Cong trinh Khoa hpc
MO HINH DU* BAO XUONG C A P LOCAL MIXTURE HAZARD MODEL AP DUNG NGHIEN ClTU SO SANH TIEN TRIEN
HAN LUN MAT DU^OfNG BE TONG NHU^A TREN CAC TUYEN QUOC LO
NGUYEN DiNH THAO B(J mon Dudng Otd & San bay Trudng Dgi hgc Giao Ihdng Van tai Tom tat: Hien nay, hien luang han liin mgi dudng be long nhira dang dien ra rat phuc lap trin nhiiu tuyin quoc 16 d nudc ta gdy dnh hudng nghiem irgng den luoi thg mat dudng. lam suy gidm mire do phuc vu vd dieu kien ATGT. Nghien cuu du bdo lien triin hien tugrig ndy nhdm khuyen nghi cdc gidi phdp Idu ddi d cdp mgng ludi cSng nhu djnh hirdng xu ly cu the d muc du dn trong do co vi4c xdc dinh phgm vi tru lien xir ly Id can thiet. Bdi bdo trinh bdy nghien cuu mo hinh du bdo xuong cdp Local Mixture Hazard Model vd dp dung de xdc dinh quan hf luang doi vi toe do xuong cdp mat dudng cho cdc tuyen quoc Id theo chi liiu hdn litn.
Summary: Pavement rutting is the serious distress that has been progressing widely on national roads with negative effects on reduction of road serviceability, traffic safety and pcevemenl life span Researching on prediction such deterioration progress to make recommendations of long-term solutions, policies at network level as well as direction and orientation for counlermeasures at project level is needed. The paper presents Local Mixture Hazard Model and its application in the empirical study to clarify comparative deterioration speeds of national routes in the Northern in term of rutting distress
I. MO HINH DV BAO XUONG CAP LOCAL MIXTURE HAZARD MODEL 1.1. Mo hinh du* bao xuong cap Markov Hazard Model
Trong tgp miu ldn la cac doan dudng dupc xet, qua trinh tiln triln mit mat dudng dugc xem la qua trinh ngiu nhien hay la mgt xich Markov thuin nhit dugc xac djnh bdi ba ylu to ca ban la: tap hgp trang thai ciia he, ma tran xac suit chuyen trang thai ciia h? va trang thai ban diu ciia hf Ggi X(t) la dac tinh lam viec ciia h? tai thdi dilm t. Tgp hgp cac gia tri dac trung cho d5c tinh ciia he ggi la khong gian trang thai I. Tai thdi dilm hien tgi t, trang thai ciia he la i va trudc thdi dilm nay (trong qua khir), he d mgt trgng thai nao do. Bai toan dat ra la xac djnh xac suat de den thdi diem T trong tuang lai (T > t) trang thai ciia he la j . Nlu xac suit nay chi phy thugc vao cac tham sd t, T, i, j thi sy tien triln cua he trong tuang lai chi phy thugc vao hien tgi va dpc lap vdi qua khu. Do la tinh Markov va he co tinh chat nhu vay dugc ggi la he co tinh Markov. Trong qua trinh nay, tai thoi dilm TQ , mat dudng d trang thai tot irng vdi thang trang thai i = 1. Theo thdi gian, qua trinh xuIng cip diln rava thang trgng thai i (i = 1,...,I) tang dan din cac trang thai kem han. Khao sat mat dudng dugc thyc hien vao cac thdi dilm cy thi z^ va TB. Nhu v^y dya tren s6 lieu co dupc trong cac lin khao sat, cin phai dy bao dugc trang thai ciia m$t dudng trong tuang lai d thdi dilm T,. Tir s6 li^u thu thap dugc trong hai lin khao sat tinh 30 Tgp chi KHOA HOC GIAO THONG VAN TAI S6 47 - 08/2015
Cong trinh Khoa hoc tr^ng mat dircmg: h(TA) = i tai thai diem TA va h(TB) = j tai tliai diem TB, ta xay dirng dirac ma tran chuyen trang thai Markov riy.
P r o b { h ( t , ) = j|h(TA) = i} = 7t,
|7t,j>0 (i,j = I,...l) (2); Vai diSu kien: J n.^ = 0 (khi i > j)
( I )
(3)
Trong nghien ciru ciia minh nam 2006, Y.Tsuda da tinh toan xac dmh dugc cac xac suat trong ma tran tren dya vao ly thuyet xac suat va thong ke nhu sau lam ca sd tinh toan dugc thdi gian ton tai ciia mat dudng d tirng trgng thai. Ket qua la tuoi thg mat dudng va dudng cong xuong cap dugc xac dinh nhu trong hinh 1 cho mat dudng tren 21 tuyen dudng qudc lg d phia Bac nudc ta (xem thong ke ten tuyen trong hinh 2),.
7i,(z) = Prob{h(xB) = j | h ( T 0 = i) = X n ^ - ^ e x p ( - X , z )
=in n. exp(-X.|Z) (4)
(5)
trjng thai
[11
(21 13) [4]
[5]
[61 Chieu s3u
(mm)
[0;101
|10,20) (20:30) 130:40) (40:50)
^50 xuong
1-079 0^1974 0-195 0.3712 0-5815
Ti)iJ\ gian trgng thai
0 93 5 07 5.13 2 69 1.72
T h i l giSR ton tai den trgng
thai ET, (nam)
0 93 5.99 11 12 13.81 15,53
Thoi gian khai Ihac (nam) 0 5 10 15 20
.a ^°
O 30
40
, 50
\
\
\
\
Hinh I. Dudng cong xuong cdp trung binh ciia todn bg cdc tuyen dudng 1.2. Mo hinh du bao xuong cap Local Mixture Hazard Model
Mo hinh Markov Hazard Model d tren giiip dy bao dugc dien bien xuong cap chung ciia ca h?; tuy nhien trong thyc te, tap mlu thudng gom rat nhilu ddi tugng dugc dac trung bang cac
Tgp chi KHOA HOC GIAO THONG VAN TAI S6 47 - 08/2015 31
trudng so lieu. Trong do nhieu mau cd cac thupc tinh gidng nhau cd the phan thanh tirng nhom nhu nhom cac phan doan mat dudng dac trung tren mgng ludi dutmg theo loai kit ciu, tuoi tho khai thac, dilu kien tai trgng, che dp thiiy nhiet,,.. Khi do, viec du bao dugc diln biln xuong cap hoac thay doi trang thai ciia tiing nhom dac trung trong he co y nghTa rit ldn trong viec phan tich, danh gia so sanh dac diem xuIng cap rieng ciia tirng nhom giiip xac dinh dugc nguyen nhan, muc dp tac dgng cCia cac nhan td gay xuong cap dac biet ddi vdi cac nhdm cd toe dp xu6ng cip bat thudng. Phan tich so sanh nhu tren dugc ggi la phan tich Benchmarking thudng dugc dimg nhilu trong quan ly tai san kit ciu ha tang, dua ra cac khuyin nghj can thay ddi de hoan hien ban chu trinh quan ly PDCA (PlanLgp ke hogch - DoThuc hiin - CheckKtim tra - ActHdnh dgng). Vdi kit cau mat dudng, ket qua phan tich Benchmarking giup lua chgn va thilt kl kit ciu hgp ly cho tirng dilu kien ap dung vl: tai trgng, khi hau, dja chit, thuy van,...
Dap ling nhu ciu phan tich Benchmarking, mo hinh du bao xuong cip Local Mixture Hazard Model (Mo hinh dy bao xuIng cip h6n hgp dja phuang) da dupc nhdm nghien ciiu do GS. Kiyoshi Kobayashi va cac cgng sy phat triln va dua vao ung dung. Trong quan ly mgt dudng, toan bp tap mlu c6 thi phan thanh K nhdm khac nhau theo cac tieu chf danh gia thuan nhit khac nhau vl: logi kit ciu, loai vat lieu, dilu ki?n moi trudng tac dgng, dieu kien tai trpng tac dgng, tuyen dudng, dan vj quan ly,.... Trong nhom thir k (k = ],...,K), tdng so mau co trong nhom la Sk. He sd khong thuan nhat ciia moi nhom rieng ky hieu ia ^, bieu thi su thay doi miic.
xuong cap irng vdi tirng trang thai i (i =1,...,1 - 1) ling vdi tirng nhom mau s^. Cong thiic ciia ham xudng cap trong (3) dupc viet dudi dang tong hgp nhu sau:
x;" =i;'-E'0 = U--,l-l;k = l,-",K;s^ =1,- -,5,) (6) v l bilu diln do dugc, gia trj ciia E^ (k = 1, ,K) dugc mo ta bing vec-ta t^, vdi thanh
ngang ( ) chi sy do dugc. Nhu vgy, la ham tin tgi ^(;'*)theo mire xudng cip hon hgp xac dinh theo (6) nhu sau:
^(yf) = exp(-?:.ry:') (7) Tuang ty, xac suit chuyen trang thai Markov xac djnh theo cong thuc (3), (4) dugc vilt lai
nhu sau:
7t|;(z'' :£*') = exp(-A,;'e''z'') (8) 7t;;(z'':e')-£n^^^^^exp(-iyz')-2^y;/^'')exp(-^,S'^z'') (9)
Vdi
<(^'^ = nxrrxr (10)
Trong nghien ciiru nay, mo hinh ap dyng dugc xet trong trudng hgp trj so e^co mien pftSn tan h?p va mo hinh ngau nhien trong trudng hgp nay ggi la md hinh x u l n g c i p hdn hgp dja phuang (Local mixture model). Theo hg ham mu f(x; e), he h§n hgp dja phuang dugc dinh nghia bieu thj tham so hoa theo gia tri trung binh ciia no ^'':
g(x;p):=f(x;£) + ^ f ' ( x ; e ) vdi ISVE) = 1^I(X.E) ( H j Khai triln cac phuang trinh trong (10) co thi dugc bilu diln dudi dgng chuSi Taylor. Do
3 2 Tgp chi KHOA HOC GIAO THONG VAN TAI S6 47 - 08/2015
Cong trinh Khoa hoc ham hgp ly (Likehood) ciia xac suit chuyln trang thai Markov trong (11) thudc hp ham mu nen CO thi tinh gin diing xac suit chuyln trgng thai theo dang phan bd hon hgp dia phuong-
S„(z) = Jj7i,/z:8)f(E)de ( i - l , - , I - i ) (12) D I thuan tien trong tinh toan, xac suat chuyen trgng thai hon hgp dja phuang dugc gia
thuyit CO dang ham mu f,ni:s(e,z,>.), vdi mix dugc ky hieu cho md hinh hon hgp. Ham hon hgp f,nix(E,z,X.) CO the dupc bieu thi bang gia tri. trung binh ciia ham chuan f(e,z,^) va phan bo H(e).
Phucmg trinh (12) dugc don gian hem dudi dang:
f,„,j£,z,X) = jf(e,z,X)dH(e) (13) Vdi f(e,z,A.) - exp(-elz). Ham fl;epsilon,z, lambda) cd the dugc coi la ham ciia epsilon ve
gia tri trung binh ciia no. De khong mat di tinh tong quat vdi dilu kien trj s5 trung binh tin tgi, phuang trinh (11) cd the dupc khai trien tiep va viet lai nhu dudi day:
exp(-EXz) = e-^(l + (E-1 )(-Xz) +^^~'^ (-Xz)' +..,) (14) Day la chuoi Taylor. Do dd dang toan phuang dugc chap nhan dung de tinh xap xi. Ket qua
la ham hien ciia xap xi c6 the dugc tinh toan de xac dinh xac suat chuyen trang thai Markov:
E(e-'^)^e-'^{l + ^ ^ ^ } (15) 2
S„(z) = e - ^ ' { U ^ ^ } (16) 2!
^ ( z ) = i v : , ( M e - ' ' ' < I + ^ ^ ^ } ( i = l - . - I - l J = ' + U - . - I ) (17)
II. iTNG DUNG MO HINH LOCAL MIXTURE HAZARD MODEL DANH GIA QUA TRINH XUONG CAP MAT D U ^ N G THEO HU HONG H A N LUN TREN CAC TUYEN QUOC LO 6" PHIA BAG NUOC TA
Mo hinh dy bao dya tren ly thuyet dy bao Local Mixture Hazard Model da dugc ditng lam thuat toan dl xay dung phin mim tinh toan. Phan mem duoc viet bing ngon ngCf lap trinh Fortran nhim dam bao toe do xii ly cac phep ti'nh phuc tgp tren tap so li?u ldn. Cong tac chuan bj so lieu: tir kit qua khao sat tinh trgng mat dudng, 6 thang trgng thai ung vdi tinh trgng nut mat dudng tiJ "Rit T6t" din "Rit Xiu" (bang 2) dugc djnh nghTa nhim rdi rac hoa tinh trgng mat dudng theo cac thang danh gia dl ap dung mo hinh tinh tren. Thang trang thai tren da dugc sir dung trong cac nghien ciiu cung nhu thyc tiln tgi Nhat Ban. Tai Viet Nam, khi lap thii ke hoach sua chOa mat dudng nam 2014 bing mo hinh Kyoto Model ciia Tong cue DBVN cung ap dung thang trang thai danh gia nay vdi chieu sau hin kin gidi hgn de tinh toan tuoi thg mat dudng la 50mm. Ngoai ra, ngudi dimg c6 thi dinh nghTa thang trang thai mdi khi ap dyng cho phii hgp.
Xac suit chuyen giira cac trgng thai tren dugc tinh toan dua tren so lieu tinh trgng mat dudng dugc xac dinh tai it nhit hai thdi dilm khac nhau. Trong nghien ciru nay, hai tap so lieu ve tinh trang mgt dudng dugc thiet lap: (1) tinh trang mat dudng dupc thu thap nam 2012 va (2) tinh trgng mat dudng tdt nhat irng vdi trang thai [1] cd dugc tgi thai diem hoan thanh xay dyng mdi mat dudng hogc lin sua chira Idn gin day nhit can cir vao du lieu lich sir bao tri mat
Tap chi KHOA HOC GIAO THONG VAN TAI S6 47 - 08/2015 33
dudng, Toan bp so lieu khao sat va thu thap ciia 52411 phan dogn mat dudng c6 chieu dai phan doan trung binh 100m thupc 21 tuyin qu6c 16 da dugc tong hgp tgo tep dff lieu dau vao cua phin mem phan tich phat trien tren ngon ngiJ Fortran (bang 1). Dir lieu dugc tai vao chuang trinh phan mim cd cau true tep dang .csv. Nhd ap dyng mo hinh Local Mixture Hazard Model, miic xuIng cap Xf'' ciia tirng tuyin dudng dugc xac dinh tuang irng vdi tirng trang thai tinh trang mat dudng lam ca sd xac dinh dugc tuli thg mat dudng. Kit qua tinh toan dugc the hien tren bang 2, hinh 2 c6 bilu thj tuong quan vdi mice xuIng cip chung ciia tit ca cac tuyen {irirdng hgp Benchmark).
Bdng 1. Bdng dit lieu phuc vji phdn lich
TT
] 2
52411
.;"L
QLI OLl
^79
Ly trinh doan Tit km
0 0
115 m 10 100
500 DSn km
0 0
115 m 100 200
600
Nam dira dudng vao khai thac gan day nh^t (sau Nay dimg hogc sau cai
2001/01 2001/01
1995/01 Thai diem linh irsng m^t dirtnig 2012/10 2012/10
2012/08 U n
1 1
1 Chien sSu
(mm) 31 00 13 00
33 00 ( T 2 - T 1 )
(thang) M.S 118
13 6
Thang tr^ng thai tinh tr^ng m|it
diicmR Tai thoi digmTI 1 1
1 Tgi thoi dieiiiT2 4 2
4
Bang 2. Miic xuong cdp A vd thai gian mat dudn^ ton tgi d mo Irgng thdi ciia tirng luyen dudng
TT
W„
Triing tliai Clue
1 2 3 4 5 6 7 8 9 ID 11 12 13 14 15 16 17 18 19 20 2\
saiihanluii(mm) Bench mark
Q L I V D 3 Q L 2 0 L 3 QL4E
Q L 5 Q L 6 OL.a 2 QL6 3 QL 10 QL 1 1 QL 15 QL IS NB-BN H C M QL37 QL.38 QL-38B QL43 QL70 QL279
Mire xuung c^p A. ling vdi tCrng tr^ng thai 1
[0,10) 1 079 Q5179 1 2567 1 2225 1 2S1S 0 7214 1 31E 1 1039 0 9816 1 3454 0 9064 8 171 0S456 0 3706 0 4779
0 8219 2 0414 1 0026 2.2839 1 5021
1 [10.20)
0 1974 0 1 13 0 3399 0 2236 0 2345 0 132 02411 0 2019 0 !796 0 2461 0 1658 1 4949 0 1547 0 0678 0 0874
0 1504
0 1834 04178 0 2748
3 ' [20,30)
0 195 0 1117 0 2271 0 2209 0 2316 0 1304 0 2382 0 1995 0 1774 0 243!
0 1638 1 4767 0 1528 0 067 0 0864
0,1485
0 1812 04128 0 2715
*4 . :30 ,40) 03713 0 2126 0 4323 0 4306 0 441 0 2482 0 4534 0 3798 0 3377 0 4638 031 18 2 811 0 2909 0.1275 U 1644
0 2828
0 3449 0 7857 05168
5 40; 50) 0 5815 0 333 0 6773 0 6588 0 6908 0 3888 0 7103 0 5949 0 539 0 725 0,4885 4,4036 0 4557 0 1997 0 2575 0 690H 0 2354 0 4439 1 1002 0 5403 1 2308 0 8095
T h » , g i 1 [ 0 ; l O )
0 93 1,62 0 80 0 82 0 78 1 39 0 76 0 9 1 1 02 0 74 1 10 0 12 I 18 2 70 2 09 0 78 2 29 1 22 0 49 1 00 0 44 0.67
n ton ta 2 [ I 0 ; 2 0 )
5 07 8 85 4.35 4 47 4 26 7 58 4 15 4.95 5.57 4 06 6.03 0 67 6 46 14 75 11 44 4 26 12 51 6.65 2.68 5 45 2.39 3.64
3 :20 , 30)
5 13 8.95 4 40 4 53 4 32 7 67 4 20 5.01 5 64 4 I I 6 10 0 68 6 54 14 93 11 5g 4 32 12 67 6 73 2,71 5 52 2 42 3.68
rang thai (nam) 4 (30 ,40)
2 69 4 70 2 31 2 38 2 27 4,03 2 31 2 63 2.96 2 16 3.21 0 36 3 44 7 84 6 08 2 27 6,65 3 54 I 42 2 90 1 27 1 94
S [40 , 50J
1 72 3 00 1 48 1 52 1 4 5 2 57 1 41 1 68 1 89 1,38 2,05 0 23 2 19 5,01 3 88 1 4 5 4 25 3,26 0 9 1 1 85 0,81 1 24
Tuoi th9 (nam)
E 'S.53
^ ^7.13 E '3 34
E "^.'i
B '3-08 Bfc; 1 23.23
B 'i-''^
E l 15.18 P n 17.08 B '2-"*
E '«•'•'
1 2.05 w ^ i9S2
m^mts.23 i ^ asios
^ 13 08
^ ^^ 7
^ J 20.39 U 8.21 m] 16.72 D 7.34
0 TiA6
34 Tap clil KHOA HOC GIAO THONG VAN TAI S6 47 - 08/2015
Cong trinh Khoa hoc
Hinh 2. Dudng cong xudng cdp cua tirng tuyin dudng theo chi tiiu hdn lun vet bdnh xe Ket qua phan tich Benchmarking d3 cho thay ro mire do xudng cap khac nhau cua mat dudng tren mdi tuyen lam ca sd de cac ca quan quan ly dudng xac dinh dugc cac doan tuyen can luu y dac biet (khdo sdt chi tiit cudng dg. xdc dinh nguyen nhdn. dua ra gidi phdp xit ly, kien nghi cdi tien....) khi c6 dien bien xuong cap nhanh bat thudng.
So sanh vdi tuoi tho trung binh ciia mat dudng la 15.53 nam, cac tuyen QL18, OL37 {lan dirge khdo sdt cgnh ddi phdn cdch) cd tuoi thp cao r6 ret. Trong khi do mat dudng tuyen QLI.!
tire la doan noi QLI ra cang Ninh Phiic co tdc dp phat trien han iiin rat nhanh, chi sau hem 2 nSm, m^t dudng da han liin sau den 50mm. Tir ket qua nay, khao sat bo sung cho thay tinh hinh xe tai n^ng hoat dong tren tuyen dudng nay trong thdi gian vira qua rat phirc tap. Vdi cac tuyen CO t6c dp xu6ng cap d mire can trung binh nhu QL2, QL3, QL5, dudng H6 Chi Minh,... can tang cudng kl6m tra h^n ch6 cac nguyen nhan tac dpng bat lai gay hu hong mat dudng nhu kiem soat tai trpng phuang tien ddng thdi trien khai cong tac bao tri du phong de litm cham dien tien xuong cap tren.
Ngoai ra, kSt qua du bao tren QLI cho thay tu6i tho theo chi tieu hfin lim kha cao (27.13 nam); tuy nhien day la ket qua phan tich c6 dupc tir dif lieu khao sat cua lan sat dai phan each.
Quan sat thuc te tren QLI d ian ngoai, hu hong hin liin nghiem trpng han nhieu so vdi lan sat dai phan each. Day la ca sd de kien nghj dieu chinh each chpn lan khao sat cho chieu dudng co nhi6u lan xe: can khao sat tit ca cac lan hoac lan dac trung co miic dp hu hong nang hon.
Tir ket qua du bao xuong cSp cho tirng tuySn nhu trong hinh 2, co the tiep tuc ap dung mo hinh Local Mixture Hazard Model de phan tich danh gia xu6ng cap cho cac nhom phan doan dac trung tfong m6i tuyen dudng do theo timg ki-16-met, theo tirng Ian, theo cac dieu kien thiiy nhi?t,...
(Xem liep trang 18) Tap chi KHOA H O C GIAO THONG VAN TAI S6 47 - 08/2015 35
