2020 IEEE Student Conference on Electric Machines and Systems (SCEMS) | 978-1-7281-5622-4/20/$31.00 ©2020 IEEE | DOI: 10.1109/SCEMS48876.2020.9352407
""!
.' ' "%&" $%#$#%'#" # *" $#*%
"%'#""'$#*%%'%"#!"&&")# ' ',#
*" $#*% "%'#" ) !#% " !#% &%#(& !$'
#" ' $#*% % #$%'#" %#% (%' *" $#*%
#%&'" & " &&"' (%"' #% ' $#*% &,&'!&
& " &' #$%'#" " $#*% & !" , ' ,
*"&$&#$%&#%&'"#*"&$&!$%')
)"'"&("'(&#"#%!'#",(%%"'*"&$
#%&'" !'#& '& $$% !& ( (& # "#%!'#"
"'*#!"&#"&#'!"&$ '$%#$#&&!'##
$ %"" & )&( - *" &$ !'%+ #%&'"
!# #%*"$#*%#%&'" %&''*"&$!'%+
& #%! , +'%'" ' *" &$ ' ("% %"'
##%"'&#" ,'*"&$!'%+&#")%'"'#
%, ! # *" &$ , )&( -'#" !'# !$$"% '#"&$'*"'$+ &"'%,!"
''( *"&$&&' &#")# ('#" "(% "'*#% #%'!"$('&&%&#*"&$!&
" !& #%&'" '# #'" ' #%&' *" &$
!& " (&& ' !$$" % '#"&$ '*" $+ & "
*"&$'#''#%&'*"&$' " ,'
%&( '& % #!$% *' ' #" &#%''%! !!#%,
!'#&!( '#"%&( '&&#*'''!'#
$%#$#& " '& $$% & % #%&'" (%, "
''% %#(&'"&& " ' $%# *" *" &$ ('('&
* ,
'"
!'(%
$(&"!%
''
@?G@=FE:@?2='6FC2='6EH@C<
(-
(9@E@G@=E2:4
'.(
'F>6C:42=.62E96C(C65:4E:@?
66A-@I6==@H
-
LSTM
Long Short-Term Memory
RMSE
Root Mean Squared Error
&(
&62?3D@=FE6(6C46?E286CC@C
" "!'%"('"!
.:E9 E96 56A=6E:@? @7 7@DD:= 6?6C8J :? C646?E J62CD =@@<:?8 7@C C6?6H23=6 6?6C8J E@ C6A=246 EC25:E:@?2= 7@DD:=
6?6C8J 92D 364@>6 2 E@A:4 E92E >FDE 36 DEF5:65 0 1 642FD6 @7 :ED H:56 5:DEC:3FE:@? =@H 4@DE 4=62? C6?6H23=6 2?5 C6=2E:G6=J >2EFC6 A@H6C 86?6C2E:@? E649?@=@8J H:?5
A@H6C 92D 366? H:56=J FD65 0 1 J E96 6?5 @7 9:?2D4F>F=2E:G6:?DE2==6542A24:EJ@7H:?5A@H6CC624965
. 244@F?E:?87@C2AAC@I:>2E6=J @7E96H@C=5D
E@E2= :?DE2==65 42A24:EJ .:?5 A@H6C 86?6C2E:@? 92D E96
492C24E6C:DE:4D @7 C2?5@>?6DD :?E6C>:EE6?E ?6HD 2?5
978-1-7281-5622-4/20/$31.00 ©2020 IEEE
G@=2E:=:EJ %2C86 D42=6 H:?5 A@H6C :?E68C2E:@? H:== :?4C62D6
E9692C>@?:44@?E6?E@7E968C:52?527764EE96A@H6CBF2=:EJ *@ :ED G6CJ :>A@CE2?E E@ 4@?D:56C E96 DE23:=:EJ @7 E96 D>2CE
8C:5:?E6C>D@756>2?5C6DA@?D6E92E244FC2E6H:?5A@H6C
AC65:4E:@? C6DF=ED 0 1 +96 H:?5 DA665 92D E96 >@DE
D:8?:7:42?E :?7=F6?46 @? E96 244FC24J @7 H:?5 A@H6C
7@C642DE:?8 +96C67@C6 E@ @3E2:? 9:89 AC64:D:@? H:?5 A@H6C
7@C642DE:?8 C6DF=ED E96 7@C642DE:?8 @7 H:?5 DA665 :D
:?4C65:3=J :>A@CE2?E +96 4FCC6?E H:?5 DA665 7@C642DE:?8
>6E9@5D2C6>2:?=J5:G:565:?E@EH@EJA6DE:>64@CC6=2E:@?
2?5 DA2E:2= 4@CC6=2E:@? %:E6C2EFC6 0 1 FD6D DE2E:DE:42=
E649?:BF6D E@ >@56= E96 H:?5 DA665 2E 2 D:?8=6 DA2E:2=
=@42E:@?FD:?8E964@CC6=2E:@?@7E:>6D6C:6DH:?5DA66552E2 +9:D >6E9@5 C6BF:C6D 76H6C 52E2 2?5 72DE 42=4F=2E:@? DA665 3FE :E FD6D =6DD :?7@C>2E:@? 2?5 :E :D?E 62DJ E@ @3E2:? 9:89
7@C642DE:?8244FC24J %:E6C2EFC6017:CDE4=FDE6CD?F>6C:42=
H62E96C AC65:4E:@? '.( 52E2 3J 4=FDE6C:?8 >6E9@5 2?5
D6=64ED D2>A=6D H:E9 EJA:42= 492C24E6C:DE:4D +96 '.( 52E2
H:E9 46CE2:? 762EFC6D :D :?AFE :?E@ E96 =@?8 D9@CE E6C>
>6>@CJ %*+& 7@C642DE:?8 AC@8C2> E@ @3E2:? E96
7@C642DE:?8 C6DF=E +96 D:>F=2E:@? G6C:7:6D E96 67764E:G6?6DD
@7E96>6E9@5 !@H6G6C E9:DEJA6@7AC@46DD@?=J4@?D:56CD
E96 E:>6 D6C:6D :?7@C>2E:@? 2?5 5@6D ?@E 4@?D:56C E96
4@CC6=2E:@? :? 25;246?E DA246D %:E6C2EFC6 01 E2<6D H:?5
DA665 2?5 H:?5 5:C64E:@? 2D :?AFE 2?5 FD6D E96
2FE@4@CC6=2E:@?2?54C@DD 4@CC6=2E:@?36EH66?E96H:?57:6=5
2?5 DFCC@F?5:?8 @3D6CG2E:@? A@:?ED E@ :>AC@G6 H:?5 DA665
7@C642DE:?8 244FC24J E9C@F89 7FKKJ >@56=D +9:D >6E9@5
FD6D DA2E:2= 4@CC6=2E:@? :?7@C>2E:@? 3FE 5F6 E@ E96 D>2==
?F>36C@7@3D6CG2E:@?A@:?ED E96:>AC@G6>6?E67764E:D?@E
D:8?:7:42?E EAC6D6?E 7@C642DE:?832D65@?:>286D92D366?
H:56=JFD65:?E96A9@E@G@=E2:4(-7:6=50 1 %:E6C2EFC6
01FD6D29J3C:5>@56=4@>A@D65@74@?G@=FE:@?2=?6FC2=
?6EH@C<D 2?5 @E96C EJA6D @7 ?6FC2= ?6EH@C<D E@ 6DE23=:D9 2
>2AA:?8 >@56= 36EH66? D<J :>286D 2?5 8C@F?5 DFC7246
:CC25:2?46 "E42?36D66?7C@>E96D:>F=2E:@?C6DF=EDE92EE96
4@>3:?2E:@? @7 '' 2?5 @E96C 566A =62C?:?8 2=8@C:E9>D @7
E96 9J3C:5 >@56= 92D 9:896C 7@C642DE:?8 244FC24J E92? ;FDE
@?6 >6E9@5 H9:49 2=D@ G6C:7:6D E96 25G2?E286D @7 '' :?
AC@46DD:?8 :>286D %:E6C2EFC6 01 AC@A@D65 2 566A 6?5 E@
6?5 ?6EH@C< 66A -@I6= =@H - 7@C G:56@ 7C2>6
DJ?E96D:D +9:D>6E9@5:>AC@G65E96@AE:42=7=@HE649?@=@8J
2?5 :>AC@G65 E96 =2E6DE '' E649?@=@8J 7@C :?E6CA@=2E:@?
2?5G:56@6IEC2A@=2E:@? +967@C642DE:?8C6DF=E@7E96:>286
:D:>AC@G65:?BF2?E:EJ2?5BF2=:EJ4@>A2C65H:E9E96AC:@C
2CE !@H6G6C E9:D >6E9@5 6IEC24ED 762EFC6D H9:49 H:==
C65F46E96:>286DC6D@=FE:@?2?542FD6D@>6:?7@C>2E:@?E@
36 5:D42C565 D@ :E :D?E 62DJ E@ 249:6G6 9:89 244FC24J 642FD6@7E96A@H6C7F=25G2?E286D@74@?G@=FE:@?2=?6FC2=
?6EH@C<D :? :>286 7@C642DE:?8 E9:D A2A6C AC@A@D6D 2 H:?5
DA665 :>286 7@C642DE:?8 >6E9@5 32D65 @? 4@?G@=FE:@?2=
952
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
?6FC2= ?6EH@C<D :CDE E9:D A2A6C 4@>A@D6D E96 H:?5 DA665
52E2 F?56C 5:776C6?E =2E:EF56D 2?5 =@?8:EF56D :?E@ 2 H:?5
DA665 >2EC:I "E A6C7@C>D G:DF2=:K2E:@? AC@46DD:?8 2?5
@3E2:?DE968C2J D42=6:>286@7H:?5DA665 "E6DE23=:D96DE96
>2AA:?8C6=2E:@?D9:A36EH66?E96H:?5DA665:>286DA:I6=D
2?5 E96 4@CC6DA@?5:?8 A@:?E H:?5 DA665 *64@?5=J E96
4@?G@=FE:@?2=?6FC2=?6EH@C<:DFD65E@7@C642DEE967@C>65
H:?5 DA665 :>286 2?5 E96 7@C642DE65 H:?5 DA665 :>286 :D
@3E2:?657:?2==J E964@CC6DA@?5:?8H:?5DA665:D42=4F=2E65
E9C@F89 E96 >2AA:?8 C6=2E:@?D9:A 36EH66? A:I6=D 2?5 H:?5
DA665 +964@?EC:3FE:@?D42?36DF>>2C:K652D7@==@HD
+9:D A2A6C >2<6D 7F== FD6 @7 E96 DA2E:@E6>A@C2=
4@CC6=2E:@? 492C24E6C:DE:4D @7 C68:@?2= H:?5 DA665 52E2
E9C@F89G:DF2=:K2E:@?E649?:BF6 +9:D A2A6C FD6D '' E@ C62=:K6 E96 7@C642DE:?8 @7
H:?5DA665:>286 J6IEC24E:?8E967@C642DE65:>286A:I6=D 2?5 E9C@F89 E96 >2AA:?8 C6=2E:@?D9:A 36EH66? A:I6=D 2?5
H:?5DA665 E96G2=F6@7H:?5DA665:D@3E2:?65 +96 >@56=D A6C7@C>2?46 :D 4@>A2C65 F?56C E96
D46?6 @7 G:@=6?E H:?5 DA665 7=F4EF2E:@? 3J FD:?8 E96
>62DFC65 52E2 H9:49 G6C:7:6D E96 67764E:G6?6DD @7 E96
AC@A@D65>@56= "" &'"&
$ )"$"&$"#"% "
+96 7=@H 492CE @7 E96 >6E9@5 AC@A@D65 :? E9:D A2A6C :D
D9@H? :? :8FC6 :CDE H:?5 DA665 52E2 F?56C 5:776C6?E
4@@C5:?2E6D2C6FD65E@7@C>2H:?5DA66552E2>2EC:I H9:49
:D G:DF2=:K65 E@ 7@C> 2 8C2J D42=6 :>286 2?5 E96 >2AA:?8
C6=2E:@?D9:A 36EH66? A:I6=D 2?5 H:?5 DA665 :D 6DE23=:D965 *64@?5=J E96 8C2J :>286 :D FD65 2D E96 :?AFE @7 E96 ''
>@56= E@ 7@C642DE E96 8C2J :>286 :?2==J E96 7@C642DE65
:>286DA:I6=D2C66IEC24E65 2?5E967@C642DE65H:?5DA665:D
@3E2:?65E9C@F89E96>2AA:?8C6=2E:@?D9:A 86 !4C@=<0:2=<<42B8=<;=34
"E 42? 36 D66? 7C@> :8FC6 E92E H96? E96 ?F>36C @7
?6FC@?D:?E96: E9=2J6C:D2?5E96?F>36C@7?6FC@?D:?
E96: E9=2J6C:D E967F==J4@??64E654@??64E:@?>6E9@5:D
25@AE65 2?5 E96 ?F>36C @7 4@??64E:@?D 36EH66? E96 EH@
=2J6CD :D +92E :D E@ D2J E96C6 2C6 H6:89E A2C2>6E6CD
E92E?665E@36EC2:?65H96?E964@??64E:@?>@56@7A2CE:2=
4@??64E:@?:D25@AE65E96=@42=C646AE:G67:6=5DH:5E9:D E96C6 :D 2 4@??64E:@? 36EH66? 6249 ?6FC@? :? E96 : E9 =2J6C
2?5 E96 25;246?E ?6FC@?D :? E96 : =2J6C +96 ?F>36C @7
4@??64E:@?D36EH66?E96EH@=2J6CD:D "E42?36D66?E92E
FD:?8 A2CE:2= 4@??64E:@?D 42? C65F46 E96 ?F>36C @7 H6:89E
A2C2>6E6CD .96?E96?F>36C@7?6FC@?D:D=2C86 E9667764E
@7 A2CE:2= 4@??64E:@?D @? C65F4:?8 E96 H6:89E A2C2>6E6CD :D
>@C6 @3G:@FD "? 255:E:@? E96 C646AE:G6 7:6=5 @7 E96 :E9
=2J6C7@CE96: E9=2J6C:?E96A2CE:2=4@??64E65?6EH@C<:D
E96?6FC@?:?E96:E9=2J6C42?@3E2:?E96@FEAFED:8?2=D@7
E96 ?6FC@?D :? E96 : E9 =2J6C FE 7@C E96 : E9 =2J6C E96
C646AE:G6 7:6=5 :D D E96 ?6EH@C< =6G6=D 4@?E:?F6 E@
:?4C62D6 9:89 =6G6=?6FC@?D42?4@G6C2?5@3E2:?D:8?2=D:?2
=2C86CC2?86 +9:DDECF4EFC667764E:G6=JD:>F=2E6DE96H@C<:?8
>6E9@5D@7?6CG646==D:?E963:@=@8:42=G:DF2=4@CE6I 0C::G2=<<42B431#0@B80::G2=<<42B43
$&%
*92C65 H6:89ED 6?23=6 2== ?6FC@?D :? E96 D2>6 ?6EH@C<
=2J6C E@ FD6 E96 D2>6 D6E @7 H6:89E A2C2>6E6CD H:E9:? E96:C
C646AE:G6 7:6=5 E96C63J 7FCE96C C65F4:?8 E96 ?F>36C @7
?6EH@C< A2C2>6E6CD +96 DECF4EFC6 @7 D92C65 H6:89ED :D
D9@H?:?:8FC6 '':D5:776C6?E7C@>@E96C?6FC2=?6EH@C<D:?E6C>D@7
E964@??64E:@?@7?6FC@?D 2DD9@H?:?:8FC6 86 :=E270@B=5B74>@=>=A43;=34:
'6IE E9:D A2A6C :?EC@5F46D E96 '' >@56= D @?6 @7
E96 >@DE H:56=J FD65 566A =62C?:?8 2=8@C:E9>D '' 92G6
366? H:56=J FD65 :? :>286 AC@46DD:?8 2?5 =2?8F286
AC@46DD:?8 0 1 @>A2C65 H:E9 @E96C ?6FC2= ?6EH@C<D ''92DE967@==@H:?8492C24E6C:DE:4D 0C::G2=<<42B431A70@43E4867BA
86 *4867B>0@0;4B4@
+96?6EH@C<@?E96=67E:?:8FC6:D7F==J4@??64E65 E96
?F>36C @7 4@??64E:@?D 36EH66? ?6FC@?D :D 2?5 E96
"#&(%
953
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
?6EH@C< 4@?E2:?D H6:89E A2C2>6E6CD E96 ?6EH@C< @? E96
C:89E 25@AED D92C65 H6:89ED 32D65 @? A2CE:2= 4@??64E:@?D E@
>2<6 E96 : E9 =2J6C 2?5 E96 +96 ?F>36C @7 A2C2>6E6CD
36EH66? E96 : =2J6CD :D C65F465 E@ E96 D2>6 =:?6 D92A6
>62?DE92EE96D2>6H6:89EA2C2>6E6CD2C6FD65 @>A2C65
H:E9 E96 7F==J 4@??64E65 ?6EH@C< E96 ?F>36C @7 H6:89E
A2C2>6E6CD:D@?=J .96?E96?6EH@C<:D4@>A=6I ''
FD6D A2CE:2= 4@??64E:@?D 2?5 D92C65 H6:89ED E@ C65F46 E96
?F>36C @7 H6:89E A2C2>6E6CD E92E ?665 E@ 36 EC2:?65 3J
D6G6C2= @C56CD @7 >28?:EF56 H9:49 :D @7 8C62E D:8?:7:42?46
7@C :>286 AC@46DD:?8 AC@3=6>D H:E9 2 9F86 2>@F?E @7
42=4F=2E:@? "!("'&"!
@?G@=FE:@?:DE964@C6@7'' 2?5A2CE:2=4@??64E:@?D
2?5 D92C65 H6:89ED 2C6 C62=:K65 E9C@F89 E96 4@?G@=FE:@?
DECF4EFC6 "?E964@?G@=FE:@?2==2J6C E96:?AFE762EFC6>2A:D
4@?G@=G65 H:E9 E96 4@?G@=FE:@? <6C?6= +96 4@?G@=FE:@?
C6DF=E A2DD6D E9C@F89 E96 24E:G2E:@? 7F?4E:@? 2?5 E96
AC@46DD:?8C6DF=E@7E96AC@465FC6:DE96@FEAFE762EFC6>2A
@7E96=2J6C +96 4@?G@=FE:@? <6C?6= :D 2 < @C56C >2EC:I 2?5 :E
4@?E2:?D <N< EC2:?23=6 A2C2>6E6CD 7E6C 4@?G@=FE:@? @7 2?
:?AFE 762EFC6 >2A H:E9 2 C6D@=FE:@? @7 >N? 2?5 2 <N<
4@?G@=FE:@?<6C?6= E96C6D@=FE:@?@7E96@FEAFE762EFC6>2A
:D> <N? < :8FC6D9@HDE964@?G@=FE:@?AC@46DD
@7 2 N 4@?G@=FE:@? <6C?6= @? 2? :?AFE :>286 H:E9 2
C6D@=FE:@?@7>N? 86 #==:8<6>@=24AA
+96C62C6EH@4@>>@?=JFD65A@@=:?8AC@46DD ?2>6=J >62? A@@=:?82?5>2I A@@=:?8 +96 42=4F=2E:@? 7@C>F=2 @7 >62? A@@=:?8 :D D9@H? :?
6BF2E:@? = &2I A@@=:?8:DD9@H?:?6BF2E:@? = "?255:E:@? A@@=:?842?>2<6E96?6EH@C<:?D6?D:E:G6E@
=@42=492?86D:?E96:>286 D@E92EE96?6EH@C<>2:?E2:?D2
46CE2:?568C66@7:?G2C:2?46E@492?86D:?E96:?AFE:>286 &(&"!'!&"!
+96 42=4F=2E:@? 7@C>F=2 @7 E96 4@?G@=FE:@? AC@46DD :D
D9@H?:?6BF2E:@? D:K6 "7E96D2>A=:?8<6C?6=D:K6:D%N% E96?%:?86?6C2= (@@=:?8 42? C65F46 E96 C6D@=FE:@? @7 762EFC6 >2AD E96C63J
C65F4:?8 4@>AFE2E:@?2= 4@>A=6I:EJ :8FC6 D9@HD E96
A@@=:?8AC@46DD@72?:>286H:E92C6D@=FE:@?@7NFD:?82
N D2>A=:?8 4@C6 7E6C A@@=:?8 E96 :>286 C6D@=FE:@? :D
C65F465 E@ N "E 42? 36 D66? E92E A@@=:?8 42? C65F46 E96
D42=6@7DF3D6BF6?E42=4F=2E:@?D = ∑
∈
× + H96C6C6AC6D6?EDE964@?G@=FE:@?2==2J6C :DE96 E9
86 =<D=:CB8=<>@=24AA
+96 42=4F=2E:@? AC@46DD @7 4@?G@=FE:@? :D D9@H? :?
6BF2E:@? = ∑∑ × = =
'' FD6D E96 4@?G@=FE:@? <6C?6= E@ 249:6G6 A2CE:2=
4@??64E:@? 2?5 D92C65 H6:89E H9:49 :D 2=D@ 2? 6DD6?E:2=
724E@C E92E 5:DE:?8F:D96D '' 7C@> @E96C ?6FC2= ?6EH@C<D +96D:K6@7E964@?G@=FE:@?<6C?6=C67=64EDE96C2?86@7=@42=
4@??64E:@?D +96 DF3 C68:@?D :? E96 :?AFE 762EFC6 >2A H:E9
E96D2>6D:K62DE964@?G@=FE:@?<6C?6=2C6E964@CC6DA@?5:?8
?6FC@?D C646AE:G6 7:6=5D :? E96 @FEAFE 762EFC6 >2A "? E96
4@?G@=FE:@? =2J6C E96 D2>6 4@?G@=FE:@? <6C?6= :D 2=:8?65 +96 :?AFE 762EFC6 >2AD 2C6 4@?G@=G65 E@ 6IEC24E 2 D6E @7
:>286 762EFC6D 2?5 H6:89E D92C:?8 :D C62=:K65 *:?46 2
4@?G@=FE:@?<6C?6=42?@?=J6IEC24E2D6E@76=6>6?ED@7E96
:?AFE 762EFC6 >2A E96 4@?G@=FE:@? =2J6C 86?6C2==J C6BF:C6D
>F=E:A=64@?G@=FE:@?<6C?6=D;@:?E24E:@?E@6IEC24EDF77:4:6?E
:>286762EFC6D ""!
(@@=:?8 :D E@ >2A E96 DF3 C68:@?D @7 E96 :?AFE 762EFC6
>2A H:E9 E96 D2>6 D:K6 2D E96 D2>A=:?8 <6C?6= H:E9 2 DE6A
@FEAFE 762EFC6 >2A @7 E96 E9 =2J6C :D E96 E9 :?AFE
762EFC6 >2A @7 E96 E9 =2J6C 2?5 − :D E96
4@?G@=FE:@?<6C?6= %:DE963:2DE6C> :DE96D6E@7:?AFE
762EFC6>2AD 2?5 ⋅ :DE9624E:G2E:@?7F?4E:@? +96 24E:G2E:@? 7F?4E:@? 42? 36 2 D:8>@:5 7F?4E:@? E2?9
7F?4E:@? D@7EA=FD 7F?4E:@? 2?5 )6%, 7F?4E:@? +96
6I:DE6?46 @7 E96 24E:G2E:@? 7F?4E:@? 42? @AE:>:K6 E96
AC@46DD:?8 C6DF=ED @7 E96 ?6FC2= ?6EH@C< 7@C ?@?=:?62C
4=2DD:7:42E:@?AC@3=6>D )6%,92D?@D2EFC2E:@?K@?62?5?@
8C25:6?E 5:D2AA62C2?46 AC@3=6> E96C6 :D ?@ 4@>A=:42E65
6IA@?6?E:2= @A6C2E:@? +96 42=4F=2E:@? :D D:>A=6 2?5 E96
677:4:6?4J:D:>AC@G65E9624EF2=4@?G6C86?46DA665:D72DE6C >F49 72DE6C E92? *:8>@:5 E2?9 :E :D >@C6 :? =:?6 H:E9
3:@=@8:42= ?6FC2= 24E:G2E:@? >6492?:D> E92? *:8>@:5 +96C67@C6 E96 24E:G2E:@? 7F?4E:@? FD65 :? E9:D 2CE:4=6 :D E96
)6%,7F?4E:@? +96 )6%, 7F?4E:@? 42? EFC? 2== ?682E:G6 G2=F6D :?E@ H9:=6A@D:E:G6G2=F6DC6>2:?F?492?865 +96)6%,7F?4E:@?
42?36C6AC6D6?E653J2A:646H:D6=:?62C7F?4E:@? +92E:DE@
D2J H96? E96 :?AFE :D ?682E:G6 :E H:== @FEAFE E96? E96
?6FC@? H:== ?@E 36 24E:G2E65 +9:D >62?D E92E :? E96 D2>6
E:>6 >@DE @7 E96 ?6FC@?D H:== ?@E 36 24E:G2E65 2?5 @?=J 2
D>2== ?F>36C @7 ?6FC@?D A2CE:4:A2E6 :? E96 24E:G:EJ E9FD
954
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
6?DFC:?8 E96 DA2CD:EJ @7 E96 ?6EH@C< "? EFC? :E :D G6CJ
677:4:6?E 7@C 42=4F=2E:@?D 642FD6 @7 E9:D F?:=2E6C2=
:?9:3:E:@? ?6FC@?D :? E96 ?6FC2= ?6EH@C< 2=D@ 92G6 DA2CD6
24E:G2E:@? DA64:2==J :? 566A ?6FC2= ?6EH@C< >@56=D DF49
2D '' H96? E96 >@56= 255D ' =2J6CD E96@C6E:42==J E96
24E:G2E:@?C2E6@7)6%,?6FC@?DH:==564C62D63JE:>6DE96
'E9A@H6C +96:>286@7E96)6%,7F?4E:@?2?5E96:>286
@7:ED56C:G2E:G62C6D9@H?:?:8FC6 &$'&'$""!("'&"!'$&)"$
'' :D 2 ?6FC2= ?6EH@C< H:E9 2 >F=E: =2J6C DECF4EFC6 +96=@H6C=2J6C:D4@>A@D65@724@?G@=FE:@?2==2J6C2?52
A@@=:?8=2J6C "E:D2?:>A@CE2?EA2CE@7E96?6EH@C<E@6IEC24E
:>286 762EFC6D "7 E96 FAA6C =2J6C 4@?E2:?D 2 4=2DD:7:6C :E
86?6C2==JFD6D27F==J4@??64E654@??64E:@?>6E9@5 :8FC6
D9@HD 2 4@>>@? '' >@56= +96 ?6EH@C< 4@?E2:?D 4@?G@=FE:@?2==2J6CD2?5 A@@=:?8=2J6CD* * 2?5
7F==J4@??64E65=2J6C ('&"! !&"$%
"? E9:D A2A6C )&* 2?5 &( :?56I6D 2C6 FD65 E@
6G2=F2E6 E96 H:?5 DA665 7@C642DE:?8 C6DF=ED 2D D9@H? :?
BF2E:@? 0%4(14@8D0B8D4
86 %4(5C<2B8=<
+96 42=4F=2E:@? 7@C>F=2 @7 )6%, :D D9@H? :? BF2E:@?
−
∑ =
∧
− ∑ × = )6%,>2ILI M
∧
H96C6 :D E96 ECF6 G2=F6 :D E96 7@C642DE:?8 G2=F6 2?5>:DE96?F>36C@77@C642DE:?8A@:?ED 86 '74AB@C2BC@4=5!!
""" &*'(,
"? E9:D D64E:@? 2 42D6 DEF5JG6C:7:6D E9667764E:G6?6DD @7
E96 AC@A@D65 >6E9@5 This paper uses Python 3.6.1 with
Keras to build a CNN forecasting model.
&%&
+96 52E2 :? E9:D A2A6C 4@>6D 7C@> E96 @A6C?:4FD
=:>2E62E2*E@C601 H9:495@H?=@25DH:?5DA66552E2
2E > 23@G6 E968C@F?5 +96 =2E:EF56 2?5 =@?8:EF56 @7 E96
52E2 2C6 E96 =2E:EF56 :D E96 C6D@=FE:@? @7
E96 4@@C5:?2E6D :D E96 E:>6 :D 7C@> #2?F2CJ E@
#2?F2CJ 2?5E96E:>6C6D@=FE:@?:D9 &$#$"%%!
"? @C56C E@ @3E2:? 2 36EE6C 7@C642DE:?8 67764E E9:D 2CE:4=6
7:CDE ?@C>2=:K6D E96 H:?5 DA665 >2EC:I 52E2 +96 DA64:7:4
7@C>F=2:DD9@H?:?6BF2E:@? =
H96C6 2?5 C6AC6D6?E E96 H:?5 DA665 52E2
367@C62?527E6C?@C>2=:K2E:@?@A6C2E:@? C6DA64E:G6=J ⎡ ⎢
⎢
⎢
⎢
⎢ ⋅⋅⋅
⎢
⎢
⎢
⎢
⎣ ⋅⋅⋅
⋅⋅⋅
⋅⋅⋅
⎤
⎥
⎥
⎥
⎥
⋅⋅⋅ ⎥
⎥
⎥
⎥
⎥⎦
86
0>>8<65C<2B8=<
H:?5 DA665 >2EC:I 4@>A@D65 @7 H:?5 DA665D 2E
5:776C6?E 4@@C5:?2E6D 2E E96 D2>6 E:>6 +96 H:?5 DA665
>2EC:I:DG:DF2=:K65:?E967@C>@728C2JD42=6:>286 2?5E96
>2AA:?8C6=2E:@?D9:A36EH66?H:?5DA665>2EC:I2?5A:I6=D
@7E96H:?5DA665:>286:D>256 2DD9@H?:?:8FC6 "? E96 :8FC6 + C6AC6D6?ED E96 A:I6= 2?5 * C6AC6D6?ED
E96H:?5DA665 +96C67@C6 E96G2=F6@742?36@3E2:?653J
42=4F=2E:@? "$%&!
642FD6:E:DE@7@C642DEE96:>286@7E96D2>6D:K6 2?5
:?@C56CE@6?DFC6E92EE96A:I6=:?7@C>2E:@?:?E96:>286:D
955
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
?@E =@DE E9:D A2CE ?@ =@?86C 25@AED E96 DECF4EFC6 @7 A@@=:?8
=2J6C2?57F==4@??64E:@?=2J6C "?E9:DA2A6C 2 =2J6CE9C66
5:>6?D:@?2=4@?G@=FE:@?DECF4EFC6:D25@AE65E@C62=:K6:>286
762EFC6 6IEC24E:@? E9C@F89 4@?G@=FE:@? 2?5 E96 =6?8E9 2?5
H:5E9 @7 E96 4@?G@=FE:@? <6C?6= 2C6 +96 :?AFE :>286
D6BF6?46 :? E9:D A2A6C :D 2 E9C66 5:>6?D:@?2= :>286 >2EC:I 2?5E9C@F892D6C:6D@74@?G@=FE:@?@A6C2E:@?D E96AC65:4E65
:>286>2EC:I:D@FEAFE 2DD9@H?:?:8FC6 "E42?36D66?7C@>:8 E92EH:E9:?E96:>286C2?86 E96 7@C642DE65 H:?5 DA665 :>286 2?5 E96 E2C86E H:?5 DA665
92G6 2 D:>:=2C D92A6 H9:49 AC@G6D E92E E96 4@CC6DA@?5:?8
A:I6=G2=F6D2C6:56?E:42=:?D:K6 "E42?2=D@36D66?7C@>E96
7:8FC6E92EE96AC@A@D65>6E9@542?7@C642DEE96H:?5DA665
2E2?J4@@C5:?2E6A@:?E E92E:D :E42?7@C642DEE96H:?5DA665
@7 H:?5 A@H6C 4=FDE6C '@H 6IEC24E E96 A:I6= D:K6 :? E96
7@C642DE65 :>286 2?5 FD6 E96 7F?4E:@?2= C6=2E:@?D9:A E@
42=4F=2E6E96H:?5DA665 "? E9:D A2A6C H6 6IA6C:>6?E65 H:E9 D:I >@?E9 H:?5
DA665 :>286D :? E@E2= +96 7:CDE 2C6 FD65 7@C
EC2:?:?8 E96 2C6 FD65 7@C G6C:7:42E:@? 2?5 E96
2C6FD657@CE6DE:?8 ,D6E96>6E9@5AC@A@D65:?
E9:D 2CE:4=6 E@ D:>F=2E6 E96 24EF2= :>286 2?5 7@C642DE65
:>2862C6D9@H?:?:8FC6 86 '74AB4>A=5!!8;0645=@420AB8<6
%'&%!!+%%
"#$#
!"
"
!!
0
86
=;>0@8A=<=5E8<3A>4435=@420AB8<6@4AC:BA
+96H:?5DA665C6DF=E@72A2CE:4F=2C4@@C5:?2E6A@:?E:D
4@>A2C65 H:E9 E96 H@C< 7@C642DE65 3J E96 %*+& >6E9@5 +96 4@>A2C:D@? 36EH66? E96 EH@ >6E9@5D 2?5 E96 24EF2=
H:?5DA665:DD9@H?:?:8FC6 1
86 =;>0@8A=<=55=@420AB0<3B0@64B@4AC:BA
'
* & !"!
"E 42? 36 D66? 7C@> :8FC6 E92E E96 %*+& E:>6
7@C642DE:?8 >6E9@5 92D 2 DA64:7:4 E:>6 56=2J :? E96
7@C642DE:?8 @7 H:?5 DA665 +96 >6E9@5 AC@A@D65 :? E9:D
A2A6C 92D 36EE6C EC24<:?8 @7 H:?5 DA665 492?86D 2?5 92D 2
9:896C 7@C642DE:?8 244FC24J +96 DA64:7:4 52E2 :D D9@H? :?
+23=6 2?5E966G2=F2E:@?:?5:42E@CD2C6D9@H?:?+23=6P ) ('#""'#%
%#$#&!'#
!'#
'
!"!
"E42?36D66?7C@>+23=6O2?5+23=6PE92EE96AC@A@D65
>6E9@5:?E9:DA2A6C92D29:89244FC24JF?56C3@E9:?56I6D H9:=6E96AC@A@D65>6E9@5:>AC@G6D3J F?56C)&*
:?56I6D "?E9:DA2A6C E96H:?5DA665G2=F6:D=2C86 D@E96
&(:?5:42E@C67764E:D?@E@3G:@FD :?4C62D653J "- "!(&"!
:G6? E96 :>A@CE2?46 @7 H:?5 DA665 7@C642DE:?8 7@C
@3E2:?:?8 9:89 AC64:D:@? H:?5 A@H6C 7@C642DE:?8 2?5
6?DFC:?8 E96 A@H6C DJDE6>D DE23=6 @A6C2E:@? "? E9:D A2A6C E96 9:DE@C:42= H:?5 DA665 52E2 :D 7:CDE :?E68C2E65 +96 H:?5
956
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
DA66552E2:D7@C>65:?E@E96H:?5DA665>2EC:I3JFD:?8E96
:?7@C>2E:@?7C@>EH@5:>6?D:@?D@7E:>62?5DA246 2?5E96
G:DF2= AC@46DD:?8 :D 42CC:65 @FE :? E96 7@C> @7 2 8C2JD42=6
>2A *64@?5=J 244@C5:?8 E@ E96 A:I6=D H:?5 DA665 2?5
4@CC6DA@?5:?8 A@:?ED @7 E96 8C2JD42=6 :>286 E96 >2AA:?8
C6=2E:@?D9:A 36EH66? E96 A:I6=D 2?5 E96 H:?5 DA665 :D
6DE23=:D965 +9:DA2A6CE96?FD65''E@7@C642DEE96H:?5
DA665:>2862?586EE967@C642DE:?8H:?5DA665:>286 2?5
E96>2AA:?8C6=2E:@?D9:A:DFD65E@7:?5E96H:?5DA66552E2
:?G6CD6=J :?2==J :E:DG6C:7:653JD:>F=2E:@? +96D:>F=2E:@?
C6DF=ED D9@H E92E 4@>A2C65 H:E9 E96 %*+& >6E9@5 E96
>6E9@5 AC@A@D65 :? E9:D A2A6C H9:49 FD65 E96 H:?5 DA665
:>286 E@ 7@C642DE E96 H:?5 DA665 92D 9:896C 244FC24J +96
>6E9@5AC@A@D65:?E9:DA2A6C42?7@C642DEE96H:?5DA6652E
2?J 4@@C5:?2E6 A@:?E 2E E96 D2>6 E:>6 2?5 42? C62=:K6 E96
H:?5 DA665 7@C642DE:?8 @7 E96 H:?5 A@H6C 4=FDE6C E9FD
AC@G:5:?82DEC@?8DFAA@CE7@CE969:89 AC64:D:@?H:?5A@H6C
4=FDE6CA@H6C7@C642DE:?8C6DF=ED +96 7FEFC6 H@C< @7 E9:D A2A6C :D E@ FD6 E96 >2AA:?8
C6=2E:@?D9:A36EH66?H:?5DA6652?5H:?5A@H6CE@6DE23=:D9
2>2AA:?8>@56=7C@>H:?5DA665:>286E@H:?5A@H6C J
:?AFEE:?8 E96 AC65:4E65 H:?5 DA665 :>286 :?E@ E96 >2AA:?8
>@56= E96 7@C642DE:?8 @7 H:?5 A@H6C :D C62=:K65 ?5
4@?D:56C:?8E967=F4EF2E:@?@7:?;64E65H:?5A@H6C E96D276
2?5DE23=6@A6C2E:@?@7D>2CE8C:532D65@?56>2?5C6DA@?D6
:DDEF5:65 !"* !'
+9:D H@C< H2D DFAA@CE65 3J E96 '2E:@?2= $6J )
(C@8C2> @7 9:?2 +649?@=@8J 2?5 2AA=:42E:@? @7 H:?5
A@H6C A9@E@G@=E2:4 A@H6C AC65:4E:@? 7@C AC@>@E:?8
C6?6H23=66?6C8J4@?DF>AE:@? / )%!&
. / *0<6 8 8C - 8 &705849707 0<3 #& 0B0:I=
K&G<27@=<=CA >0BB4@< ;0B278<6 >@8<28>:4 10A43 @4A834<B80: 34;0<3
@4A>=<A4 10A4:8<4 4AB8;0B8=< 4270<8A; 0<0:GA8A 0<3 0>>@=027
34A2@8>B8=<L D=: <= >> !=D . / *0<6+80<68+408#47670<80<K&;0@B
=CA47=:3AM66@460B430>028BG=@420AB8<65=@=0366@460B=@A
(<34@ <24<B8D40A43 4;0<3 %4A>=<A4 #@=6@0;AL D=: <= >> 0@27>@8: . / ,0<-70<6,8C&0<80<3-CK=@420AB8<6B74
7867 >4<4B@0B8=< =5 E8<3 >=E4@ =< ;C:B8>:4 A20:4A CA8<6 ;C:B8B=
;C:B8 ;0>>8<6L D=: <= >> 0G . / --74<&#0<6*0<68-8%4< &7058497070<3
#&0B0:I=K#0BB4@<2:0AA85820B8=<0<3#&"=>B8;0:E4867BA10A43
A9G 8;064A 2:=C3 ;=B8=< A>443 20:2C:0B8=< ;4B7=3 5=@ A=:0@ #)
>=E4@5=@420AB8<6L'@0<A<3>>:D=: <= >>
J
C:C6 . / *0<6--70<68C,,C&#0<60<3!C8K4<4@0B8D4
03D4@A0@80: <4BE=@9A 0<3 2=<D=:CB8=<0: <4C@0: <4BE=@9A 10A43
E40B74@ 2:0AA85820B8=< ;=34: 5=@ 30G 07403 A7=@BB4@; >7=B=D=:B082
>=E4@5=@420AB8<6L<4@6G=<D4@A 0<06D=: >>
J 41 ./ 08 + C *0<6 # 47670<80< 0<3 % '0<6 K@=0320AB
6=AA8> 0:6=@8B7;A 5=@ 38AB@81CB43 >44@B=>44@ 2=<B@=: 8< ;82@=6@83AL '@0<A <3 >>: D=: <= >>
J
0GC< ./ , *C # &C< ' *C =<6 0<3 , 0AA0< K#@=1018:8AB82
E8<3>=E4@ 5=@420AB8<6 CA8<6 E40B74@ 4<A4;1:4 ;=34:AL D=: <=>> !=D42 ./
=1=0<3&0<274HK%468=<0:E8<3>=E4@5=@420AB8<610A43
=< A;==B78<6 B427<8?C4A E8B7 0>>:820B8=< B= B74 &>0<8A7 >4<8<AC:0@
AGAB4;L D=: <= >> !=D
./ , *C & 70<6 0<3 # 0<30: K@83=<<42B43 *8<3 #=E4@
#:0<BA &C@D4G =< B74 <B46@0B8=< %4?C8@4;4<BA 8< =34@< @83
=34AL D=: <=>> !=D
42 . / 0 ,0<6 + 0< 0<3 - 8 K(:B@0&7=@B'4@; *8<3
4<4@0B8=< =@420AB 0A43 =< C:B8D0@80B4 ;>8@820: G<0;82
=34:8<6L D=: <= >> 0@27>@8: . / ,0<6 , 8< 0<3 + 0< K#@=1018:8AB82 *8<3 4<4@0B8=<
=@420AB 0A43 =< &>0@A4 0G4A80< :0AA85820B8=< 0<3 4;>AB4@J
&7054@'74=@GL D=: <= >> 0GC<4 . / *0< -70= 0<3 , &=<6 K70<24 =<AB@08<43 FB@4;4
40@<8<6 0278<4 5=@ !=<>0@0;4B@82 #@4382B8=< <B4@D0:A =5 *8<3
#=E4@ 4<4@0B8=<L D=: <= >>
&4>B . / -70= *0< 0<3 , &=<6 K< 30>B8D4 8:4D4: #@=6@0;;8<6
=34: 5=@ !=<>0@0;4B@82 #@4382B8=< <B4@D0:A =5 *8<3 #=E4@
4<4@0B8=<L D=: <= >>
0< . / +C8+C*0<6--7=C0<3,-70<6KC<30;4<B0:A
0<3 1CA8<4AA ;=34: 5=@ @4A=C@24 066@460B=@ =5 34;0<3 @4A>=<A4 8<
4:42B@828BG;0@94BALD=: > C6 . / 8*0<6- 8 =BC788@CH0103!C80<3'*0<6
K0>028BG 0<3 =CB>CB >=E4@ 4AB8;0B8=< 0>>@=027 =5 8<38D83C0:
1478<3B74;4B4@ 38AB@81CB43 >7=B=D=:B082 AGAB4; 5=@ 34;0<3
@4A>=<A4 10A4:8<4 4AB8;0B8=<L >>: <4@6G D=:
@B <=
!=D . / *0<6+4#,0<68- 8#&80<=0<3!C8K0G
07403=>B8;0:18338<60<3A2743C:8<6AB@0B4684A5=@%066@460B=@
2=<A834@8<6 @4A>=<A8D4 C<24@B08<BG C<34@ @40:B8;4 >@828<6L <4@6G
D=:
@B<= 42 . / - +C0< + 0= 8 *0<6 + 4 0<3 , =C K#)=03
42=C>:8<6 0A43 4;0<3 %4A>=<A4 0A4:8<4 =03 AB8;0B8=<
>>@=027 5=@ %4A834<B80: CAB=;4@ E8B7 8AB@81CB43 #) &GAB4;L
'@0<A <3 >>: D=: <= >> !=D42
. / +C , 8< + -70<6 0<3 *0<6 K#=E4@ AGAB4; >0@0;4B4@
0BB0295=@58<0<280:>@=58BA8<4:42B@828BG;0@94BAL'@0<A&;0@B
@83D=: <= >>
C: . / $74<*0<6 =364-70<6-8 &705847070<3
# & 0B0:I= KG<0;82 >@824 D42B=@ 5=@;0B8=< ;=34:10A43
0CB=;0B82 34;0<3 @4A>=<A4 AB@0B46G 5=@ #)0AA8AB43 ) 270@68<6
AB0B8=<AL'@0<A&;0@B@83D=:<=>> J !=D
. / 0;0: 0<3 , - 05@8 K'8;4 A4@84A ;=34:A B= A8;C:0B4 0<3
5=@420AB7=C@:G0D4@0643E8<3A>4438<$C4BB0#098AB0<L D=: <= >> C: . / ) &08<8 % C;0@ 0B7C@ 0<3 &0F4<0 K&7=@B B4@;
5=@420AB8<6 10A43 =< 7=C@:G E8<3 A>443 30B0 CA8<6 344> :40@<8<6
0:6=@8B7;AL 8< @3 <B4@<0B8=<0: =<54@4<24 =< ;4@68<6
'427<=:=684A 8< =;>CB4@ <68<44@8<6 0278<4 40@<8<6 0<3
<B4@<4B=5'78<6A'08>C@<380 >> . / 0;=CA8A :4F8038A '74=270@8A 0<3 # &
=9=>=C:=A K 5CHHG ;=34: 5=@ E8<3 A>443 >@4382B8=< 0<3 >=E4@
64<4@0B8=< 8< E8<3 >0@9A CA8<6 A>0B80: 2=@@4:0B8=<L D=: <= >>
C< . / *0<6 - +C0< - -74< , 8 8 -70= &705849707
0<3#&0B0:I=K;8<CB4:GA=:0@8@@0380<245=@420AB8<6;4B7=3
10A43 =< @40:B8;4 A9G 8;0648@@0380<24 ;0>>8<6 ;=34:L D=: >
&4> . / *0<6 - +C0< - -74< 8 ' *0<6 0<3 &78 K 30G
07403#)>=E4@5=@420AB8<6;4B7=310A43=<&' %!!;=34:0<3
B8;4 2=@@4:0B8=< ;=385820B8=< C<34@ >0@B80: 308:G >0BB4@< >@4382B8=<
5@0;4E=@9L D=:
>
0G
. / - -74< - +C0< *0<6 % &C< ! C8 0<3 ' 8< K;064
>70A4A785B8<D0@80<2410A43;C:B8B@0<A5=@;5CA8=<;4B7=35=@2:=C3
;=B8=<38A>:024;4<B20:2C:0B8=<CA8<6A9G8;064AL<4@6G=<D4@A
0<06D=: @B<=
"2B . / --74<8C--70<6*0<6708,,C+C'*0<6
0<3 , 8<K44>:40@<8<6 10A43 AC@5024 8@@0380<24 ;0>>8<6 ;=34:
5=@ A=:0@ #) >=E4@ 5=@420AB8<6 CA8<6 A9G 8;064L D=: <= >> C:GC6 957
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.
. / -8C%,47+'0<6,8C0<360@E0:0K)834=5@0;4
AG<B74A8ACA8<6344>D=F4:5:=EL >> "2B . / -70<6,8C,0<&0<80<3$=<6K;>@=D43344>
;8FBC@4 34<A8BG <4BE=@9 5=@ @468=<0: E8<3 >=E4@ >@=1018:8AB82
5=@420AB8<6L D=: <= >>
C: . / 8< ' 20<< @=CAB4G 0<3 (<A4@ K44>
=<D=:CB8=<0: !4C@0: !4BE=@9 5=@ <D4@A4 #@=1:4;A 8< ;068<6L
D=: <=>> &4>B . / , 70<6 ,0< 74< 0<6 0<3 & -7=<6 K'E=&B064
=<D=:CB8=<0:!4C@0:!4BE=@95=@ 43820:!=8A4%4;=D0:D80;064
42=;>=A8B8=<L D=:<=>> C<4 . / =>4@<82CA :8;0B4 0B0 &B=@4 ."<:8<4/ D08:01:4
7BB>A23A2:8;0B42=>4@<82CA4C
958
Authorized licensed use limited to: Carleton University. Downloaded on June 05,2021 at 19:20:25 UTC from IEEE Xplore. Restrictions apply.