
𝑘1	13476	13660	1.4	13800	2.4	14022	4.0	14132	4.9
𝑘2	13476	13660	1.4	13604	0.9	13516	0.3	14011	4.0
𝑘3	13476	13403	−0.5	13339	−1.0	13224	−1.9	12015	−10.8
𝑘8	13476	13309	−1.2	13545	0.5	13884	3.0	13338	−1.0
𝑘9	13476	13124	−2.6	12722	−5.6	12037	−10.7	12318	−8.6
𝑘10	13476	13612	1.0	13796	2.4	14257	5.8	15219	12.9
𝑘15	13476	11407	− 15.4	9610	− 28.7	7085	− 47.4	1496	− 88.9
𝑘16	13476	13343	−1.0	12960	−3.8	12372	−8.2	11843	−12.1
𝑘17	13476	13453	−0.2	13197	−2.1	12958	−3.8	10902	−19.1
𝑘4	14553	14850	2.0	15135	4.0	15635	7.4	16068	10.4
𝑘5	14553	14612	0.4	14657	0.7	14757	1.4	15803	8.6
𝑘6	14553	14471	−0.6	14366	−1.3	14096	−3.1	13402	−7.9
𝑘7	14553	14184	−2.5	13952	−4.1	13491	−7.3	12110	−16.8
𝑘11	14553	14558	0.0	14985	3.0	15573	7.0	14642	0.6
𝑘12	14553	14706	1.1	14796	1.7	14743	1.3	14370	−1.3
𝑘13	14553	14929	2.6	14924	2.5	15081	3.6	18502	27.1
𝑘14	14553	14292	−1.8	14098	−3.1	13938	−4.2	13103	−10.0
𝑘18	14553	14682	0.9	15029	3.3	15415	5.9	14668	0.8
𝑘19	14553	14417	−0.9	14477	−0.5	14466	−0.6	15039	3.3
𝑘20	14553	14651	0.7	14847	2.0	15158	4.2	18497	27.1
𝑘21	14553	14905	2.4	14745	1.3	14660	0.7	12948	−11.0
𝐑𝑡𝑘	10^−4
w		1000		1000		1000		10