Thuat toan mat dap ufng cai tien tifng dung trong phan tkh md ket cau coc chju tai trong ngang
The response surface improvement algorithm applied in fuzzy structure analysis in problem of cross bearing piles
Ngay nhan bai: 22/3/2017 Ngay SLi^ bai: 11/4/2017 Ngay chip nhan dang: 5/5/2017
Nguyen Hung Tuan, Le Xuan Huynh, Ha Manh Hung
T 6 M TAT :
Btii b i o nay de xuat mpt thuat toan phan tich md ket cau, ilng dung vao bai toan coc chiu tai trong ngang. Thuat toan de xuat dfla tren cO sd phflong phap mat dap ifng trong ly thuyet xac suat- thSng ke toan hoc, vdi mdt so cai ti^n trong mo hinh thay the Thong qua vi du so minh hoa. so sanh ket qua dat difcfc vdi cac thuat toan khac da difdc cong bo, cho thay hieu qua ciia thu§t toan de xuat.
Td khoa: Phan tich md kSt cau, coc chiu tai trong ngang, phUdngphap mat dap ufng
ABSTRACT:
This paper proposes a algorithm to fiizzy structure analysis, applied to the problem of cross bearing piles.
Proposed algorithm based on response surface method in probability theory, with some improvements in the alternative model. Through some numerical examples, the results compared with other published algorithms shows the effectiveness of the proposed algorithm.
Keywords: fuzzy structure analysis, cross bearing piles, response surface method
TS. Nguyen Hung Tuan
Tritdng Dai hoc Thiay lai, 175 T5y Sdn, Ha Noi
GS.TS Le Xuan Huynh, TS. Ha Manh Hiing Trddng Dai hgc Xay dung, 55 Dudng Giai Phong, Ha Npi
I.Datvandl
Coc chiu t^i trong ngang la bai to^n thudng gap trong thi^t k^, chan Soan ky thuat cong trinh. B&n canh viec tinh toSn silc chiu tai cCia coc, mot yeu cau quan trong 1^ phSi xSc dinh ehuyen vi ngang tai dinh coc, til 36 kiem tra yeu cau ve do cilng (chuyin vi ngang cho phep), dudc quy dinh trong eac tieu chuan, quy chuan ky thuSt. Be ph§n tich ket cau coc chiu tSi trong ngang, vtic sd dung phL/ong phap phan tir hu'u han (PTHH) la thuan tien va hop ly hcfn d. do sd dung du'oc "cong cu so" vi khd nang tinh toan cCia may tinh Tuy nhien, phifong pViSp PTHH chl duoc thi/e hien khi cac tham so dau vao- mo dun 3in hoi cua v | t lihi, kich thudc tiet dien coc, tSi trong tac dung, c h i l u dhy cua cac Iflp Sii, de tham s6 co hoc cua dat n l n (tham sd chiu n^n ks, tham so chm cSl kl)... la dc so thUc. Trong thyc te, cac dai luong nay khong t h i difOc xac cljnh mot each chinh xac hoan toan, dUoc goi la cac dai lUOng bSt ctinh.
Khi CO su thieu hut thdng tin, chSng han, do tinh khong thuan nhat ciia cac ldp dat nen va viec lay cac mSu t h i nghiem ehi dUoe thUe hien dmot so diem dac biet, viSe sd dung ly thuyet m d [1], [2]], de mo tS cac dai lu'ong bat dinh nSy la hop ly hon cS. Tdviee md ta cac tham so d l u vao du'di dang sd md, cic nhS khoa hoc Viet Nam va tren the gidi da nghien cClu, d l xuat cSc thuat todn PTHH m d trong phan tieh k i t cau 13-11).
Bai bao nay se trinh bay mdt thuat toan PTHH md ph3n tfch tinh k i t cau, apdung trong bai toan coc chju tai trang ngang.ThuSt toan de xuat dUa tren co sd nghien cifu cua tac gia tai eac tai iiiu [12], [13 ], [14]. Thdng qua vi du sd minh hoa, so sanh k i t qua vdi cac thuat toan khac da 3uac cdng bo, cho thay hieu quS eua thuat toan de xuat.
2. Thuat tpan phan t k h md ket cau
2.1 .Phu'cmg phap PTHH do! vdi bai toan coc chju tdi trong ngang [15]
V l mat CO hoc, coc ehiu tSi trong ngang thuoc ldp bai toan d i m tren n l n dan hdi. Ddi vdi bai loan nay, trong ket du xSy dung thiTcmg sil dung md hinh nen Winkler, phSn li/c dan hoi cua dat nen tai mdt diem ty le t h u | n vdi chuyin vi cua dilm tai d i l m do, he sd t^ le dUoc goi la hfi sd do cuYig ki. Tuy nhien, theo [15], mdt trong nhCrng nhu'Oc d i l m Idn cua mo hinh Winkler la tinh khong ll^n tuc cua chuyin vi xu^t hl^n giOa phSn d | t tai trong va phan khong dat tai trong cua be mat nen. De khSc phuc nhu'Oc d i l m cDa md hinh nen Winkler, rat nhieu nha khoa hoc tren the gidl da kiln nghi cac mo hinh nen kh^c nhau, trong dd cac mo hinh n l n hai tham sd (two-parameter models) la mo hinh n l n sat th^c te, vi da khac phuc du'oc nhupc diem eua mo hinh n l n Winkler.
Theo [15], phuong trinh co sd eda md hinh nen hai tham so l a : d ' w d ' w
E A — r - ' ^ , - T + K w = q(x) (1) dx dx
trong do: Eb lb - do ciing chdng udn cCia d i m ;
OO.iSnni^ilHiV 0 5 . 2 0 1 7
k, - tham sd n6n eda n l n , tuong dUong he sd dan hdi trong md htnh nen Winkler;
kl - tham sd cSt cilia nen,
De t h i l t l^p phitong trinh bien thien, x^t dam trong md hinh nen hai tham so cd c h i l u dai I, chiu t^e dung lUe phan bd q(x) va cac lu'c ndt Qi, Ml, Qi, M j . C h i l u dUdng quy Ude duoc the hien tren Hinh 1.
^•J::' .7,..:. "-.X^ '"•
Hinh 1. Phan tilrnau mo hinti nln hai tham so Vec t o chuyen VI :{d,} = {wi fit W2 QzV V^c to lite n i i t : {Se} = {Qi Mi Qj M:}^
Chon ham chuyen vi Id da thde b l e 3, ^p dung phUOng phcip Galerkin de cUc tieu hda phan dU„ bien ddi ta dUOe phuong t r i n h :
{w+^.]+[>':]){<i.}-{s.)-{R.) (2)
trong dd [ke] la ma tran dd cdng cua phSn t d d a m chju udn, [kcj la ma tran do cdng ciia tham sd n l n t h d nhat;
[k«] ia ma tran do cdng cua tham sd nen t h d 2;
w- M-i
W-
•12 -61 12 -6 61 21^ -61 4
"156 221 54 221 41= 131
-36 -31 36 -31
nhi§n, thuat toan nSy tuong ddi phde tap, ddi hdi khoi luong tinh toan Idn. CSc muc sau se trinh bay cac di tien trong viec thiet lap ham thay the phCi hop ddi vdl ccic thanh phin ehuyin vi tai cac nOt d l giSm thdi gian tfnh toan trong vl^e giin cac bin toan tdi Uu.
2.2. Xac djnh c^c b i l n mdchuan trong md hinh thay the Theo [16], sd dung bien ehuan trong md hinh thay the se lam giSm sai sd do lam trdn so khi tfnh toan cac he sd hdi quy. Trong [12], tren co sd nguyen ly thdng tin khdng dily dCi (insufficient reason) tai [17^19], ehung tdi da t h i l t l|p cdng thdc xac flinh b i l n m d chuan X j ddi vdi b i l n md gdc la sd md tam gilc cSn X^ = (a,l,l)LB ta xac djnh bien chuan theo cdng thdc sau;
X = ^ ^ ^ (6) 1/3
Vdi phep ddi b i l n tren, t i l b i l n md gdc ban d^u X, = (a, I, Dm ta chuyen sang b i l n md ehuan X, = (0,3,3)ui. Ndi each khlc, t d bien md gdc ban dau cd mien xac ^ n h r i t khae nhau, da chuyen thSnh cac b i l n chuan cd ciing m i l n x l e dinh. Mgc dii duoc thue hi§n trgn co sd chuyen ddi t d dai lUOng md sang dai lUOng ngau nhi€n tuong du'ong, tuy nhien cd t h i xem bien md chuan la k i t q u i mot ph^p b i l n d i i hinh hgc t d b i l n md gdc ban dau, dUoc v | n dung tUong tif nhU khdi niem b i l n chuan trong ly thuyet thdng ke t o l n hoe. Khlc vdi elc thuSt toan trong [10], thuat toan d l x u l t dUoc thUe hien trong khdng gian elc bien md chuan, do do khdng gay ra sai l&ch do chuyen ddi t d dai ludng md sang dai luong ngau nhien (vdi cac tham sd dau v i o ) va ngU^c lai, tir dai luong ngau nhien quay t r d lai dai luong md {vdi d l u ra la ddp dng k i t cau) trong qua trinh tinh t o l n . Trong vi du minh hoa tai [14], viec sd dung b i l n md chuSn cho k i t q u i sal ISch vdi nghiem "chfnh xae" tu'ong ddi b^ (nhd hon 4% d tat ci cac tieu chi so sinh), cdn bien md gde cho ket q u i sai lech tuong ddi Idn (Idn hon 60%).
2.3. Lua chon md hinh thay the (mo hinh m i t dap dng) Trong ly t h u y l t thdng ki, mdt sd md hinh thay t h i thudng dUoc sCl dung I I : md hinh hdi quy da thde (polynomial regression model PRG), md hinh Kringing (Kringing model KRG), h i m eo sd hu'dng tam {radial basis functions RBF). Trong cle md hinh nay, md hinh hdi quy da thOrc thudng du'oc sCr dyng d l x l y dung ham mat dap dng do don g i l n va t h u i n ti^n trong tfnh toan Trong [12], chi:ing tdi da sd dyng md hinh hdi quy da thdc ble 2 khdng day dCi lam md hinh thay t h i . Tuy nhien, cd the nhan thay, md hinh hdi quy da thdc b l e 2 d l y du se mang tinh tdng q u i t hon. Do do, thuat toan de xuat sd dung md hinh hoi quy da thdc bpcfta/cfoyiJuddi vdl elc bien md ehuan lam m d h i n h thay t h i , eho dap dng k i t cau la cac chuyin vi md:
V ^ t o {RJ phu thude vao dang eda t l i trpng p h i n bd tren d i m TrUdng hop t l i trpng phan bd deu q(x)=q=const, cd:
• '' [2 12 2 1 2 j
(4)
y(X) = a + S a , ' < , + 2 : a , X , X , + S a . x : (7)
Thuc hien ghdp ndi eac ma tran do edng va vecto t l i trong, nhan du'oc phuong trinh cCia phUdng phap PTHH trong hi toa dd tdng t h i :
[K]{W} = {F) (5) trong dd [K] I I ma tran dd cdng tdng t h i , {W} la v i c t o chuyen vj ndt,
{F}= [Se) - (fcl la v^c t o t i i trong nut tuong dUong. De g i l i phuong trinh (5), can dua vao cle dieu ki?n bien.
Khi eac dai luong d l u v i o nhU md dun dan hdi eila vat lieu, kich thudc tiet dien coc, t l i trpng t i c dung, c h i l u day eda cle Idp dat, elc tham sd co hoc cua dat nen la cac sd md, dap dng k i t cau (ndi lUc, chuyen vi...) cung la cac sd md. De nhan dupc dap dng k i t cau, mdt trong nhuTig phUOng phap thudng dupc sd dung la t h u i t t o l n tdi Uu mdc a [4], g i l i cle bai t o l n tdi Uu tren d i p Ung thUc cua k i t cau. Tuy
Vdl viSc sd dung bien chuan, a,, fluoc xac djnh theo phudng t r i n h : y(X=0) = a„
(8)
CIc he sd edn lai trong (8) duoc x l e dmh theo phUtJng phap binh phuong tdi thieu.
2.4.Thietkemauthur
Tuong t u nhU elc bin b i o [12], [13], [14], trong bai n l y ehiing tdi chon thiet ke mau Box- Behnken, Trong thiet ke mau Box - Behnken, cac fliem thiet k l hole n i m tai t i m l i p phuong hole tai trung diem cua cac eanh l i p phUOng. Thiet ke mau Sox - Behnken vdi 3 bien sd dau vao duoc the hien tr&n Hinh 2, trong dd k;^ hi§Li ±1 chi Vi do d l i khoSng bien thien ciia b i l n . Odi vdi bien chuan xle dmh theo cdng thdc (6), sd dung quy t i c 3o ta lay khoing bien thien cua bien chuan la (-3, •i-3)a.
05.2017aU!inffi[|H!i|l01
Hinh 2.1hiet kf mau Box- Behnken vfli ba bien 56 2.5. l/dc l u m g sai lech va chon lUa phUOng an
Ude luong sai lech danh gia chat lupng ciia md hinh thay the v l dimg de lUa chon phuong an phii hop giUa cac phuong an tfnh toan.
Cac dang Ude luong sai lech thudng sd dung la : phuong p h i p mau don (split sample), phuong p h i p kiem tra cheo [cross - validation) va phuong p h i p mdi (bootstrap!ng), Trong cac phuong p h i p tren, phuong p h i p mau don va phuong p h i p kiem tra chio de sddung de lua chpn cle phuong I n hon c l . Trong thuat toan de xuat, chiing tdi sir dung phuong p h i p k i l m tra cheo rdi bd mot t|ip (leave - one - out cross - validation), trong dd mdi diem phan dng flupc k i l m tra mdt lan va thd k - 2 l l n (do m i u trung t i m d l sd dung de xac djnh ao theo cdng thdc (8)).
L/u d l l m ciia phuong p h i p n l y theo [20] la dUa den Ude luong khdng chSeh ciia sai lech tdng va phuong sai tUOng titig se giam khi so sinh vdi phuong p h i p m i u don. NhUpc d i l m ciia phuong phap n l y Ia ddi hdi tinh t o l n n h i l u l l n cle md hinh thay the. Tuy nhien, nhuoc diem n l y cd t h i khae phuc n l u l i p trinh tU flong hoa lua chpn c i c td hop mSu t u c i c m i u cho trudc 3i dUa v i o md hinh hoi quy Lfdc luong sai lich eda phuong an thU j ( s d dung X<" lam t i p k i l m tra) x i c dinh theo cdng thUe:
G S E , = ( y , - 19)
2.6. XAc dinh dip utig m d k e t cau
Trong [12], chUng tdi da sd dung phUdng phap chuyin ddi (transformation method) [7], cai t i l n vdi sd t d hpp it hdn do sd dung ph^p dao h i m de xle dmh dap Ung md k i t cau. D l y la mdt each tinh flon g i l n , t h u l n tiin sd dung trong thyc te. Tuy nhi§n, ddi vdi ham thay t h i la md hinh hdi quy da thdc bae 2 flay flu, viec sd dung dao ham d l tim cac d i l m cue tri ctia dap utig md k i t cau tren elc l i t cat a se trd nen khd khan. Oe khie phuc d i l u nay, chiing toi sd dung thuat g i l i di truyin (genetic algorithm) GA [21], I I mdt thuat toan thudc nhdm t h u i t t o l n tdi Uu theo quan t h i {population-based optimization). Vf du minh hoa sd dung t h u i t toan GA trong (\rtatlab 7.12. CIc t h u i t toan tdi uu theo quan the khlc, nhU thuat toan tdi Uu hda b i y dan PSO (particle swam optimization) [22], thujjt toan t i l n hda vi p h i n DE [differential evolution) [23], duoc xem la cac cdng cu hdu hieu fll giai b l i toan quy hoach phi tuyen, xac dinh d i p dng md ket cau
^r^ »
l c , - p « J « . 4 ) „ M P ^ l : i - t a , S * ) u M P »
k,=0M,XiJ£f.tt,-&SJ2A)^lSHi
W p 3 H , - 3 l c
| [ , ^ 1 9 ) U P i , k , ^ K a i F i
1C,^ UWMFa. k,== m U P a
H'inh 3 Vidu mmh hoa
3. V i d u minh hoa
X^t coc chiu t l i trong ngang F = 300KN, M = 1 OOKNm tai dinh coc.
Dat nen cd 4 Idp, moi Idp cd chieu day K = 5m (i = 1,...,4).
Cle he sd nen eda Idp 1 va Idp 2 la cle sd md tam gile c i n , cac h^
sd nen ciia Idp 3 va Idp 4 la sd td, Cac sd lieu dupe t h i hien trin Hinh 3.
Yeu c l u : xac dmh chuyin vi m d (chuyen vi ngang w i , chuyen vi xoay9i) t^i dinh coc
Thyc hien tinh t o l n theo thuat to^n de xuat, k i t qua cac chuyin v]
md wi va Si the h i f n tiin Bing 1, Bing 2 va Hinh 4, Hinh 5.
Be kiem tra do tin c i y ciia thu$t t o l n d l xuat, so sinh k i t qua cila t h u | t t o l n de x u l t vdi t h u i t t o l n tdi Uu hoa mdc a. [4] theo cic tieu chl trong [14]. K i t qua t h i hien tren Bing 1, Bang 2 va Hinh 3, Hinh 4.
Tfnh t o l n theo thuat t o l n [12], so s i n h vdi thuat toan tdi uu hda mdc a. Ket qua the hien t r l n Bing 3, Bing 4 v l Hinh 3, Hinh 4.
Bang 1. Chuyin vi rigang dinh cpc Wi theo thu^t t o l n d l xuat tatcSt
a
0,0000 02DDD 04000 p_.60K_
_0-8000_
1.0000 Thu^ttoande
(mm) 45327 4.6777 4.8816 51446 5.4667 5,3478
(mm) 8.6404 7.9634 7.3457 67B72 _ 6 ^ e 7 9 _
5.8478 Thuit t o j n toi UU
hoa mile a
(mm) 4.4S70 4.7010 493S5 5.2059 5 5 0 5 4 5.8478
(mm) _ 8 6 M 1 _
7,8964 7.2422 _6_Jtl07 62418 5B478
Sailech A E , . . { H )
1.02 0.50 1.15
i.ie 0.70 0.00
Sai Ikh AE-™(%)
0.66 0.85 143 1.29 0.74 0,00
Sallkli IE(%)
245
Bang 2 C h u y i n v i x o Latc^
0,0000 02000 0.400O 0.6000 0,8000 1.0000
Thuattoan de xual
(rad) -0.0046 -0,0043 -0,0041 -0.0039 -0,0037 -O0O36
(rad) -0.0030 -0,0031 -0,0032 -00053 -0,0034 -0,0036
ay dinh coc 01 theo thuat t o l n d l x u l t Thuat toantoi uu
hda miic a 0,™,, (rad) -0,0046 -0,0043 -0,0041 -0.0039 -0,0037 -00036
(rad) -0.0030 -0.0031 -0.0032
^).OD33 -0.O034 -D0D36
AEe™[%)
000 0.00 0.00 0.00 000 0.00
Sailed!
AEe„„(%)
0.00 0.00 0.00 000 0.00 0,00
Sai -i Ikh ^ IE[%1 .
000
Bing 3. Chuyen VI n Litc3t
ODODO 0.2000 0.4OOO 0.6000 0.8000 1,0000
Thuattoan[12]
(mm) 4,3721 4,5749 4.8239 5.1191 5.4604 5.8478
Wl,n.
[mm) 8.4775 7,8592 72870 5,7611 6,2814 5.8478
;iang d i n h coc w i Thuat toan toi Uu hoa mile a
W i n w . (mm) 44S70 4 701O 49385 5,2059 5,5054 5.8478
Vl\rm (mm) 8.6981 7.8964 7.2422 6.7007 62418 58478
t h e o t h u a t t o a n [12]
Sai Ikh A£™{%}
2.56 2,68 2,32 1,67 0.82 0.00
Sailech AE™(%)
2.54 0.47 0.62 0.90 0.63 000
• "'"^
m
1 1
BInq 4. Chuyin vi xoay dinh coc fii theo t h u i t toan [12]
Latest a 0.0000 OiOOO 04000 O60O0 OiOOO 1.0000
Thuat toan [12]
(rad) -0.0045 -0.0043 -0.0041 -0.0039 -00037 -0.0036
(rad)
•0.0029 -0.0030 -0.0031 -0.0033 -0,0034 -0,0036
ThuSttodntSiuu hiamilca B i n . (rad) -0,0046 -0,0043 -0.0041 -0.0039 -0.0037 -0.0036
(rad) -00030 -0.0031 -0.0032 -0.0033 -0.0034 -O.0O36
Sai i k h AE»,.(%)
2.5!
0.00 0.00 0.00 0.00 0.00
Sai I k h AE™(%)
211 1.76 3.49 0,00 0.00 000
Sai lech IE(%)
3.27
\ 131
• ei(rad) PA - thuat toan d l x u a t ; OA - t h u i t t o l n tdi Uu hda mdc a; A[12] - thuat t o l n [12].
Thdng qua vi du minh hpa t r l n , nhan thay mot sd d i e d i l m sau eda thuat toan d l xuat:
- T h u i t toan fle xuat eho k i t qua tfnh t o l n s i t vdi thUe te va cd sai lech b^ (sai lech Idn nhat nhd hon 3%). Odi vdi chuyin vi xoay Si, t h u i t toan de xuat cho k i t q u i trung vdi k i t q u i eiia thuat t o l n tdi Uu hda mdc a. So sanh vdi k i t q u i tinh diuyen vj ngang ui tai [11] (trudng hop 2, cd cung c l e g i l tri eda tham sd m d dau vao), thuat t o l n d l xuat cho cle sai lech be hon [sai lech Idn nhat trong [11] so vdi k i t q u i "chfnh xac" 11 hon 13%).
- Thuat t o l n fll xuat cho k i t q u i t d t hon thuat t o l n [12]. Do fld, fldi vdi d i p Utig k i t cau la e l c ehuyen vj md, md hinh hoi quy da thde bae 2 flay dil la md hinh thay t h i phd hop hon md hinh hdi quy fla thUe b l e 2 khdng d l y dd.
4. Kit luan
Bai bao da d l xuat mdt t h u i t toan m d e l i tien, utig dung vao phan tfch k i t c l u coc chiu t l i trpng ngang. Thuat t o l n de xuat la su k i t hpp eda c i c noi dung: sd dung b i l n chuan trong md hinh hdi quy da thdc ble 2 d l y dii, lUa chpn chuyen vi phuong p h i p kiem tra ch^o rdi bd mdt tap v l dua ra tieu ehi ude luong sai l§ch tdi t h i l u , sd dung thuat g i l i di t r u y i n GA de g i l i bai toan tdi Uu x l e dinh d i p dng ket cau. Lfu diem cOa thuat toan d l xuat la sd lupng cac b l i toan PTHH tat dinh g i l m , ma van d i m b i o d o tin c|y trong tinh t o l n .
Hudng nghien cdu t i l p theo la phat t r i l n thuat toan fll x u l t ddi vdi bai t o l n dn djnh cua he thanh, phan tich m d ket eau phi tuyen, v l m d rdng thuat t o l n ddi vdi c l e sd m d dau vao cd dang tam g i l e khdng can
TAI LteU THAM K H A O
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