Application of neural network predictive control methods to solve the shipping container sway control problem in quay cranes

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 This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ 78253 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 78254 VOLUME 9, 2021 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. 78256 VOLUME 9, 2021 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 VOLUME 9, 2021 78257 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). 78258 VOLUME 9, 2021 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) VOLUME 9, 2021 78259 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 78260 VOLUME 9, 2021 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 VOLUME 9, 2021 78261