Ci a ion: William, M.V.A.; Ramesh,
S.; Cep, R.; Mahalingam, S.K.;
Elango an, M. DPGWO Based
Fea u e Selec ion Machine Lea ning
Model o P edic ion o C ack
Dimensions in S eam Gene a o
Tubes. Appl. Sci. 2023,13, 8206.
h ps://doi.o g/10.3390/
app13148206
Academic Edi o : Ki-Yong Oh
Recei ed: 21 June 2023
Re ised: 11 July 2023
Accep ed: 13 July 2023
Published: 14 July 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
applied
sciences
A icle
DPGWO Based Fea u e Selec ion Machine Lea ning Model o
P edic ion o C ack Dimensions in S eam Gene a o Tubes
Ma hias Vijay Albe William 1, Sub amanian Ramesh 2, Robe Cep 3,* , Si a Kuma Mahalingam 4
and Muniyandy Elango an 5,6,*
1Depa men o Elec onics and Communica ion Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D
Ins i u e o Science and Technology, A adi 600062, India
2Depa men o Elec ical and Elec onics Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D Ins i u e o
Science and Technology, A adi 600062, India
3Depa men o Machining, Assembly and Enginee ing Me ology, Facul y o Mechanical Enginee ing,
VSB-Technical Uni e si y o Os a a, 70800 Os a a, Czech Republic
4Depa men o Mechanical Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D Ins i u e o Science and
Technology, A adi 600062, India
5Depa men o Biosciences, Sa ee ha School o Enginee ing, Sa ee ha Naga , Thandalam 602105, India
6Depa men o R&D, Bond Ma ine Consul ancy, London EC1V 2NX, UK
*Co espondence: [email p o ec ed] (R.C.); muniyandy[email p o ec ed] (M.E.)
Abs ac :
The selec ion o an app op ia e numbe o ea u es and hei combina ions will play a
majo ole in imp o ing he lea ning accu acy, compu a ion cos , and unde s anding o machine
lea ning models. In his p esen wo k, 22 g ay-le el co-occu ence ma ix ea u es ex ac ed om
magne ic lux leakage images cap u ed in s eam gene a o ubes’ c acks a e conside ed o de el-
oping a machine lea ning model o p edic and analyze c ack dimensions in e ms o hei leng h,
dep h, and wid h. The pe o mance o he models is examined by conside ing R
2
and RMSE alues
calcula ed using bo h aining and es ing da a se s. The F Sco e and Mu ual In o ma ion Sco e
me hods ha e been applied o p io i ize he ea u es. To analyze he e ec o di e en machine
lea ning models, hei numbe o ea u es, and hei selec ion me hods, a Taguchi expe imen al
design has been implemen ed and an analysis o a iance es has been conduc ed. The dynamic
popula ion g ay wol algo i hm (DPGWO) has been adop ed o selec he bes ea u es and hei
combina ions. Due o he wo con adic o y na u es o pe o mance me ics, Pa e o op imal solu ions
a e conside ed, and he bes one is ob ained using Deng’s me hod. The e ec i eness o DPGWO is
p o ed by compa ing i s pe o mance wi h G ey Wol Op imiza ion and Mo h Flame Op imiza ion al-
go i hms using he F iedman es and pe o mance indica o s, namely in e ed gene a ional dis ance
and spacing.
Keywo ds: machine lea ning model; ea u e selec ion me hods; op imiza ion algo i hms; F iedman
es ; Deng’s me hods; pe o mance indica o s
1. In oduc ion
In nuclea powe plan s, c i ical componen s such as s eam gene a o ubes (SGT),
eed wa e hea e s, and p essu e essels ha e s ingen design equi emen s due o he high
empe a u e, p essu e, and adia ion-exposing en i onmen , which induce s ess co osion
c acking, pi ing, ouling, and mechanical e ing [
1
]. Apa om ha , s eam gene a o
ube up u e (SGTR) leads o he ine i able elease o adia ion in o he en i onmen [
2
].
Fo he sa e y and eliable ope a ion o he plan , i is necessa y o go o online moni o ing
and pe iodic inspec ion [
3
,
4
]. Non-des uc i e es ing (NDT) is a mode o es ing ha has
been adop ed by indus ies o mo e han a decade o es mass-manu ac u ed p oduc s o
anomalies. This p ocess is inc easingly being used by sec o s such as ae ospace, oil and
gas, pe oleum, nuclea , and cons uc ion indus ies [
5
–
7
]. Mo e pa ailu es occu due
Appl. Sci. 2023,13, 8206. h ps://doi.o g/10.3390/app13148206 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2023,13, 8206 2 o 33
o he complexi y o he de ices p oduced. To a oid such hings, NDT indings o ecas
ailu e and enhance he sa e y and economy o en e p ises. Sump uous non-des uc i e
e alua ion echniques ha e been es ablished o majo sys ems such as powe plan s
and ai planes o con i m he du abili y o he NDT es and hei sa e y. Singh e al. [
8
]
p oposed he magne ic lux leakage (MFL) echnique o iden i y he localized aul s in
he SGT. Zhang e al. [
9
] implemen ed he MFL echnique o de ec bo h shallow su ace
and deep sub-su ace de ec s in e omagne ic ma e ials. Su esh e al. [
10
,
11
] sugges ed
he MFL app oach o he de ec ion o de ec s and subsu ace c acks in small-diame e
SGT. The expe imen al se up o he measu emen o MFL is de ailed in Su esh e al. [
10
].
Daniel e al. [
12
] designed an ANN model o o ecas he SGT’s de ec in e ms o he leng h,
b ead h, and dep h o he c ack by p o iding he g ay-le el co-occu ence ma ix (GLCM)
in o ma ion ex ac ed om he MFL images.
Wang e al. [
13
] s udied a de ailed e iew o he applica ion o ML models in p edic ing
he ou comes o s oke wi h s uc u ed da a. The andom o es (RF) ML algo i hm has been
implemen ed o p edic he ou come o endo ascula ea men [
14
] and acu e s oke [
15
]
and imp o e p edic ion accu acy in Ischemic s oke pa ien s. Decision ee (DT) and
ex eme g adien boos ing (XGB) ML algo i hms we e implemen ed o imp o e he accu acy
o he p edic ion o Ischemic s oke pa ien s [16].
In ML, ea u e selec ion, a me hod o selec ing independen pa ame e s, educes he
compu a ion ime and complexi y o he p oblem by elimina ing i ele an , no -use ul,
and edundan ea u es. Due o i s combina o ial na u e, ea u e selec ion is ea ed as
a non-polynomial ha d p oblem, which c ea es he oppo uni y o he esea che s o
implemen me a-heu is ic algo i hms. De i e al. [
17
] p oposed a new a ian o he
Golden Jackel Op imiza ion (GJO) algo i hm called Imp o ed GJO (IGJO) o sol e he
ea u e selec ion p oblem in ML. Qa aad e al. [
18
] in oduced quad a ic in e pola ion
wi h a salp swa m-based local escape ope a o in he ea u e selec ion o 19 da ase s and
conduc ed F iedman and Wilcoxon es s o analyze he esul s. Houssein e al. [
19
] imple-
men ed a cen oid mu a ion-based sea ch and escue op imiza ion algo i hm o ea u e
selec ion in 15 disease da a se s wi h di e en ea u e sizes ex ac ed om he UCI ma-
chine lea ning eposi o y and compa ed he pe o mance wi h six exis ing me a-heu is ic
algo i hms. Fil e -based and w appe -based echniques a e he wo basic ca ego ies un-
de which ea u e selec ion may be classi ied [
20
,
21
]. While he w appe -based s a egy
bases i s e alua ion o he solu ion h oughou he sea ching and op imiza ion p oce-
du es on he lea ning algo i hm, he il e -based app oach uses he co ela ion be ween
he da a and he ele an class label wi hou consul ing he lea ning algo i hm. The
w appe -based echnique is he mos equen ly employed ea u e selec ion me hod as
compa ed o he less compu a ionally expensi e il e -based app oach due o i s highe
pe o mance accu acy [22,23].
In his wo k, he ML model is o be de eloped o p edic he SGT’s de ec in e ms o
leng h, wid h, and dep h o c ack om he gi en g ay le el co-occu ence ma ix ea u e
om he MFL image. The ea u e selec ion me hod and he numbe o selec ed ea u es
will a ec he pe o mance o he ML models. The R
2
and oo mean squa e e o (RMSE)
alues a e conside ed me ics o measu e he pe o mance o he ML models. Mul iple con-
adic o y pe o mance measu es equi e he con e sion o mul iple objec i es in o a single
objec i e, which ini ia ed he implemen a ion o a mul i-c i e ion decision-making me hod,
namely Deng’s me hod. The dynamic popula ion g ay wol op imiza ion (DPGWO) algo-
i hm is implemen ed o selec he numbe o ea u es and hei combina ions o minimize
he p edic ion e o . The e ec i eness o he DPGWO algo i hm is p o ed by compa ing
i s pe o mance wi h he g ay wol op imiza ion (GWO) Algo i hm [
24
] and mo h lame
op imiza ion algo i hm (MFO) [
25
] by implemen ing a non-pa ame ic F iedman es [
25
]
and pe o mance indica o s.
The pape is o ganized as ollows. Sec ion 2desc ibes he p oblem s a emen , and
Sec ion 3desc ibes he p oposed me hodology and he a ious s ages, namely p io i izing
he ea u es, Taguchi o hogonal a ay expe imen al design [
25
], analysis o Va iance
Appl. Sci. 2023,13, 8206 3 o 33
(ANOVA) Tes , and me a-heu is ic algo i hms o ea u e selec ion in ol ed in sol ing he
p oblem. Sec ion 4deals wi h he esul s and discussion, including a compa ison o he
pe o mance o he DPGWO algo i hm wi h he MFO and GWO algo i hms. Finally, he
conclusion pa o he pape gi es u u e scope.
2. P oblem S a emen
Any model mus be app op ia ely selec ed o ma ch he equi emen s o he applica-
ion. Decision-make s analyze he beha io o da a using p edic ion models. Reg ession
models, a i icial neu al ne wo ks, and suppo ec o machines a e a ew echniques used
o build p edic ion models. Each echnique has i s own p os and cons based on he size
o he da ase . Recen ly, machine lea ning echniques ha e assis ed esea che s in de el-
oping mo e accu a e p edic ion models. The ype o machine lea ning (ML) model will
di e om p oblem o p oblem. The same ML model may no gi e simila pe o mance
ac oss applica ions. Hence, he selec ion o a sui able ML model o he gi en p oblem is a
challenging ask.
Apa om ha , he selec ion o app op ia e ea u es will play a majo ole in imp o -
ing he lea ning accu acy, compu a ion cos , and unde s anding o he model. O e i ing
o models is one o he majo p oblems ha will educe he applica ion o ML in a ious
ields. The p oblem conside ed in his wo k will be de eloping an accu a e ML model
wi h a smalle numbe o ea u es o p edic he c ack dimensions om 22 GLCM ea u es
ex ac ed om 105 MFL c ack images p esen ed by Daniel e al. [12].
3. Me hodology
The main ocus o he p esen wo k is o implemen a sui able ML Model wi h an
app op ia e selec ion o ea u es and hei combina ions o p edic he c ack dimensions
mo e accu a ely as compa ed wi h he exis ing ANN model. Daniel e al. [
12
] om he
gi en 22 GLCM ea u es ex ac ed om 115 MFL c ack images. This has been ca ied
ou in ou s ages. In he i s s age, he ea u es a e p io i ized based on F Sco e (FS)
and Mu ual In o ma ion Sco e (MIS) alues. L16 Taguchi o hogonal a ay design [
25
]
has been cons uc ed by conside ing ea u e selec ion me hods (FSM), machine lea ning
models (MLM), and numbe o ea u es as pa ame e s and R
2
and RMSE alues as esponse
alues. Fo each expe imen , py hon codes a e execu ed using he co esponding MLM,
FSM, and a ge numbe o ea u es as de e mined by he Taguchi a ay o de e mine
he co esponding R
2
and RMSE alues o bo h aining and es da a se s. To analyze
he e ec o pa ame e s and hei in e ac ion on he esponse alues, an ANOVA es
has been ca ied ou in he hi d s age. The esponses, namely R
2
and RMSE alues, o
he aining and es ing da a se s, a e di e en o each expe imen , which is simila o
di e en al e na i es among mul iple design p oblems. To selec he bes design, hese
mul iple esponses a e o be con e ed in o a single alue. Hence, in his wo k, a simila i y-
based mul i-c i e ion anking me hod called Deng’s me hod [
26
] is in oduced o selec he
bes ML model in he hi d s age. In he ou h s age, me a-heu is ic algo i hms, namely
MFO, GWO, and DPGWO, a new a ian o GWO p oposed in his wo k, ha e been
implemen ed o selec he numbe o ea u es and hei combina ions. Also, Pe o mance
indica o s and F iedman’s es ha e been conduc ed in he ou h s age o p o e he e ec-
i eness o he DPGWO, along wi h s a is ical analysis o con i m he esul s. The p oposed
me hodology is shown in Figu e 1. The s ep-by-s ep algo i hm o he p oposed wo k is
gi en below.
Appl. Sci. 2023,13, 8206 4 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 4 o 35
Figu e 1. P oposed Me hodology.
Figu e 1. P oposed Me hodology.
Appl. Sci. 2023,13, 8206 5 o 33
S ep 1:
Read he GLCM ea u es and hei co esponding c ack dimension da ase s.
S ep 2:
P io i ize he ea u es’ o de based on
(a) Mu ual In o ma ion Sco e (MIS)
(b) F Sco e (FS)
S ep 3:
A ange he ea u es based on MIS.
S ep 4:
Selec he i s 15 ea u es and ix one o he c ack’s dimensions as he a ge alue.
S ep 5:
Se a machine lea ning model and selec R
2
and RMSE as pe o mance me ics o he
machine lea ning model.
S ep 6:
Se he size o a aining da a se , and based on ha , sepa a e he aining and es ing
da a se s along hei a ge alues.
S ep 7:
Fi he ML model o he da a se and p edic bo h aining and es ing a ge alues.
S ep 8: Compu e he esponse alues (pe o mance me ics, namely R
2
and RMSE) o he ML
model o bo h he aining and es ing da a se s.
S ep 9:
Repea s eps 5 o 8 by changing he di e en ML models.
S ep 10:
Repea s eps 4 o 9 by changing he numbe o ea u es o 17, 19, and 21.
S ep 11:
Repea s eps 3 o 10 by a anging he ea u es based on he F Sco e.
S ep 12:
Conduc an ANOVA and s a is ical es o es he signi icance o he pa ame e s on
he esponse alues.
S ep 10: Implemen Deng’s me hod o selec he bes machine lea ning model based on R2 and
RMSE alues.
S ep 11:
Tune he hype -pa ame e s o he bes machine lea ning model.
S ep 12: Implemen he MFO, GWO, and DPGWO algo i hms by andomly selec ing he gi en
ea u es along wi h hei a ge alues be ween 15 and 21.
S ep 13:
Compa e he pe o mance o algo i hms using pe o mance indica o s (In e ed
Gene a ional Dis ance and Spacing) and F iedman’s Tes . Selec he bes numbe o
ea u es and hei combina ions.
S ep 14:
Repea he s eps om 3 o 15 o o he dimensions o he c ack, like c ack dep h and
c ack wid h.
3.1. S age 1: P io i izing he Fea u es
Conside a ion o all ea u es in machine lea ning may lead o poo pe o mance, excess
compu a ion ime, and o e i ing o he p edic ion model. To a oid his, ea u e selec ion
echniques ha e been used in ML. Since he w appe me hod o ea u e selec ion is an
i e a i e p ocess and slow in na u e, in his wo k wo il e me hods, namely, he F sco e
(FS) and he mu ual in o ma ion sco e (MIS), ha e been in oduced o selec ion. In he
F sco e me hod, ea u es a e selec ed s a is ically by iden i ying he ela ionship be ween
pa ame ic ea u es and a ge ea u es, whe eas in he mu ual in o ma ion sco e me hod,
ea u es a e selec ed based on hei en opy. Table 1 ep esen s he lis o 22 GLCM ea u es
ex ac ed om MFL images o c ack dimensions. Figu e 2 ep esen s he p io i ized ea u es
o c ack dimensions. I is unde s ood ha in Figu e 2a, he 3 d ea u e is gi en p io i y and
he 2nd ea u e is gi en leas he p io i y in he F-Sco e-based p io i ized me hod, whe eas
in he MIS me hod, he 1s ea u e has i s p io i y and he 19 h ea u e has he leas p io i y
in c ack leng h p edic ion. In c ack wid h p edic ion, he 7 h ea u e has i s p io i y in
bo h p io i ized me hods. Di e en ea u es, namely he 20 h and 6 h ea u es, ha e he
leas p io i y in c ack dep h p edic ion [27].
Table 1. GLSM Fea u e De ails (Daniel e al. [12]).
FNo. FName Fea u e Name
0 UNF Ene gy/Uni o mi y
1 ETR En opy
2 DSL Dissimila i y

Appl. Sci. 2023,13, 8206 6 o 33
Table 1. Con .
FNo. FName Fea u e Name
3 CST Con as
4 ID In e se Di e ence
5 CN Co ela ion
6 H Homogenei y
7 AC Au o co ela ion
8 CS Clus e shade
9 CP Clus e p ominence
10 MP Maximum P obabili y
11 SS Sum o squa es
12 SA Sum a e age
13 SV Sum Va iance
14 SE Sum en opy
15 DV Di e ence Va iance
16 DE Di e ence en opy
17 IMC (1) In o ma ion measu e o co ela ion1
18 IMC (2) In o ma ion measu e o co ela ion 2
19 MCC Maximal Co ela ion Coe icien
20 INN In e se Di e ence No malized
21 IDN In e se di e en momen no malized
FNo.—Fea u e Numbe and Fname—Fea u e Name.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 6 o 35
3
CST
Con as
4
ID
In e se Di e ence
5
CN
Co ela ion
6
H
Homogenei y
7
AC
Au o co ela ion
8
CS
Clus e shade
9
CP
Clus e p ominence
10
MP
Maximum P obabili y
11
SS
Sum o squa es
12
SA
Sum a e age
13
SV
Sum Va iance
14
SE
Sum en opy
15
DV
Di e ence Va iance
16
DE
Di e ence en opy
17
IMC (1)
In o ma ion measu e o co ela ion1
18
IMC (2)
In o ma ion measu e o co ela ion 2
19
MCC
Maximal Co ela ion Coe icien
20
INN
In e se Di e ence No malized
21
IDN
In e se di e en momen no malized
FNo.—Fea u e Numbe and Fname—Fea u e Name.
(a)
(b)
(c)
(d)
Figu e 2. Con .
Appl. Sci. 2023,13, 8206 7 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 7 o 35
(e)
( )
Figu e 2. P io i ized ea u es o c ack dimensions. (a) F Sco e-based p io i ized ea u es o C ack
Leng h. (b) MIS-based p io i ized ea u es o C ack Leng h. (c) F Sco e-based p io i ized Fea u es
o C ack Dep h. (d) MIS-based p io i ized ea u es o C ack Dep h. (e) F Sco e-based p io i ized
Fea u es o C ack Wid h. ( ) MIS-based p io i ized ea u es o C ack Wid h.
3.2. S age 2: Taguchi O hogonal A ay Expe imen al Design o ML Model Selec ion
In his wo k, a o al o six di e en ML models ha e been used, in which a di e en
combina ion o ou models is conside ed o each c ack dimension. The ML models’
names a e desc ibed in Table 2. The pa ame e s and hei le els conside ed o c ack
leng h a e ep esen ed in Table 3. The ML models conside ed o c ack dep h and c ack
wid h a e ep esen ed in Tables A1 and A4. Table 4 ep esen s he expe imen al pa ame e
se ings o he L16 Taguchi o hogonal a ay o he gi en combina ion o le els o pa am-
e e s men ioned in Table 3, ob ained using Mini ab 19 So wa e, whe e 16 ep esen s he
minimum numbe o expe imen al uns equi ed o conduc he expe imen s and o ind
he bes pa ame e se ings [28]. Fo each expe imen al un co esponding o i s pa ame e
se ings, Py hon code has been execu ed o he aining da a se wi h a sample size o 95
images’ ea u es and es ed wi h a da a size o 20 images. The pe o mance o he ML
model is eco ded o each expe imen based on he R2 and RMSE alues o bo h he ain-
ing and es ing da a se s. Deng’s me hod has been implemen ed o selec he bes ML
model based on he o e all pe o mance index calcula ed using R2 and RMSE alues,
which a e lis ed in Table 4. L16 Taguchi o hogonal a ay and Deng’s alues o c ack
dep h and c ack wid h a e p esen ed in Tables A2 and A5.
Table 2. Lis o Machine Lea ning (ML) Models Used in C ack Leng h.
Model
Name
DT
Decision T ee Reg esso
LoR
Logis ic Reg esso
LiR
Linea Reg esso
XGB
Ex eme G adien Boos e
ABR
Adap i e Boos e Reg esso
RF
Random Fo es Reg esso
Table 3. Pa ame e s and I s Le el o C ack Leng h.
Pa ame e
No. o Le els
Le els
1
2
3
4
FSM
2
FS
MIS
MLM
4
DT
LiR
LoR
XGB
NoF
4
15
17
19
21
Figu e 2.
P io i ized ea u es o c ack dimensions. (
a
) F Sco e-based p io i ized ea u es o C ack
Leng h. (
b
) MIS-based p io i ized ea u es o C ack Leng h. (
c
) F Sco e-based p io i ized Fea u es
o C ack Dep h. (
d
) MIS-based p io i ized ea u es o C ack Dep h. (
e
) F Sco e-based p io i ized
Fea u es o C ack Wid h. ( ) MIS-based p io i ized ea u es o C ack Wid h.
3.2. S age 2: Taguchi O hogonal A ay Expe imen al Design o ML Model Selec ion
In his wo k, a o al o six di e en ML models ha e been used, in which a di e en
combina ion o ou models is conside ed o each c ack dimension. The ML models’ names
a e desc ibed in Table 2. The pa ame e s and hei le els conside ed o c ack leng h a e
ep esen ed in Table 3. The ML models conside ed o c ack dep h and c ack wid h a e ep-
esen ed in Tables A1 and A4. Table 4 ep esen s he expe imen al pa ame e se ings o he
L16 Taguchi o hogonal a ay o he gi en combina ion o le els o pa ame e s men ioned
in Table 3, ob ained using Mini ab 19 So wa e, whe e 16 ep esen s he minimum numbe
o expe imen al uns equi ed o conduc he expe imen s and o ind he bes pa ame e
se ings [
28
]. Fo each expe imen al un co esponding o i s pa ame e se ings, Py hon
code has been execu ed o he aining da a se wi h a sample size o 95 images’ ea u es
and es ed wi h a da a size o 20 images. The pe o mance o he ML model is eco ded
o each expe imen based on he R
2
and RMSE alues o bo h he aining and es ing
da a se s. Deng’s me hod has been implemen ed o selec he bes ML model based on
he o e all pe o mance index calcula ed using R
2
and RMSE alues, which a e lis ed in
Table 4. L16 Taguchi o hogonal a ay and Deng’s alues o c ack dep h and c ack wid h
a e p esen ed in Tables A2 and A5.
Table 2. Lis o Machine Lea ning (ML) Models Used in C ack Leng h.
Model Name
DT Decision T ee Reg esso
LoR Logis ic Reg esso
LiR Linea Reg esso
XGB Ex eme G adien Boos e
ABR Adap i e Boos e Reg esso
RF Random Fo es Reg esso
Table 3. Pa ame e s and I s Le el o C ack Leng h.
Pa ame e No. o Le els
Le els
1 2 3 4
FSM 2 FS MIS
MLM 4 DT LiR LoR XGB
NoF 4 15 17 19 21
Appl. Sci. 2023,13, 8206 8 o 33
Table 4. L16 OA—Pe o mance o ML o C ack Leng h.
E.No. FSM MLM NoF R2T R2T RMSET RMSET Deng’s Value
1 FS DT 15 0.2619 0.3737 0.9684 1.4000 0.4569
2 FS DT 17 0.1998 0.4572 1.0000 1.3000 0.4771
3 MIS DT 19 0.6100 0.1434 1.0278 1.6440 0.4879
4 MIS DT 21 0.5940 0.1429 1.0282 1.6446 0.5040
5 FS LiR 15 0.9596 0.6091 0.2346 1.2090 0.4434
6 FS LiR 17 0.9592 0.6209 0.2389 1.1815 0.4616
7 MIS LiR 19 0.9221 0.6109 0.3917 1.1977 0.4643
8 MIS LiR 21 0.9078 0.5437 0.4225 1.2860 0.4248
9 MIS LoR 15 0.6002 0.1449 0.8200 1.6425 0.5484
10 MIS LoR 17 0.6120 0.1441 0.8150 1.6433 0.5360
11 FS LoR 19 0.5860 0.1434 0.8008 1.6441 0.5324
12 FS LoR 21 0.3960 0.1430 0.8400 1.6445 0.5408
13 MIS XGB 15 0.8652 0.8646 0.4410 0.6942 0.6073
14 MIS XGB 17 0.8757 0.8705 0.4055 0.6869 0.6444
15 FS XGB 19 1.0000 0.5988 0.0005 1.1801 0.6263
16 FS XGB 21 1.0000 0.5841 0.0006 1.2013 0.6326
3.3. S age 3: ANOVA Tes
The ANOVA Tes is used o analyze he di e ences among he means o di e en
g oups using a iance and o p o e which g oups a e s a is ically signi ican . To p o e ha
he pe o mance is signi ican ly di e en o a ious ML models, an ANOVA es [
24
] is
implemen ed in his wo k. Figu e 3 ep esen s he p obabili y plo o pe o mance measu es
o he ML model ob ained by execu ing he Py hon codes. I is unde s ood ha he alues
o R
2
and RMSE o bo h aining and es ing a e wi hin he 95% con idence in e al and
ha hei p obabili y alues a e g ea e han 0.005. This shows ha he expe imen a ion
esul s a e accep able o c ack leng h p edic ion. Simila ly, o c ack dep h and c ack
wid h, he p- alue shown in Figu e A1 and Table A6 is g ea e han 0.005, which e eals
ha he expe imen al esul s ob ained a e accep able.
The main and in e ac ion e ec plo s o pa ame e s a e depic ed in Figu e 4a–h o
c ack leng h p edic ion. I is in e ed om Figu e 4a,b ha he mean alue o R2T is highe
when he pa ame e s a e MIS, 15, and XGB, whe eas in R2T he pa ame e s a e FS and 18,
espec i ely. I is unde s ood om Figu e 4c,d, ha o ge ing he lowe mean alue o
RMSET and RMSET , he pa ame e s a e o be se in a di e en way han R2T and R2T .
F om Figu e 4e, , i is no ed ha inc easing he NoF alue dec eases he R2T alue o all
ML models, whe eas in R2T excep MLM and DT in all o he models, i inc eases. Using
XGB, a lowe RMSE is epo ed in Figu e 4g,h.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 8 o 35
Table 4. L16 OA—Pe o mance o ML o C ack Leng h.
E.No.
FSM
MLM
NoF
R2T
R2T
RMSET
RMSET
Deng’s Value
1
FS
DT
15
0.2619
0.3737
0.9684
1.4000
0.4569
2
FS
DT
17
0.1998
0.4572
1.0000
1.3000
0.4771
3
MIS
DT
19
0.6100
0.1434
1.0278
1.6440
0.4879
4
MIS
DT
21
0.5940
0.1429
1.0282
1.6446
0.5040
5
FS
LiR
15
0.9596
0.6091
0.2346
1.2090
0.4434
6
FS
LiR
17
0.9592
0.6209
0.2389
1.1815
0.4616
7
MIS
LiR
19
0.9221
0.6109
0.3917
1.1977
0.4643
8
MIS
LiR
21
0.9078
0.5437
0.4225
1.2860
0.4248
9
MIS
LoR
15
0.6002
0.1449
0.8200
1.6425
0.5484
10
MIS
LoR
17
0.6120
0.1441
0.8150
1.6433
0.5360
11
FS
LoR
19
0.5860
0.1434
0.8008
1.6441
0.5324
12
FS
LoR
21
0.3960
0.1430
0.8400
1.6445
0.5408
13
MIS
XGB
15
0.8652
0.8646
0.4410
0.6942
0.6073
14
MIS
XGB
17
0.8757
0.8705
0.4055
0.6869
0.6444
15
FS
XGB
19
1.0000
0.5988
0.0005
1.1801
0.6263
16
FS
XGB
21
1.0000
0.5841
0.0006
1.2013
0.6326
3.3. S age 3: ANOVA Tes
The ANOVA Tes is used o analyze he di e ences among he means o di e en
g oups using a iance and o p o e which g oups a e s a is ically signi ican . To p o e
ha he pe o mance is signi ican ly di e en o a ious ML models, an ANOVA es [24]
is implemen ed in his wo k. Figu e 3 ep esen s he p obabili y plo o pe o mance
measu es o he ML model ob ained by execu ing he Py hon codes. I is unde s ood ha
he alues o R2 and RMSE o bo h aining and es ing a e wi hin he 95% con idence
in e al and ha hei p obabili y alues a e g ea e han 0.005. This shows ha he expe -
imen a ion esul s a e accep able o c ack leng h p edic ion. Simila ly, o c ack dep h
and c ack wid h, he p- alue shown in Figu e A1 and Table A6 is g ea e han 0.005, which
e eals ha he expe imen al esul s ob ained a e accep able.
(a)
(b)
Figu e 3. Con .
Appl. Sci. 2023,13, 8206 9 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 9 o 35
(c)
(d)
Figu e 3. P obabili y Plo o Pe o mance Measu es o ML Models in C ack Leng h. (a) P obabili y
Plo o C ack Leng h-R2T . (b) P obabili y Plo o C ack Leng h-R2T . (c) P obabili y Plo o C ack
Leng h-RMSET . (d) P obabili y Plo o C ack Leng h-RMSET .
The main and in e ac ion e ec plo s o pa ame e s a e depic ed in Figu e 4a–h o
c ack leng h p edic ion. I is in e ed om Figu e 4a,b ha he mean alue o R2T is
highe when he pa ame e s a e MIS, 15, and XGB, whe eas in R2T he pa ame e s a e FS
and 18, espec i ely. I is unde s ood om Figu e 4c,d, ha o ge ing he lowe mean
alue o RMSET and RMSET , he pa ame e s a e o be se in a di e en way han R2T
and R2T . F om Figu e 4e, , i is no ed ha inc easing he NoF alue dec eases he R2T
alue o all ML models, whe eas in R2T excep MLM and DT in all o he models, i in-
c eases. Using XGB, a lowe RMSE is epo ed in Figu e 4g,h.
(a)
(b)
(c)
(d)
Figu e 3.
P obabili y Plo o Pe o mance Measu es o ML Models in C ack Leng h. (
a
) P obabili y
Plo o C ack Leng h-R
2
T . (
b
) P obabili y Plo o C ack Leng h-R
2
T . (
c
) P obabili y Plo o C ack
Leng h-RMSET . (d) P obabili y Plo o C ack Leng h-RMSET .
Appl. Sci. 2023, 13, x FOR PEER REVIEW 9 o 35
(c)
(d)
Figu e 3. P obabili y Plo o Pe o mance Measu es o ML Models in C ack Leng h. (a) P obabili y
Plo o C ack Leng h-R2T . (b) P obabili y Plo o C ack Leng h-R2T . (c) P obabili y Plo o C ack
Leng h-RMSET . (d) P obabili y Plo o C ack Leng h-RMSET .
The main and in e ac ion e ec plo s o pa ame e s a e depic ed in Figu e 4a–h o
c ack leng h p edic ion. I is in e ed om Figu e 4a,b ha he mean alue o R2T is
highe when he pa ame e s a e MIS, 15, and XGB, whe eas in R2T he pa ame e s a e FS
and 18, espec i ely. I is unde s ood om Figu e 4c,d, ha o ge ing he lowe mean
alue o RMSET and RMSET , he pa ame e s a e o be se in a di e en way han R2T
and R2T . F om Figu e 4e, , i is no ed ha inc easing he NoF alue dec eases he R2T
alue o all ML models, whe eas in R2T excep MLM and DT in all o he models, i in-
c eases. Using XGB, a lowe RMSE is epo ed in Figu e 4g,h.
(a)
(b)
(c)
(d)
Figu e 4. Con .
Appl. Sci. 2023,13, 8206 16 o 33
se s. Ea ly con e gence is eco ded in i e a ion numbe s 16, 18, 30, and 28 in he cases
o R
2
T , RMSET , R
2
T , and RMSET , espec i ely, in Figu e A5b,c,e, . Simila kinds o
Pa e o solu ion and con e gence plo s a e ob ained in he case o c ack wid h, as shown
in Figu e A6a– . I is also obse ed ha a majo di e ence in RMSE alue is achie ed in
DPGWO as compa ed o MFO and GWO in Figu e A6c, . The p- alue shown in Figu e A4
con i ms ha he esul s ob ained o 25 uns a e no mally dis ibu ed and accep able. Pe -
o mance indica o s a e used o compa e he pa e o solu ions gene a ed by he algo i hms.
In his wo k, wo di e en pe o mance indica o s, namely in e ed gene a ional dis ance
(IGD) and spacing (SP), a e implemen ed o check he e ec i eness o he algo i hms. Fo
p oblems wi h mo e han h ee objec i es, IGD is used o measu e he quali y o pa e o
op imal solu ions in e ms o dis ibu ion and con e gence, whe eas SP is used o measu e
he dis ibu ion and sp ead o pa e o op imal solu ions. In bo h cases, he lowe he alue,
he be e he pe o mance o he algo i hm. F om Table 12, i is con i med ha he DPGWO
algo i hm has lowe alues o IGD and SP as compa ed o he o he wo algo i hms, hence
i is ou pe o med.
Table 12. Pe o mance Indica o s o Algo i hms [30].
C ack Dimension Algo i hm IGD SP
C ack Leng h
MFO 0.10066 0.05977
GWO 0.10413 0.04707
DPGWO 0.09652 0.04558
C ack Leng h
MFO 0.23810 0.49592
GWO 0.21844 0.24535
DPGWO 0.19339 0.08908
C ack Leng h
MFO 0.20932 0.15989
GWO 0.34371 0.13514
DPGWO 0.08245 0.06335
To u he suppo he pe o mance o he algo i hms, F iedman’s es , a non-pa ame ic
es , has been implemen ed in his wo k. This es is used o de e mine whe he s a is ically
signi ican di e ences exis be ween he means o h ee o mo e g oups. In his wo k, he
Deng’s alues ob ained by 25 uns using h ee algo i hms a e conside ed o anking and
he calcula ion o mean alues. Using he “F iedman ()” unc ion in Ma lab, his es is
conduc ed. Table 13 ep esen s F iedman’s Tes alues and he mean anking o each algo-
i hm. All he p obabili y alues o c ack dimensions a e less han 0.05, which shows ha
he algo i hm’s pe o mance di e s om each o he , i.e., a signi ican e ec will be he e
on he selec ion o algo i hms. Usually, a lowe alue will be allo ed ank 1 in F iedman’s
Tes . Bu in his wo k, he highe he Deng’s alue, he be e he solu ion; he highe he
mean ank alue, he highe he pe o mance o he algo i hm; hence, i is p o ed ha he
mean ank alue o 2.24 in he case o c ack leng h p edic ion using DPGWO ou pe o med
as compa ed o he mean ank alues o 2.2 and 1.56 o he MFO and GWO algo i hms,
espec i ely. Simila ly, in he case o c ack dep h and wid h p edic ion, he mean ank o
DPGWO will be 2.23 and 2.12, which a e highe han he mean ank o MFO and GWO.
Table 13. F iedman’s Tes Values and Mean Ranking o Algo i hms [25].
C ack Dimensions
Mean Rank P obabili y
MFO GWO DPGWO
C ack Leng h 2.2 1.56 2.24 0.0263
C ack Dep h 1.98 1.78 2.23 0.0049
C ack Wid h 1.84 2.04 2.12 0.0093

Appl. Sci. 2023,13, 8206 17 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 17 o 35
(a)
(b)
(c)
(d)
(e)
( )
Figu e 7. Pa e o and Con e gence Plo o C ack Leng h. (a) Pa e o Plo o T aining Da a Se —C ack Leng h. (b) R2 Con e gence Plo o T aining Da a Se —
C ack Leng h. (c) RMSE Con e gence Plo o T aining Da a Se —C ack Leng h. (d) Pa e o Plo o Tes ing Da a Se —C ack Leng h. (e) R2 Con e gence Plo o
Tes ing Da a Se —C ack Leng h. ( ) RMSE Con e gence Plo o Tes ing Da a Se —C ack Leng h.
Figu e 7.
Pa e o and Con e gence Plo o C ack Leng h. (
a
) Pa e o Plo o T aining Da a Se —C ack Leng h. (
b
) R
2
Con e gence Plo o T aining Da a Se —C ack
Leng h. (
c
) RMSE Con e gence Plo o T aining Da a Se —C ack Leng h. (
d
) Pa e o Plo o Tes ing Da a Se —C ack Leng h. (
e
) R
2
Con e gence Plo o Tes ing
Da a Se —C ack Leng h. ( ) RMSE Con e gence Plo o Tes ing Da a Se —C ack Leng h.
Appl. Sci. 2023,13, 8206 18 o 33
The numbe o ea u es and hei combina ions ob ained by implemen ing he MFO,
GWO, and DPGWO o each c ack dimension a e p esen ed in Table 14, along wi h ea-
u es conside ed in he Taguchi O hogonal A ay Me hod (TM) and Desi abili y Me hod
(DM). In Table 14, ‘N’ ep esen s ha he pa icula ea u e is no selec ed by he me h-
ods/algo i hms.
Table 14. Lis o Fea u es Conside ed in Va ious Me hods.
FNo. Fname
C ack Leng h C ack Dep h C ack Wid h
TM DM
OT
TM DM
OT
TM DM
OT
MFO GWO DPGWO MFO GWO DPGWO MFO GWO DPGWO
0 UNF N N N
1 ETR N N N N N N N
2 DSL N N N N N
3 CST N N N N N N N
4 ID N N N N N N N
5 CN N N N N N N
6 H N N
7 AC N N N N N N N N
8 CS
9 CP
10 MP
11 SS
12 SA
13 SV
14 SE
15 DV
16 DE N N N N
17 IMC(1) N N N N
18 IMC(2) N
19 MCC
20 INN N
21 IDN N N N N N N N N N N
No. o Fea u es 19 17 17 17 17 19 21 17 17 17 17 19 17 17 17
The ea u e ha has a highe coun o ‘N’ is decided o be an impo an ea u e. The
lis o no -impo an ea u es compa ed by a ious me hods is p esen ed in Table 15. A
o al o 5 ou o 22 ea u es a e no conside ed impo an ea u es.
Table 15. No Impo ance Fea u es.
FNo. FName
1 ETR
3 CST
4 ID
7 AC
21 IDN
The pe o mance me ics o he sample conside ed in he exis ing li e a u e by
Daniel e al. [
12
] a e calcula ed based on he numbe o ea u es and hei combina ions
gi en in Table 16. Figu es 8–10 ep esen he ac ual c ack dimensions o he sample along
wi h he calcula ed c ack dimensions using he exis ing me hods, MFO, GWO, and DPGWO.
I is clea ha all he dimensions calcula ed by DPGWO a e e y close o he ac ual di-
mensions. Table 16 ep esen s he compa ison o he pe o mance me ics wi h exis ing
and p oposed algo i hms o he sample da a se conside ed by Daniel e al. I is obse ed
ha he R
2
alue is highe in DPGWO as compa ed wi h he exis ing me hods, MFO,
and GWO. In he mean ime, o he me ics like RMSE, MAE, and MAPE a e also lowe
in DPGWO as compa ed wi h o he s. I shows ha he DPGWO pe o med well. The
s a is ical compa ison o compu a ion ime o he p oposed DPGWO wi h MFO and GWO
is shown in Table 17. I is unde s ood ha he minimum compu a ion imes o DPGWO,
MFO, and GWO will be 32.1 s, 29.6 s, and 89.6 s, espec i ely. Due o he in oduc ion o
li e, ep oduc ion, and disease s a egies in DPGWO, he compu a ion ime is 8.4% highe
han he GWO algo i hm and 64.2% lowe han he MFO algo i hm.
Appl. Sci. 2023,13, 8206 19 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 19 o 35
GWO. In he mean ime, o he me ics like RMSE, MAE, and MAPE a e also lowe in
DPGWO as compa ed wi h o he s. I shows ha he DPGWO pe o med well. The s a is-
ical compa ison o compu a ion ime o he p oposed DPGWO wi h MFO and GWO is
shown in Table 17. I is unde s ood ha he minimum compu a ion imes o DPGWO,
MFO, and GWO will be 32.1 s, 29.6 s, and 89.6 s, espec i ely. Due o he in oduc ion o
li e, ep oduc ion, and disease s a egies in DPGWO, he compu a ion ime is 8.4% highe
han he GWO algo i hm and 64.2% lowe han he MFO algo i hm.
Figu e 8. Expe imen al VS P edic ed Value o C ack Leng h Using Di e en Algo i hms (EV-Expe -
imen al Value; P_EM-P edic ed alue using he exis ing me hod; P_MFO, P_GWO and P_DPGWO-
P edic ed alues based on he numbe o ea u es and i s combina ion ob ained using MFO, GWO,
and DPGWO algo i hms.
Figu e 9. Expe imen al VS P edic ed Value o C ack Dep h Using Di e en Algo i hms.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
12345678910 11 12
CRACK LENGTH IN MM
SAMPLE NO.
EV P_EV P_MFO P_GWO P_DPGWO
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
12345678910 11 12
CRACK DEPTH IN MM
SAMPLE NO.
EV P_EM P_MFO P_GWO P_DPGWO
Figu e 8.
Expe imen al VS P edic ed Value o C ack Leng h Using Di e en Algo i hms (EV-
Expe imen al Value; P_EM-P edic ed alue using he exis ing me hod; P_MFO, P_GWO and
P_DPGWO-P edic ed alues based on he numbe o ea u es and i s combina ion ob ained us-
ing MFO, GWO, and DPGWO algo i hms.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 19 o 35
GWO. In he mean ime, o he me ics like RMSE, MAE, and MAPE a e also lowe in
DPGWO as compa ed wi h o he s. I shows ha he DPGWO pe o med well. The s a is-
ical compa ison o compu a ion ime o he p oposed DPGWO wi h MFO and GWO is
shown in Table 17. I is unde s ood ha he minimum compu a ion imes o DPGWO,
MFO, and GWO will be 32.1 s, 29.6 s, and 89.6 s, espec i ely. Due o he in oduc ion o
li e, ep oduc ion, and disease s a egies in DPGWO, he compu a ion ime is 8.4% highe
han he GWO algo i hm and 64.2% lowe han he MFO algo i hm.
Figu e 8. Expe imen al VS P edic ed Value o C ack Leng h Using Di e en Algo i hms (EV-Expe -
imen al Value; P_EM-P edic ed alue using he exis ing me hod; P_MFO, P_GWO and P_DPGWO-
P edic ed alues based on he numbe o ea u es and i s combina ion ob ained using MFO, GWO,
and DPGWO algo i hms.
Figu e 9. Expe imen al VS P edic ed Value o C ack Dep h Using Di e en Algo i hms.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
12345678910 11 12
CRACK LENGTH IN MM
SAMPLE NO.
EV P_EV P_MFO P_GWO P_DPGWO
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
12345678910 11 12
CRACK DEPTH IN MM
SAMPLE NO.
EV P_EM P_MFO P_GWO P_DPGWO
Figu e 9. Expe imen al VS P edic ed Value o C ack Dep h Using Di e en Algo i hms.
Appl. Sci. 2023,13, 8206 20 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 20 o 35
Figu e 10. Expe imen al VS P edic ed Value o C ack Wid h Using Di e en Algo i hms.
Table 16. Compa ison o Pe o mance wi h exis ing and p oposed algo i hms.
Pe o mance Me ics
EM
MFO
GWO
DPGWO
R2
0.9970
0.9987
0.9981
0.9992
0.9938
0.9975
0.9966
0.9989
0.9969
0.9993
0.9990
0.9994
RMSE
0.101
0.066
0.078
0.050
0.032
0.020
0.023
0.014
0.208
0.099
0.126
0.089
MAE
0.0872
0.0563
0.0568
0.0417
0.0247
0.0147
0.0135
0.0099
0.1922
0.0792
0.1028
0.0727
MAPE
2.93
1.88
1.60
1.38
3.09
1.72
1.60
1.16
2.25
0.91
1.09
0.91
Table 17. Compa ison o compu a ion ime o algo i hms.
Va iable
Samples
Mean
S De
Va iance
Minimum
Q1
Median
Q3
Maximum
Skewness
Ku osis
DPGWO
12
45
8.23
67.68
32.1
39.95
43.7
52.77
59.6
0.22
−0.65
GWO
12
38.4
6.98
48.75
29.6
31.62
39.25
41.38
51.8
0.57
−0.09
MFO
12
108.42
15.64
244.77
89.6
95.93
103.75
126
133.7
0.42
−1.36
5. Conclusions
In his wo k, he bes ML model sui able o p edic he c ack dimensions om he
gi en 22 GLCM ea u es ex ac ed om MFL images epo ed by Daniel e al. [12], was
de e mined using he Taguchi L16 o hogonal a ay expe imen al design. Ou o six ML
models, he XGB model is iden i ied as he bes sui ed o he p oposed p oblem. Apa
om ha , wo- il e -based ea u e selec ion me hods a e implemen ed o p io i izing he
ea u es. The pe o mance o he ML models is examined based on he numbe o ea u es
and hei combina ions. Me a-heu is ic algo i hms, namely MFO, GWO, and a new a i-
an o GWO called DPGWO, a e implemen ed o iden i y he numbe o ea u es and hei
combina ions o achie e be e pe o mance o he selec ed XGB ML model. The p oposed
me hod p o ed ha by elimina ing 23% o he numbe o ea u es as compa ed wi h he
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
12345678910 11 12
CRACK WIDTH IN MM
SAMPLE NO.
EV P_EM P_MFO P_GWO P_DPGWO
Figu e 10. Expe imen al VS P edic ed Value o C ack Wid h Using Di e en Algo i hms.
Table 16. Compa ison o Pe o mance wi h exis ing and p oposed algo i hms.
Pe o mance Me ics EM MFO GWO DPGWO
R2
0.9970 0.9987 0.9981 0.9992
0.9938 0.9975 0.9966 0.9989
0.9969 0.9993 0.9990 0.9994
RMSE
0.101 0.066 0.078 0.050
0.032 0.020 0.023 0.014
0.208 0.099 0.126 0.089
MAE
0.0872 0.0563 0.0568 0.0417
0.0247 0.0147 0.0135 0.0099
0.1922 0.0792 0.1028 0.0727
MAPE
2.93 1.88 1.60 1.38
3.09 1.72 1.60 1.16
2.25 0.91 1.09 0.91
Table 17. Compa ison o compu a ion ime o algo i hms.
Va iable Samples Mean S De Va iance Minimum Q1 Median Q3 Maximum Skewness Ku osis
DPGWO 12 45 8.23 67.68 32.1 39.95 43.7 52.77 59.6 0.22 −0.65
GWO 12 38.4 6.98 48.75 29.6 31.62 39.25 41.38 51.8 0.57 −0.09
MFO 12 108.42 15.64 244.77 89.6 95.93 103.75 126 133.7 0.42 −1.36
5. Conclusions
In his wo k, he bes ML model sui able o p edic he c ack dimensions om he
gi en 22 GLCM ea u es ex ac ed om MFL images epo ed by Daniel e al. [
12
], was
de e mined using he Taguchi L16 o hogonal a ay expe imen al design. Ou o six ML
models, he XGB model is iden i ied as he bes sui ed o he p oposed p oblem. Apa
Appl. Sci. 2023,13, 8206 21 o 33
om ha , wo- il e -based ea u e selec ion me hods a e implemen ed o p io i izing he
ea u es. The pe o mance o he ML models is examined based on he numbe o ea u es
and hei combina ions. Me a-heu is ic algo i hms, namely MFO, GWO, and a new a ian
o GWO called DPGWO, a e implemen ed o iden i y he numbe o ea u es and hei
combina ions o achie e be e pe o mance o he selec ed XGB ML model. The p oposed
me hod p o ed ha by elimina ing 23% o he numbe o ea u es as compa ed wi h he
exis ing me hod, i was possible o ge good pe o mance using he XGB ML model. Also,
in his wo k, i is iden i ied ha he ea u es ETR, CST, ID, AC, and IDN a e no impo an
ea u es, i.e., hese ea u es a e elimina ed du ing he p edic ion o c ack dimensions.
The e ec i eness o he p oposed DPGWO is p o ed by compa ing F iedman’s Tes and
pe o mance indica o s’ alues, iz., IGD and SP wi h MFO and GWO. Also, he p oposed
me hod is implemen ed on he 12- es da a se ca ied ou by Daniel e al. [
12
]. As compa ed
o he exis ing me hod, he p oposed DPGWO pe o med well in calcula ing pe o mance
me ics like R
2
, RMSE, MAE, and MAPE. App oxima ely 0.2 o 0.5% imp o emen s in R
2
alue, 50% o 57% imp o emen in RMSE alue, 52% o 62% imp o emen in MAE alue,
and 53% o 63% imp o emen in MAPE alues a e epo ed by using a smalle numbe
o ea u es, i.e., 17 and i s combina ions, and implemen ing a new a ian o GWO called
DPGWO. As a u he scope, he w appe me hod o ea u es selec ion along wi h he
mul i- eg esso concep o ML models may be conside ed o imp o e pe o mance. Apa
om ha , he c ack dimensions may be changed om nume ical o ca ego ical da a ype,
and ML classi ie s can be in oduced ins ead o ML eg esso s. The p oposed DPGWO may
be implemen ed o cons ained enginee ing p oblems.
Au ho Con ibu ions:
Concep ualiza ion, M.V.A.W., S.R., R.C., S.K.M. and M.E.; da a cu a ion,
M.V.A.W.; Fo mal analysis, M.V.A.W.; in es iga ion, M.V.A.W.; me hodology, S.R. and M.E.; esou ces,
R.C. and S.K.M.; so wa e, S.R., R.C., S.K.M. and M.E.; isualiza ion, M.V.A.W. and S.R.; w i ing—
o iginal d a , M.V.A.W. and S.R.; w i ing— e iew and edi ing, R.C., S.K.M. and M.E. All au ho s
ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This wo k was suppo ed by he p ojec SP2023/088 suppo ed by he Minis y o Educa-
ion, You h, and Spo s, Czech Republic.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
The da a p esen ed in his s udy a e a ailable upon eques h ough
email o he co esponding au ho .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Appendix A
Gi Hub Link: h ps://gi hub.com/lawansisa/ML_MFO_GWO_DPGWO (accessed
on 1 June 2023).
Table A1. Pa ame e s and I s Le el—C ack Dep h.
Pa ame e No. o Le els
Le els
1 2 3 4
FSM 2 FS MIS
MLM 4 ABR LiR RF XGB
NoF 4 15 17 19 21

Appl. Sci. 2023,13, 8206 22 o 33
Table A2. L16 OA—Pe o mance o ML o C ack Dep h.
E.No. FSM MLM NoF R2T R2T RmseT RmseT Deng’s Value
1 FS ABR 15 0.7741 0.0441 1.3924 3.0091 0.3319
2 FS ABR 17 0.8537 0.1680 1.2802 3.3972 0.4154
3 MIS ABR 19 0.8699 0.0221 1.1833 3.1780 0.3480
4 MIS ABR 21 0.9154 0.0446 0.9110 3.2148 0.3941
5 FS LiR 15 0.5956 0.3609 1.8665 3.5540 0.4292
6 FS LiR 17 0.6049 0.2698 1.8390 3.3689 0.3965
7 MIS LiR 19 0.6883 0.4080 1.6204 3.6648 0.4693
8 MIS LiR 21 0.7274 0.2882 1.5332 3.5175 0.4361
9 MIS RF 15 0.9207 0.0444 0.8105 3.1208 0.4061
10 MIS RF 17 0.9228 0.0584 0.7603 3.0285 0.4208
11 FS RF 19 0.9330 0.0469 0.6982 3.2378 0.4224
12 FS RF 21 0.9412 0.0455 0.6224 3.0668 0.4325
13 MIS XGB 15 1.0000 0.4452 0.0006 3.6458 0.6737
14 MIS XGB 17 1.0000 0.4829 0.0005 3.7246 0.6806
15 FS XGB 19 1.0000 0.5153 0.0006 3.9049 0.6836
16 FS XGB 21 1.0000 0.4663 0.0004 3.7602 0.6761
Appl. Sci. 2023, 13, x FOR PEER REVIEW 22 o 35
9
MIS
RF
15
0.9207
0.0444
0.8105
3.1208
0.4061
10
MIS
RF
17
0.9228
0.0584
0.7603
3.0285
0.4208
11
FS
RF
19
0.9330
0.0469
0.6982
3.2378
0.4224
12
FS
RF
21
0.9412
0.0455
0.6224
3.0668
0.4325
13
MIS
XGB
15
1.0000
0.4452
0.0006
3.6458
0.6737
14
MIS
XGB
17
1.0000
0.4829
0.0005
3.7246
0.6806
15
FS
XGB
19
1.0000
0.5153
0.0006
3.9049
0.6836
16
FS
XGB
21
1.0000
0.4663
0.0004
3.7602
0.6761
(a)
(b)
(c)
(d)
Figu e A1. S a is ical In e ence o ML Models’ Pe o mance o C ack Dep h P edic ion. (a) P oba-
bili y Plo o C ack Leng h-R2T . (b) P obabili y Plo o C ack Leng h-R2T . (c) P obabili y Plo
o C ack Leng h-RMSET . (d) P obabili y Plo o C ack Leng h-RMSET
Figu e A1.
S a is ical In e ence o ML Models’ Pe o mance o C ack Dep h P edic ion. (
a
) P obabil-
i y Plo o C ack Leng h-R2T . (
b
) P obabili y Plo o C ack Leng h-R2T . (
c
) P obabili y Plo o
C ack Leng h-RMSET . (d) P obabili y Plo o C ack Leng h-RMSET .
Appl. Sci. 2023,13, 8206 23 o 33
Appl. Sci. 2023, 13, x FOR PEER REVIEW 23 o 35
(a)
(b)
(c)
(d)
(e)
( )
Appl. Sci. 2023, 13, x FOR PEER REVIEW 24 o 35
(g)
(h)
Figu e A2. Fac o ial and In e ac ion Plo s o Pe o mance o ML Models o C ack Dep h P edic-
ion. (a) R2 Fac o ial Plo o T aining Da ase —D. (b) R2 Fac o ial Plo o Tes ing Da ase —D. (c)
RMSEFac o ial Plo o T aining Da ase —D. (d) RMSEFac o ial Plo o Tes ing Da ase —D. (e) R2
In e ac ion Plo o T aining Da ase —D. ( ) R2 In e ac ion Plo o Tes ing Da ase —D. (g) RMSE
In e ac ion Plo o T aining Da ase —D. (h) RMSE In e ac ion Plo o Tes ing Da ase —D.
Figu e A2.
Fac o ial and In e ac ion Plo s o Pe o mance o ML Models o C ack Dep h P e-
dic ion. (
a
) R
2
Fac o ial Plo o T aining Da ase —D. (
b
) R
2
Fac o ial Plo o Tes ing Da ase —D.
(
c
) RMSEFac o ial Plo o T aining Da ase —D. (
d
) RMSEFac o ial Plo o Tes ing Da ase —D. (
e
) R
2
In e ac ion Plo o T aining Da ase —D. (
) R
2
In e ac ion Plo o Tes ing Da ase —D. (
g
) RMSE
In e ac ion Plo o T aining Da ase —D. (h) RMSE In e ac ion Plo o Tes ing Da ase —D.
Appl. Sci. 2023,13, 8206 24 o 33
Table A3. ANOVA o C ack Dep h P edic ion.
Sou ce DF R2T R2T RMSET RMSET
Adj SS Adj MS F-Value p-Value Adj SS Adj MS F-Value p-Value Adj SS Adj MS F-Value p-Value Adj SS Adj MS F-Value p-Value
Reg ession 13 0.29005 0.02231 87.17000 0.01100 0.54741 0.04211 65.07000 0.01500 6.58227 0.50633
753.53000
0.00100 1.22728 0.09441 8.76000 0.10700
NoF 1 0.00018 0.00018 0.70000 0.49100 0.00530 0.00530 8.20000 0.10300 0.00054 0.00054 0.81000 0.46300 0.03826 0.03826 3.55000 0.20000
FSM 1 0.00001 0.00001 0.02000 0.89300 0.00028 0.00028 0.44000 0.57700 0.00329 0.00329 4.90000 0.15700 0.00192 0.00192 0.18000 0.71400
MLM 3 0.00416 0.00139 5.42000 0.16000 0.02247 0.00749 11.57000 0.08100 0.05840 0.01947 28.97000 0.03400 0.10052 0.03351 3.11000 0.25300
NoF*NoF 1 0.00000 0.00000 0.00000 0.98300 0.00336 0.00336 5.20000 0.15000 0.00377 0.00377 5.60000 0.14200 0.02372 0.02372 2.20000 0.27600
NoF*FSM 1 0.00001 0.00001 0.03000 0.88400 0.00005 0.00005 0.08000 0.80900 0.00236 0.00236 3.51000 0.20200 0.00001 0.00001 0.00000 0.98100
NoF*MLM 3 0.00241 0.00080 3.14000 0.25100 0.01630 0.00543 8.39000 0.10800 0.01977 0.00659 9.81000 0.09400 0.08768 0.02923 2.71000 0.28100
FSM*MLM 3 0.00113 0.00038 1.47000 0.42900 0.02182 0.00727 11.24000 0.08300 0.00680 0.00227 3.37000 0.23700 0.09859 0.03287 3.05000 0.25700
E o 2 0.00051 0.00026 0.00129 0.00065 0.00134 0.00067 0.02154 0.01077
To al 15 0.29057 0.54870 6.58361 1.24882
Appl. Sci. 2023,13, 8206 25 o 33
Table A4. Pa ame e s and I s Le el—C ack Wid h.
Pa ame e No. o
Le els
Le els
1234
FSM 2 FS MIS
MLM 4 ABR LiR RF XGB
NoF 4 15 17 19 21
Table A5. L16 OA—Pe o mance o ML o C ack Wid h.
E.No. FSM MLM NoF R2T R2T RMSET RmseT Deng’s Value
1 FS ABR 15 0.8447 0.2031 0.1349 0.3008 0.4569
2 FS ABR 17 0.8633 0.2435 0.1240 0.2896 0.4771
3 MIS ABR 19 0.8573 0.3026 0.1271 0.2798 0.4879
4 MIS ABR 21 0.8789 0.3411 0.1191 0.2724 0.5040
5 FS LiR 15 0.6983 0.3227 0.1795 0.2604 0.4434
6 FS LiR 17 0.7047 0.3961 0.1781 0.2391 0.4616
7 MIS LiR 19 0.7382 0.3611 0.1663 0.2561 0.4643
8 MIS LiR 21 0.7632 0.1582 0.1518 0.2909 0.4248
9 MIS RF 17 0.9351 0.3889 0.0820 0.2648 0.5484
10 MIS RF 19 0.9361 0.3163 0.0800 0.2822 0.5360
11 FS RF 19 0.9328 0.2949 0.0800 0.2665 0.5324
12 FS RF 21 0.9337 0.3332 0.0793 0.2635 0.5408
13 MIS XGB 15 1.0000 0.1967 0.0006 0.2825 0.6073
14 MIS XGB 17 1.0000 0.4196 0.0006 0.2440 0.6444
15 FS XGB 19 1.0000 0.3050 0.0005 0.2688 0.6263
16 FS XGB 21 1.0000 0.3386 0.0006 0.2570 0.6326
Table A6. S a is ical Analysis o ML Models’ Pe o mance o C ack Wid h P edic ion.
Va iable Mean S De Va iance Minimum Q1 Median Q3 Maximum Range p-Value
R2T 0.8804 0.1061 0.0113 0.6983 0.7836 0.9058 0.9840 1.0000 0.3017 0.0950
R2T 0.3076 0.0743 0.0055 0.1582 0.2564 0.3195 0.3561 0.4196 0.2614 0.3030
RmseT 0.0940 0.0648 0.0042 0.0005 0.0203 0.1006 0.1476 0.1795 0.1790 0.0750
RmseT 0.2699 0.0170 0.0003 0.2391 0.2579 0.2676 0.2825 0.3008 0.0617 0.9400
Appl. Sci. 2023, 13, x FOR PEER REVIEW 26 o 35
Table A4. Pa ame e s and I s Le el—C ack Wid h.
Pa ame e
No. o Le els
Le els
1
2
3
4
FSM
2
FS
MIS
MLM
4
ABR
LiR
RF
XGB
NoF
4
15
17
19
21
Table A5. L16 OA—Pe o mance o ML o C ack Wid h.
E.No.
FSM
MLM
NoF
R2T
R2T
RMSET
RmseT
Deng’s Value
1
FS
ABR
15
0.8447
0.2031
0.1349
0.3008
0.4569
2
FS
ABR
17
0.8633
0.2435
0.1240
0.2896
0.4771
3
MIS
ABR
19
0.8573
0.3026
0.1271
0.2798
0.4879
4
MIS
ABR
21
0.8789
0.3411
0.1191
0.2724
0.5040
5
FS
LiR
15
0.6983
0.3227
0.1795
0.2604
0.4434
6
FS
LiR
17
0.7047
0.3961
0.1781
0.2391
0.4616
7
MIS
LiR
19
0.7382
0.3611
0.1663
0.2561
0.4643
8
MIS
LiR
21
0.7632
0.1582
0.1518
0.2909
0.4248
9
MIS
RF
17
0.9351
0.3889
0.0820
0.2648
0.5484
10
MIS
RF
19
0.9361
0.3163
0.0800
0.2822
0.5360
11
FS
RF
19
0.9328
0.2949
0.0800
0.2665
0.5324
12
FS
RF
21
0.9337
0.3332
0.0793
0.2635
0.5408
13
MIS
XGB
15
1.0000
0.1967
0.0006
0.2825
0.6073
14
MIS
XGB
17
1.0000
0.4196
0.0006
0.2440
0.6444
15
FS
XGB
19
1.0000
0.3050
0.0005
0.2688
0.6263
16
FS
XGB
21
1.0000
0.3386
0.0006
0.2570
0.6326
Table A6. S a is ical Analysis o ML Models’ Pe o mance o C ack Wid h P edic ion.
Va iable
Mean
S De
Va iance
Minimum
Q1
Median
Q3
Maximum
Range
p-Value
R2T
0.8804
0.1061
0.0113
0.6983
0.7836
0.9058
0.9840
1.0000
0.3017
0.0950
R2T
0.3076
0.0743
0.0055
0.1582
0.2564
0.3195
0.3561
0.4196
0.2614
0.3030
RmseT
0.0940
0.0648
0.0042
0.0005
0.0203
0.1006
0.1476
0.1795
0.1790
0.0750
RmseT
0.2699
0.0170
0.0003
0.2391
0.2579
0.2676
0.2825
0.3008
0.0617
0.9400
(a)
(b)
Figu e A3. Con .
Appl. Sci. 2023,13, 8206 32 o 33
4.
Liu, H.; Yue, Y.; Liu, C.; Spence , B.; Cui, J. Au oma ic ecogni ion and localiza ion o unde g ound pipelines in GPR B-scans
using a deep lea ning model. Tunn. Unde g . Space Technol. 2023,134, 104861. [C ossRe ]
5.
Xia, Y.; Shi, M.; Zhang, C.; Wang, C.; Sang, X.; Liu, R.; Zhao, P.; An, G.; Fang, H. Analysis o lexu al ailu e mechanism o
ul a iole cu ed-in-place-pipe ma e ials o bu ied pipelines ehabili a ion based on cu ing empe a u e moni o ing. Eng. Fail.
Anal. 2022,14, 106763. [C ossRe ]
6.
Wang, Y.-Y.; Lou, M.; Wang, Y.; Wu, W.-G.; Yang, F. S ochas ic Failu e Analysis o Rein o ced The moplas ic Pipes Unde Axial
Loading and In e nal P essu e. China Ocean Eng. 2022,36, 614–628. [C ossRe ]
7.
Zeng, L.; L , T.; Chen, H.; Ma, T.; Fang, Z.; Shi, J. Flow accele a ed co osion o X65 s eel g adual con ac ion pipe in high CO
2
pa ial p essu e en i onmen s. A ab. J. Chem. 2023,16, 104935. [C ossRe ]
8.
Singh, W.S.; Rao, B.P.; Thi una ukka asu, S.; Mahade an, S.; Mukhopadhyay, C.; Jayakuma , T. De elopmen o magne ic lux
leakage echnique o examina ion o s eam gene a o ubes o p o o ype as b eede eac o . Ann. Nucl. Ene gy
2015
,83, 57–64.
[C ossRe ]
9.
Zhang, J.; Liu, X.; Xiao, J.; Yang, Z.; Wu, B.; He, C. A compa a i e s udy be ween magne ic ield dis o ion and magne ic lux
leakage echniques o su ace de ec shape econs uc ion in s eel pla es. Sens. Ac ua o s A Phys. 2019,288, 10–20. [C ossRe ]
10.
Su esh, V.; Abudhahi , A.; Daniel, J. De elopmen o magne ic lux leakage measu ing sys em o de ec ion o de ec in small
diame e s eam gene a o ube. Measu emen 2017,95, 273–279. [C ossRe ]
11.
Su esh, V.; Abudhahi , A.; Daniel, J. Cha ac e iza ion o de ec s on e omagne ic ubes using magne ic lux leakage. IEEE T ans.
Magn. 2019,55, 6200510. [C ossRe ]
12.
Daniel, J.; Abudhahi , A.; Paulin, J.J. Magne ic Flux Leakage (MFL) based de ec cha ac e iza ion o s eam gene a o ubes using
a i icial neu al ne wo ks. J. Magn. 2017,22, 34–42. [C ossRe ]
13.
Wang, W.; Kiik, M.; Peek, N.; Cu cin, V.; Ma shall, I.J.; Rudd, A.G.; Wang, Y.; Doui i, A.; Wol e, C.D.; B ay, B. A sys ema ic e iew
o machine lea ning models o p edic ing ou comes o s oke wi h s uc u ed da a. PLoS ONE 2020,15, e0234722. [C ossRe ]
14.
Liu, M.; Gu, Q.; Yang, B.; Yin, Z.; Liu, S.; Yin, L.; Zheng, W. Kinema ics Model Op imiza ion Algo i hm o Six Deg ees o F eedom
Pa allel Pla o m. Appl. Sci. 2023,13, 3082. [C ossRe ]
15.
Xie, L.; Zhu, Y.; Yin, M.; Wang, Z.; Ou, D.; Zheng, H.; Liu, H.; Yin, G. Sel - ea u e-based poin cloud egis a ion me hod wi h a
no el con olu ional Siamese poin ne o op ical measu emen o blade p o ile. Mech. Sys . Signal P ocess.
2022
,178, 109243.
[C ossRe ]
16.
Lu, H.; Zhu, Y.; Yin, M.; Yin, G.; Xie, L. Mul imodal Fusion Con olu ional Neu al Ne wo k Wi h C oss-A en ion Mechanism o
In e nal De ec De ec ion o Magne ic Tile. IEEE Access 2022,10, 60876–60886. [C ossRe ]
17.
De i, R.M.; P emkuma , M.; Ki u higa, G.; Sowmya, R. IGJO: An imp o ed golden jackel op imiza ion algo i hm using local
escaping ope a o o ea u e selec ion p oblems. Neu al P ocess. Le . 2023, 1–89. [C ossRe ]
18.
Qa aad, M.; Amjad, S.; Hussein, N.K.; Elhosseini, M.A. An inno a i e quad a ic in e pola ion salp swa m-based local escape
ope a o o la ge-scale global op imiza ion p oblems and ea u e selec ion. Neu al Compu . Appl.
2022
,34, 17663–17721.
[C ossRe ]
19.
Houssein, E.H.; Sabe , E.; Ali, A.A.; Waze y, Y.M. Cen oid mu a ion-based Sea ch and Rescue op imiza ion algo i hm o ea u e
selec ion and classi ica ion. Expe Sys . Appl. 2022,191, 116235. [C ossRe ]
20.
Ganesh, N.; Shanka , R.; ˇ
Cep, R.; Chak abo y, S.; Kali a, K. E icien ea u e selec ion using weigh ed supe posi ion a ac ion
op imiza ion algo i hm. Appl. Sci. 2023,13, 3223. [C ossRe ]
21.
Hu, F.; Qiu, L.; Xiang, Y.; Wei, S.; Sun, H.; Hu, H.; Weng, X.; Mao, L.; Zeng, M. Spa ial ne wo k and d i ing ac o s o low-ca bon
pa en applica ions in China om a public heal h pe spec i e. F on . Public Heal h 2023,11, 1121860. [C ossRe ]
22.
Dai, X.; Xiao, Z.; Jiang, H.; Alazab, M.; Lui, J.C.S.; Min, G.; Dus da , S.; Liu, J. Task O loading o Cloud-Assis ed Fog Compu ing
Wi h Dynamic Se ice Caching in En e p ise Managemen Sys ems. IEEE T ans. Ind. In o m. 2023,19, 662–672. [C ossRe ]
23.
P iyada shini, J.; P emala ha, M.; ˇ
Cep, R.; Jayasudha, M.; Kali a, K. Analyzing Physics-Inspi ed Me aheu is ic Algo i hms in
Fea u e Selec ion wi h K-Nea es -Neighbo . Appl. Sci. 2023,13, 906. [C ossRe ]
24. Mi jalili, S.; Mi jalili, S.M.; Lewis, A. G ey Wol Op imize . Ad . Eng. So w. 2014,69, 46–61. [C ossRe ]
25.
Mahalingam, S.K.; Naga ajan, L.; Velu, C.; Dha ma aj, V.K.; Salunkhe, S.; Hussein, H.M.A. An E olu iona y Algo i hmic
App oach o Imp o ing he Success Ra e o Selec i e Assembly h ough a No el EAUB Me hod. Appl. Sci.
2022
,12, 8797.
[C ossRe ]
26.
Deng, H. A simila i y-based app oach o anking mul ic i e ia al e na i es. In Ad anced In elligen Compu ing Theo ies and
Applica ions. Wi h Aspec s o A i icial In elligence: Thi d In e na ional Con e ence on In elligen Compu ing, ICIC 2007, Qingdao, China,
21–24 Augus 2007; Huang, D.S., Heu e, L., Loog, M., Eds.; Lec u e No es in Compu e Science; Sp inge : Be lin/Heidelbe g,
Ge many, 2007; Volume 4682, pp. 253–262.
27.
Mi jalili, S.; Alja ah, I.; Ma a ja, M.; Heida i, A.A.; Fa is, H. G ey Wol Op imize : Theo y, Li e a u e Re iew, and Applica ion
in Compu a ional Fluid Dynamics P oblems. In Na u e-Inspi ed Op imize s; Sp inge : Cham, Swi ze land, 2019; pp. 87–105.
[C ossRe ]
28.
A i alagan, S.; Sappani, R.; ˇ
Cep, R.; Kuma , M.S. Op imiza ion and Expe imen al In es iga ion o 3D P in ed Mic o Wind Tu bine
Blade Made o PLA Ma e ial. Ma e ials 2023,16, 2508. [C ossRe ]

Appl. Sci. 2023,13, 8206 33 o 33
29.
Sa emi, S.; Mi jalili, S.Z.; Mi jalili, S.M. E olu iona y popula ion dynamics and g ey wol op imize . Neu al Compu . Appl.
2015
,
26, 1257–1263. [C ossRe ]
30.
Khalilpou aza i, S.; Nade i, B.; Khalilpou aza y, S. Mul i-Objec i e S ochas ic F ac al Sea ch: A Powe ul Algo i hm o Sol ing
Complex Mul i-Objec i e Op imiza ion P oblems. So Compu . 2019,24, 3037–3066. [C ossRe ]
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