Nghiên cứu ứng dụng công nghệ mạng nơron tế bào vào giải phương trình truyền nhiệt 2 chiều (Luận văn thạc sĩ)

i

IH
IH

LU

N

U

C

NG D

M NG N

I

RUY N NHI T 2 CHI U

H

PH M THANH H I
ng d n: TS.

- 2016

S

T B

c li u


ii

ng k t qu
lu

mb tc

s h

t

t Vi t Nam. N

nhi

t.

14

4

lu

Ph m Thanh H i

S

c li u

16


iii

T
i

i th
t

lu

ng d

om

u ki

t nghi p.
ng d

h ct pt

t th i gian
o

u ki

c
p th l p Cao h

t lu n

ng c g ng nh
h

lu

nh

cs

i gian

u thi

n ch nh

a th

n.

14

H

S

c li u

4

Ph m Thanh H i


iii

M CL C
L

..............................................................................................ii

L IC

..................................................................................................iii

DANH M

VI T T T ..............................................................iii

DANH M

NG............................................................................... vi

DANH M

..............................................................................vii

M C L C........................................................................................................iii
M

U........................................................................................................... 1
V

GI

N NHI T B NG

M

...................................................... 3

1.1. Gi i thi u v

................................................. 3
nv

........................... 3
p hai v i hai

bi

c l p ....................................................................................................... 4
.................................................................. 4
..................................................................................... 6
n nhi t 2 chi u.............................................................. 8

m

................................................................. 12
m

1.3.2 Ki

nv
ng ki

1.3.4. M t s

o.................................................. 12
m

................................ 13

ng CNN ............................................................. 14

ng d ng c

CNN.................................................. 20

GI

N NHI T HAI CHI U ........ 24

2.1. M i quan h gi a m

........ 24

m

ron t

......................................................................................................... 28

2.2.1. M

t k m u.............................................................................. 28
S

c li u


iv

2.2.2.

ng d

2.2.3. S

-UM trong m t s

n............ 29

nh c a m ng CNN ................................................................... 39
n nhi t hai chi

c............................. 50

n nhi t .................................................... 50
u ki
2.4. Gi

u ki

..................................................... 53

n nhi t 2 chi u b ng CNN.................................. 54
n nhi t hai chi u............ 54

2.4.2. Thi t k m
2.4.3. Ki

n nhi t hai chi u ............... 54
n t cu m

n nhi t hai

chi u ................................................................................................................ 55
2.5. K t lu n .................................................................................................... 57
NG GI

N

NHI T HAI CHI U ....................................................................................... 58
.................................................................................... 58
t qu

................................................................................ 59

K T LU N ..................................................................................................... 69
U THAM KH O............................................................................... 71

S

c li u


v

Vi t t t

Ti ng Anh

CNN

Cellular Neural Network

PDE

Partial Difference Equation

Ti ng Vi t
m

Ma tr n c ng logic l

FPGA

Field Programmable Logic Array

VLSI

Very Large Scale Intergrated

pm

VHDL

Very High Description Language

c t ph n c

S

c li u

c
cao


vi

B

u c a nhi

trong t m ph ng th c nghi m ........... 60

B

c

nh ........................................ 61

B

c

nh ........................................ 62

B ng 3.4. K t qu

........................................................ 63

nhi
B

.............................................................. 63

c

nh ........................................ 64

nhi

.............................................................. 64

B

c

nh ........................................ 65

B

c

nh ........................................ 66

B ng 3.8. K t qu

S

......................................................... 67

c li u


vii

n..................................................................... 13
c c a m ng CNN................................................. 14
t s ki

n ............................................... 14
u 3 l p ....................................................... 15
t bi n v

c

ng ................................... 18

a CNN t

................................. 19

i ti p b ng 0: C(0,B,z) ...................................................... 19
nc

i ti p b ng 0 C(0,B,z)........................... 19
ng 0, C(A,0,z)...................................................... 20
ng 0:C(A,0,z)................................... 20

ch CNN hai l p. L

n l p v ...................... 25

u...................................................................... 26
i h PDE ........................................ 28
r

i (LLM, GW, GCL) ..... 30

r

.......................... 31

t

....................................................... 32
x

.................................................. 33
p TEM1 (a,b).............................................................. 35

N p k t qu

................................................................. 36

nh k t qu x

m

uc

p............................... 38

................................................. 39

nh k t qu nghi m c

....................................... 39

a m ch phi tuy

.. 45

ng ch c c a m
......................................................................................................................... 46
S

c li u


viii

ng c a m

i

a g(t). ......................................................................... 50
u c a m t kh
kh i CNN 2D cho gi
ix
m ph

n nhi t.............. 56

h c c a m ng CNN gi

n nhi t .56

c nghi m .......................................................... 58

nhi

u................................................................... 61

nhi

............................................................... 62

nhi

.............................................................. 63

nhi

.............................................................. 64

nhi

............................................................ 65

c a nhi
nhi

S

................... 50

........................................................ 66
sau 10 gi y ............................................................ 67

c li u

1

M
Trong nhi

U

hoa h

ng bi

nhi u tham s

c t p theo

u ki n ngo i c

quy

gi i

n vi c gi

m

u lo

ti n h

ng hi

gi

it

h n ch , m t s

ng h

c

v i ng d ng trong th i gian th c.
Vi

m
it

n thi

u tri n v

i gian th c.
u ng d

m

n nhi t hai chi u

mm

ngh m

thu t thu t th c hi n

gi

n nhi t hai chi u b

th c hi n

m

i dung sau:
V

m

gi
:

h truy n nhi t b
c

m
n nhi t hai chi

ng d ng th c

ti n.
Gi

n nhi t hai chi u:

gi
chi

n nhi t hai
c gi i b

m
ng th c nghi m:
t qu .

S

xu

c li u

t qu


2

Lu

uv im

um

m i ng d ng

trong vi c gi

c.

t nhu c u r t quan tr ng trong th

n khoa h

uh

c bi u

di n b

n ph c t

chi m s

ng l n. Vi c gi

d

cv
Trong n i dung c a lu

n nhi t hai chi

t ng

n.
cs

r

i nh ng thi u
lu

S

c li u


3

V

GI

N NHI T B
NGH M

1.1. Gi i thi u v
m

nv

a hai hay nhi

n ph
u
x
2

u
x2

u
y
2

u
y2

u
z

[7,8]

:
(1.1)

0
2

u
z2

u

(1.2)

u(x,y,z);
C pc
p 1; c p c

pc

p cao nh

c pc a

p 2.
cg
xu t hi n v i lu th a b c nh

a

i nhau.
D ng t

iv

bi
2

A( x, y )

2

2
u
u
u
2
B
(
x
,
y
)
C
(
x
,
y
)
2
x
x y
y2

D( x, y)

N u G(x,y)

n nh t, n

n nh t.

S

u
u
E ( x, y ) F ( x, y)u G( x, y)
x
y

c li u

(1.3)


4

Nghi m c
cm

ng nh t th

x+3y32z

nghi m c

: u(x,y) = x + y

mc

lo
bi

p hai v i hai

cl p
D ng t

p hai, trong
c l p ( x, y)

t ph thu c hai bi
2

A( x, y )

2

u
x2

2

u
x y

2 B( x, y )

C ( x, y )

u
y2

i ta ch

D ( x, y )

u
x

E ( x, y )

u
y

F ( x, y)u

c r ng m

G ( x, y )

(1.4)

ng (1.4) nh

nh

m t trong ba d ng sau:

a) N u

trong m t mi

h

ng mi n y v d ng
2

2

u
2

u

D1

2

u

u

E1

F1u

(1.5)

G1 ( , )

ng h

i eliptic.

b) N u

trong m t mi

n

d ng
2

2

u
2

u

D2

2

u

u

E2

F2 u

G2 ( , )

ng h

(1.6)
i hypebolic.

c) N u

trong m t mi

i n

d ng
2

u

D3

2

u

E3

u

F3 u

ng h
S

G3 ( , )

(1.7)
i parabolic.

c li u


5

ng
minh c

id

chu

iv im ts

c bi

ng h p [5,7]

iv

ng h

s bi
nb tk

n,

ng minh c

t ph c t p. Trong nh

c

ng h

m ph i d a

ig
gi i quy t v
p

gi i quy t v
ti

th sau.

a, b v i a < b.
QT

a

x

b; 0 t

T ;

QT

a

x

b;0 t

T .

u(x, t) tho
2

u
t

Lu

u

x2

u( x,0)

g ( x)

u ( a, t )

g a (t )

f ( x, t )

(1.8)

a
u (b, t )

b
T

t

h

S

0 t

g b (t )

Ch n hai s

x

b a
N

xi

a ih

T
M

tj

j.

c li u

i
j

0,1,2,....,N
0,1,2,....,M

(1.9)
(1.10)


6

Ta chia mi n QT

ng th ng x

i nh

cg

xi , t

tj , m

m

.M

mg

.

g
g

i gian.

QT .

i, j t

T pt tc
X px

u ( xi , t j 1 ) u ( xi , t j 1 )
2

u
( xi , t j ) o( )
t

u ( xi 1 , t j ) 2u ( xi , t j ) u ( xi 1 , t j )
h

2

T

(1.11)

2

u
( xi , t j ) o(h 2 )
2
x

px
thay th

mg

u ( xi , t j 1 ) u ( x i , t j )

* Xu

vij

u( xi , t j ) .

u
( xi , t j ) o( )
t

suy ra

u ( xi , t j 1 ) u ( xi , t j )

u ( xi 1 , t j ) 2u ( xi , t j ) u ( xi 1 , t j )
h2

u
( xi , t j )
t
S

2

u
( x i , t j ) o(
x2
c li u

h2 ) .

(1.12)


7

vij

v

i 1..N 1, j

vi0

g ( xi )

i

0..M 1 (1.13)
(1.14)

1..N 1

(1.15)
t

vij

h2
1

(

(1 2 )vij

h2

1
2

(1.13)

(vij 1 vij 1 )

f ( xi , t j )

(1.16)

m v ij 1 , vij , vij 1

T (1.16) ta th y n u bi
ki

c vi

c

l p th

j

u ( xi , t j 1 ) u ( x i , t j )

u
( x i , t j 1 ) o( )
t

v

u

0

(1.14).
* N u ta xu

u ( xi 1 , t j 1 ) 2u ( xi , t j 1 ) u ( xi 1 , t j 1 )
h2

u ( xi , t j 1 ) u ( xi , t j )

2

u
( x i , t j 1 ) o( h 2 )
2
x
u ( xi 1 , t j 1 ) 2u ( xi , t j 1 ) u ( xi 1 , t j 1 )

h2

T

S

c li u


8

vi0
v0j
t

g ( xi ) i 1..N 1
g a (t j ) v Nj

T

vi0

0.v1j

1

1

vij 11

1

h

vij

f ( xi , t j 1 )

ga (t j 1 )

y n u bi t

g ( xi )

j 1..M

v d ng sau:

h2

vij 11 (1 2 )vij

v0j

g b (t j )

j 0..M 1

vij

c

vij 11 , vij 1 , vij 11

v i

.

Vi c gi i h

c th c hi n b
n nhi t 2 chi u
t

bi

a nhi

t

s

t mi

c qua th i gian [7,8].

Gi s

u

(x, y)

nhi

t ib

i theo th i gian khi nhi t truy

kh

cs d

c

nh s

i

u theo th i gian.
M t trong nh

tc a

l n nh t c a u ho
c a mi

nhi t
th

c
ng nhi

S

c li u

nh lu t maximum

ho c nhi

nt


9

m t ngu

th

c t o ra t

tc a
ch ng minh.
M

n

gian kh

ut=

u

s ngay l p t

c t i th i
c kh

t > t0. Ch ng h n, n u m t thanh kim lo

t

cg nv
ngay l p t c nhi

t

mn

th c a nhi

ch

0

n 100. V m t v
c truy

iv nt

n, s

ch t c

lu t
a s truy n nhi

cho nhi u m

ct ,s

b qua.
c s d

ng

(random wal

Bi u di
h

di n t
ng trong

h a cho nghi m c a m

c bi t khi nhi t truy

nh t

ng

t v t li u

-chi u
S

c

c li u

ng

ng


10

(1.17)

v i:
theo th

i c a nhi
b

t im

i gian;

n nhi t) c a nhi

theo

ng x, y, theo th t .
k

t h s ph thu

t li u ph thu

d n nhi t, m t

t.
qu c a
N

nh lu t Fourier cho d n nhi t.

ng truy

gi i
n ph

s

u ki

t c
n ph i gi thi t m t ch

v

id

p

m.
Nghi m c

nhi

is
u do m

nhi t truy n t

a m t v t th . M

nh
u tr

u ki

u

t tr

l

c t nghi

u ki

u t

t lu
u ki n nhi t hi n th

ph
parabolic.
c li u

ng

th i gian s

trong m t kho ng th i gian r t ng n.

S

nc a

bi n c a

ts


11

S d ng

Laplace

v

t

c l y theo bi
s
t ho
ng trong t

lan truy n c a th

n kinh. M

n ch

ng t

ts

b ng m

t

t. N

hi

cs d

ng x y ra trong

Black-Scholes

Ornstein-Uhlenbeck
t

nh phi tuy

cs d

nh.
t, v m t k thu

b

n

mc

m thuy

n nhi u lo

u ki

u ki

i h p,

c kh c.

u:

u ki

u ki n tham s

Trong v

t r ng mu

trong v t

m i th

b nhi

trong v t

u ki

c nhi

t im

m

n ph i bi

th

nhi

s c a v t.

cho b ng nhi

* Cho bi t nhi
*T im
u
n

mP c

t im

mc
2

s cho bi

u |S

S

t

q

S

( P, t )

k

( P, t )
u
n v

(1.18).

u ki n
(1.19)

( P, t )

S

2

1

q ( P, t )
k

c.

c li u

12

sc av
nhi

c

i nhi t v

uo

u ki
u
n

N

s

h(u u 0 )

u
n

h=0 suy ra (1.20) tr
n nhi t trong m t v t r
mc

u ut

ki

( x, y, z)

0

(1.20)

0
S

0
S

ng ch t truy n nhi

ng

(1.17) tho

u

u ki

m
nh

m
tv m

ts

c v ki
m

CNN:

n 2-, 3- ho c n- chi u c a nh ng ph n t
t

ng [10,11]:

ng gi ng nhau (g

- cell)

b) M i t
- Ch
- M i bi n tr

c
ch phi tuy

h nt

ct ob ic p

tv

tm
l

cl

i ph n t

pg

nh t,

u, c u v.v... H CNN c

h

c t sau:
h nt

ng h

at

theo th

ng.
S

c li u

i

13

2) Lu t ti p h p trong CNN bi u di n s
c

c b trong t ng c

ng, m i t

-

u ki

c a bi

ir

u ki n

n th

c hay r i r c.
th

n c a tr

a m i cell

n Nr
Nr(i,j) = {C(k,l)|max{|k-i|,|l-j|}

r, 1 k

M

M, 1

l

M}

s d
tk

1.3.2 Ki

c

n.

nv

m

M t ki

m

ch nh

tm

i to
C t
1

2

3

N

j

1
2
3
C(i,j)

M

n
M
ki

t m ng hai chi

chip x

tc cb v
S

c li u

it

t


14

u t o gi ng h t nhau g
tuy

n tr , t tuy

phi tuy

n

ng ph c t p trong nhi u ng d

n ho

ng d a

c c a m ng CNN
ng ki

ng CNN
ng

V m

ng m

i CNN
i thi

ts

u:

ng nh t: (NUP

it

tr

b

-

t ki u t

n (MNS-CNN: Multiple Neighborhood Size
hai ki

. M i chip trong m

CNN): CNN

c u t o ph n c ng

gi

n
ic

r=1;

-

nh ng l

a
ng theo h

th ng t

ng h

c bi t c a MNS-CNN v i hai ki

c n ch ch a m t chip trong l

uk tn it

u t o r t linh ho
S

c li u

u gi i quy t x


15

am

-CNN. Lo i

MSN-

bi n ch s d ng trong m t s

nh

p.

+ Ki

p:

ph

u bi

it

u bi n tr

i

i ta c n m t h

ul pg i

p. Trong c
m

c bi t cho

c, m t l

t bi n tr
h

ng h

u bi n tr
p nh n m

trong m t l p, gi

ns

n

th

c a nhi u l

th p

p ch

m tl

p.
u bi n tr

ch n nhi u ki

ng

th i cho m i bi n tr

ck

linh ho

i quy t nh
2
3

2
2

c li u

S
2
1

c t p.


16

M

t
k
j

um il p
l p (n

l

cc a

n 2 chi

s c a l p.
2
1,

t h CNN hai chi u 3 l
2
3

2
2,

il
cc

b ch s k, ch

j ( j) v i m i j {1,2,...n}. Ta th y m i t
tv

s

1
tv

i. M

cc

c am it

n

m il

i theo th i gian x

-Discrete-Time Cellular Neural Network (DT-CNN): X

ur i

r c theo th i gian
-Continuous-Time Cellular Neural Network (CT-CNN): X

u

c theo th i gian

+ CNN tuy

u tuy n
c s d ng cho x

cho m t s

n trong x

u tuy
nh tuy

u:
A(i,j;l,k);
S

c li u

B(i,j;k,l)

tp
u CNN tuy

p