Optimization of the Cyclone Separator Geometry via Multimodel Simulation

CIplus
Band 9/2016
Op imiza ion o he Cyclone Sepa a o
Geome y ia Mul imodel Simula ion
Thomas Ba z-Beiels ein, Ho s S enzel, Ma in Zae e e , Bea e B ei-
de ho , Quoc Cuong Pham, Dimi i Gusew, Aylin Mengi, Ba is Kaba-
cali, Je ome Tün e, Lukas Büsche , Sascha Wüs lich, Thomas F iesen
A
Op imiza ion o he Cyclone Sepa a o Geome y ia Mul imodel
Simula ion
THOMAS BARTZ-BEIELSTEIN, TH K¨
oln
HORST STENZEL, TH K¨
oln
MARTIN ZAEFFERER, TH K¨
oln
BEATE BREIDERHOFF, TH K¨
oln
QUOC CUONG PHAM, TH K¨
oln
DIMITRI GUSEW, TH K¨
oln
AYLIN MENGI, TH K¨
oln
BARIS KABACALI, TH K¨
oln
JEROME T ¨
UNTE, TH K¨
oln
LUKAS B ¨
USCHER, TH K¨
oln
SASCHA W ¨
USTLICH, TH K¨
oln
THOMAS FRIESEN, TH K¨
oln
Cyclone sepa a o s a e popula de ices used o il e dus om he emi ed lue gases. They a e applied
as p e- il e s in many indus ial p ocesses including ene gy p oduc ion and g ain p ocessing acili ies. In-
c easing compu a ional powe and he a ailabili y o 3D p in e s p o ide new ools o he combina ion o
modeling and expe imen a ion, which necessa y o cons uc ing e icien cyclones. Se e al simula ion ools
can be un in pa allel, e.g., long unning CFD simula ions can be accompanied by expe imen s wi h 3D
p in e s. Fu he mo e, esul s om analy ical and da a-d i en models can be inco po a ed. The e a e un-
damen al di e ences be ween hese modeling app oaches: some models, e.g., analy ical models, use domain
knowledge, whe eas da a-d i en models do no equi e any in o ma ion abou he unde lying p ocesses.
A he same ime, da a-d i en models equi e inpu and ou pu da a, whe eas analy ical models do no .
Combining esul s om models wi h di e en inpu -ou pu s uc u e is o g ea in e es . This combina ion
inspi ed he de elopmen o a new me hodology. An op imiza ion ia mul imodel simula ion app oach, which
combines esul s om di e en models, is in oduced. Using cyclonic dus sepa a o s (cyclones) as a eal-
wo ld simula ion p oblem, he easibili y o his app oach is demons a ed. P os and cons o his app oach
a e discussed and expe iences om he expe imen s a e p esen ed. Fu he mo e, echnical p oblems, which
a e ela ed o 3D-p in ing app oaches, a e discussed.
CCS Concep s: Compu ing me hodologies →Modeling me hodologies;
Addi ional Key Wo ds and Ph ases: Combined simula ion, mul imodeling, simula ion-based op imiza ion,
me amodel, su oga e model, s acking, esponse su ace me hodology, 3D p in ing, compu a ional luid dy-
namics
ACM Re e ence Fo ma :
Thomas Ba z-Beiels ein, Ho s S enzel, Ma in Zae e e , Bea e B eide ho , Quoc Cuong Pham, Dimi i
Gusew, Aylin Mengi, Ba is Kabacali, Je ome T¨
un e, Lukas B¨
usche , Sascha W¨
us lich, and Thomas F iesen,
2016. Op imiza ion ia Mul imodel Simula ion – Combining Analy ical, Su oga e, CFD, and 3D-p in ing
Modeling. ACM V, N, A icle A (No embe 2016), 23 pages.
DOI: h p://dx.doi.o g/10.1145/0000000.0000000
This wo k is suppo ed by he Bundesminis e ium ¨u Wi scha und Ene gie unde he g an s
KF3145101WM3 und KF3145103WM4. This wo k is pa o a p ojec ha has ecei ed unding om he
Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og am unde g an ag eemen No 692286.
Au ho ’s add esses: T. Ba z-Beiels ein, Facul y o Compu e Science and Enginee ing Sciences, TH K¨
oln.
Pe mission o make digi al o ha d copies o all o pa o his wo k o pe sonal o class oom use is g an ed
wi hou ee p o ided ha copies a e no made o dis ibu ed o p o i o comme cial ad an age and ha
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lish, o pos on se e s o o edis ibu e o lis s, equi es p io speci ic pe mission and/o a ee. Reques
pe missions om [email p o ec ed].
c
2016 ACM. 0000-0000/2016/11-ARTA $15.00
DOI: h p://dx.doi.o g/10.1145/0000000.0000000
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
A:2 Thomas Ba z-Beiels ein e al.
1. INTRODUCTION
Simula ion is a widely used me hod o s udying complex eal-wo ld sys ems, because
many sys ems canno be comple ely desc ibed by analy ical (ma hema ical) models
and expe imen a ion wi h he eal sys em is in easible o expensi e. Fu he mo e,
simula ion allows he es ima ion o sys em pe o mance unde new condi ions as well
as he compa ison o di e en ope a ing condi ions and pa ame e iza ions, e.g., new
geome ies.
Howe e , he e a e also some p oblems ela ed o simula ion-based app oaches. Sim-
ula ion models a e usually mo e expensi e han analy ical models. Each simula ion
desc ibes only one single se ing. Se e al epea s wi h a ying inpu da a a e neces-
sa y, whe eas an analy ical model allows he calcula ion o he exac cha ac e is ics o
he sys em o se e al se ings. An inapp op ia e le el o model de ail, ailu e o col-
lec adequa e sys em da a, and using w ong pe o mance indica o s o compa isons
a e only h ee common pi alls in simula ion s udies. The eade is e e ed o Law
and Kel on [2000] o a de ailed discussion o hese issues.
Inc easing compu a ional powe and he a ailabili y o 3D p in e s p o ide ools
o new modeling app oaches. Se e al simula ions can be un in pa allel, e.g., long
unning compu a ional luid dynamics (CFD) simula ions can be accompanied by ex-
pe imen s wi h 3D p in e s, whe eas he analy ical model is e alua ed as a baseline.
Combina ions o he ollowing app oaches a e possible: (i) ield expe imen s, (ii) lab ex-
pe imen s, (iii) complex simula ions, (i ) model based simula ions, and ( ) analy ical
models. Two ques ions a ise in his con ex :
Q-1 A e he e any bene i s in combining di e en simula ion app oaches?
Q-2 Can he weakness o one app oach be compensa ed by o he app oaches?
To answe hese ques ions, a me hodology o combining hese esul s is necessa y.
This a icle p esen s a new app oach o handling se e al simula ion models in pa al-
lel. I combines bene i s om di e en wo lds. The p oposed me hodology can be used
as he cen al pa o a new simula ion-op imiza ion app oach [Fu 1994]. To exempli y
ou app oach, a well es ablished eal-wo ld simula ion p oblem is used: cyclone dus
collec o s.
Cyclone dus collec o s a e used o il e dus om he emi ed lue gases. Re e se-
low ype de ices wi h a angen ial inle (slo o w ap-a ound) and a cylinde -on-cone
body shape will be e e ed o as cyclones in he emainde o his a icle. Since hey a e
ela i ely simple o ab ica e and main ain, cyclones a e popula in many indus ies.
Ho mann and S ein [2007a] lis he ollowing indus ies, which make use o cyclones:
— oil and gas
— powe gene a ion
— incine a ion plan s
— i on and s eel indus y/blas u naces
and non- e ous indus ies
— o e sin e ing plan s
— wood chip, wood mill and building ma-
e ial plan s
— sand plan s
— cemen plan s
— coking plan s
— coal i ed boile s
— lead, e osilicon, calcium ca bide, ex-
panded pe li e, ca bon black plan s,
e c.
— g ain p ocessing acili ies such as lou
mills (whea , ice, e c.)
— ‘chemical’ plan s (plas ics, elas ome s,
polyme s, e c.)
— ca alys manu ac u ing plan s
— ood indus y.
The main goal o a cyclone is o il e a maximal amoun o dus om he lue gas
(high deg ee o sepa a ion), while minimizing he p essu e loss. They can be applied
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
Op imiza ion ia Mul imodel Simula ion A:3
in ex emely ha sh and demanding en i onmen s, bu show a ela i ely low sepa a-
ion compa ed o elec os a ic dus collec o s. I pa icles a e la ge han 5 µm, cy-
clones a e e icien . The e o e, cyclones a e used as p e-cleane s o o he il e ech-
niques [Swamee e al. 2009]. Many pa ame e s de e mine he pe o mance o cyclones.
Fo p ac i ione s, i is o impo ance o know which pa ame e s a e impo an and
which a e no , in any gi en si ua ion. E en wi h oday’s mode n ools, he complexi y
o cyclone beha io is such ha expe imen al s udies a e necessa y o a solid unde -
s anding o he phenomena go e ning hei beha io .
Cyclones use a conical geome y o in oduce a cen i ugal o ce ha sepa a es dus
om gas. The p essu e d op (Eule numbe ) and he collec ion e iciency a e well es ab-
lished pe o mance indica o s o cyclones. The la e is ela ed o he cu -o diame e
(S okes numbe ). Bo h indica o s a e de e mined by se e al pa ame e s, including he
geome y o he cyclone. Hence, an e icien cyclone equi es he op imiza ion o he
geome y pa ame e s.
Fo he pu pose o op imiza ion, he pe o mance could be es ima ed by ull-scale,
eal-wo ld expe imen s. Due o he ex ensi e cos s, his is no easible. Ra he , a ious
physics-d i en and da a-d i en models a e ypically used. These include (i) analy -
ical models, (ii) CFD simula ions, and (iii) me amodeling o su oga e model based
app oaches.
The analy ical app oaches de eloped by Ba h [1956], which we e u he ex ended
by Muschelknau z [1972] and co-wo ke s, can be conside ed as s anda d in li e a-
u e [Ho mann and S ein 2007b]. This app oach enables an unde s anding o cyclone
pe o mance as a unc ion o i s geome y, eed p ope ies, and low a es.
CFD simula ions ha e p o en o be use ul o s udying he luid and pa icle lows
in cyclones [Hoeks a e al. 1999; G i i hs and Boysan 1996; Gimbun e al. 2005b;
Elsayed and Laco 2010; Elsayed 2011; Gimbun e al. 2005a; O e camp and Man ha
1998; Elsayed and Laco 2014; Di go and Lei h 2007; Sole o and Coghe 2002; Ho -
mann and S ein 2007a; Swamee e al. 2009]. They ha e clea ad an ages o unde -
s anding he de ails o he low in cyclones, bu also limi a ions in e ms o modeling
cyclone sepa a ion pe o mance accu a ely [Ho mann and S ein 2007a]. Nume ical
simula ions a e pe o med by sol ing he uns eady-s a e, h ee-dimensional Reynolds
a e aged Na ie -S okes (RANS) equa ions combined wi h a closu e model o he u -
bulen s esses and he la ge eddy simula ion app oach. The physical laws go e ning
he beha io o cyclones we e es ablished in he wo ks o New on and S okes, which
lay he ounda ions o desc ibing he o ces ac ing on a pa icle a eling in a luid
medium.
Compu a ional luid dynamics simula ions a e compu a ionally expensi e. Da a-
d i en models o cyclone sepa a o s, which a e subs an ially cheape o e alua e, can
be used ins ead. The me amodeling o su oga e-based modeling app oach is well-
known o accele a ing op imiza ion asks. I a su oga e model is in eg a ed in o
he op imiza ion p ocess, he me hod is e e ed o as su oga e based op imiza ion
(SBO) [Ba z-Beiels ein 2016a].
As a new app oach owa ds cyclone geome y op imiza ion, we p opose small-scale
expe imen s, based on 3D-p in ed cyclones. Tha is, 3D-p in ed small-scale cyclones
will be used o pe o m ac ual eal-wo ld expe imen s. While 3D p in ing educes he
cos o expe imen s signi ican ly (compa ed o ull-scale as well as complex CFD), he
expe imen s hemsel es a e s ill ime-consuming and equi e ma e ial esou ces. Wi h
he cos o expe imen s, noise o e alua ion (due o manu ac u ing as well as measu e-
men inaccu acies), and he inhe en complexi y o he sea ch-space due o i s combi-
na o ics, he modeling based on 3D-p in ed cyclones poses a majo challenge. Despi e
o his p oblems, we expec combining esul s om he 3D-p in ing expe imen s wi h
esul s om o he modeling app oaches migh imp o e he o e all model quali y. This
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.

A:4 Thomas Ba z-Beiels ein e al.
imp o emen migh (i) accele a e he op imiza ion p ocess and (ii) lead o new insigh s
in o he beha io o cyclones.
This a icle p esen s esul s om an expe imen al s udy, which combines esul s
om a ious modeling app oaches. The s udy can be ega ded as a p oo -o -concep
o a new, in eg a ed mul imodel app oach, in eg a ing 3D-p in ing based modeling in
he cyclone simula ion and op imiza ion loop. I combines ou di e en modeling ap-
p oaches, namely (M-A) analy ical, (M-S) su oga e, (M-C) CFD, and (M-P) 3D-p in ing
modeling.
This pape is s uc u ed as ollows: Sec ion 2 desc ibes ela ed wo k. Sec ion 3 de-
sc ibes he simula ion-op imiza ion loop. Sec ion 4 in oduces cyclone design and ge-
ome y conside a ions. Sec ion 5 compa es esul s om di e en modeling app oaches.
The analy ical (M-A), he su oga e modeling (M-S), he CFD modeling (M-C), and he
3D-p in ing (M-P) app oaches a e desc ibed. Expe imen al esul s a e p esen ed in
Sec ion 6. How o combine esul s om a ious models ia ensemble building is shown
in Sec ion 7. Sec ion 8 desc ibes he me amodel-based op imiza ion. Sec ion 9 gi es
a conclusion and p esen s ecommenda ions based on ou expe iences made in his
s udy.
2. RELATED WORK
The idea o using di e en models wi h di e en esolu ion has been discussed in he
li e a u e o many yea s. Zeigle and O en [1986] desc ibe mul iple le els o model ag-
g ega ion ( esolu ion, abs ac ion). These le els depend on he objec i es, knowledge,
and he a ailable budge ( esou ces, e.g., ime). They claim ha he e is “an unde ly-
ing uni y ha binds di e en models oge he —namely hei common o igin.” An en-
i onmen “can suppo he in eg a ion o models so ha a cohe en whole eme ges.”
Fishwick and Zeigle [1992] p esen a o malism and a me hodology o de eloping
mul iple, coope a i e models o physical sys ems om quali a i e physics.
S ayma es e al. [2013] p esen he design and cha ac e iza ion o a s eamlined,
high- olume pa icle impac o in ended o use wi h ace chemical analysis. Compu-
a ional luid dynamics was used as a ool o op imize he ae odynamic pe o mance
o he impac o by i e a i ely edesigning he geome y and cu a u e o he in e nal
walls. By elimina ing eci cula ion zones wi hin he low ield o he impac o and using
low ield s eamlines as new walls, successi e designs e ealed a signi ican educ ion
in he p essu e d op ac oss he impac o . Pa icle ajec o ies we e simula ed in he
impac o and he 50% cu poin was de e mined. They ab ica ed a p o o ype impac o
wi h a 3D apid p o o yping p in e and cha ac e ized in e ms o pa icle cu -o di-
ame e using es ae osols gene a ed by an Ink Je Ae osol Gene a o and luo escence
in ensi y measu emen s.
Cyclone geome y and design op imiza ion using CFD can be conside ed as a s an-
da d echnique [Ce necky and Plando o a 2013]. The cyclone modeling, simula ion,
and op imiza ion app oach p esen ed in ou s udy is ela ed o he wo k om P een
and Bull [2014], who op imized e ical-axis wind u bines using minia u ized 3D-
p in ed wind u bines. A e y gene al app oach o in eg a ing 3D p in ing in o he
op imiza ion loop is p esen ed by Eiben and Smi h [2015]. These au ho s desc ibe he
eme ging a ea o a i icial e olu ion in physical sys ems. Chaudhu i e al. [2015] de-
sc ibe a lapping wing op imiza ion ask. They used mul iple su oga es, mul iple in-
ill c i e ia, and mul iple poin s o he same expe imen al da a se o add mul iple
poin s in a cycle o op imiza ion. In he con ex o eal wo ld applica ions, Kazemi
e al. [2016] use di e en machine lea ning app oaches o c ea e simple and eliable
models o p edic ing g anule size dis ibu ions. Thei models we e de eloped based
on a da a se om labo a o y. An i e a i e p ocedu e assis ed by c oss alida ion was
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
Op imiza ion ia Mul imodel Simula ion A:5
implemen ed o ind ou he bes model among housands. Gene ic p og amming and
neu al ne wo ks pe o med bes .
In gene al, he e a e wo op ions o deal wi h mul iple models: (i) selec ion o he
bes model and (ii) combina ion o esul s om se e al models. Simpson e al. [2012]
p esen a hough ul e iew o se e al mul imodel app oaches. They s a e ha “ he
use o mul iple su oga es (i.e., a se o su oga es and possibly a weigh ed a e age
su oga e) is e y appealing in design op imiza ion due o he ac ha he bes su -
oga e may no lead o he bes esul ; and complemen a y because i ing many su -
oga es and epea ing op imiza ions is cheap compa ed o cos o simula ion.” Yang
[2003] s a es ha selec ion can be be e when he e o s in p edic ion a e small and
combina ion wo ks be e when he e o s a e la ge. Fu he mo e, co-k iging, which is
a popula me hod ha combines esul s om ine and coa se g ained models, can be
men ioned in his con ex [Fo es e e al. 2007].
The app oaches desc ibed so a y o selec one model, whe eas ou app oach com-
bines esul s om se e al models using s acked eg ession. In addi ion, ou app oach
is able o combine esul s om models wi h di e en un imes (s eady s a e p op-
e y) [Nowos awski and Poli 1999]. The app oaches men ioned abo e use in o ma ion
om su oga e models o selec new design poin s o he manu ac u ing p ocess o
CFD simula ion. Ou s udy p esen s an in eg a ed simula ion and expe imen a ion
me hodology on a ious scales (o laye s), namely
(M-A) analy ical models,
(M-S) su oga e models,
(M-C) CFD simula ion, and
(M-P) 3D p in ing.
Simula ion and op imiza ion o cyclones we e pe o med sepa a ely on each o hese
laye s. To bes o ou knowledge, an in eg a ed app oach ha combines expe imen a-
ion and simula ion a di e en le els and ha uses a s acked gene aliza ion app oach
o gene a e one me a-model was no applied o his (o simila ) simula ion and op i-
miza ion asks. Since 3D p in e become mo e and mo e a o dable, e alua ing he p os
and cons o hei in eg a ion in o he simula ion-op imiza ion amewo k is desi able.
3. OPTIMIZATION VIA MULTIMODEL SIMULATION IN THE LOOP
Simula ion is o g ea in e es o p ac i ione s planning o op imize a sys em, which
equi es he speci ica ion o a numbe o decision o inpu a iables. In many si u-
a ions, he inpu a iables a e also subjec o cons ain s. Fu he mo e, he e is an
objec i e unc ion o be minimized (o maximized), which is a unc ion o one o se -
e al simula ion ou pu a iables and o ce ain inpu a iables. In his se ing, he
goal o op imiza ion is o pe o m uns o he simula ion model in an e icien manne
and o de e mine hose inpu a iables, which esul in an op imal (o nea op imal)
solu ion [Law and Kel on 2000; Fu 1994]. This se ing is known as op imiza ion ia
simula ion. Ou app oach ex ends he s anda d op imiza ion ia simula ion se ing by
in eg a ing esul s om se e al model ypes. I will be e e ed o as op imiza ion ia
mul imodel simula ion in he ollowing.
The gene al concep o op imiza ion ia mul imodel simula ion is illus a ed in Fig-
u e 1. He e, we conside he op imiza ion o he cyclone’s geome y pa ame e s, which
should be dis inguished om he p ocess pa ame e s. I consis s o he ollowing s eps:
(S-1) Selec an ini ial design. Se = 1, whe e deno es he numbe o pa ame e se s.
The i s se o pa ame e s, ~x( )
g, which desc ibe he geome y, is gene a ed.
(S-2) Speci y he p ocess pa ame e s ~xp. Fo example, he inle eloci y and he pa -
icle size dis ibu ions ha e o be speci ied o he simula ion model. The p ocess
pa ame e s a e no changed du ing he op imiza ion.
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Legend
(S-3)
Selec unsupe ised
models
(S-7)
Selec supe ised
models
(S-1)
Ini ial design
(S-5)
E alua e models
(S-11)
S o e op imized
design
(S-4)
Build models
(S-2)
P ocess
pa ame e s
Ex e nal da a
(S-6)
Collec esul s
(S-9)
Op imize on
me amodel
(S10)
Te mina e?
P ocess
Pa allel
P ocesses
Da abase
(S-8)
Build me amodel
Fig. 1. Op imiza ion ia mul imodel simula ion in he loop. Se e al simula ion models a e used in pa allel.
Elemen s o he i s se o models, i.e., du ing s eps (S-3), (S-4), and (S-5), can be one o se e al CFD
simula o s, analy ical models, o expe imen s based on 3D-p in ed objec s. Resul s om hese di e en
models a e collec ed and op ionally combined wi h addi ional esul s, which we e s o ed in a da abase. The
second se o models is build du ing s ep (S-8). Models om he second se a e classical su oga e models, e.g.,
neu al ne wo ks, linea eg ession models, o K iging models. Resul s om hese models can combined in
se e al ways. We desc ibe an app oach ha is based on s acked gene aliza ion [Wolpe 1992]. Op imiza ion
is pe o med on he s acked model (S-9).
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Op imiza ion ia Mul imodel Simula ion A:7
(S-3) Selec unsupe ised models (e.g., CFD, analy ical). The whole pa ame e se ,
~x( )= (~x( )
g, ~xp)will be used o build he models. No e, hese models a e simila o
unsupe ised models in he machine lea ning communi y, because no in o ma ion
abou he dependen (ou pu ) a iables yis needed.
(S-4) Build models. In his s ep, one o se e al models ( 1, . . . , p) om he se o unsu-
pe ised models, which comp ehends 3D-p in ed objec s, ma hema ical model o -
mulas, o CFD simula ion models, a e gene a ed. The cons uc ion p ocess esul s
in se e al models, which use he same se o pa ame e s ~x( ).
(S-5) E alua e models. The models a e e alua ed, i.e., each model gene a es an ou -
pu : j:~x( )→y( )
j. No e, some models gene a e a de e minis ic ou pu , e.g., CFD
models, whe eas o he , e.g., 3D-p in ed models, gene a e s ochas ic (noisy) ou pu s.
The e o e, epea s should be conside ed o he s ochas ic models, o imp o e he
quali y o he measu ed alues.
(S-6) Collec esul s. Besides he se o pai s {(~x(k), y(k)
j)}, o k= 1, . . . , and j=
1, . . . , p, addi ional esul s {(~x(m), y(m)
l)}, o m= 1, . . . , s and l= 1, . . . , q, e.g., om
his o ical da a o da a om he li e a u e, can be used in he cons uc ion o he
me amodels.
(S-7) Selec supe ised models. The whole inpu pa ame e se , ~x( )= (~x( )
g, ~xp)as well
as he co esponding ou pu alues a e needed o hese models. In gene al, se -
e al design poin s and hei co esponding ou pu alues om one o mo e models
(i= 1, . . . , n), i.e., {~x(k), y(k)
i}s
k=1 a e manda o y o building models. Fo example,
a simple linea eg ession model o se en independen a iables ~xg={x1, . . . , x7}
equi es eigh design poin s (s= 8).
(S-8) Build me amodel. The me amodel combines in o ma ion om se e al models,
say Fi, which equi e he speci ica ion o independen a iables, ~x, and dependen
a iables, yi. The me amodel will be e e ed o as F∗. Using me hods desc ibed
by Ba z-Beiels ein [2016b], he models could be s acked. Ins ead o s acking, a
weigh ed combina ion o models Fican be used. Al e na i ely, co-k iging, which is
also a popula me hod ha combines esul s om ine and coa se g ained models,
can be used.
(S-9) Op imize on he me amodel. The model F∗is used as a su oga e o pe o ming
he op imiza ion s ep. The op imiza ion esul s in a new se o p omising geome y
pa ame e s, which will be e alua ed in he ollowing s ep. The e o e, he coun e o
he numbe o pa ame e se s is inc emen ed and he new design can be e e ed
o as ~x( )
g. Ins ead o inc easing by one, se e al new design poin s can be added o
he pa ame e se . Fo a la ge numbe o expe imen al op imiza ion p oblems, he
cos o objec i e unc ion e alua ions plays an impo an ole. Expe imen s may e-
qui e ime, wo king-hou s o an ope a o o ma e ial esou ces. Hence, op imiza ion
algo i hms should equi e as ew e alua ions as possible.
(S-10) Check he e mina ion c i e ion. I he budge , i.e., simula ion ime, is ex-
haus ed o he desi ed solu ion quali y is eached, he p ocess is s opped and he
esul is p esen ed. The a ious models may ha e dis inc e mina ion c i e ia. Fo
example, he a ailabili y ime o a 3D p in e , o he a ailabili y o ma e ial e-
sou ces may be dis inc om he compu e simula ions.
(S-11) S o e he op imized design. Op ionally, i can be added o a da abase.
To illus a e his me hodology, we will conside he cyclone op imiza ion p oblem.
Ob iously, he op imiza ion ia simula ion me hodology is no es ic ed o he cyclone
op imiza ion p oblem. Resul s om ou s udy can be ans e ed o many o he appli-
ca ions.
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
A:14 Thomas Ba z-Beiels ein e al.
Table V. Summa y o he esul s om di e en modeling app oaches. O e all collec ion e iciency E(in %) as
de ined in Eq. 5 o h ee di e en cyclone ypes, h ee di e en ou le pipe imme sions (h ), and ou di e en
modeling app oaches (M-A), (M-C), (M-P), and (M-S). 3D-p in column (M-P) shows mean (and s anda d de ia ion)
om i e epea s. The column (M-P∗) con ains he same alues as (M-P), whe e h ee ob ious ou lie s we e
emo ed. Values in column (M-S) a e based on Eq. (6).
Type h (M-A) (M-C) (M-P) (M-P∗) (M-S)
L¨
o le 0 90.19 97.98 86.8(±4.39) 86.8(±4.39) 89.80
L¨
o le 35 89.49 97.89 94.5(±6.92) 92.13(±5.12) 88.95
L¨
o le 44 89.27 98.03 90.83(±3.84) 90.83(±3.84) 88.73
Muschelknau z 0 91.14 97.37 72.53(±17.79) 78.92(±12.27) 92.13
Muschelknau z 35 90.37 97.92 86.83(±9.55) 86.83(±9.55) 91.28
Muschelknau z 44 90.15 98.15 92.87(±2.94) 92.87(±2.94) 91.06
S ai mand 0 89.33 96.17 90.53(±5.68) 90.53(±5.68) 88.79
S ai mand 35 88.70 97.8 95.43(±2.81) 94.29(±1.34) 87.93
S ai mand 44 88.45 97.8 95.5(±2.5) 95.5(±2.5) 87.71
●
●
●
●
0.L 35.L 44.L 0.M 35.M 44.M 0.S 35.S 44.S
50 60 70 80 90 100
Collec ion e iciency
Fig. 4. Box plo s o he 3D-p in da a. The da a a e g ouped acco ding o h ∈ {0,33, , 45}and cyclone ype
(L = L¨
o le , M= Muschelkna z, S= S ai mand). The y-axis shows e iciency (%).
5.4. 3D-p in ing Model (M-P)
Expe imen s used s anda d labo a o y equipmen : E lenmeye lask, s and, p essu e
gauge, p ecision scale, and a acuum cleane . The expe imen al se up is illus a ed in
Figu e 5.
The ini s ep (S-1) comp ehends he selec ion o an ini ial design, ~xg. This design
is also used o o he model ypes, e.g., (M-C) and (M-A). I no expe imen al da a is
a ailable, s anda d geome ies om he li e a u e as shown in Table II can be used
as s a ing poin s. Design o expe imen me hodology can be used i planned expe -
imen s a e possible. Table III shows he pa ame e s o he p in ed cyclones. P ocess
pa ame e s, ~xp, as desc ibed in Table I a e used in addi ion.
The model building s ep (S-3) consis s o he (i) 3D compu e model gene a ion and
he (ii) p in ing s ep. The 3D models, desc ibed in he STe eoLi hog aphy, S anda d
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.

Op imiza ion ia Mul imodel Simula ion A:15
Fig. 5. Expe imen s using he 3D-p in ing model as desc ibed in Sec ion 5.4. Schema ic illus a ion o he
expe imen al se up.
Tessella ion Language (STL) a e c ea ed using a Py hon sc ip .1The Py hon sc ip
uses he F eeCad Py hon lib a y.2The sc ip c ea es a cyclone based on he geome y
pa ame e s. Cons uc ion o composi e objec s is s aigh o wa d. Fo example, i s a
unc ion o gene a e a solid body wi h a gi en heigh , diame e , and posi ion is used. To
gene a e a hollow objec , a second sligh ly bigge cylinde is c ea ed and he di e ence
o bo h is compu ed. The esul ing objec is a hollow pipe wi h he speci ied wall hick-
ness and heigh . The cylinde has o be used o all o he pa s, so he model is one
p in able objec and no a collec ion o sepa a e pa s. Finally, he model is expo ed o
an .STL ile. The .STL o ma is a 3D model which can be p in ed on a b oad numbe
o 3D p in e s. The h ee de i ed cyclone models a e shown in Figu e 6.
Today, a b oad a ie y o 3D p in e s as well as di e en ma e ials a e a ailable o
p in he cyclone. The p in ing echnique as well as he ma e ial ha e o mee ce ain
equi emen s. The cyclone has o be obus , because i is ixed in o posi ion o he
expe imen s and i has o wi hs and he low o ai and dus . Due o he hollow shape
o he cyclone a P oJe CJP 660p o p in e was chosen, which uses gypsum powde
(Visije PXL) as p in ing subs a e. This way he en i e cyclone can be p in ed in one
s ep, no suppo s uc u es ha e o be emo ed, and i is no necessa y o assemble he
p in e om pa s which would lea e seams ha could hinde he ai low. The gypsum
powde has o be ha dened a e su plus gypsum powde has been emo ed om he
in e io . A p oblem ha could a ise is buildup o s a ic cha ge in he cyclone. I he ma-
e ial is s a ically cha ged and he dus adhe es o i , he esul s a e unusable, because
i leads o luc ua ions and educed e iciency. Tha is why we used cyan ac yla e (“Col-
o Bon”), which yielded a su icien ly smoo h, hough s ill somewha ough su ace, a
he same ime gi ing he cyclone su icien s abili y. While many eal-wo ld cyclones
ha e o deal wi h ho lue gases, he expe imen s we e pe o med a oom empe a u e.
Signi ican ly highe empe a u es may equi e a di e en choice o ma e ial.
1h ps://www.py hon.o g/
2h p://www. eecadweb.o g
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A:16 Thomas Ba z-Beiels ein e al.
Fig. 6. F om le o igh : L¨
o le , Muschelknau z, S ai mand cyclones. The co esponding geome ies, ~xg,
a e speci ied in Table III.
P in ing a single cyclone model his way akes abou h ee hou s o he p in ing
p ocess, one hou o e inishing, dus emo al and in il a ion, and ano he hou o
cu ing.
Besides he selec ion o a p in e and ma e ial, he cha ac e is ics o he dus ha e o
be selec ed. The dis ibu ion o pa icle sizes should no a y o p e en luc ua ions in
he esul s. I he pa icles a e oo la ge, hey may be oo easy o sepa a e om he gas.
I he e a e oo many, hey may e en block he low inside he cyclone. I he pa icles
a e oo small, he ask o sepa a ion may become nea o impossible. The chosen dus is
silica sand wi h a maximal pa icle size o 63µm. I s pa icle size dis ibu ion is shown
in Table IV.
Fu he mo e, he measu emen s ha e o be clea ly speci ied. The same amoun o
dus , he e: 6 g, has o be used in e e y expe imen . The amoun o dus il e ed ou o
he ai de e mines he e iciency o a cyclone. I can ei he be measu ed by he amoun
in he ai a e i passes h ough o by he amoun in he ecep acle. I is easie o
measu e he second op ion. The ai p essu e has o be he same in each es . O he wise
he esul s a e no compa able. I can be measu ed in on o behind he cyclone.
To measu e he e iciency o di e en cyclones, he cyclones ha e o be in e change-
able. The dep h o he ou le pipe can be a iable. The dus ecep acle has o be e-
mo able o measu e i s con en s a e a es . The es o he se up is ixed o minimize
luc ua ions.
The expe imen s we e pe o med ollowing a s anda dized i e-s ep p ocedu e,
which can be summa ized as ollows:
(1) The cyclone is pu in o posi ion a he desi ed ou le pipe dep h.
(2) The weigh o he ecep acle is measu ed and used as a s a ing poin o he ol-
lowing es s. The ecep acle is hen pu in o posi ion and sealed. Meanwhile 6g o
dus , wi h a ole ance o 0.05g, a e p epa ed.
(3) The acuum cleane is s a ed. The p essu e gauge akes some ime o measu e. I
he p essu e is o , he sealing be ween he connec ion is checked. The se up is hen
adjus ed un il he p essu e eaches an accep able le el.
(4) A cons an a e o he dus is hen pu in o he cyclone h ough he inle pipe. A e
all dus is inse ed, he cyclone akes a ew seconds o p ocess he ai . The acuum
cleane is hen u ned o .
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
Op imiza ion ia Mul imodel Simula ion A:17
Table VI. Resul s om he 3 D p in ing expe imen s (M-P). De e mina ion o he collec ion e iciency o he L¨
o le
cyclone wi h ~xg aken om Table III. Simula esul s we e ob ained o he Muschelknau z and he S ai mand
cyclones.
Recep acle be-
o e (g)
Recep acle a -
e (g)
Di e ence (g) Dep h ou le
pipe (mm)
E iciency (%) A e age (%)
415.35 420.44 5.09 0 84.83
420.44 425.36 4.92 0 82
425.36 430.64 5.28 0 88
430.64 436.26 5.62 0 93.67
436.26 441.38 5.13 0 85.5 86.8(±4.39)
387 392.13 5.13 35 85.5
392.13 397.6 5.57 35 91.17
397.6 403.45 5.85 35 97.5
403.45 409.69 6.24 35 104
409.69 415.35 5.66 35 94.33 94.5(±6.92)
359.66 364.89 5.23 44 87.17
364.89 370.23 5.25 44 87.5
370.23 375.64 5.41 44 90.17
375.64 381.23 5.59 44 93.17
381.23 387 5.77 44 96.17 90.83(±3.84)
All 90.71
(5) The ecep acle is emo ed and weighed again. The di e ence be ween he s a -
ing weigh and he second weigh is calcula ed. The esul shows how e icien he
cyclone wo ked. The second weigh is used as he base weigh o he nex es .
Resul s om he 3D-p in ing expe imen s a e shown in column (M-P) in Table V. Box-
plo s, which isualize hese esul s a e shown in Figu e 4.
6. EXPERIMENTAL RESULTS
We discuss esul s om he 3D p in ing (M-P) expe imen s i s . As can be seen in Ta-
ble VI, he e iciency o he L¨
o le cyclone is app oxima ely 90%. Two measu emen s
wi h high e iciency alues (104% and 97.5%) a e lis ed in his able. This can be a
esul s o insu icien cleaning o he cyclone be ween es s. The p essu e migh also
lead o sligh ly highe o lowe e iciency, because i has o be modi ied du ing expe i-
men a ion. The highes a e age e iciency (94.5%) was eached wi h a dep h o 35mm.
Ze o imme sion dep h lead o he lowes esul (86,8%).
Summa ized esul s om he expe imen s wi h he Muschelknau z cyclone a e
shown in Table V. The e iciency o he Muschelknau z cyclone is a ound 84%. Ex-
eme ou lie s can be ound a a dep h o 0mm. The esul s a 35mm dep h luc ua e
hea ily as well. The bes a e age e iciency is eached wi h a dep h o 44 mm. The
e iciency lowe s ela i e o he dep h, as can be seen in Figu e 4.
Acco ding o he (M-P) column in Table V, he S ai mand cyclone has he highes a -
e age e iciency. The e iciency a e e y dep h is highe han he p e ious wo cyclones
wi h he same dep h. The e a e ewe luc ua ions in he esul s. The only ou lie s can
be ound a he beginning o e e y se ies o es s. These ou lie s may be caused by dus
pa icles om p e ious expe imen s. The cyclone has no la ge di e ence be ween a
dep h o 35 and 44 mm, as can be seen in Figu e 4.
A e emo ing ob ious ou lie s, e.g., e iciencies la ge han 100%, he alues om
column (M-P∗) we e ob ained. Resul s om he 3-D p in ing expe imen s (M-P) can
be summa ized as ollows: (i) he e a e high a iances in he measu ed alues, and
(ii) he expe imen al esul s indica e ha he collec ion e iciency, E, inc eases wi h
inc easing o ex inde imme sion (h ) alues.
In addi ion o he discussion o he esul s om he 3D p in ing expe imen s, we
conside esul s om he CFD simula ions and om he analy ical model. E iciency
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
A:18 Thomas Ba z-Beiels ein e al.
alues, which a e based on he CFD simula ions a e gene ally highe han alues om
o he simula ions. Again, he e a e high a iances in he measu ed alues, and he
expe imen al esul s indica e ha he collec ion e iciency inc eases wi h inc easing
o ex inde imme sion alues. In e es ingly, da a om he analy ical model (M-A)
show a nega i e e ec o he imme sion leng h, h , on he e iciency: smalle h alues
esul in an inc eased collec ion e iciency E.
O e all, he e a e se e al inconsis encies in he da a ha ha e o be cla i ied. The
equi ed s eps o ix hese p oblems a e ob ious: he a iance in he (M-P) model can
be educed by imp o ing he expe imen al p ocedu e, e.g., by keeping he ope a ing pa-
ame e s cons an du ing expe imen a ion. Addi ional ecommenda ions will be p e-
sen ed in Sec ion 9. Howe e , e en i he da a i sel do no enable o d aw eliable
conclusions o designing an op imal cyclone geome y, hey a e sui able o demon-
s a ing he op imiza ion ia mul imodel simula ion app oach.
7. ENSEMBLE BUILDING
S ep (S-8) o he p oposed me hodology uses an ensemble engine o combine esul s
om se e al models. I uses he collec ed esul s om s ep (S-6). In con as o he
model ypes used in s eps (S-3) o (S-5), he models in s ep (S-8) equi e da a wi h inpu
and ou pu alues. This co esponds o supe ised lea ning in machine lea ning. I can
be b ie ly ou lined as ollows: The ich a ie y o su oga e models includes app oaches
such as eg ession ees and andom o es , leas angle eg ession (LARS), and K ig-
ing. The ensemble engine uses c oss alida ion o selec an imp o ed model om he
po olio o candida e models [ an de Laan and Dudoi 2003]. I implemen s me hods
o c ea ing a weigh ed combina ion o se e al su oga e models o build he imp o ed
model and me hods, which use s acked gene aliza ion o combine se e al le el-0 mod-
els o di e en ypes wi h one le el-1 model in o an ensemble [Wolpe 1992]. The
le el-1 aining algo i hm is ypically a ela i ely simple linea model. The s acked
gene aliza ion app oach is de ailed in Ba z-Beiels ein [2016b]. As le el-0 models, a
simple eg ession model (lm), a eg ession ee ( ) , a andom o es ( ), and a K ig-
ing (k ) model we e used in his s udy. The le el-1 model, which combines esul s om
he le el-0 models, uses he ollowing coe icien s:
Ensemble (le el-1) :−213.41 + 0.31 lm + 0.77 −1.95 −0.45k
i.e., he s acked model uses mainly he in o ma ion om he eg ession ee ( ) su -
oga e (le el-0) model, bu includes in o ma ion om he o he su oga e models as
well.
8. METAMODEL-BASED OPTIMIZATION
The me amodel F∗ om Sec ion 7 can be used o op imizing he geome y pa ame e s
~xg. This is s ep (S-9) in he op imiza ion ia mul imodel simula ion app oach. To illus-
a e he op imiza ion s ep, he R package SPOT2 can be used. The package SPOT2 is
he mos ecen e sion o he sequen ial pa ame e op imiza ion (SPO), which imple-
men s se e al ools o he analysis and op imiza ion o complex p oblems. I combines
me hods om design o expe imen s, esponse su ace me hodology,design and analy-
sis o compu e expe imen s, and eg ession ees o he analysis o algo i hms [Ba z-
Beiels ein e al. 2005]. The R sc ip ba 16eOp imiza ionViaMul imodelSimula ion.R,
which explains he op imiza ion s ep can be downloaded om he au ho ’s webpage.
On he same page, he SPOT2 package can be ound.
A e collec ing esul s (s ep S-6) om he di e en models, e.g., (M-P), (M-C), o (M-
A), he esul s a e collec ed and can be loaded as an R da a. ame. A se o su oga e
models ha e o be chosen (s ep S-7). To exempli y his s ep, a linea eg ession model, a
andom o es , a eg ession ee and a K iging model, we e chosen. The SPO2 unc ion
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
Op imiza ion ia Mul imodel Simula ion A:19
he be D h hz Da Du
lowe
op imum
uppe
pa ame e
0 20 40 60 80 100 120
Fig. 7. Op imiza ion on he me amodel (S-9). Ba plo o he op imized geome y pa ame e s. Compa ing
lowe and uppe bound o decision space wi h op imum.
buildEnsembleS ack implemen s he me amodel building s ep (S-8). A e gene a ing
an objec i e unc ion om he i , an op imize can be applied. In ou example, di e -
en ial e olu ion was use, bu any o he op imize is ine.
Resul s om he op imiza ion a e as ollows: he= 0.13,be= 0.06,D = 0.06,h =
0.29,hz= 0.19,Da= 0.73,Du= 0.03. All alues a e ela i e o he cyclone heigh
h0= 160mm. This geome y esul s in an es ima ed e iciency o 95.35 %. The alues
a e also shown in he las ow o Table II. Resul s om his op imiza ion a e shown
in Figu e 7. This igu e illus a es he ecommenda ions om he op imiza ion on he
me amodel. Fo example, he imme sion leng h, h , should be inc eased, whe eas he
diame e o he o ex inde , D should be dec eased.
I he e mina ion c i e ia a e no ul illed, hese ecommenda ions can be used o
p in a new cyclone (M-P) o o pe o m a CFD simula ion and s a he nex i e a ion
o he op imiza ion ia mul imodel simula ion loop as in oduced in Figu e 1.
9. CONCLUSIONS
This a icle explo es a new app oach o combining di e en simula ion app oaches.
Based on a s acking, a lexible me hodology o combining esul s om di e en models
is p esen ed. I is demons a ed, how esul s om wo di e en modeling app oaches,
namely,
(1) models ha equi e only inpu alues, i.e. (M-A), (M-P), and (M-C), and
(2) models, ha equi e inpu and ou pu alues, i.e., (M-S),
can be combined. I da a is sca ce and simula ion is expensi e, he p oposed op imiza-
ion ia mul imodel simula ion is a p omising way. Howe e , esea ch ques ion (Q-1)
“A e he e any bene i s in combining di e en simula ion app oaches?” canno be con-
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.

A:20 Thomas Ba z-Beiels ein e al.
clusi ely answe ed. The expe imen e s, who ca ied ou he 3D p in ing expe imen s,
aced unp edic able echnical di icul ies. Expe ience om p ac ice plays a c ucial ole
o hese expe imen s. Fi s esul s indica e ha he weakness o one app oach can be
compensa ed by o he app oaches, bu needs u he in es iga ions. This ques ion was
o mula ed as esea ch ques ion (Q-2) in he in oduc ion.
This emainde o his a icle summa izes impo an expe iences om ou s udy.
Fi s , we discuss p oblems ela ed o he 3D-p in ing app oach. Then, we will discuss
he op imiza ion ia mul imodel simula ion app oach.
9.1. Technical Recommenda ions (3D-p in ing)
One impo an goal o his s udy was he explo a ion o di icul ies in eg a ing a 3D-
p in ing app oach in o he op imiza ion loop, using u ili ies om a s anda d labo a-
o y.
(1) I was possible o 3D p in wo king cyclones wi h a ying pa ame e s. Once he
p ocedu e is cla i ied, i is easy (bu ime consuming) o c ea e new cyclones.
(2) One possible p oblem is he used ma e ial in he 3D-p in ing p ocess. The chosen
ma e ial has a a he ough ex u e, which collec s dus and p oduces luc ua ing
esul s. A be e al e na i e would be a smoo he su ace. This can be achie ed
h ough a di e en ma e ial, sealing he ough su ace o modi ying he p in ing
p ocess.
(3) The e we e high luc ua ions in he esul s because he cyclones we e no cleansed
o dus a e each es s. Doing so would ha e esul ed in a high wo kload and sp ead-
ing he dus in he lab.
(4) Gua an eeing a cons an ai p essu e was a di icul ask. Fluc ua ions in he p es-
su e caused high a iance in he expe imen al esul s. The used p essu e migh be
o low o usable esul s. A highe p essu e would equi e a p essu e gauge ha can
measu e in a highe ange o ensu e ha he p essu e s ays cons an .
(5) The chosen dus has a speci ic size dis ibu ion. O he ma e ial, e.g., sawdus ,
migh need highe p essu e o low h ough he cyclone. This is because di e en
dus pa icles can ha e a ying size, shape, o densi y.
(6) The sealing could be imp o ed and he suc ion powe should be kep cons an .
(7) While es ing he i s cyclone (L¨
o le ), i was ha d o inse he dus in o he
cyclone. To simpli y he in ill p ocedu e new cyclones we e p in ed wi h ounded
opening ha poin s o he op. This design was chosen, because i does no a ec
he low inside and makes i easie o inse dus . The di e en cyclones we e hen
measu ed o hei e iciency in a se ies o es s. I would also be bene icial o ind
an au oma ed, mo e uni o m dus inse ion p ocedu e.
(8) The cyclones ha we e p in ed a e o small size. La ge cyclones (h > 200 mm)
migh esul in a obus beha io o he cyclone.
Besides hese echnical di icul ies om he 3D-p in ing app oach, he e a e addi-
ional p oblems, which e e o he o he models as well. Recommenda ions based on
ou expe iences can be lis ed as ollows.
9.2. S a is ical Recommenda ions
(1) Collec ion e iciency alues, which a e based on he analy ical model (M-A) and he
3D-p in ing models a e in he same ange (app oxima ely 90%). Su p isingly, alues
om he CFD-based models (M-C) a e signi ican ly highe . These esul s indica e,
ha a model alida ion is necessa y. Valida ion analyzes he au hen ici y o he
model, i.e., how closely he model ep esen s a eal sys em. Model assump ions a e
e iewed by expe s, a ious da a se ings a e es ed, and independen es da a a e
used o compa ison [Law and Kel on 2000].
ACM Jou nal Name, Vol. V, No. N, A icle A, Publica ion da e: No embe 2016.
Op imiza ion ia Mul imodel Simula ion A:21
(2) Expe imen s should be epea ed i unusual alues occu . O , hese da a should no
be conside ed i a plausible explana ion o his beha io can be gi en. Only a e y
mode a e da a p ep ocessing was pe o med in his s udy. Fo example, expe imen-
al esul s which a e e y implausible we e emo ed. This esul s in he alues
epo ed in column (M-P∗) in Table V. Each expe imen was epea ed i e imes. As
a ule o humb, we ecommend ha each expe imen should be epea ed a leas
en imes.
(3) I was no possible o de e mine a ule o humb o an e icien cyclone. The esul s
show ha he e was no pe ec cyclone, bu some cyclones we e be e a di e en
ou le pipe dep hs. Based on columns (M-C) and (M-P) om Table V, he S ai mand
cyclone wi h 35 and 44 mm imme sion dep h has a highe e iciency han he o he
cyclones. A dep h o 0 mm usually p oduces highe luc ua ions han a dep h o 35
o 44 mm. Al hough esul s a e app oxima ely in a simila ange (90-95%), no alid
conclusions could be d awn based on hese da a.
The esul s o he p oo o concep show he alidi y o he op imiza ion ia mul-
imodel simula ion app oach. Due o insu icien expe ience wi h he expe imen al
se up, he esul s in his a ea a e no ye conclusi e, bu hey demons a e how o
collec da a and how o combine esul s om di e en modeling app oaches.
This s udy was conside ed as a p oo -o -concep o he op imiza ion ia mul imodel
simula ion app oach. All s eps o he simula ion-op imiza ion amewo k we e es ed
and e alua ed. As a consequence o he posi i e e alua ion o his amewo k, u u e
wo k should deal wi h an ex ensi e op imiza ion ia mul imodel simula ion s udy,
which ocuses on he imp o ed cyclone geome ies.
APPENDIX
In his appendix, we desc ibe he supplemen a y R sou ce iles and he se o expe i-
men al da a, which was used in ou s udy.
(1) Ba 16eAllDa a.cs : This CSV ile con ains all da a used in his s udy.
(2) SPOT2 0.1. a .gz: R so wa e package equi ed o unning he analysis. To ins all
he package om sou ce, you can ei he use he R-command-line call:
ins all.packages(pkgs="SPOT2 0.1. a .gz", epos=NULL, ype="sou ce")
O you can use he RS udio IDE o ins all ia ”Tools - Ins all Packages ...”. No e,
ha you may equi e RTools i you ins all sou ce packages unde Windows: h ps:
//c an. -p ojec .o g/bin/windows/R ools/.
(3) ba 16eEda.R: This R sc ip was used o gene a e he boxplo s and o calcula e
means and s anda d de ia ions o he 3D-p in ing da a, i.e., columns (M-P) and
(M-P∗), in Table V.
(4) ba 16eOp imiza ionViaMul imodelSimula ion.R: This R sc ip was used o build
he me amodel and o un he op imiza ion s ep (S-9) on he me amodel F∗. The R
unc ions, which a e necessa y o building he me amodel, a e implemen ed in he
R package SPOT2.
The sou ce iles and he open sou ce R so wa e package SPOT2 can be downloaded
om he au ho ’s webpage: h p://www.gm. h-koeln.de/∼ba z/Ba 16e.d. The so wa e
package SPOT2 will also be made a ailable on CRAN (h ps://www. -p ojec .c an.o g).
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