Thiet k e tci irti k e t cau du^a t r e n dc tin c a y bana aiai thuat di truyen
(*) NGUYEN HlTU LOC (**) DINH LE CAO KY
TOM TAT
Muc tieu cua bai bao la ap dung giai thuat di truyen (GA) vao toi Uu hinh dang l<e't ca'u diia tren do tin cay. Thiet ke toi Uu theo do tin cay dam bao l<etcau lam viec trong dieu kien an toan nhat dinh trong khi cac dai iugng thiet ke tuan theo mot quy luat phan phoi nao do. Giai thuat di truyen (GA) da ap dung va thanh cdng cho mot so bai toan toi Uu. Ap dung GA giup tiet kiem thdi gian tinh toan hdn so vdi cac giai thuat khac. IVlot so tiet dien mat cat ngang Suae xet trong bai bao gom: tru dac, tru rong, chuf nhat dac, chQ nhat rong, chQ I, chQT
1. TONG QUAN
Gia thanh san pham chu yeu phu thugc vao gia thanh vat lieu sir dung. Viec tiet kiem vat lieu ma van dam bao kha nang lam viec la cdng viec quan trgng, giup tiet kiem thdi gian gia cdng, chi phi van chuyen, nhan cdng thuc hien...
Mdt so cdng trinh lien quan den tuih toan thiet ke tdi uu: ap dung phuong phap mat do va phuong phap tien hda tdi uu kieu dang ket cau [2], ap dung giai thuat di truyen tdi uu cho nhieu mat cat ngang ciia ket cau [3]...
Cac giai thuat dugc su dung cho bai toan tdi uu ket cau: giai thuat leo ddi, giai thuat md phdng luyen thep, giai thuat di truyen, giai thuat quan the...
Trong cac giai thuat, giai thuat di truyen dugc xem la cdng cu tim kiem ldi giai tdi uu hieu qua nhat.
Mac du van cdn nhieu han che nhung giai thuat di truyen da ap dung cho nhieu bai toan va cho ket qua dang tin cay.
Ngoai ra, cac gia tri nhu tai trgng tac dung, irng suat gidi han ciia vat lieu deu la cac dai lugng ngau nhien, tuan theo mgt quy luat phan phdi nao dd. De dam bao ket cau van lam viec trong dieu kien an toan, can xet cac chi tieu do tin cay vao bai toan tdi uu. Viec ap dung cac chi tieu ve dp tin cay ciing dugc neu trong mgt sd
(*) Khoa Ca khi, Truong Dai hoc Bach khoa TP Ho Chi Minh (**) Khoa Co khi, Truang Dai hoc Cong nghiep Thuc phim TP H6 Chi Minh
cdng trinh: ap dimg md phdng Monte Carlo cd xet den do tin cay cho cho bai toan tdi uu kich thude ket cau [1], ap dung phuong phap be mat dap irng va md phdng Monte Carlo tdi uu ket cau dua tren do tin cay...
Ngi dung ciia bai bao la ap dung giai thuat di tmyen vao bai toan tdi uu ket can cd xet den cac chi tieu do tin cay va so sanh ket qua vdi phuong phap Monte Carlo [ 1].
2. BAI TOAN TOI UU KET CAU 2.1. Bai toan toi uu theo do tin cay
Dang cua bai toan tdi uu:
(1) Tim X{dj. d^,..., dJ de f(X) dat gia tri nhd nhat.
Dieu kien ham rang huge:
h/X)<0: l/X) = 0; d;<d<dl'
vdij = 1, 2, ...,«., i= 1, 2, ..., n, k = 1, 2, ...,n^.
X: bien thiet ke, f(X): ham muc tieu Rang huge do tin cay:
(2) P(g/X, p) ^ 0))' R
Vdi: p - vecto' tham sd ngau nhien, g - ham trang thai tdi han thir j , R - do tin cay mong mudn
2.2. Phan loai ket cau
Kich thude, hinh dang, kieu dang cua than may phu thugc vao nhieu yeu td nhu: tai trgng tac dung, vat lieu che tao, cdng dung chirc nang cua may, trinh do thiet ke che tao, dien tich khdng gian nha xudng...
Trong cac yeu td ke tren, tai trgng tac dung va vat ^
TAP C H i c a KHi VIET NAM • > So 09-Tiiang 9 nam 2010
lieu che tao (irng suat gidi han) dugc coi la hai nhan td anh hudng nhieu nhat den kich thude, hinh dang, kieu dang than may.
iTng suat (US) sinh ra trong than may do tai trgng tac dung len than may cd the chia lam hai dang: iing suat don (keo (nen), udn, xoan), irng suat phirc tap (keo-udn, xoan-udn, keo-xoan...).
Xet ket cau than may phay dung (hinh la) khi gia cdng xuat hien ba luc Fx, Fy, Fz tac dimg len than may.
US sinh ra trong phan 1 (hinh lb) gdm: US udn, keo, cat. Theo ly thuyet sire ben, chi can xet US udn-keo, US cat thudng bd qua.
Tuong tu vdi phan 2 (hinh le) va phan 3 (hinh Id), US sinh ra gdm: xoan, udn, nen, cat. Cd the bd qua US nen, cat chi xet den US xoan-udn.
Ket qua ciia bai toan US phirc tap la td hgp cac ldi giai cua bai toan US don. Do dd, chi can xet bai toan US don cu the: keo, udn, xoan.
%
Fy-
% Fy.
b)
Fx Fz 3
Fx Fz . M x l
Fr
Fx'
Mx3
^X
\Fy^ M y l a)
Fx Fz c)
Fz
d) y i Mxl -3
Hinh 1: Than may phay diing console
2.3 Bai toan toi uu ket cau
Bai toan tdi uu ket cau cd the chia lam ba dang chinh:
tdi uu kich thude, tdi uu hinh dang, tdi uu kieu dang.
Tuy theo yeu can thiet ke ma cd the ap dung mdt hoac ket hgp nhieu dang tdi uu tren.
3. GIAI THUAT DI TRUYEN Trinh tu thuc hien giai thuat:
Budc 1: Ma hda cac bien thiet ke dudi dang ma nhi phan, thap phan hay ma Gray.
Budc 2: Khdi tao quan the ban dau, sd Iugng quan the ban dau va sd lugng ca the cd trong quan the dd phu thugc vao do Idn cua khdng gian tim kiem.
Budc 3: Danh gia do thich nghi ciia cac ca the trong quan the vdi mdi trudng hien tai thdng qua ham muc tieu.
Budc 4: Chgn lgc cac ca the cd do thich nghi cao
hon, cd nhieu phuang phap chgn lgc nhu: theo ty le, theo xep hang, theo banh xe Roulette...
Budc 5: Chgn hai ca the cha me lai ghep vdi nhau, tao ra mdt hay nhieu ca the con cho the he tiep theo. Lai ghep bao gom: lai mgt diem, lai nhiSu diem, lai ghep deu, lai matna...
Budc 6: Dot bien mdt hay nhieu gen vdi cac kieu:
thay the, hoan vi, dao doan, chen them...
Budc 7: Kiem tra dieu kien dirng ciia giai thuat, n8u thda dirng lai. Neu khdng, lap lai budc 3 vdi quan the mdi dugc sinh ra d budc 6.
Dieu kien dirng giai thuat bao gdm: dirng theo ket qua mong mudn, diing theo sd the he, dirng theo thdi gian thuc hien giai thuat hay td hgp ciia nhieu each tren.
IMS hoa c d the
Khd i tqo q u d n t h ^
Tqo qudn the mcii
, .
£xjt bien
, .
Ddnh gid c d the
^.^\€m tta digu^~^I{'°°
T K h o n g t h d a Chon loc
Cd the tot nhdt
G i d i ^ md
Ket qud tdi uu
Hinh 2: Trinh tir thuc hien giai thuat
4. KET QUA TINH TOAN
Xac dinh tiet dien thanh la nhd nhat vdi rang bugc do ben, do cirng (chuyen vi) thda xac suat la R=0.955, tai trgng tac dung va iing suat gidi han deu la dai lugng ngau nhien dugc neu trong bang.
Tinh toan vdi rang huge do ben cho cac trudng hgp, sau dd kiem tra lai vdi rang bugc do cimg (chuyen vi).
Fx
1=1000
F \ ^
1=1000 1=1000 : ^
a) Keo (nen) b) Uon hai phuang c) Xoan Hinh 3. Tai trong tac dung len thanh
Trudng hcrp chju uon: Tdi uu hinh dang thanh chiu udn hai phuong (hinh 3b).
TAP CHI c a KHI VIET NAM V So 09-Thang 9 nam2010
Bang 1
Dai lugng
Luc tac dung F Luc tac dung F Ung suat gidi han s^j^
Gia trj trung binh
3000 N 4000 N 500 MPa
Sai lech binh phuffng trung binh
300 N 400 N 50 MPa
D
D
b
JZ
Ham muc tieu: A (dien tich thanh)
m m ^ • ^
Dieu kien rang bugc:
a) Tru dac b) Tru rong c)Chu nhat dac
Do ben: P 1 F l l
W„
y a , , < 0 > R
Dp cimg: P ^ ( f ; + f;) - [ f ] < o V R
Xet cac tiet dien hinh 4a, b, c, d, e, f.
•I- JZ
I d I
b
- ^ sz d
b
d) Chu nhat r6ng e) Chii I f) ChQT Hinh 4: Cac dang tiet dien thanh
Tir bang 2, bai toan udn theo hai phuang, thanh chir T cho ket qua la tdi uu nhat. Tuy nhien, tiet dien cira thanh chir T khdng ddi xirng nen khi lap dat can phai chii y phuong ciia tai trgng tac dung nen it sir dung ma thudng gap la thanh chir I.
Bang 2: Ket qua tinh toan thanh chiu uon hai phuang vdi cac tiet dien khac nhau STT
1 2
- t 0
4
5
6
Tiet dien thanh
Tru dac Tru rdng Chii nhat dac Chii nhat rdng
Chii I
ChiiT
Bien thiet ke (mm)
D=58.545
D=69.787;d=55.8296 b=42.3742; h=56.4224 b=47.9396;h=152.2627 d=23.9698; t=26.1313 b=49.2030; h=98.4050 d=5;t=5.007
b=49.097; h=97.667 d=5;t=5.009
Gia trj toi uu (mm^) 2691.9655
1377.0120 2390.7570 1879.0943
934.6702
709.2175
Tir bang 3, ket qua tir giai thuat di truyen thu dugc sai lech so vdi phuong phap Monte Carlo khoang 0.2% la rat nhd. Tuy nhien, thdi gian giai bai toan ciia giai thuat di truyen nhd hon nhieu so vdi phuong phap Monte Carlo.
Btog 3 : So sanh kit qu^ 3 d bang 2 vdi cac phuang phap khac trong bai bao [1]
STT
1 2
Ten phuomg phap
Md phdng Monte Carlo va gradient Md phdng Monte Carlo va budc nhay
Ket qua toi uu vdi do tin cay 0,995 b
42.7260 42.1900
h 56.4002 56.7800
Dien tich A 2395.4639 2395.5482
Sai lech, % 0.0035 0
TAP C H i c a KHi VIET NAM • > Sd 09-Thang 9 nam 2010
3 4 5
Be mat dap irng bac hai, md phdng Monte Carlo va budc nhay
Be mat dap ung bac hai, Monte Carlo va gradient Giai thuat di truyen
42.6600 42.4726 42.3724
56.1600 56.4002 56.4224
2395.7856 2395.4631 2390.7570
0.0099 0.0035 0.2004 Trudng hgp chju keo: Tdi uu hinh dang thanh chiu keo diing tam (hinh 3a).
B^ng4 Dai lirong
Luc tac dung F Ung suat gioi han ey^^^
Gia tri trung binh 500 kN 400 MPa
Sai lech binh phiromg trung binh 50 kN
40 MPa Ham muc tieu: A (dien tich thanh)
mm ^ • ^
Dieu kien rang budc:
Dieu kien rang huge:
Ddben: P A
- C l e h ^ O > R
Do Cling: p j l — [ 8 ] < o ] > R Xet cac tiet dien hinh 4a, b, c, d, e, f.
Cac ket qua trong trudng hgp nay deu hdi tu d gia tri 1819.5462 (mm-) cho thay, dien tich A khdng phu thugc vao hinh dang tiet dien. Mat khac ciing cho thay giai thuat di truyen cd do hdi tu cao, thich hgp vdi cac bai toan cd mdt hay nhieu bien thiet ke.
Trudtig hup chju xoan: Tdi uu hinh dang thanh chiu xoan (hinh 3 c).
Ddben: p
V
Dd cimg: P T W p "
fTl l ^ J p
lim
J
- [(p]<0
J
> R
> R
Xet cac tiet dien nhu: tru dac, rdng, chu nhat dac, chii rdng hinh 4a, b, c, d.
Bang 6: Ket qua tinh toan thanh chiu xoan thuan tuy vdi cac tiet dien khac nhau
Bang 5 Bai luong
Moment xoin T U'ng suat gidi han
"••lim
Gia tri trung binh
10% Nm 40 MPa
Sai lech binh phucmg trung binh
W5 Nm 4 MPa
STT 1 2
3
4
Tiet dien thanh Tru dac Tru rdng
Chii nhat dac
Chu nhat rong
Bien thiet ke (mm) D=57.015 D=67.963;
d=54.3704 b=40.8519;
h=85.1782 b=40.6880;
h=l 12.9730 d=22.3830;
t=44.7660
Gia trj toi mi (mm^) 2551.8075 1305.9812
3479.6948
3594.3980
Ham muc tieu: A (dien tich thanh)
Tir bang 6, vdi bai toan xoan thi thanh tru rdng dugc xem la tdi uu nhat. Dieu nay phu hgp vdi vdi mdt sd ket cau da tinh toan, che tao va sir dung trong thuc te nhu true chinh cua may tien.
Trudng hop chju uon-keo: Tdi uu hinh dang thanh
chiu udn-keo (hinh 5a). [
J TAP CHI c a KHI VIET NAM V Sd 09 - Thang 9 nam 2010
/
/
Ml
\= 1000
^
d b
^
a) U6n-keo b)Tiet dien 2 niia chu nhat Hinh 5: Thanh chiu uon-keo
Bang 7 Dai luong
Luc tac dimg F Moment M U'ng su§t gidi han s_,^
Gia tri trung binh 1000 N lOM Nmm
400 MPa
Sai lech binh phuong trung binh
100 N WS Nimn
40 MPa Ham muc tieu: A (dien tich thanh)
mm ^ • '
Dieu kien rang huge:
(r
W - V f -
A
[W
a, <0
>R
Bang 8 : Ket qua tinli toan thanh chiu xoan-keo vdi cac tiet dien khac nliau
STT
1 2
4
5
Tiet dien thanh
Tru dac Tru rdng Chii nhat dac
Chu nhat rdng
2 nua chir nhat
Bien thiet ke (mm) D=33.3890 D = 3 9 . 8 5 3 0 ; d=31.8824 b=10;h=46.9110 b = 2 5 . 0 8 3 5 ; h=49.8111 d = 2 0 . 0 6 6 8 ; t=39.8489
b = 1 1 . 7 5 1 0 ; h=66.4475 t=6.7510
Gia tri toi uu (mm^) 875.5818 449.0695 469.0987
449.7989
332.2376 Tir bang 8, vdi bai toan xoan-keo d trudng hgp tren thi thanh 2 nira chir nhat la tdi uu nhat.
5. K E T L U A N
vdi ket cau than may cd xet den cac chi tieu do tin cay cd the chgn cac tiet dien irng vdi cac trudng hgp sau:
- Than may cMu keo dung tam cd the chgn tiet dien tru dac, rong, chii nhat dac, rdng, chii I, T deu cho ket qua tdi uu nhu nhau.
- Than may chiu uon hai phuong, tiet dien chir T cho ket qua la tdi uu nhat. Trong thuc te thudng dimg thanh chii I do tinh chat ddi xirng.
Hinli 6. Ket cau chiu uon trong thuc te
- Than may chiu xoan, tiet dien tru rdng la tdi uu nhat.
- Than may chiu udn-keo, tiet dien 2 nua chii nhat la tdi uu nhat.
d b
_c
Hinh 7. KSt cau chiu uon-keo trong thuc te
Tir 3 trudng hgp tren cd the thay, giai thuat di truyen ap dung dugc cac bai toan tdi uu trong ky thuat, cd mdt hay nhieu bien, cho ket qua dang tin cay vdi thdi gian thuc hien nhanh hon phuang phap Monte Carlo vdi ket qua sai khac khoang 0.2%. *>
Tai lieu tham khao:
1. Nguyen Him Loc, Nguyen Tnmg Dimg; Tliiet ke tdi uu kich thude tiieo do tin cay, Ky yen Hoi nghi Ca hoc Toan qu6cl4ntiiir 8,2007.
2. Bill Hoang Giang, Nguyen Hieii Loc; Toi uu hoa kieu dang ket can theo phuang phap mat do va phuang phap tien hoa, Tap chi Phat trien Khoa hoc va Cong nghe. 03/2008, Tap 11. Tr 57-68.
3. Yoshimiira, M., Nishiwaki, S., andIziii, K.; AMuitiple Cross-Sectional Shape Optimization Method for Automotive Body Frames, J. Mecli. Des., 2005, pp. 49-57.
4. Kaymaz Irfan, McMalwn Chris, Meng Xianyi;
Reliability-Based Stmctiual Optimization Using The Response Surface Method and Monte Carlo Simulation, 8"' International Macliine design and Production Conference, Ankara (1998).
5. Nguyen Mini Loc; Thiet ke va phan tich he thong theo do tin cay, NXB Khoa hoc va Ky thuat, 2005.
TAP C H i c a KHi VIET NAM %• Sd 09-Thang 9 nam2010
