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Applica ion o machine lea ning modeling o p edic ing he eliabili y o
solde join s unde he mal cycling
Qiulin Yua,b,e,∗, Chinmay Nawghane c, Zihan Zhang d, Ba Vande elde c, Ka l Fend a,
Thomas K i eca, Die e P. G ube b,e
aAus ia Technologie & Sys em echnik Ak iengesellscha , Fab iksgasse 13, Leoben, 8700, S y ia, Aus ia
bChai o Ma e ials Science and Tes ing o Polyme s o Mon anuni e si ae , O o-Glöckel-S aße 2, Leoben, 8700, S y ia, Aus ia
cImec, Kapeld ee 75, Leu en, 3001, Flemish B aban , Belgium
dDepa men o Mic oelec onics, Del Uni e si y o Technology, Mekelweg 5, Del , 2628 CD, Ne he lands
ePolyme Compe ence Cen e Leoben GmbH, Sau augasse 1, Leoben, 8700, S y ia, Aus ia
A R T I C L E I N F O
Keywo ds:
Machine lea ning
Mic oelec onics
Solde join
The mal cycling
Su oga e modeling
Reg ession analysis
A B S T R A C T
In his s udy, Machine Lea ning (ML) me hods combined wi h Op una hype pa ame e op imiza ion we e
in es iga ed o p edic c eep s ain in solde join s o mul ilaye chip capaci o s. Ma e ial p ope ies, geome y
and he mal loading condi ions we e a ied in simula ions using Fini e Elemen Modeling. E alua ed ML
models included Random Fo es , G adien Boos ing, Suppo Vec o Reg ession (SVR) and A i icial Neu al
Ne wo k (ANN). The esul s demons a ed a p edic ion accu acy o 96%, pa icula ly o SVR and ANN. The
model pe o mance signi ican ly imp o ed wi h inc easing da a size up o a ound 600 simula ions. In he
ea u e and hype pa ame e impo ance analysis, solde s and-o heigh and componen leng h mos in luenced
ANN p edic ions, wi h lea ning a e being he key hype pa ame e , while o SVR, he egula iza ion pa ame e
o ke nel unc ion was mos c i ical.
1. In oduc ion
Solde join s in elec onic packaging endu e subs an ial mechanical
and he mal s esses du ing ope a ion. Due o he low s eng h and
elas ic modulus o solde ma e ials, solde join s a e ypically he mos
ulne able componen s and a e highly suscep ible o low cycle a igue
(LCF) [1,2]. The a igue ailu e o a solde join can gene ally be di ided
in o wo main s ages: c ack ini ia ion and c ack p opaga ion. C ack
ini ia ion gene ally ollows h ee s ages: he o ma ion o a mic oc-
ack, i s nuclea ion, and inally, he ini ia ion o a signi ican physical
c ack [3–5]. In some cases, c acks can o m due o o e loading, whe e
an acciden al o ce o p e-exis ing oid in he c ack egion igge s hei
de elopmen . Howe e , in a igue es ing, c ack ini ia ion p ima ily
esul s om he cyclic de o ma ion o he solde join unde s ess [6].
Du ing exposu e o he mal cycling, he momechanical s esses and
s ains a e gene a ed due o he misma ch in he coe icien o he mal
expansion (CTE) be ween he p in ed ci cui boa d (PCB) and elec onic
componen s, which d i e p og essi e c eep de o ma ion and e en ually
esul in a igue ailu e o he solde join s [7,8]. O e he p oduc ’s li e
cycle, hese epea ed he mal cycles con ibu e o c ack ini ia ion and
p opaga ion, g adually deg ading he mechanical in eg i y o he solde
join s and educing he o e all eliabili y o he elec onic assembly.
∗Co esponding au ho a : Aus ia Technologie & Sys em echnik Ak iengesellscha , Fab iksgasse 13, Leoben, 8700, S y ia, Aus ia.
E-mail add ess: [email p o ec ed] (Q. Yu).
To assess and p edic he long- e m du abili y o solde join s unde
eal-wo ld ope a ing condi ions, accele a ed he mal cycling es s a e
commonly employed [9]. These es s subjec elec onic componen s
o apid and ex eme empe a u e luc ua ions, eplica ing yea s o
he mal cycling wi hin a signi ican ly sho e pe iod. By analyzing he
ailu e mechanisms and a igue li e obse ed in accele a ed he mal
cycling es s, enginee s can de elop p edic i e models o es ima e he
ac ual se ice li e o solde join s and op imize ma e ial and design
choices o enhance eliabili y [10]. Howe e , expe imen al es ing o
elec onic package ypically akes 3 o 4 mon hs o comple e, equi ing
signi ican cos s and esou ces. This is whe e Fini e Elemen Modeling
(FEM) comes in o play, p o iding a mo e e icien way o model
complex enginee ing p oblems. A p ope Fini e Elemen (FE) model
wi h la ge nonlinea i ies o ma e ial and geome y usually equi es
specialized modeling expe ise o esea che s and high compu a ional
powe o ha dwa e de ice [11–13].
In o de o o e come his issue, he in eg a ion o a i icial in-
elligence (AI) echniques wi h FEM simula ions has eme ged as an
e ec i e app oach o achie ing eliable p edic ions in he mic oelec-
onics indus y [14–17]. This me hodology, e e ed o Fig. 1, is known
as he AI-assis ed design-on-simula ion p ocedu e. I in ol es a ying
h ps://doi.o g/10.1016/j.mic o el.2025.115900
Recei ed 16 May 2025; Recei ed in e ised o m 6 Augus 2025; Accep ed 27 Augus 2025
Mic oelec onics Reliabili y 174 (2025) 115900
A ailable online 6 Sep embe 2025
0026-2714/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
Q. Yu e al.
Fig. 1. A chi ec u e o AI-assis ed design-on-simula ion p ocedu e.
geome y, ma e ial pa ame e s and bounda y condi ions h oughou
he simula ions o co e he design space and ep esen eal scena ios.
A comp ehensi e da ase is hen gene a ed ia FEM simula ions o
AI aining pu poses. Once he model is de eloped, designe s only
need o inpu he equi ed pa ame e s o ob ain he a ge alues [18].
Se e al s udies ha e employed his me hodology o assessing solde
join eliabili y, which will be u he discussed in Sec ion 2. Howe e ,
mos exis ing s udies use only one ype o modeling app oach, and
he e is a lack o compa a i e analysis be ween di e en machine
lea ning models o p edic ing solde join eliabili y. Addi ionally, he
selec ion and op imiza ion o hype pa ame e s p esen a signi ican
challenge, as imp ope uning can lead o subop imal model pe o -
mance [19]. Ano he c i ical limi a ion is he unce ain y ega ding he
op imal da ase size o FEM-gene a ed da a. Due o his unce ain y,
esea che s o en gene a e la ge da ase s o ensu e su icien aining
samples. Howe e , he ma ginal bene i o inc easing da ase size be-
yond a ce ain h eshold emains unclea , and excessi e da a collec ion
may esul in unnecessa y compu a ional cos s wi hou a p opo ional
imp o emen in model accu acy. Despi e hese challenges, he e is a
lack o sys ema ic in es iga ions in o how di e en machine lea ning
models espond o a ying da ase sizes and whe he hei p edic i e
pe o mance s abilizes beyond a ce ain da a olume.
The e o e, his s udy aims o conduc a comp ehensi e compa ison
o a ious machine lea ning algo i hms, u ilizing Op una as an e icien
hype pa ame e op imiza ion amewo k. Fu he mo e, i sys ema i-
cally examines he ela ionship be ween da ase size and model pe -
o mance, assessing whe he inc easing he olume o FEM-gene a ed
da a consis en ly enhances p edic i e accu acy o i pe o mance gains
diminish beyond a c i ical h eshold. The indings o his s udy will con-
ibu e o a deepe unde s anding o he ade-o be ween da a olume
and p edic i e e iciency, p o iding aluable insigh s o op imizing
FEM-based AI modeling in he eliabili y assessmen o solde join s.
2. P edic i e modeling echniques in solde join s
Se e al s udies ha e in es iga ed me hods o p edic li e cycles
o solde join in ea ly design s age and unde s and how package
design pa ame e s a ec he solde join in eg i y. The mos commonly
used solde join a igue models a e c eep s ain-based and ene gy-
based li e models, which a e de eloped by in eg a ing ini e elemen
modeling wi h empi ical eliabili y es da a [20–23]. Schube e al.
demons a ed he impac o a ious solde in e connec alloys and
package ypes on he a igue li e o solde h ough bo h simula ions
and expe imen al s udies [22]. Liu e al. p esen ed a hyb id me hod
ha combines analy ical and ene gy-based app oaches o p edic solde
join geome y and analyze he mal s ess/s ain beha io in lip-chip
packaging [24]. The esul s demons a e ha op imizing solde ball
size and pad con igu a ion can signi ican ly educe he mal s ess,
enhancing he eliabili y o solde join s in ad anced elec onic pack-
aging applica ions. Liu e al. u he applied his combined me hod
o p edic s ando heigh s and geome y p o iles o he solde join s,
which is u he alida ed by expe imen s [25]. Xu e al. u ilized ini e
elemen simula ions and esponse su ace app oxima ion o e alua e
he he mo-mechanical pe o mance in he design op imiza ion p oce-
du e [26]. Thei indings consis en ly demons a ed a s ong co ela ion
be ween simula ion ou comes and expe imen al da a . This ag eemen
ein o ces he alidi y o simula ion-based me hodologies and p o-
ides a obus g ound u h o aining machine lea ning models in
p edic i e eliabili y assessmen .
In ecen yea s, ML-based modeling echniques ha e been widely
used in a ious esea ch domains o elec onics [27–29]. In pa icula ,
he combina ion o machine lea ning and simula ion has signi ican ly
educed bo h cos and ime, demons a ing s ong abili y o analyze
complex sys ems [15]. Yuan e al. combined bo h he ecu en neu al
ne wo k (RNN) and he ga e-ne wo k long sho - e m memo y (LSTM)
wi h 81 FE da a pai s o assess he solde join he mal cycling pe o -
mance in Glass Wa e Le el Chip Scale Package, whe e die hickness,
glass hickness and PI hickness a e conside ed [30]. Fe ando-Villalba
e al. de eloped an a i icial neu al ne wo k o p edic inelas ic s ain in
PCB Assembly solde join unde he mal cycling [31]. A o al o 1017
pa ame e ized simula ions we e conduc ed, inco po a ing 15 a iables
ac oss a ious scena ios, including subs a e/solde /die geome ies,
ma e ial p ope ies o he subs a e and solde , and pi ch a ia ions.
The ANN p edic ions exhibi ed a s anda d de ia ion o app oxima ely
15% compa ed o he simula ed s ain alues.
Al hough machine lea ning based echniques ha e been widely
applied o p edic solde join eliabili y, esea che s ypically ely on
ex ensi e simula ions o gene a e aining da a and spend signi ican
ime manually sea ching o op imal hype pa ame e s. This wo k aims
o compa e a ious models and de elop a amewo k ha simpli ies hy-
pe pa ame e uning while also in es iga ing he ela ionship be ween
da ase size and model pe o mance, ul ima ely educing he esou ces
equi ed o simula ion and modeling in he hype pa ame e uning.
3. Me hodology
3.1. Da ase gene a ion ia ini e elemen simula ions
The p ima y goal o his esea ch is o de elop a machine lea ning
(ML) model capable o p edic ing he c eep s ain in solde join s
o mul ilaye chip capaci o s (MLCC). To achie e his, a subs an ial
amoun o da a is impe a i e, which is subsequen ly gene a ed using
FE simula ions. We use ini e-elemen modeling o simula e a s anda d
MLCC elec onics package wi h solde join s. The inpu pa ame e s
o hese simula ions include a ious ma e ial p ope ies, geome ic
con igu a ions, loading condi ions, and en i onmen al a iables, all
o which a e chosen based on hei signi icance o he solde join
pe o mance. These pa ame e s a e sys ema ically a ied o c ea e a
comp ehensi e da ase . The key ou pu a iable om hese simula ions
is he a e age c eep s ain measu ed unde di e en scena ios, which
se es as he a ge a iable o ou ML model.
The FEM s uc u e was gene a ed wi h a bo om-up app oach using
he comme cial so wa e MSC Ma c [32]. This me hod in ol es build-
ing he model om he mos basic elemen s such as poin s, lines, 2D
planes and expanding hem o a 3D s uc u e. A pa ame ic sc ip is
de eloped o build such FE models, which allows good con ol o e
he mesh and enables he de ini ion o consis en mesh e en wi h
di e en geome y pa ame e s. This ensu es ha he mesh quali y
emains high and uni o m, ega dless o he a ia ions in he geome ic
con igu a ions o he MLCC package. The pa ame ic sc ip ing app oach
enhances lexibili y and e iciency in modeling, as i au oma es he gen-
e a ion o he mesh based on p ede ined pa ame e s. This au oma ion
educes he likelihood o human e o and ensu es consis ency ac oss
mul iple simula ions. By adjus ing he geome ic pa ame e s wi hin he
Mic oelec onics Reliabili y 174 (2025) 115900
2
Q. Yu e al.
Fig. 2. Illus a ion o DASC model and FOSC model wi h showing mesh and
c i ical solde a ea.
sc ip , a ious con igu a ions can be quickly modeled and analyzed,
he eby accele a ing he da ase gene a ion p ocess. Fu he mo e, he
pa ame ic sc ip acili a es he explo a ion o a wide ange o scena -
ios, as i can sys ema ically a y inpu pa ame e s o s udy hei e ec s
on he pe o mance o he solde join s. This comp ehensi e explo a ion
is c ucial o c ea ing a obus da ase ha accu a ely cap u es he
beha io o he componen s unde di e se condi ions. Ul ima ely, his
me hodological app oach signi ican ly con ibu es o he de elopmen
o a eliable and p edic i e machine lea ning model by p o iding
high-quali y and consis en simula ion da a.
To educe compu a ional ime and gene a e a la ge da ase e i-
cien ly, he ini ial 3D model is simpli ied o a 2D model. This simpli ica-
ion is achie ed by applying s uc u al plane s ain geome y p ope ies
o he 2D model, which e ec i ely p o ides he necessa y hickness
o he model wi hou he need o a ull 3D ep esen a ion. This
app oach is pa icula ly ad an ageous because i simpli ies he complex
3D p oblems in o mo e manageable 2D p oblems, allowing o as e
compu a ions and easie handling o he da a. By simpli ying he 3D
model o a 2D model, he ini ial compu a ional ime was signi ican ly
educed om 4 h o jus 15 min in ou simula ion a emp s. This d as ic
educ ion in compu a ion ime enabled he e icien gene a ion o a
la ge da ase , which is essen ial o aining obus machine lea ning
models.
I is also impo an o no e ha FE simula ions a e pe o med in wo
essen ial s eps o ob ain accu a e esul s. The i s s ep in ol es c ack
p opaga ion unde he componen a ea, speci ically a ge ing he solde
join loca ed below he chip componen . The second s ep add esses
c ack p opaga ion wi hin he solde ille a ea. To e ec i ely implemen
his p ocess, wo dis inc FE models a e de eloped. In Dual-a ea Solde
Co e age (DASC) model, solde is p esen bo h unde he componen
and wi hin he ille . In con as , Fille -Only Solde Co e age (FOSC)
model assumes a ully c acked solde join below he componen ,
hus emo ing he solde om benea h he componen a ea. Fig. 2(a)
illus a es DASC model, while Fig. 2(b) depic s FOSC model, along
wi h hei espec i e meshes. The mesh in hese models is ca e ully
e ined in he solde join a ea o accu a ely cap u e he c eep s ain.
To main ain consis ency ac oss a la ge numbe o simula ions, a c i ical
solde a ea is de ined. The a e age c eep s ain is calcula ed om his
p ecisely de ined a ea, ensu ing uni o mi y and eliabili y in he da a.
This calcula ed a e age c eep s ain is subsequen ly used as he a ge
a iable in he machine lea ning model, which aims o p edic he
pe o mance and beha io o solde join s unde a ious condi ions.
3.2. Fini e elemen modeling o MLCC
3.2.1. Inpu pa ame e de ini ion
The inpu ea u es selec ed o his s udy encompass a a ie y o
ma e ial p ope ies, geome ic con igu a ions, and loading condi ions.
The selec ion o hese ea u es is mo i a ed by hei c i ical in luence
on he pe o mance and eliabili y o solde join s in MLCCs. The co -
esponding pa ame e anges we e de e mined based on manu ac u e
da ashee s, ele an indus y s anda ds, and expe knowledge d awn
om p io s udies and p ac ical expe ience.
(a) Ma e ial P ope ies
Ma e ial p ope ies play a c ucial ole in de e mining he me-
chanical beha io and du abili y o solde join s unde di e en
ope a ing condi ions. Key ma e ial p ope ies conside ed in his
s udy include he coe icien o he mal expansion, which e lec s
he misma ch be ween componen and PCB. This misma ch can
induce he mal s esses, leading o c eep s ain and e en ual ail-
u e o he solde join s. Elas ic/Young’s modulus (E-modulus),
ep esen ing he s i ness o he ma e ials in ol ed, a ec s he
s ess dis ibu ion and de o ma ion beha io o he solde join s.
(b) Geome ic Con igu a ions
Geome ic pa ame e s a e c ucial in de ining he physical dimen-
sions and s uc u al cha ac e is ics o he MLCC package and
solde join s. This s udy includes s anda d MLCC sizes anging
om C1005 o C7563, based on manu ac u e da ashee s, o en-
su e model gene alizabili y ac oss a ying capaci o dimensions.
Va ia ions in solde s and heigh impac he o e all heigh o he
solde join , in luencing i s he mal and mechanical beha io .
The leng h o he coppe pads a ec s he ille o ma ion o he
solde join s, which in u n in luences he s ess dis ibu ion and
de o ma ion beha io .
(c) Loading Condi ions
Loading condi ions simula e he ope a ional en i onmen and
he mo-mechanical s esses expe ienced by he solde join s. The
minimum and maximum empe a u es a e de ined as c i ical
inpu pa ame e s, encompassing he s anda d he mal cycling
condi ions anging om −55 ◦C o 100 ◦C. This ange en-
compasses ep esen a i e empe a u e windows (e.g., –40 ◦C
o 100 ◦C, 0 ◦C o 100 ◦C) aligning wi h indus y s anda ds
like ECSS-Q-ST-70-04C o space applica ions and AEC-Q007-
001 o au omo i e con ex s. As such, he model ensu es b oad
applicabili y ac oss a ious eal-wo ld scena ios.
Table 1 p o ides a de ailed lis o he pa ame e s along wi h he
ange o alues simula ed in his s udy. The geome ic pa ame e s,
c ucial o accu a ely depic ing he physical dimensions and s uc u al
cha ac e is ics o he MLCC package, a e isually ep esen ed in Fig.
3. The design o expe imen s o his s udy was conduc ed using he
La in hype cube sampling me hod. This me hod is e ec i e in his
con ex as i ensu es a comp ehensi e and uni o m explo a ion o he
design space, he eby educing he numbe o simula ions needed o
achie e accu a e esul s. As shown in Fig. A.13, he dis ibu ion o
all inpu pa ame e s a e illus a ed by hei his og ams. A o al o
1481 simula ions we e conduc ed o each o he wo models, esul -
ing in an agg ega e o 2962 simula ions. The simula ion p ocess was
au oma ed using Noesis Op imus so wa e [33], which allows se ing
up he design o expe imen s based on he la in hype cube me hod
and pe o ms he simula ions sequen ially. The s udy ocused on 13
Mic oelec onics Reliabili y 174 (2025) 115900
3
Q. Yu e al.
Table 1
Lis o inpu pa ame e s used in he simula ions along wi h hei anges.
Type Inpu pa ame e s Nominal Min Max
Geome y
Componen leng h (lc) 4.5 mm 0.6 7.5
Componen wid h
(wc)
3.2 mm 0.3 6.3
Componen hickness
( c)
2.8 mm 0.3 3
End e mina ion
leng h (le )
0.61 mm 0.1 0.7
Solde s and-o
heigh ( s )
0.045 mm 0.01 0.07
Pa ial Coppe pad
leng h (ls 1)
0.3 mm 0.1 0.4
Pa ial Coppe pad
leng h (ls 2)
0.35 mm 0.2 0.6
Ma e ial p ope y
Componen CTE
(Cap_CTE)
9 ppm/◦C 5 10
PCB CTE X/Y
(PCB_CTE)
15 ppm/◦C 12 18
PCB hickness ( pcb) 1.6mm 0.8 3.2
PCB young’s modulus
(PCB_E)
23000 MPa 23000 50000
Loading p o ile
Min empe a u e
(Tmin)
−55 ◦C−55 20
Max empe a u e
(Tmax)
100 ◦C 80 120
Fig. 3. Schema ics o MLCC wi h geome ical pa ame e s.
inpu a iables, each signi ican ly in luencing he ou come. These inpu
a iables p oduced wo main ou pu s: c eep s ain in DASC model
and c eep s ain in FOSC model. By ca e ully selec ing hese inpu
ea u es, he s udy aims o c ea e a comp ehensi e and ep esen a i e
da ase ha cap u es he key ac o s in luencing he c eep s ain in
solde join s. This app oach ensu es ha he machine lea ning model
de eloped can accu a ely p edic he pe o mance o solde join s unde
di e se condi ions, he eby enhancing he eliabili y and obus ness o
he MLCC elec onics package.
3.2.2. Ou pu pa ame e de ini ion
The s udy iden i ies wo p ima y ou pu pa ame e s: a e age c eep
s ain om DASC model and a e age c eep s ain om FOSC model.
In Fig. 4, he esul s o he ini e elemen (FE) simula ion a e depic ed,
showcasing he c eep s ain obse ed in each FE model o a ull he -
mal cycle o −55 ◦C o 100 ◦C. The A e age c eep s ain is calcula ed
om he c i ical a eas de ined o each model, as p e iously illus a ed
in Fig. 2. The a e age c eep s ain ob ained om hese simula ions
se es as he a ge pa ame e in he subsequen ML models.
3.3. Da ase isualiza ion and p ep ocessing
3.3.1. Co ela ion ma ix
A co ela ion ma ix is a abula ep esen a ion ha displays co -
ela ion coe icien s, indica ing he s eng h and di ec ion o linea
Fig. 4. FE analysis esul s showing a e age c eep s ain o a he mal cycle o
−55 ◦C o 100 ◦C.
Fig. 5. Co ela ion ma ix o inpu ea u es o ou pu s o DASC model and
FOSC model.
ela ionships be ween a iables in a da ase [34]. Co ela ion alues
close o 1 o −1 indica e a s ong ela ionship, while alues nea 0
sugges a weak o no ela ionship. Posi i e alues mean bo h a iables
inc ease oge he , while nega i e alues show one ises as he o he
alls. Fig. 5 shows he co ela ion be ween he inpu ea u e and he
a e age c eep s ain in DASC model and FOSC model. I shows ha he
leng h o capaci o (lc) and CTE o PCB (PCB_CTE) posi i ely impac
bo h a ge s. Solde s and-o heigh ( s ) is a s ong nega i e p edic-
o , especially o FOSC model. The capaci o ’s coe icien o he mal
expansion (Cap_CTE) also has a nega i e e ec on bo h models, hough
o a lesse ex en . Tmin show s a weake co ela ion wi h bo h models,
especially FOSC model, indica ing lowe minimum empe a u es lead
o lowe a e age c eep s ain. Tmax has a weak posi i e co ela ion
wi h bo h models, sugges ing highe maximum empe a u es sligh ly
inc ease a e age s ain. Fea u es like capaci o wid h (wc), Pa ial
coppe pad Leng h (ls 1 and ls 2) migh be less impo an due o weak
co ela ions.
3.3.2. Min-max scale
The Min-Max Scale is a da a p e-p ocessing echnique ha scales
each ea u e o a gi en ange, usually [0, 1]. I adjus s each alue based
on he ea u e’s minimum and maximum using he o mula [35]:
𝑋𝑠𝑐𝑎𝑙𝑒𝑑 =𝑋−𝑋𝑚𝑖𝑛
𝑋𝑚𝑎𝑥 −𝑋𝑚𝑖𝑛
whe e 𝑋 deno es he o iginal alue, 𝑋𝑚𝑖𝑛 and 𝑋𝑚𝑎𝑥 a e he minimum
and maximum o he ea u e column, 𝑋𝑠𝑐𝑎𝑙𝑒𝑑 a e he scaled alue
be ween 0 and 1. In his wo k, he Min-Max Scale was applied o
no malize he inpu ea u es.
Following da a no maliza ion, he da ase was spli in o aining and
es subse s. Fo each simula ion g oup, a consis en es se comp ising
113 da a poin s was employed o ensu e compa abili y. The aining se
was used o hype pa ame e op imiza ion h ough Op una ( e e ed
Mic oelec onics Reliabili y 174 (2025) 115900
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Fig. 6. A chi ec u e o he modeling p ocedu e.
Table 2
Hype pa ame e s o he RF model uned in his s udy [36–39].
Hype pa ame e Desc ip ion Sea ch ange
n_es ima o s Numbe o ees in he
o es .
[10, 200]
max_dep h Maximum dep h o each
ee.
[50, 100]
min_samples_spli Minimum numbe o
samples o spli an in e nal
node.
[2, 10]
min_samples_lea Minimum numbe o
samples equi ed a a lea
node.
[1, 15]
max_ ea u es Me hod o selec ea u es
a each spli .
[‘sq ’, ‘log2’, None]
o Sec ion 3.4.2), esul ing in an op imized model ained on he
same aining se . Finally, he pe o mance o his ained model was
e alua ed on he es se o acili a e compa ison wi h o he models.
3.4. Machine lea ning models
The ML models used in his s udy a e ained on labeled da ase s,
whe e inpu pa ame e s (inpu da a) and co esponding ou pu al-
ues (ou pu da a) a e p o ided. This app oach, known as supe ised
lea ning, encompasses echniques such as Random Fo es (RF), eX eme
G adien -boos ing (XGB), Suppo Vec o Reg ession SVR and A i icial
Neu al Ne wo k (ANN). Fig. 6 illus a es he schema ic a chi ec u e o
he ML models employed o p edic ing a e age c eep s ain.
3.4.1. E alua ed machine lea ning models
The i s echnique employed in his s udy is he andom o es
(RF). RF is an ensemble lea ning me hod ha consis s o se e al ee
p edic o s whe e each ee is gene a ed using a andom ec o sampled
independen ly om he inpu ec o [40]. In eg ession analysis, RF
model compu es he a e age p edic ions om mul iple decision ees
o gene a e he ou pu [41]. Consequen ly, as he numbe o ees
inc eases, he gene aliza ion e o app oaches a s able limi [42]. Table
2 indica es he hype pa ame e s and sea ch anges o he decision ee
model used in his s udy [36–39]. As shown in Table 2, hype pa am-
e e s con ain he numbe o ees in he o es (n_es ima o s), he max
numbe o le els in each decision ee (max_dep h), and he numbe o
da a poin s placed in a node be o e he node is spli (min_samples_spli ).
RF is a basic ee-based machine lea ning algo i hm, while eX eme
G adien -boos ing (XGB) is an ad anced model o g adien -boos ing
decision ees [43]. XGB combines wo key echniques o ensemble
lea ning: bagging and boos ing. Bagging ains mul iple models in pa -
allel, wi h each model gene a ed om independen ly sampled subse s
o he da a. This app oach educes a iance and imp o es model s abil-
i y and accu acy by combining he p edic ions o all models. Boos ing
Table 3
Hype pa ame e s o he XGB model uned in his s udy [46,47].
Hype pa ame e Desc ip ion Sea ch ange
n_es ima o s Numbe o ees in he ensemble. [30, 400]
max_dep h Maximum dep h o each ee. [3, 12]
lea ning_ a e S ep size sh inkage du ing aining. [0.01, 0.1]
subsample Subsample a io o aining ins ances. [0.6, 0.9]
colsample_by ee Subsample a io o columns pe ee. [0.6, 0.9]
eg_alpha L1 egula iza ion e m on weigh s. [0.01, 10]
eg_lambda L2 egula iza ion e m on weigh s. [0.01, 10]
Table 4
Hype pa ame e s o he SVR model uned in his s udy [48].
Hype pa ame e Desc ip ion Sea ch ange
ke nel Ke nel unc ion used o
map inpu da a o a
highe -dimensional space.
[‘linea ’, ‘poly’, ‘ b ’, ‘sigmoid’]
CRegula iza ion pa ame e
con olling he ade-o
be ween smoo hness and
accu acy.
[1e−3, 50]
epsilon Tole ance ma gin o e o
in he insensi i e loss
unc ion.
[1e−7, 1e−3]
gamma De ines he in luence o a
single aining example in
non-linea ke nels.
[‘scale’, ‘au o’]
builds models sequen ially, whe e each ee is cons uc ed o add ess
he e o s o he p e ious one. This i e a i e p ocess e ines he model
by ocusing on he poo ly lea ned pa e ns, he eby enhancing o e all
p edic i e pe o mance [44,45]. Table 3 p esen s he hype pa ame e s
and he sea ch anges o he XGB model in his s udy [46,47].
Suppo ec o eg ession (SVR) is a supe ised machine lea ning
algo i hm ha uses he p inciples o Suppo Vec o Machines (SVM) o
pe o m eg ession asks by inding a unc ion ha p edic s con inuous
alues while main aining a ma gin o ole ance a ound he p edic ed
alue and minimizing model complexi y [49]. I iden i ies suppo ec-
o s (da a poin s closes o he ma gin) o de ine he decision bounda y,
enabling obus p edic ions e en in high-dimensional spaces o wi h
non-linea ela ionships when combined wi h ke nel unc ions [50].
Table 4 illus a es hype pa ame e s and he sea ch anges o he SVR
model in his s udy [48].
An A i icial Neu al Ne wo k (ANN) is a machine lea ning model
inspi ed by he human b ain, designed o lea n and map complex ela-
ionships in da a [51]. I consis s o an inpu laye ha ecei es da a,
hidden laye s whe e neu ons compu e weigh ed sums o inpu s, add
biases, and apply ac i a ion unc ions o cap u e non-linea pa e ns,
and an ou pu laye ha p oduces p edic ions. Du ing aining, he
ne wo k minimizes he e o be ween p edic ions and ac ual alues us-
ing backp opaga ion, whe e g adien s a e compu ed o upda e weigh s
and biases i e a i ely h ough an op imiza ion algo i hm [51–53]. This
i e a i e p ocess enables ANNs o lea n om da a, making hem highly
e ec i e o asks like image ecogni ion, na u al language p ocessing,
and p edic i e analy ics [54]. Table 5 illus a es hype pa ame e s and
he sea ch anges o he ANN model in his s udy [55,56].
3.4.2. Op una o selec ing hype -pa ame e s o machine lea ning models
Hype pa ame e uning is essen ial o ge ing he bes pe o mance
om machine lea ning models, as e ec i e uning can g ea ly imp o e
bo h accu acy and obus ness [19,57]. Howe e , adi ional uning
me hods (G id Sea ch and Random Sea ch) o en equi e use s o de ine
a s a ic sea ch space in ad ance, which limi s lexibili y [58]. Op una,
p oposed by Akiba e al. [59], is a hype pa ame e op imiza ion ame-
wo k designed o add ess hese limi a ions h ough a dynamic ‘‘de ine-
by- un’’ applica ion p og amming in e ace (API). This API allows use s
o build sea ch spaces in e ac i ely du ing he op imiza ion p ocess [59,
Mic oelec onics Reliabili y 174 (2025) 115900
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Fig. 7. The basic p ocedu e o hype pa ame e s selec ion in Op una.
Table 5
Hype pa ame e s o he ANN model uned in his s udy [55,56].
Hype pa ame e Desc ip ion Sea ch ange
num_laye s Numbe o hidden laye s in
he ne wo k.
3
hidden_dim1 Numbe o neu ons in he i s
hidden laye .
[16, 256]
hidden_dim2 Numbe o neu ons in he
second hidden laye .
[32, 128]
hidden_dim3 Numbe o neu ons in he
hi d hidden laye .
[16, 128]
d opou _ a e D opou a e o p e en
o e i ing.
[0.0, 0.4]
ba ch_no m Whe he o apply ba ch
no maliza ion a e each laye .
[T ue, False]
lea ning_ a e Lea ning a e con olling he
upda e s ep in aining.
[1e−5, 1e−2]
weigh _decay Regula iza ion o penalize
la ge weigh s.
[1e−6, 1e−3]
epochs Numbe o aining epochs. [50, 200]
60]. Meanwhile, i ea u es e icien sampling and p uning algo i hms
wi h suppo o use cus omiza ion. Sampling in ol es wo ypes:
independen (e.g., T ee-s uc u ed Pa zen Es ima o ) and ela ional
(e.g., Co a iance Ma ix Adap a ion E olu ion S a egy), enabling lex-
ible and dynamic sea ch space explo a ion. P uning sa es esou ces
by moni o ing in e media e esul s and e mina ing unp omising ials
ea ly, wi h Op una implemen ing he s a e-o - he-a Asynch onous
Successi e Hal ing Algo i hm (ASHA) o asynch onous and scalable
p uning. By combining e icien sampling o iden i y p omising a eas
and p uning o ocus esou ces, Op una op imizes pe o mance while
educing compu a ional o e head [59]. Op una’s inal design ea u e
is i s easy se -up, making i simple o use o e e y hing om small
expe imen s o la ge-scale dis ibu ed asks, suppo ed by i s lexible
and adap able a chi ec u e [59,61,62].
Fig. 7 illus a es he key s eps in ol ed in hype pa ame e op i-
miza ion o machine lea ning models using Op una. The p ocess s a s
wi h selec ing he hype pa ame e s o each model and de ining hei
espec i e sea ch spaces. Nex , he objec i e unc ion is con igu ed, ol-
lowed by speci ying he op imiza ion di ec ion. Finally, he numbe o
Op una ials is de e mined. In his s udy, hype pa ame e op imiza ion
is pe o med o e 100 ials wi h he objec i e o minimizing he MSE,
e alua ed h ough 5- old c oss- alida ion. This app oach helps mi iga e
o e i ing and ensu es model obus ness and gene alizabili y.
3.5. E alua ion me ics
To assess he p edic ion accu acy o di e en machine lea ning
models, h ee s a is ical me ics a e employed: Mean Squa ed E o
(MSE), Roo Mean Squa ed E o (RMSE), and he Coe icien o De-
e mina ion (R2). These me ics p o ide complemen a y insigh s in o
model pe o mance, om e o magni ude o a iance explana ion.
The Mean Squa ed E o (MSE) is de ined as he mean o he
o e all squa ed p edic ion e o s [63]. When he MSE is ze o, he
es ima o p ecisely p edic s he pa ame e ’s esponse. As he MSE
dec eases, he model’s accu acy imp o es, educing he disc epancy
be ween p edic ed and ac ual alues. I is de ined as:
𝑀𝑆𝐸 =1
𝑁𝑡𝑒𝑠𝑡
𝑁𝑡𝑒𝑠𝑡
∑
𝑖=1
(𝑦𝑖−𝑦𝑖)2
, whe e 𝑦i ep esen s he ac ual alue, 𝑦i deno es he p edic ed alue
ob ained om he cons uc ed su oga e model and 𝑁 es indica es he
o al numbe o e i ica ion samples. In his s udy, iden i ica ion o
op imal model pa ame e s using Op una is conduc ed by minimizing
he MSE o c oss alida ion da a.
The Roo Mean Squa ed E o (RMSE) is de i ed om he MSE and
p o ides a mo e easily in e p e able measu e o p edic ion e o , due
o ha ing he same uni s as he a ge a iable. I e lec s he s anda d
de ia ion o he esiduals and is use ul o unde s anding he ypical
magni ude o p edic ion e o s. A lowe RMSE sugges s a be e i
o he model o he da a [63], and i is used he e o compa e he
pe o mance o he ou machine lea ning models unde conside a ion.
I is de ined as
𝑅𝑀𝑆𝐸 =√
√
√
√1
𝑁𝑡𝑒𝑠𝑡
𝑁𝑡𝑒𝑠𝑡
∑
𝑖=1
(𝑦𝑖−𝑦𝑖)2
The Coe icien o De e mina ion (R2) e alua es how well he p e-
dic ed alues app oxima e he ac ual da a by quan i ying he p o-
po ion o a iance in he a ge a iable ha is explained by he
model [64]. R2 akes alues wi hin he ange [0, 1], wi h highe
alues indica ing be e p edic i e pe o mance. In his wo k, R2 is used
alongside RMSE o compa e he e ec i eness o he di e en models,
p o iding insigh in o how well each model cap u es he unde lying
pa e ns in he da a. I is ma hema ically de ined as
𝑅2=∑𝑁𝑡𝑒𝑠𝑡
𝑖=1 (𝑦𝑖−𝑦𝑖)2
∑𝑁𝑡𝑒𝑠𝑡
𝑖=1 (𝑦𝑖−𝑦𝑖)2
, wi h he e m 𝑦i e e ing o he mean o he ue alues [65].
4. Resul s and discussions
4.1. Model pe o mance compa ison
A e hype pa ame e op imiza ion wi h Op una, he op imal pa-
ame e s o each model we e iden i ied, and models con igu ed wi h
hese op imal pa ame e s we e subsequen ly applied o he es se
o e alua e hei pe o mance. Fou eg ession models we e assessed
and compa ed based on hei pe o mance on DASC model, using
RMSE, and R2 as e alua ion me ics. The esul s, including i ed locally
weigh ed sca e plo smoo hing ends, a e p esen ed in Fig. 8. As he
numbe o simula ions inc eases, all models gene ally imp o e, wi h
lowe p edic ion e o s (RMSE) and highe accu acy (R2). The esul s
show ha ANN pe o ms bes in he small sample egime, wi h a
apid inc ease in R2 and a s eep dec ease in RMSE, indica ing s ong
nonlinea modeling capaci y and good gene aliza ion. As he aining
size inc eases, SVR demons a es obus and s eadily imp o ing pe o -
mance, ul ima ely sligh ly ou pe o ming ANN in he la ge da asiye
egime, making i one o he mos s able models o e all. XGBoos shows
mode a e and consis en pe o mance h oughou , while RF unde pe -
o ms signi ican ly, especially wi h small da ase s, and con inues o
all behind o he models e en as mo e da a is in oduced. No ably,
all models exhibi diminishing e u ns in pe o mance imp o emen
as he aining da a size inc eases. Speci ically, when he numbe o
aining samples eaches app oxima ely 700, he R2 alues o ANN
and SVR pla eau and RMSE educ ion slows, indica ing ha u he
imp o emen s a e limi ed. The e o e, ocusing esou ces on ANN o
Mic oelec onics Reliabili y 174 (2025) 115900
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Fig. 8. Compa ison o 4 models on es se , o DASC model.
Fig. 9. Compa ison o 4 models on es se , o FOSC model.
SVR and main aining simula ion coun s a ound o sligh ly abo e 700
would p o ide op imal balance and e iciency.
Fig. 9 shows he same compa ison o FOSC model wi h DASC model.
The esul s indica e ha SVR consis en ly ou pe o ms o he models,
achie ing he highes R2 and he lowes RMSE ac oss mos aining
sizes, especially in he la ge-da a egime. ANN pe o ms compe i i ely,
pa icula ly excelling in small o medium aining sizes, and emains
close o SVR as he da a size g ows. XGBoos shows mode a e pe -
o mance, imp o ing s eadily wi h mo e da a bu alling sho o SVR
and ANN. Random Fo es pe o ms he wo s , especially in low-da a
scena ios, and exhibi s limi ed imp o emen e en wi h inc eased da a.
A clea s abiliza ion poin is also obse ed: SVR and ANN each pe -
o mance sa u a ion a ound 500–600 aining samples, wi h ma ginal
gains beyond ha poin . XGBoos s abilizes close o 700–800 samples,
while Random Fo es shows no dis inc sa u a ion end. This sugges s
ha , o he FOSC ask, a aining size o app oxima ely 600 samples
is su icien o achie ing nea -op imal model pe o mance.
An impo an obse a ion ac oss all models is he phenomenon o
diminishing e u ns. While all models bene i om an ini ial inc ease
in aining da a (especially om 10 o 400 samples), he i ed cu es
show ha beyond app oxima ely 600 samples, he pe o mance gains
begin o pla eau. The slope o he pe o mance cu es becomes in-
c easingly shallow, indica ing ha addi ional da a poin s con ibu e
less and less o imp o ing model accu acy. This end is pa icula ly
e iden in ANN and SVR, whose pe o mance me ics app oach hei
asymp o ic limi s. I means ha simply inc easing he da ase size does
no inde ini ely lead o signi ican imp o emen s in pe o mance [66].
Nume ically in Figs. 8and 9, SVR consis en ly achie es he bes
pe o mance ac oss bo h models, wi h RMSE nea 0.004 and R2 con-
sis en ly a ound o exceeding 0.96, especially a highe simula ion
coun s. ANN closely ollows SVR, pe o ming s ongly wi h he bu
sligh ly behind wi h RMSE nea 0.005 and R2 abou 0.94. All models
we e ained on a local machine equipped wi h an In el® Co e™ i7
CPU and 32 GB RAM, using CPU-only compu a ion. Unde his se up
(da ase size = 1200), he a e age op imiza ion ime o 100 ials was
app oxima ely 2 min o RF, 9 min o SVR, 3 min o ANN, and 1 min
o XGBoos .
4.2. In e p e a ion o esul s
4.2.1. SHAP analysis in ANN
The SHapley Addi i e exPlana ions (SHAP) amewo k is conside ed
o explain he machine lea ning models [67,68]. I assigns each ea u e
an impo ance alue, called a SHAP alue, based on he concep o
Shapley alues om coope a i e game heo y [68,69]. A SHAP alue
indica es how much each inpu ea u e con ibu es, posi i ely o neg-
a i ely, o c eep s ain p edic ions. In his s udy, SHAP alues we e
compu ed using he Ke nelExplaine om he SHAP Py hon lib a y,
which is model-agnos ic and well-sui ed o explaining non- ee-based
models such as he ANN used he e [70]. The explaine es ima es
ea u e con ibu ions by pe u bing inpu alues and obse ing he
co esponding changes in he model’s ou pu . The magni ude o a SHAP
alue e lec s he s eng h o he ea u e’s in luence on he p edic ion,
while he sign indica es whe he he ea u e inc eases (posi i e) o
dec eases (nega i e) he p edic ed ou pu . In summa y plo s, he colo
ep esen s he ac ual alue o he ea u e, p o iding insigh in o how
high o low ea u e alues a ec he model’s ou pu .
Fig. 10 depic s he SHAP analysis o ANN on bo h models. In bo h
models, solde s and-o heigh ( s ) and componen leng h (lc) a e con-
sis en ly he mos in luen ial p edic o s, showing wide dis ibu ions o
SHAP alues. Highe alues o solde s and-o heigh ( s ) gene ally
inc ease p edic ions signi ican ly in bo h models. Fea u es such as CTE
o capaci o s (Cap_CTE) and CTE o PCB (PCB_CTE) main ain ela i ely
high impo ance in bo h models, e lec ing s able in luence. Specially
in DASC model, Max empe a u e (Tmax) and end e mina ion leng h
(le ) a e ela i ely mo e in luen ial, indica ing ha peak empe a u es
and ho izon al s uc u e a e mo e c i ical o solde c acking below
componen (in he solde s ando a ea). In FOSC model, minimum
empe a u e (Tmin) becomes no ably mo e in luen ial han maximum
empe a u e (Tmax), sugges ing ha low empe a u e e ec s (e.g., con-
ac ion, s ess eco e y) play a la ge ole a e c acking. Pa ial coppe
pad leng h a ille a ea (ls 2) gains signi icance, consis en wi h he
ocus shi ing o he ou e solde egion. End e mina ion leng h (le )
in FOSC model becomes less impo an , indica ing educed in luence as
FOSC model assumes ull ac u e a solde below componen . O e all,
PCB hickness ( pcb), PCB young’s modulus (PCB_E), pa ial coppe
Mic oelec onics Reliabili y 174 (2025) 115900
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Fig. 10. SHAP alues o each ea u e in he ANN model.
Fig. 11. Compa ison o SVR pe o mance ac oss wo da ase s: DASC and FOSC.
pad leng h unde componen (ls 1), componen wid h (wc) a e lowe
anked and ha e li le in luence on he solde join c eep s ain in
ou cu en loading scena ios. This esul is consis en wi h ha o
co ela ion ma ix in Sec ion 3.3.1.
4.2.2. Hype pa ame e impo ance analysis in SVR and ANN
Op una’s hype pa ame e impo ance ea u e helps o iden i y
which hype pa ame e s ha e he mos impac on model pe o mance
[59]. I analyzes comple ed ials and calcula es each pa ame e ’s
in luence on he objec i e alue. I helps sa e ime and esou ces by
ocusing op imiza ion on impo an pa ame e s. Fig. 11 p esen he
hype pa ame e impo ance o SVR models ained on he DASC and
FOSC da ase s, espec i ely. In he DASC model, he mos in luen ial
hype pa ame e is C (0.57), indica ing ha egula iza ion s eng h
signi ican ly a ec s model pe o mance. The ke nel pa ame e also
plays a mode a e ole (0.25), while gamma and epsilon ha e ela i ely
mino impac s (0.11 and 0.08, espec i ely). In con as , he FOSC
model is mos sensi i e o he ke nel choice (0.55), making i he key
ac o in uning. epsilon and C ollow wi h mode a e impo ance (0.17
and 0.15), and gamma emains he leas impac ul (0.12).
Fig. 12 shows a de ailed analysis compa ing he ANN hype pa am-
e e impo ance o DASC model and FOSC model. In bo h, lea ning
a e is he mos in luen ial pa ame e —especially in DASC Model (0.63
s. 0.39). DASC model is also mode a ely a ec ed by weigh decay and
ba ch no maliza ion, while a chi ec u al pa ame e s ha e li le impac .
In con as , FASC model is mo e in luenced by ba ch no maliza ion,
numbe o neu ons in hidden laye 3, and d opou a e, indica ing
g ea e sensi i i y o a chi ec u e and egula iza ion.
Th ough SHAP analysis, we can iden i y he mos in luen ial design
ea u es a ec ing model pe o mance. In his case, solde s and-o
heigh ( s ) and he capaci o leng h (lc) a e he mos impo an ea-
u es, hus a oiding unnecessa y expe imen al designs in u u e s udies.
Addi ionally, hype pa ame e impo ance analysis e eals which hy-
pe pa ame e s signi ican ly impac model pe o mance in SVR and
ANN. SVR models show model-dependen sensi i i y o ei he he
egula iza ion pa ame e C o he ke nel unc ion, while ANN models
a e consis en ly d i en by he lea ning a e, wi h FOSC addi ionally
in luenced by a chi ec u al ac o s like ba ch no maliza ion, enabling
a mo e e icien op imiza ion p ocess.
4.3. Limi a ions and u u e wo k
A key limi a ion o his s udy is he absence o expe imen al alida-
ion. The p oposed amewo k elies exclusi ely on high- ideli y ini e
elemen analysis da a o ain and es he machine lea ning models.
This syn he ic da a app oach enables e icien explo a ion o pa ame e
spaces and acili a es he cons uc ion o accu a e and compu a ionally
e icien su oga e models. Howe e , i inhe en ly lacks di ec co e-
la ion wi h physical es esul s. Al hough simula ion da a p o ide a
consis en and con olled en i onmen o model de elopmen , hey
may no ully cap u e he a iabili y and complexi y o eal-wo ld
he mal cycling beha io .
To mi iga e his conce n, we emphasize ha he FEA modeling
app oach adop ed in his s udy builds upon well-es ablished simula ion
me hodologies ha ha e p e iously demons a ed excellen ag eemen
wi h expe imen al obse a ions in simila con ex s [71–74]. None he-
less, we ully acknowledge ha simula ion-based p edic ions, ega dless
o hei ideli y, canno subs i u e o expe imen al alida ion. C i i-
cal ac o s such as ma e ial a iabili y, p ocess-induced de ec s, and
en i onmen al unce ain ies a e di icul o cap u e ully in nume ical
models alone. As such, expe imen al co ela ion emains an essen ial
nex s ep. In u u e wo k, we aim o collabo a e wi h indus ial pa ne s
o ob ain accele a ed he mal cycling es da a, which will enable
di ec compa ison and alida ion o he su oga e model’s p edic i e
capabili y unde eal-wo ld ope a ing condi ions.
Mic oelec onics Reliabili y 174 (2025) 115900
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Q. Yu e al.
Fig. 12. Compa ison o ANN pe o mance ac oss wo da ase s: DASC and FOSC.
Fig. A.13. His og am plo s o inpu pa ame e dis ibu ions.
Mic oelec onics Reliabili y 174 (2025) 115900
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