Journal of Science and Technology.-N. 166(2-2015) - Mililary University of Science and Technology
SU* DUNG THUAT TOAN DE TINH TOAN TOI UtJ KET CAU CHAN DE CONG TRINH BIEN VA DANH GIA D Q TIN CAY
CUA KET QUA BANG MO PHONG MONTE - CARLO
Nguyen Qudn Thdng ; Hodng Mgnh Khang, Biii Due Ndng Bai bao trinh bay hifu qua ap dung thu^t toan tiln h6a vi phSn (Differential Evolution - DE) giai bai toan tii uu k^t ciu chan dl cong trinh biln vai trgng lugng circ tigu. Dii lugng nghiSn cu-u la chan dl ciia mpt trong c^c c6ng trinh DKI da dugc xSy dyng. Tai trgng moi truimg khi thilt kl tii uu cQng nhu khi kilm tra theo TCVN 6170-3:1998 co tham khao tieu chuSn ciia API RP 2A-WSD 2005. Kit qua cua phucmg an thifit kl va phuong An tii uu dtrgc danh gia ve gioi han d6 tin cJiy bAng phucmg phSp mo phong Monte - Carlo 1. Dat van de
Phin chan dk eua cac cdng trinh biln cd dinh la bp phan rit quan trpng, day la ket ciu do toan bp phin thugng tang va chju tae dpng Hen tue cua mdi trudng. Chan de ciing la phin chiem ty trgng Idn trong gia thanh toan bp cdng trinh, do vay viec hoach dinh kit ciu chan dl hgp ly cd y nghia kinh tl ky thuat cao d tat ca cac budc thiet ke.
Tir trudc den nay, qua trinh nay dugc tien hanh theo phuang phap "thii - sai". Do tinh phiic tap cua bai toan nen viec so sanh lira chpn chi thuc hien trong mgt vai phuang an, ket qua cung vi the ma han che va phu thugc nhieu vao kinh nghiem cua can bg thiet ke.
Cae tai lieu nude ngoai [2, 3, 4] da cdng bd mpt sd ket qua nghien ciiu thiet ke toi uu ket cau chan de cae cdng trinh bien cd djnh trong ITnh vuc khai thac dau khi, tram phat dien gid... Trong dd, cac tac gia da dung mpt sd thuat toan tdi uu nhu quy hoach phi tuyen, phuong phap nhan tir Lagrang, thuat toan di truyln... Tuy vay, viee ling dung nhiing ket qua nghien ciiu nay cho tinh toan cdng trinh cu thi edn gap nhilu khd khan.
Tren co sd ket qua nghien ciru trudc day [8], cae tac gia lua chgn sii dung thuat toan tiln hda vi phan DE giai bai toan tdi uu vl trgng lugng cho phuang an chan dl cong trinh bien vdi hinh dang da dugc thiet kl. Vi du tinh la md hinh chan dl cdng trinh DKI da dugc xay dung tren cac bai san hd ngim cua vung bien Trudng Sa.
2. Xay dung bai toan toi u'u chan de cong trinh bien
v l ly thuyet, mgt phuang an tdi uu kit ciu diy du phai dam bao tinh tdi uu vl ciu true ve hinh dang va tilt dien ngang, bai toan tdi uu kit ciu theo tilt dien ngang thuong [ B T L Cong binh.
" Hpc vien KTQS.
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Tgp chi Khoa hgc vd Ky ihudt.-Sd 166(2-2015) - Hgc vien KTQS
duge giai sau khi phuang an hinh dang va cau tnic da dugc lira chgn. Viec giai ddng thdi vdi ba muc tieu tr6n g$p nhilu khd khan nen thdng thuong tirng bai toan dugc giai mgt each dgc lap. Trong [2, 5, 6], cac tac gia thuong tap trung vao giai bai toan tdi uu tiet dien ngang vdi cae dieu kien rang budc khac nhau. Vdi ket cau he thanh, bai toan dugc viet dudi dang chung:
Cue tieu hoa ham: W(x)= ^p^.AJ, (1)
vdi cac dieu kien rang budc: gj =Cj-Cj > 0
trong dd, W - trgng lugng toan bg ket can; p, - ty trgng cua vat lieu lam p h i n tii /;
A, ' dien tich mat cat ngang ciia phan tii thanh (cae bien thiet ke i =1 -^ n); I, - chieu dai ciia phan tir; n - tong sd phan tii trong ket can; gj - bieu diln cac dieu kien han che v l hinh hpc hoac eo hgc; Q - trang thai cho phep eua cae dieu kien rang bugc; C, - trang thai thuc ciia ket cau dang xem xet.
Cac dieu kien rang bugc cua bai toan (1) dugc hieu la nhiing gidi ban ve eo hgc, hinh hpc va cong nghe. Ciing cd the tir nhiing dac diem rieng khi thi cdng ma xuat hien nhung yeu cau ve cau tao va nhiing rang budc rat chat che ve mat hinh hpc. De Idi giai bai toan tdi uu la kha thi, trong thuc te phai xem xet ky nhung dieu kien rang huge nay eiing vdi nhung rang bugc dam bao an toan khi su dung.
* Cdc dieu kien rdng bugc:
+ Dieu kien rang bugc vdi tiet dien (kich thudc ngang) cua cac phan tir:
A,^D{A,) (2) D la mien cho phep cua tiet dien ngang, dugc xae
dinh bdi tat ca cac gia trj eo thS chgn, eo the la mien lien tue hoac mien gdm cae gia tri rdi rac.
Mgt dac diem rieng khac ciia chan de cdng • trinh bien ed dang nhu hinh 1 la khi thi cdng he cgc dugc long vao dng chan de trong qua trinh ddng. Do vay, dudng kinh ngoai cua cgc (D„c) phai nhd ban dudng kinh trong ciia dng chan d l (Died) hay:
D - A = D n i ^ " ^ ^- ^dfgket cdu chdn de dien hinh cua cdc trgm dich vu DKI dirge vdi A - khoang hd cdng nghe cin thilt. xay dmg vdo nhOng ndm 1990
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Journal of Science and Technology.-N. 166(2-2015) - Mililary University of Science and Technology
Tliuc tl, kieh thudc eac 6ng ed the lira chgn la mgt danh sach dinh sin (theo API [5]).
Do vay, bai toan (1) se dugc giai vdi cac bien rdi rgc va dilu kien cdng nghg (3).
+ De cdng trinh boat dgng an toan, he ket cau va cac phin tu phai thda man cac dieu kien rang bugc ve ben ciing nhu do eiing tdng the.
- Dieu kien ben: o, < [a]; f = 1 ^ w (4) trong dd, cr,;[o-] lan lugt la ling suat tinh toan va ling suat cho phep; n la sd phan tir
eua he.
- Dilu kien cimg: (A^,Aj,,A.)^ <[A\;j = \-^m (5) trong do, ( A ^ , A J , , A . ) ^ ; [ A J lan lugt la chuyen vi theo cac phuong tai niit thiiy va
chuyen vj cho phep; m la tdng sd niit cua he ket cau.
- Dilu kien 6n dinh: N, < [A^,"' ]; (" ^ U « (6) trong do, A',;rjV,'''1 lan lugt la luc nen va luc nen tdi han cho phep trong phin tir thii /
(tinh theo Ole chi cho cac phin tii chju nen).
De cd dugc thdng tin xii Iy cac dilu kien rang huge tren, ta tiln hanh phan tich kit can bing phuong phap phin tu hiiu ban (PTHH) cd nghia la giai he phuang trinh sau:
W{«} = {f} (7) vai [K]; {«}; {f} lin luat la ma tran dp cilng, vecta chuySn vi mit, vecta tai cua he
ket cau.
Klii giai he (7) se nhSn dugc ngi luc trong tung phin tu, chuySn vi a tit ca cac nut va nhu vay, co thS chgn dugc cac phuong an "cho phep" vS mat co hgc. Trong nhi6u bai toan toi uu ket ciu he thanh da dugc giai, vecta tai {F} thuang dugc xem nhu khong doi trong toan bg qua trinh tinh toan t6i uu khi bo qua trgng lugng ban than cua k6t ciu.
Tuy nhien, vol cong trinh biSn vecta tai {F) thay d6i a timg buoc lap khi giai bai toan toi uu. Su thay doi nay thu nhit do tinh dgn trgng lugng ban than, thu hai do tai trgng song va dong chay phu thugc vao kich thuoc tiSt dien cua cac phin tu ngap nuac [7].
3. T h u a t toan DE voi bien l<hdng lien tue
Thuat toan DE trong truang hgp cac biSn dgc lap la thuc va lien tuc da dugc trinh bay tai nghien cuu [8]. Tren ca sa sa do nguyen ly tuong tu, sau day trinh bay m6t phien ban khac cua thuat toan DE vol bidn khong lien tuc, ngi dung nhu sau:
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Tgp chi Khoa hgc vd Ky ihudt.-SS 166(2-2015) - Hgc vien KTQS
a. Xay dirng qudn thi ban dau
[X\g=j dugc xay dung ngiu nhiSn trong mien cho phep eiia eac bien dgc lap theo cdng thiic:
x^ = mt(rand(OA)*(n^,„„J)+\ (8) trong do, x,j - b i l n y ciia ea the i thugc quan the [X] vdi / = 1 , 2 , . . . , np (np - tdng sd
eac ea t h e ) ; / = 1, 2,..., nx (nx - tdng sd cae bien); int() - lay phan nguyen cua bieu thiie trong dau ngoae; rand{0,\) - sd ngau nhien phan bd deu trong khoang (0,1); nchoose - so kha nang lua chgn theo danh sach.
Nhu vay, theo (8), Xy ludn nhan mgt each ngau nhien cac gia trj trong [1, ndwose]- b. Dot bien
Toan tii dot bien se tao ra quan the \y\g tir [X\g theo cdng thirc sau:
v^^ =x„,^ + i n t ( f *(x,,^^ -^.2.j)) (9) vdi F - he sd td hgp sai sd F={Q, 1.0) va i ?^ro ^ri ^r2', i - chi sd xac dinh ca the thii /
trong quan the mdi [ V\^., TQ, ri, r2 - chi sd eua ba ca the dugc chpn ngau nhien trong quSn the \X\g.
c. Lai ghep
Tren co sd hai quan the [X\g va [V\g tien hanh lai ghep theo cdng thiic (10), ta dugc quan the mdi [U]g .
v„; if randiO, I) < C„ or j = rand(nx)
" » = , . • ' ' " '
x^j; otherwise
dday, C^ = (0,1) -xac suat lai ghep; rand(nx) -sd ngau nhien phan bd dSu trong tap [J, nx], d. Chgn Igc
Tren co sd hai quSn the [X\g va {U\g tien hanh chgn loc theo cdng thiic (11), ta duge quan the {Y\g bao gdm eac ea thS ed gia trj ham nhd ban,
if f{u,^)<f{x,^) otherwise
e. Tdi sinli
Thuc hien phep gan {X\gt, = [Y]g ta dugc thS he he moi. Qua trinh tiSn hoa se lap lai tir buac 1 cho dSn khi dilu kien dirng (11) thoa man.
/ Biiit liien dirng
Dilu kien dimg cua thuat toan DE dugc xay dung theo bilu thiic:
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Journal of Science and Technology.-N. 166(2-2015) - Military University of Science and Technology
lip
eps- -IMIIX^) (12)
4. Ket hop thuat toan DE vol phuong phap phan t\x huu han giai bai toan to! u'u ket can chan de cong trinh bien
Tuong tu cae thuat toan tii uu riln hda khac, thuat toan DE thuc hien cac toan tir dot bien, lai ghep, chpn Igc, tai sinh tren mgt tap eac ca thS thda man cac diSu kien rang budc. Vdi bai toan tdi uu kit ciu la mpt tap cac phuang an ket cau thda man tat ca cae dilu kien (1)^(6). Npi dung su dung thuat toan DE va phuang phap PTHH de giai bai toan tdi uu kit ciu chan dl cdng trinh bien ^VKJC trinh bay tren hinh 2 bao gdm 6 bude, trong dd ein luu y kilm tra tinh dugc phep eiia tirng ea the (KTTDP) tai cae bude 2, 3 va 4 vdi thii tiic KTTDP eiia phuang an theo so dd hinh 3.
C KT i n i > - Kwm tiu Huh diim plii-p L »a iiiiin cu ilu-)
Hinh 2. Sa dd thugt todn gidi bdi todn tdi iru ket cdu
Khi kiem tra tinh duge phep cua mgt phuang an ket cau, trudc tien phai dam bao eac bien thiet ke hay cac loai tilt dien cua mgt phuong an phai thda mSn eac dilu kiSn gidi ban (2) va (3). Sau dd, thdng qua ba khdi tinh toan chinh.
148
Tap chi Khoa hoc va Ky thuat -Sd 166(2-2015) • Hoc vien KTQS
Truac hit, phai xay dung lai vecto tai ma trong do tai trgng song va dong chay dong vai tro chu dao. Ap dung ly thuylt song Stock bac 5, phuang trinh Morison [1] vai cac he s6 Cd. Cm iiy theo chi din cua API [5] c6 ke den mirc do ha bam.
Bitn hiet ke ( MOt ci the mdi)
Tint) iai tai trong song va dung chay cho phirong an ket cau mdi
- Cac tlioiig so ktit cau - Dieu kien moi tririnig bien
• Cac tru6iig hop tui trong (kliung doi 6 mui p/a ket cau)
• Tieu chuan kiem tra.
Phan tich ket cau b^ng phuung phap PTHH
I'hu'uiig an khong duuc phep Quay lai tim phuoiig an mdi
Hmh 3. Cdc budc kiem tra tinh dugc phep ciia phuang dn ket cdu
Phan tich tTnh he ket eau bang phuong phap PTHH duge viet cho he thanh khdng gian cd bac tu do d mdi nut bang 6. Ket qua cho chuyen vi nut va ngi luc trong timg phan tir. Sii dung ket qua phan tich ket cau kiem tra cac dieu kien rang bugc theo cac bieu thirc (4), (5) va (6) h-en co sd quy djnh cua TCVN 6170-3:1998 va tieu chuin API RP 2A-WSD 2005 [5]. Ket qua sau thii tue nay cho biet phuong an cd dugc phep hay khdng.
S . V i d u t i n h
De lam ro hon nhiing ngi dung da trinh bay, ta xet mgt bai toan cu the. Hinh 4 la so do ket cau ciia mgt dang chan d l DKI da duge xay dung vao nhung nam 90 the ky XX.
(^
A L S L
1 '5^
O)
^) © / ® 1 a
i 1
Hinh 4. SaM tinh ctia niQt dgng kit cau chan de diin htnh
Journal of Science and Technology.-N. 166(2-2015) - Military Umversity of Science and Technology
Chan dl hinh chop cut voi do nghiSng cac 5ng chinh la 1:12,7. T6ng chieu cao chan dl (tinh tir day biln) la 26,3 m. Cac phin tit dugc chia thanh 5 nhom tiet dien:
Nhom 1 - cgc; Nhom 2 - 6ng chinh cua chan de; Nhom 3 - cac phin tic lien ket a khoang 1;
Nhom 4 - cac phin tir lien kit o khoang 2; Nhom 5 - cac phin tu lien kit 6 khoang 3.
Dilu kien moi truong biln: Chieu sau nuac tinh 15 m; chilu cao song co nghia Hs = 8,58 m; chu ky cit khong To= U s; chilu cao song a trang thai sir dung Hs = 11,7 m;
• chu ky song T = 12,27 sec; dong chay mat 3,2 m/s; dong chay day 1,7 m/s.
Tai trgng do phin thugng ting tac dung ISn khIi chan de: Theo phuang thing dirng Pz = 305500 kg; theo phuong nim ngang P^ = 34530 kg.
Tinh vol so do ngam co chilu sau ngam kh6ng d6i liy bing 2 m so voi day biln.
Bang cac loai duong kinh 5ng dugc lira chgn g6m 22 loai ca ban theo tieu chuin Ing API CO kich thuoc (duang kinh D x chilu day 5) tit 273x18,26 din 1422,4x31,75.
Ci phuong an thilt kl, cgc da dugc tang cuong them bang mgt 6ng long (1)530x12.
Cac tham s6 dilu khiln sir dung khi giai bai toan toi uu: So bien dgc lap (so nhom tilt dien) nx = 5; S6 ca thi (s6 phuang an) trong quan the np = 25; He so to hgp sai so F = 0,25; Xac suit lai ghep Cr = 0,75. Cac dang tilt dien da sur dung khi thilt ke va kit qua sau khi giai bai toan toi uu cho a bang 1.
Bang 1. Ket qud linh todn lira chon tiet dien cdc nhom phdn tir vd tong trpng lucmg ctia chdn de Cac phirang an
Phuang an thiet ke Phuong an bai toan toi uu
Nhom 1 720x32 720x20
Nhom 2 812x20,63
863x25,4 Nhom 3 609,6x24,4
406x17,5 Nhom 4 508x19,08 355x12,7
Nhom 5 377x12,0 323x12,7
G(Tan) 121,0 95,03
Chuong trinh viet bang ngon ngir C'*'^ hgi tu sau 35 the he trong khoang thai gian tit 1,5 din 2 phut.
6. Banh gia do tin cay cua hai phuwng an
6.1. Phu'&ng phdp mo phong Monie - Carlo ddnh gid do tin cay kit can chdn di Chan de cong trinh bien la mgt he ket cau phiic tap, chiu tac dgng thuang xuyen cua song bien. Trang thai dugc xem xet khi danh gia do tin cay chinh la nhirng phan irng ciia timg phan tu ddi voi tai trgng tac dgng. Trgng [6, 7] trinh bay nhilu phuang phap danh gia do tin cay cua phin til va he thdng. Vcri he kit cSu philc tap, trang thai dugc phan tich thong qua phuang phap PTHH thi phii hgp nhit la sii dung phuong phap mo phong Monte - Carlo. Ngi dung cua phuang ph4p khi ap dung cho doi tugng la chan de cong trinh bien c6 thi torn tat nhu sau:
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Tap chi Khoa hoc vd Ky thudl.-So 166(2-2015) - Hgc vien KTQS
1) Chuin bj cac sd lieu ban diu: Sd lieu vl kit cau, nhiing sd lieu can thiet ve moi trudng biln d khu vuc xay dung cdng trinh. Cac thanh phin tai trgng khdng mang dac tinh ngiu nhien. Sd liSu vl tinh chit eo hge eiia vat lieu va dac tinh ngiu nhien eua eac dai lugng nay. Cho sd Ian thii nghiem n,esi.
2) Md phdng trang thai bien ngau nhien theo pho sdng P-M, xac djnh chieu cao sdng cue dai va chu ky sdng tuong img T cua trang thai bi6n dang xem xet. Tinh tai trgng sdng tac dung len cdng trinh theo cac ly thuyet sdng da biet.
3) Td hgp tai trgng theo tieu chuan, phan tich ung x\x eiia ket cau chan de theo eac sd lieu da cd tir bude 1 va 2.
4) So sanh trang thai chuyen vi eua eac niit, trang thai ben, dn dinh cua mdi phan td vdi trang thai cho phep. Ghi lai nhung trudng hgp hu hdng eua moi nut va mdi phan tu n/,.
5) Kilm tra sd lin thir, nlu chua dat quay lai bude 2, neu thda man chuyen sang budc 6.
6) Xir Iy sd lieu da cd, xac dinh xae suat pha hdng ddi vdi timg phan tir P.- = —^.
Vdi ea he kit ciu, gidi han tren va gidi ban dudi cua xac suat an toan duge xac djnh:
MaxP^^={\-MaxPj,) (13)
MinP,,=Y[[\-Pi) 04) vdi Pss - xac suit an toan cua he; Pfi - xac suat hu hdng cua phan tu.
6.2. Danh gid do tin cay cua hai phirang dn
Tir chuang trinh danh gia gidi ban do tin cay ciia he kit ciu da cd [8], duge phat trien ddi vdi kit ciu chan dl cdng trinh bien. Hai dai lugng ngau nhien cd tac dgng nhieu nhat din do tin cay cua kit ciu cdng trinh bien la gidi ban chay eiia vat lieu va tai trgng sdng bien da duge xir ly trong qua trinh sir dung phuang phap md phon"
Monte - Carlo. Kit qua tinh cho d bang 2.
Bdng2. So sanh giai hgn dg tin cdy cua hai phuang dn (n,eti=10.000 Idn)
Cac thong so Phuang an thiet ke Phuang an toi uu
Huong chinh dien PsMax (%)
98,63 100
P.M,«(%) 97,52
100
Huong 45°
P.M„(%) 96,72 99,94
PsMiiiC/o) 96,53 99,94
Journal of Science and Technology.-N. 166(2-2015) - Mililary University of Science and Technology
7. Ket luan
- Bing each ket hgp thuat toan tien hda vi phan DE vdi phuong phap PTHH va tren co sd thu tuc thiet ke cong trinh bien, da xay dung dugc p h i n m I m giai bai toan tdi uu tilt dien ngang ket cau chan de vdi trgng lugng cue tilu.
- Phuang an tdi uu da giam 21,4% trgng lugng cua khdi chan de, giam tai trgng ngang theo hudng chinh dien do song va ddng chay gay ra 18,2% (3340 kN & 2987 kN).
Dieu nay dan tdi viec giam nhe tai trgng len h^ cgc, tang do tin cay cua he ket cau.
- Kit qua danh gia do tin cay cua phuong an thiet ke va phuong an tdi uu bang phuong phap md phdng Monte - Carlo sau 10.000 lan thir cho thay do tin cay ciia phuong an tdi uu eao ban phuang an thiet ke trudc day.
- Do ket cau cdng trinh bien chju tac dgng cua nhiSu yeu td ngau nhien nen can tiep tue nghien cdu xae djnh do tin cay cua he thdng, tiSn tdi tdi uu theo dieu kien rang huge la do tin cay dam bao e6iig trinh an toan trong nhiing dieu kiSn khac nghiSt eiia moi trudng.
T a i lieu t h a m k h a o
1. Thomas H. Dawson. Offshore Structural Engineering. Prentice Hall Inc., 1983.
2. Lotliar Birk, Gunther F. Clauss, June Y. Lee. Practical Application of Global Optimization lo the Design of Offshore Structure. Proceedings of OMAE04; 23"" International Conference on Offshore Mechanics and Arctic Engineering, June 20-25,2004.
3. M. Mohammad Nejad, M. D. Pirooz, Mohammad Daghigh. Optimization of Legs Batter in Fixed Offshore Platforms. Proceedings of the 20th International Offshore and Polar Engineering Conference; Beijing, China, June 20-25, 2010.
4. Nijat Mastanzade. Optimization Scheme of Offshore Steel Structures. Journal of Istanbul Kiiitur University, 1/2002, pp. 75-80.
5. Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - WorkingStess Design. American Petroleum Institute (API), 2003.
6. Le Xuan Huynh. Tinh todn ket cdu theo ly thuyet loi ini, Tieu chuan do tin cdy, Thugt gidi di truyen. Nxb Khoa hgc va Ky thuat. Ha Ngi, 2006.
7. Phan Van Khoi. Tuoi thg mdi ciia ket cdu thep ngoai bien. Nxb Khoa hgc va Ky thuat.
Ha Ngi, 1997.
8. Biii Diic Nang, Hoang Manh Khang, Nguyen Quan Thang. Tdi ivu ket cdu dan vai diSu kien rimg bugc Id ciu sd do lin cdy tren ca sa phuang phdp PTHH ngau nhien (SFEM) vd thugt todn toi icii DE. Tuyen tap cong trinh hgi nghi Co hgc Ky thuat toan quoc ky niem 35 nam ngay thanh lap Vien Co hgc. Ha Ngi, 09/04/2014, tr. 331 -336.
Ngay nhgn bdi: 10 thdng 10 ndm 2014 Ngay nhgn bdn sira idn cudi: 18 ihdng II nam 2014
