THIET KE TOI iTU KICK THlTdC KET CAU THEO DO TIN CAY
ThS. Le Quang Thdnh Trung tdm Khdo thi vd Kiim dinh chdt lugng.
Tdm tdt: Trong thiet ke vd che tao ket cdu, ca tinh vd kich thudc thay ddi mgt cdch ngau nhien.
Nguyen nhdn su khdc nhau ndy Id do su thay ddi cua tdi trgng tdc dung, ca tinh vgt lieu vd chdt lugng gia cdng (dung sai kick thudc). Bdi bdo trinh bdy img dung cdc phuang phdp toi uu vd be mat ddp ung de thiet ke tdi uu kich thuac cdc mat cat ngang trin ca sa do tin cdy. Cdc kit qud tinh todn so sdnh dugc thuc hien tren chucmg trinh mdy tinh tu thiet lap.
Abstract- In the design of structure for mass-production every item produced will be different.
Uncertainties or variability in load, materials and manufacturing quality are caused this different Introduce theory fundamentals of reliability analysis and reliability based - design of structure using optimum and response surface methods Establish reliability - based analysis and design computer program.
Keywords: optimization of structure, reliability
1. T6ng quan
Do sy canh lranh thi trudng ndn cac san
pham thiet kd khdng chi thda man cac chi 77mX = J i (1) tidu vd kha nang lam viec, ma cdn phai ihigi
ke tdi im theo dp tin cay vdi myc dich dat do tin cay, an toan va chat lugng cao nhat, vat lieu dugc sir dung it nhat. \
Ngu nhu trudc day ta chi tidn hanh danh gia phan tich do tin cay cho cac ket cau san c6 thi trong cac nam gan day la cd thg dua cac chi tidu do tin cay vao giai doan dau tidn cua qua trinh thidt kd.
Phuong phap thidt kd ldi uu dua trdn co sd dg lin cay ngay cang dugc ung dung rgng rai lrong cac nganh ky thuat xay dyng, co khi, hang khdng...
Phuong phap bd mat dap ung (RSM) dugc sir dyng thay the ham trang thai ldi han bang cac ham da thuc va dua theo ham nay dd tim nghiem tdi uu theo phuong phap gradient va xac dinh do tin cay theo cac phuang phap xdp xi.
Trong bai bao nay chiing tdi dua ra giai thuat dng dung phuong phap gradient va bd mat dap ung dd thidt ke tdi im kich thudc kdt cdu, cu thd la thidt kd tdi uu mat cat ngang kdt cau.
2. Bai toan toi uu tren co sd do tin c^y Bai loan toi uu theo dp tin cay cd dang ham muc tidu nhu sau:
dd f(X) dat gia tri nhd nhat.
Didu kien rang bugc la:
p ( a ( x , p ) > o ) > R j hoac
P(gj(X,p) > 0) - O(-Pj) > 0; j - 1,2,...,ng.
h k ( X , m p ) < 0 ; k = 1, 2,...,nh.
d,'<d, < d " ; i = l , 2 , . . . , n . Trong dd: d, - bign Ihigl ke (cd the la don djnh hoac ngau nhidn) thur i; X - vecto bidn thidt kd (bao gdm don djnh va ngau nhidn); p - veclo tham sd ngau nhidn, hay cdn ggi la cac he sd nhidu, cd gia tri trung binh mp; f(d) - ham muc tidu; gj - ham trang thai tdi han thir j ; n- sd bien thiet ke; nh- sd rang bugc xac suat; Rj - do tin cay mong mudn; d,', di" - gidi han dudi va lren cua bidn thidt kd thir I; ^- dugc ggi la chi sd do tin cay.
Dd thda man dieu kien rang bugc P(gj(X, p) < 0) > Rj thi ta phai phan tich do tin cay, su dung phuong phap md phdng Monte Carlo, phuong phap xap xi bac nhat (FORM) vdi tim kiem didm xac suat ldn nhat (MPP).
Theo FORM thi ta phai giai bai loan tdi uu lim chi sd do lin cay P lheo MPP:
Tim gia tri nhd nhat ||ui| vdi:
lu|| = V>.?+u!-H...-^u5 (2) la do dai ciia vecto u
Didu kien rang bugc g(U) > 0.
Khoang each yff = L ' dugc ggi la chi sd do tin cay.
Giai thuat tim MPP duoc trinh bay trdn (hinh 1).
( B i t dlu ( Ganai^mbandau|[/„y~)
(Utrc iKiyng h^m lrgng thail l^ gi6i hgn G J
Hinh 2 - Giai thuat tim MPP phan tich do tin cay ngirgc
Dd dua cac didu kien rang budc phan tich do tin cay thanh rang bugc don dinh ta cd thd su dung phuong phap phan tich dg tin cay ngugc.
Giai thuat tim MPP phan tich do tin cay ngugc trinh bay trdn (hinh 2).
3. Giai bai toan toi un theo dq tin c^y Dd giai bai toan tdi im theo do tin cay (1) ta phai sir dung phuong phap hai vdng Ijip tdi uu long vao nhau. Vdng ngoai la thiet ke tdi tm, vdng trong la phan tich do tin cay nhu (hinh 3).
Phan tich ngifgic' IJQ tin cgy RB 1
Ph^n tich ngippc.
• dg hn cgy RB m |
Hinh 3 - Phuong phap hai vong lap
Tuy nhidn cac phuong phap trdn chi giai dugc khi ham trang thai gidi ban don gian va cd the lay dao ham dugc. Dd giai bai toan tdi im tdng quat ta sir dyng phuang phdp bd mat dap ung va phuong phap gradient theo so do (hinh 4).
i p b i n i j l d a p L > n g j 1
Dung phirang ph^p quy cfluyin hSm Ir^ng lh j l
Dung phinmg phdp gradienl v^ phucmg phip |
' iibacnliild«1lni
Hinh 4 - Giai thuat giai bai toan t6i uu tren co so dg tin cay
Giai thuat giai bai toan tdi uu hai vong lap vdi vdng trong la FORM vdi MPP trinh bay trdn (hmh 5). Phuang phap thidt kg tdi uu theo hai vdng l^p Idng vao nhau nhu (hinh 4 va 5) tdn rdt nhidu thdi gian. Hai tac gia Du va Chen [4] da dd nghi phuang phap danh gia do tin cay va tdi uu lidn bic, hay ggi la phuang phap tudn ty. Phuang phap nay thuc hien vdng lap don vdi hang loat danh gia do 54
tin cay va tdi im ndi tidp nhau (hinh 6).
Trong mdi loat tdi uu va danh gia do tin cay dgc lap Ian nhau, khdng cd sy danh gia do tin cay nao dugc yeu cau trong qua trinh tdi im va danh gia do tin cay thuc hidn sau khi toi
Giai thuat giai bai toan tdi uu theo phuang phap tudn tu trinh bay tren (hinh 7).
Y tudng chinh cua phuang phap nay la sy thay ddi dudng bao cua cac rang budc do tin cay bang rang budc don dinh.
Hinh 5 - Trinh ty giai bai toan toi uu theo hai vong lap long vao nhau Vong 2
T O I U'U 1 —
Phan tich ngi j o' c ) d p lm cay 1 p
Phan tfch ngu'p'c]
30 tin cgy m
z-V^^-^i
Phan tich ngu'Cc do tin c§y 1
PhSn tich ngu-pc dO tin c^y ""
r^^i
Hinh 6 - Thiet ke toi uu theo hai vong lap long vao nhau
Hinh 7 - Giai thuat giai bai toan toi uu theo phuong phap tuan tu
Trong nhidu ung dung ky thuat vide udc cac ham lrang thai tdi hgn ban dau. Khi udc lugng ham trang thai gidi han tdn nhigu thdi lugng hoac danh gia ham thay thg se tdn it gian va cdng sdc, phan tich sy thay ddi can thdi gian va cdng sue ban la ham trang thai nhidu cac udc lugng nay. Mdt Idi giai cho bai tdi han ban dau.
toan nay la tao md hinh thay thd de thay thd
Qua trmh thay thd nay dugc thuc hidn b^ng phuang phap bd mat dap ung. Khi da thu dugc ham thay thd thi ta se su dung cac phuang phap da khao sat nhu md phdng Monte Carlo, x§p xi chudi Taylor bac nhat, xap xi chuoi Taylor bac hai... de phan tich do tin cay.
4. Mo phong ti'nh toan
Trong muc nay trinh bay kdt qua giai cac bai toan ±idt kd ldi uu trdn co sd do tin cay.
Chiing tdi da thuc hien nhidu bai toan cho cac md hinh khac nhau dd cd the so sanh va danh gia tdng quan vd cac phuong phap tmh toan.
Trong gidi ban cua bai bao, chiing ldi xin dua ra mgt bai toan vi dy cu the. Bai toan nay thyc hi?n vdi muc tidu la so sanh giira cac phucmg phap linh. Tien hanh thyc hien theo 11 phuong phap khac nhau. Ket cau la d4m cdng xdn cd lidt didn ngang hmh chu nhat chiu tac dung lyc F^ va Fy nhu hinh 8.
dai lugng nglu nhien co gia tri cho trong b ^ g 1. Chidu dai thanh 1= 1000 mm.
Bang 1 - Gia tn cac dai luong ngau nhien
Dai lirong
Lire tac dung F„ N Lire tac dung Fy, N tTng suat gidi han OcbMPa
Gia tri trung
binh 3000 4000 500
Sai l^ch binh phuvng
trung binh 300 400 50 Xac diiih kich thudc b, h de tidt dien lhanh la nhd nhdt dam bao do tin cay R = 0,995.
Bai toan tdi im cd dang:
Ham muc tieu:
Xac dinh gia tri nhd nhat cua ham:
A = bh Digu kidn rang budc:
I b h l l
b h • 0,1,^0 >R,Lyc tac dung Fx, Fy, kich thudc b, h, mddun dan hdi E, iing suat gidi ban la cac
10<b<100 10<h<100
Kdt qua giai vdi cac phuong phap khac nhau frinh bay trong (bang 2).
Bang 2 - Ket qua tinh loan voi cac phuong phap khac nhau
s
TT 1 2 3 4 5 6 7 8 9
10
Ten phlTffng phap Mo phong Monte Carlo va gradient Mo phong Monte Carlo va buac nhay MPP va gradient
MPP va buac nhay
Be mat dap ung bac nhat, MPP va buoc nhay
Be tnat dap ung bac nhat, Monte Carlo va budc nhay
Be mat dap ting bac hai, mo phong Monte Carlo va buac nhay Be mat dap ung bac hai, Monte Carlo va gradient
Be mat dap img bac nhat day du, MPP va buac nhay
Be mat dap ung bac hai, MPP va gradient
Kit qua toi mi voi do tin cay 0,995 b
42,7260 42,1900 42,3369 42,1500 42,2500 42,1500 42,6600 42,4726 42,1500 42,3369
h 56,4002 56,7800 56,4493 56,7000 55,5100 56,7000 56,1600 56,4002 56,7000 56,4492
Difn tich A 2395,4639 2395,5482 2389,8843 2389,9050 2345,2975 2389,9050 2395,7856 2395,4631 2389,9050 2389,8843
Sai If ch, % 0,0035 0 0,2364 0,2356 2,0977 0,2356 0,0099 0,0035 0,2356 0,2364
s
TT 11
T§n phinrag phap Theo phuong phap tuan tu theo phuong phap 10
Ket qua toi uu voi do tin cay 0,995 b
42,4267 h 56,3395
Dien tich A 2390,2991
Sai Ifch, % 0,2191 So sanh cac kdt qua trdn khi su dung cac
be mat dap ung bac nhat hoac bSc hai thi sai lech so vdi phuang phap 2 (chinh xac nhat) la khdng dang kd. Do dd ta cd the thay thd cac ham giai tich bang be mat dap ung bac nhat hoac bac hai van dam bao tinh chinh xac tinh toan va thdi gian tinh toan giam di dang kd.
5. Ket luan
Ta cd the sir dyng cac phuang phap md phdng sd de danh gia do tin cay kdt cau, tuy nhidn dd dat do chinh xac mong mudn thi cac phuang phap trdn ddi hdi khdi lugng tinh toan ldn. Do do chi thich hgp img dung khi lap cac phan mem tinh loan lrdn may tinh.
Ddi vdi cac md hinh tinh phiic tap ta cd the sir dung phuong phap bd mat dap iing de thay the chiing bang cac phuang trinh hdi quy bac nhSt hoac bac hai, tir do sir dung cac phuong phap xap xi hoac md phdng Monte Carlo dd dd dang phan tich hoac thidt kd lheo do tin cay. Tren ca sd nay chimg tdi xay dyng phuang phap giai bai toan tdi uu nhidu bidn trdn CO sd do tin cay sii dung phuang phap gradient va be mat dap iing. Kdl hgp phuang phap trinh bay vdi cac phuang phap ldi im khac nhau dd tdi uu hinh dang va kidu dang kdt c4u tren co sd do tin cay.
Tki lieu t h a m khao
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Mississippi State University (2001).
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University of Iowa (2002).
[3] Du X., Sudjianto A., Chen W., An integrated framework for probabilistic optimization using inverse reliability strategy. Joumal Mechanical Design, July 2004. p 562-570.
[4] Du X., Chen W. Sequential optimization and reliability assessment method for efficient probabilistic design. ASME 2002 Design Engineering Technical conferences and computers and information in engineering conference. 9/2002.
Montreal, Canada.
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University of Notre Dam (2004).
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[7] Kaymaz Irfan, McMahon Chris, Meng Xianyi. Reliability-Based Structural Optimization Using The Response Surface Method and Monte Carlo Simulation. S^ Intemational Machine design and Production Conference, Ankara (1998).
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Ngay nhan bai: 08/10 nam 2013 Ngay chap nhan dang: 20/10/2013 Phan bifn: TS. Nguyen Van Nhanh
