Research Article
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 (%) |
| | | | | | | | | | |
| 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 (%) |
| | | | | | | | | | | | | |
| 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
| |
13476 |
11613 | |
26952
|
19915
| |
40121
|
28042
| |
59503
|
39672
| | |
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
|
| | 10−4 |
| w | 1000 | 1000 | 1000 | 10 |
|
|