KHOA HOC CONG NGHE
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Toi uu hoa hinh hpc va trpng lupng cau gian thep quy mo Ion
sCr dung thuat toan to! uu hoa bay dan
I KS. L £ H O A I N A M - Cdng ty Co phdn Dau tdXay ddng Hoai Nam I ThS. H 6 K H A C H A N H - SdGiao thong van tdi tinh Nghe An
• TS. NGU Y I N T H I C A M NHUNG; Lg X U A N T H A N G - TrUdng Dai hoc Giao thong van tai
TOM TAT: Bai b i o trinh bay mdt each tiep can de tdi uu hda hinh hpc va trong luqng cda mpt cay cau gian quy mo Idn dya tren p h i n tich tTnh ket hop vdi tdl uu hda bay dan (PSO). PSO la mgt thuat toan tien hda duqe ap dung thanh cong trong nhieu van de toi uu hda trong nhung thap ky qua, Cac bien thiet ke bao gdm kich thudc mSt cSt ngang cda cac thanh gian va cac t i i trpng tac dpng len ket cau.
Cac rang bupe ddi v6i ung suat cda cac thanh gian dupe chpn la mpt ham muc tieu di giSm thieu su khac biet giua cac dng suit tinh t o i n va cac dng suat cho phep. Ket q u i chi ra ring, phuong phap de xuat da g i i m dupe trpng luqng cCia cau so vdi thiet ke ban dau.
TL/ KHOA; Tdl uu hda, toi uu hda hinh hpc, toi uu hda bay dan, cau gian thep quy md Idn.
ABSTRACT: This paper presents an approach to geometnc and weight optimization of a large-scale truss bndge based on static analysis combined with particle swarm optimization (PSO). PSO is an evolutionary algonthm applied successfully in numerous optimization problems in the last decades. Design variables consist of the cross- sectional dimensions of truss members, and the redundant forces acting on the structure.
Constraints on member stresses are selected as an objective function to minimize the difference between calculated stresses and permissible ones.
The results indicate that the proposed method can provide the considered bridge with a lighter weight than that of the original design
KEYWORDS: Optimization, geometry and weight optimization, particle swarm optimization, large-scale truss bndge
I . O A T V A N O i
Trong nhieu thap k^y- gan day, tdi Uu hda d i trd t h i n h mdt chd de nghien cdu n h i n ddpc nhieu sU quan t i m t d cpng dong khoa hpc trong rat nhieu ITnh
vUe, tdi du hda thiet ke la mdt trong sd dd. Bai b i o xem xet van de tdl Uu hda hinh hpe eua cic g i i n bang each tdi Uu hda eie mat cat ngang eac thanh, t d dd g i i m trong luong ket eau. Cae van de don gian nhat ve tdi Uu hda gian thep da dUOc dUa ra trong Haug va cac cdng su [1] nhung eie kieu eua mat cat ngang thanh khdng ddaexicdinh.SergeyevviMroz[2] da apdyng ky thuat lap trinh bae hai tuan t u d e thiet ke tdi uu ket cau khung vdi c i hai bien hinh dang va kich thUde. Cic thuat toan de g i i i quyet cac bai toan phi tuyen eung duoc ap dyng nhU thuat t o i n di truyen dupe gidi thieu bdi Hayalioglu [3-4] dng dyng cho ket cau thanh gian d i n hoi. Zheng va cae edng sU [5] dng dyng de tim ra vj tri ndt v i kich thUde thanh phan tdi Uu, nhU v i y trpng lupng hoic khdi lupng vat lieu cua ket cau se dupe giam thieu. Thuit toan ldi Uu hda b i y dan dupe phat trien bdi R. C. Eberhart and J. Kennedy [6] v i dUpc Gomes, Herbert Martins[7] ap dung vdi viee tdi Uu hda ket c i u gian ve kich thudc v i hinh dang duoc thue hien cd xet den eie ring budc ve tan sd. Tdi Uu hda ket cau ve hinh dang va kieh thUdc la eie v i n de tdi Uu hda phi tuyen tinh do viec tdi Uu hda ve lUpng m i u thuan vdi eic r i n g budc tan sd. Trong b i i b i o nay, cac g i i i p h i p cho cie v i n de tdi Uu hda dupe thUe hien bang each sd dung mdi trudng lap trinh t o i n hpc MATLAB. Vdi viec ap dung thuat t o i n tdi uu hda bay d i n (Particle Swarm Optimization - PSO) ket hop cic dieu kien r i n g budc, phuong p h i p lap ddi vdi tdng p h i n tdsau moi lan thUe hien ket q u i mdi dUOc dem so sanh vdi ket q u i eu, t d dd ta thu duoc eae thdng sd mdi tdi uu hon nhung van dam b i o cac dieu kien ve mat chju lUc va dn dinh.
& Viet Nam, tdi Uu hda bay dan da b i t dau dUOc i p dung cho mot sd ITnh vUe trong thdi gian gan day.
Nguyen Thi Hoang PhUPng [8] trinh bay ve viec x i y dung va danh g i i hieu q u i md hinh t h d nghiem ddi vdi phuong p h i p loe cpng tac sddung md hinh lang gieng v i phan cum Ipe edng t i e tdi Uu trpng sd sd dyng PSO tren tap d d l i e u MovieLens 100k. Tran Thai Bio [9] Udc lupng dupe ehi phi va no lUc de p h i t tnen p h i n mem gan chinh xac nhat; g i i m thdi gian trong viee Ude lupng, d i m bao thdi gian hoan t h i n h d u i n kip tien dp, d i m b i o dupe ehi phi trong q u i trinh phat trien. Tuy
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nhien, viee dng dung tdi Uu hda, cu the sd dung t h u i t toan tdi Uu hda bay dan (PSO) d e g i i i quyet cae van de thude ITnh vuc xay dung ndi ehung va ITnh vUc thiet ke ket cau tdi uu hinh hpe eua ket cau ndi rieng cdn han che, vdi rat it eic tai lieu cung nhu eic xua't ban lien quan den linh vue nay.
Dua tren cic k h i nang tim kiem trong pham vi rpng cua t h u i t toan tdi uu hda bay d i n (PSO), trong bai b i o nay ehung tdi de xuat sd dyng PSO de tdi Uu hda hinh hpe eua ket cau g i i n thep, vdi edng trinh thue le dUOc xem xet den la eau Chuong Duong se dupe md ta chi tiet d phan 3.1.
Phan edn lai cua bai bao nay duoc td chdc nhu sau:
Thuat toan tdi Uu hda bay dan (PSO) gidi thieu trong trong phan 2. Phan 3: L/ng dung cua tdi Uu hda v i o cdng trinh eau gian thep nhip Idn. Cuoi eung, mot sd ket luan dUde rut ra trong phan 4.
2. THUAT TO AN TOI UU H 6 A B A Y 0 A N (PARTICLE SWARM OPTIMIZATION - PSO)
Thuat t o i n PSO lan dau tien dupe gidi thieu bdi Eberhart, Russell and James Kennedy [6]. T h u i t t o i n nay dupe lay e i m hdng i d cae hien tuong t u nhien.
Cae ca nhan t r i i rdng trong khdng gian tim kiem dUdi dang cie hat. Moi hat di ehuyen trong khdng gian tim kiem ca nhan tdt nhat loan cau. Vi t r i hat dUpc cap n h i t nhusau:
A-,"' = x; + Vi'^ (1) Trong do:
X f - V i tri hien tai cua hat t h d i;
V'*^ -Van tdc cua hat t h d i sau khi tinh toan.
Moi hat/ed VI tri tdt n h i t cua rieng ndduoc bleu thj l i •pbes!'^, trong dd / la so lan lap. Vi tri tdt nhi't t o i n cau trong eie lan l i p la gbesi'. Van tdc hat bao gdm ba p h i n : v i n tdc ban dau, vi tri -pbesfva vi tri gbesf. Van tdc mdi dugc cap nhat nhU sau:
[/,'+' = w'V^ + c^r^{pbest\ ~ K\) + Cir^igbest', - Xf) (2) Trong do: r^vir^-Gia tri ngau nhien [ 0 < r , , r ^ < l ] ; c , va Cj - Lan luot la cac tham sd ty le n h i n thdc va xa hdi va
«/•-Trpng luong q u i n tinh dupe sddyng de g i i m tdc do trude dd cua hat dupe b i o t o i n .
Hinh 3.1: Cau Chuong Duong 3.2. Mo hinh phin tit huTu han
Trong nghien edu ta nghien cUu ehi tiet 01 nhip dien hinh cua cau Chuong Duong. Md hinh phan td hdu ban chi liet 01 nhjp cau (Hinh 3.2) vdi tong ehieu dai nhjp la 89,28m.
Hinh 3.2: MP hinh nhjp cau Chuong Duong Trong dd, t i p trung md hinh 5 loai thanh: thanh xien, thanh dung - treo, dam ngang, dam dpc, he giang tren - dudi. Chi tiet c i u tao thanh duac md t i theo Hinh 3.3.
2@760X12 —f H—
ill
3. 17NG DUNG VAO C 6 N G TRINH CAU G I A N THEP NHjP LdN
3.1 .Tong quan ve cong trinh cau
Cau Chuong Duong b i e qua sdng Hdng, tren QLl A tai k m l 70-t-200, dta phan Thu do H i Ndi. Day la eay cau Idn lan dau tien dUOc thiet ke va thi edng tat Viet Nam khdng cdsU tro giup ky thuat cua eac ky sUnUdc ngoai.
Td day, eie ky sU eau dudng eua Viel Nam t u t h d sde minh de cd the t y thiet ke v i thi cdng cie ciy cau Idn khac. Chieu dat eau 1.230m gdm 21 nhip: 11 nhip thep, 10 nhip betdng, trong dd 7 nhip d phia Ha Ndi v i phfa Gia Lam cd 3 nhip; tai trpng: H30. Cau chia lam 4 lan xe chay hai ehieu. Phia ngoii cung cd lan dudng danh cho xe m i y rdng 1,5m.
60
= _ _ X 2@240X10
HE GIANG TREN - Dddl
Hi
4L@200X125X16l - f V
l ~ I
t
Hinh 3.3: Chi tiit cic thanh trong md hinh eau Tai trpng gia thiet t o i n bd eie nut gian phia dUdi deu chju 01 lue tap trung F = 100 kN.
Cae tinh chat vat lieu eua gian thep dupe het ke nhU Bdng 3.1.
KHOA HOC CONG NGHE
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Bang 3.1. Oac trung vat lieu ciia kit ciu giin thep Thanh phan
Md-dun dan hoi
Gia tri 2x10«
Trong lugng the tich 7850
He so poisson 0,3
Oomvi KN/m^
Kg/m^
khdi luong trong Hinh 3.5 va dien tieh dupe liet ke va tdng hpp khoi luong tai Bang 3.4.
Gidi han eUdng dp chju nen j Gidi han cUdng dp chiu keo
53000 KN/m^
45000 KN/m=^
Md hinh phan t d hdu han cua g i i n thep dupe x i y dung bang cich sddung toolbox Stabil trong p h i n mem MATLAB cic thanh gian va d i e trUng hinh hpc cua nd duoc x i y dung dUa tren yeu to hinh hpc g i i djnh. Cie bd phan tuong dUOng 5 loai phan t d l i ket eiu chinh (thanh xien, thanh ddng - treo, dam ngang, dam dpc, he g i i n g tren dUdl) dUoc md hinh hda vdi cie phan t d thanh ehi chju keo nen. Dien tieh mat cat 5 loai phan t d dupe g i i djnh dupe md t i dudi Bdng 3.2.
Bing 3.2. Chi tiet thupc tinh phin tddupc mP hinh trong Matlab Phan ta
Thanh xien Thanh d d n g - t r e o Dam ngang Dam doc He g i i n g tren-dudi
Gii tri dien tich 0,012 0,013152 0,0055 0,05984 0,0064
Donvi m' m^
m^
m^
m^
Ta ed the de dang tinh t o i n dUgc dng suat keo va nen max trong ket cau trong Bang 3.3:
Bing 3.3. Bang tinh toin dng suit Idn nhat trong kit eiu O^ng suat Idn nhat
Keo Nen
Giatr|(KN/m') 42386,30338 52982,87923 Tong trong lUpng thep toan nhjp la: 236.203 (tan) thep.
3.3. Ap dung toi Uu hoa vao ket cau va ket q u i nghien cuiXi
Vdi 5 thanh duoc md hinh ta ehia vao 5 nhdm tat ca deu dupe lay gia trj dien tieh trong khoing 0,005 - 0,06ml Qua trinh ehay t h u i t toan b i n g MATLAB nhU trong Hinh 3.4.
Hinh 3.4: Qui trinh chay thuit toan trong MATLAB Sau khi ehay t h u i t t o i n tdi Uu PSO cae thay doi ve
Hinh 3.5: Bang bien thien khoi lupng sau khi chay thuat toan Bing 3.4. Chi tiet mat cat cac phan sau khi ehay toi uu hda PhSn tuT
Thanh xien Thanh ddng-treo Dam ngang Dam doc He giang tren-dudi
Gia tri dien t k h 0,011996194
0,005 0,005 0,020229057 0,005
Donvi m^ m' m^ m^ m^ Bing 3.5. Bing tinh toan ung suit Idn nhit trong kit ciu
iing suat Idn nhd't Keo Nen
Gia tr| (KN/iri') 42399,75117 52999,91971 Tdng trpng lupng thep t o i n nhip la: 116.304 (tan) thep.
Nhu vay ed the thay, so vdi ban dau giim dupe:
119.899 (tan),-50.761% khdi luong so vdi ket eau ban dau va van d i m bao dieu kien ve eUdng dd chiu nen va keo.
4. KET L U A N
Trong bai bio, thuat loan tdi uu tien hda bay d i n da dupe ap dyng de tdi Uu hda hinh hpe cho mdt cau gian thep quy md Idn. Vdi mye dieh tim trpng lUPng va kich thudc tdl Uu cho ti't ea eic phan t d cua ket cau ma van d i m bao eac dieu kien rang bude. Ket q u i sau khi ehay tdi Uu eho thay, so vdi cac yeu td hinh hoc ban dau, trong lupng ket eau ban dau 236.203 (tan) thep, cac thdng sd mdi, trong lUpng eua ket eau mdi 116.304 (tan) thep da g i i m dang ke 119.899 (tan) thep nhung van gid dugc yeu cau tdi thieu ma bai toan dat ra ve eUdng do chiu nen v i keo. Tuy nhien, bai b i o nay mdi chi xet den bai toan tdi Uu hda yeu td hinh hoc cua eau gian thep. Nhdng nghien cdu tiep theo se dugc trien khai de tdi uu hda lien ket, sd dung eae loai phan t d khac cung nhu tdi Uu hda hinh hpc cho eie ket cau khic.
Tai lieu tham khao
[1 ]. Arora, J. 5. and E. J. Haug (1979), Applied optimal design: mechanical and structural systems. A Wiley-inter Science Publication, 506.
[2], Goremikins, Vadtms, K. Rocens and D. Serdjuks (2010), Rational structure of trussed beam, Goremikins.
[3]. Hayalioglu, M. S.; Degertekin, S. 0. (2004), Design of Non-Linear Steel Frames for Stress and Displacement Constraints with Semi-Rigid Connections vio Genetic Optimization, Structural and Multidisciplinary
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Optimization 27(4): 259-271, http-//dx.doi.org/10.1007/
sOOl 58-003-0357-9.
[4]. Hayalioglu, M. S. (2000), Optimum Design of Geometrically NonLinear Elastic-Plastic Steel Frames Via Genetic Algorithm, Computers & Structures 77(5): 527- 538, http-y/dx.doi.org/10.1016/S0045-7949(99)00221-7.
[5]. Zheng, Q.Z„ 0. M. Querin and D. C. Barton (2006), Geometry and sizing optimisation of discrete structure using the genetic programming method. Structural and Multidisciplinary Optimization 31.6,452-461.
[6] J. Kennedy, R. Eberhart (1995), Particle swarm optimization. In: Proc IEEE International Conference on Neural Networks, Perth, Australia, pp.1942-1948.
[7]. Gomes, Herbert Martins (2011), Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Systems vwith Applications 38.1, 957-968.
[8]. Nguyen Thj Hoing PhUOng (2018), Nghien cdu dng dung thugt todn to! du bdy dan vdo hi thong ggi y.
Diss,TrUdng Oai hoc Bach khoa-Dai hpe O i Ning.
[9], Tran Thai Bio (2017), Dd dodn no luc phdt trien phan mem theo quy tr'inh Agile sddung thugt todn toi Uu bdy dan, Diss, TrUdng Dai hoe Bich khoa - Dai hpc Da NSng.
Ngiy nhan bai: 03/12/2019 Ngay chap nhan dang: 27/12/2019 Ngudi phSn bi@n: TS. Nguyin Van Hau
TS. Hoang Vi^t Hai