Structures
1. 2D structure (Rao et al., 2004)
2. 2D structure (Kim, 2013)
3. 3D structure (Kim, 2013)
Test cases
| Structures | 1 (Rao, 2004) | 2 (Kim, 2013) | 3 (Kim, 2013) |
|---|---|---|---|
| Nb. members | 11 | 16 | 36 |
| Nb. nodes | 6 | 8 | 12 |
| Case a | 1a. alpha(i) = 1 | 2a. undamaged (X) | 3a. undamaged (X) |
| Case b | 1b. alpha(3) = 0.7, alpha(6)=0.3 | 2b. alpha(9) = 0.7 | 3b. alpha(5) = 0.6, alpha(13) = 0.7 |
| Case c | 1c. alpha(10) = 0 | 2c. alpha(13) = 0.6 | 3c. alpha(1) = o.7, alpha(21) = 0.5 |
alpha = ones(size(mbs,1),1); % Init and all case A
% alpha(3) = 0.3; alpha(6) = 0.7; % Rao case 1B
% alpha(10) = 0; % Rao Case 1C
% alpha(9) = 0.3; % Kim 2D case 2B >> Wrong
% alpha(9) = 0.7; % Kim 2D case 2B >> Correct
% alpha(5)=0.4; alpha(13)= 0.3; % Kim 2D case 2C >> Wrong
% alpha(5)=0.6; alpha(13)= 0.7; % Kim 2D case 2C >> Correct
% alpha(13) = 0.4; % Kim 3D case 3B >> Wrong
% alpha(13) = 0.6; % Kim 3D case 3B >> Correct
% alpha(1) = 0.3; alpha(21) = 0.5; % Kim 3D case 3C >> Wrong
% alpha(1) = 0.7; alpha(21) = 0.5; % Kim 3D case 3C >> Correct
Objective 1: Damage detection
placeholder for numerical result
- result 1
- result 2
- result 3
Objective 2: With experimental noise
Intoducing 2% and 3% error in frequencies and mode shapes
1a
0.98602774 0.99999537 0.99999659 0.97790755 0.99529354 0.99999459 0.99999926 0.99999993 0.99999994 0.99951465 0.99999964
0.99999769 0.97869903 0.99999841 0.98441354 0.99061495 0.99999700 0.99999860 0.98643643 0.99476770 0.99999946 0.97696022
0.99999990 0.99999521 0.99813132 0.99999690 0.99999977 0.99999967 0.99999974 0.99999445 0.99999874 0.99999994 0.99999810
1.00000000 0.99999996 0.99999980 0.99999989 0.99999920 0.99999891 0.97561556 0.99999946 0.99999417 0.99999990 0.99999043
0.99999993 0.97590535 0.99583471 0.97339347 0.98021801 0.98011224 0.97708295 0.99998244 0.97261923 0.99998954 0.97828362
1b
0.99999992 0.99997251 0.29716514 0.99999995 0.99999946 0.68390794 0.93840275 0.99999910 0.99999983 0.99999594 0.96438564
0.99999999 0.99999955 0.29995739 0.99999906 0.99999966 0.70528334 0.98018799 0.99999999 0.99999482 0.99999998 0.99999890
0.99999987 0.99999997 0.30279037 0.99992235 0.99045979 0.71398673 0.99999828 0.99608873 0.98597680 0.98660262 0.99999566
0.97082634 0.99999979 0.29652679 0.99999998 0.99400867 0.69516530 0.93568642 0.99999991 0.99999953 0.99999997 0.98930952
0.99999894 0.99999926 0.29872920 0.99999985 0.99808212 0.67661343 0.95543034 0.99999886 0.99018471 0.99999980 0.98653848
1c
0.99999999 0.99999981 0.99324331 0.96758383 0.99207263 0.99999995 0.99999815 0.99999936 0.99999979 0.00526743 0.96793524
0.99280398 0.99999677 0.99998397 0.99999917 0.99999866 0.99516414 0.99999232 0.99999963 0.99491477 0.00066950 0.99999985
0.98058810 0.99999991 0.99445604 0.99610331 0.99999872 1.00000000 0.99999994 0.98985805 0.99202538 0.00000133 0.99999900
0.99999770 0.99572150 0.99999309 0.99999987 0.99444005 0.99999995 0.99999946 0.99999746 0.99007390 0.00890209 0.97991378
2b
0.99033274 0.99999994 0.99979286 0.99999841 0.98499279 0.99507554 0.99999875 0.99999926 0.69959041 0.99416776 0.99053050 0.99555828 0.99999992 0.99999852 0.99999984 0.99999935
0.99999719 0.98122961 0.99999993 0.99963661 0.99999569 0.99999998 0.97968871 0.99883320 0.69882062 0.99999882 0.99999970 0.99999974 0.97812610 0.98586483 0.99999956 0.99554702
0.99999218 0.99999979 0.99999858 0.99999921 0.99999924 0.99999972 0.99212473 0.98456048 0.68958808 0.99998818 0.99999895 0.99999961 0.99999959 0.99999964 0.99999764 0.99999999
0.98731508 0.99260911 0.99999902 0.99999996 0.99999932 0.99999967 0.99401181 1.00000000 0.70242891 0.99760689 0.99999960 0.99127127 0.99999990 0.98839435 0.99999575 0.98723457
0.96043265 0.98754251 0.98471883 0.99915065 0.99870121 0.99999978 0.99999973 0.99999799 0.69540866 0.99057611 0.98689594 0.99998871 0.99999955 0.99999554 0.99999997 0.98735809
2c
0.99999952 0.99999986 0.99999565 0.99579418 0.60104796 0.99188636 0.99480870 1.00000000 0.99999970 0.99087411 0.99329587 0.98629785 0.70780523 0.99255558 0.99999985 0.97552356
0.99999957 0.97821994 0.99813586 0.99999847 0.59106479 0.99932839 0.99705954 1.00000000 0.99714356 0.99506400 0.99999938 0.99999942 0.71443390 0.99464713 0.99773248 0.99842577
0.99930661 0.99999981 0.99999996 0.99999931 0.59153941 0.99999982 0.99104153 0.99081575 0.99999593 0.98677714 0.99725024 0.99999789 0.67643222 0.97864347 0.99999592 0.99999993
0.99949465 0.99998485 0.99999987 0.99999984 0.59231571 0.99999957 0.99999875 0.98975366 0.98914152 0.99505058 0.98059486 0.99999938 0.69280754 0.99999995 0.97849973 0.99499560
0.99999990 0.99446805 0.99999986 0.98939098 0.60295792 0.99124378 0.99999463 0.99999849 0.99999983 0.99999931 0.99999967 0.97203054 0.70249916 0.99999839 0.99999972 0.99502817
3b
0.98346770 0.99999631 0.99999996 0.99999993 0.98602208 0.99998649 0.99999992 0.99999984 0.99999989 0.98986443 0.98489964 0.99999972 0.61216722 0.99999674 0.99030815 0.97977661 0.97985580 0.99999996 0.98226962 0.99999889 0.99999950 0.99127383 0.99876988 0.99634170 0.99738216 0.99999874 0.99999984 0.99999998 0.99999972 0.99999987 0.97474908 0.99999921 0.99999737 0.99999979 0.99480509 0.99999529
0.98865093 0.98039195 0.99999852 0.98697344 0.99999996 0.99999970 0.99999932 0.99999377 0.99999268 0.97984276 0.99999987 0.99999965 0.59778632 0.99999998 0.99999993 0.99999273 0.99999999 0.99999628 0.99999980 0.99449693 0.99999983 0.99175973 0.98307132 0.99999829 0.99999997 0.99999429 0.99999870 0.99999275 0.99152336 0.99999358 0.99999924 0.99999759 0.99999972 0.99999980 0.99999997 0.99999894
0.99999933 0.99999806 0.99999978 0.99999900 0.99999932 0.99999991 0.99999765 0.99999851 0.99999994 0.99999983 0.99999963 0.99999991 0.59974622 0.99999984 0.99999892 0.99999853 0.99999926 0.99998846 0.99999915 0.99999940 0.95688503 0.99999962 0.99743582 0.99999066 0.99783362 0.99999803 0.99999997 0.99999990 1.00000000 0.99999991 0.99999876 0.99999962 0.99999989 0.99999951 0.99999618 0.99999777
0.99999959 0.98424928 0.99969984 0.98896048 0.98697410 0.99999928 0.99999966 0.99999895 0.99999848 0.99294177 0.99999936 0.97888545 0.60769903 0.99892572 0.99999613 0.99999582 0.99346307 0.99380529 0.99999980 0.99999442 0.99999997 0.98912000 0.99999983 0.98677364 0.99999825 0.99999998 0.99998685 0.99999575 0.99999942 0.99502999 0.98431444 0.99999987 0.99853815 0.99201875 0.98580379 0.99999940
0.97548955 0.99999984 0.99999926 0.99999596 0.99999977 0.99999781 0.99417957 0.99999994 0.99999751 0.99818731 0.99999184 0.99999937 0.60013862 0.99999802 0.99999717 0.99997221 0.97981988 0.99999641 0.99999886 0.99999985 0.99999999 0.99999972 0.99999665 0.99997424 0.99999359 0.97358281 0.98757369 0.99999972 0.99999998 0.99999213 0.99999971 0.99999979 0.99999975 0.99999822 0.99999923 0.99999960
3c
0.70378826 0.99182466 0.99999848 0.98631520 0.99379132 0.98787283 0.99999974 1.00000000 0.99999953 0.99460063 0.99313320 0.99999988 0.99999186 0.99366123 0.99309125 0.98579416 0.98758677 0.99999998 0.99999566 0.96493946 0.47308704 0.99658780 0.99999997 0.99999735 0.99999967 0.99042080 0.99998820 0.99999991 0.99999993 0.99999997 0.99101219 0.99999999 1.00000000 0.99999952 0.99999967 0.99999944
0.70571863 0.99999956 0.99999989 0.99999843 0.98604550 0.99999867 0.99999983 0.99999751 0.99999949 0.99999996 0.99999851 0.99825982 0.99470476 0.99185044 0.99999813 0.98455601 0.97431656 0.99966822 0.99999956 0.99999944 0.50486037 0.99999972 0.99999992 0.99999967 0.99999941 0.96760136 0.98098869 0.99999998 0.99694844 0.99999872 0.99999945 0.99681778 0.98388754 0.99999881 0.99999940 0.99200666
0.71966949 0.99999768 0.99999983 0.99998933 0.99999963 0.99999943 0.99999723 0.99999999 0.99999932 0.99999991 0.99999794 0.99998727 0.99999919 0.99798056 0.99999995 0.99999790 0.99999951 0.99999687 0.99371099 0.99999972 0.52434768 0.99999936 0.99999995 0.99999998 0.99999855 0.99999938 0.99999951 0.99498481 0.99999964 0.99999873 0.99999980 0.99999982 0.99999974 0.99913401 0.99999965 0.99999786
0.69977279 0.99999983 0.99999936 0.99999688 0.98059629 0.99999721 0.99999999 0.99998195 0.99999696 0.99999926 0.99999975 0.98452045 0.99999928 0.99999971 0.99999939 0.99999840 0.99999975 0.99999925 0.99999572 1.00000000 0.51996030 0.98647055 0.99999702 0.99999728 0.99248321 0.99633691 0.99999968 0.99999992 0.99999920 0.99999961 0.99999728 0.99999903 0.99999797 0.99999952 0.99029455 0.99999951
0.70060791 0.99399114 0.98928364 0.99046030 0.99999813 0.99769043 0.99999980 0.99999564 0.99999989 0.99999300 0.99999329 0.99999984 0.99828859 0.99999965 0.99999980 0.99688524 0.98569001 0.99999956 0.99532056 0.99393617 0.48040683 1.00000000 0.99999969 0.99502272 0.99415969 0.99999997 0.99999712 0.99999913 0.99999910 0.99999600 0.98795462 0.99999797 0.99999974 0.99999957 0.99999948 0.99999943
0.69529678 0.99998826 0.99445465 0.99999948 0.97383870 0.99014956 0.99999879 0.97691440 0.99247995 0.99999748 0.99863624 0.98319432 0.99923687 0.98816625 0.99749535 0.99325272 0.99941518 0.99607116 0.99103788 0.99999960 0.51075809 0.98636846 0.99999914 0.99999582 0.99999516 0.99999572 0.99999998 0.99999999 0.99998977 0.99999822 0.99499407 0.99999488 0.99999906 0.99324839 0.98374103 0.99999996
0.70404018 0.99999408 0.98897026 0.99999923 0.99999997 0.99999958 0.99999998 0.99999836 0.99999725 0.99999934 0.98703286 0.99999941 0.99999972 0.99999759 0.99999826 0.99999908 0.99044870 0.99950339 0.99159538 0.99965165 0.49273733 0.97169305 0.99999643 0.99999860 0.99999766 0.99999689 0.99999995 0.99999660 0.99999890 0.99999993 0.99999895 0.99999906 0.99999794 0.99396075 0.99311455 0.98230861
0.69840631 0.99900096 0.99719322 0.99999997 0.99171231 0.99999844 0.99540081 0.99999943 0.99682402 0.99266943 0.99999973 0.99999987 0.99546463 0.99999180 0.99999698 0.98439768 0.97072566 0.97253911 0.98951435 0.95666007 0.49745246 0.98975430 0.97037588 0.99999994 0.99998823 0.99999997 0.96544712 0.99999889 0.98725228 0.99999963 0.99999965 0.98330103 0.99999941 0.99999994 0.98045065 0.99434935