Ship Performance and Navigation Data Compression and Communication under Autoencoder System Architecture

JournalofOceanEngineeringandScience3(2018)133–143

www.elsevier.com/locate/joes

Ship performance and navigation data compression and communication under autoencoder system architecture

Lokukaluge P. Perera

, B. Mo

aUiTTheArcticUniversityofNorway,Tromso,Norway

bSINTEFOcean,Trondheim,Norway

Received7October2017;receivedinrevisedform16January2018;accepted13April2018 Availableonline21April2018

Abstract

Modernvesselsare designedtocollect, storeand communicate largequantities ofship performanceand navigationinformationthrough complexonboarddatahandlingprocesses.Thatdatashouldbetransferredtoshorebaseddatacentersforfurtheranalysisandstorage.However, theassociatedtransfercostin large-scaledatasetsisamajor challengefortheshippingindustry,today.Thesamecostrelatestotheamount of data thatare transferringthrough variouscommunicationnetworks (i.e.satellites and wirelessnetworks), i.e.between vesselsand shore baseddata centers. Hence, this studyproposes to useanautoencoder systemarchitecture (i.e.adeep learning approach)to compress ship performanceand navigation parameters(i.e.reducethe numberofparameters) and transferthroughthe respectivecommunicationnetworks asreduceddatasets.Thedata compressionisdoneunderthelinearversionofanautoencoderthatconsistsofprincipalcomponentanalysis (PCA), wherethe respectiveprincipalcomponents(PCs)representthestructureofthe dataset.Thecompresseddatasetisexpandedby the samedata structure(i.e.anautoencodersystemarchitecture)atthe respectivedata centerrequiringfurtheranalysesandstorage. Adataset ofshipperformanceandnavigationparametersinaselectedvesselisanalyzed(i.e.datacompressionandexpansion)throughanautoencoder system architecture and the resultsare presented in this study.Furthermore,the respectiveinput and output valuesof the autoencoder are alsocomparedasstatisticaldistributionsand samplenumberseriestoevaluate itsperformance.

© 2018Shanghai JiaotongUniversity.Publishedby ElsevierB.V.

Thisisanopenaccess articleunderthe CCBY-NC-NDlicense.(http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords:Autoencoder;Shipperformanceandnavigationinformation;Shipenergyefficiency;Datacompression;Datacommunication;Principalcomponent analysis.

1. Introduction

1.1. Performance and navigationdata

Theshipenergyefficiencymanagementplan(SEEMP)[1], i.e. amandatoryrequirement, enforcesvesselstocollectship performanceandnavigationinformationbyimplementingvar- ious onboard sensors and data acquisition (DAQ) systems.

These DAQ systems are designed to collect, store andcom- municatelargequantities ofship performanceandnavigation informationthrough complexdata handling processes. Those arealsofacilitatedbyintegratedbridgesystems(IBSs),where

∗Correspondingauthor.

E-mailaddresses:[email protected](L.P.Perera), [email protected](B.Mo).

variousnavigationandautomation systemsareconnected[2]. These DAQ systems can create large-scale data sources and introduceadditionalchallengesinonboarddatahandling pro- cesses. The same issues have often been identified as “Big Data” challenges by various industrial applications due to theirvolume,variety,veracityandvelocityconsiderations[3]. Suchbigdatasetscanalsocreateadditionalchallengesduring data transmission processes (i.e. between vessels and shore based data centers). e.g. the associated costs to transfer of suchdatasetsthroughvarioussatellitenetworksarerelatively expensiveinshipping. Hence, effective approaches toreduce the amount of data that communicate through such satellite networks are considered by the shipping industry in recent yearsandthat reduce the associated datatransfercosts.

https://doi.org/10.1016/j.joes.2018.04.002

2468-0133/© 2018ShanghaiJiaotongUniversity.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense.

(http://creativecommons.org/licenses/by-nc-nd/4.0/)

In general,the mostpreferred methodby the shipping in- dustry is to increase the length of the sampling period (i.e.

alower samplingrate) inwhich reducesthe numberof data samples collected with a selected time period. This method reducesthesizeofshipperformanceandnavigationdatasets, thereforethe associateddatatransfercostscanbeminimized.

However, such data sets may not consist of all relevant in- formationonshipperformanceandnavigationconditionsdue tothe lower datasampling rate. Furthermore, that canintro- duce additionalchallenges inparameter estimation processes [4],where estimationalgorithms can divergefrom the actual valuesdue to inadequate data samplingrates. Therefore, the actualperformance andnavigationparameterscannotbe esti- matedfrom suchdata setsinsomesituations.e.g.the engine fuelandpowerconsumptionvaluesinvesselscannotbecom- pared,adequately duetothe lower samplingrate of the data sets.

1.2.Recent studies

Various ship performance andnavigation monitoring sys- tems with sensors and DAQs are implemented by the ship- pingindustry.Theseon-boardsystems as apart of IBSscol- lectvariousshipperformance andnavigationparametersfrom navigationandautomationsystems.Thesameparameters(i.e.

collect as big data sets) represent ship operational and nav- igation information that can be used under various decision supportsystems.Thesesystemscanoftenbedividedintotwo categoriesofsafetyandperformancemonitoringsystems.The safetymonitoring systems focus onimprovingthe navigation safetyinshipping.Shipon-boardsystemstoimprovethenav- igation safety under rough weather conditions are presented in[6] and [7]. In addition, ship collision avoidance systems withdecisionsupport featuresare presented[8–12].The per- formancemonitoringsystemsfocusonimprovingenergyeffi- ciencyandreducingemissionsinshipping [5].Similarly, ship on-board systems to improve vessel energy efficiency under variousoperationalconditionsare presentedbytheauthorsin [13–15].

However, these systems have not been designed to han- dle big data sets and that may limit to small or moderate data sets. Therefore, the decision support features in such systemsmay oftensuffer under largescaleship performance and navigation data sets. This study proposes a methodol- ogy as a part of both safety and performance monitoring systems to overcome the same challenges in shipping. The methodology consists of pre-processing of ship performance and navigation data sets, where the size of data sets is re- duced. Therefore, the resulted data sets can be conveniently transferred to shore based data centers in a reduced format.

One should note that the proposed pre-processing step con- sists of implementing adimensionality reduction method on ship performance and navigation data sets. Furthermore, the structurefor ship performance andnavigationdatais discov- eredthrough thesamemethodandused toreducethe sizeof therespective datasets (i.e.dimensionality reduction method or datacompression). Even though thesize of therespective

datasetisreduced,theamountof shipperformance andnav- igation informationispreserved(i.e. or approximately equal) during this data compression process. Since the size of the data sets can be reduced, the samplingrate of the samecan be increased. Therefore, the information quality of ship per- formance andnavigation datasets can befurther improved.

1.3. Autoencoder

The proposed approach consists of implementing an au- toencoder system architecture in an onboard data handling system that collects ship performance and navigation infor- mation. The autoencoder system architecture introduces a dimensionality reduction method, i.e. while preserving the amount of ship performance and navigation information, for the same data sets as the main contribution of this study.

An overview of an autoencoder system architecture is pre- sented inFig.1 consistingdatacompression, communication andexpansionsteps.Autoencoderisanunsupervisedlearning methodthatisimplementedasafeed-forwardneuralnetwork ([16] and [17]), which is also categorized as the linear ver- sion of deep learning [18]. Autoencoders are the fundamen- tal building blocks of deep learning and that may associate with additional linear and/or nonlinear functions. Such au- toencodersarecapabletocompressandexpandtherespective informationthat istheinputstothesame.Deeplearningcon- sists of learning the respective information from the bottom layeroftheneuralnetworkratherthanthetoplayer(i.e.back- propagation approach). Hence, that can be aslight deviation from conventional neural networkapproaches. However, this approach is illustrated as a better learning method for neu- ral networksby the recent studiesof other transport systems [19]. Since this study focuses on the linear version of deep learning, the proposed neural networks consists of a linear function (i.e. under the proposed autoencoder system archi- tecture).Ingeneral,theautoencoderrecreatestheinputof the neural network at its output. The neural networks consistof hiddenlayerstocompress andexpandtherespectivedataand the hidden layerslocate betweenthe input andoutput layers of the autoencoder (see Fig. 1). The difference between the input(i.e.theactualparameters)andoutput(i.e.theestimated parameters) data sets can be used toevaluate the success of the neural network(i.e. the comparison/expansion accuracy).

An autoencoder system architecture consists of two sec- tions (see Fig. 1): encoder and decoder. The inputs to the encoder are ship performance and navigation data collected from various onboard sensors. The input data sets are com- pressed by the encoder under the respective linear function of the autoencoder(i.e. the hiddenlayercompressesthe data sets). Then,the compresseddatasets are transmittedthrough communicationnetworkstoshorebaseddatacentersfor stor- age and further analyses. The compressed data sets are re- ceived by the decoder of the autoencoder located in shore based data centers, where the data sets are expanded (see Fig. 1) under the same linear function of the autoencoder.

Therefore, the outputs of the decoder consist of estimated ship performance and navigation data sets. These data sets

Fig.1. Autoencodersystemarchitecture.

(i.e. estimated ship performance and navigation information) canfurtherbeanalyzedforotherapplications,i.e.shipenergy efficiency, emission, and system reliability, at the respective data centers. The measured and estimated ship performance andnavigationdatasets mayhavesomeparametervariations that reflect the autoencoder performance. However, some er- roneous conditionscanalso beintroducedinto thesamedata setduring thisprocess(i.e. data compressionandexpansion) and that may relate to the respective linear function.There- fore,an appropriate linearfunctionshould beassigned under the autoencodersystemarchitecture. Oneshouldnotethat an autoencodersystemarchitecture(i.e.theencoderanddecoder) facilitates toextract alow dimensionalhigh-level representa- tionfromahigh-dimensionalshipperformanceandnavigation data sets. It is believed that such representation can also be used toevaluate the respectiveship performance andnaviga- tionconditions.Furthermore,thesame(i.e.alowdimensional high-level representation) can also be expanded back to the high-dimensional ship performance and navigation data sets set by considering the respective linear function of the au- toencoder. Hence, the respective linear function under data compression/expansion steps of an autoencoder playsan im- portant role.

Autoencodersthatarealsoapartofdeeplearningareoften associated with various linear and nonlinear approaches that relate to the respective application domains [20]. Liner ap- proaches consistof real,complex andfinitefieldapplications of autoencoders. Nonlinear approaches consist of Boolean, Boolean/linear, neuralnetworksandBoltzmannmachines ap- plications of autoencoders. However, linear approaches con- sist of linear functions for both encoder and decoder sides andthisstudy also focusesonthe same. Thislinearfunction proposed in this study for the autoencoder system architec- ture isderivedfrom principalcomponent analysis(PCA) and the respective derivation of thisfunction is also presented in the following sections. Oneshould notethat the linear func- tion under PCA represents asetof vectors,i.e. singular val- ues and vectors, and these vectors relate to the structure of the ship performance and navigation data set. Hence, such structural information, i.e. principal components, in the ship performance and navigation data set is used for both com- pression andexpansionsteps of theautoencoder. Oneshould

note that the data structure represents various relationships among the respective ship performance and navigation pa- rameters. Those parameters relate to onboard sensors of the vessels,therefore the datastructure can representan abstract modelofthevesselandshipsystems.Sincevesselsconsistof possiblecombinations of differentautomation andnavigation systems,suchdatastructuresshouldfurtherbeinvestigatedto understandvessel andship systembehavior.

1.4. Principal componentanalysis

PCAisanon-parametricmethodforextractingrelevantin- formation from data sets. That transforms the parameterset, i.e. sensor measurements, of the respective data into a lin- early uncorrelated parameter set, i.e. the new basis, which canbeused asalowdimensional representationof the origi- naldata set.The linearlyuncorrelatedparametersof the data setmayimprove thecontent visibilityinsomesituations, be- cause thoserepresent the most important parameter relation- ships, i.e. thecorrelations amongparameters, inthe dataset.

One should note that the new basis, i.e. the linearly uncor- relatedparameters, is representedby the respectiveprincipal components (PCs), i.e. singular values and vectors, of the data set. Singularvalues andvectors are fundamental build- ing blocks of multi input multiple-input and multiple-output electricalandmechanicalsystemsaccordancewiththesystem theory.The respective PCs that havealinear combinationof therespectiveshipperformanceandnavigationparametersare derived from the sensor measurements. The encoder and de- coderoftheautoencoderarebasedonthesePCs.Thenumber ofPCsthatshouldimplementunderthehiddenlayers,i.e.the encoder and decoder, of the autoencoder should be selected, appropriatelyby consideringthe respective application. Such selection should be made by considering the singular values and that represent the percentage of the information content oftheparameterrelationshipsinthedataset.Furthermore,the respective number of PCs relate to the number of nodes in the hiddenlayersof the autoencoder,where the mostimpor- tant information in the data set should be preserved. Hence, thisapproachreducesthedimensionalityofshipperformance andnavigationdatasetbyconsideringitsstructure(i.e.PCs).

Furthermore,thesamePCscanbeusedtovisualizeshipper-

formance and navigation data under a different set of pa- rameters, where the information visibility can be improved.

Finally, the reduced data sets of ship performance and nav- igation information communicate through satellite networks, where the respectivetransfercosts canbe minimized.

There are several steps that should be taken on the data sets, prior to implementing PCA. Firstly, any erroneous re- gions (i.e. sensor faults and noise and system abnormal events) in the data sets should be removed to improve the dataintegrity,ifpossible.Furthermore,slowmaneuveringsit- uations of the vessels should be removed from the respec- tiveshipperformance andnavigationdatasets, thereforelow signal-to-noiseratio situations canbe avoided. Secondly, the scalingofshipperformanceandnavigationdatasetsshouldbe done to reduce uneven parameter contributionsduring PCA.

e.g.theparameterswithlargevariancesmayhavebiggercon- tributions in the data analysis and that should be avoided.

Such situations can be avoided by standardizing the respec- tiveparametersinshipperformance andnavigationdatasets, where each parameter is assigned with zero mean and 1.0 variance values. Hence, each parameter has an equal vari- ance(i.e. 1.0), thereforethat influencesequallyinPCA [21]. Eventhough asetof unit-lessparametersare introducedinto PCAbythisstep,therespectiveunitscanbepreserved,sepa- rately[22].However,thisapproachmayincreasesensornoise in some situations and that degrades the outcome of PCA.

That is another reason to remove slow vessel maneuvering situations (i.e. highsensor noise situations) from the respec- tiveshipperformance andnavigationdata sets,as mentioned before.

Each PC represents an important variance direction that isorthogonal to each succeeding variance. The top principal component represents the largest variance direction and the bottom principal component represents the smallest variance directionof thedataset. ThemostimportantPCs(i.e.thetop PCs)inadatasetcanbeselectedtorepresentthe entiredata set, i.e. alowerdimensional representationthat isdefined as data compression in this study. An accumulated percentage of variances (i.e. the summation of the respective singular values) in the data set can be used as a guideline to select themostimportantPCs.Therefore,ahigherpercentageofthe informationon ship performance andnavigation data canbe preservedby selectingan appropriate numberof PCs.

Additional advantages have also been noted by selecting anappropriatenumberofPCs.Itisobservedthatdataanoma- liesare oftengrouped into the bottom principalcomponents, therefore the bottom PCs can also be used to identify such erroneousdataregions[23].Therespectiveerroneousregions, i.e.dataanomalies,canbeisolatedandrecoveredinsomesit- uationsto improve the quality of shipperformance andnav- igation data by consideringthe respective PCs. Furthermore, redundant parameters (i.e. redundant sensor measurements) within the data sets can also be identified by observing the PCs.Therefore, PCA has often been adopted by many “Big Data” applications in various industrial platforms [24] as a partof their datahandling processes.

2. Mathematical formulation 2.1. Autoencoder development

A mathematical overview of an autoencoder with respect toPCA ispresented inthis section.The encoder compresses the measured data set of ship performance and navigation parametersas mentioned before.The inputto the encoder is X(t), i.e. a measured ship performance and navigation data set, denoted as:

X(t)=

x1(t) x2(t) ... xn(t)

(1)

where x1(t),x2(t),. . .,xn(t) with xi(t)∈R^d represent the re- spective ship performance and navigation parameters. One should note that X(t) should a normalized data set derived fromactualshipperformanceandnavigationparameters. The output of theencoder is Y(t),a compresseddataset, denoted as:

Y(t)=

y1(t) y2(t) ... ym(t)

(2)

where n>m andy₁(t),y₂(t),. . .,ym(t)with yi(t)∈R^d repre- sent a setof new parametersthat are derived from the mea- suredshipperformanceandnavigationdatasetbyconsidering PCA. The compresseddata set, Y(t), mayconsist of less pa- rameters than the actual data set, X(t), due to the selected number of PCs. It is expected that the compressed data set is delivered todata centers through the respectivecommuni- cationnetworks. The encoder of thisneural network(i.e. the data compression)canbe denoted as:

Y(t)= fe(WeX(t)+be) (3)

where fe(·)isthe respectivelinearfunction,Weistheweight matrix andbe isthe bias vectorof the encoder. On theother hand, the decoder expands the compressed data set of ship performanceandnavigationparameters.Theoutputofthede- codersideisXˆ(t),thedatasetofestimatedshipperformance andnavigation parametersdenoted as:

Xˆ(t)= ˆ

x1(t) xˆ2(t) ... xˆn(t)

(4)

where xˆ₁(t),xˆ₂(t),. . .,xˆn(t) with xˆi(t)∈R^d represent a set ofestimatedshipperformanceandnavigationparameters.The decoder of this neural network (i.e. the data expansion) can be written as:

Xˆ(t)= fd(WdY(t)+bd) (5) wherefd(·)isthe respectivelinearfunction,Wd istheweight matrix and bd is the bias vector of the decoder. One should notethatfe(·)andfd(·)caneitherbelinearornonlinearfunc- tions. However, a linear function is considered in this study as mentionedbefore.The actualdata setinshipperformance andnavigationinformationisnormalizedwithzeromeanand 1.0 variance values (i.e. be≈bd≈0), previously. Hence, the respective encoder and decoder functions in (3) and (5) can be simplifiedas:

Y(t)=WeX(t)

Xˆ(t)=WdY(t) (6)

Considering(6),thedatacompressionandexpansionsteps can besummarized as:

Xˆ(t)=WdWeX(t) (7)

Therefore,(7)representsanexpressionbetweentheactual and estimated data sets of ship performance and navigation parameters. One should note that some variationsin the ac- tual and estimated data sets can be observed under the data compression and expansion steps. Such parametervariations introduce someerroneous conditionsthat can bedenoted by:

E(t)=

e1(t) e2(t) ... en(t)

(8) where e₁(t),e₂(t),. . .,en(t) with ei(t)=xi(t)− ˆxi(t),∈R^d representasetof shipperformance andnavigationparameter errors.Considering (7),(8)can bewritten as:

E(t)=X(t)− ˆX(t)=(I−WdWe)X(t) (9) If We≈WdT, then WdWe=WdW_d^T≈I and (9) can be written as:

E(t)≈0 (10)

Therefore, We can be derived from Wd to minimize the errorsbetween themeasured andestimatedship performance and navigation parameters. One should note that We≈WdT

is considered to approximate measured and estimated ship performance and navigation parameters. Hence, the weight matrix, Wd,should furtherbe calculatedanddenoted as:

Wd =

w₁ w₂ ... wn

(11)

where w1,w2,...,wn with wi∈R^m represent the respective parametersin the weightmatrix.

2.2. Principal componentcalculations

The respective errors between actual and estimated ship performance and navigationparametersshouldbe minimized under the weight matrix of the autoencoder. Hence, the re- spective orthonormal basis of E(t) that minimizes the mean least square error can be calculated by the following mini- mization problem:

Min.E(t)² =Min.X(t)− ˆX(t)²

=Min.X(t)−WdW_d^TX(t)² (12) The minimization problemin (12)can be also written as:

Min n

i=1

xi(t)− ˆxi(t)²=Min.trace

I−WdW_d^T

X(t)X^T(t)

(13) Oneshouldnotethat(13)canbemodifiedasthefollowing maximization problem:

Min n

i=1

xi(t)− ˆxi(t)²⇒Max.trace

W_d^TX(t)X^T(t)Wd

(14) Consideringthe method of Lagrange multipliers,(14) can bemodified as:

L=trace

W_d^TX(t)X^T(t)Wd

+trace

I−WdW_d^T

(15) where=^T ∈R^d×d istheLagrangemultipliermatrix.The gradientof(15)iszeroatitsstationarypoints.Thesestation- ary pointsrepresent the respective solutions to (14) andthat canbe written as:

X^T(t)X(t)Wd =Wd

WdWdT =I (16)

Hence, (16) satisfy the required conditions in (10) and the objective functionin(16) canalso be denoted as:

W_d^TX^T(t)X(t)Wd = (17)

OneshouldnotethattheLagrange multipliermatrix,,is selectedasadiagonalmatrix,whichisalsosymmetric.Since theLagrangemultipliermatrixisasymmetricdiagonalmatrix thatalsorepresentstheeigenvaluesofX^T(t)X(t)[25].Thetop andbottom eigenvaluesandeigenvectorsof X^T(t)X(t)issame as the top and bottom singular values and vectors of X(t).

Hence,the singularvalue decomposition(SVD)for the mea- sureddatasetofshipperformanceandnavigationparameters, X(t), is considered to derive the Lagrange multiplier matrix.

The respective SVD of the same data set canbe written as:

X(t)=UV^T (18)

where is the singular value matrix and U and V are the respective left and right singular vectors. Hence, the SVD of the data set gives the optimal solution to the minimiza- tion problem in (13). One should note that the left-singular vectorsofX(t)aretheeigenvectorsofX(t)X^T(t)andtheright- singularvectorsof X(t)are theeigenvectorsof X^T(t)X(t).The non-zero singular values of X(t) are the square roots of the non-zero eigenvaluesof bothX(t)X^T(t) andX^T(t)X(t).Hence, the respective PCs of the ship performance and navigation datasets canbe calculatedbySVDas anefficientalgorithm.

Thesesingular values and vectorsthat representthe PCs are orthogonalto each other. Oneshould note that the same ap- proachminimizes the least mean square reconstruction error andmaximizesthe projectionvariance betweentheinputand output data sets of ship performance and navigation param- eters. The top PC (i.e. the vector with the highest singular value)representsthelargestvariance andthebottom PC(i.e.

thevectorwiththelowestsingularvalue)representsthesmall- estvariance that is orthogonal. Hence, the respective weight matrixis selected as:

Wd ≡U (19)

By considering (19), the respective encoder and decoder functions, fe(·) andfd(·), canbe derived.

2.3.Optimal values

Considering (19),(6) canbe modified as:

Y(t)=(t)⁻¹U_t^T

=W_e

X(t) (20)

where We is the modified weight matrix that consists of the respective singular values and vectors. Furthermore, t and Ut represent thematricesthat consistof the toph-numberof singularvaluesandvectors(i.e. PCs) from andU,respec- tively. One should note that (20) represents the linear func- tion of the data compression step (i.e. the encoder side) of theautoencoder.Themodifiedweightmatrixisintroducedby assumingthat themost importantinformationonthe dataset (i.e.shipperformanceandnavigationparameters)ispreserved by the respective singular values and vectors. It is expected that 95−99% of the ship performance and navigation infor- mationof the data setshould be preserved during this com- pressionandexpansion stepsofthe autoencoder.Thatcanbe donebyselectinganappropriatesetofPCs(i.e.singular val- ues andvectors) from the respective data set. Considering a situation,where α%ofthevarianceshouldberetainedwithin theselectedPCs,therespectivesingularvaluecalculationcan bewritten as:

1−^h

i=1Si/^d

i=1Si≤1− α

100 (21)

whereSiis thei-thsingularvalueandthetotalandtopnum- bersof singularvaluesare denotedby dandh ,respectively.

Therefore,(21)can be simplifiedas:

h i=1Si/^d

i=1Si≥ α

100 (22)

The top PCs should be selected to accommodate α% of the actual information of ship performance and navigation parameters.Hence, (6)can bewritten as:

Xˆ(t)=WdY(t)=Utt

=W_d

Y(t) (23)

One should note that (23) represents the modified linear function of the data expansion step (i.e. the decoder) of the autoencoder.Hence,(20)and(23)areusedastheoptimallin- earfunctionsforthedatacompressionandexpansionstepsof theautoencoderandtheresultsarepresentedinthefollowing section.

3. Dataanalysis

3.1.Vessel instrumentation

Therespectivedatasetofshipperformanceandnavigation parametersiscollectedfromabulkcarrierwithfollowingpar- ticulars:shiplength:225(m),beam:32.29(m),grosstonnage:

38.889 (tons), deadweight at max draft: 72.562 (tons). The vessel ispowered by 2 stroke main engine(ME) with maxi- mumcontinuousrating(MCR)of7564(kW)attheshaftrota- tionalspeedof105(rpm).Furthermore,thevesselhasafixed

Table1

MinandMax.Valuesofshipperformanceandnavigationparameters.

Parameter Mini. Max.

1.Avg.draft(m) 0 15

2.STW(Knots) 3 20

3.MEpower(kW) 1000 8000

4.Shaftspeed(rpm) 20 120

5.MEfuelcons.(Tons/day) 1 40

6.SOG(Knots) 0 20

7.Trim(m) −2 6

8.Rel.windspeed(m/s) 0 25

9.Rel.winddirection(deg.) 2 360

10.Aux.fuelcons.(Tons/day) 0 8

pitchpropeller,diameter6.20(m),with4blades[26,27].The data setconsists of the following parameters:average (Avg.) draft,speed through water(STW), main engine(ME) power, shaftspeed,MEfuelconsumption (cons.),speedover ground (SOG),trim,relative(rel.)windspeedanddirection(dir.)and auxiliary (aux.) enginefuel consumption (cons.).

Several data pre-processing steps are implemented inthis analysis to improve the quality of the ship performance and navigation data set. Firstly, the parameter variations within theselectedmaximum(max.)andminimum(min.)valuesare consideredandpresentedinTable1.Theparametervariations beyondthe normal operationalregions (i.e.beyondmax. and min.values) areremoved bythisstep.Secondly, the dataset isnormalized(i.e.standardization)toequallycenterandscale parameters, where each parameter is subtracted and divided bythesamplemeanandstandarddeviationvaluesofthedata set.

3.2. PC calculations

The PCs of the ship performance and navigationdata set arecalculatedandtherespectivesingularvalues(SV)arepre- sentedinthetopplotof Fig.2inascendingorder.Then,each singular value is divided by the sum of singular values and presented in the middle plot of the same figure. That shows the percentage of ship performance and navigation informa- tion thateach singular vectorconsists of.The valuesthat are derived in the previous step are subtracted from 1 and pre- sentedinthebottom plotof thesamefigure.Thisplotshows that the percentage of the actual ship performance and navi- gation information that can preserve by removing each prin- cipal component. The results can be interpreted as: the top 10, 9, 8, 7 and 6 principal components can preserve 100%, 99.92%,99.48%,97.86% and94.03%of the actualshipper- formanceandnavigationinformation.Therespective99%and 95%linesarealsopresentedinthesameplot.Thetop7prin- cipalcomponentsareselected asthebenchmark levelforthis dataanalysis andthat canpreserve approximately 97.86%of theshipperformance andnavigationinformation.Oneshould note that this step reduces a 10 parameter data set of ship performance and navigation information into a 7 parameter data sets (i.e. compressed data set of 7 new parameters).

Fig.2. Autoencodersystemarchitecture.

Therefore, the compressed data set can be approximated to 70%ofitsoriginalsizewith98%preservedshipperformance and navigation information. This can also be seen as a sit- uation, where 30% of the ship performance and navigation data setis reduced with2% of informationloss. Oneshould note that the information loss may relate to data anoma- lies and sensor noise, therefore that can negligible in some situations.

The data compressionratio, i.e. the ratio betweenthe un- compressed size andcompressed size, is independent of the autoencoder systemarchitecture, but the distribution and re- dundancy of sensor measurements. If the ship performance and navigation parameters are distributed with low correla- tions, then the compression ratio may decrease by preserv- ing the same percentage of information. If each parame- ter is measured by several sensors (i.e. data redundancy), then the compression ratio may increase by preserving the same percentage of information. One should note that such correlationsamongshipperformance andnavigationparame- tersalsorepresenttherespectivedatastructure.Therespective PCsrepresentthestructureof theshipperformanceandnavi- gationdataset,thereforeaproperstructureimprovesthedata compressionratio.However,data anomaliesandsensor noise conditions can degrade the compression ratio in some situa- tions.Ingeneral,shipperformance andnavigationparameters are often related to each other (i.e. speed-power conditions, trim-draftconditions),thereforeagoodcompressionratiohas beenobservedinthisstudy.Furthermore,thecompressionra- tiocanfurtherbeincreasedbyintroducingmultiplesensorsto monitor the most importantship performance andnavigation parameters andthat may relate to the respective application.

The data compression ratio may increase in such situations, however the numberof ship performance and navigationpa- rameters in the datasets mayalso increase.

3.3. Measuredand estimated data

The respectivehistograms for ship performance andnavi- gationparametersarepresentedintheplotsofthefirstcolumn inFig.3.Thesameparametersarenormalized (i.e.standard- ization) to use under PCA [28–30] as a part of the autoen- codersystemarchitectureandtheresultsare presented inthe plots of the second columnin the same figure.The new pa- rametersarederivedbyprojectingmeasuredshipperformance andnavigationparametersintotherespectivePCsandthere- sultsarepresentedintheplotsofthethirdcolumninthesame figure. That are denoted by XP1(t), XP2(t), ..., XP10(t) and a decreasing trend on the variance values of these parameters canalso be noted because the singularvalues are decreasing inthesameorder.Thenewparametersderivedbyconsidering the top 7 PCs (i.e. the compressed data set) are selected to communicate fromthe encoder tothedecoder of the autoen- coder inthisstudy. One shouldnote that thesePCs preserve 98% of the ship performance and navigation information in thisdataset.

The compressed data set is transferred to the decoder of the autoencoder, where the respective dataset should be ex- pendedtoitsoriginalparameters.Thedecoderreceivesadata setof7parametersandthatshouldbetransformedintoadata set of 10 parameters. The same PCs (i.e. the data structure) are used to expand the compressed data set of ship perfor- manceand navigationparameters. The outputof the decoder is categorized as estimated ship performance and navigation data set. The respective histograms for each estimated (Est.) shipperformance and navigationparametersare presented in the plots of the fourthcolumn of Fig. 3. The histogramsfor measuredshipperformanceandnavigationparameters(Msd.) are also presented in the same plots. One should note that theseare the initial ship performance and navigationparam- eters that are measured by the onboard sensors. Some vari- ations among measured and estimated histograms (i.e. ship performance and navigation parameters) can be observed in these plots. The estimated ship performance and navigation datarepresent someparameter degradation conditions dueto thedatacompressionandexpansionstepsofthe autoencoder.

The measured and estimated ship performance and nav- igation parameters with respect to the sample number are presented in Fig. 4. The time duration between two consec- utive data points is 15 (min). However, some data intervals are not continuous because erroneous data intervals are re- movedfrom thisdataanalysis,initially. Ingeneral,measured andestimatedshipperformanceandnavigationparametersare approximatelysimilar.However,somerelativelysmallparam- etervariationscanalsobeobservedinthisfigureandthat are introduced by the data compression and expansion steps of the autoencoder.

3.4. Datacompression ratio

It is noted that estimated ship performance and nav- igation parameters represent approximately Gaussian type distributions in a majority of the situations due to PCA.

Fig.3. PCAofshipperformanceandnavigationparameters.

Furthermore, measured ship performance andnavigation pa- rameters that haveapproximately Gaussian typedistributions have low information loss in comparison to the parameters withNon-Gaussian type distributions. Ifthe parameters con- sistsGaussian typedistributions, theneach PC isan asymp- totically consistent unbiased estimate for the respective data set [31]. Therefore, the parameters with Non-Gaussian type distributionsinsuchdatasetsshouldbetransferredintoGaus- sian type distributions in possible situations to improve the

data compression ratio. It is also noted that the autoencoder transforms ship performance and navigation parameters into approximatelyGaussiantypedistributions,whenthoseparam- eters are not parallel to any PC. If the PCs are not parallel to the respective parameters, then the same parameters con- sists of a stronger correlation. Therefore, a negligible data compressionratio (i.e. equal measured and estimated param- eter values) can be observed under the autoencoder, i.e. the parametersare parallel toPCs.

Fig.4. Measuredandestimatedparametersofshipperformanceandnavigationdata.

The central limit theorem states that, givencertain condi- tions, any independentrandom variablecanbe approximated to a Gaussian distribution with well-defined mean and vari- ancevalues,regardlessoftheactualdistributionoftherespec- tive parameter [32]. The autoencoder also approximates the variance of each ship performance and navigationparameter into an approximateGaussian distribution, where the respec- tiveinformationcanretainwithintherespectivePC.Itisalso recommendedthat each ship performance andnavigationpa-

rameter should be transformed into approximately Gaussian typedistributions,thereforethedatacompressionratiocanbe increased. e.g. rel.wind direction sensor measurements may notconsist of aGaussian typedistribution(see Fig.3).That can be transformed to a Gaussian type distribution by con- sidering an appropriate angle transformation. Therefore, this canbean iterative process,wherethe amountof information loss vs the parameter compressionratio should be compared toevaluatetheautoencoderperformance.Theoutcomeofthis

studyshowsthat 98% ofthe varianceisretained withthe re- spective7 PCs. Therefore,only2%of ship performance and navigationinformationhaslostduringthesedatacompression andexpansion stepsof the autoencoder.

3.5.Improvements indatacompression

There are various septs that can be taken to improve the quality of the data compression and expansion steps of the autoencoder.Asdiscussed before,that can bedone bytrans- formingtherespectiveparametersintoGaussiantypedistribu- tionsandselectingaminimalnumberofPCsthatcanpreserve required ship performance and navigation information. Ship performance andnavigation parameterscan be rearranged to create Gaussian type distributions in some situations. How- ever,shipperformanceandnavigationparametersmaynotvi- sualizeGaussiantypedistributionsinthosesituations.Various dataclusteringapproachesinahighdimensionalspaceshould beconsidered to identify appropriate Gaussiantype distribu- tionsthesesituations[30].E.g.marineenginesofoceangoing vesselsmayhaveseveraloperationalpoints,thereforshipper- formance andnavigation parameterscanbe clustered around Gaussiantypedistributions undertheseoperational points, in whichshouldbe identifiedby additionalalgorithms.Thisap- proachshows that ship performance and navigationparame- ters may consist of a combination of several approximately Gaussiantype distributions andthat should be identified be- forePCA. Ship performance andnavigation datasets should be separated into such Gaussian type distributions and each distribution(i.e. data cluster) shouldsend separately through the autoencoder to improve the compression ratio in those situations[2].

Those data clusters can be compressed and expanded by theautoencoderwithapproximately similarmeasuredandes- timateddatasets.Oneshouldnotethat thecompressionratio canbehigher withlowerinformation lossinsuch situations.

Some ship performance andnavigation parameters are more importantthanothers,thereforeadditionsensorscanbeintro- ducedto monitor thoseparameters. That step canstrengthen the most important ship performance and navigation param- eters within the respective data sets and PCA can identify suchsituations,i.e.redundantparametermeasurements.How- ever, data anomalies, i.e. sensor andDAQ faults and system abnormal events, can degrade the data compression ratio of the autoencoder. Such data anomalies can often be outliers of PCs and that can be detected by using adequate outlier detection filters with the bottom PCs [33]. Since the PCs represent the respective data structure of ship performance and navigation parameters, that can also be used to recover somedataanomalies.Therefore,suchdataanomaly detection and recovery filters can also be a part of the autoencoders, i.e. self-cleaning autoencoders,and that will further improve the quality of the respective data sets. However, additional hardware erroneous conditions (i.e. channel errors and fad- ing)can be introducedinto ship performance and navigation parametersduringdatacommination processes.It isbelieved thatsuchconditionscanalsobeidentified,isolatedandrecov-

eredby aself-cleaning autoencodersystemarchitecture[34]. However, such additional features will be integrated into the proposed autoencodersystem architecturein the futurework of thisstudy.

Oneshouldnotethatself-cleaning autoencoderscanbean important part of onboard data handling processes of mod- ern vessels. When vessels are equipped be such large num- ber of onboard sensors, these steps discussed in this section can make aconsiderablecontribution toimprove the respec- tivedata handlingprocesses. Furthermore, autoencoderswith a good compression ratio can help the data handling pro- cessestoreducetherequiredcomputationalpowerinonboard vessels.

4. Conclusion

Ship owners often use the average values of ship perfor- mance and navigation parameters and that reduce the size and cost of transferring, handling and analyzing the respec- tive data sets. The main objective in this study is to show that ship performance and navigation data sets can be re- duced in their sizes by the autoencoder system architecture, while having ahigh sampling rate. Therefore, the respective ship performance and navigation parameters can be stored and analyzed with a high data sampling rate in such situa- tions. The will further improve the information visibility of vessel operational andnavigationconditions.

An autoencoder system architecture compresses and ex- pands data sets of ship performance and navigation parame- ters,whichshouldbetransferredthroughcommunicationnet- works as reduced data sets but with a considerable amount of information. The encoder and decoder should develop as software functions, therefore the autoencoder system archi- tecturemaynotdepend,extensivelyon thehardware systems of modern vessels. In general,the encoder should be imple- mented inonboardvessels andthe decoder shouldbe imple- mentedinonshoredatacenters.Thedatatransmissionprocess also plays an important role under the autoencoder system architecture. In general, some vessels transmit ship perfor- manceandnavigationdata undersatellitecommunicationsto data centers, while the respective bandwidth is free. Other vessels transmit ship performance andnavigation data under wirelesscommunicationtodatacenters,whilethevessels are within port areas. Therefore, the respective data centers can locatewithin the port areaswiththe required infrastructures, where the proposed autoencoder system architecture can be implemented.

Autoencodersderive anewreducedset ofparametersthat is another representation of measured ship performance and navigation parameters. These new parameters consist of a considerable amount of ship performance andnavigation in- formation, therefore the capabilities of using those parame- ters to quantify ship performance and navigation conditions instead of using measured parameters should be further in- vestigated. Hence, optimal vessel operational and navigation situations can be identified to archive the respective energy

efficiencyrequirementsinshippingbyconsideringtheautoen- coder systemarchitecture.

Acknowledgment

This work has been conducted under the project of “SFI Smart Maritime (237917/O30) – Norwegian Centre for im- provedenergy-efficiencyandreducedemissionsfromthemar- itime sector” that is partly funded by the Research Council of Norway.Aninitialversionofthispaperispresentedatthe 35th International Conference on Ocean, Offshore and Arc- tic Engineering (OMAE 2016), Busan, Korea, June, 2016, (OMAE2016-54093).

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