configurations in view of assessing stability characteristics. Vasilis A. ... starting from existing designs is a non linear procedure. ... assumptions inherent in engineering aeroelastic tools only dealt ... variable speed machine for which full scale ... function of the displacement vector u[5]. ..... modeling of the drive train system.
$GYDQFHGDHURHODVWLFPRGHOLQJRIFRPSOHWHZLQGWXUELQH FRQILJXUDWLRQVLQYLHZRIDVVHVVLQJVWDELOLW\FKDUDFWHULVWLFV
9DVLOLV$5L]LRWLVDQG6S\URV*9RXWVLQDV 1DWLRQDO7HFKQLFDO8QLYHUVLW\RI$WKHQV +HURRQ3RO\WHFKQHLRXVWU$WKHQV*UHHFH YDVLOLV#IOXLGPHFKQWXDJUVS\URV#IOXLGPHFKQWXDJU
$EVWUDFW 7KHDHURHODVWLFSUREOHPRIWKHFRPSOHWHZLQGWXUELQH FRQILJXUDWLRQ LVUHFRQVLGHUHGLQYLHZRIDVVHVVLQJWKH VLJQLILFDQFH RI FHUWDLQ QRQOLQHDU IOXLGVWUXFWXUH LQWHUDFWLRQ PHFKDQLVPV ZKLFK DUH W\SLFDOO\ QHJOHFWHG LQ PRVW VWDWHRIDUW DHURHODVWLF WRROV 7R WKLV HQG DHURG\QDPLFV LV DFFRXQWHG IRU E\ D ' IUHHZDNH YRUWH[ PHWKRG LQVWHDG RI WKH FRPPRQO\ XVHG EODGH HOHPHQW PRPHQWXP PRGHO ZKLOH D QG RUGHU QRQ OLQHDUEHDPPRGHOLVXVHGLQIRUPXODWLQJWKHVWUXFWXUDO G\QDPLFHTXDWLRQVLQVWHDGRIWKHOLQHDUFODVVLFDOEHDP WKHRU\ 7KH WZR DUH QRQOLQHDUO\ FRXSOHG DQG WLPH GRPDLQVLPXODWLRQVDUHSHUIRUPHG6WDELOLW\DQDO\VLVLV WKHQ FDUULHG RXW VLJQDO SURFHVVLQJ RQ WKH ORDGV WLPH VHULHVIRUWKHFRPSOHWHFRQVWUXFWLRQ$VVHVVPHQWRIWKH VLJQLILFDQFHQRQOLQHDULWLHVKDYHRQVWDELOLW\LVFDUULHG RXW WKURXJK FRPSDULVRQV ZLWK UHVXOWV REWDLQHG IURP GLIIHUHQW OLQHDUL]HG PRGHOV ZKLOH FRPSDULVRQV ZLWK IXOO VFDOH PHDVXUHPHQWV RQ D PXOWL 0: PDFKLQH YDOLGDWHWKHWKHRUHWLFDOGHYHORSPHQWV .H\ZRUGV DHURHODVWLF VWDELOLW\ URWRU DHURHODVWLFLW\ IUHHZDNHDHURG\QDPLFPRGHOLQJ
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α DQG ' DHURG\QDPLF HII
GDWD 2I FRXUVH WKH ZDNH G\QDPLFV ZLOO EH LQFRUSRUDWHG LQWR WKH HVWLPDWLRQ RI α ZKLFK LV DQ HII
LPSURYHPHQW ZLWK UHVSHFW WR %(0 DQDO\VLV 7KH IDFW WKDW PRVW RI WKH QHZ GHVLJQV DUH XVLQJ SLWFK FRQWURO VWUDWHJ\DGGVWRWKHFRQILGHQFHLQWKLVDSSUR[LPDWLRQ 7KHDVVHVVPHQWLVFDUULHGRXWRQD0:SLWFK YDULDEOH VSHHG PDFKLQH IRU ZKLFK IXOO VFDOH
PHDVXUHPHQWV DUH DYDLODEOH 7KUHH VHWV RI VLPXODWLRQ UHVXOWV DUH FRPSDUHG 7KH ILUVW VHW LV REWDLQHG E\ D VWDWHRIDUWDHURHODVWLFWRROZKLFKFRPELQHV%(0DQG OLQHDUEHDPWKHRULHV³*$675$)7OLQ´ 7KLVVHWLV XVHG DV UHIHUHQFH PDLQO\ EHFDXVH LW FDQ EH IXOO\ OLQHDUL]HG VR WKDW VWDELOLW\ DQDO\VLV FDQ EH FDUULHG RXW LQDHLJHQYDOXHFRQWH[W7KHVHFRQGVHWLVREWDLQHGE\ WKH QRQOLQHDU YHUVLRQ RI WKH SUHYLRXV RQH ³*$675$)7 QRQOLQ´ DQG ILQDOO\ WKH WKLUG VHW LV REWDLQHG E\ WKH IUHHZDNH DHURG\QDPLF PRGHO FRPELQHG ZLWK QG RUGHU EHDP WKHRU\ ³*$67*(1893´
2XWOLQHRIWKHDHURHODVWLFPRGHO 8VLQJPXOWLERG\DSSURDFKLQGHVFULELQJWKHG\QDPLFV RI WKH ZLQG WXUELQH V\VWHP FRQVLVWV RI FRQVLGHULQJ HDFKFRPSRQHQWVHSDUDWHO\DQGGHILQLQJLWVNLQHPDWLFV ZLWKUHVSHFWWRWKHIL[HGV\VWHP)LJXUH U*N = N + N ⋅ UN
\ ] [ 2
[
\
2
\*\
U*N
]
N
2*2 ]*]
[*[
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
)LJXUH%HDPFRRUGLQDWHV\VWHPGHILQLWLRQ
⎧X ⎫ ⎧ X ⎫ ⎧ ξ ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪Y ⎪ U = ⎨ \ + Y ⎬ + (X ⋅ ⎨−λ∂ \θ ⎬ X = ⎨ ⎬ ⎪ Z ⎪ ⎪ ζ ⎪ ⎪ Z⎪ ⎩ ⎭ ⎩ ⎭ ⎪⎩θ ⎪⎭
ZKHUH GHQRWHV WKH ZDUSLQJ IXQFWLRQ RI WKH FURVV VHFWLRQ DQG ( LV WKH WUDQVIRUPDWLRQ PDWUL[ EHWZHHQ Ο[\] DQG Ο′ξηζ ZKLFK LV GHILQHG DV D QRQOLQHDU IXQFWLRQ RI WKH GLVSODFHPHQW YHFWRU X >@ 8VLQJ WKH VWUDLQ WHQVRU LV ILUVW REWDLQHG ZKLFK LV WKHQ LQWURGXFHG LQWR +RRNH¶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
WQ
=W
WQ+
= WQ + ∆W
)LJXUH9RUWH[EOREVUHSUHVHQWDWLRQRIWKHZDNH
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
: \
8 \
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
0 ([ )⋅ [Ö + &[ ⋅ [Ö + .[ ⋅ [Ö = 4[ ZKHUHWKHPDVVGDPSLQJDQGVWLIIQHVVPDWULFHV0&
.DVZHOODVWKHORDGYHFWRU4GHSHQGRQWKHVROXWLRQ LQFOXGLQJ LWV WLPH GHULYDWLYHV KHUH GHQRWHG E\ DQ Ö LVWKHYHFWRURIWKHGLVFUHWHGRIDQGD XQGHUWLOW [ GRWGHQRWHVWLPHGHULYDWLRQ,Q WKHIORZERXQGDU\ FRQGLWLRQV ZKLFK GHWHUPLQH WKH LQYLVFLG SDUW RI WKH IORZDUHQRWLQFOXGHG'XHWRWKHLUOLQHDUFKDUDFWHUWKH FRUUHVSRQGLQJGRIFDQEHHOLPLQDWHG'XHWRLWVQRQ OLQHDU QDWXUH V\VWHP LVVROYHGLQWLPHKHUHXVLQJ WKH 1HZPDUN QG RUGHU VFKHPH 1RQOLQHDULWLHV RULJLQDWH IURP WKH PXOWLERG\ IRUPXODWLRQ WKH QG RUGHU EHDP PRGHO DQG WKH DHURG\QDPLF FRXSOLQJ
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
SLWFKH[FLWDWLRQ WRZHUIRUFHH[FLWDWLRQ
P O S LV G O D LQ G WX L J Q R O S R W U H Z WR
WRZHUWRSODWHUDOGLVSOP
)LJXUH7RZHUWRSGLVSODFHPHQWVLQSLWFKDQGODWHUDO WRZHUIRUFHH[FLWDWLRQZLQGVSHHGPV
([FLWDWLRQ DQG LGHQWLILFDWLRQPHWKRGV
GDPSLQJ
,Q7DEOHWKHDQDO\VHGPRGHVDUHOLVWHGWRJHWKHUZLWK WKH IUHTXHQF\ WKH DPSOLWXGH DQG WKH SKDVH ZKHQ DSSOLFDEOH RIWKHH[WHUQDOH[FLWDWLRQDVDSSOLHGRQWKH
REWDLQ WKHSHDNSORW'DPSLQJLVWKHQHVWLPDWHGIURP WKHVORSHRIDOLQHDUOHDVWVTXDUHILWWRWKLVSHDNSRLQWV SORW
0: PDFKLQH FRQVLGHUHG $ SLWFK DQJOH YDULDWLRQ RI ±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
0RGH WRZHUODWHUDO
WRZHUORQJ
)UHT +]
P 1 W Q H P R P
H
H
H
H
H
H
VKDIWWLOW WRZHUWRSWLOW
H
P 1 G D H OR I R 7 ) )
H
H
WRZHUIRUFHH[FLW IUHT DPSOLWXGH1W +]
ODW
ORQJ
UHJURWRUIODS
UHJURWRUODJ SURJURWRU ODJ
7DEOH7KHH[FLWDWLRQPDWUL[
)LJXUH 7UDQVLHQW WLPH VHULHV DQG ))7 RI GLIIHUHQW ORDGV LQ FDVH RI WKH UHJUHVVLYH URWRU OHDGODJ PRGH H[FLWDWLRQZLQGVSHHGPV
IODS
IUHTXHQF\+]
WRZHUWRUVLRQ
SURJURWRU
VKDIW\DZ
H
H
WLPHV
VKDIWWLOW WRZHUWRSWLOW
SKDVH GHJ
VKDIW\DZ WRZHUWRUVLRQ
VKDIWWRUVLRQ
FROURWRUIODS
SLWFKH[FLW $PSOLWXGH GHJ
H
ORDG WRZHUERWWRPODW EHQGLQJPRP WRZHUERWWRPORQJ EHQGLQJPRP VKDIWWRUTXH VKDIW\DZEHQGLQJ PRP EODGHURRWIODSZLVH EHQGLQJPRP VKDIW\DZEHQGLQJ PRP WRZHUWRSORQJ PRP WRZHUWRSORQJ PRP
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
H
WUDQVLHQWVLJQDO HQYHORSHVLJQDO
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³*$675$)7 QRQOLQ´ DQG ³*$67*(1893´ VKRZ VLPLODU EHKDYLRXU ZLWK WKH IUHH ZDNH PRGHO JLYLQJ VOLJKWO\ ORZHU GDPSLQJ YDOXHV$VGLVFXVVHGLQWKHVHTXHOVLPLODUEHKDYLRXULV REWDLQHG LQ DOO WKH PRGHV WKDWDUHDVVRFLDWHGZLWKWKH URWRUHGJHZLVHDHURG\QDPLFORDGLQJ
HQYHORSHVLJQDOH[SILW P 1 . W Q H P R P J LQ G Q H E W OL W S R W U H Z R W
H
*$675$)7 OLQ *$675$)7 QROLQ WRZHU H[FLW *$67*(1893 WRZHU H[FLW PHDV 20$ PHDV JHQHUDWRU H[FLW
] + \ F Q H X T H U I
H
H
)LJXUH 'HFD\ HQYHORSH VLJQDO RI WKH WRZHU WRS WLOWLQJPRPHQW
WLPHV
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
J Q L S P D G
D
ZLQG VSHHG PV
W Q H P H U F H G J R O Q L
ZLQG VSHHG PV E
)LJXUH 7RZHU ODWHUDO EHQGLQJ PRGH IUHTXHQFLHV DQG GDPSLQJ QRQOLQHDU GDPSLQJ FDOFXODWHG ZLWK PRYLQJEORFNPHWKRG
*$675$)7 OLQ *$675$)7 QROLQ SLWFK H[FLW *$675$)7 QROLQ WRZHU H[FLW *$67*(1893 SLWFK H[FLW PHDV 20$ PHDV SLWFK H[FLW
] + \ F Q H X T H U I
ZLQG VSHHG PV
D
W Q H P H U F H G J OR Q L J Q L S P D G
ZLQG VSHHG PV E
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³*$675$)7´ QRQOLQHDU FRXQWHUSDUW RI WKH OLQHDU VWDELOLW\ WRRO JLYH VLPLODU UHVXOWV XS WR WKH ZLQG VSHHG RI PV %H\RQG WKDW VSHHG D VLJQLILFDQW UHGXFWLRQ RI GDPSLQJ LV REWDLQHG ZLWK WKH QRQ OLQHDU FRGHV UHJDUGOHVV WKH H[FLWDWLRQ PHWKRGXVHGEODGHVSLWFKRUWRZHUIRUFH 7KHUHDVRQ
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³VWURQJ´VSHFWUDOO\FORVHPRGHGDPSLQJLGHQWLILFDWLRQ PD\ EH SUREOHPDWLF 7KH GDPSLQJ REWDLQHG ZLWK ³*$67*(1893´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³*$675$)7´ FRGH DUH LQ EHWWHU DJUHHPHQW ZLWK WKH GDWD FRPLQJ IURP WKH H[FLWDWLRQ WHVW DW OHDVW XS WR WKH ZLQG VSHHG RI PV ZKHUH VXIILFLHQW DPRXQW RI GDWD SRLQWV DUH DYDLODEOH ZKLOH WKH IUHHZDNH FRGH JLYHV GDPSLQJ SUHGLFWLRQV FORVHU WRWKH20$ UHVXOWV+RZHYHULWLVQRWHGWKDWLQWKH 20$ UHVXOWVKLJKHUGDPSLQJYDOXHVDUHDQWLFLSDWHG DV D UHVXOW RI WKH FORVH ORRS RSHUDWLRQ WKH FRQWURO V\VWHPLVDFWLYH $VDJHQHUDOUHPDUNWKHSUHGLFWLRQV RIDOOWKHWRROVXVHGDUHZLWKLQWKHUDQJHGHILQHGE\WKH
PHDVXUHG GDWD SRLQWV ZKLFK DV LQ WKH SUHYLRXV FDVH GHPRQVWUDWHDODUJHVFDWWHU$VUHJDUGVWKHIUHTXHQF\ RI WKH PRGH WKH SUHGLFWLRQV DUH LQ JRRG DJUHHPHQW ZLWKWKHGDWDFRUUHVSRQGLQJWRWKHH[FLWDWLRQWHVWZKLOH WKH20$ JLYHVVRPHKRZKLJKHUIUHTXHQF\YDOXHVLQ DOOZLQGVSHHGV P 1 W ( Q H P R( P J Q LG ( Q HE J ( Q R O P R WW ( R E UH ( Z R WI R 7 ) )
PV PV
IUHTXHQF\ +]
)LJXUH ))7 RI WKH WRZHU ERWWRP ORQJLWXGLQDO EHQGLQJPRPHQWDWDQGPV
U5
XQVWHDG\ VWHDG\QDFD VWHDG\QDFD
W Q LH F LI I H R F W I OL / &
DQJOHRIDWWDFNGHJ
U5
XQVWHDG\
VWHDG\QDFD VWHDG\QDFD W Q H L F LI I H R F W LI O
/ &
DQJOHRIDWWDFNGHJ
)LJXUH 8QVWHDG\ OLIW FRHIILFLHQW ORRSV REWDLQHG ZLWKWKHIUHHZDNHFRGH
,Q )LJXUH DQG )LJXUH UHVXOWV IRU WKH URWRU OHDGODJ PRGHV DUH SUHVHQWHG 7KH PLUURU EHKDYLRXU EHWZHHQWKHOLQHDUDQGWKHQRQOLQHDUGDPSLQJUHVXOWV REWDLQHG LQ WKH WRZHU ODWHUDO EHQGLQJ PRGH LV DOVR QRWLFHG LQ WKH FDVH RI WKH OHDGODJ PRGHV XS WR WKH UDWHG ZLQG VSHHG )RU KLJKHU ZLQG VSHHGV ERWKOLQHDU DQG QRQOLQHDU UHVXOWV DJUHH WKDW WKH GDPSLQJ RI WKH OHDGODJ PRGHV UDSLGO\ LQFUHDVHV DV D UHVXOW RI WKH VWUXFWXUDO FRXSOLQJ RI WKH HGJHZLVH ZLWK WKH IODSZLVH PRGHV LQWURGXFHG E\ WKH EODGHV SLWFKLQJ 7KH DERYH PHQWLRQHG FRXSOLQJ LV LOOXVWUDWHG LQ )LJXUH ZKHUH WKHDHURHODVWLFPRGHVKDSHRIWKHSURJUHVVLYHOHDGODJ PRGHLVVKRZQIRUWKHZLQGVSHHGVRIDQGPV ,WLVFOHDUWKDWDWWKHZLQGVSHHGRIPVDVLJQLILFDQW IODSSLQJ FRPSRQHQW LV GHWHFWHG $V UHJDUGV WKH FRPSDULVRQZLWKPHDVXUHPHQWVDEHWWHUFRUUHODWLRQLV REWDLQHG ZLWK WKH QRQOLQHDU VLPXODWLRQV 7KH PHDVXUHG GDWD LGHQWLI\ WKDW IRU ZLQG VSHHGV EHORZ UDWHG WKH GDPSLQJ RI WKH WZR DV\PPHWULF HGJHZLVH PRGHV VOLJKWO\ LQFUHDVHV ZLWK WKH ZLQG VSHHG %RWK QRQOLQHDU PRGHOV ³*$675$)7 QRQOLQ´ DQG ³*$67*(1893´ JLYH JRRGGDPSLQJSUHGLFWLRQV IRU WKH SURJUHVVLYH HGJHZLVH PRGH XS WR WKH UDWHG VSHHG )RU KLJKHU VSHHGV WKH UHVXOWV RI WKH IUHH ZDNH FRGH VHHP WR EH LQ EHWWHU DJUHHPHQW ZLWK WKH PHDVXUHPHQWVDOWKRXJKWKHQXPEHURIPHDVXUHGGDWD SRLQWV DYDLODEOH LV OLPLWHG ZKHUHDV WKH ³*$675$)7 QRQOLQ´ PRGHO XQGHUHVWLPDWHV GDPSLQJ YDOXHV EH\RQG WKH ZLQG VSHHG RI PV ,Q WKH FDVH RI WKH UHJUHVVLYH OHDGODJ PRGH ³*$675$)7 QRQOLQ´ JLYHV EHWWHU GDPSLQJ SUHGLFWLRQV XS WR WKH UDWHG VSHHG ZKHUHDV DJDLQ XQGHUHVWLPDWHVWKHGDPSLQJRIWKHEH\RQGUDWHGVSHHG UHJLRQ 2Q WKH FRQWUDU\ ³*$67*(1893´ XQGHUHVWLPDWHVGDPSLQJXSWRWKHZLQGVSHHGRIPV DQGJLYHVEHWWHUUHVXOWVEH\RQGWKDWVSHHG,WLVQRWHG WKDW WKH GDPSLQJ FXUYHV IRU WKH WZR OHDGODJ PRGHV SURYLGHG E\ ³*$675$)7´ ERWK OLQHDU DQG QRQ OLQHDU YHUVLRQV H[KLELW D YHU\ VOLJKW VHSDUDWLRQ 7KH DERYH UHVXOW LV DOVR VXSSRUWHG E\ WKH PHDVXUHG GDWD 2QWKHFRQWUDU\WKHVHSDUDWLRQRIWKHGDPSLQJFXUYHV REWDLQHGZLWK³*$67*(1893´LVUHODWLYHO\ODUJH HVSHFLDOO\ IRU WKH ZLQG VSHHG UDQJH EHOORZ WKH UDWHG ZLQGVSHHG$SRVVLEOHUHDVRQRIWKLVGLIIHUHQFHLVWKDW WKH VKDIW EHQGLQJ ZDV QRW WXQHG ZLWK UHVSHFW WR WKH VWDQGVWLOO PRGDO WHVW ZKHQ XVLQJ WKH QG RUGHU PRGHO 7KLV LV HVSHFLDOO\ WUXH VLQFH EHQGLQJ VWLIIQHVV RI WKH VKDIWLVLGHQWLILHGDVRQHRIWKHSDUDPHWHUVWKDWFRQWURO WKH GDPSLQJ VHSDUDWLRQ RI WKH DV\PPHWULF OHDGODJ PRGHV >@ $V UHJDUGV IUHTXHQFLHV WKH\ DUH ZHOO SUHGLFWHG E\ DOO PRGHOV 6OLJKWO\ EHWWHU UHVXOWV DUH REWDLQHG ZLWK WKH ³*$67*(1893´ PRGHO DV D UHVXOW RI WKH XVH RI WKH QG RUGHU EHDP PRGHO 7KH IUHTXHQF\ UHVXOWV SURYLGHG E\ WKH ³*$675$)7 QRQOLQ´ PRGHO DOPRVW FRLQFLGH ZLWK WKRVH RI WKH HLJHQYDOXHDQDO\VLV
*$675$)7 OLQ *$675$)7 QROLQ SLWFK H[FLW *$67*(1893 SLWFK H[FLW PHDV 20$
] + \ F Q H X T H U I
*$675$)7 OLQ *$675$)7 QROLQ SLWFK H[FLW *$67*(1893 SLWFK H[FLW PHDV 20$
] + \ F Q H X T H U I
ZLQG VSHHG PV
D
LQ J Q L S P D G
ZLQG VSHHG PV
D
W Q H P H U F H G J R O Q L
J Q L S P D G
W Q H P H U F H G J OR
ZLQG VSHHG PV E
ZLQG VSHHG PV E
)LJXUH 5RWRU UHJUHVVLYH OHDGODJ PRGH IUHTXHQFLHV DQG GDPSLQJ QRQOLQHDU GDPSLQJ FDOFXODWHGZLWKPRYLQJEORFNPHWKRG
)LJXUH 5RWRU SURJUHVVLYH OHDGODJ PRGH IUHTXHQFLHV DQG GDPSLQJ QRQOLQHDU GDPSLQJ FDOFXODWHGZLWKPRYLQJEORFNPHWKRG
1H[W FRPSDULVRQ RI WKH WZR GDPSLQJ LGHQWLILFDWLRQ PHWKRGV LV SUHVHQWHG ,Q )LJXUH WKH GDPSLQJUHVXOWVRIWKHWRZHUODWHUDOEHQGLQJPRGHDUH SURYLGHG DV FDOFXODWHG E\ WKH WZR QRQOLQHDU DHURHODVWLFWRROVDQGERWKGDPSLQJHVWLPDWLRQPHWKRGV LHPRYLQJEORFNDQG+LOEHUW ,WLVFOHDUWKDWWKHWZR GDPSLQJPHWKRGVJLYHDOPRVWLGHQWLFDOUHVXOWVIRUWKLV ORZGDPSHGPRGH7KHVDPHFRQFOXVLRQLVDOVRPDGH IRU WKH UHVW RI WKH PRGHV H[KLELWLQJ ORZ GDPSLQJ YDOXHV LH WKH URWRUOHDGODJPRGHV 'LIIHUHQFHVDUH QRWHG LQ WKH GDPSLQJ HVWLPDWLRQ RI WKH WRZHU ORQJLWXGLQDO EHQGLQJ PRGH 7KHVH DUH RQO\SUHVHQWLQ WKH ³*$675$)7 QRQOLQ´ VLPXODWLRQV %DVHG RQ WKH UHVXOWV RI WKH +LOEHUW PHWKRG WKH GLIIHUHQFHV LQ WKH GDPSLQJ SUHGLFWLRQVRIWKHWZRDHURHODVWLFWRROVIUHH ZDNH DQG EODGH HOHPHQW IRU ZLQG VSHHGVEHOORZWKH UDWHG VSHHG DUH QRW DV KLJK DV VXJJHVWHG E\ WKH PRYLQJ EORFN PHWKRG +RZHYHU VLJQLILFDQW GLIIHUHQFHV DUH VWLOO REWDLQHG LQ WKH UDQJH RI ZLQG VSHHGVEH\RQGUDWHG
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
FDOFXODWHG WLPH VHULHV LV QRW VR KLJK DQG WKDW WKH GDPSLQJ YDOXH IRU ERWK RI WKHP LV FHUWDLQO\ KLJKHU WKDQ
W Q H P H U F H G J OR
FRVLQH ODJ FRVLQH IODS VLQH ODJ VLQH IODS
LQ J LQ S P D G
P P H G X W L Q J D P
*$675$)7 OLQ *$675$)7 QROLQ PRYLQJ EORFN *$675$)7 QROLQ +LOEHUW *$67*(1893 PRYLQJ EORFN *$67*(1893 +LOEHUW
UDGLXV P
8 PV
ZLQG VSHHG PV
)LJXUH &RPSDULVRQ RI GDPSLQJ HVWLPDWLRQV RI PRYLQJ EORFN DQG +LOEHUW PHWKRGV IRU WKH WRZHU ORQJLWXGLQDOEHQGLQJPRGH H *$675$)7WUDQVLHQW
*$67*(1893WUDQVLHQW
FRVLQH ODJ FRVLQH IODS VLQH ODJ VLQH IODS
0 1 W Q H P R P J LQ G Q H E O D LQ G X W L J Q OR P R W W R E U H Z R W
P P H G X W L Q J D P
UDGLXV P
W Q H P H U F H G J OR LQ J LQ S P D G
ZLQG VSHHG PV
H
H
H
H
)LJXUH&RPSDULVRQRIWUDQVLHQWUHVSRQVHV
'LVFXVVLRQDQG&RQFOXVLRQV
*$675$)7 OLQ *$675$)7 QROLQ PRYLQJ EORFN *$675$)7 QROLQ +LOEHUW *$67*(1893 PRYLQJ EORFN *$67*(1893 +LOEHUW
WUDQVLHQWG
WLP HV
)LJXUH 0DJQLWXGH RI WKH F\FOLF FRPSRQHQWV VLQH DQGFRVLQH RIWKHURWRUSURJUHVVLYHOHDGODJPRGHIRU WKHZLQGVSHHGVRIPVDQGPV
*$67*(1893HQYHORSH
8 PV
*$675$)7HQYHORSH H
)LJXUH &RPSDULVRQ RI GDPSLQJ HVWLPDWLRQV RI PRYLQJ EORFN DQG +LOEHUW PHWKRGV IRU WKH WRZHU ODWHUDOEHQGLQJPRGH
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
$FNQRZOHGJHPHQWV 7KLV ZRUN ZDV VXSSRUWHG E\ WKH (XURSHDQ &RPPLVVLRQXQGHUFRQWUDFW11.&7
5HIHUHQFHV >@ ³:LQG (QHUJ\ WKH )DFWV DQ DQDO\VLV RI ZLQG HQHUJ\LQWKH(8´(:($UHSRUW >@ 6FKHSHUV -* ³9(:7'& 9HULILFDWLRQ RI (XURSHDQ :LQG 7XUELQH 'HVLJQ &RGHV´ )LQDO 5HSRUW RI -25&7 -RXOH ,,, SURMHFW (&1 >@ 5L]LRWLV9$DQG9RXWVLQDV6*³9DOLGDWLRQRI WKH6WDELOLW\WRROVDQG$HURHODVWLF&RGHV´178$ UHSRUW >@ 5L]LRWLV 9$ DQG 9RXWVLQDV 6* ³*$67 $ JHQHUDO DHURG\QDPLF DQG VWUXFWXUDO SUHGLFWLRQ WRRO IRU ZLQG WXUELQHV´ (:(&¶ 'XEOLQ ,UHODQG >@ +RGJHV '+ DQG 'RZHOO (+ ³1RQOLQHDU (TXDWLRQVRI0RWLRQIRUWKH(ODVWLF%HQGLQJDQG 7RUVLRQ RI 7ZLVWHG 1RQXQLIRUP 5RWRU %ODGHV´ 1$6$71' >@ %HOHVVLV 0$ &KDVVDSR\LDQQLV 3, 9RXWVLQDV 6* ³)UHHZDNH PRGHOOLQJ RI URWRU DHURG\QDPLFV 5HFHQW GHYHORSPHQWV DQG IXWXUH SHUVSHFWLYHV´ 3URF RI (:(&¶ &RSHQKDJHQ'HQPDUN >@ 3HWRW ' ³'LIIHUHQWLDO HTXDWLRQ PRGHOLQJ RI G\QDPLFVWDOO´5HFKHUFKH$HURVSDWLDOHSDSHUQR
>@ &KDYLDURSRXORV 3. ³)ODS/HDG±ODJ $HUR HODVWLF 6WDELOLW\ RI :LQG 7XUELQH %ODGHV´ - :LQG(QHUJ\± >@ 6PLWK &% DQG :HUHOH\ 10 ³7UDQVLHQW $QDO\VLV IRU 'DPSLQJ ,GHQWLILFDWLRQ LQ 5RWDWLQJ &RPSRVLWH %HDPV ZLWK ,QWHJUDO 'DPSLQJ /D\HUV´ 6PDUW 0DWHU 6WUXFW SS >@7DVNHU )$ DQG &KRSUD , ³$VVHVVPHQW RI 7UDQVLHQW $QDO\VLV 7HFKQLTXHV IRU 5RWRU 6WDELOLW\´ -RXUQDO $P +HOLFRSWHU 6RF >@6LPRQ 0 DQG 7RPOLQVRQ *5 ³8VH RI WKH +LOEHUW 7UDQVIRUP LQ 0RGDO $QDO\VLV RI /LQHDU DQG1RQOLQHDU6WUXFWXUHV´-RXUQDORI6RXQGDQG 9LEUDWLRQ >@)XJOVDQJ 3 ³$HURHODVWLF 6WDELOLW\ DQG &RQWURO RI /DUJH :LQG 7XUELQHV ± 67$%&21´ 3URFHHGLQJV RI WKH (XURSHDQ :LQG(QHUJ\ &RQIHUHQFH DQG ([KLELWLRQ 0DGULG 6SDLQ -XQH ± >@5L]LRWLV9$9RXWVLQDV6*3ROLWLV(6DQG &KDYLDURSRXORV 3. ³$HURHODVWLF 6WDELOLW\ RI :LQG 7XUELQHV 7KH 3UREOHP WKH 0HWKRGV DQG WKH,VVXHV´-:LQG(QHUJ\± >@+DQVHQ 0+ ³,PSURYHG 0RGDO '\QDPLFV RI :LQG 7XUELQHV WR $YRLG 6WDOO,QGXFHG 9LEUDWLRQV´-:LQG(QHUJ\±