Recei ed Ma ch 19, 2021, accep ed Ap il 24, 2021, da e o publica ion May 26, 2021, da e o cu en e sion June 3, 2021.
Digi al Objec Iden i ie 10.1109/ACCESS.2021.3083928
Applica ion o Neu al Ne wo k P edic i e Con ol
Me hods o Sol e he Shipping Con aine Sway
Con ol P oblem in Quay C anes
SERGEJ JAKOVLEV 1,2, TOMAS EGLYNAS1,
AND MIROSLAV VOZNAK 1,2, (Senio Membe , IEEE)
1Ma ine Resea ch Ins i u e, Klaipeda Uni e si y, 92294 Klaipeda, Li huania
2Depa men o Telecommunica ions, Facul y o Elec ical Enginee ing and Compu e Science, VSB–Technical Uni e si y o Os a a, 708 00 Os a a,
Czech Republic
Co esponding au ho : Se gej Jako le (s.jako le [email p o ec ed])
This wo k was suppo ed by he Eu opean Regional De elopmen Fund h ough he Resea ch Council o Li huania (LMTLT) unde P ojec
01.2.2-LMT-K-718-03-0001.
ABSTRACT Sma con ol sys ems a e mos ly applied in indus y o con ol he mo emen s o hea y
machine y while op imizing o e all ope a ional e iciency. Majo shipping companies use la ge quay c anes
o load and unload con aine s om ships and s ill ely on he expe ience o on-si e ope a o s o pe o m
anspo a ion con ol p ocedu es using joys icks and isual con ac me hods. This pape p esen s he
esea ch esul s o an EU- unded p ojec o he Klaipeda con aine e minal o de elop a no el con aine
anspo a ion secu i y and ca go sa e y assu ance me hod and sys em. I was concluded ha many isks a ise
du ing he con aine handling p ocedu es pe o med by he quay c anes and ope a o s. To minimize hese
isks, he au ho s p oposed con olling he sway o he sp eade using a model p edic i e con ol me hod
which applies a mul i-laye pe cep on (MLP) neu al ne wo k (NN). The pape analyzes cu en neu al
ne wo k a chi ec u es and case s udies and p o ides he enginee ing communi y wi h a unique case s udy
which applies eal ope a ion s a is ical da a. Se e al key aining algo i hms we e es ed, and he ini ial esul s
sugges ha he Le enbe g–Ma qua d (LM) algo i hm and a iable lea ning a e backp opaga ion pe o m
be e han me hods which use he mul i-laye pe cep on neu al ne wo k s uc u e.
INDEX TERMS Neu al ne s, da a mining, con ol sys ems.
I. INTRODUCTION
The logis ics sec o is cons an ly looking o a be e way o
dec ease he cos s associa ed wi h po handling ope a ions,
including main enance cos s, long ope a ional delays, and
human e o du ing echnical p ocedu es. Mos con aine s
a e handled by hea y machine y and ope a ed unde e en
less op imal s anda dized p ocedu es and con ol sys ems,
including hose applied a he Klaipeda con aine e minal.
Fac o s such as di e en con aine weigh s, wind gus s, ope -
a o expe ience and con ol ou ines o en cause con aine s
o sway chao ically du ing hei anspo a ion om ships.
I is inc easingly challenging o s abilize con aine s ca ied
by quay c ane sp eade s because o hei la ge weigh s and
sizes [1]. Enginee ing and indus y communi ies ha e dedi-
ca ed much a en ion o he examina ion and imp o emen o
The associa e edi o coo dina ing he e iew o his manusc ip and
app o ing i o publica ion was Xiaosong Hu .
mechanical c ane s abiliza ion sys ems, cons uc ion o new
componen s and de elopmen o new sma con ol sys ems
o mo emen and speed p edic ion sub- ou ines. Howe e ,
less a en ion has been paid o he ull au onomy o c ane
con ol ope a ions [2]. New con ol sub- ou ines mus ake
in o accoun he ull spec e o he na u e o he con aine
swinging p oblem [3]. Expe ienced on-si e ope a o s who
pe o m con aine -handling p ocedu es ha e yea s o expe-
ience and a e eady o espond o con inuous changes.
Howe e , due o a lack o knowledge o some c ucial
elemen s o con ol, hese ope a o s end o lea n alse in o -
ma ion. Visual eedback is used o aid in posi ioning he
con aine below he quay c ane. The e o e, i is necessa y o
con ol sudden changes in accele a ion o he con aine du -
ing i s anspo a ion along wi h he mo emen o he c ane,
which esul s in a change in he high ampli ude accele a ion.
The ollowing sec ion add esses he applica ion o p edic i e
con ol and neu al ne wo k (NN) me hods and sys ems.
VOLUME 9, 2021
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
II. LITERATURE REVIEW
A. RECENT ADVANCEMENTS IN CRANE SPREADER AND
CARGO STABILIZATION
Recen ad ances in a i icial in elligence, AI machine lea n-
ing [4], [5], and deep lea ning [6] ha e p esen ed new oppo -
uni ies o use in he indus y o sol e complex con ol and
scheduling p oblems. Many enginee ing p oblems om he
pas can now be sol ed using ad anced knowledge ex ac ion
me hods and big da a (BD) analy ics ools.
Many academic au ho s ely solely on he heo e ical
achie emen s in he ele an ield, while o he s p esen
s ong p ac ical applica ions in he a ea o anspo a-
ion, dealing wi h delay op imiza ion and a ious pa e n
p edic ions [7]–[11].
We analyzed ecen me hods o compensa ing he sway
o con aine s du ing mo emen [12] ( om ship o sho e
and sho e o ship ia quay c anes) and minimizing he
o e all anspo a ion p ocess [13]. We examined some
gene al me hodologies, including he use o key on-si e
sa e y and secu i y egula ions. The heo e ical pa o he
p esen ed model was based on esea ch ideas om he
ollowing au ho s. Zhang e al. [14] de eloped a model-
independen con ol me hod, called p opo ional-de i a i e
sliding mode con ol, o 3D o e head c ane sys ems o
achie e simul aneous olley posi ioning and payload swing
supp ession o quay c anes. Golo in and Palis [15] p esen ed
a obus con ol-based app oach o ac i e damping o elas ic
s uc u al ib a ions in gan y c anes. Yongming e al. [16]
analyzed he in luence o e ical de o ma ion in c anes on
an i-sway con ol; hey c ea ed a no el h ee-mass h ee-
deg ee-o - eedom elas ic dynamic model o he olley
sys em o sol e he sway p oblem. Ileš e al. [17] p e-
sen ed an asymp o ically s abilizing sequen ial dis ibu ed
model p edic i e con ol (MPC) o a 3D owe c ane.
Abdullahi e al. [18] p oposed a new online adap i e ou pu -
based command shaping (AOCS) echnique o e ec i e
payload sway educ ion in an o e head c ane. Smoczek and
Szpy ko [19] de eloped a new e olu iona y-based algo i hm
o a uzzy logic-based da a-d i en p edic i e model o ime
be ween ailu es (TBF) o an adap i e c ane con ol sys em.
Finally, Maghsoudi e al. [20] p esen ed an imp o ed uni y
magni ude ze o ib a ion (UMZV) shape o payload sway
educ ion o an unde ac ua ed 3D o e head c ane wi h hois -
ing e ec s.
B. RECENT ADVANCEMENTS IN CRANE PREDICTIVE
CONTROL
Au ho s Nelson and Johnson [21] de eloped wo model
p edic i e con ol app oaches o op imizing mic og id
dispa ch. Yang e al. [22] p oposed a model p edic i e con-
ol sys em wi h adap i e machine-lea ning-based building
models o building au oma ion and con ol applica ions.
Zeng e al. [23] aimed o inc ease he con ol pe o -
mance o a selec i e ca aly ic educ ion (SCR) deni i i-
ca ion sys em h ough modeling and dis u bance ejec ion.
Beckenbach e al. [24] analyzed model-based p edic i e
con olle s used o manage con ol asks wi h cons ain s on
he s a e. Bünning e al. [25] de eloped a model p edic i e
con ol me hod o oom empe a u e con ol in buildings.
Li e al. [26] explo ed a hie a chical model p edic i e con ol-
based ene gy managemen s a egy o uel cell hyb id con-
s uc ion ehicles. Liu e al. [27] p esen ed a no el ini e
con ol-se model p edic i e con ol (FCS-MPC) s a egy
o sol ing he well-known challenges in p edic i e con ol
egula ed NNPC. De León Puig e al. [28] p oposed a sim-
ple adap i e-p edic i e con ol scheme o a DC-DC buck
con e e . Hu e al. [29] de eloped gene alized p edic i e
con ol (GPC) o supp ess he e ec o ime- a ying delay
and pa ame e iden i ica ion e o du ing obo -assis ed ca -
dio ascula su ge y. Wang e al. [30] a emp ed o op imize
con ol pe o mance o he mean alue model o a uel-
powe ed ai c a engine; he au ho s designed an adap i e
uzzy adial basis unc ion (RBF) neu al ne wo k o pe o m
p edic i e ai - uel a io con ol o op imize pe o mance
and educe exhaus emissions in uel-powe ed unmanned
ae ial ehicles (UAVs). Ma aoui and Bouz a a [31] p o-
posed a dis ibu ed model p edic i e con ol based on a
game heo y amewo k o nonlinea sys ems wi h non-
linea ly coupled dynamics. Oyama and Du and [32] de el-
oped economic model p edic i e con ol (EMPC) which
in eg a es p ocess con ol and economic op imiza ion and
can po en ially allow ime- a ying ope a ing policies o
maximize economic pe o mance. Yin e al. [33] p esen ed
a da a-d i en mul i-objec i e p edic i e con ol app oach
o inc ease powe p oduc ion and educe a igue loads in
wind a ms using e olu iona y op imiza ion. Shi e al. [34]
analyzed he au onomous ehicle ajec o y planning me h-
ods and cons uc ed an adap i e model p edic i e con ol
(AMPC) ajec o y acking sys em which conside s dis-
u bances in he pa h cu a u e. Gao e al. [35] p oposed
a da a-d i en p edic i e con ol s a egy o a nonlinea
sys em, es ed on a con inuous s i ed ank hea e (CSTH)
benchma k. Maza and Rezaiezadeh [36] employed a model
p edic i e con olle (MPC) o minimize boile ac i a ion
ime. Pozzi e al. [37] add essed ba e y pack managemen
and de eloped non-linea model p edic i e con ol (NMPC).
Rami ez e al. [38] also de eloped a as model-based p edic-
i e con ol (MPC), designed o con ol ac i e and eac i e
powe exchanged by a g id-connec ed MMC, p o iding a as
dynamic esponse, low cu en THD, and cons an swi ching
equency. Vallianos e al., [39] p esen ed an expe imen al
and nume ical s udy o p edic i e con ol o a hyb id en-
ila ion sys em in an ins i u ional building, wi h an empha-
sis on he mal com o . Wang and Wang [40] discussed
he possibili ies o adop MPC in he au omo i e indus y.
Yin e al. [41] p esen ed a eliabili y awa e mul i-objec i e
p edic i e con ol s a egy o wind a ms based on machine
lea ning and heu is ic op imiza ions.
C. JUSTIFICATION OF THE SELECTED PREDICTION
METHOD
A deepe analysis o he scien i ic publica ions e ealed
posi i e esul s om he adop ion o ce ain a i i-
cial neu al ne wo k (ANN) aining algo i hms o sol e
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
p edic ion p oblems ia ime-se ies o ecas ing, espe-
cially, a modi ied Le enbe g–Ma qua d (LM) algo i hm by
Ga oosiha e al. [42]. Two au ho s de eloped his algo i hm
independen ly: Le enbe g [43] and Ma qua d [44].
O he esea ch eams ound LM use ul and e icien
enough o sol e complex asks in ime-cons ained si -
ua ions [45]. Billah e al. [46] p oposed an imp o ed
Le enbe g–Ma qua d (LM) aining algo i hm o a i i-
cial neu al ne wo ks o p edic he possible day-end clos-
ing s ock p ice. Keong e al. [47] de eloped an LM
back-p opaga ion a i icial neu al ne wo k model o p edic
loods. Au ho s Mul azam e al. [48] discussed new ends
and sou ces o enewable ene gy and p oposed a wind
speed p edic ion backp opaga ion neu al ne wo k (BPNN)
wi h he Le enbe g–Ma qua d algo i hm o weigh upda es.
Qiao e al. [49] de eloped an adap i e LM-algo i hm-based
echo s a e ne wo k (ALM-ESN) o chao ic ime-se ies p e-
dic ions. Zhang and Behe a [50] p oposed a p edic i e model
based on ecu en neu al ne wo ks ained wi h he LM back-
p opaga ion lea ning algo i hm o o ecas sola adia ion.
Mammadli [51] p oposed he use o a i icial neu al ne wo ks
using he LM op imiza ion algo i hm o he p edic ion o
inancial ime se ies. Finally, Shi e al. [52] p oposed an
imp o ed ecu si e Le enbe g–Ma qua d algo i hm (RLM)
o mo e e icien ly ain mul i-laye neu al ne wo ks and
achie e eliable e iciency in enginee ing asks.
LM algo i hms in combina ion wi h ad anced neu al ne -
wo k a chi ec u es can b ing posi i e esul s o p edic he
sway o he sp eade du ing mo emen and minimize he
ime delays du ing li e con ol ope a ions using MPC, by
con e ging mo e o en and accele a ing aining o be quick
enough in eal scena ios, unde eal con ol ope a ions.
D. WORKING HYPOTHESIS
Based on a e iew o he cu en ends in AI and sway con-
ol, we p opose a echnological solu ion capable o sol ing
he p oblem o con aine sway caused by lack o expe ience in
on-si e c ane ope a o s, by de eloping an MPC-based me hod
o p edic sp eade speed du ing unloading ope a ions. In his
pape , we p esen a gene ic wo k hypo hesis consis ing o wo
s a emen s:
– Despi e hei adap abili y in sol ing only gene ic cu e-
i ing p oblems and inding only a local minimum, LM algo-
i hms can be used in machine y con ol ope a ions whe e his
minimum is su icien o pe o m anspo a ion ope a ions
mo e e icien ly.
– By es ima ing speed ac o s and p edic ing ca go sway
scena ios o he p edic i e con ol model, LM is mo e obus
and can mo e e icien ly con e ge [53].
III. DESCRIPTION OF THE STATISTICAL DATA
ACQUISITION SYSTEM AND THE DATA ACQUISITION
PROCESS
A. DESCRIPTION OF THE EQUIPMENT USED TO COLLECT
THE TRAINING DATA
To acqui e he necessa y s a is ical da a o ain he algo-
i hm, we de eloped a senso y sys em and applied i o eal
ans-shipmen ope a ions using quay c anes, sp eade sys-
ems, AGVs, and ucks [54]. The sys em’s design and expe -
imen al backg ound we e modeled acco ding o he me hods
p esen ed by Ha ison e al. [55].
In he expe imen al sec ion, a DL1 PRO da a log-
ge /analyze acqui es and ans e s he da a. I uses a h ee-
axis accele ome e (6 g) o de ec he mo emen ec o .
Accele ome e wo king pa ame e s: 3-axis wo k modes wi h
a gua an eed 6 gminimum ull scale on all axes, and
maximum esolu ion o 0.005 g. We examined he dynamic
cha ac e is ics o he con aine s wi h di e en masses du ing
mo emen and placemen on AGVs/ ucks. The accele a ion
da a p o ed o be e y in e es ing and in o ma i e o he ana-
ly ical sec ion. The esea ch eam also examined he sp eade
and i s posi ion abo e he AGVs / ucks du ing con aine
handling ope a ions.
The mo emen de ec ion speed was calcula ed up o
100 imes pe second due o se e al echnology limi a ion ac-
o s. The da a logging accu acy o he expe imen al ha dwa e
sys em was se o 1 % due o possible i egula i ies in he
elec onics. Figu e 1 shows he da a logge ’s ha dwa e, and
Figu e 2 indica es i s placemen on he sp eade du ing he
expe imen .
This da a logging echnology (DL1 PRO da a logge ) was
selec ed o se e al key pa ame e s. Fi s , i eco ded accu a e
da a e e ences wi h exac ime s amps and h ee-dimensional
posi ions in space du ing mo emen . Second, i possesses su -
icien echnological compa ibili ies wi h o he in o ma ion
and communica ion echnologies (ICT). The logge i sel has
IP50 en i onmen al p o ec ion.
The expe imen was pe o med a he Klaipeda po con-
aine e minal – LKAB ‘‘Smel e’’. Du ing he da a acqui-
si ion expe imen , he necessa y equipmen was moun ed
on he sp eade o he quay c ane (Fig. 2). The quay
c ane pe o med con aine anspo a ion p ocedu es om he
ship on op o he AGV (Ship- o-Sho e ope a ions). Du ing
he sp eade ’s mo emen s, he accele a ion da a om he
accele ome e we e collec ed by he sys em and s o ed on
an SD ca d. The con aine and o he s a is ical in o ma ion
we e collec ed, including he mass o he con aine and he
ope a o s who con olled he mo emen s o he sp eade . The
en i e da a acquisi ion p ocess ook nine hou s o comple e
due o ba e y usage limi a ions. This da a was used o
he p esen esea ch (in o al, 200 sepa a e ope a ions we e
eco ded).
B. DESCRIPTION OF THE ACQUIRED DATA
Figu e 3 plo s measu ed da a om he expe imen al case
s udy o a shipping con aine unloading p ocedu e pe o med
by a quay c ane a he Klaipeda con aine po . Each mea-
su emen aken du ing he case s udies had i s own s a is ical
and ope a ional de ia ions and echnological i egula i ies,
mainly due o he s ic ules p esen ed in he ope a ions man-
ual o c ane ope a o s. Each ‘‘bes con ol choice’’ scena io
was pe o med wi hou ope a ional p oblems. Each con aine
a ied in mass, al hough de ia ions om he 20,000 kg li ing
VOLUME 9, 2021 78255
S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
FIGURE 1. DL-1 PRO Da alogge wi h GPS an enna ( he special p o ec i e
case was designed o wi hs and a ha sh physical en i onmen ).
FIGURE 2. Placemen o he da a acquisi ion senso y ha dwa e on he
quay c ane sp eade .
ope a ional s anda d we e minimal; i did no a ec he qual-
i y o he measu emen s. Figu es 4 depic s key s ages du ing
anspo a ion/unloading:
– Con aine aising wi h hooking
– Ve ical aising o he con aine
– Bias aising o he con aine
– Ho izon al anspo a ion o con aine
– Bias lowe ing o he con aine
– Ve ical lowe ing o he con aine
– Con aine placemen on he anspo means
( uck o AGV)
Figu e 3 p esen s he sway speed o he sp eade and
he con aine . This in o ma ion is e y impo an because
highe alues co ela e wi h he ac ual speed o he ca go
du ing anspo a ion and ship unloading a a designa ed po .
The da a indica e ha he o e all anspo a ion p ocess is
FIGURE 3. Compa ison o ou cases wi h de ec ed sp eade speed ac oss
he X-axis du ing con aine anspo a ion om he ship o he AGV.
FIGURE 4. Quay c ane wi h sp eade mo emen along h ee axes.
p olonged due o compensa ion o sway, he eby c ea ing
ime delays. Figu e 4 depic s quay c ane ca go anspo a ion
along all axes, he X-axis used o p edic ion p io i y due o
high sway speeds.
The li e a u e highligh s he e iciency o se e al
algo i hms used o ain neu al ne wo ks also used in a -
ious p edic i e con ol scena ios, i.e. a iable lea ning a e
backp opaga ion, scaled conjuga e g adien , ecu si e p e-
dic ion e o me hods, and he Le enbe g–Ma qua d me h-
ods. We discuss hese algo i hms in he ollowing sec ions
and apply hem o p edic he speed o he sp eade along
he X-axis using he MLP ne wo k s uc u e. To se he
inpu alues, we collec ed da a om en s a is ically simila
p ocedu es using con aine s o simila mass and he same
c ane ope a o . In he modeling phase, we assume ha all
con aine s a e anspo ed om a single poin in space ( om
he ship), wi hou de ia ions in hei ac ual placemen om
each ano he . In p ac ice, planning is pe o med wi h a delay
in mind, hus minimizing he e iciency o he e minal [56].
Mos ope a ions a e also synch onized wi h he on-si e
ope a o ’s ac ions o uck and AGV secu e mo emen s and
CO2 egula ions [57]. Such delays occu daily, and we aim o
demons a e he p oblem o he academic en i onmen , o he
enginee s wo king in his ield, and o show he capabili ies o
new AI p edic ion me hods o sol e he possible sway con ol
p oblems on-si e.
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
Jako le e al. [58] p esen ed he ini ial esul s, which
sugges ed he ollowing:
– Quay c ane ope a o s did no main ain uni o m ho i-
zon al mo emen speed o he con aine . The ladde shape
p esen ed in Figu e 3 indica es he ac ual dec ease in speed.
– Ope a o s ini ia ed sudden con ol mo emen s o he
joys ick o s op he con aine anspo a ion p ocess o sho
pe iods.
– Ope a o s ini ia ed co ec ions o mo emen s and he eby
p olonged he con aine anspo a ion p ocess.
– Lack o expe ience among ope a o s and low e iciency
in he echnological synch oniza ion and planning me hods
o quay c anes, ucks and AGVs led o addi ional unneces-
sa y oscilla ions o he ca go, up o he inal se en h s age o
he anspo a ion [59].
– Because he maximum speed o he sp eade is egula ed
by ISO ope a ional s anda ds, each con aine was anspo ed
wi h an a e age o 8.1 seconds delay o he en i e pe iod
o measu emen , he a e age con aine anspo a ion speed
being 40.4 seconds. Acco ding o he ope a ional manual,
he wo king e iciency o hese p ocedu es achie ed a me e
80 %.
– Each quay c ane is limi ed only by he human ac o ,
he e o e p omp ing new ad ancemen s in he ele an a ea
o enginee ing [60].
I is wo h men ioning ha he expe imen al s a is ical
da a which desc ibes he unde lying ne wo k and he sway
p ocess h oughou i sope a ing angewasassignedasui able
sampling equency in ad ance, while also elimina ing e o s.
IV. METHODOLOGY FOR THE PREDICTION MODEL
A. INTRODUCTION OF THE MODEL PREDICTIVE CONTROL
(MPC) STRATEGY
Fo he sp eade sway con ol s a egy, we p opose he appli-
ca ion o an MPC which uses an in e nal sys em model
o make single-s ep p edic ions o he sys em beha io and
compu e he con aine sway o e a p ede ined p edic ion
pe iod, aking in o accoun he ope a ional cons ain s o he
c ane. MPC can adequa ely measu e he dynamics o ene gy
consump ion de ices (mo o s) and he cha ac e is ics o he
mechanical componen s used o mo e he sp eade . New
measu emen s o he sys em and new p edic ions a e added
con inuously o he sys em.
Figu e 5 schema ically illus a es he main componen s o
cen alized model p edic i e con ol (CMPC), de ailing he
op imiza ion c i e ia o he model in Figu e 6.
MPC is a mul i a iable con ol algo i hm which uses:
•An in e nal dynamic model o he sp eade con ol
p ocess
•A his o y o pas sp eade mo emen s (speed alues)
•Op imiza ion c i e ia and he unc ion J, which collabo-
a e o e he eceding p edic ion ho izon and apply he
bes AI unc ions and me hods.
Gene al MPCs a e based on i e a i e, ini e-ho izon op i-
miza ion models. In he cu en s a e, a ime n, he sp eade
FIGURE 5. Desc ip ion o he MPC con ol s a egy o he quay c ane
(sys em) o de ec he speed o he sp eade along he X-axis du ing
con aine anspo a ion om he ship o AGV and o p edic he op imal
speed o his p ocedu e wi h ime s eps k+1[61].
s a e (speed) is sampled and a cos -minimizing con ol
s a egy is compu ed ( ia a nume ical minimiza ion algo-
i hm wi h he op imiza ion block shown in Fig. 5 and
Equa ions 1–3) o a ela i ely sho ime ho izon in he
u u e o he sampling pe iod T. Speci ically, an AI en iched
p edic ion s a egy calcula ion is used o explo e sp eade
speed de ia ions which emana e om he con ol cu en s a e
and ind a cos -minimizing con ol s a egy un il ime o
compu a ional pe iod Tc. A e he sp eade speed con ol
s a egy is applied, he sp eade speed is sampled again and
he calcula ions a e epea ed, yielding a new con ol and
new p edic ed speed. The p edic ion ho izon is con inuously
shi ed o wa d, and o his eason, MPC is also called
Receding Ho izon Con ol [62]. Al hough his app oach is no
op imal, in p ac ice i has gi en e y good esul s [63].
The de ined single con olle de e mines he sys em’s
inpu s. Fi s , a each con ol s ep, he CMPC con olle mea-
su es he cu en s a e o he quay c ane con ol sys em
(measu es he speed o he sp eade ) and de e mines which
alue con ol inpu s (speed con ol indica o s) o p o ide o
he sys em using p e-de ined nume ical op imiza ion models.
The model consis s o p edic ion algo i hms based on a neu al
ne wo k s uc u e, de ined in he ollowing sec ion.
P edic ion alues (desi ed speed o he sp eade ) a e linked
o he objec i e unc ion o minimize he o e all anspo a-
ion ime o he ca go by he sp eade . These op imum alues
de e mine he ac ions which p o ide he bes -p edic ed pe -
o mance acco ding o a gi en objec i e unc ion minJ:
min J ( T,T)=XT=n
T=1
ST
T
,(1)
whe e Jis he o al minimized anspo a ion ime, Tis he
desi ed pe iod o he con ol p ocedu e o ake e ec ( o
each p edic ion s ep k+1), nis he numbe o pe iods in a
anspo a ionp ocess om heship o he AGV,Sis he ans-
po a ion dis ance, and is he anspo a ion speed (ob ained
by he sys em om he p oposed da a acquisi ion uni ).
The e o e, he e ec i eness o he MPC can be desc ibed
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
FIGURE 6. Schema ic o he MPC Con olle op imiza ion algo i hm wi h
he op imiza ion objec i e o he con ol ac ion, i.e.,
o inc ease/dec ease he ca go anspo a ion speed.
as (2) and (3):
min MPC (T,Tc)=(min J,min C),(2)
min C (Tc)=XT=n
T=1CTc,(3)
whe e Tcis he compu a ion pe iod o each new p edic ion.
This s a egy includes he con ol a iables de e mined o
he i s p edic ion s ep applied o he sys em, a e which he
cycle epea s. The goal o his con ol s a egy is o de e mine
he op imal con ol alues so ha he sp eade s abiliza ion
ime delay and ene gy consump ion cos s a e minimized.
Hence, he p edic i e con ol p oblem is s a ed as de e mining
he inpu alues so ha he con ol objec i es a e achie ed
op imally while sa is ying he o e all mechanical and elec i-
cal quay c ane con ol sys em cons ain s. The p oposed MPC
solu ion does no ha e eal- ime p ope ies. Delays occu ing
due o he compu a ional imes o each pe iod Tdec ease
he eal- ime p ope ies, i.e., an inc ease in he numbe o
pe iods inc eases he o e all compu a ional ime o he en i e
ope a ion; howe e , i can dec ease he anspo a ion ime o
each con aine .
The hea o he con olle is a model M( ), pa ame e ized
by a da a se (consis ing o ime-se ies da a samples o
sp eade speed momen um alues zk– inpu da a samples
o he neu al ne wo k o each inpu node. These a e ec o s
FIGURE 7. Schema ic o he ANN MLP s uc u e used in his s udy.
o he app op ia e dimensions used o p edic he mo emen
speed o he sp eade . He e, kis he numbe o desi ed inpu
nodes. Op imiza ion is subjec o he cons ain s o he con-
olle a iables (CVs). The e ec i eness o he MPC sys em
in hese con ol asks is om he ad an ages o he implici
closed-loop con ol law. Only he i s o he se o con ol
alues, i.e., , is ansmi ed o he p edic ion model, a e
which he comple e op imiza ion and p edic ion p ocedu e
is epea ed using he cu en speed alue ou pu , he eby
imp o ing he esul s a each i e a ion, a e each pe iod T.
B. MODEL STRUCTURE SELECTION
The aim o his s udy is o analyze and discuss he pe o -
mance o an a i icial neu al ne wo k, i.e., a mul i-laye pe -
cep on (MLP), in he p edic ion and es ima ion o con aine
sway du ing a quay c ane unloading p ocess. The modeling
p oblem was de ined as a ime se ies o ecas ing unc ion
app oxima ion p oblem. MLP can model complex unc-
ional ela ionships and app oxima e any complex nonlinea
unc ion.
To es he unc ionali y and e iciency o he LM
algo i hm, we compa ed i o se e al o he con en ional
algo i hms:
– Recu si e p edic ion e o me hod
– Scaled conjuga e g adien
– Va iable lea ning a e backp opaga ion
The ne wo k inpu s we e he sp eade speeds om he
p esen ed case s udies. A each new phase, he ne wo k is
ained using he p e ious ‘‘bes -case’’ expe ience om he
da a se , adding he new node zn, upg ading he da a se θ
and elimina ing he ‘‘wo s -case’’ scena ios, while keeping
he numbe o pa ame e s and he size o he da a se θcon-
s an . We designed a ully connec ed wo-laye eed o wa d
MLP-ne wo k con aining ou inpu s o each speed alue,
along wi h a a ying numbe o hidden uni s, and a single
ou pu uni , o he p edic ion o X-axis sp eade sway speed
(Fig. 7).
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
FIGURE 8. Implemen a ion o he Le enbe g–Ma qua d algo i hm in
NNSYSID.
The ne wo k ou pu is he p edic ed speed o he sp eade
acco ding o he c ane ope a o ’s con ol ac ions. ANN ain-
ing da a ZNconsis s o inpu s o he ne wo k u( )and
FIGURE 9. In es iga ed indices o sys em o de s om 1 o 6.
co esponding desi ed ou pu s y( ):
ZN={[u( ),y( )]|i=1. . . N}.(4)
The de ined MLP ne wo k consis s o a hidden laye and
hype bolic angen sigmoid ac i a ion unc ions ( ,F):
ˆyi(w,W)=FiXq
jWij jX2
l=1wjlzl+wj0+Wi0.
(5)
In his case, he MLP hidden laye (.) o each hidden
neu on zj,wjis p esen ed as:
jzj,wj=2
1+e−2P2
j=1zj·wji+wj0
−1.(6)
The ou pu o he neu al ne wo k wi h nnodes in a hidden
laye is de ined as:
yiyij,Wij=FXi=1yij ·Wij +W0j.(7)
The weigh s (speci ied by he ec o θand by he ma ices
wand W) a e he adjus able pa ame e s o he MLP ne wo k
de e mined h ough he neu al ne wo k aining p ocedu e.
The objec i e o he aining is hen o de e mine a mapping
om he se o aining da a o he se o possible weigh s:
ZN→ˆ
θ. (8)
MLP p oduces he p edic ions ˆyi( ). MLP uses he p edic-
ion e o app oach, which measu es closeness in e ms o a
mean squa e e o c i e ion:
VNθ, ZN=1
2·NXN
i=1yi− ˆyi|θT
yi− ˆyi|θ.(9)
The weigh s o he p edic ions a e:
ˆ
θ=a g min
θVNθ, ZN.(10)
By an i e a i e minimiza ion scheme:
θi+1=θi+µi· i,(11)
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
FIGURE 10. In es iga ed indices o sys em o de s om 1 o 6 o pas
inpu s and pas ou pu s.
FIGURE 11. One-s ep ahead p edic ion o an NN wi h 10 hidden neu ons
and a 3 d o de model using he LM algo i hm.
whe e θispeci ies he cu en i e a e, and iis he sea ch
di ec ion wi h he s ep size µi.
The selec ed MLP neu al ne wo k s uc u e and ma h-
ema ical de ini ion is he mos -o en conside ed choice
o p edic ion p oblems [64] which use only one hidden
laye . In pa icula , we selec ed he LM e sion o Bap is a
and Mo gado-dias [53] o aining since i p o ed e ec-
i e in sol ing simila asks. The di e ence be ween he
Ma qua d [44] and he cu en i e a ion o LM is in he ol-
lowing adjus men s by Fle che [65]. The size o he elemen s
FIGURE 12. P edic ion e o s o an NN wi h 10 hidden neu ons and a 3 d
o de model using he LM algo i hm.
o he diagonal ma ix added o he Gauss–New on Hessian
is acco ding o he size o he a io be ween ac ual dec ease
and p edic ed dec ease:
i=VNθi,ZN−VNθi+ ji,ZN
VNθi,ZN−Liθi+ ji,(12)
Lθi+ ji=VNθi,ZN+ TB(θi)+ +1
2 TB(θi) ji,
(13)
whe e Bdeno es he g adien o he c i e ion conce ning he
weigh s, and Ris he so-called Gauss-New on app oxima-
ion o he Hessian. The ollowing NNSYSID algo i hm was
applied o he LM (Fig. 8):
A. Selec an ini ial pa ame e ec o θ0and an ini ial
alue δ0;
B. De e mine he sea ch di ec ion om [R(θi+δi·I)]·
ji = −G(θi), whe e Iis a uni ma ix;
C. I he p edic ed dec ease is close o he ac ual dec ease,
le he sea ch di ec ion app oach he Gauss–New on sea ch
di ec ion while inc easing s ep size, i>0.75 →δi=δi
2;
D. I a p edic ed dec ease is a om he ac ual dec ease,
le he sea ch di ec ion app oach he g adien di ec ion while
dec easing s ep size, i<0.25 →δi=2·δi;
E. I VNθi+ ji,ZN<VNθi,ZN, hen θi+1=θi+ ji
as a new i e a e and le δi+1=δi,i=i+1.
F. I he s opping c i e ion is no sa is ied, go o 2).
The weigh s a e adjus able, and hey a e upda ed h ough
ne wo k aining. The objec i e o he aining is hen o
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S. Jako le e al.: Applica ion o NN P edic i e Con ol Me hods
FIGURE 13. One-s ep ahead p edic ion o an NN wi h 10 hidden neu ons
and a 3 d o de model using he ecu si e p edic ion e o me hod.
de e mine a mapping om he se o aining da a o he se
o possible weigh s.
Many me hods a e a ailable o selec he numbe o
nodes in a hidden laye [66], howe e no gene al ule exis s
which mee s e e y case o neu al ne wo k design. The e o e,
we designed se e al NN s uc u es: 5, 10, 15, and 20 hidden
neu ons in each case. We de ined he no mal dis ibu ion
o andom ini ial weigh s o each ial and pa i ioned he
aining and es da a. T aining was pe o med on he i s
70 % o he sequence and he es on he inal 30 %. Each
algo i hm was p og ammed o ain un il he squa ed e o
h eshold was less han 0.005.
V. COMPUTATIONAL RESULTS
The neu al ne wo k was ained using MATLAB so wa e.
Fi s , he aining se was scaled o a ze o mean and a a iance
o one, and hen he es se was scaled wi h he same con-
s an s. Nex , we add essed he p oblem o inding he o de
o he sys em (Fig. 9).
I is di icul o conclude any hing ce ain om his igu e.
The added measu emen noise in all ou da a samples co -
up ed he measu emen s. Figu e 10 cha s he o de index
co ela ion wi h pas inpu s and ou pu s.
We can assume ha he sys em can be modeled by a 3 d
o de model since he slope o he cu e dec eases o model
o de s ≥3. Figu es 11 o 18 indica e he e iciency o he
aining algo i hms o one-s ep-ahead p edic ions.
A compa ison o he plo s o he aining and es se s
o all ou algo i hms was sa is ac o y. The compu a ional
FIGURE 14. P edic ion e o s o an NN wi h 10 hidden neu ons and a 3 d
o de model using he ecu si e p edic ion e o me hod.
FIGURE 15. One-s ep ahead p edic ion o an NN wi h 10 hidden neu ons
and 3 d o de model using scaled conjuga e g adien .
esul s sugges ha he ne wo ks do no o e i he da a in
each case. The e o e, we conclude ha he selec ed MLP
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