Ci a ion: Cha es, E.; Ba on ini, A.;
Mendes, N.; Compán, V.; Lou enço,
P.B. Me hodologies and Challenges
o Op imal Senso Placemen in
His o ical Mason y Buildings.
Senso s 2023,23, 9304. h ps://
doi.o g/10.3390/s23239304
Academic Edi o s: F ancesc Pozo,
Mohammad N Noo i, S e en
Cha e on and Jose Al onso
An onino-Da iu
Recei ed: 19 Oc obe 2023
Re ised: 15 No embe 2023
Accep ed: 17 No embe 2023
Published: 21 No embe 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
senso s
A icle
Me hodologies and Challenges o Op imal Senso Placemen
in His o ical Mason y Buildings
Es e anía Cha es 1,*, Albe o Ba on ini 1, Nuno Mendes 1, Víc o Compán2and Paulo B. Lou enço 1
1Depa men o Ci il Enginee ing, ISISE, ARISE, Uni e si y o Minho, 4800-058 Guima ães, Po ugal;
[email p o ec ed] (A.B.); [email p o ec ed] (N.M.); [email p o ec ed] (P.B.L.)
2
Depa men o Building S uc u es and Geo echnical Enginee ing, Uni e si y o Se ille, 41012 Se ille, Spain;
[email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac :
As ageing s uc u es and in as uc u es become a global conce n, s uc u al heal h moni-
o ing (SHM) is seen as a c ucial ool o hei cos -e ec i e main enance. P omising esul s ob ained
o mode n and con en ional cons uc ions sugges ed he applica ion o SHM o his o ical mason y
buildings as well. Howe e , his p esen s peculia sho comings and open challenges. One o he
mos ele an aspec s ha dese e mo e esea ch is he op imisa ion o he senso placemen o ackle
well-known issues in ambien ib a ion es ing o such buildings. The p esen pape ocuses on he
applica ion o op imal senso placemen (OSP) s a egies o dynamic iden i ica ion in his o ical ma-
son y buildings. While OSP echniques ha e been ex ensi ely s udied in a ious s uc u al con ex s,
hei applica ion in his o ical mason y buildings emains ela i ely limi ed. This pape discusses he
challenges and oppo uni ies o OSP in his speci ic con ex , analysing and discussing eal-wo ld
examples, as well as a nume ical benchma k applica ion o illus a e i s complexi ies. This a icle
aims o shed ligh on he p og ess and issues associa ed wi h OSP in mason y his o ical buildings,
p o iding a de ailed p oblem o mula ion, iden i ying ongoing challenges and p esen ing p omising
solu ions o u u e imp o emen s.
Keywo ds:
op imal senso placemen ; dynamic iden i ica ion; s uc u al heal h moni o ing; he i age
buildings; his o ical mason y
1. In oduc ion
In ecen decades, he e has been a g owing ocus on and in es men in ools and
s a egies o moni o ing s uc u al beha iou . This inc eased in e es , especially in de el-
oped coun ies, s ems om a signi ican numbe o c i ical acili ies, in as uc u es and
buildings being close o o beyond he end o hei design li e. As hei eplacemen is im-
p ac ical and una o dable, s akeholde s inc easingly u n o s uc u al heal h moni o ing
(SHM) solu ions o in o m main enance and es o a ion ac i i ies, op imising ime and
esou ce alloca ion. SHM a ose as a ield o esea ch whose aim is o de elop and alida e
me hodologies and ools ha p o ide in o ma ion abou he s uc u e and i s beha iou
o e ime. SHM me hods mainly ocus on he p omp au oma ed de ec ion o damage,
os e ing in e en ions in he ea lies s age possible and in he mos e ec i e way. This
aims o a oid mode a e and se e e damage o e en sudden ailu es and ensu e p ope
ope a ion and conse a ion o buildings [1–3].
The p omising esul s ob ained in he ields o mechanical, ae ospace and ci il en-
ginee ing ega ding mode n s uc u es sugges ed he applica ion o SHM s a egies o
his o ical cons uc ions as well [
4
]. Indeed, he i age buildings no only ha e a ele an
economic alue bu also a signi ican social one due o hei meaning o cul u al oo s,
belie sys ems and indi idual iden i ies [
5
]. Thei conse a ion is, he e o e, undamen al,
bu is commonly mo e challenging han o o he ypes o ci il s uc u es due o hei
Senso s 2023,23, 9304. h ps://doi.o g/10.3390/s23239304 h ps://www.mdpi.com/jou nal/senso s
Senso s 2023,23, 9304 2 o 23
complexi y in e ms o geome y, ma e ials and e olu ion o e ime. In pa icula , se e al
unce ain ies a ise due o he lack o knowledge o he cons uc ion echniques employed,
pas in e en ions o haza dous e en s ha hey may ha e su e ed [6].
Cu en ly, pu chasing and main aining he equi ed so wa e and ha dwa e com-
ponen s, including ins umen a ion, licenses, s o age pla o ms and p ocessing sys ems,
equi e a signi ican in es men . Fo hese easons, he de elopmen o a cos -e ec i e SHM
sys em is pa amoun . Wi h his pu pose, op imal senso placemen (OSP) eme ges as a
me hodology ha s udies he op imisa ion o he senso ne wo k, namely, he minimisa ion
o he numbe o senso s used and he de e mina ion o hei op imal loca ions, wi hou
comp omising he e ec i eness o he sys em. Mo e speci ically, he OSP is composed
o eigh main s eps, as desc ibed in he amewo k de eloped by Os achowicz e al. [
7
]:
(1) de ini ion o he demands, (2) choice o senso ype, (3) de ini ion o he ope a ional
pa ame e s, (4) de e mina ion o he objec i e unc ion, (5) choice o he OSP echnique,
(6) de ini ion o he inpu s, (7) OSP esolu ion and (8) deploymen .
S eps 1 o 6 consis o he de ini ion o all he main aspec s o se he speci ic p oblem
ins ance and he OSP algo i hm ins ance, whe eas in he las wo s eps, namely, 7 and 8,
he OSP is ca ied ou and he ne wo k is deployed o e he in es iga ed sys em. Mo e in
de ail, he de ini ion o he scope o he moni o ing (s ep 1) and he ope a ional pa ame e s
(s ep 3), as well as he selec ion o he ype o senso s (s ep 2), a e essen ial o iden i y
he expec ed use o he moni o ing sys em, including he moni o ing goals [
8
] and he
inal se up o he quali a i e and quan i a i e p oblem-speci ic equi emen s. These can be
ela ed o he moni o ed sys em and i s condi ions, he budge a ailable, he cha ac e is ics
o he expec ed scena ios in case o damage de ec ion, and he moni o ing sys em and
i s componen s [
7
–
9
]. I is wo h no ing ha poin s 2 and 3 a e s ongly in e connec ed,
as he senso ype should be selec ed based no only on he demands bu also on he
ope a ional pa ame e s and, a he same ime, he used senso s in luence he de ini ion
o he ope a ional pa ame e s, which depend on he sensing ne wo k and i s ins alla ion.
In he ield o OSP, mos o he a en ion has been ocused on ib a ion moni o ing and
dynamic iden i ica ion [
7
]. Indeed, ib a ion moni o ing h ough accele ome e s o , mo e
a ely, elocime e s, is a well-known global echnique ha is commonly adop ed o
s uc u al iden i ica ion and SHM, e en in he ield o his o ical buildings, since his
echnique p o ides gene al in o ma ion abou he sys em beha iou wi hou causing any
damage o i [1].
Se e al examples in he li e a u e demons a ed he applica ion o OSP echniques o
he loca ion o accele ome e s in eal s uc u es, as in [
10
,
11
] o [
12
]. Howe e , he use o
hese me hodologies in his o ical buildings emains ela i ely limi ed. E en hough he e
exis some e iew s udies ha analysed di e en OSP app oaches, ypes o moni o ing,
me ics and op imisa ion algo i hms [
7
,
13
,
14
], hey mos ly ocused on ci il s uc u es
and in as uc u e. A ca e ul analysis o he sho comings ha a ise when es ablished
me hods o con en ional sys ems a e applied o his o ical ones is missing. To his end,
he p esen wo k aimed a b idging his gap, analysing he exis ing applica ions o OSP o
his o ical buildings, o mo e speci ically, OSP me hods used o op imise he placemen o
ansduce s ha a e deployed in con ac wi h he s uc u e o dynamic iden i ica ion, such
as accele ome e s, elocime e s o displacemen ansduce s o ou pu -only acquisi ions.
The me hods discussed in he manusc ip we e o iginally de eloped o op imally place
wi ed senso s; howe e , he same me hods can be used o wi eless senso s as long as
addi ional equi emen s unique o his ype o senso a e aken in o conside a ion.
The aim was o iden i y success ul adap a ions o he buil he i age o hese echniques
bo n in he con ex o mechanical, ae ospace and mode n ci il enginee ing asse s and o
highligh he limi a ions me , poin ing ou p og ess made and open challenges, as well
as iden i ying p omising u u e ends o he de elopmen o success ul enhanced and
ailo -made s a egies.
Se e al ypes o his o ical s uc u es made o di e en ma e ials and cons uc ion
echniques exis . Some o hem ha e been he subjec o OSP. To ensu e a clea analysis and
Senso s 2023,23, 9304 3 o 23
syn hesis o he esul s, he p esen wo k speci ically ocused on he applica ion o OSP o
his o ical buildings made o mason y, hus excluding applica ions o buil he i age made
o o he ma e ials, like imbe [
15
,
16
] o conc e e [
17
], and in as uc u es such as me allic
b idges [
18
], mason y b idges [
19
] and aqueduc s [
20
]. Mo eo e , he scope o he OSP
applica ions he e in es iga ed was limi ed o he de e mina ion o he op imal accele ome e
placemen o dynamic iden i ica ion and, in a ew cases, damage iden i ica ion, wi h his
being he objec i e o all he analysed s udies.
The emainde o he pape is o ganised as ollows. Sec ion 2de ails he de ini ion
and o mula ion o he OSP p oblem. I s applica ion o mason y his o ical buildings is
discussed in Sec ion 3based on he a ailable li e a u e, and a simple nume ical case s udy
is p esen ed in Sec ion 4 o be e cla i y he challenges. The main open issues a e p esen ed
and analysed in Sec ion 5 o p opose p omising s a egies o u u e imp o emen s. Finally,
in Sec ion 6, he main conclusions a e d awn and u u e scopes a e ou lined.
2. Op imal Senso Placemen
The OSP can be o mula ed as a nume ical op imisa ion p oblem in which one o mo e
p ope ly de ined objec i e (o cos ) unc ions
obj
a e maximised o minimised depending
on he adop ed me ics. In pa icula , conside ing ha minimising
obj
is equi alen o
maximising − obj [21], wi hou loss o gene ali y, he nume ical op imisa ion p oblem is
min
w∈Ω obj,i(w),(i=1, 2, . . . , M)(1)
subjec ed o:
hj(w)=0, (j=1, 2, . . . , J)
gk(w)≤0, (k=1, 2, . . . , K)
whe e
obj,i(w):D1×. . . ×Dn→R+
is he
i
h objec i e unc ion in he p oblem;
D1×. . . ×Dn
is he sea ch space gi en by he a iable domain
Ω⊆Rn
, namely, he egion
o easible solu ions in he sea ch space; and
hj(w)
and
gk(w)
a e cons ain unc ions,
namely, bina y e alua ions ega ding speci ic equi emen s ha he solu ion mus sa is y
o be easible. All he unc ions depend on he design ec o
w=(w1,w2, . . . , wn)T∈Ω
whose componen s
wi
a e called design o decision a iables. Such a iables can be con in-
uous, disc e e o a mix u e o bo h. A easible solu ion sis [22]
s=a g
D1×...×Dnmin
w∈Ω obj,i(w),(i=1, 2, . . . , M)(2)
I
M=
1, he p oblem is called a single-objec i e p oblem, whe eas i
M>
1, i is
called a mul i-objec i e p oblem. The bes solu ion o he op imisa ion p oblem is he
a gumen o he op imum o he objec i e unc ion.
In OSP, he e exis u he limi a ions o he op imisa ion amewo k p esen ed abo e.
In pa icula , he only design a iable is he se o loca ions and o ien a ions, namely,
he ins umen ed deg ees o eedom (DOFs), which assume only disc e e alues and
whose selec ion is mu ually exclusi e. This can be seen as a specialised Knapsack p oblem,
namely, a cons ained combina o ial p oblem in which a gi en numbe o senso s
nsens
a e placed in a ew loca ions and o ien a ions among a la ge se o candida es (
ncand
),
hus 1
≤nsens ≤ncand
o a se o gi en objec i es. A solu ion o his p oblem is a
ec o o spa ial nodal coo dina es
d={x1,y1,z1,δ1, . . . , xnsens ,ynsens ,znsens ,δnsens }
, whe e
δi={ui, i,wi}
is he o ien a ion o he
i
h senso and
{xi,yi,zi}
co esponds o i s
loca ion in he e e ence sys em o he geome ical space. A simple de ini ion is achie ed
by eso ing o a disc e isa ion o he in es iga ed sys em and he enume a ion o he
candida e DOFs: d={d1,δ1, . . . , dnsens ,δnsens }∈D.
Senso s 2023,23, 9304 4 o 23
The dimension o
D
, namely, he domain o he solu ions, o a gi en numbe o
senso s nsens and candida e loca ions ncand is
|D|=ncand!
nsens!(ncand −nsens)!(3)
In he li e a u e, di e en c i e ia a e commonly used o o mula e he objec i e
unc ion and/o assess he sui abili y o he placemen a pos e io i [
23
]. To his end, he
no ewo hy wo k o Kamme [
24
] has been pa amoun , as i cen ed he ocus on he
o mula ion o objec i e unc ions, which ensu es no only hei obse abili y bu also hei
absolu e iden i iabili y, which is an essen ial equi emen o co ec dynamic iden i ica ion.
This has led o a p oli e a ion o me hods based on he Fishe in o ma ion ma ix (FIM),
modal assu ance c i e ion (MAC), singula - alue decomposi ion a io (SVD ), modal kine ic
o s ain ene gy (MKE and SE) o in o ma ion- heo y- ela ed me ics [
25
–
28
]. These me ics
a e mainly based on he mode shape ma ix pa i ioned a he candida e senso loca ions
and a p e-de ined se o a ge modes. In any case, i is wo h no ing ha he objec i e
unc ion is no known analy ically and, consequen ly, he OSP is a black box op imisa ion
p oblem. Mo eo e , he objec i e unc ion is likely non-con ex, p esen ing many local
op ima. The e o e, he objec i e unc ion alue a a speci ic poin can be calcula ed only
by unning a simula ion, and he adi ional app oach o OSP equi es he exis ence o a
p elimina y nume ical model, which is commonly a simpli ied ini e elemen model (FEM),
o he in es iga ed sys em.
Add essing black box op imisa ion s ongly limi s he iable op imisa ion s a egies [
29
].
These a e mos ly sub-op imal and, depending on hei o mula ion, can be subdi ided
in o de e minis ic o s ochas ic [
7
]. De e minis ic me hodologies ea he design a iables
as de e minis ic inpu s. A wide ange o me hods ha e been de eloped o speci ically
add ess he op imisa ion o gi en me ics, le e aging ad hoc, non-gene alisable s a egies.
These me hods a e he so-called heu is ics, namely, a class o sequen ial senso placemen
(SSP) algo i hms, which i e a i ely add o o ejec candida es om a p ede ined loca ion
se un il inding he op imal solu ion [
30
]. Besides hese me hods, well-es ablished ech-
niques o ackle black-box op imisa ion, namely, he so-called me aheu is ic algo i hms,
ha e been success ully applied o OSP. These a e also sub-op imal me hods bu a e no
cons ained by a speci ic o mula ion o he objec i e unc ion, and hus, hey allow o
op imising mo e complex objec i e unc ions and conside some p oblem ins ances ha a e
di icul o include in a heu is ic p ocess, such as mul i-objec i e op imisa ion p oblems [
7
].
Mul i-objec i e op imisa ion o e s a powe ul app oach o simul aneously de e mining
he op imal placemen o senso s unde mul iple po en ially con lic ing goals, such as max-
imising co e age, minimising edundancy and con olling cos s. Me hods ha a e easible
o mul i-objec i e op imisa ion p oduce a se o al e na i e solu ions known as a Pa e o
on . Thei comp ehensi e explo a ion o he solu ion domain, coupled wi h sensi i i y
analysis capabili ies, p o ides a pi o al unde s anding o how di e en pa ame e s and
objec i es in luence op imal senso con igu a ions.
On he o he hand, s ochas ic me hodologies ha e been de eloped o ea he nu-
me ical pa ame e s as andom, conside ing he limi ed ep esen abili y o he p elimina y
model adop ed due o simpli ica ions and limi ed knowledge o he physical and me-
chanical p ope ies o he in es iga ed s uc u e. These me hodologies may employ he
a o emen ioned sub-op imal echniques wi hin a p obabilis ic amewo k ha epea s he
op imisa ion upon sampling he alues o he andom a iables om p ede ined dis i-
bu ions, ensu ing an unce ain y analysis in he op imisa ion p oblem [
7
]. Ins ead, no el
s ochas ic app oaches a e based on a o mula ion o OSP in he gene al amewo k o
expe imen al design using a Bayesian app oach [
31
], in which he goal is he maximisa ion
o he alue o he da a collec ed h ough moni o ing and he op imisa ion o ime and cos
equi emen s [
32
]. Finally, he necessi y o dealing wi h se e al sou ces o unce ain ies
ha a ec no only he model bu also he expe imen al s age o moni o ing has ecen ly
led o no el app oaches ha ci cum en he issues in he p elimina y model by elying on
Senso s 2023,23, 9304 5 o 23
a da a-d i en op imisa ion. Such app oaches iden i y he bes placemen o he senso s
among a la ge numbe o ins umen ed DOFs, eso ing o p elimina y moni o ing, hus
conside ing eal ieldwo k signals [33,34].
3. OSP Applica ions o His o ical Mason y Buildings
In he p esen sec ion, a comp ehensi e analysis o he OSP applica ions o his o ical
mason y buildings iden i ied in he li e a u e is p o ided, highligh ing and compa ing he
main ea u es o he op imisa ion p ocess. The in es iga ed case s udies (Figu e 1) comp ise
six eligious buildings and wo ci il cons uc ions, namely, he San a Ma ia chu ch in Via in
Came ino, I aly [
35
]; he Collegia a o San a Ma ia in Visso, I aly [
36
]; he bell owe o San a
Ma ia and San Gio enale Ca hed al in Fossano, I aly [
37
]; he clois e o he monas e y o
San Je ónimo de Buena is a in Se ille, Spain [
38
]; he clois e o he monas e y o San a
Ma ia in Salzedas, Po ugal [
39
]; he Ca hed al o Sain John he Di ine in New Yo k [
40
];
he Slo s jell owe in Tønsbe g, No way [
19
]; and a p o o ype o Venice palace inspi ed
by Ca’ Lo edan in Venice, I aly [
41
]. No ably, excep o he monas e y o San a Ma ia in
Salzedas, all he case s udies employed a model-based OSP app oach. Fou cases op imised
he placemen o he comple e building [
19
,
35
,
36
,
41
], whe eas ou ocused on single
po ions, such as he bell owe [37], he clois e s [38,39] o a bay [40].
Senso s 2023, 23, x FOR PEER REVIEW 5 o 24
a da a-d i en op imisa ion. Such app oaches iden i y he bes placemen o he senso s
among a la ge numbe o ins umen ed DOFs, eso ing o p elimina y moni o ing, hus
conside ing eal ieldwo k signals [33,34].
3. OSP Applica ions o His o ical Mason y Buildings
In he p esen sec ion, a comp ehensi e analysis o he OSP applica ions o his o ical
mason y buildings iden i ied in he li e a u e is p o ided, highligh ing and compa ing
he main ea u es o he op imisa ion p ocess. The in es iga ed case s udies (Figu e 1)
comp ise six eligious buildings and wo ci il cons uc ions, namely, he San a Ma ia
chu ch in Via in Came ino, I aly [35]; he Collegia a o San a Ma ia in Visso, I aly [36]; he
bell owe o San a Ma ia and San Gio enale Ca hed al in Fossano, I aly [37]; he clois e
o he monas e y o San Je ónimo de Buena is a in Se ille, Spain [38]; he clois e o he
monas e y o San a Ma ia in Salzedas, Po ugal [39]; he Ca hed al o Sain John he Di ine
in New Yo k [40]; he Slo s jell owe in Tønsbe g, No way [19]; and a p o o ype o Venice
palace inspi ed by Ca’ Lo edan in Venice, I aly [41]. No ably, excep o he monas e y o
San a Ma ia in Salzedas, all he case s udies employed a model-based OSP app oach. Fou
cases op imised he placemen o he comple e building [19,35,36,41], whe eas ou o-
cused on single po ions, such as he bell owe [37], he clois e s [38,39] o a bay [40].
Figu e 1. Loca ion o he Eu opean case s udies.
The objec i e o he op imisa ion p ocess a ies o diffe en case s udies, conside ing
he ype o building, le el o damage (e.g., he Collegia a o Visso and San a Ma ia in
Came ino we e signi ican ly damaged by he Cen al I aly 2016 seismic sequence), p e i-
ous in e en ions and main enance ac i i ies (e.g., he ex ensi e s eng hening a he
Salzedas monas e y), he ype o senso s ( iaxial o uniaxial accele ome e s), among o he
pa ame e s. Howe e , in gene al, he op imisa ion applied o he case s udies aimed o
efficien ly design he senso layou o ensu e a co ec modal iden i ica ion wi h a educed
numbe o senso s and, consequen ly, imp o ed cos effec i eness. The inal senso s we e
na u al candida es o long- e m moni o ing, hus allowing o he de ec ion o a damage
ou b eak. To his end, i is wo h no ing ha he OSP a he Fossano bell owe explici ly
included damage iden i ica ion by op imising he senso placemen in undamaged and
expec ed damaged scena ios.
Rega ding he selec ion o he candida es, he numbe and loca ions a y depending
on he chosen app oach. In he only da a-d i en applica ion (i.e., he Salzedas monas e y),
he candida es co esponded o he moni o ed DOFs, which we e a o al o o y acqui ed
Figu e 1. Loca ion o he Eu opean case s udies.
The objec i e o he op imisa ion p ocess a ies o di e en case s udies, conside ing
he ype o building, le el o damage (e.g., he Collegia a o Visso and San a Ma ia in
Came ino we e signi ican ly damaged by he Cen al I aly 2016 seismic sequence), p e ious
in e en ions and main enance ac i i ies (e.g., he ex ensi e s eng hening a he Salzedas
monas e y), he ype o senso s ( iaxial o uniaxial accele ome e s), among o he pa ame-
e s. Howe e , in gene al, he op imisa ion applied o he case s udies aimed o e icien ly
design he senso layou o ensu e a co ec modal iden i ica ion wi h a educed numbe
o senso s and, consequen ly, imp o ed cos e ec i eness. The inal senso s we e na u al
candida es o long- e m moni o ing, hus allowing o he de ec ion o a damage ou b eak.
To his end, i is wo h no ing ha he OSP a he Fossano bell owe explici ly included
damage iden i ica ion by op imising he senso placemen in undamaged and expec ed
damaged scena ios.
Rega ding he selec ion o he candida es, he numbe and loca ions a y depending
on he chosen app oach. In he only da a-d i en applica ion (i.e., he Salzedas monas e y),
he candida es co esponded o he moni o ed DOFs, which we e a o al o o y acqui ed

Senso s 2023,23, 9304 6 o 23
DOFs e enly dis ibu ed o e hi y- wo poin s. In he case o he San Je ónimo monas e y
in Spain, an FEM was calib a ed based on a p elimina y acquisi ion and i was used o
he OSP by conside ing he same candida e poin s as he dynamic campaign, namely,
hi y- wo poin s in h ee di ec ions, summing up o nine y-six candida e DOFs.
Fo he o he cases, he numbe o candida es is usually highe (Figu e 2), as hey
a e selec ed om he FEM i sel . A common s a egy o limi he candida es is based on
he accessibili y o he a eas. Fo example, conside ing he applica ion in he Came ino
chu ch, a andom sampling app oach was used o selec candida e DOFs exclusi ely om
he ex e nal su ace. The ini ial se comp ised o e 250,000 DOFs, which we e la e e ined
o 25,000 h ough andom sampling. This educ ion se ed o educe he compu a ional
bu den while ensu ing a ep esen a i e subse o analysis. This app oach was also applied
o he Ca hed al o Sain John, ob aining a o al o 781 candida e posi ions om he comple e
se o accessible nodes o he FEM. The o he applica ions ollowed a simila end, selec ing
he candida es among he accessible DOFs o he FEM bu limi ing he numbe by manually
excluding he a eas wi h lowe in e es , o he e ical di ec ion when e ical componen s
o he mode shapes we e deemed unin luen ial o no a ge ed.
Senso s 2023, 23, x FOR PEER REVIEW 6 o 24
DOFs e enly dis ibu ed o e hi y- wo poin s. In he case o he San Je ónimo monas e y
in Spain, an FEM was calib a ed based on a p elimina y acquisi ion and i was used o
he OSP by conside ing he same candida e poin s as he dynamic campaign, namely,
hi y- wo poin s in h ee di ec ions, summing up o nine y-six candida e DOFs.
Fo he o he cases, he numbe o candida es is usually highe (Figu e 2), as hey a e
selec ed om he FEM i sel . A common s a egy o limi he candida es is based on he
accessibili y o he a eas. Fo example, conside ing he applica ion in he Came ino
chu ch, a andom sampling app oach was used o selec candida e DOFs exclusi ely om
he ex e nal su ace. The ini ial se comp ised o e 250,000 DOFs, which we e la e e ined
o 25,000 h ough andom sampling. This educ ion se ed o educe he compu a ional
bu den while ensu ing a ep esen a i e subse o analysis. This app oach was also ap-
plied o he Ca hed al o Sain John, ob aining a o al o 781 candida e posi ions om he
comple e se o accessible nodes o he FEM. The o he applica ions ollowed a simila
end, selec ing he candida es among he accessible DOFs o he FEM bu limi ing he
numbe by manually excluding he a eas wi h lowe in e es , o he e ical di ec ion
when e ical componen s o he mode shapes we e deemed unin luen ial o no a ge ed.
Figu e 2. Numbe o candida e loca ions pe di ec ion o each case. Loga i hmic scale. In Sain John
Ca hed al, he esul an o he h ee di ec ions was used. No a ailable in o ma ion o he Slo s jell
owe .
Ano he impo an inpu o he op imisa ion is he numbe o a ge modes. I is
in e es ing o no e ha mos applica ions se his o i e (Figu e 3). In mos cases, all o
hem ep esen ed global modes o he in es iga ed building (i.e., he chu ch o San a Ma-
ia in Came ino and he Slo s jell owe ) o in es iga ed building po ions (i.e., he San
Je ónimo monas e y). The global modes o he chu ch o San a Ma ia in Came ino we e
wo longi udinal, one ans e sal and wo o sional. Fo he Slo s jell owe , he i s and
he second modes we e i s bending, he hi d mode was o sional, and he ou h and
i h modes we e second bending. A he Salzedas monas e y, he p esence o wo local
e ical modes o he slab o he in es iga ed galle y o he clois e was add essed by ca -
ying ou one op imisa ion by conside ing he i e iden i ied modes, and ano he one con-
side ing jus he h ee global modes, namely, wo ans e sal, single and double bending
modes, and a longi udinal mode. The op imisa ion conduc ed o he Vene ian palace in-
cluded one local mode o he in e nal cou ya d wi hin he i e a ge ed. He e, he global
modes we e one longi udinal, one ans e sal, one o sional and a highe mo e complex
global mode. In he Ca hed al o Sain John, only he global modes (nine ou o he i s
wen y) we e conside ed. Fo he Fossano bell owe , 10 modes we e used o he op imi-
sa ion. In his case, he modes we e local bu in ol ed he comple e in es iga ed
Figu e 2.
Numbe o candida e loca ions pe di ec ion o each case. Loga i hmic scale. In Sain
John Ca hed al, he esul an o he h ee di ec ions was used. No a ailable in o ma ion o he
Slo s jell owe .
Ano he impo an inpu o he op imisa ion is he numbe o a ge modes. I is
in e es ing o no e ha mos applica ions se his o i e (Figu e 3). In mos cases, all
o hem ep esen ed global modes o he in es iga ed building (i.e., he chu ch o San a
Ma ia in Came ino and he Slo s jell owe ) o in es iga ed building po ions (i.e., he San
Je ónimo monas e y). The global modes o he chu ch o San a Ma ia in Came ino we e
wo longi udinal, one ans e sal and wo o sional. Fo he Slo s jell owe , he i s and
he second modes we e i s bending, he hi d mode was o sional, and he ou h and i h
modes we e second bending. A he Salzedas monas e y, he p esence o wo local e ical
modes o he slab o he in es iga ed galle y o he clois e was add essed by ca ying ou
one op imisa ion by conside ing he i e iden i ied modes, and ano he one conside ing
jus he h ee global modes, namely, wo ans e sal, single and double bending modes,
and a longi udinal mode. The op imisa ion conduc ed o he Vene ian palace included
one local mode o he in e nal cou ya d wi hin he i e a ge ed. He e, he global modes
we e one longi udinal, one ans e sal, one o sional and a highe mo e complex global
mode. In he Ca hed al o Sain John, only he global modes (nine ou o he i s wen y)
we e conside ed. Fo he Fossano bell owe , 10 modes we e used o he op imisa ion.
In his case, he modes we e local bu in ol ed he comple e in es iga ed mac oelemen .
Simila ly, a he Collegia a o Visso, he h ee a ge s we e all local modes o he bell owe ,
wo ans e se in each di ec ion and one o sional.
Senso s 2023,23, 9304 7 o 23
Senso s 2023, 23, x FOR PEER REVIEW 7 o 24
mac oelemen . Simila ly, a he Collegia a o Visso, he h ee a ge s we e all local modes
o he bell owe , wo ans e se in each di ec ion and one o sional.
Figu e 3. Numbe o global and local modes used in he op imisa ion in each case s udy.
The algo i hms used o mos o he case s udies we e heu is ics. The Fassano bell
owe was he only excep ion by employing a me aheu is ic algo i hm. Mos o he appli-
ca ions elied on he effec i e independence (E I) me hod as he unique op imisa ion al-
go i hm (i.e., Sain John Ca hed al, San a Ma ia chu ch in Came ino, he Collegia a o
Visso and he Vene ian palace) o in compa ison wi h al e na i e ones. This was he case
o he Slo s jell owe , whe e E I was compa ed wi h he i e a i e Guyan educ ion (IGR),
he no malised modal displacemen (NMD), he no malised kine ic (NKE) me hod and
he off-o -diagonal MAC (offMAC). In he San Je ónimo monas e y, he E I was used and
compa ed wi h he E I weigh ed me hod (E Iwm), he kine ic ene gy and he s ain ene gy
ma ix ank op imisa ion (KEMRO and SEMRO). Finally, o wo cases, E I was no con-
side ed. In he Salzedas monas e y, i e heu is ic me hods we e used: eigen ec o com-
ponen p oduc (ECP), mode shape summa ion plo (MSSP), a e age d i ing poin esi-
due (ADPR), weigh ed a e age d i ing poin esidue (WADPR) and QR decomposi ion
(QRD).
Fo he Fassano bell owe , a me aheu is ic app oach was used, namely, a mul i-ob-
jec i e gene ic algo i hm (MOGA) wi h cos unc ions based on MAC a ia ions, i.e., bo h
he au o-MAC, which compa es he modes o a s uc u e be ween hemsel es, and he
c oss-MAC, which compa es he modes o wo diffe en s uc u es o wo diffe en s uc-
u al con igu a ions o he same s uc u e. In pa icula , he op imisa ion was ca ied ou
by conside ing wo po en ially con lic ing goals upon damage onse : on he one hand,
ensu ing he iden i iabili y o he modes o a gi en condi ion o he owe , and on he
o he hand, ob aining ai ly dis inc mode shapes in diffe en condi ions. The wo com-
bined objec i e unc ions gua an eed ha he senso pa e n emains op imal h oughou
he li e ime o he s uc u e, which is an impo an issue, especially o complex mason y
buildings in high-haza d zones. In his s udy, he mul i-objec i e me hod was compa ed
wi h ano he me aheu is ic echnique, a single objec i e gene ic algo i hm (SOGA), as well
as o he heu is ic me hods: he en opy in o ma ion (EI), ECP and ADPR me hods.
When mo e han one op imisa ion algo i hm is used, a leas one alida ion me ic is
de ined o compa e he esul s om he diffe en me hods. Fo he Salzedas monas e y,
he compa ison was conduc ed in e ms o SVD , he de e minan o he FIM (de FIM) and
he maximum offMAC alue o he au o-MAC ma ix. Mo eo e , he dynamic iden i ica-
ion was ca ied ou again, conside ing only he senso s ecommended by he ou pe o m-
ing me hod, and he esul s we e compa ed wi h he iden i ica ion conduc ed wi h all he
measu emen poin s, alida ing he esul s h ough expe imen al da a.
0
2
4
6
8
10
San Je ónimo
monas e y
Salzedas
monas e y
Sain John
Ca hed al
Came ino
chu ch
Visso
collegia a
Venice
palace
Fossano
bell owe
Global Local
Figu e 3. Numbe o global and local modes used in he op imisa ion in each case s udy.
The algo i hms used o mos o he case s udies we e heu is ics. The Fassano bell
owe was he only excep ion by employing a me aheu is ic algo i hm. Mos o he ap-
plica ions elied on he e ec i e independence (E I) me hod as he unique op imisa ion
algo i hm (i.e., Sain John Ca hed al, San a Ma ia chu ch in Came ino, he Collegia a o
Visso and he Vene ian palace) o in compa ison wi h al e na i e ones. This was he case
o he Slo s jell owe , whe e E I was compa ed wi h he i e a i e Guyan educ ion (IGR),
he no malised modal displacemen (NMD), he no malised kine ic (NKE) me hod and
he o -o -diagonal MAC (o MAC). In he San Je ónimo monas e y, he E I was used and
compa ed wi h he E I weigh ed me hod (E Iwm), he kine ic ene gy and he s ain ene gy
ma ix ank op imisa ion (KEMRO and SEMRO). Finally, o wo cases, E I was no consid-
e ed. In he Salzedas monas e y, i e heu is ic me hods we e used: eigen ec o componen
p oduc (ECP), mode shape summa ion plo (MSSP), a e age d i ing poin esidue (ADPR),
weigh ed a e age d i ing poin esidue (WADPR) and QR decomposi ion (QRD).
Fo he Fassano bell owe , a me aheu is ic app oach was used, namely, a mul i-
objec i e gene ic algo i hm (MOGA) wi h cos unc ions based on MAC a ia ions, i.e.,
bo h he au o-MAC, which compa es he modes o a s uc u e be ween hemsel es, and
he c oss-MAC, which compa es he modes o wo di e en s uc u es o wo di e en
s uc u al con igu a ions o he same s uc u e. In pa icula , he op imisa ion was ca ied
ou by conside ing wo po en ially con lic ing goals upon damage onse : on he one hand,
ensu ing he iden i iabili y o he modes o a gi en condi ion o he owe , and on he o he
hand, ob aining ai ly dis inc mode shapes in di e en condi ions. The wo combined
objec i e unc ions gua an eed ha he senso pa e n emains op imal h oughou he
li e ime o he s uc u e, which is an impo an issue, especially o complex mason y
buildings in high-haza d zones. In his s udy, he mul i-objec i e me hod was compa ed
wi h ano he me aheu is ic echnique, a single objec i e gene ic algo i hm (SOGA), as well
as o he heu is ic me hods: he en opy in o ma ion (EI), ECP and ADPR me hods.
When mo e han one op imisa ion algo i hm is used, a leas one alida ion me ic is
de ined o compa e he esul s om he di e en me hods. Fo he Salzedas monas e y, he
compa ison was conduc ed in e ms o SVD , he de e minan o he FIM (de FIM) and he
maximum o MAC alue o he au o-MAC ma ix. Mo eo e , he dynamic iden i ica ion
was ca ied ou again, conside ing only he senso s ecommended by he ou pe o ming
me hod, and he esul s we e compa ed wi h he iden i ica ion conduc ed wi h all he
measu emen poin s, alida ing he esul s h ough expe imen al da a.
In he case o he San Je ónimo monas e y, he compa ison was ca ied ou in e ms o
equency e o be ween he esul s ob ained om he dynamic iden i ica ion conside ing
he comple e se o candida es and he senso s ob ained in he esul s. This is, indeed, he
only model-based wo k ha alida es he esul s o he op imisa ion p ocess based on
Senso s 2023,23, 9304 8 o 23
expe imen al da a. In he cases o he wo owe s whe e mo e han one me hod was used,
he me ic o he analysis o he inal con igu a ion was he o MAC alue.
In mos o he applica ions, as is common in he adi ional OSP o mula ion, he
numbe o senso s o be placed was p ede e mined, as shown in ligh o ange in Figu e 4.
This was he case o he Slo s jell owe , whe e se en uniaxial senso s we e selec ed. Since
o some algo i hms, he minimum numbe o senso s o place is equal o he numbe
o a ge modes, his is he p e-se alue. This c i e ion was adop ed in he San a Ma ia
chu ch and he monas e y in Salzedas. Fo he Vene ian palace, he minimum numbe
equal o he a ge modes (i.e., i e) was i s used, de ining a se o so-called i al senso s.
Then, con igu a ions wi h an inc easing numbe o senso s, up o en, we e conside ed.
De eloping a obus s a egy o op imise he numbe o senso s is cu en ly an open
challenge. Some au ho s achie ed his by selec ing a ange o he numbe o senso s
and analysing he esul s by means o some pe o mance me ics. This was he case o
he Collegia a o Visso, whe e he senso s a ied be ween h ee and six. The ace and
he de e minan o he FIM, he SVD and he maximum o MAC alue we e used as
pe o mance me ics, and based on hem, he bes numbe o senso s was iden i ied as
ou . Fo he Fassano bell owe , a minimum numbe o ou een was de ined as op imal
wi hou losing pe o mance in e ms o o MAC alues. A he San Je ónimo monas e y,
he minimum numbe o senso s, be ween wo and six een, was de ined based on he
analysis o he e o in e ms o equencies be ween he iden i ica ion using he da a
om he dynamic campaign and he iden i ica ion using jus he esul an senso s o he
op imisa ion. The au ho s concluded ha he e o was s abilised o a numbe o senso s
g ea e han eigh .
Senso s 2023, 23, x FOR PEER REVIEW 9 o 24
Figu e 4. Numbe o senso s selec ed. Da k o ange ep esen s he cases whe e he numbe o senso s
was op imised. Ligh o ange ep esen s he cases whe e he minimum numbe was p e-de ined.
A ele an issue o OSP o he i age buildings is he le el o unce ain ies in ol ed in
he de ini ion o he model. In all cases, excep one (i.e., he Vene ian palace), he FEM
used o he op imisa ion was upda ed based on dynamic iden i ica ion es s o minimise
his issue. In mos cases, piezoelec ic accele ome e s we e used o he iden i ica ion, ex-
cep o he San Je onimo monas e y, whe e o ce balance accele ome e s we e used. Mo e
de ails ega ding he senso s adop ed in hese case s udies a e epo ed in Table 1.
Table 1. Cha ac e is ics o he senso s adop ed o he dynamic iden i ica ion o he in es iga ed
case s udies.
Case Type Axis Model Sensi i i y Accel. * Poin s **
San Je ónimo monas e y Fo ce balance Uni KINEMETRICS ES-U2 10 V/g 8 32
Salzedas monas e y Piezoelec ic Uni PCB 393B12 10 V/g 12 40
Sain John Ca hed al Piezoelec ic Uni PCB 393A03 1 V/g 7 7
Came ino chu ch Piezoelec ic Uni PCB 393B31 10 V/g 16 28
Visso collegia a Piezoelec ic T i - 1 V/g 4 11
Fossano bell owe Piezoelec ic Uni PCB 3701G3FA3G 1 V/g 20 20
* Numbe o accele ome e s used, ** numbe o posi ions measu ed.
In he Vene ian palace, ins ead, he sou ces o unce ain y in he model we e included
in he op imisa ion using an ex ensi e Mon e Ca lo simula ion (MCS), ea ing se e al
unknown ea u es o he model and sampling 200 se s o alues o hem. Con inuous
dis ibu ion was used o he a iables ela ed o he walls, namely, elas ic modulus and
shea modulus wi h a log-no mal p obabili y dis ibu ion unc ion (PDF) and mass den-
si y and hickness wi h a no mal PDF. Disc e e dis ibu ions we e used o he loo p op-
e ies and he connec ion be ween walls, conside ing h ee alues wi h uni o m p obabil-
i y in each case. Then, he op imisa ion was ca ied ou o each sample, and he p elimi-
na y esul s we e discussed wi hou p o iding, a his s age, a s a egy o he de ini ion
o he o e all bes placemen .
A simila s ochas ic app oach was used a he San Je ónimo monas e y, whe e he
MCS conside ed he elas ic modulus o he b ick and he s one mason ies o be s ochas ic
wi h no mal dis ibu ion o gene a e he samples. Fo his case, he de e mina ion o he
op imal numbe o samples was de ined by analysing he dispe sion pe cen age, which
was s abilised o a numbe o samples g ea e han 64. In his case, he p obabili y o
senso selec ion was compu ed o each me hod, ob aining he mos ecu en posi ions.
A simple app oach o include unce ain ies was p esen ed o he Slo s jell owe ,
whe e only wo scena ios we e analysed and compa ed: one whe e he owe was ixed
0
10
20
30
40
50
60
70
80
San Je ónimo
monas e y
Salzedas
monas e y
Sain John
Ca hed al
Came ino
chu ch
Visso
collegia a
Venice palace Fossano
bell owe
Slo s jell
owe
Figu e 4.
Numbe o senso s selec ed. Da k o ange ep esen s he cases whe e he numbe o senso s
was op imised. Ligh o ange ep esen s he cases whe e he minimum numbe was p e-de ined.
In he case o he Ca hed al o Sain John, a iabili y analysis o h ee po en ial me ics
was conduc ed, namely, he loss o in o ma ion measu ed by he de e minan o he FIM,
he MAC and he E I alue. I is impo an o no e ha he loss o in o ma ion me ic is
ela i e and s ic ly depends on he ini ial candida e se ’s cha ac e is ics. The MAC me ic
seems o be mo e sui able when dealing wi h a subs an ial numbe o senso s. As a esul ,
he E I alue is a ou ed, and e en hough he p ima y objec i e o his me hod is no he
de ini ion o he minimum numbe o senso s, his me ic is used o se ing an a bi a y
h eshold o 0.1 o de e mine he numbe o senso s.
As can be seen in Figu e 4, a emp s o de e mine a minimum alue o he numbe
o senso s based on he me ics (cases highligh ed in da k o ange in he g aph) gene a ed
e y di e en esul s. This was likely a ec ed by he p oblem inpu , such as he numbe
and selec ion o a ge modes o he numbe and loca ion o candida e nodes, as well
as he choice o he me ic i sel . Mo eo e , i is po en ially in luenced by he way he
Senso s 2023,23, 9304 9 o 23
adop ed algo i hm explo ed he domain o easible solu ions in he ollowing i e a ions. I
is he e o e essen ial o de ine obus s a egies o sol e his open issue wi hin he OSP.
A ele an issue o OSP o he i age buildings is he le el o unce ain ies in ol ed in
he de ini ion o he model. In all cases, excep one (i.e., he Vene ian palace), he FEM used
o he op imisa ion was upda ed based on dynamic iden i ica ion es s o minimise his
issue. In mos cases, piezoelec ic accele ome e s we e used o he iden i ica ion, excep o
he San Je onimo monas e y, whe e o ce balance accele ome e s we e used. Mo e de ails
ega ding he senso s adop ed in hese case s udies a e epo ed in Table 1.
Table 1.
Cha ac e is ics o he senso s adop ed o he dynamic iden i ica ion o he in es iga ed
case s udies.
Case Type Axis Model Sensi i i y Accel. * Poin s **
San Je ónimo monas e y Fo ce balance Uni KINEMETRICS ES-U2 10 V/g 8 32
Salzedas monas e y Piezoelec ic Uni PCB 393B12 10 V/g 12 40
Sain John Ca hed al Piezoelec ic Uni PCB 393A03 1 V/g 7 7
Came ino chu ch Piezoelec ic Uni PCB 393B31 10 V/g 16 28
Visso collegia a Piezoelec ic T i - 1 V/g 4 11
Fossano bell owe Piezoelec ic Uni PCB 3701G3FA3G 1 V/g 20 20
* Numbe o accele ome e s used, ** numbe o posi ions measu ed.
In he Vene ian palace, ins ead, he sou ces o unce ain y in he model we e included
in he op imisa ion using an ex ensi e Mon e Ca lo simula ion (MCS), ea ing se e al
unknown ea u es o he model and sampling 200 se s o alues o hem. Con inuous
dis ibu ion was used o he a iables ela ed o he walls, namely, elas ic modulus and
shea modulus wi h a log-no mal p obabili y dis ibu ion unc ion (PDF) and mass densi y
and hickness wi h a no mal PDF. Disc e e dis ibu ions we e used o he loo p ope ies
and he connec ion be ween walls, conside ing h ee alues wi h uni o m p obabili y in
each case. Then, he op imisa ion was ca ied ou o each sample, and he p elimina y
esul s we e discussed wi hou p o iding, a his s age, a s a egy o he de ini ion o he
o e all bes placemen .
A simila s ochas ic app oach was used a he San Je ónimo monas e y, whe e he
MCS conside ed he elas ic modulus o he b ick and he s one mason ies o be s ochas ic
wi h no mal dis ibu ion o gene a e he samples. Fo his case, he de e mina ion o he
op imal numbe o samples was de ined by analysing he dispe sion pe cen age, which
was s abilised o a numbe o samples g ea e han 64. In his case, he p obabili y o
senso selec ion was compu ed o each me hod, ob aining he mos ecu en posi ions.
A simple app oach o include unce ain ies was p esen ed o he Slo s jell owe ,
whe e only wo scena ios we e analysed and compa ed: one whe e he owe was ixed o
he soil, and a second one whe e he soil–s uc u e in e ac ion (SSI) was conside ed. Finally,
he OSP applica ion o he Ca hed al o Sain John included he unce ain ies acco ding o
an enhanced e sion o he E I p oposed in [
42
], which conside ed he possible inaccu acies
o he nume ical model by assuming a 5% e o in he model inpu pa ame e s. Thus,
i e new FEMs we e gene a ed wi h a 5% educ ion in he elas ic modulus o one o each
ma e ial ype a he ime (assigned o ibs/a ches, aul webbing, ubble su cha ge, pie s
and walls) o be compa ed agains a e e ence model.
4. OSP in His o ical Mason y Buildings—Insigh om a Simple Nume ical Benchma k
To illus a e he a o emen ioned ou s anding challenges, his sec ion demons a es
he use o wo main OSP echniques on a simple bu e ec i e benchma k, namely, he
nume ical model o a h ee-na e mason y chu ch wi h a pi ched oo , win owe s a he
sides o he açade, a ansep and an apse wi h wo seconda y chapels. The openings we e
asymme ical in bo h he ansep and in he owe s o include mo e complexi y. The o e all
Senso s 2023,23, 9304 16 o 23
Senso s 2023, 23, x FOR PEER REVIEW 16 o 24
(a) (b)
(c) (d)
Figu e 12. OSP esul s o he al e na i e scena ios: (a) SCN01; (b) SCN02; (c) SCN03; (d) SCN04.
The numbe o senso s placed was 15 and he op imisa ion me hod was based on he
offMAC me hod. This app oach was p e e ed since o he E I, he minimum numbe o
senso s canno be less han he numbe o modes, which in hese scena ios, would exceed
15 and be a iable, p e en ing a ai compa ison.
In gene al, he senso s we e loca ed and dis ibu ed h oughou he building wi hou
exhibi ing clus e ing. This could be a ibu ed o he inclusion o a b oade ange o modes
in he op imisa ion and was pa icula ly e iden o he owe s. As he numbe o local
modes o he owe s was balanced by a la ge numbe o modes in ol ing he o he com-
ponen s, hei ole became less ele an , leading o a educ ion in he numbe o senso s
placed he e.
The es o he senso s we e dis ibu ed mainly along he leng h o he building. The
açade con ained one senso in SCN01 and SCN04, bu , as expec ed, i gained impo ance
when i was disconnec ed om he owe s in SCN02, con aining mo e senso s in he inal
placemen . The only case whe e a e ical senso was in oduced was in he scena io ep-
esen ing he so soil and was loca ed in he cen e o one o he a cades. This was likely
due o he way he soil–s uc u e in e ac ion was modelled, allowing o he occu ence o
e ical modal displacemen . Finally, SCN04 inco po a ed wo senso s in a side chapel a
he disconnec ion poin . Due o he poo e in ol emen o he apse in he mode shapes,
no senso s we e placed in his a ea in any o he scena ios.
The au o-MAC was calcula ed o all he esul s (Figu e 13). When compa ing hese
ou comes wi h Figu e 10, he imp o emen in he iden i iabili y o he modes was e iden ,
as hese we e a ge ed in he op imisa ion, esul ing in less indis inguishable couples o
modes.
Figu e 12. OSP esul s o he al e na i e scena ios: (a) SCN01; (b) SCN02; (c) SCN03; (d) SCN04.
Senso s 2023, 23, x FOR PEER REVIEW 17 o 24
(a) (b)
(c) (d)
Figu e 13. Au o-MAC ables conside ing he esul om he offMAC 15-senso 179-node op imisa-
ion o (a) SCN01, (b) SCN02, (c) SCN03 and (d) SCN04. MAC alues ep esen ed by colou scale:
ed ep esen s 1, whi e ep esen s 0.
5. Main Open Issues in OSP o His o ical Mason y Buildings
Upon he comp ehensi e analysis o he li e a u e and he applica ion o he nume -
ical benchma k discussed in he p e ious sec ion, a clea se o ele an open issues and
challenges ha hinde a success ul applica ion o OSP me hodologies o his o ical ma-
son y buildings we e iden i ied and he ea e discussed. Such challenges can be classi ied
acco ding o he h ee main componen s o he OSP s a egy: model- ela ed, expe imen -
ela ed and op imisa ion- ela ed challenges.
Commonly, he OSP p oblem is add essed be o e a de ailed in es iga ion o he
s uc u e, wi h he goal being he iden i ica ion o he bes measu emen poin s o maxim-
ise he in o ma ion quali y and minimise he esou ces needed o he acquisi ion. To his
end, a p elimina y model ha is sufficien ly ep esen a i e o he s uc u e is used o p e-
dic he expec ed beha iou . The gene a ion o a eliable model in ol es he de ini ion o
nume ous pa ame e s ha usually p esen a high le el o unce ain y [48]. Such pa ame-
e s comp ise ma e ial p ope ies, complex geome ies, connec ion be ween elemen s,
p esence o damage and soil s uc u e in e ac ion, among o he s [19]. To minimise he
unce ain ies ela ed o geome y, ad anced su eying echniques, such as pho og amme-
y o lase scanning, a e commonly employed. These ools can p o ide de ailed alues o
de o ma ions and damage loca ions, as well as accu a e in o ma ion o he de ini ion o
he s uc u al nume ical model. Howe e , a oiding unce ain ies in he de ini ion o he
o he pa ame e s is no so simple. One o he undamen al challenges in modelling his o -
ical mason y s uc u es is he accu a e cha ac e isa ion o he ma e ial p ope ies o aged
and wea he ed mason y [49]. T adi ional cons uc ion ma e ials o en lack he homogene-
i y and consis ency seen in mode n ma e ials, making i difficul o de ine eliable alues
o he analysis. The cons uc ion echniques employed in his o ical mason y buildings
Figu e 13.
Au o-MAC ables conside ing he esul om he o MAC 15-senso 179-node op imisa ion
o (
a
) SCN01, (
b
) SCN02, (
c
) SCN03 and (
d
) SCN04. MAC alues ep esen ed by colou scale: ed
ep esen s 1, whi e ep esen s 0.

Senso s 2023,23, 9304 17 o 23
5. Main Open Issues in OSP o His o ical Mason y Buildings
Upon he comp ehensi e analysis o he li e a u e and he applica ion o he nume -
ical benchma k discussed in he p e ious sec ion, a clea se o ele an open issues and
challenges ha hinde a success ul applica ion o OSP me hodologies o his o ical mason y
buildings we e iden i ied and he ea e discussed. Such challenges can be classi ied acco d-
ing o he h ee main componen s o he OSP s a egy: model- ela ed, expe imen - ela ed
and op imisa ion- ela ed challenges.
Commonly, he OSP p oblem is add essed be o e a de ailed in es iga ion o he s uc-
u e, wi h he goal being he iden i ica ion o he bes measu emen poin s o maximise he
in o ma ion quali y and minimise he esou ces needed o he acquisi ion. To his end, a
p elimina y model ha is su icien ly ep esen a i e o he s uc u e is used o p edic he
expec ed beha iou . The gene a ion o a eliable model in ol es he de ini ion o nume ous
pa ame e s ha usually p esen a high le el o unce ain y [
48
]. Such pa ame e s comp ise
ma e ial p ope ies, complex geome ies, connec ion be ween elemen s, p esence o damage
and soil s uc u e in e ac ion, among o he s [
19
]. To minimise he unce ain ies ela ed o
geome y, ad anced su eying echniques, such as pho og amme y o lase scanning, a e
commonly employed. These ools can p o ide de ailed alues o de o ma ions and damage
loca ions, as well as accu a e in o ma ion o he de ini ion o he s uc u al nume ical
model. Howe e , a oiding unce ain ies in he de ini ion o he o he pa ame e s is no so
simple. One o he undamen al challenges in modelling his o ical mason y s uc u es is he
accu a e cha ac e isa ion o he ma e ial p ope ies o aged and wea he ed mason y [
49
].
T adi ional cons uc ion ma e ials o en lack he homogenei y and consis ency seen in
mode n ma e ials, making i di icul o de ine eliable alues o he analysis. The con-
s uc ion echniques employed in his o ical mason y buildings can a y signi ican ly om
con empo a y p ac ices. These echniques may no be well documen ed and unde s anding
hem is c ucial o c ea ing accu a e models. Addi ionally, his o ical mason y s uc u es
ha e o en unde gone modi ica ions and epai s o e he yea s. Documen ing hese al e -
a ions and unde s anding hei impac on s uc u al beha iou is essen ial bu cumbe some.
Nume ical models should be able o accu a ely accoun o hese changes. De e mining
he load his o y o a mason y s uc u e is also challenging, especially when conside ing
long- e m e ec s, such as se lemen , c eep and he mal cycling [
50
]. Ob aining accu a e
load da a o his o ical s uc u es is o en impossible, and assump ions need o be made,
which can in oduce unce ain ies in o he nume ical model.
This kind o unce ain y undoub edly comp omises he quali y o he esul s ob ained
using he OSP me hodologies i a pu ely de e minis ic app oach is ollowed. As shown
in he benchma k applica ion, sligh changes o he o iginal assump ions and unexpec ed
con igu a ions a e ha dly iden i iable and dis inguishable when hei main ea u es a e
no accoun ed o in he p elimina y model used o he OSP. Simila ly, including he
unce ain ies in he op imisa ion, as demons a ed by se e al applica ions (i.e., Venice
palace, San Je ónimo monas e y, Slo jell owe and he nume ical benchma k), leads
o dis inc op imised placemen s, calling o he de ini ion o a obus s a egy o selec
a inal o e all op imal localisa ion. The de e minis ic applica ions in li e a u e y o
ci cum en he p oblem by employing a nume ical model calib a ed o he expe imen al
esponse o he building. Howe e , his solu ion equi es a p elimina y acquisi ion, ailing
o ul il he o iginal p emise o p o iding an op imised placemen be o e conduc ing
any es . On he o he hand, s ochas ic app oaches y o include unce ain y analysis in
he op imisa ion p oblem by simula ing a wide ange o possible scena ios. Two o he
in es iga ed applica ions p oposed he MCS echnique o sample se e al di e en ins ances
om p e-se p obabilis ic unc ions o each s ochas ic a iable [
21
,
22
]. Howe e , his
app oach is much mo e compu a ionally demanding, and se e al aspec s a e no ully
ag eed upon and need mo e esea ch, such as he de ini ion o he numbe o samples,
he a iables and hei s a is ical dis ibu ions, and he inal con igu a ion conside ing he
dispe sion o he esul s.
Senso s 2023,23, 9304 18 o 23
Da a-d i en me hods cons i u e a qui e no el and comple ely al e na i e app oach
o a oid p oblems wi h unce ain ies ela ed o he de ini ion o he model. In his case,
he a o emen ioned p emise o OSP is comple ely sub e ed and he aim becomes he
de e mina ion o he op imal placemen s a ing om a la ge numbe o measu emen
poin s eco ded du ing an ex ensi e ambien ib a ion es . This app oach, indeed, opens a
new scena io, in which he s akeholde s p e e o in es in a la ge es ing p og amme and
a e y high le el o knowledge o he s uc u e is ob ained, making he gene a ion o he
nume ical model unnecessa y o he op imisa ion pu pose. This implies a oiding he cos s
o c ea ing a eliable nume ical model, he complexi y o dealing wi h he unce ain ies,
and he need o he necessa y skill and expe ise o he nume ical simula ion. On he
o he hand, his app oach p esen s clea sho comings, such as he cos o conduc ing
a la ge es ing p og amme in ad ance ha o i s scale, may in e e e wi h he egula
unc ioning o he building. Mo eo e , he lack o p e ious in o ma ion abou he dynamic
beha iou o he s uc u e may hinde p ope es planning. A discussion o hese wo
al e na i e scena ios (i.e., da a-d i en, high le el o knowledge and expe imen ally in en-
si e wi hou nume ical simula ions equi ed s. model-based, low le el o knowledge and
compu a ionally in ensi e wi hou p elimina y expe imen s) has been p o ided in [34].
The analysis o he da a-d i en app oach leads o he discussion on expe imen - ela ed
issues [
39
]. Such issues a ec he campaign conduc ed be o e he applica ion o da a-d i en
OSP bu also he p elimina y es o nume ical calib a ion pu poses in model-based
app oaches [
38
]. Mo eo e , such issues should be aken in o accoun while conduc ing he
op imisa ion, i espec i e o he adop ed app oach, o enhance he op imised moni o ing.
His o ical mason y buildings possess unique cha ac e is ics ha g ea ly impac he
modal analysis p ocess [
51
]. These s uc u es a e o en massi e and exhibi po en ially
nonlinea esponses and complex damping mechanisms due o ageing, ma e ial deg ada-
ion and s uc u al modi ica ions, making hem inhe en ly di e en om mo e mode n,
homogeneous cons uc ions. Fu he mo e, hey can exhibi b i le beha iou , and hei
complex layou s, as seen in s uc u es like chu ches, de y he simpli ying assump ion o
box-like beha iou .
The challenges p esen ed by hese peculia i ies ex end o he domain o expe imen al
modal analysis [
52
]. His o ical mason y building high and local modes a e no easily
exci ed, and hus, can be ha dly iden i ied. Howe e , he e y essence o hese s uc u es
calls o an op imisa ion o he senso placemen d i en no only by he global modes bu
also by he local ones, which a e o en o e looked due o he complexi y hey in oduce
bu play a key ole in he s uc u al esponse. A homogeneous selec ion o modes om
di e en componen s and all majo di ec ions is also essen ial o a oid biases ha a ise
om a selec ion ha p io i ises ce ain mac oelemen s o mode shapes. All hese issues
can be obse ed in he applica ion o he benchma k. Since all hese decisions signi ican ly
in luence he inal con igu a ion, i is impo an o de ine a global s a egy ha can be
ex apola ed o o he cases o mason y buildings, despi e he case-speci ic peculia i ies.
In ligh o hese s uc u al complexi ies, he e a e se e al o he p essing issues o
con end wi h. Ambien ib a ion sou ces in he icini y o such his o ical buildings may be
weak, exace ba ing he challenges in acqui ing eliable modal da a. These buildings o en
s and in es ic ed a eas o , in gene al, a om hea ily a icked a eas, whe e ambien
ib a ions a e ypically mo e subs an ial. Mo eo e , he ope a ions a ound hese he i age
s uc u es may in oduce non-s a iona y inpu s, including he pe iodic olling o bells,
mic o- emo s and o he spo adic dis u bances. T adi ional ou pu -only modal analysis
echniques, which a e p ima ily designed o s a iona y and ime-in a ian inpu s, s uggle
o handle hese a iable o ces e ec i ely [52].
P ac ical conside a ions a e equally signi ican . His o ical mason y buildings o en
ope a e wi hin cons ain s imposed by hei signi icance. This means ha he ins alla ion
and ope a ion o he sensing de ices mus be minimally in asi e and isually unob usi e
o comply wi h he conse a ion p inciples o hese cul u al asse s, namely, p ese ing
hei isual and s uc u al in eg i y. This limi s, in many cases, he easible candida e
Senso s 2023,23, 9304 19 o 23
loca ions. Howe e , selec ing a su icien numbe o candida e poin s o ensu e he adequa e
pe o mance o he op imisa ion s a egy is pa amoun [39].
No only he inpu o he op imisa ion p ocess poses a p oblem bu also he op i-
misa ion algo i hm i sel . Rega ding he op imisa ion- ela ed issues, he impo ance o
he selec ion o he echnique was demons a ed, which is a complex decision because o
he la ge numbe o a ailable al e na i es, wi h all o hem ha ing di e en ad an ages
and disad an ages. The applica ions in he li e a u e ha compa e se e al op imisa ion
me hods, as in he case o he monas e y in Salzedas, concluded ha qui e la ge a iabili y
in he es ima ion o he ele ance o each candida e acco ding o dis inc me ics eme ged,
especially when he global and local modes we e a ge ed.
In he case o he San Je ónimo monas e y, among he ou OSP algo i hms analysed,
he E I me hod p o ided a solu ion ha allowed o he iden i ica ion o na u al equencies
wi h less e o , whe eas he solu ion o he KEMRO me hod was he one ha ga e he g ea -
es e o in he modal iden i ica ion. When unce ain ies we e conside ed o his s uc u e,
he SEMRO me hod was he one ha p esen ed he lowes dispe sion in i s solu ion o all
he scena ios analysed. The di e en esul s and conclusions exposed he lack o obus ness
in OSP, as di e en me hods p o ided e y dis inc placemen s and p esen ed signi ican
a iabili y in he pe o mance o a ious scena ios and in es iga ed cases.
Fo he Fassano bell owe , mul i-objec i e op imisa ion was add essed using gene ic
algo i hms. In his case, he me ics we e based on MAC unc ions. In pa icula , wo
objec i e unc ions we e combined o ensu e ha he senso pa e n emained op imal
h oughou he li e ime o he s uc u e, allowing o he success ul de ec ion o damage
onse e lec ed in he al e a ion o he mode shapes. Al hough his app oach o e s se e al
ad an ages, i equi es he de ini ion o mo e inpu pa ame e s and he selec ion o he
inal single op imal solu ion is challenging, as a ade-o be ween po en ially compe ing
objec i es mus be ound, which in ol es choosing among Pa e o-op imal solu ions ha
o e a ying ad an ages in dis inc aspec s.
An addi ional in e ence o d aw pe ains o he necessi y o es ablishing a me hodol-
ogy o de e mining he op imal numbe o senso s o place. In mos cases, no op imisa ion
was conduc ed, and he numbe was p ede ined based on speci ic demands, such as he
a ailabili y o he senso s o a limi a ion o he budge . Indeed, he p oblem o op imis-
ing he ne wo k cos , possibly conside ing pu chasing and ins alla ion cos s o di e en
ypes o senso s ( i-, bi- and uniaxial), e en in combina ion, and he ease o access o
he measu emen poin s ha e no a ac ed much a en ion ye [
37
]. Thus, a ecu en
s a egy o de e mine he numbe o senso s o place was o se i equal o he numbe o
a ge ed modes. Mo e complex app oaches analyse he e olu ion o one o mo e me ics
o a a iable numbe o senso s [
38
]. Howe e , by lacking a benchma k o he minimum
necessa y alue o hese me ics, he iden i ica ion o hei op imum can p o ide an un eal-
is ic numbe o senso s in complex cases, gene a ing edundan in o ma ion. This la e
p oblem o en eme ges, e en o a a he limi ed numbe o senso s, due o he endency o
se e al algo i hms o clus e hem. Indeed, as demons a ed by he benchma k applica ion
bu also by he in es iga ed li e a u e (i.e., monas e y o Salzedas and Venice palace), he
adop ed me ics o en ewa d he poin wi h la ge modal displacemen , whe eas hey end
o penalise nodes o he modes ha would o en be equally impo an o he in e p e a ion
o he shapes wi h mo e in lec ion poin s. As shown in he benchma k, his p oblem also
depends on he numbe o modes chosen o op imisa ion, and hus, a wide selec ion
o local and global modes and hei p opo ion ela i e o he numbe o senso s could
minimise his p oblem. In he Ca hed al o Sain John, o add ess his issue, he E I me hod
was imp o ed, including a dis ance-based c i e ion (DBC) o ejec senso s close han a
minimum dis ance. Al hough he au ho s analysed a ious minimum dis ances om 0 o 3
m and he me hod p o ided p omising esul s, i equi ed a case-speci ic de ini ion o he
DBC ha is ha dly gene alisable and applicable o o he cases.
Senso s 2023,23, 9304 20 o 23
6. Conclusions
In he p esen pape , a comp ehensi e o e iew o OSP me hods o his o ical mason y
buildings is p esen ed, which in ol es an in oduc ion o he OSP p oblem, including an
explana ion o he in ol ed s eps and p oblem o mula ion. The pape comp ises a e iew
o eigh applica ions ound in he li e a u e. The examined case s udies encompass six
eligious buildings and wo ci il cons uc ions. Fou cases op imised he placemen o
he comple e s uc u e, while ou ocused on speci ic po ions o i . The analysis co e ed
objec i es, inpu de ini ion, candida e and mode selec ion, op imisa ion algo i hms, esul
alida ion me ics, minimum senso selec ion and unce ain y inco po a ion, aiming a
iden i ying he un esol ed issues associa ed wi h applying his echnique o his o ical
mason y buildings.
Based on hese iden i ied issues, a nume ical benchma k was gene a ed o illus a e
he challenges mo e e ec i ely. Two me hods, namely, E I and o MAC, we e u ilised,
compa ing a ious ini ial candida e loca ions and senso quan i ies. Addi ionally, i e
scena ios (i.e., one e e ence and ou al e na i es) we e de ined h ough sligh a ia ions
in he nume ical model o accoun o ypically expec ed unce ain ies due o limi ed
knowledge o he in es iga ed his o ical building.
The analysis o he eigh pape s and he esul s ob ained om he nume ical bench-
ma k yielded signi ican insigh s in o he challenges associa ed wi h OSP in his o ical
mason y buildings. These challenges could be ca ego ised in o h ee p ima y aspec s:
model- ela ed, expe imen - ela ed, and op imisa ion- ela ed challenges:
•
Model- ela ed p oblems s em om he unique cha ac e is ics o hese buildings and
he al e a ions ha likely a ec ed hem o e ime, making he modelling ask ex emely
challenging and a ec ed by signi ican sou ces o unce ain y, which, i no p ope ly
add essed, may lead o a simula ed beha iou no being ep esen a i e o he eal one.
•
Expe imen - ela ed p oblems o igina e om common peculia i ies o he his o ical
mason y buildings ha a ec he in e p e a ion o ambien ib a ion es da a, such as
he b i le beha iou and nonlinea esponse, he di icul y in exci ing high and local
modes despi e hei ele ance, and he a ailabili y o mos ly weak ib a ion sou ces
wi h non-s a iona y inpu s. Mo eo e , conse a ion p inciples p e en he adop ion
o in asi e and ob usi e senso ins alla ions.
•
Op imisa ion- ela ed issues depend on he op imisa ion algo i hms and p ocedu es,
as exis ing me hodologies ail o p o ide a uni ocal answe o he main goals o
OSP. Va iabili y in he op imised loca ions o he same applica ion h ough dis inc
me hods is signi ican and obus s a egies o op imise he numbe and he o e all
cos s along wi h he placemen a e s ill missing.
Building on he insigh s gained om his s udy, u u e esea ch in he ield o OSP
o his o ical mason y buildings should ocus on add essing he iden i ied challenges
and explo ing no el echniques o op imising he senso placemen while conside ing
he unique cha ac e is ics o he his o ical mason y s uc u es. One po en ial a enue o
u he in es iga ion is he de elopmen o cos -e ec i e echniques ha accoun o he
unce ain ies wi hin he op imisa ion. Addi ionally, esea ch could del e in o inno a i e
OSP me hods o include cos s and budge - ela ed aspec s. In his espec , one o he majo
p oblems consis s o he selec ion o an op imal minimum numbe o senso s. To his
end, mul i-objec i e op imisa ion s a egies could o e some ad an ages by allowing o
managing se e al po en ially con lic ing objec i es a he same ime.
Finally, i is impo an o men ion he need o explo e issues ela ed o expe imen a ion,
such as he di icul ies in expe imen ally exci ing and iden i ying speci ic modes and
de ining iable solu ions o accoun o hem wi hin he op imisa ion p ocess.
Au ho Con ibu ions:
Concep ualiza ion, E.C., A.B. and N.M.; me hodology, E.C., A.B. and N.M.;
so wa e, E.C.; alida ion, E.C.; o mal analysis, E.C. and A.B.; in es iga ion, E.C., A.B. and N.M.; da a
cu a ion, E.C.; w i ing—o iginal d a p epa a ion, E.C. and A.B.; w i ing— e iew and edi ing, A.B.
and N.M.; isualiza ion, V.C. and P.B.L.; supe ision, N.M., V.C. and P.B.L.; p ojec adminis a ion,
Senso s 2023,23, 9304 21 o 23
A.B. and N.M.; unding acquisi ion, E.C., A.B., N.M., V.C. and P.B.L. All au ho s ha e ead and ag eed
o he published e sion o he manusc ip .
Funding:
This wo k was pa ly inanced by FCT/MCTES h ough na ional unds (PIDDAC) unde
he R&D Uni Ins i u e o Sus ainabili y and Inno a ion in S uc u al Enginee ing (ISISE), unde e -
e ence UIDB/04029/2020, and unde he Associa e Labo a o y Ad anced P oduc ion and In elligen
Sys ems ARISE unde e e ence LA/P/0112/2020. This wo k was pa ly inanced also by na ional
unds h ough FCT—Founda ion o Science and Technology, unde g an ag eemen 020.07164.BD
a ibu ed o he i s au ho .
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : The da a a e a ailable on eques .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Re e ences
1.
Mascio a, M.G.; Ramos, L.F. Dynamic iden i ica ion o his o ic mason y s uc u es. In Long-Te m Pe o mance and Du abili y o
Mason y S uc u es: Deg ada ion Mechanisms, Heal h Moni o ing and Se ice Li e Design; Else ie : Ams e dam, The Ne he lands,
2018; pp. 241–264.
2.
Palla és, F.J.; Be i, M.; Ba oli, G.; Palla és, L. S uc u al heal h moni o ing (SHM) and Nondes uc i e es ing (NDT) o slende
mason y s uc u es: A p ac ical e iew. Cons . Build. Ma e . 2021,297, 123768. [C ossRe ]
3.
Lamonaca, F.; Oli i o, R.S.; Po zio, S.; Cami, D.L.; Scu o, C. S uc u al Heal h Moni o ing Sys em o Mason y His o ical
Cons uc ion. In P oceedings o he 2018 Me ology o A chaeology and Cul u al He i age (Me oA chaeo), Cassino, I aly, 22–24
Oc obe 2018; pp. 330–335. [C ossRe ]
4.
Ramos, L.F.; De Roeck, G.; Lou enço, P.B.; Campos-cos a, A. Vib a ion Based Damage Iden i ica ion o Mason y S uc u es. In
P oceedings o he 5 h In e na ional Con e ence o S uc u al Analysis o His o ical Cons uc ions, Delhi, India, 6–8 No embe
2006; pp. 641–650.
5.
Mascio a, M.G. Damage Iden i ica ion o S uc u es Based on Spec al Ou pu Signals. Ph.D. Thesis, Uni e si y o Minho, B aga,
Po ugal, 2015.
6.
Ce a olo, R.; Pis one, G.; F agona a, L.Z.; Masse o, S.; Abbia i, G. Vib a ion-based moni o ing and diagnosis o cul u al he i age:
A me hodological discussion in h ee examples. In . J. A chi . He i . 2016,10, 375–395. [C ossRe ]
7.
Os achowicz, W.; Soman, R.; Malinowski, P. Op imiza ion o senso placemen o s uc u al heal h moni o ing: A e iew. S uc .
Heal h Moni . 2019,18, 963–988. [C ossRe ]
8.
Ba on ini, A.; Mascio a, M.G.; Ramos, L.F.; Amado-Mendes, P.; Lou enço, P.B. An o e iew on na u e-inspi ed op imiza ion
algo i hms o S uc u al Heal h Moni o ing o his o ical buildings. P ocedia Eng. 2017,199, 3320–3325. [C ossRe ]
9.
Fa a , C.R.; Pa k, G.; Allen, D.W.; Todd, M.D. Senso ne wo k pa adigms o s uc u al heal h moni o ing. S uc . Con ol Heal h
Moni . 2006,13, 210–225. [C ossRe ]
10.
Li, B.; Li, D.; Zhao, X.; Ou, J. Op imal senso placemen in heal h moni o ing o suspension b idge. Sci. China Technol. Sci.
2012
,
55, 2039–2047. [C ossRe ]
11.
Yang, Y.; Chadha, M.; Hu, Z.; Vega, M.A.; Pa no, M.D.; Todd, M.D. A p obabilis ic op imal senso design app oach o s uc u al
heal h moni o ing using isk-weigh ed -di e gence. Mech. Sys . Signal P ocess. 2021,161, 107920. [C ossRe ]
12.
C uz, A.; Vélez, W.; Thomson, P. Op imal senso placemen o modal iden i ica ion o s uc u es using gene ic algo i hms-a case
s udy: The olympic s adium in Cali, Colombia. Ann. Ope . Res. 2010,181, 769–781. [C ossRe ]
13.
Hassani, S.; Dacke mann, U. A Sys ema ic Re iew o Op imiza ion Algo i hms o S uc u al Heal h Moni o ing and Op imal
Senso Placemen . Senso s 2023,23, 3293. [C ossRe ]
14.
Liu, K.; Yan, R.J.; Soa es, G. Op imal senso placemen and assessmen o modal iden i ica ion. Ocean Eng.
2018
,165, 209–220.
[C ossRe ]
15.
Zhang, C.; Chun, Q.; Leng, J.; Lin, Y.; Qian, Y.; Cao, G.; Dong, Q. Op imal placemen me hod o mul i-objec i e and mul i- ype
senso s o cou ya d-s yle imbe his o ical buildings based on Me a-gene ic algo i hm. S uc . Heal h Moni . 2023. [C ossRe ]
16.
Zhang, C.; Chun, Q.; Lin, Y.; Qian, Y.; Cao, G.; Dong, Q. Resea ch on Op imal Senso Placemen Me hod o T adi ional Chinese
Timbe Dwellings Based on Mul i-objec i e Moni o ing. In RILEM Bookse ies, P oceedings o he SAHC: In e na ional Con e ence on
S uc u al Analysis o His o ical Cons uc ions, Kyo o, Japan, 1–15 Sep embe 2023; Sp inge : Cham, Swi ze land, 2023; Volume 47,
pp. 188–196. [C ossRe ]
17.
Len icchia, E.; Ce a olo, R.; An onaci, P. Senso Placemen S a egies o he Seismic Moni o ing o Complex Vaul ed S uc u es
o he Mode n A chi ec u al He i age. Shock Vib. 2018,2018, 3739690. [C ossRe ]
18.
Qua an a, G.; Ma ano, G.C.; T en adue, F.; Mon i, G. Nume ical s udy on he op imal senso placemen o his o ic swing b idge
dynamic moni o ing. S uc . In as uc . Eng. 2014,10, 57–68. [C ossRe ]

Senso s 2023,23, 9304 22 o 23
19.
Shabani, A.; Kiouma si, M. Op imal senso placemen echniques o modal iden i ica ion o his o ical mason y s uc u es.
P ocedia S uc . In eg . 2022,42, 147–154. [C ossRe ]
20.
Dogh i, W.; Saddoud, A.; Chaa i, L. Op imal Senso Placemen S a egy o S uc u al Heal h Moni o ing wi h Applica ion o
he Aqueduc El Hnaya o Ca hage. In P oceedings o he 2023 15 h In e na ional Con e ence on De elopmen s in eSys ems
Enginee ing (DeSE), Baghdad & Anba , I aq, 9–12 Janua y 2023; pp. 137–142. [C ossRe ]
21.
Yang, X.-S. In oduc ion o Algo i hms. In Na u e-Inspi ed Op imiza ion Algo i hms; Academic P ess: Camb idge, MA, USA, 2021;
pp. 1–22.
22.
Blum, C.; Roli, A. Me aheu is ics in Combina o ial Op imiza ion: O e iew and Concep ual Compa ison. ACM Compu . Su .
2003,35, 268–308. [C ossRe ]
23.
Yuen, K.V.; Kuok, S.C. E icien Bayesian senso placemen algo i hm o s uc u al iden i ica ion: A gene al app oach o
mul i- ype senso y sys ems. Ea hq. Eng. S uc . Dyn. 2015,44, 757–774. [C ossRe ]
24.
Kamme , D.C.; Yao, L. Enhancemen o on-o bi modal iden i ica ion o la ge space s uc u es h ough senso placemen . J. Sound
Vib. 1991,171, 119–139. [C ossRe ]
25.
Yi, T.H.; Li, H.N. Me hodology De elopmen s in Senso Placemen o Heal h Moni o ing o Ci il In as uc u es. In . J. Dis ib.
Sens. Ne w. 2012,2012, 11. [C ossRe ]
26.
Lian, J.; He, L.; Ma, B.; Li, H.; Peng, W. Op imal senso placemen o la ge s uc u es using he nea es neighbou index and a
hyb id swa m in elligence algo i hm. Sma Ma e . S uc . 2013,22, 095015. [C ossRe ]
27.
Meo, M.; Zumpano, G. On he op imal senso placemen echniques o a b idge s uc u e. Eng. S uc .
2005
,27, 1488–1497.
[C ossRe ]
28.
Cas o-T igue o, R.; Mu ugan, S.; Gallego, R.; F iswell, M.I. Robus ness o op imal senso placemen unde pa ame ic unce ain y.
Mech. Sys . Signal P ocess. 2013,41, 268–287. [C ossRe ]
29. Eiben, A.E.; Smi h, J.E. In oduc ion o E olu iona y Compu ing; Sp inge : Be lin/Heidelbe g, Ge many, 2015.
30.
Tan, Y.; Limao, Z. Compu a ional Me hodologies o Op imal Senso Placemen in S uc u al Heal h Moni o ing: A Re iew.
S uc . Heal h Moni . 2020,19, 1287–1308. [C ossRe ]
31.
Papadimi iou, C. Op imal senso placemen me hodology o pa ame ic iden i ica ion o s uc u al sys ems. J. Sound Vib.
2004
,
278, 923–947. [C ossRe ]
32.
Huan, X.; Ma zouk, Y.M. Simula ion-based op imal Bayesian expe imen al design o nonlinea sys ems. J. Compu . Phys.
2011
,
232, 288–317. [C ossRe ]
33.
Capella i, G. Op imal Design o Senso Ne wo ks o S uc u al Heal h Moni o ing. Ph.D. Thesis, Poli ecnico di Milano School o
Managemen , Milan, I aly, 2017.
34.
Imposa, G.; Ba on ini, A.; Russo, S.; Lou enço, P.B. Fi s hypo hesis o Op imized Moni o ing S a egy h ough Ambien
Vib a ions in his o ic buildings. P ocedia S uc . In eg . 2022,44, 1608–1615. [C ossRe ]
35.
A ezzo, D.; Nicole i, V.; Ca bona i, S.; Ga a, F. Op imal Senso Placemen o he Dynamic Moni o ing o a His o ical Mason y
Chu ch in Cen al I aly. In P oceedings o he 9 h IOMAC In e na ional Ope a ional Modal Analysis Con e ence, Vancou e , BC,
Canada, 3–6 July 2022; pp. 247–256.
36.
Gio dano, E.; Clemen i, F.; Ba on ini, A.; Gio anna, M.; Cha zi, E.; Luís, F. Damage de ec ion and op imal senso placemen in
heal h moni o ing o “ Collegia a di San a Ma ia ” in Visso ( Cen al I aly). In P oceedings o he XVII Con egno Anidis, Ascoli
Piceno, I aly, 15 Sep embe –19 Oc obe 2019; pp. 44–53.
37.
Ci e a, M.; Peco elli, M.L.; Ce a olo, R.; Su ace, C.; Zano i F agona a, L. A mul i-objec i e gene ic algo i hm s a egy o obus
op imal senso placemen . Compu . Ci . In as uc . Eng. 2021,36, 1185–1202. [C ossRe ]
38.
Pachón, P.; In an es, M.; Cáma a, M.; Compán, V.; Ga cía-Macías, E.; F iswell, M.I.; Cas o-T igue o, R. E alua ion o op imal
senso placemen algo i hms o he S uc u al Heal h Moni o ing o a chi ec u al he i age. Applica ion o he Monas e y o San
Je ónimo de Buena is a (Se ille, Spain). Eng. S uc . 2020,202, 109843. [C ossRe ]
39.
Vila-Chã, E.; Ba on ini, A.; Lou enço, P.B. Implemen a ion o a Condi ion Moni o ing S a egy o he Monas e y o Salzedas,
Po ugal: Challenges and Op imisa ion. Buildings 2023,13, 719. [C ossRe ]
40.
P abhu, S.; A am u k u , S. Selec ion o Op imal Senso Loca ions Based on Modi ied E ec i e Independence Me hod: Case
S udy on a Go hic Re i al Ca hed al. J. A chi . Eng. 2013,19, 288–301. [C ossRe ]
41.
Imposa, G.; Ba on ini, A.; Lou enco, P.B.; Russo, S. A S a egy o Op imal Senso Placemen o Dynamic Iden i ica ion in Cul u al
He i age. In RILEM Bookse ies, P oceedings o he SAHC: In e na ional Con e ence on S uc u al Analysis o His o ical Cons uc ions,
Kyo o, Japan, 1–15 Sep embe 2023; Sp inge : Cham, Swi ze land, 2023; Volume 47, pp. 309–321. [C ossRe ]
42.
Kamme , D.C. E ec o model e o on senso placemen o on-o bi modal iden i ica ion o la ge space s uc u es. J. Guid.
Con ol Dyn. 1992,15, 334–341. [C ossRe ]
43.
DIANA FEA. DIsplacemen Me hod ANAlyse . Use ’s Manual, Release 10.7, The Ne he lands. 2023. A ailable online: h ps:
//diana ea.com/ (accessed on 15 No embe 2023).
44.
Ramos, L.F.; Alaboz, M.; Aguila , R.; Lou enço, P.B. Dynamic iden i ica ion and FE upda ing o S. To ca o Chu ch, Po ugal. In
Con e ence P oceedings o he Socie y o Expe imen al Mechanics Se ies; Sp inge : New Yo k, NY, USA, 2011; Volume 4, pp. 71–80.
[C ossRe ]
45.
Macwilliam, K.; Nunes, C. S uc u al Analysis o His o ical Cons uc ions; Sp inge : Be lin/Heidelbe g, Ge many, 2019; Volume 18,
pp. 1949–1958. [C ossRe ]
Senso s 2023,23, 9304 23 o 23
46.
Ramí ez, R. S uc u al Analysis o he Chu ch o he Monas e y o São Miguel de Re ojos. Mas e ’s Thesis, Uni e si y o Minho,
B aga, Po ugal, 2016.
47.
Aguila , R.; Noel, M.F.; B iceño, C.; A ce, D.; Cas añeda, B.; Ramos, L.F. Geoma ics’ p ocedu es and dynamic iden i ica ion o
he s uc u al su ey o he chu ch o ‘San Juan Bau is a de Hua o’ in Pe ú. In B ick and Block Mason y: T ends, Inno a ions and
Challenge, P oceedings o he 16 h In e na ional B ick and Block Mason y Con e ence, IBMAC, Pado a, I aly, 26–30 June 2016; CRC P ess:
Boca Ra on, FL, USA, 2016; pp. 815–820. [C ossRe ]
48.
As e is, P.G.; Ple is, V.; Sa hosis, V.; Papaloizou, L.; Mohebkhah, A.; Komod omos, P. Nume ical Modeling o His o ic Mason y
S uc u es; IGI Global: He shey, PA, USA, 2015.
49.
Be i, M.; O lando, M.; Vignoli, A. S a ic beha iou o an I alian Medie al Cas le: Damage assessmen by nume ical modelling.
Compu . S uc . 2011,89, 1956–1970. [C ossRe ]
50.
D’Al i, A.M.; de Mi anda, S.; Cas ellazzi, G.; Glisic, B. Nume ical modelling-based damage diagnos ics in cul u al he i age
s uc u es. J. Cul . He i . 2023,61, 1–12. [C ossRe ]
51.
Koçak, A.; Toydemi , B.; Bulgu , M. De e mina ion o cha ac e is ic Pa ame e s o mason y S uc u es ia Ope a ional Modal
Analysis. In . J. Eng. Sci. 2019,12, 120304. [C ossRe ]
52.
Pau, A.; Ves oni, F. Dynamic Cha ac e iza ion o Ancien Mason y S uc u es. In Ad ances in Vib a ion Analysis Resea ch; Eb ahimi,
F., Ed.; In echOpen: Rijeka, C oa ia, 2011.
Disclaime /Publishe ’s No e:
The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .