Neural networks in mechanics of structures and materials ± new results and prospects of applications Zenon Waszczyszyn a, * , Leonard Ziemia nski b a Institute of Computer Methods in Civil Engineering, Cracow University of Technology, Krakow, Poland b Chair of Structural Mechanics, Rzesz ow University of Technology, Rzesz ow, Poland Abstract Basic ideas of back-propagation neural networks BPNNs) are presented in short. Then BPNN applications in analysis of the following problems are discussed: 1) bending analysis of elastoplastic beams, 2) elastoplastic plane stress problem, 3) estimation of fundamental vibration periods of real buildings, 4) detection of damage in a steel beam, 5) identi®cation of loads applied to an elastoplastic beam. Regularization neural network is brie¯y discussed and its application to estimation of concrete fatigue durability it shown. A modi®ed Hop®eld network is used to the analysis of an elastic angular plate with unilateral constraints. In the end some conclusions and prospects of neurocomputing applications are pointed out. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Neural network; Applications; Mechanics; Structures; Materials 1. Introduction In recent years the interest in transferring methods developed in one discipline to the analysis of problems in other disciplines has evidently increased. Such a co-dis- ciplinary approach can give solutions which are dicult to achieve by methods specialized to the analysis of in- ward-disciplinary oriented problems. Development of computer hardware and software causes beyond of doubt formulation of new, nonstandard methods of data processing. From among these methods soft computing has to be mentioned as an approach related to the so- called intelligent methods and especially to `biologi- cal' methods of information processing. Arti®cial neural networks ANNs), evolutionary strategies ES) and Fuzzy inference systems FIS) make a background for `intelligent computing'. ANNs and neurocomputing re- lated to them have especially rich possibilities of appli- cations. ANNs simulate biological neural systems very loosely. They are massively parallel, they can process not only crisp but also noisy or incomplete data. ANNs can be used for the mapping of input to output data without known `a priori' a relationship between those data. ANNs can be applied in optimum design, classi- ®cation and prediction problems. ANNs advantages oer, in fact, complementary possibilities to standard, von Neuman type computers. In such a way hybrid systems with neural procedures open the door to new computational strategies. On the base of above remarks it is clear why ANNs have been recently widely introduced to the analysis of increasing number of problems in science and techno- logy. Of course, ANNs have also been applied in me- chanics of structures and materials. It seems that paper [1] by Adeli and Yeh was the ®rst to be published in 1989 in an archival journal. During the last ten years ANNs applications in mechanics grew so rapidly that now it would be dicult to point out those problems of me- chanics in which ANNs have not been used yet. Only a rough re¯ection of actual situation in this ®eld can be Computers and Structures 79 2001) 2261±2276 www.elsevier.com/locate/compstruc * Corresponding author. E-mail addresses: [email protected] Z. Waszczyszyn), [email protected] L. Ziemia nski). 0045-7949/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0045-794901)00083-9
NNSMA
Sep 26, 2015
mechanics of structures
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
-
!! !!
C40!" # $ !
% C40&" C40'"
C40(" ) C40*"
C40+" , # - .
# / , 0,
# 1
# '22& 3) 4 # / )#
" 5 /5 65 45 6
1
)
) # 4
) 7
)
# 8)
# 9
:
; # /,
C40/" ) C4034"
9 C40914"
: ;# /
)
#
/ )
# $ )
# /
: ;
# /
, # / )
&? / @ , &ABA
) C# 8 /
7
/ ) # =
. ,
D 4 EA C40'22&" ''F&''EF
#)#GG
D #
# " H### C40# "
H## C40# "#
22*+EA*AG2&GI '22& 3) 4 # / )#!11% 422*+ EA*A C402& "222B( A
-
## -# >'(?
## -# >*?#
1
D) 3
8 D - J)
$# =
#
9 !; ,
>+?
, , %
/# % K L )
C4064"
#
/# % K ) 64 L#
# $% K L
64#
$ L) /
#
-# >*?# 1
C40!"
# $ !
) 4 '# = C40
0, " .
4 (#
4 ' )
! ; # 3
L
# $
!
% C40" C40
"
! C40
" # $
L )
#
4 (
/# $ )
#
%&'& (#
$ ! ##
) ## ) # $
& !& &
& & # $
C40"
# 1 9# &
# 1 ) )
) %
&
'
) #
9 ) )
%
C40"
C40 "
&& L 2 & 2 (
C40"
& L& L & & 2 (
1 9# & # $
)# 3
) M
# / L
9# & *((' ##
* 5 0& ( 0' (
9# C40" 4 C40" #
''F' *& +!!! ,& * - ./ C40%11'2 %%3'4%%.3
-
' # $ C40 " &
$ )
) C40"#
/ # $
) C40
# 9# '"%
& * ) #
9 ) %
& &
+
$
## # 9# /
) )
&'
&
&
' F
8F?# $ - )
& # ! #
=
# 9# ' ! # 1 9# '
) 643N#
9# '# C40" 8
-
$
C40 9# '"
)
# 9# '#9 !
%
5
'# C40
"5
(# 5
*# #
$ M
::;;
#
%&%& ( 5 4
M M%
&2
6 )
L )
) ) , #
3M# C40&2" )
%
&&
1 L# $
#
1 %
'( &'( & & &(' &
&'
*'2 '2 &(
$ 3M# C40&'"%
2 2
F?# $ '222
# $ +22 ) )
&O#
$ ! 986 M# 1
986G!
# = )
) #
/ L ) # $
% 22&' 22'+ ' &2 '& &2+ 6! 2 '&2 6! C ) # $ 9# *
M & 2& & % 2 & ' & & *'2 ' *'2 *(2 +F2 # $ 986G! )
986#
%&7& 8 5 4
/ ) M
, C40936"
,
)# $
)
-
C40-6/"# 1
9# +%
!! &*
! ( )) ( )! ( ( A? ! -6/#
! !
9# +
% C40"
) 6
C40
" )
M . )#
!
)%
" " &+
" A?# / 9#
F# $ B ,
P
# $ 93
9# F#
$ 9# F#
$ 22(' M
) 2 22E#1
/K/ /K/0
222+ F+ 22' # 1 /K/ E* &*+ # $
/K/0 (B
B( # $
22E# $ EB &*F /K/ , F*
&&E /K/0 L#
9# *# 3M & ) 2 & ' & C40 2&" C40 &"#
9# +# C40" -6/ C40" C40" ! #
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''F+
-
%&9& 5
5 5 4 #
$ )
L
# $
# ## -#
>&2? )
# 1 ) /
#
4 !
)
! # /
+ &( C
) # $ 1 9# E
) #
) L , L)
M # 99$
)
6 C40) )
)"# 1 ::;;
) $ &
#
1 -# >&&?
)
# $
L 7 )
.
#$# $ )
%
& 2AB#$
(
&F
1 B $ & C40&F"
)#
1 -# >&2?
5 ) # 9# E
) # 1
-
$
&
9
)
8
!
G
&C40
"
&
&22O
'(
&
(*
&
**
&3
&'
(*
+F
EB
8=
61
=F
BC401
"$
)
&
2#'
+F
*#B
*#E
F#*
'#F
#
'
2#'
(2
+#+
2#F
&F
8=
61
=B
FC401
1"$
)
(
2#'
+F
*#B
*#E
F#*
'#F
#
*
2#'
(2
+#+
2#F
&F
J
9$
FE4
#/#GN
$
)
+
2#'
+(
+#A
+#+
B#&
+#2
#
F
2#'
2*
F#2
'#A
F
''#*
J
9P
$B*
C401"
$
)
E
2#&
E+
(#*
(#(
'#A
(#+
4
#1
#
B
2#&
B+
B#E
B#(
+#+
+#*
4
#11
$
)
A
2#&
B2
2#+
2#E
*
A#(
#
&2
2#&
FA
'A#A
&2#&
B#F
2#2
J
9P
$B*
C4011"
$
)
&&
2#&
+E
*#B
F#&
E#E
(#&
4
#1
#
4
#11
$
)
&'
2#&
B2
B#F
E#'
*#*
&2#E
#
&(
2#&
EE
''#F
2#(
(
B#B
DG6
@
GNC401
"$
)
&*
2#&
E'
A#B
E#B
F#+
&(#B
#
&+
2#&
A'
&2#B
A#B
+
'F#A
DG6
@
GNC401
1"$
)
&F
2#&
B+
F#B
+#B
'#A
A
#
&E
2#'
&(
'#2
'
'#'
&E#2
DG6
@
GNC401
11"
$
)
&B
2#'
'E
2#+
2#B
'#+
&*
#
&A
2#'
((
2#(
&
&(#A
4K
C401"
$
)
'2
2#&
++
E#B
+#2
(
+
4
#1
#
'&
2#'
((
B#E
2#'
(
+(#+
4
#11
$
)
''
2#&
++
E#B
F#(
2#E
+
#
'(
2#'
((
A#+
'#2
&
+(#+
4K
C4011"
$
)
4
#1
#
4
#11
$
)
'*
2#&
+F
E#&
+#F
2#&
(#&
#
'+
2#'
((
A#+
'#2
&
+(#+
!$
)
'F
2#'
E2
'#2
'#'
(
+#*
#
'E
2#'
A*
&E#F
&'#&
&'#2
&*#E
$
)
'B
2#'
A*
A#A
&2#(
A#F
&*#E
#
'A
2#'
F(
2#+
*
'#F
K
E2
$
)
(2
2#'
+F
(#*
(#'
(#A
2#2
#
(&
2#'
EE
F#F
*#&
&*
G
%
5%
)
5%
#
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''FE
-
- ) C40643 643N"
(2 &2* # -# >&'?#1 $ & )
& L &22O &A1 !% '(& L L (2O C )
&2O # 9# B# $ , )
!% (*& L &'O# /
-
% C40&" > C40'" (C40(" ) # 9# &
$ ,
,
M # $ !
936 /81/
>&+?# $
F (2 B 93 #
$ ) -#
>&F? ,L )# $ -# >&E?
:; ! #
$
**2 A2 )# / ) -
44 # =
?
)
# $
) )
L , M )
, 3M# C40'&" &2 #
$
! 9# &'# @# !
) F L ) C40'2"#
$ ! !
1 11 111# $ ! 1 ! 11 !
111 ) ! 1
! 11 ) B&
( (
1 9# &( )
!# 1 )
, ) >
( M # 1, ) )
! C40 9# &( 7
)"#
7&'& !
- C40-"
9# A# C40" $ C40" ) C40" M C40" )
, !#
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''FA
-
# -
),
L# $ M 0
>&B? -
/
>&A?#
$ -
C40-9" # 9# &*#
$ L %
&
& ''
P ) %
& L '
L
&
'
2 '(
1 9# &* )
& * * L *' &''
1 -# >&A? P
M
# $ M%
'*
9# &2# , % % C40" C40" 936#
9# & 8 #
''E2 *& +!!! ,& * - ./ C40%11'2 %%3'4%%.3
-
&& & && ' && &' & &' ' &'
& & & ' &
&
&' & & ' '+
) & #1
M %
-463 &
&
' 'F
A ) )#
1 P C40'(" # $
)
%
-643 '
'E
9 -643 ' )L
## # $ )
- )
-# >'2? -9 #
$ -9
#
7&%& 5 4
==
$ C
) -# >'&?# 1
L ) *22
,
-# >''?# 1
#
$ ) ) -# >'&''?# $ )
)%
*& 'B
L 7 M =
#
3L 9# &+
-# >'&?# / )
C40
"#
1 '&B &2A ' &2A )
)# 1 9# &F
) -643C40" # $
2A+ -643 C40 ' "# 19# &F ) ) # 1 ,) 7 '
) #
$ ) - )
! # $
*+*&
*222 -# >''? 7 M%
2B+E ' 2B'F#$ -
! -
# /
M !#
9# &'# C40" =) ! C40" ) !#
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''E&
-
1 9# &+
) -# >'&?#
7&7& ?$
$ 0, C400"
## # $
0 9# &E# = )
) 2 ,L )
& #1 , 0
#
# 1
C40
" #
9# &(# D ) ) ( (( ( ( ) ) % C40" =) ! C40" D!#
''E' *& +!!! ,& * - ./ C40%11'2 %%3'4%%.3
-
! ## #
$ )
0 #$ 0
# $ ?== C40 0,
$ " ## # $
) 0
#
0 ,
## )
C40 )
"# $ ) 0
M
# $
); #
9# &*# C40" - C40" P #
9# &+# - M -# >'&? % C40" / 6 C40&A+A" &22 6G6' 2'+( &22 0 C40" 9 C40&AE+" 'B2 6G6' 22'+ &22 0#
9# &F# C40" -643 C40" - ) #
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''E(
-
9 0 ,%
&'
&
&
2
& 'A
9 C40'A" )
M%
&
& (2 # 3M# C40(2" M
0 0 *'(? ) 0
M
%
&'$
2 ('
936 % *?
# 1 -# >'*? !
)# 3M# C40(*"
M# $ 7 M
C %
&
$
$&&
(+
) %
2 %
(F
- C40(F"
,#
1 -# >'*? L
# 9# &B# $ &E 93# J
# & & 22( # E2BB %E2 %BB 22' # / 8=9 ) & E2BB C403M# C40(+"" -K + F
>'+?# / L & &&2A %C401" & &2 &2 & C4011" ' &2 & & # $
)
#
- &&
1 ) 11# 1
F(2 # 1
& C40) ) 5 9#
&B" *222 #
$
-
/
, M
)
# 8 3M# C40(+"
, #
9&'&
= )
%
! 7
#
'# 7
) M#
(# / L
#
*# !
)#
+# 8
) ,
64#
F# -
# -
!#
E# 0 7
# $
#
9&%& 8==
/
7 )
C40,
936"# / )
%
4 ,
)
: ; #
$
# -# >'F?#
'# / L )
L
#
(# /
# $
>'(?#
*# 0 /
C40## "
#
+# / L
/
.L
#
F# Q
/ ,
# 3)
7 /#
9 )
7
/ # -# >*?#
$ L
8 3# ! K# K 6# 3# 0 6# K# 6# # 6 -# !
L
#
-
, ! D
9# &B# C40" 8 93 C40" ) #
*& +!!! ,& * - ./ C40%11'2 %%3'4%%.3 ''E+
-
4, - P # B $&&9 2'' &* E
$2E/ 22( &(# $ L
#
>&? / 0 @ D# ! #
6 D) 3 &ABA5*%'*E+F#
>'? # 4
) # 1% $
0N # /)
# 3% D)D !5 &AAF# # *(+B#
>(? # 4
)
# 1% $ 0N # /)
% D)D !5 3
# &AAB# # &E(BE#
>*? #
# D146 D #
*2*# @% 45 &AAA#
>+? ! $#
, # 4 N &AA(5&%&EE
AA#
>F? / # 44 4 #
J; 6 )# *#& 1 ! 8
0 ! 4 - # FGA+ J
) 4 &AA+#
>E? D D - 6# 4
, # /% 3)5
&AA*#
>B? 6 P # 0 G
# ! &( ! D D 6 6 !&AAE# # A*A+*#
>A? ! 3# 0 G936
# D /
6 3 4 &AAA5F%&EEBB#
>&2? D - K K 6 3 $ $# 3
# /) D) 3 &AA'5(B%'A&A#
>&&? 6 3# 3L ) &'? K K # ! , # 1%
- $ - # !
9 D $ /
D &AAA# # (**A#>&(? R # $
# ! &( !
D D 6 ! &AAE# # &**E+*#>&*? R # 8 C40
!"# =, ! -C - &AAA#
>&+? / 1 6# /! 6# /81/ -S8
1# &AA'#
>&F? 6 ! P #
, # D / 6
3 4 &AAA5F%**AFE#
>&E? 6 ! P # 1, # 1% -
$ - # ! 9
D $ /
D &AAA# # (F(B#>&B? 0 4# ) #
@% 65 &AA*#
>&A? / 0 6# -
# Q D 3 6
&AAB5&'*%&B'*#
>'2? ! - # ,
# ! 9
1 D 3 /
&AAA# # 'BFA
>'&? 9 K# 4 C C40
!"# /) D) 3 &AB*5(2%FEEAB#
>''? K Q J / 9 K#
C40 !"# ! *+
! D) 3 D K &AAA# )# *
# ''(*#
>'(? $ !4 ! !8#
# D 6 / 6 3
&AA(5&2F%'&('B#
>'*? ! 3# / 0,
# 1% R
# ! &* ! D D 6 6
- &AAA# # (B(*#>'+? 30 P J 9#
D# % 45 &AAF#
>'F? 6 ! P# 8 # ! 9
1 D 3 /
&AAA# # &EEB'#
''EF *& +!!! ,& * - ./ C40%11'2 %%3'4%%.3