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

Table 4

Stiffness parameter (EI/L) identification for defect 3 using GILS-EKF-UI.

4 (a) Stage 1: Identification of substructure

Member	Nominal/Theoretical	Identified (EI/L) values in (kN-m) for the substructure
		Locating the defective member		Additional node at mid-span of		Additional node at 3.07 m right of		Additional node at 2.07 m right of
				member 16		node 10		node 10
		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	14564	0.08	14563	0.07	14563	0.07	14564	0.07
k15	13476	13486	0.08	13486	0.07	13486	0.07	13486	0.07
k18	14553	14564	0.08	14563	0.07	14563	0.07	14564	0.07

4 (b) Stage 2: Identification of whole frame

Member	Identified (EI/L) values in (kN-m) for the whole frame
	Locating the defective member			Additional node at mid-span of			Additional node at 3.07 m			Additional node at 2.07 m
				member 16			right of node 10			right of node 10
	24 DDOFs			30 DDOFs			30 DDOFs			30 DDOFs
	Nominal/Theoretical	Identified	Error (%)	Nominal/Theoretical	Identified	Error (%)	Nominal/Theoretical	Identified	Error (%)	Nominal/Theoretical	Identified	Error (%)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
k1	13476	13387	−0.7	13476	13581	0.8	13476	13611	1.0	13476	13265	−1.6
k2	13476	13430	−0.3	13476	13608	1.0	13476	13496	0.1	13476	13472	0.0
k3	13476	13917	3.3	13476	13435	−0.3	13476	13600	0.9	13476	13691	1.6
k8	13476	13076	−3.0	13476	13233	−1.8	13476	13552	0.6	13476	13382	−0.7
k9	13476	14418	7.0	13476	13331	−1.1	13476	13126	−2.6	13476	13577	0.8
k10	13476	12863	−4.5	13476	13215	−1.9	13476	13332	−1.1	13476	13446	−0.2
k15	13476	13157	−2.4	13476	13210	−2.0	13476	13505	0.2	13476	13208	−2.0
𝑘16a	13476	11613	−𝟏𝟑.𝟖	26952	19915	−𝟐𝟔.𝟏	40121	28042	−𝟑𝟎.𝟏	59503	39672	−𝟑𝟑.𝟑
𝑘16b				26952	30381	12.7	20292	21220	4.6	17422	17135	−1.6
k17	13476	13649	1.3	13476	12798	−5.0	13476	13044	−3.2	13476	13251	−1.7
k4	14553	14227	−2.2	14553	14856	2.1	14553	14840	2.0	14553	14110	−3.0
k5	14553	14178	−2.6	14553	14813	1.8	14553	14621	0.5	14553	14325	−1.6
k6	14553	14616	0.4	14553	14310	−1.7	14553	14317	−1.6	14553	14746	1.3
k7	14553	15543	6.8	14553	14508	−0.3	14553	14770	1.5	14553	14944	2.7
k11	14553	14316	−1.6	14553	14609	0.4	14553	14931	2.6	14553	14560	0.0
k12	14553	15107	3.8	14553	14960	2.8	14553	14871	2.2	14553	15329	5.3
k13	14553	14351	−1.4	14553	15139	4.0	14553	14689	0.9	14553	14338	−1.5
k14	14553	14509	−0.3	14553	13495	−7.3	14553	13788	−5.3	14553	14374	−1.2
k18	14553	14620	0.5	14553	14300	−1.7	14553	14522	−0.2	14553	14518	−0.2
k19	14553	14863	2.1	14553	14683	0.9	14553	14653	0.7	14553	15198	4.4
k20	14553	13709	−5.8	14553	14840	2.0	14553	14565	0.1	14553	14458	−0.7
k21	14553	15137	4.0	14553	14389	−1.1	14553	14604	0.4	14553	14376	−1.2
𝐑𝑡𝑘	10^−4
w	1000			1000			1000			10