Expe Sys ems Wi h Applica ions 208 (2022) 118039
A ailable online 8 July 2022
0957-4174/© 2022 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-
nc-nd/4.0/).
Sensi i i y analysis: A ool o ailo ing en i onmen ally iendly ma e ials
Da id Seidl
a
,
*
, I an Ruˇ
ziak
b
, Zo a Koˇ
s ialo ´
a Janˇ
cíko ´
a
a
, Pa el Koˇ
s ial
a
a
Facul y o Elec ical Enginee ing and Compu e Science, VSB Technical Uni e si y o Os a a, Czech Republic
b
Facul y o Wood Sciences and Technology, Technical Uni e si y, Z olen, Slo akia
ARTICLE INFO
Keywo ds:
Rubbe blends
Plas icize s
A i icial neu al ne wo ks
Sensi i i y analysis
P edic ions
ABSTRACT
In his a icle, we examine he use o sensi i i y analysis o he op imiza ion o selec ed physical p ope ies in
ubbe compounds and de e mine objec i e c i e ia which allow o he educ ion o en i onmen al load du ing
ubbe compound p oduc ion. The sensi i i y analysis shows how signi ican ly each inpu alue a ec s he
ou pu alue, and he esponse g aphs exp ess he e ec o he selec ed pa ame e on he ou pu alue. The
solu ions desc ibed in he a icle a e applicable o o he p oduc ion echnologies. We p esen a sensi i i y
analysis based on he p edic ion o selec ed mechanical p ope ies o ubbe mix u es composed o S anda d
Malaysian Rubbe (SMR). Two blends we e p e- pa ed by mixing SMR and oleic acid and di e en concen a ions
o su ac an (2, 4, 6, 8, 10, 20, 30 w %). Tensile s eng h R
m
and moduli M100, M200, M300 we e measu ed and
e alua ed. The sensi i i y analysis showed he signi icance o ce ain ing edien s which a ec he measu ed
mechanical p ope ies.
1. In oduc ion
Technological ea men s and he agen s o ille s added o ubbe
ha e a s ong e ec on se e al p ope ies o ubbe mix u es. Ca bon
black is an ac i e ille which is used o inc ease elec ical and he mal
p ope ies due o i s s ong in e ac ion wi h na u al ubbe . Plas icize s
play an impo an echnological ole in he ubbe indus y. Rubbe is a
mul icomponen ma e ial which is e y sensi i e o many chemical
species, and especially o echnological ea men . Fo mul icomponen
sys em inpu s and ou pu s associa ed wi h he op imiza ion o chemis y
o echnological p ocesses, i is con enien o use an a i icial neu al
ne wo k (ANN).
ANNs a e equen ly applied in ma e ial analysis, and in some cases
also ha e success ully eplaced des uc i e es ing in ibe composi es
(Fa hana e al., 2016).
T ue s ess/s ain cu es we e success ully calcula ed o he au o-
mobile indus y (Doh, Lee, & Lee, 2016), whe e he au ho s op imized
in e connec ion weigh s ob ained wi h hidden laye s and ou pu laye s.
A ma hema ical model o he ma e ial’s beha io was sugges ed h ough
his eed- o wa d neu al ne wo k.
The s udy Le, Y onne , and He (2015) applied a ini e elemen
me hod and an ANN o desc ibe su ace s ess in ma e ials.
A combina ion o an ANN and FEM was applied in a s udy o he
dynamic p ope ies in glass lamina es wi h di e en ma e ial shaping
(Seidl e al., 2011). Shape modes we e p esen ed o di e en ib a-
ional exci a ions.
ANNs we e used wi h success o op imize he composi ion o op ical
glasses (Seidl e al., 2011) and ob ain equi ed op ical p ope ies.
Feed o wa d neu al ne wo ks a e used o he classi ica ion o laye s
o coal and shale coal acco ding o ash and mois u e con en (Janˇ
cíko ´
a,
Boˇ
s´
ak, Zimný, Legoue a, Min´
a ik, Koˇ
s ial, & Poulain, 2014).
The wo k Ghosh, Cha e jee, and Shanke (2016) applied an ANN
and neu o- uzzy in e e ence sys em which sepa a ed pe mea e lux and
sal con en .
A mul i esolu ion analysis o ime-dependen da a se s ob ained
h ough Wa ele de- composi ion and e alua ed using an ANN was
applied o he managemen o enewable ene gy sou ces in he s udy
Salehi and Raza i (2016).
A sound s a is ical model analysis was de eloped based on deep
neu al ne wo ks. Using a new algo i hm on con en ional da a, he au-
ho s a ained subs an ially be e esul s (Doucou e, Agbossou, & Ca -
denas, 2016).
A discolo a ion p ocess analysis was conduc ed wi h he applica ion
o h ee in e media e laye s, a backp opaga ion lea ning algo i hm, and
a sigmoid ac i a ion unc ion implemen ed in Fo an. Th ee neu ons in
he in e media e laye p o ided he bes esul s Hwang, Pa k, and Chang
(2016).
Technological ea men s and he agen s o ille s added o ubbe
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (D. Seidl), [email p o ec ed] (I. Ruˇ
ziak), [email p o ec ed] (Z. Koˇ
s ialo ´
a Janˇ
cíko ´
a), [email p o ec ed] (P. Koˇ
s ial).
Con en s lis s a ailable a ScienceDi ec
Expe Sys ems Wi h Applica ions
jou nal homepage: www.else ie .com/loca e/eswa
h ps://doi.o g/10.1016/j.eswa.2022.118039
Recei ed 7 Feb ua y 2022; Recei ed in e ised o m 13 May 2022; Accep ed 30 June 2022
Expe Sys ems Wi h Applica ions 208 (2022) 118039
2
ha e a s ong e ec on se e al p ope ies o ubbe mix u es. The main
addi i es and hei unc ions we e desc ibed in Lenzi e al. (2016).
The pape Jonˇ
s a e al. (2011) examines he e ec o nano-s y ene
bu adiene ubbe in phenolic nanocomposi es. When applied in he
amoun o only se e al pe cen , hese nanopa icles subs an ially in-
c ease he no ched impac s eng h wi hou a signi ican change in
lexu al pe o mance.
The applica ion o ul asound du ing he ex usion p ocess o
di e en ubbe ypes showed changes due o die p essu e (Liu, Ma,
Zhan, & Wang, 2015). Inc easing he ul asound ampli ude dec eased
he die p essu e o bo h na u al ubbe and mix u es o na u al and
s y ene bu adiene ubbe . In he case o s y ene-bu adiene ubbe , he
die p essu e inc eased.
In (Choi & Isaye , 2015), he au ho s p esen ed liquid isop ene as a
eplacemen o oil plas icize . In his case, liquid isop ene educed bo h
Mooney and appa en iscosi y and supp essed plas icize mig a ion.
The wo k (Ren, Zhao, Li, Zhang, & Zhang, 2015) p esen ed an
imp o emen in he mechanical p ope ies o silica- illed ubbe caused
by a ing opening be ween ubbe chains and Si-OH g oups. Ring
opening p ocesses occu ed du ing bo h he ulcaniza ion and mixing
p ocesses.
Polye hylene-co- inyl ace a e, na u al ubbe and o ganoclay mix-
u es we e s udied in (Xu, Jia, Luo, Jia, & Peng, 2015). The addi ion o
o ganoclay supp essed he na u al ubbe amoun and aised Young’s
modulus and yield s ess. Elonga ion a b eak and s ess a b eak we e
dec eased.
The pape (Raza i-Nou i & Ka ami, 2014) s udied he pe cola ion
e ec and u he elec ic anspo phenomena caused by he p esence
o g aphi e.
Mansou , Hussein, and Moha am (2014) desc ibed he in luence o
ille s on na u al ubbe p ope ies. The esul s o di e en ille s
(including ca bon nano ubes) showed an inc ease in iscosi y c oss-link
densi y, modulus and ha dness and a dec ease in cu e ime. The plas i-
cize s in a ubbe blend inc eased hei p ocessing p ope ies. Ne e -
heless, hey o en mig a ed om he ubbe ma ix and caused poo
s abili y in he ubbe blend in he long e m. The ad e se en i on-
men al impac o his p ocess was also subs an ial.
Kopal e al. (2022) ha e p edic ed cu ing cha ac e is ics which play
a signi ican ole in he ulcaniza ion p ocess o ubbe blends using
ANN. Al hough some s udies, e.g. (Lubu a e al., 2021), (Sa a e al.,
2019), (Vodka & Pog ebnyak e al., 2020) and (Lopes, Sil a, & Machado,
2021), ha e used ANN ne wo ks o he p edic ion o di e en p ocesses
in ubbe echnology, hey ocused on he p edic ion o di e en pa-
ame e s bu none o hem ake in o accoun he en i onmen al aspec o
ubbe echnology. As he p oduc ion o ubbe compounds also has i s
en i onmen al impac , i is necessa y o ocus on he op imiza ion o
chemical compounds.
The aim o his pape is o e alua e he in luence o exis ing chem-
icals on he mechanical p ope ies o he mix u e in o de o educe
en i onmen al e ec s in he p oduc ion p ocess o ubbe compounds,
whe e he en i onmen al aspec is he main con ibu ion o his
esea ch. In he esea ch, we deal wi h he e ec o plas icize and he
amoun o su ac an on ce ain mechanical p ope ies such as s eng h
R
m
and moduli M100, M200, M300. The analysis me hod we applied
was based on ou p e ious expe imen al wo k (Ruˇ
ziak e al., 2018).
The a icle is s uc u ed as ollows: Sec ion 2 summa izes he heo y
o a i icial neu al ne wo ks. Sec ion 3 desc ibes he expe imen al con-
di ions. Sec ion 4 gi es a de ailed o e iew o esul s, and Sec ion 5 lis s
he conclusions a ising om he esea ch.
2. Theo y
A i icial neu al ne wo ks a e used o p edic ma e ial p ope ies
when an analy ical ma hema ical app oxima ion canno be ound. Using
his e y obus ma hema ical ool, ma e ial p ope ies can be p edic ed.
A i icial neu al ne wo ks use di e en opologies which, in mos
cases, con ain h ee o ou laye s. Th ee ypes o neu ons occu in hese
ne wo ks:
•inpu neu ons
•hidden neu ons
•ou pu neu ons.
Inpu neu ons con ain in o ma ion abou he pa ame e s which
change in ou da ashee , such as ma e ial composi ion, he mal ea -
men , and o he s. Ou pu neu ons co espond o he ma e ial p ope ies
we wan o p edic . Some o he inpu neu ons a e used o aining and
o he s a e used o gene alizing.
The ad an age o a neu al ne wo k is ha i can bo h lea n and
gene alize. The main disad an age o a neu al ne wo k is ha i needs
mo e alues o one o mo e pa ame e s which change in each inpu
da ase han equi ed by s anda d i ing p ocedu es such as he leas
squa es and o he me hods.
The use o an ANN is es ed wi h he s a is ical pa ame e s REL_RMSE
and R
2
, which a e de ined by Eqs. (1) and (2).
RMSE =
∑n
i=1(yi−oi)2
n.(n−1)
√(1)
R2=(E(y).E(o)
E(y.o))2
(2)
whe e:
y
i
−measu ed alues o
i
−p edic ed alues.
n −numbe o inpu alues.
E (y) −s a is ical mean alue o inpu s.
E (o) −s a is ical mean alue o p edic ed alues.
E (y.o) −mean alue o mul iplica ion o p edic ed and inpu alues.
3. Expe imen al condi ions
3.1. Ma e ials
Plas icize s play an impo an ole in ubbe echnology and ha e an
e ec on he blend mixing. We he e o e p esen he e ec o he amoun
o plas icize on selec ed mechanical p ope ies such as s eng h R
m,
modulus M100, M200 and M300. The expe imen al alues we e
measu ed on he appa a us Z250 All oundLine (250 kN). The ensile
s eng h R
m
and moduli M100, M200, M300 measu emen s we e pe -
o med on his de ice by ensile es .
The chemical composi ion o s anda d ubbe mix u e in PHR (pa s
pe hund ed o ubbe ) is shown in Table 1. The ubbe was SMR
(S anda d Malaysian Rubbe ).
Sul enax is used in ubbe indus y in p ocessing o na u al and
syn he ic ubbe in ubbe compounds as a as accele a o o ulcani-
za ion wi h delayed ac ion. I p o ides good physical and mechanical
p ope ies, high c osslinking e iciency and good modulus. N339 CB is a
ype o ca bon black (CB) and Gumodex is a plas icize .
The gene al p ocedu e o he ubbe ulcaniza es p epa a ion is as
ollows and is p o ec ed by he manu ac u e . In he wo-s age mixing,
which we used in ou case, he mix u e is p epa ed in he i s phase a a
Table 1
Chemical composi ion o s anda d ubbe mix u e.
Ing edien PHR con en
SMR 100
Sulphu 2
ZnO 5
S ea ine 2
Sul enax 2
N339 CB 50
Gumodex 10
D. Seidl e al.
Expe Sys ems Wi h Applica ions 208 (2022) 118039
3
empe a u e o abou 150◦C. The p essu e exe ed by he kneading
wedge is abou 3 MPa and he mixing ime is 4 o 4.5 min. These pa-
ame e s depend on he ype o mix u e. The hickness o he bel is
de e mined by he gap be ween he olle s. To p e en he mix u e om
s icking, i is imme sed in a we ing ba h con aining a sepa a ion
solu ion. The empe a u e o he e luen mix u e is a maximum o 36◦C.
In he second s age o mixing he mix u e ( inal mix u e), he mix u e
is weighed again in he o m o a chopped honeycomb. I is i s p o-
cessed in a mixe , and when he equi ed plas ici y is eached, he
ulcanizing agen and o he subs ances a e added. The empe a u e o
he mixing chambe is lowe han in he p e ious mixing (abou 110◦C)
and he mixing akes a e y sho ime.
The e e ence samples we e mixed wi h oleic acid plas icize wi h a
con en o 1 PHR and 3 PHR, oge he wi h weigh pe cen age o su -
ac an (0, 2, 4, 6, 8, 10, 20, 30 w %). The su ac an was sodium 1-
Table 2
Numbe o hidden uni s.
Type o ne wo k Minimum hidden inpu s Maximum hidden inpu s
Radial basis unc ion RBF 1 8
Th ee-laye MLP, laye 2 1 16
Fou -laye MLP, laye 2 1 16
Fou -laye MLP, laye 3 1 16
Table 3
Bes neu al ne wo ks.
P ope y De ails o ne wo k
R
m
[MPa] MLP 2:2–16-6:6
M100 [MPa] MLP 2:2–16-6:6
M200 [MPa] MLP 2:2–16-16–6:6
M300 [MPa] MLP 2:2–16-16–6:6
Fig. 1. MLP2:2-16-6:6 is bes ne wo k o he p edic ion o ensile s eng h R
m
and modulus M100.
Fig. 2. MLP2:2-16-16-6:6 id he bes ne wo k o moduli M200 and M300.
Table 4
Slope be ween he p edic ed and measu ed cha ac e is ics, pe cen age de iance,
co ela ion coe icien R and mean squa ed e o RMSE.
P ope y Slope Pe cen age di e ence (%) R RMSE (MPa)
R
m
[MPa] 1,048 +4,8 0,982 0,082
M100 [MPa] 0,983 −1,7 0,985 0,028
M200 [MPa] 0,999 −0,1 0,978 0,068
M300 [MPa] 0,938 −6,2 0,981 0,095
Table 5
Sensi i i y coe icien s o he inpu pa ame e s o all he s udied mechanical
cha ac e is ics.
P ope y/Sensi i i y coe icien Su ac an w % Oleic acid amoun
R
m
[MPa] 2.491 1.163
M100 [MPa] 2.632 1.159
M200 [MPa] 2.931 1.203
M300 [MPa] 2.514 1.073
Fig. 3. Es ima ed R
m
alues e sus he eal measu ed alues in he subg oup o
16 alues.
Fig. 4. Es ima ed M100 alues e sus he eal measu ed alues in he subg oup
o 16 alues.
D. Seidl e al.
Expe Sys ems Wi h Applica ions 208 (2022) 118039
4
nonyl-2-(2-nonylphenoxy benzene sul a e). These amphiphilic sub-
s ances educe he su ace ension o he luids and he in e acial en-
sion be ween wo liquids. The use o oleic acid plas icize as a subs i u e
o gumodex has a lowe ecological impac .
3.2. Sensi i i y analysis
The sensi i i y analysis me hod applied in he s udy allows o a
s a is ical analysis o he e ec o echnological p ocesses on he me-
chanical p ope ies o he ubbe blend (in his case). The esponse
g aphs, which a e addi ional esul s om he ANN p ocedu es, indica e
he alues o he s udied p ope ies in combina ions o inpu pa ame e s
which we e no measu ed.
Neu al ne wo ks we e c ea ed in STATISTICA – Neu al Ne wo ks
so wa e. Neu al ne wo k so wa e enables he execu ion o a sensi i i y
analysis and he c ea ion o esponse g aphs. The sensi i i y analysis
e eals how signi ican ly each inpu alue a ec s he ou pu alue, and
he esponse g aphs exp ess he e ec o he selec ed pa ame e on he
ou pu alue.
A neu al ne wo k conduc s a sensi i i y analysis by ea ing each
inpu a iable in u n as i i we e “una ailable”. Each model de ines a
missing alue subs i u ion p ocedu e o allow p edic ions in he absence
o alues o one o mo e inpu s. To de ine he sensi i i y o a pa icula
a iable, we i s un he ne wo k on a se o es cases and accumula e
he ne wo k e o . We hen un he ne wo k again using he same cases,
bu his ime eplace he obse ed alues wi h he alue es ima ed by he
missing alue p ocedu e, and again he ne wo k e o accumula es.
Gi en ha we e ec i ely emo e some in o ma ion which he
ne wo k p esumably uses (i.e., one o i s inpu a iables), we would
easonably expec some de e io a ion in e o o occu . The basic mea-
su e o sensi i i y is he a io o he e o wi h he missing alue sub-
s i u ion and he o iginal e o . The mo e sensi i e he ne wo k is o a
pa icula inpu , he g ea e he de e io a ion we can expec and
he e o e he g ea e he a io. I he a io is one o less, hen making he
a iable “una ailable” ei he has no e ec on he pe o mance o he
ne wo k o enhances i s pe o mance. This means ha he s udied
p ope y is no a unc ion o he “missing” inpu pa ame e .
Fig. 5. Es ima ed M200 alues e sus he eal measu ed alues in he subg oup
o 16 alues.
Fig. 6. Es ima ed M300 alues e sus he eal measu ed alues in he subg oup
o 16 alues.
Fig. 7. P edic ion o ensile s eng h R
m
e sus su ac an amoun .
D. Seidl e al.
Expe Sys ems Wi h Applica ions 208 (2022) 118039
5
Fo he neu al ne wo k inpu pa ame e s, we used he su ac an
amoun as a con inuous neu on inpu and he oleic acid amoun as a
ca ego ical neu on inpu . We selec ed oleic acid as a ca ego ical inpu
because he s udied ma e ials only con ain wo di e en alues o his
inpu pa ame e , which is a e y low le el o lea ning and gene aliza-
ion. The measu ed alues o he mechanical p ope ies we e used as
con inuous neu on ou pu s. Since he concen a ions o he su ac an
equaled 0, 2, 4, 6, 8, 10, 20, and 30 w % and he wo concen a ions o
oleic acid we e 1 PHR and 3 PHR, he neu al ne wo ks lea ned wi h 16
inpu neu ons.
The o al analyzed neu al ne wo ks o each a iable and each s a e
consis ed o en neu al ne wo ks, om which we used he bes i e
neu al ne wo ks. The selec ion c i e ion o e ain a ne wo k was he
lowes e o . The ypes o ne wo k which we applied we e linea , PNN o
GRNN, Radial Basis unc ion, h ee laye and ou -laye pe cep on.
The minimum and maximum alues o he hidden inpu s o each
Fig. 8. P edic ion o modulus M100 e sus su ac an amoun .
Fig. 9. P edic ion o modulus M200 e sus su ac an amoun .
D. Seidl e al.

Expe Sys ems Wi h Applica ions 208 (2022) 118039
6
ne wo k a e shown in Table 2.
4. Resul s
We p esen de ails o he imp o ed eal ime ne wo ks.
In he inal s ep, we compu ed he p edic ions o all i e bes neu al
ne wo ks and com- pa ed hem o he measu ed alues in he eaching
subse . As he bes neu al ne wo k, we used a neu al ne wo k in which
he co ela ion be ween he measu ed and ANN ap- p oxima ed ne wo k
we e closes o 1 by sus aining he oo mean squa e e o be ween he
measu ed and app oxima ed alues closes o ze o. The bes neu al
ne wo ks o each a iable a e lis ed in Table 3.
whe e MLP e e s o he mul ilaye pe cep on ne wo k.
Figs. 1 and 2 p esen he bes ne wo k o moduli 100, 200 and 300.
Table 4 p esen s he slope alues be ween he p edic ed alues o he
s udied mechanical cha ac e is ics and he eal measu ed alues. The
able also p esen s de iances o his slope om he alue o 1 (i cha -
ac e izes he de iance) and he co ela ion coe icien , oge he wi h he
mean squa ed e o RMS.
Based on he esul s p esen ed in Table 4, we can d aw he ollowing
conclusions:
The maximal size o he e o in de e mining he mechanical cha -
ac e is ics by neu on ne wo ks in a 16-membe base is 6.2% ( o he
M300 cha ac e is ic), which is below he measu ing e o limi o he
s a ed mechanical cha ac e is ics o ubbe compounds.
Since he e o in de e mining mechanical cha ac e is ics o neu al
ne wo ks is smalle han he measu ing e o , we can s a e ha ANN a e
able o p edic ensile s eng h and s eng h o he M100, M200, M300
samples be o e ageing.
The s a ed conclusion is also suppo ed by high alues o he co e-
la ion coe icien – a leas 0.978.
The maximal mean squa ed e o be ween he p edic ed and
measu ed alues o he mechanical cha ac e is ics is 0.095 MPa, which
is a he measu abili y limi o he gi en cha ac e is ics.
Mo e use ul pa ame e o assessing he di e ences be ween he
p edic ed and measu ed alues o mechanical cha ac e is ics is he
ela i e mean squa ed e o , de ined as a quo ien o he mean squa ed
e o and he minimal alue o he gi en.
This pa ame e amoun s o 0.005; 0.008; 0.009 and 0.009 o he
ensile s eng h and he M100, M200 and M300 moduli, which co e-
spond o he pe cen age de ia ion o 0.5% o he ensile s eng h, 0.8%
o he M100 modulus and 0.9% o he M200 and M300 moduli.
•These alues ep esen he maximal de iance be ween he p edic ed
and measu ed cha -ac e is ics, wi h he s ipula ion ha hey a e a
leas 10 imes smalle han he unce ain ies in de e mining he
s udied mechanical cha ac e is ics.
•The heo e ical e o in de e mining he mechanical p ope ies o
ubbe compounds based on a leas 10 es specimens is app oxi-
ma ely equal o 5%. The expe imen ally de ec ed e o s in he
de e mina ion o Rm, M100, M200 and M300 o all measu ed
sample ypes and all p ope ies do no exceed he e o alue o 5%.
Based on diag ams 3 o 6, we can d aw he ollowing conclusions:
All he s udied ma e ial p ope ies inc eased along wi h a ise in he
amoun o oleic acid and su ac an .
•Tensile s eng h inc eased app ox. 29% o 1 PHR and 22% o 3
PHR.
•Modulus M100 inc eased app ox. 53% o 1 PHR and 46% o 3PHR.
•Modulus M200 inc eases app ox. 51% o 1 PHR and 44% o 3PHR.
•Modulus M300 inc eases app ox. 53% o 1 PHR and 45% o 3PHR.
Fig. 10. P edic ion o modulus M300 e sus su ac an amoun .
Table 6
To al sha e o he sha e o he su ac an and he olume o oleic acid o he
s udied mechanical cha ac e is ics.
P ope y/Sensi i i y coe icien Su ac an w % Oleic acid amoun
R
m
[MPa] 68.2 % 31.8 %
M100 [MPa] 69.4 % 30.6 %
M200 [MPa] 70.9 % 29.1 %
M300 [MPa] 70.1 % 29.9 %
D. Seidl e al.
Expe Sys ems Wi h Applica ions 208 (2022) 118039
7
•All hese inc eases a e highly abo e he p ope y measu emen un-
ce ain y; he e o e, he su ac an weigh pe cen age has a signi i-
can ole in he ensile s eng h and moduli.
•The di e ences be ween 1 PHR and 3 PHR in inc ease we e 7%, 7%,
7%, and 8%, which a e all below he measu emen e o s o hese
ypes o ubbe blends, and we can he e o e conclude ha he e ec
o su ac an weigh pe cen age is app oxima ely he same o 1 PHR
and 3 PHR mix u es, which is also suppo ed by a e y high co e-
la ion coe icien .
•be ween he p edic ions and measu emen s o bo h 1 PHR and 3
PHR mix u es.
•The inc ease in R
m
was p obably caused by a highe deg ee o
s uc u e c oss- linking Sk obak e al. (2016).
In he ollowing esul s, we show p edic ions o he s udied p ope -
ies. Because o same inc ease in he s udied mechanical p ope ies o 1
PHR and 3 PHR oleic acid mix u es, we show he p edic ion o he
a e age alues o p ope y e sus su ac an amoun .
Fo each neu al model esponse, g aphs we e c ea ed. The esponse
g aphs exp ess he in luence o he chosen inpu pa ame e on he p e-
dic ed ou pu pa ame e – see Figs. 7-10. These g aphs exp ess he in-
luence o he su ac an amoun on he p edic ed mechanical
p ope ies. Fig. 7 shows he p edic ion o ensile s eng h, while Figs. 8-
10 show he p edic ion esul s o modulus M100, M200 and M300
espec i ely.
Based on Figs. 7-10, we can d aw he ollowing conclusions:
•The bigges change in he s udied mechanical cha ac e is ics wi h a
change in he sha e o he su ac an can be obse ed wi hin he
weigh pe cen age ange o 0 o 10%; he e ec o he su ac an is
educed o e 10%.
•An inc ease in he alues o he s udied mechanical cha ac e is ics o
up o 10% ep e- sen s 12%; 27%; 26% and 22%, while he inc ease
o up o 30% in he weigh pe cen age o he su ac an only co e-
sponds o inc eases o 25.5%; 49.5%; 47.5% and 49%.
•An inc ease in he sha e o he su ac an by 1/3 o he o e all in-
c ease leads o a 48% inc ease o he o al inc ease o he ensile
s eng h R
m
.
•An inc ease in he sha e o he su ac an by 1/3 o he o e all in-
c ease leads o a 55% inc ease in he o al inc ease o he M100
modulus.
•An inc ease in he sha e o he su ac an by 1/3 o he o e all in-
c ease leads o a 55% inc ease in he o al inc ease o he M200
modulus.
•An inc ease in he sha e o he su ac an by 1/3 o he o e all in-
c ease leads o a 45% inc ease in he o al inc ease o he M300
modulus.
•On he o he hand, an inc ease in he su ac an by 2/3 o he o e all
inc ease leads o an inc ease in he ensile s eng h and o he M100,
M200 and M300 moduli by 82.5%; 85%; 87.5% and 91%.
•Such an inc ease o a 20% sha e o he su ac an is su icien o
imp o ing he s udied mechanical cha ac e is ics and, a he same
ime, educing he sha e o he su ac an has a posi i e impac on he
en i onmen al bu den o he inal mix u e o e ime since he inal
mix u e as well as su ac an age due o he impac o hea and ime.
Below, we discuss he sensi i i y analysis ob ained om he p edic-
ion using he ANN ne wo ks. Table 5 shows he sensi i i y coe icien s
o he inpu pa ame e s o all he s udied mechanical cha ac e is ics.
Based on Table 5, we can s a e ha :
•The inc ease in he e o by omi ing he sha e o he oleic acid (in
he way he sensi i i y coe icien s o neu al ne wo ks a e calcula ed)
amoun s o 16%, 16%, 20% and 7% o R
m
, M100, M200 and M300,
which is close o he measu ing e o , i.e., he change in he me-
chanical cha ac e is ics wi h a change in he sha e o he su ac an
can be desc ibed by a single unc ion o bo h concen a ions o he
oleic acid, which can be also deduced om Figs. 3-6.
•On he o he hand, he same ope a ion o he sha e o he su ac an
leads o, a leas , a 149% inc ease in he mechanical cha ac e is ics,
which means ha he su ac an has a signi ican ly g ea e e ec on
he mechanical cha ac e is ics.
In Table 6 we calcula ed he o e all sensi i i y coe icien s o bo h
inpu pa ame e s and all s udied mechanical cha ac e is ics.
I is clea based on Table 6 ha he sha e o he su ac an has
app oxima ely a 70% e ec on he s udied mechanical cha ac e is ics.
Oleic acid has a nega i e en i onmen al impac especially du ing he
ageing p ocess. Based on he esul s p esen ed in he able, we can hus
ecommend a educ ion in he sha e o he so ene wi h a simul aneous
inc ease in he sha e o he su ac an o be e en i onmen al mix u es
wi h he same mechanical cha ac e is ics.
5. Conclusion
Based on he esul s o he p edic ion o he mechanical cha ac e -
is ics o ubbe com- pounds wi h a ious olume sha es o oleic acid
and a ious weigh sha es o he su ac an , using a s a is ical se o 16
samples, we can d aw he ollowing conclusions:
•ANN ne wo ks a e sui able ools o he p edic ion o ensile s eng h
and modulus o ubbe mix u es con aining oleic acid, wi h a co -
ela ion o a leas 0.98 and REL_RMSE maximum 0.8 %.
•The dependence o mechanical p ope ies e sus su ac an amoun
can be desc ibed by a single unc ion o 1 PHR and 3 PHR mix u es.
•ANN ne wo ks can also p edic he mechanical p ope ies o non-
measu ed concen a- ions o su ac an .
•F om he p edic ion o mechanical p ope ies, we can conclude ha
he le el o su - ac an amoun a 20 w % inc eases he mechanical
p ope ies o a leas 80 % o he le el o inc ease o 30 w % o
su ac an , and he e o e wi h he aid o ANNs, we can lowe he
en i onmen al impac o he mix u es, especially as he ma e ial
ages.
•F om he sensi i i y analysis, we can conclude ha unca ing he
changes in he oleic acid amoun leads only o a maximum 20 %
inc ease in e o , he e o e we can conclude ha he oleic acid
amoun in he egion o 1 PHR o 3 PHR does no ha e a signi ican
e ec on he s udied mechanical p ope ies.
•T unca ing he changes o su ac an amoun , howe e , leads o an
inc ease in e o o a leas 150 %, he e o e we can conclude ha he
su ac an amoun s be ween 3 w % and 30 w % ha e a e y la ge
e ec on he mechanical p ope ies.
•No malizing he sensi i i y coe icien s leads o a 70 % e ec on
mechanical p ope ies by he su ac an amoun and only a 30 %
e ec by he oleic acid.
•The lesse e ec o oleic acid is because oleic acid is mainly used in
ubbe mix u es o imp o e he p ocessing o mix u es which a e no
c ea ed o any speci ic mechanical p ope ies.
•Su ac an s, howe e , bond wi h ille s, and he e o e he amoun o
su ac an has a signi ican e ec on mechanical p ope ies.
•The submi ed s udy demons a es he possibili ies o how o op i-
mize he ma e ial composi ion o p oduc s o ma e ial ailo ing wi h
an accen on he en i onmen al bu den.
Decla a ion o Compe ing In e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
D. Seidl e al.
Expe Sys ems Wi h Applica ions 208 (2022) 118039
8
Acknowledgemen s
The esea ch was suppo ed by G an o SGS No. SP2022/81, VSB –
Technical Uni e si y o Os a a, Czech Republic.
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