Environmental effects on the dynamic characteristics of a historic cathedral

(19,5210(17$/())(&76217+('<1$0,&

&+$5$&7(5,67,&62)$+,6725,&&$7+('5$/

&DUPHOR*HQWLOHDQG$QWRQHOOR5XFFROR _{3ROLWHFQLFRGL0LODQR'HSDUWPHQWRI$UFKLWHFWXUH%XLOWHQYLURQPHQWDQG&RQVWUXFWLRQHQJLQHHULQJ} 3LD]]D/HRQDUGRGD9LQFL0LODQ,WDO\ HPDLOFDUPHORJHQWLOH#SROLPLLW _{3ROLWHFQLFRGL0LODQR'HSDUWPHQWRI$UFKLWHFWXUH%XLOWHQYLURQPHQWDQG&RQVWUXFWLRQHQJLQHHULQJ} 3LD]]D/HRQDUGRGD9LQFL0LODQ,WDO\ DQWRQHOORUXFFROR#SROLPLLW

.H\ZRUGV $XWRPDWHG PRGDO LGHQWLILFDWLRQ &DWKHGUDO RI 0LODQ &RQGLWLRQEDVHG

PDLQWHQDQFH&RQWLQXRXVPRQLWRULQJ7HPSHUDWXUH

$EVWUDFW The maintenance and preservation of the Milan Cathedral is traditionally

performed through well-established and time-scheduled programs of visual inspection and architectural restoration of surfaces, decorations, and statues in Candoglia marble. On the other hand, the structural condition assessment and preservation turns out to be a challenging task due to the dimensions and complexity of the building, the usual uncertainties on the material properties and also the difficulty in inspecting several structural elements. Therefore, a structural monitoring system was recently designed and installed in the Milan Cathedral to assist the condition-based structural maintenance of the monument. The monitoring system includes different sensing technologies to allow appropriate tracking of different long-term structural behavior. The dynamic monitoring of the horizontal response of selected piers is complemented by the static monitoring of the tilt of the same piers and of the strain in selected tie-rods. In addition, the indoor and outdoor environmental parameters are extensively measured as well.

After a concise historic background on the historic monument and the description of the dynamic monitoring system installed in the Milan Cathedral, the paper focuses on the dynamic characteristics of the monument, that were identified in the first hours of continuous monitoring, Subsequently, the results of the first year of dynamic monitoring are presented and discussed, with special attention being given to the influence of environmental parameters on the variations observed in the resonant frequencies and mode shapes. In more details, the presented results highlight that: (a) 8 global vibration modes are automatically detected in the frequency range 1.0-5.0 Hz; (b) the variations observed in the resonant frequencies are mainly driven by temperature, with the effect of thermal changes being very peculiar; (c) the mode shapes and the related mode complexity do not exhibit appreciable fluctuations associated to the environmental changes, so that an appropriate strategy of SHM should be based also on the time invariance of those parameters.



 ,1752'8&7,21

7KH 0LODQ &DWKHGUDO LV D ZRUOGZLGH NQRZQ +HULWDJH PRQXPHQW ZKRVH VWUXFWXUDO FRQVWUXFWLRQ WRRN PRUH WKDQ  FHQWXULHV IURP WKH DSVH HUHFWLRQ LQ  XQWLO WKH IDoDGH ILQDOL]DWLRQLQ>@6XEVHTXHQWO\WKHDUFKLWHFWXUDOZRUNVFRQWLQXHGXQWLOWKHLQVWDOODWLRQ RIWKHODVWLURQJDWHLQDQGWKLV\HDULVXVXDOO\LQGLFDWHGDVWKHRIILFLDOFRPSOHWLRQRIWKH EXLOGLQJ ZRUNV 6LQFH  DOO RSHUDWLRQDO DVSHFWV UHODWHG WR WKH FRQVWUXFWLRQ PDLQWHQDQFH DQG UHVWRUDWLRQ RI WKH FDWKHGUDO DUH PDQDJHG E\ WKH KLVWRULF ,QVWLWXWLRQ QDPHG Veneranda Fabbrica del Duomo di Milano >@ DQG GHQRWHG DV Fabbrica LQ WKH IROORZLQJ $IWHU WKH FRQVWUXFWLRQ RI WKH PDLQ VWUXFWXUHV RI WKH FDWKHGUDO WKH Fabbrica PDLQ PLVVLRQ PRYHG WR FRQWLQXRXVLQVSHFWLRQPDLQWHQDQFHDQGSUHVHUYDWLRQRIWKHPRQXPHQW ZLWKWKRVHDFWLYLWLHV EHLQJHVSHFLDOO\UHODWHGWRVXUIDFHVGHFRUDWLRQVDQGVWDWXHVLQ&DQGRJOLDPDUEOH

$IWHUWKHUHFHQWDVVHVVPHQWRIWKHVWDWHRISUHVHUYDWLRQDQGWKHWHQVLOHIRUFHRIWKHPHWDOOLF WLHURGVRIWKH0LODQ&DWKHGUDO>@WKHLGHDRIDGRSWLQJD6WUXFWXUDO+HDOWK0RQLWRULQJ6+0 VWUDWHJ\KDVEHHQWDNLQJVKDSHWRFRQWLQXRXVO\DVVLVWWKHVWUXFWXUDOFRQGLWLRQDVVHVVPHQWDQG SUHVHUYDWLRQ RI WKH PRQXPHQW &RQVHTXHQWO\DMRLQWUHVHDUFKVWDUWHGEHWZHHQWKHFabbrica DQG3ROLWHFQLFRGL0LODQRDQGDVWUXFWXUDOPRQLWRULQJV\VWHP>@ZDVGHVLJQHGDQGLQVWDOOHG LQ WKH FDWKHGUDO ZLWK WKH REMHFWLYHV RI SURYLGLQJ WKH LQIRUPDWLRQ QHHGHG IRU WKH FRQGLWLRQ EDVHGVWUXFWXUDOPDLQWHQDQFHDQGWKHFUHDWLRQRIDODUJHDUFKLYHRIH[SHULPHQWDOGDWDXVHIXOWR HQKDQFHWKHNQRZOHGJHRIWKHPRQXPHQW 7KHORQJWHUPPRQLWRULQJV\VWHP>@IXOO\FRPSXWHUEDVHGDQGZLWKHIILFLHQWWUDQVPLVVLRQ RIWKHFROOHFWHGGDWDLQFOXGHVVWDWLFDQGG\QDPLFPHDVXUHPHQWV7KHG\QDPLFPRQLWRULQJLV SHUIRUPHGWKURXJKVHLVPRPHWHUVHOHFWURG\QDPLFYHORFLW\VHQVRUVLQVWDOOHGDWWKHWRSRI VHOHFWHGSLHUVDQGDWOHYHOVRIWKHPDLQVSLUH7KHVWDWLFPRQLWRULQJV\VWHPFRQVLVWVRID ELD[LDOWLOWPHWHUVLQVWDOOHGDWWKHWRSRIVHOHFWHGSLHUVDQGDWOHYHOVRIWKHPDLQVSLUHE YLEUDWLQJZLUHH[WHQVRPHWHUVPRXQWHGRQWKHWLHURGVH[KLELWLQJWHQVLOHVWUHVVODUJHUWKDQ 03D >@ 6LQFH ERWK WKH ORQJWHUP VWDWLF EHKDYLRU DQG WKH WLPH HYROXWLRQ RI G\QDPLF VLJQDWXUHVDUHH[SHFWHGWREHVHQVLWLYHDOVRWRHQYLURQPHQWDOFKDQJHV>@DQGHVSHFLDOO\WKH WHPSHUDWXUHPLJKWDIIHFWWKHYDULDWLRQRIVWUXFWXUDOSDUDPHWHUVLQPDVRQU\VWUXFWXUHV>@ WKHLQGRRUDQGRXWGRRUHQYLURQPHQWDOSDUDPHWHUVWHPSHUDWXUHDQGKXPLGLW\DUHH[WHQVLYHO\ PHDVXUHG WR HVWDEOLVKLQJ FRUUHODWLRQV ZLWK WKH FKDQJHV RI VWUXFWXUDO SDUDPHWHUV >@ DQG HYDOXDWLQJWKHULVNVIRUWKHSUHVHUYDWLRQRIWKHPDLQDUWLIDFWVSUHVHQWLQWKHFDWKHGUDO>@

7KH SUHVHQW SDSHU LV PDLQO\ DLPHG DW GHVFULELQJ WKH PRQLWRULQJ V\VWHP LQVWDOOHG LQ WKH FDWKHGUDO ZLWK HPSKDVLV RQ WKH G\QDPLF PHDVXUHPHQWV WKH SURFHVVLQJ RI WKH FRQWLQXRXVO\ FROOHFWHG WLPH VHULHV DQG WKH DXWRPDWHG H[WUDFWLRQ RI G\QDPLF VLJQDWXUHV LH UHVRQDQW IUHTXHQFLHVPRGHVKDSHVDQGPRGHFRPSOH[LW\>@6LQFHWKHG\QDPLFUHVSRQVHRIWKH FKXUFKLVFRQWLQXRXVO\FROOHFWHGLQDZHOOGLVWULEXWHGPHDVXUHPHQWJULGFKDQQHOVRIGDWD WKH IHDWXUHV UHSUHVHQWDWLYH RI VWUXFWXUDO FRQGLWLRQ VKRXOG LQFOXGH WKH PRGH VKDSHV DQG QRW RQO\WKHUHVRQDQWIUHTXHQFLHV7KHXVHRIPRGHVKDSHVDQGPRGHFRPSOH[LW\ZLWKLQD6+0 VWUDWHJ\ FRQFHLYDEO\ H[KLELW DGYDQWDJHV EHFDXVH WKRVH PRGDO SDUDPHWHUV PLJKW EH OHVV VHQVLWLYHWKDQUHVRQDQWIUHTXHQFLHVWRH[RJHQRXVIDFWRUVDQGFRQWDLQLQIRUPDWLRQDOVRRQWKH ORFDOVWUXFWXUDOEHKDYLRU

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

D E

)LJXUH3DVWDDQGSUHVHQWEYLHZRIWKH0LODQ&DWKHGUDO FRXUWHV\RIVeneranda Fabbrica del Duomo di Milano

D E

)LJXUH,QQHUYLHZVRISLHUVDUFKHVYDXOWVDQGLURQWLHURGV  7+(0,/$1&$7+('5$/

7KH0LODQ&DWKHGUDO)LJVLVWKHPRVWUHSUHVHQWDWLYHODQGPDUNRIWKHFLW\RI0LODQ DQG RQH RI WKH ODUJHVW PDVRQU\ PRQXPHQWV HYHU EXLOW WKH EXLOGLQJ VSUHDGV RYHU DQ DUHD RI

PRUHWKDQPZLWKDYROXPHRIDERXWPVRWKDWLWLVWKHVHFRQGODUJHVWJRWKLF

FDWKHGUDOLQWKHZRUOGE\YROXPHDQGDUHD

7KH FKXUFK H[KLELWV D XQLTXH VW\OH RI DUFKLWHFWXUH ZKLFK LV FKDUDFWHUL]HG E\ D IXVLRQ RI (XURSHDQ *RWKLF VW\OH DQG /RPEDUG\ WUDGLWLRQ DOVR ZLWK WKH SUHVHQFH RI QHRFODVVLF QHR JRWKLF DQG HYHQ UHQDLVVDQFH LQIOXHQFHV GXHWR WKH ORQJ SHULRGUHTXLUHG E\ WKH FRQVWUXFWLRQ ZRUNV7KHFKXUFKFRQVWUXFWLRQVWDUWHGLQIURPWKHKDOIRFWDJRQDODSVHDQG(DVWFKRLU DQGSURFHHGHGZLWKWKHWUDQVHSWWKHPDLQGRPHWKHtiburioLHWKHSULVPDWLFVWUXFWXUHZLWK RFWDJRQDOEDVHZKLFKLVEXLOWDURXQGWKHPDLQGRPHDQGWKHPDLQVSLUHVXEVHTXHQWO\WKH ILYHQDYHVWUXFWXUHRYHUHLJKWED\VZDVEXLOWDQGILQDOL]HGLQZLWKDQHR*RWKLFIDoDGH $V SUHYLRXVO\ SRLQWHG RXW WKH LQDXJXUDWLRQ RI WKH ODVW JDWH -DQXDU\ K  LV JHQHUDOO\ DVVXPHGDVWKHRIILFLDOHQGLQJRIWKHPRQXPHQWEXLOGLQJ

:KHQ FRPSDUHG ZLWK RWKHU JRWKLF FDWKHGUDOV WKH 0LODQ &DWKHGUDO H[KLELWV D SHFXOLDU VWUXFWXUDOV\VWHPZLWKPHWDOOLFWLHURGVEHLQJSHUPDQHQWO\LQVWDOOHGXQGHUHDFKYDXOW)LJ DQGGHVLJQHGWRH[HUWDQDFWLYHSDUWLQUHVLVWLQJWKHODWHUDOWKUXVWV>@+LVWRULFDOGRFXPHQWV>@ WHVWLI\WKDWWKHWHQVLRQEDUVLQWKHFDWKHGUDOZHUHSHUPDQHQWO\LQVWDOOHGRQWKHWRSRIWKHSLHUV GXULQJ WKH FRQVWUXFWLRQ WR UHGXFH WKH KRUL]RQWDO WKUXVW RQ WKH ODWHUDO EXWWUHVVHV DV WKRVH

EXWWUHVVHV ZHUH MXGJHG WRR VOHQGHU E\ WKH )UHQFK DUFKLWHFW -HDQ 0LJQRW $ WRWDO RI  PHWDOOLF WLHURGV )LJ  LV QRZDGD\V SUHVHQW LQ WKH FDWKHGUDO DQG PRVW RI WKHP DUH WKH RULJLQDOHOHPHQWVGDWLQJEDFNWRWKHDJHRIFRQVWUXFWLRQ

$ORQJLWXGLQDOVHFWLRQRIWKH0LODQ&DWKHGUDOLVVKRZQLQ)LJ7KHRYHUDOOGLPHQVLRQVRI WKH/DWLQFURVVVKDSHGSODQDUHDERXWPîP)LJZLWKWKHDLVOHVDQGWKHFHQWUDO QDYHVVSDQQLQJPDQGPUHVSHFWLYHO\

)LJXUH/RQJLWXGLQDOVHFWLRQRIWKH0LODQ&DWKHGUDO

GLPHQVLRQVLQPFRXUWHV\RIVeneranda Fabbrica del Duomo di Milano

)LJXUH3ODQRIWKH0LODQ&DWKHGUDOGLPHQVLRQVLQPDQGOD\RXWRIWKHVHLVPRPHWHUVLQVWDOOHGLQWKHFKXUFK

 '<1$0,&021,725,1*6<67(0$1''$7$$1$/<6,6

,QRUGHUWRFKDUDFWHUL]HWKHKHDOWKVWDWHRIWKH0LODQ&DWKHGUDODQGWRDGGUHVVLWVFRQGLWLRQ EDVHG VWUXFWXUDO PDLQWHQDQFH WKH IROORZLQJ NH\ SDUDPHWHUV DUH FRQWLQXRXVO\ PHDVXUHG RU LGHQWLILHGIURPWKHPHDVXUHPHQWV • %LD[LDOWLOWRIWKHFDSLWDORIVHOHFWHGSLHUVLHSLHUV DQGLQ)LJDQGPDLQVSLUH • 6WUDLQRIWLHURGV DQG)LJ • ,QGRRUDQGRXWGRRUHQYLURQPHQWDOSDUDPHWHUV7KHLQGRRUWHPSHUDWXUHLVPHDVXUHGLQWKH VDPH FDSLWDOV ZKHUH WKH WLOWV DUH UHFRUGHG ZKHUHDV WKH KXPLGLW\ LV PHDVXUHG LQ WKH QHLJKERUKRRG RI LQVWUXPHQWHG WLHV 7KH RXWGRRU SDUDPHWHUV DUH FROOHFWHG WKURXJK D ZHDWKHUVWDWLRQLQVWDOOHGLQWKHPDLQVSLUH •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

7KHG\QDPLFPRQLWRULQJV\VWHPLVEDVHGRQ6$5$66VHLVPRPHWHUVHOHFWURG\QDPLF YHORFLW\WUDQVGXFHUV6LQFHWKHHOHFWURG\QDPLFVHQVRUVDUHFKDUDFWHUL]HGE\KLJKVHQVLWLYLW\ RI  9PV XQQHFHVVLW\ RI SRZHULQJ DQG H[FHOOHQW SHUIRUPDQFH LQ WKH ORZ IUHTXHQF\

UDQJHf≤+]WKRVHWUDQVGXFHUVWXUQRXWWREHHVSHFLDOO\VXLWDEOHIRUWKHDSSOLFDWLRQLQ

YLEUDWLRQWHVWLQJRUPRQLWRULQJRIFLYLOHQJLQHHULQJDQGFXOWXUDOKHULWDJH>@VWUXFWXUHV7KH G\QDPLFPRQLWRULQJV\VWHPFRQVLVWVRI

• ELD[LDOVHLVPRPHWHUVDQGPRQRD[LDOVHLVPRPHWHULQVWDOOHGDWWKHWRSRIVHOHFWHG SLHUVLQVLGHWKH&DWKHGUDO)LJDQGPHDVXULQJWKHYHORFLW\LQWKHWZRRUWKRJRQDO16 WUDQVYHUVDO DQG (: ORQJLWXGLQDO GLUHFWLRQV 7KH VHQVRUV LQVWDOOHG RQ SLHUV   DQGDUHJURXSHGDQGZLUHGWRILYH ELWGLJLWL]HUV6$5$6/(DFKGLJLWL]HULVHTXLSSHGZLWK$'FRQYHUVLRQV\VWHP*% PHPRU\V\QFKURQL]DWLRQE\*36EDFNXSEDWWHU\DQG8076PRGHPIRUGDWDWUDQVIHU • ×PRQRD[LDOVHLVPRPHWHUVLQVWDOOHGDWWKHVDPHOHYHOVRIWKHPDLQVSLUHKRVWLQJWKH ELD[LDOWLOWPHWHUVEHORQJLQJWRWKHVWDWLFPRQLWRULQJ7KHWKUHHVHQVRUVLQVWDOOHGDWHDFK OHYHODUHZLUHGWRELWGLJLWL]HUZLWKWKHGLJLWL]HUVEHLQJFRQQHFWHGWRDVZLWFKIRUGDWD WUDQVIHU

7KH YHORFLW\ GDWD DUH WUDQVIHUUHG LQ UHDO WLPH WR WKH Fabbrica ZRUNVWDWLRQ DQG VWRUHG LQ VHSDUDWHILOHVLQFRPSUHVVHGPLQLVHHGIRUPDWRIKRXU(YHU\KRXUWKHDXWRPDWLFVLJQDO SURFHVVLQJLQYROYHVWKHIROORZLQJWDVNVDSUHSURFHVVLQJWKHUDZGDWDWRFRPSHQVDWHWKH ORZIUHTXHQF\ DWWHQXDWLRQ RI WKH VHQVRU XVLQJ WKH 6(,602:,1 FRPPHUFLDO VRIWZDUH KWWSVZZZVDUDSJLW"ODQJ HQDQGVXEVHTXHQWVDYLQJRIWKHWLPHVHULHVLQWH[WIRUPDWE GDWDDQDO\VLVWRH[WUDFWWKHPD[LPXPDQGWKHURRWPHDQVTXDUHYDOXHVDQGFUHDWLRQRIDILOHLQ 0DWODE PDW IRUPDW F ORZSDVV ILOWHULQJ DQG GRZQVDPSOLQJ WR UHGXFH WKH VDPSOLQJ IUHTXHQF\IURP+]WR+]DQGFUHDWLRQRIDGDWDEDVHRIILOHVIRUWKHDSSOLFDWLRQRIWKH PRGDOLGHQWLILFDWLRQWRROVGDXWRPDWHGPRGDOHVWLPDWLRQDQGWUDFNLQJ

$IWHU WKH DXWRPDWHG PRGDO SDUDPHWHU HVWLPDWLRQ RQO\ WKH KRXUO\ HYDOXDWHG IHDWXUHV LH WKHVWDWLVWLFDOFKDUDFWHULVWLFVRIHDFKGDWDVHWDQGWKHPRGDOSDUDPHWHUVDQGDIHZWLPHVHULHV FRUUHVSRQGLQJWRPHDQLQJIXOHYHQWVDUHSHUPDQHQWO\VWRUHGLQWKHFabbricaDUFKLYHVDQGFDQ EHDFFHVVHGWKURXJKJUDSKLFDODQGUHSRUWLQJWRROV,WVKRXOGEHQRWLFHGWKDWVLPLODUWRROVDOORZ WKHPDQDJHPHQWDQGYLVXDOL]DWLRQRIWKHVWDWLFPRQLWRULQJUHVXOWV 7KHPRGDOSDUDPHWHUVRIWKHFDWKHGUDODQGRIWKHPDLQVSLUHDUHLQGHSHQGHQWO\LGHQWLILHG XVLQJ D IXOO\ DXWRPDWHG SURFHGXUH EDVHG RQ WKH FRYDULDQFHGULYHQ 6WRFKDVWLF 6XEVSDFH ,GHQWLILFDWLRQ66,&RYDOJRULWKP>@DQGGHYHORSHGLQSUHYLRXVUHVHDUFK>@7KHOHQJWK RIWKHWLPHZLQGRZDGRSWHGLQWKHDXWRPDWHGLGHQWLILFDWLRQZDVVHWHTXDOWRKV7KH DXWRPDWHGSURFHGXUH>@LQYROYHVWKHWZRPDLQVWHSVRIPRGDOSDUDPHWHUVHVWLPDWLRQ03( DQGPRGDOWUDFNLQJ07

7KH 03( LV SHUIRUPHG WKURXJK DQ DXWRPDWLF LQWHUSUHWDWLRQ RI WKH VWDELOL]DWLRQ GLDJUDP EDVHGRQWKHVHQVLWLYLW\RIIUHTXHQF\DQGPRGHVKDSHWRWKHPRGHORUGHUYDULDWLRQ)RUHDFK GDWDVHWDIWHUKDYLQJILOWHUHGWKHVSXULRXVSROHVE\FKHFNLQJWKHDVVRFLDWHGGDPSLQJUDWLRDQG PRGH FRPSOH[LW\ YDOXH >@ WKH SROHV VKDULQJ VLPLODU IUHTXHQFLHV DQG PRGH VKDSHV DUH FOXVWHUHG WRJHWKHU DQG D VHW RI UHSUHVHQWDWLYH PRGDO SDUDPHWHUV LH UHVRQDQW IUHTXHQF\ GDPSLQJDQGPRGHVKDSHLVHVWLPDWHGIRUHDFKFOXVWHU,WLVZRUWKPHQWLRQLQJWKDWWKHPRGH FRPSOH[LW\ LV FKHFNHG E\ DYHUDJLQJ WKH LQIRUPDWLRQ SURYLGHG E\ ERWK WKH 0RGDO 3KDVH &ROOLQHDULW\ 03& >@ DQG 0HDQ 3KDVH 'HYLDWLRQ 03' >@ WKURXJK WKH 0RGDO &RPSOH[LW\,QGH[0&, î>í03&03'ƒ@YDU\LQJEHWZHHQDQGZLWK LQGLFDWLQJDPRQRSKDVHEHKDYLRURIWKHLGHQWLILHGPRGHVKDSH 7KH07DLPHGDWSURYLGLQJWKHWLPHHYROXWLRQRIWKHSDUDPHWHUVRIHDFKPRGHLVEDVHG RQIUHTXHQF\DQG0$&>@YDULDWLRQZLWKUHVSHFWWRDSUHVHOHFWHGOLVWRIEDVHOLQHPRGHV,W LVZRUWKPHQWLRQLQJWKDWWKLVVWHSLVSHUIRUPHGLQDQDGDSWLYHZD\LHE\XSGDWLQJWKH0$& DQGIUHTXHQF\YDULDWLRQWKUHVKROGRIHDFKPRGHDIWHUDQHZGDWDVHWKDVEHHQDQDO\]HG ,QWKHDXWRPDWHGLGHQWLILFDWLRQRIWKHG\QDPLFFKDUDFWHULVWLFVRIWKHFDWKHGUDOFKDQQHOV RIGDWD)LJWKHWLPHODJSDUDPHWHUiZDVVHWHTXDOWRDQGWKHGDWDZHUHILWWHGXVLQJ VWRFKDVWLFVXEVSDFHPRGHOVRIRUGHUn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7KHLQVSHFWLRQRI)LJDOORZVWKHIROORZLQJFRPPHQWV

D7KH ORZHU WZR PRGHV DV H[SHFWHG DUH JOREDOVZD\PRGHVRIWKHFDWKHGUDODORQJWKH WUDQVYHUVH 16 f&  +] )LJ E DQG ORQJLWXGLQDO (: f&  +] )LJ F

GLUHFWLRQ

E7KHVXEVHTXHQWWZRPRGHVf& +])LJGDQGf& +]DQG)LJHLQYROYH

GRPLQDQW PRWLRQ LQ WKH 16 GLUHFWLRQ DQG EHQGLQJ RI WKH QDYHV ZLWK WKH GHIRUPHG VKDSHV EHLQJ FKDUDFWHUL]HG E\ RQH DQG WZR FKDQJHV RI VLJQ IURP DSVH WR IDoDGH UHVSHFWLYHO\

F7KH KLJKHU PRGHV )LJV IL DUH FKDUDFWHUL]HG E\ PRUH FRPSOH[ PRGH VKDSHV )RU H[DPSOH WKH WK PRGH f&  +] )LJ I LQYROYHV RXWRISKDVH EHQGLQJ RI WKH

1RUWKDQG6RXWKQDYHVZKHUHDVWKHWKPRGHf& +])LJJLQYROYHVRXWRI

SKDVHPRWLRQRIWKHIDoDGHDQGDSVHLQWKH(:GLUHFWLRQ

)LJXUHD$HULDOYLHZRIWKH0LODQ&DWKHGUDOIURPDSVHDQGELLGHQWLILHGYLEUDWLRQPRGHV K±

G7KH 16 PRGHV H[KLELW GDPSLQJ UDWLRV YDU\LQJ IURP  & WR  & ZKHUHDVWKHGDPSLQJRIWKH(:PRGHVUDQJHVEHWZHHQ&DQG&,W LV IXUWKHU QRWLFHG WKDW HVSHFLDOO\ WKH GDPSLQJ RI (: PRGHV VHHPV WR EH ODUJHU WKDQ JHQHUDOO\REVHUYHGDWWKHORZOHYHORIDPELHQWH[FLWDWLRQH[LVWLQJRQKLVWRULFDOEXLOGLQJV

 6(/(&7('5(68/76)5207+(&217,18286'<1$0,&021,725,1*

7KHG\QDPLFPRQLWRULQJLVDFWLYHLQWKH0LODQ&DWKHGUDOVLQFH2FWREHUWK7KLV VHFWLRQ VXPPDUL]HV WKH PDLQ UHVXOWV REWDLQHG GXULQJ WKH ILUVW \HDU RI PRQLWRULQJ IURP  WR  DQG IRU WKH VDNH RI FRQVLVWHQF\ RQO\ WKH H[SHULPHQWDO UHVXOWV FROOHFWHGLQWKHFDWKHGUDODUHSUHVHQWHGDQGGLVFXVVHGZLWKQRFRPPHQWVEHLQJSURYLGHGRQ WKHGDWDPHDVXUHGRQWKHPDLQVSLUH

$V XVXDO IRU PDVRQU\ EXLOGLQJV WKH HYROXWLRQ LQ WLPH RI HQYLURQPHQWDO SDUDPHWHUV LV ILUVWO\SUHVHQWHGLQRUGHUWRXQGHUVWDQGWKHHIIHFWVRIFKDQJLQJHQYLURQPHQWRQWKHYDULDWLRQV REVHUYHGLQWKHQDWXUDOIUHTXHQFLHVDQGPRGDOSDUDPHWHUV  (QYLURQPHQWDOSDUDPHWHUV $VSUHYLRXVO\SRLQWHGRXWDTXLWHH[WHQGHGJULGRIWHPSHUDWXUHVHQVRUVDQGK\JURPHWHUV KDVEHHQLQVWDOOHGLQVLGHWKHFKXUFKWRVXSSRUWERWKWKH6+0SURJUDPDQGWKHSUHVHUYDWLRQRI 

WKHDUWLIDFWVZKLFKDUHNHSWLQVLGHWKHPRQXPHQW7KHYDULDWLRQLQWLPHRIWKHDYHUDJHLQGRRU WHPSHUDWXUHDQGWKHRXWGRRUWHPSHUDWXUHPHDVXUHGE\WKHZHDWKHUVWDWLRQLVVKRZQLQ)LJ DZKHUHDV)LJEUHIHUVWRWKHDYHUDJHLQGRRUKXPLGLW\7KHRUDQJHOLQHLQ)LJDSUHVHQWV WKHHYROXWLRQRIWKHRXWGRRUWHPSHUDWXUHDQGKLJKOLJKWVFKDQJHVEHWZHHQ−ƒ&DQGƒ& ZLWKUHPDUNDEOHGDLO\YDULDWLRQVLQVXQQ\GD\V7KHFRUUHVSRQGLQJYDULDWLRQRIWKHDYHUDJH LQGRRUWHPSHUDWXUHLVUHSUHVHQWHGE\WKHUHGOLQHLQ)LJDDQGUDQJHVEHWZHHQƒ&DQG ƒ&LWLVIXUWKHUQRWLFHGWKDWWKHDYDLODELOLW\RIDODUJHQXPEHURIWHPSHUDWXUHVHQVRUVLQ WKHFKXUFKKLJKOLJKWV>@DORZWHPSHUDWXUHJUDGLHQWLQVSDFHZLWKWKHGLIIHUHQFHEHWZHHQ WKHH[WUHPHYDOXHVQRWH[FHHGLQJƒ&&RQVHTXHQWO\WKHORZWHPSHUDWXUHJUDGLHQWDQGWKH FRUUHODWLRQFRHIILFLHQWVDOZD\VODUJHUWKDQEHWZHHQWKHPHDVXUHGWHPSHUDWXUHVDOORZWR DVVXPH WKH DYHUDJH LQGRRU WHPSHUDWXUH )LJ D DV D UHSUHVHQWDWLYH TXDQWLW\ IRU WKH 6+0 FRUUHODWLRQV $ VLPLODU FRQFOXVLRQ LV GUDZQ IRU WKH UHODWLYH KXPLGLW\ ZKRVH WLPH VHULHV DUH KLJKO\FRUUHODWHG>@DQGH[KLELWFRUUHODWLRQFRHIILFLHQWVRIWKHRUGHURIRUODUJHU D E )LJXUH(YROXWLRQLQWLPHRIDDYHUDJHLQGRRUWHPSHUDWXUHDQGRXWGRRUWHPSHUDWXUH EDYHUDJHLQGRRUUHODWLYHKXPLGLW\  (QYLURQPHQWDOHIIHFWVRQQDWXUDOIUHTXHQFLHV 7KHUHVXOWVRIDXWRPDWHGPRGDOLGHQWLILFDWLRQDQGIUHTXHQF\WUDFNLQJGXULQJWKHILUVW\HDU RIPRQLWRULQJDUHH[HPSOLILHGLQ)LJIRUWKHORZHUPRGHVRIWKHFDWKHGUDOH[KLELWLQJWKH KLJKHU LGHQWLILFDWLRQ UDWH 7KH FRPSOHWH UHVXOWV RI DXWRPDWHG 20$ LQ WHUPV RI QDWXUDO IUHTXHQFLHVDQGGDPSLQJUDWLRVDUHVXPPDUL]HGLQ7DEOHZLWKVRPHVWDWLVWLFDOLQIRUPDWLRQ

,QPRUHGHWDLOV7DEOHOLVWVWKHLGHQWLILFDWLRQUDWHWKHPHDQYDOXHfPHDQDQGWKHVWDQGDUG

GHYLDWLRQ

_σ

IRIWKHDXWRPDWLFDOO\LGHQWLILHGIUHTXHQFLHVDQGWKHLUH[WUHPHYDOXHVfPLQfPD[

DVZHOODVWKHPHDQYDOXH

_ζ

PHDQDQGWKHVWDQGDUGGHYLDWLRQ

σ

ζRIWKHGDPSLQJUDWLR

,WVKRXOGEHQRWLFHGWKDWWKHLGHQWLILFDWLRQUDWHRIWKHIUHTXHQFLHVLQ)LJUDQJHVEHWZHHQ DQG7DEOHZKHUHDVWKHKLJKHUWZRIUHTXHQFLHVH[KLELWORZHULGHQWLILFDWLRQ VXFFHVVUDWLRVVWLOODOORZLQJWKHWUDFNLQJZLWKDQDFFHSWDEOHFRQWLQXLW\

$VH[SHFWHG>@)LJUHYHDOVFOHDUORQJWHUPYDULDWLRQVDVZHOODVGDLO\IOXFWXDWLRQVRI QDWXUDO IUHTXHQFLHV WKDW DUH FRQFHLYDEO\ DVVRFLDWHG ZLWK FKDQJLQJ WHPSHUDWXUH ,Q DGGLWLRQ WKHHQYLURQPHQWDOHIIHFWVWXUQRXWWREHYHU\GLVWLQFWLYHDQGWKLVSHFXOLDULW\LVXQGHUVWRRGIRU

H[DPSOH E\ FDUHIXOO\ LQVSHFWLQJ WKH WLPH HYROXWLRQ RI f& DQG f& LQ )LJ  7KRVH PRGHV

ZKRVHYDULDWLRQLVTXLWHHDV\WRLQVSHFWLQ)LJDUHFKDUDFWHUL]HGE\GRPLQDQWPRWLRQLQWKH ORQJLWXGLQDO(:f&DQGWUDQVYHUVH16f&GLUHFWLRQ)LJ

0RGH ,G5DWH fPHDQ+]

σ

I+] fPLQ+] fPD[+]

ζ

PHDQ

σ

_ζ &        &        &        &        &        &        &        &        7DEOH6WDWLVWLFVRIWKHQDWXUDOIUHTXHQFLHVDQGGDPSLQJUDWLRVLGHQWLILHGLQWKHILUVW\HDURIPRQLWRULQJ )LJXUH9DULDWLRQLQWLPHRIWKHQDWXUDOIUHTXHQFLHVRIWKHORZHUPRGHVGXULQJWKHILUVW\HDURIPRQLWRULQJ )LJXUHKLJKOLJKWVWKDWWKHIUHTXHQF\RIPRGH&FOHDUO\LQFUHDVHVZLWKGHFUHDVHGLQGRRU DQGRXWGRRUWHPSHUDWXUH)LJDDQGGHFUHDVHVZLWKLQFUHDVHGWHPSHUDWXUHWKLVWUHQGZKLFK LV H[DFWO\ WKH RSSRVLWH RI ZKDW H[SHFWHG IRU PDVRQU\ EXLOGLQJV >@ LV FRQILUPHG E\ SORWWLQJWKHIUHTXHQF\f&YHUVXVWKHRXWGRRUWHPSHUDWXUH)LJDDORQJZLWKWKHEHVWILWOLQH

HYHQLIIRUDJLYHQWHPSHUDWXUHDTXLWHUHPDUNDEOHIUHTXHQF\YDULDWLRQLVREVHUYHGQHJDWLYH WHPSHUDWXUHFRUUHODWLRQLVH[KLELWHGE\IUHTXHQF\f&GXULQJWKHHQWLUHPRQLWRULQJSHULRG,WLV

ZRUWK PHQWLRQLQJ WKDW D D QHJDWLYH IUHTXHQF\WHPSHUDWXUH FRUUHODWLRQ LV REWDLQHG ZLWK LQGRRU DYHUDJH WHPSHUDWXUH DQG E WKH WHPSHUDWXUH HIIHFW RQ (: PRGH f& LV UHPDUNDEO\

VLPLODUWRZKDWREVHUYHGIRUPRGHf&HVSHFLDOO\LQWKHFROGVHDVRQ)LJ

(YHQPRUHFRPSOLFDWHGWHPSHUDWXUHGULYHQPHFKDQLVPVFKDUDFWHUL]HWKHYDULDWLRQRI16

PRGHVDVVKRZQLQ)LJWKHIUHTXHQF\f&WHQGVWRLQFUHDVHERWKLQWKHFROGDQGLQWKHKRW

VHDVRQDQGDVLPLODUWUHQGLVH[KLELWHGE\16PRGHVf&f&DQGf&7KHFRUUHODWLRQEHWZHHQ

f&DQGWKHRXWGRRUWHPSHUDWXUHLVH[HPSOLILHGLQ)LJEDQGDVLWKDVWREHH[SHFWHGDQRQ

OLQHDUEHVWILWOLQHLVREWDLQHG

D E

)LJXUH&RUUHODWLRQEHWZHHQRXWGRRUWHPSHUDWXUHDQGLGHQWLILHGQDWXUDOIUHTXHQFLHVDf&DQGEf&

,WLVIXUWKHUQRWLFHGWKDWGXULQJWKHFROGVHDVRQDJHQHUDOL]HGWHQVLOHVWUDLQLQFUHDVHZLWK GHFUHDVHGWHPSHUDWXUHLVPHDVXUHGE\WKHH[WHQVRPHWHUVLQVWDOOHGLQWKHWLHURGV>@+HQFH WKHFRUUHVSRQGLQJLQFUHDVHGIRUFHVLQWKHWHQVLRQEDUVFRQFHLYDEO\H[HUWDVWLIIHQLQJDFWLRQRQ WKHRYHUDOOVWUXFWXUHVLQFHWKHPHWDOOLFWLHURGVIRUPDJULGRIVWLIIHQLQJHOHPHQWVVSUHDGRYHU WKHHQWLUHFDWKHGUDO)LJ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

,Q WKH DXWKRUV¶ RSLQLRQ WKH FRPSOH[ GHSHQGHQFH RI QDWXUDO IUHTXHQFLHV RQ WHPSHUDWXUH REVHUYHG LQ WKH 0LODQ &DWKHGUDO UHVXOWV IURP WZR WHPSHUDWXUHGULYHQ RSSRQHQW HIIHFWV WKH VWLIIHQLQJH[HUWHGGXULQJWKHFROGVHDVRQE\WKHLQFUHDVHGWHQVLOHIRUFHVLQWKHPHWDOOLFJULGRI WLHURGVDQGWKHXVXDOWKHUPDOH[SDQVLRQRIWKHPDVRQU\PDWHULDOV7KHIRUPHUHIIHFWWXUQVRXW WREHGRPLQDQWLQWKHFROGVHDVRQIRUDOOPRGHVZKHUHDVWKHODWWHUWHQGVWRRYHUFRPHLQWKH KRWVHDVRQIRU16PRGHV

1RWZLWKVWDQGLQJ WKH FRPSOH[ WHPSHUDWXUHGULYHQ EHKDYLRU RI WKH FDWKHGUDO DQG WKH GLIIHUHQFHRIWUHQGH[KLELWHGE\16DQG(:PRGHVWKHUHPRYDORIHQYLURQPHQWDOHIIHFWV FDQEHSHUIRUPHGIRUH[DPSOHE\DSSO\LQJWKHSULQFLSDOFRPSRQHQWDQDO\VLV3&$>@WR WKHIUHTXHQF\GDWDFROOHFWHGGXULQJDQDSSURSULDWHWUDLQLQJSHULRG,QWKHSUHVHQWDSSOLFDWLRQ WKHORZHUPRGHV)LJZHUHFRQVLGHUHGDQGWKHWUDLQLQJSHULRGLQFOXGHVWKHILUVW\HDURI PRQLWRULQJ

6LQFH WZR ODWHQW VRXUFHV RI WHPSHUDWXUHGULYHQ YDULDELOLW\ KDYH EHHQ VXJJHVWHG E\ WKH SUHYLRXVDQDO\VLVDQGWKRVHVRXUFHVDIIHFWGLIIHUHQWO\WKH16DQG(:PRGHVWKHILUVWIRXU 3&V DUH UHWDLQHG LQ RUGHU WR HVWDEOLVK WKH 3&$EDVHG PRGHO $V VKRZQ LQ )LJ  WKH 3&$ SURYLGHVDYHU\HIIHFWLYHUHPRYDORIWKHHQYLURQPHQWDOHIIHFWV

2QFHWKH3&$EDVHGSUHGLFWLRQPRGHOKDVEHHQHVWDEOLVKHGXVLQJWKHGDWDFROOHFWHGGXULQJ DQ DSSURSULDWH WUDLQLQJ SHULRG WKH RFFXUUHQFH RI DEQRUPDO VWUXFWXUDO FKDQJHV QRW REVHUYHG GXULQJ WKH WUDLQLQJ SHULRG LV RIWHQ GHWHFWHG E\ XVLQJ WKH UHVLGXDO HUURUV LH WKH GLIIHUHQFH EHWZHHQ WKH LGHQWLILHG IUHTXHQF\ DQG LWV SUHGLFWLRQ $QRPDO\ GHWHFWLRQ DSSURDFKHV PLJKW LQYROYHDYHULI\LQJWKDWHDFKSUHGLFWLRQHUURUGRHVQRWH[FHHGFRQILGHQFHLQWHUYDO>@ RUEXVLQJWKHSUHGLFWLRQHUURUVZLWKLQWKHIUDPHZRUNRIVWDWLVWLFDOFRQWUROFKDUWVVXFKDVWKH ZHOONQRZQ+RWHOOLQJ¶VTFRQWUROFKDUW>@

)LJXUH9DULDWLRQLQWLPHRIWKHQDWXUDOIUHTXHQFLHVRIWKHORZHUPRGHVGXULQJWKHILUVW\HDURIPRQLWRULQJ DIWHUWKH3&$EDVHGUHPRYDORIWKHHQYLURQPHQWDOHIIHFWV

)LJXUH9DULDWLRQLQWLPHRIWKH0$&RIWKHORZHUPRGHVGXULQJWKHILUVW\HDURIPRQLWRULQJ

0RGH MACPHDQ

σ

0$& MACPLQ MPCPHDQ

σ

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DQ\VXEVHTXHQWYDULDWLRQLQWKHPRGHVKDSHVFRQFHLYDEO\SURYLGHV WKHHYLGHQFHRIDVWUXFWXUDOFKDQJH>@2QWKHRWKHUKDQGHYHQLIPRGHVKDSHVFRQWDLQDOVR ORFDO LQIRUPDWLRQ RQ WKH VWUXFWXUH WKRVH SDUDPHWHUV PLJKW H[KLELW ORZ VHQVLWLYLW\ WR ORFDO VWUXFWXUDOFKDQJHV

7KH HYROXWLRQ GXULQJ WKH ILUVW \HDU RI PRQLWRULQJ RI WKH PRGH VKDSH YDULDWLRQ LQ WHUPV RI 0$&LVVKRZQLQ)LJIRUWKHORZHUPRGHV,WVKRXOGEHQRWLFHGWKDWWKH0$&LQGH[LV FRPSXWHGEHWZHHQDSUHVHOHFWHGVHWRIUHIHUHQFHPRGHVKDSHVFRUUHVSRQGLQJWRWKHVDPHVHW RI EDVHOLQH PRGHV XVHG LQ WKH DXWRPDWHG SURFHGXUH RI PRGDO LGHQWLILFDWLRQ )LJ  DQG WKH FXUUHQWO\ LGHQWLILHG PRGH VKDSHV )LJXUH  KLJKOLJKWV WKDW WKH 0$& YDOXHV LH WKH PRGH VKDSHVDUHDSSUR[LPDWHO\LQGHSHQGHQWRIWHPSHUDWXUHDQGWLPHLQYDULDQWHYHQLIWKHVWDQGDUG GHYLDWLRQ RI WKH 0$& WHQGV WR LQFUHDVH ZLWK WKH LQFUHDVLQJ PRGH RUGHU LH ZLWK WKH LQFUHDVLQJVSDWLDOFRPSOH[LW\RIWKHGLVWULEXWLRQRIPRGDOGHIRUPDWLRQV)LJ&ROXPQV RI 7DEOH  VXPPDUL]H WKH VWDWLVWLFDO FKDUDFWHULVWLFV RI WKH 0$& LQ WHUPV RI DYHUDJH YDOXH 0$&PHDQVWDQGDUGGHYLDWLRQσ0$&DQGPLQLPXPYDOXH0$&PLQ

7KH LQYHVWLJDWLRQ RQ PRGH VKDSH FKDQJHV ZDV FDUULHG RXW DOVR E\ FRQVLGHULQJ WKH PRGH FRPSOH[LW\ WKURXJK WKH 03& LH WKH FROOLQHDULW\ RI WKH PRGH VKDSH FRPSRQHQWV RI HDFK VLQJOHPRGHRQDVWUDLJKWOLQHLQWKHFRPSOH[SODQH)LJXUHDQGFROXPQVRI7DEOH GHPRQVWUDWH WKDW DOVR WKH 03& PHDVXUH RI PRGH FRPSOH[LW\ >@ LV DSSUR[LPDWHO\ WLPH LQYDULDQW HYHQ LI WKH 03& YDOXHV WHQG WR GHSDUW IURP XQLW\ SHUIHFW FROOLQHDULW\ DQG WR H[KLELWDQLQFUHDVHGGLVSHUVLRQIRUWKHKLJKHUPRGHV

 &21&/86,216

7KH SDSHU IRFXVHV RQ WKH PRQLWRULQJ SURJUDP RI WKH 0LODQ &DWKHGUDO 6SHFLDO HPSKDVLV LV JLYHQ RQ WKH G\QDPLF PHDVXUHPHQWV WKH DXWRPDWHG H[WUDFWLRQ RI PRGDO VLJQDWXUHV DQG WKH LQIOXHQFHRIHQYLURQPHQWDOFKDQJHVRQWKHYDULDWLRQVREVHUYHGLQWKHG\QDPLFFKDUDFWHULVWLFV RIWKHKLVWRULFPRQXPHQW%DVHGRQWKHUHVXOWVFROOHFWHGLQWKHILUVW\HDURIPRQLWRULQJLH EHWZHHQDQGWKHIROORZLQJPDLQFRQFOXVLRQVFDQEHGUDZQ

• 7KH DSSOLFDWLRQ RI VWDWHRIDUW WRROV IRU DXWRPDWHG RSHUDWLRQDO PRGDO DQDO\VLV DOORZV DFFXUDWHHVWLPDWHDQGWUDFNLQJRIUHVRQDQWIUHTXHQFLHVLQWKHIUHTXHQF\LQWHUYDO+]

)LJXUH9DULDWLRQLQWLPHRIWKH03&RIWKHORZHUPRGHVGXULQJWKHILUVW\HDURIPRQLWRULQJ

• 7KHDXWRPDWLFDOO\LGHQWLILHGPRGHVLQYROYHGRPLQDQWPRWLRQLQWKHPDLQWUDQVYHUVH16 DQGORQJLWXGLQDO(:GLUHFWLRQRIWKHFDWKHGUDO

• 7KHRXWGRRUDQGLQGRRUWHPSHUDWXUHWXUQHGRXWWREHDGRPLQDQWGULYHURIWKHYDULDWLRQV REVHUYHG LQ WKH IOXFWXDWLRQ RI WKH UHVRQDQW IUHTXHQFLHV RI DOO PRGHV 7KH UHODWLYH KXPLGLW\VHHPVWRVOLJKWO\DIIHFWRQO\WKHIUHTXHQF\RIWKHILUVWPRGH>@

• 7KHIUHTXHQF\WHPSHUDWXUHFRUUHODWLRQVUHYHDODGLVWLQFWLYHWUHQGZKLFKLVYHU\GLIIHUHQW IURP ZKDW UHSRUWHG LQ DOPRVW DOO ORQJWHUPVWXGLHV RQ KLVWRULFPDVRQU\ VWUXFWXUHV 7KH QDWXUDOIUHTXHQFLHVRIWKHFDWKHGUDOH[KLELWDQHJDWLYHGHSHQGHQFHRQLQGRRUDQGRXWGRRU WHPSHUDWXUH LQ WKH FROG VHDVRQ ZKHUHDV WKH FRUUHODWLRQ EHFRPHV SRVLWLYH LQ WKH KRW VHDVRQIRUWKH16PRGHVRQO\

• 7KHFRPSOH[GHSHQGHQFHRIQDWXUDOIUHTXHQFLHVRQWHPSHUDWXUH REVHUYHG LQ WKH 0LODQ &DWKHGUDO FRQFHLYDEO\ UHVXOWV IURP WZR WHPSHUDWXUHGULYHQ RSSRQHQW HIIHFWV WKH VWLIIHQLQJH[HUWHGGXULQJWKHFROGVHDVRQE\WKHLQFUHDVHGWHQVLOHIRUFHVLQWKHPHWDOOLF WLHURGV DQG WKH XVXDO WKHUPDO H[SDQVLRQ RI WKH PDVRQU\ PDWHULDOV 7KH IRUPHU HIIHFW WXUQVRXWWREHGRPLQDQWLQWKHFROGVHDVRQIRUDOOPRGHVZKHUHDVWKHODWWHUWHQGVWRUXOH WKHIUHTXHQF\YDULDWLRQRI16PRGHVLQWKHKRWVHDVRQ

• 3&$EDVHG UHJUHVVLRQ PRGHOV DUH VXLWDEOH WR UHPRYH WKH HQYLURQPHQWDO HIIHFWV IURP QDWXUDOIUHTXHQFLHV • 7KHPRGHVKDSHVRIWKHFDWKHGUDODQGWKHFRUUHVSRQGLQJPRGHFRPSOH[LW\HYDOXDWHGYLD 03&GRQRWH[KLELWDSSUHFLDEOHIOXFWXDWLRQVDVVRFLDWHGZLWKWKHHQYLURQPHQWDOHIIHFWV VRWKDWDQDSSURSULDWHVWUDWHJ\RI6+0VKRXOGEHEDVHGDOVRRQWKHWLPHLQYDULDQFHRI PRGDOGHIRUPDWLRQV $&.12:/('*(0(176

7KHVXSSRUWRIVeneranda Fabbrica del Duomo di MilanoDQGWKHSUHFLRXVFRRSHUDWLRQRI )UDQFHVFR&DQDOLLVJUDWHIXOO\DFNQRZOHGJHG7KHDXWKRUVZRXOGOLNHWRWKDQNWKHWHFKQLFDO VWDIIRI$*,6&2DQGVeneranda Fabbrica del Duomo di MilanoIRUPRXQWLQJDOOPRQLWRULQJ GHYLFHVDQGWKHWHFKQLFDOVWDIIRI6$5$(OHFWURQLFV,QVWUXPHQWVIRUWKHDVVLVWDQFHGXULQJWKH LQVWDOODWLRQDQGWKHLQLWLDORSHUDWLRQDOVHWWLQJRIWKHVHLVPRPHWHUV 5()(5(1&(6 >@ $QQDOLGHOOD)DEEULFDGHO'XRPRGL0LODQR'DOO¶RULJLQHILQRDOSUHVHQWHLQ,WDOLDQ 9HQHUDQGD)DEEULFDGHO'XRPRGL0LODQR >@ &)HUUDULGD3DVVDQR6WRULDGHOOD9HQHUDQGD)DEEULFDLQ,WDOLDQ&DVVDGL5LVSDUPLR GHOOH3URYLQFH/RPEDUGH >@ &*HQWLOH&3RJJL$5XFFROR09DVLF9LEUDWLRQEDVHGDVVHVVPHQWRIWKHWHQVLOH IRUFH LQ WKH WLHURGV RI WKH 0LODQ &DWKHGUDO International Journal of Architectural Heritage

>@ & *HQWLOH $ 5XFFROR ) &DQDOL /RQJWHUP PRQLWRULQJ IRU WKH FRQGLWLRQEDVHG VWUXFWXUDO PDLQWHQDQFH RI WKH 0LODQ &DWKHGUDO Construction and Building Materials 

>@ + 6RKQ (IIHFWV RI HQYLURQPHQWDO DQG RSHUDWLRQDO YDULDELOLW\ RQ VWUXFWXUDO KHDOWK PRQLWRULQJPhilosophical Transactions of the Royal Society A >@ /) 5DPRV / 0DUTXHV 3% /RXUHQoR * 'H 5RHFN $ &DPSRV&RVWD - 5RTXH

0RQLWRULQJ KLVWRULFDO PDVRQU\ VWUXFWXUHV ZLWK RSHUDWLRQDO PRGDO DQDO\VLV WZR FDVH VWXGLHVMechanical Systems and Signal Processing

>@ $6DLVL&*HQWLOH0*XLGREDOGL3RVWHDUWKTXDNHFRQWLQXRXVG\QDPLFPRQLWRULQJRI WKH*DEELD7RZHULQ0DQWXD,WDO\Construction and Building Materials 

>@ 0* 0DVFLRWWD -&$ 5RTXH /) 5DPRV 3% /RXUHQoR $ PXOWLGLVFLSOLQDU\ DSSURDFKWRDVVHVVWKHKHDOWKVWDWHRIKHULWDJHVWUXFWXUHVWKHFDVHVWXG\RIWKH&KXUFKRI 0RQDVWHU\RI-HUyQLPRVLQ/LVERQConstruction and Building Materials 

>@ $(O\DPDQL2&DVHOOHV35RFD-&ODSHV'\QDPLFLQYHVWLJDWLRQRIDODUJHKLVWRULFDO FDWKHGUDO6WUXFWXUDO&RQWURODQG+HDOWK0RQLWRULQJH

>@ 50$]]DUD*'H5RHFN0*LUDUGL&3DGRYDQL'3HOOHJULQL(5H\QGHUV7KH

LQIOXHQFHRIHQYLURQPHQWDOSDUDPHWHUVRQWKHG\QDPLFEHKDYLRXURIWKH6DQ)UHGLDQR EHOOWRZHULQ/XFFDEngineering Structures

>@ $.LWD1&DYDODJOL)8EHUWLQL7HPSHUDWXUHHIIHFWVRQVWDWLFDQGG\QDPLFEHKDYLRU RI &RQVROL 3DODFH LQ *XEELR ,WDO\ Mechanical Systems and Signal Processing  

>@ 1 $VWH 56 $GKLNDUL 0 %X]]HWWL 6 'HOOD 7RUUH & 'HO 3HUR +( +XHUWR &) /HRQIRUWH 0LFURFOLPDWLF PRQLWRULQJ RI WKH 'XRPR 0LODQ &DWKHGUDO ULVNVEDVHG DQDO\VLV IRU WKH FRQVHUYDWLRQ RI LWV FXOWXUDO KHULWDJH %XLOGLQJ (QYLURQPHQW    >@ 563DSSD.%(OOLRWW$6FKHQN$&RQVLVWHQWPRGHLQGLFDWRUIRUWKHHLJHQV\VWHP UHDOL]DWLRQDOJRULWKP1$6$7HFKQLFDO0HPRUDQGXP >@ >@:+H\OHQ6/DPPHQV36DV0RGDO$QDO\VLV7KHRU\DQG7HVWLQJ.8/HXYHQ %HOJLXP >@ %3HHWHUV*'H5RHFN5HIHUHQFHEDVHGVWRFKDVWLFVXEVSDFHLGHQWLILFDWLRQIRURXWSXW RQO\PRGDODQDO\VLVMechanical Systems and Signal Processing >@ $ &DEERL ) 0DJDOKmHV & *HQWLOH ¬ &XQKD $XWRPDWHG PRGDO LGHQWLILFDWLRQ DQG

WUDFNLQJDSSOLFDWLRQWRDQLURQDUFKEULGJHStructural Control Health Monitoring H

>@ 5- $OOHPDQJ '/ %URZQ $ FRUUHODWLRQ FRHIILFLHQW IRU PRGDO YHFWRU DQDO\VLV Proceedings of the 1st International Modal Analysis Conference (IMAC-I)

>@ 66KDUPD$SSOLHG0XOWLYDULDWH7HFKQLTXHV-RKQ:LOH\ 6RQV

>@ 3HHWHUV%'H5RHFN*2QH\HDUPRQLWRULQJRIWKH=±%ULGJHHQYLURQPHQWDOHIIHFWV YHUVXV JDPDJH HYHQWV (DUWKTXDNH (QJLQHHULQJ  6WUXFWXUDO '\QDPLFV   

>@ + +RWWHOLQJ 0XOWLYDULDWH TXDOLW\ FRQWURO LOOXVWUDWHG E\ WKH DLU WHVWLQJ RI VDPSOH ERPEVLJKWV7HFKQLTXHVRI6WDWLVWLFDO$QDO\VLV

>@ $ &DEERL & *HQWLOH $ 6DLVL 9LEUDWLRQEDVHG 6+0 RI D FHQWHQDU\ EULGJH D FRPSDUDWLYHVWXG\EHWZHHQWZRGLIIHUHQWDXWRPDWHG20$WHFKQLTXHVProceedings of the 9th International Conference on Structural Dynamics