AIS-Based Multiple Vessel Collision and Grounding Risk Identification

Journal of Marine Science and Engineering

Article AIS-Based Multiple Vessel Collision and Grounding Risk Identiﬁcation based on Adaptive Safety Domain

Azzeddine Bakdi 1,*, Ingrid Kristine Glad 1, Erik Vanem 1,2 and Øystein Engelhardtsen 2 1 Department of Mathematics, University of Oslo, 0851 Oslo, Norway; [email protected] (I.K.G.); [email protected] (E.V.) 2 DNV GL Group Technology and Research, 1322 Høvik, Norway; [email protected] * Correspondence: [email protected]

Received: 21 November 2019; Accepted: 17 December 2019; Published: 19 December 2019

Abstract: The continuous growth in maritime traffic and recent developments towards autonomous navigation have directed increasing attention to navigational safety in which new tools are required to identify real-time risk and complex navigation situations. These tools are of paramount importance to avoid potentially disastrous consequences of accidents and promote safe navigation at sea. In this study, an adaptive ship-safety-domain is proposed with spatial risk functions to identify both collision and grounding risk based on motion and maneuverability conditions for all vessels. The algorithm is designed and validated through extensive amounts of Automatic Identification System (AIS) data for decision support over a large area, while the integration of the algorithm with other navigational systems will increase effectiveness and ensure reliability. Since a successful evacuation of a potential vessel-to-vessel collision, or a vessel grounding situation, is highly dependent on the nearby maneuvering limitations and other possible accident situations, multi-vessel collision and grounding risk is considered in this work to identify real-time risk. The presented algorithm utilizes and exploits dynamic AIS information, vessel registry and high-resolution maps and it is robust to inaccuracies of position, course and speed over ground records. The computation-efficient algorithm allows for real-time situation risk identification at a large-scale monitored map up to country level and up to several years of operation with a very high accuracy.

Keywords: AIS; risk identiﬁcation; maritime navigation accident; multiple vessels; collision risk; grounding risk; spatial risk function; vessel maneuverability; safety domain; decision support

1. Introduction Maritime transport activities shape a new type of economic sector considered as the blue economy [1]. Since about 90% of the world’s merchandise are transported by sea [2], maritime transport plays a central and potential role in economy nowadays. In parallel, safety requirements are continuously improved to avoid hazardous accidents and ensure a sustainable growth in maritime operations. According to the recent annual review of marine casualties and incidents in 2018 [3] by the European maritime safety agency, more than 20,000 marine casualties and incidents have been reported at the European level in 2011–2017 only. Together, these accidents caused more than 680 fatalities and over 6800 injuries. Navigational accidents represent 53.1% of all casualties with ships as a combination of: grounding (16.6%), contact (16.3%) and collision (23.2%). Despite being slightly diﬀerent, the rates of maritime navigation accidents are still tragically high according to marine casualty and pollution database collected by United States Coast Guard (USCG) and provided in July 2015 (not all 2014–2015 accidents reported) by marine information and safety and law reinforcement [4]. In a total of 34,540 reported and fully investigated navigation accidents between 2000 and mid 2015, around 43.5% of the accidents were groundings, 39.6% were allisions with a static object and 16.9% were collisions

J. Mar. Sci. Eng. 2020, 8, 5; doi:10.3390/jmse8010005 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 5 22 of of 19 object and 16.9% were collisions as demonstrated in Figure 1. A high-level risk analysis on passenger as demonstrated in Figure1. A high-level risk analysis on passenger ship collisions presented in ship collisions presented in Reference [5] suggested that risk control options related to navigation Reference [5] suggested that risk control options related to navigation should be considered to reduce should be considered to reduce the overall risk of collision and that navigational aspects are the overall risk of collision and that navigational aspects are important. important.

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0 2000 2005 2010 2015 Year Figure 1. Investigated navigation accidents in USA 2000–2015. Data was from Reference [4]. Figure 1. Investigated navigation accidents in USA 2000–2015. Data was from Reference [4]. The consequences of maritime accidents can be fairly high as reported by transportation safety boardThe of Canadaconsequences [6] where of maritime the provided accidents data tablescan be includefairly high the completeas reported investigations by transportation into marine safety transportationboard of Canada occurrences [6] where inthe 2013–2019. provided data From tables the reported include 79,000the complete accidents, investigations 80.8% caused into damage, marine 9.86%transport causedation aoccurrences confirmed in pollution, 2013–2019. 7.99% From caused the reported minor injuries,79,000 accidents, 4.39% caused 80.8% seriouscaused damage, injuries, while9.86% 4.01%caused of a confirmed the accidents pollution, caused 7.99% fatalities. caused The minor reported injuries, accidents 4.39% alsocaused occurred serious during injuries, various while environmental4.01% of the accidents conditions caused as depicted fatalities. in Figure The 2 reported, in which accidents wind speed, also visibility occurred condition during and various sea stateenvironmental have weak conditions effects as accidentas depicted factors. in Figure A full 2, literature in which review wind speed, on research visibility in maritime condition accidents and sea isstate provided have weak in Reference effects as [ 7accident] which factors. lists diff Aerent full literature research methodsreview on and research data sources in maritime in this accidents context. Tois provided help reduce in Referenc the occurrencee [7] which rates lists of such different accidents, research qualitative methods research and data methods sources were in this deployed context. to understandTo help reduce the rootthe occurrence causes such rates as maritime of such navigationaccidents, qualitative risk indicators research [8] with methods explanatory were deployed variables suchto understand as vessel type the as root well causes as flag such of convenience as maritime and navigation visibility conditions, risk indicators human [8] and with organizational explanatory factorsvariables [9 ]such and includingas vessel type decision as well errors as flag due of to conditionsconvenience of and operators visibility and conditions, personnel human factors and socio-technicalorganizational factors [9] [10 ]and such including as the interactions decision errors between due shipto conditions operators. of Theoperators qualitative and personnel approach isfactors however and not socio very-technical precise as factors Figure 2 [10] shows such since as most the interactions accidents occurred between during ship good operators. conditions. The Moreover,qualitative takingapproach into is accounthowever the not tra veryffic densitiesprecise as during Figure each2 shows condition since most and itsaccidents frequencies, occurred the correlationsduring good between conditions. sea /Moreover,wind/visibility taking conditions into account and thethe numberstraffic densities of accidents during are each very condition weak as foundand its in frequencies, Reference [ 8 the]. Alternatively, correlations between the authors sea/ ofwind Reference/visibility [11 ] conditions demonstrated and thatthe numbers the general of maritimeaccidents safety are very approach weak is as reactive found andin Reference that accidents [8]. cannotAlternatively, be predicted. the authors In real time,of Reference collision and[11] groundingdemonstrated risk that depends the general on the tra maritimeffic configuration safety approach represented is reactive by the andnumber that of accidents sailing vessels cannot and be theirpredicted. locations, In real relative time, collision speed and and course grounding to each risk other depends and to on near the objects traffic andconfiguration their maneuverability represented suchby the as number the stopping of sailing distance vessels [12] and as well their as locations, the tactical relative diameter, speed maximum and course advance to each and other track and reach to definednear objects by the a Internationalnd their maneuverability Maritime Organization such as the (IMO). stopping These aspectsdistance are [12] described as well in as the the following tactical anddiameter, they are maximum incorporated advance in the and design track of reach the proposed defined by risk the identification International method. Maritime Organization (IMO). These aspects are described in the following and they are incorporated in the design of the proposed risk identification method.

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79766 accidents vs sea-state 17 (2%) 16 (0%) 1: CALM (GLASSY) - 0 meters 2: CALM (RIPPLED) - 0 to 0.1 meters 3: CONFUSED 4: HIGH - 6 to 9 meters 1 (30%) 5: ICE COVERED - HEAVY 15 (30%) 6: ICE COVERED - LIGHT 7: ICE COVERED - MODERATE 8: ICE PATCHES 9: MODERATE - 1.25 to 2.5 meters 10: PHENOMENAL - over 14 meters (a) 11: ROUGH - 2.5 to 4 meters 2 (6%) 12: SLIGHT - 0.5 to 1.25 meters 13 (5%) 14(0%) 13: SMOOTH (WAVELETS) - 0.1 to 0.5 meters 14:TIDE, RIPS - STRONG 3 (0%) 12 (7%) 4 (1%) 15: UNKNOWN 5 (2%) 9 (7%) 16: VERY HIGH - 9 to 14 meters 8 (1%) 11 (6%) 6 (1%) 17: VERY ROUGH - 4 to 6 meters 7 (1%) 10 (0%)

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FigureFigure 2. 2.Reported Reported maritimemaritime accidentsaccidents inin variousvarious environmentenvironment conditions.conditions. DataData waswas fromfrom ReferenceReference [6]: (a[)6] Sea: (a) state; Sea state; (b) Wind (b) Wind speed; speed; (c) visibility (c) visibility distance. distance.

InIn addition addition to such to such severe severe impact impact of navigation of navigation accidents, accidents, the recent the developments recent developments are continuously are increasingcontinuously the increasing traffic capacity the traffic and leadingcapacity to and new leading emerging to new technologies emerging technologies and vessels characteristics.and vessels Thischaracteristics. consequently This introduces consequently new introduces challenges new for challengesfast and early for fastrisk and identification early risk methods identification which aremethods crucial which to the are safety crucial and to the effi safetyciency and of maritimeefficiency of operations, maritime operations, especially especially in complex in complex navigation situations.navigation To situations. avoid collision To avoid and collision grounding and grounding accidents andaccidents reduce and their reduce occurrence their occurrence rates, automatic rates, riskautomatic identification risk identification and analysis and tools analysis are receivingtools are receiving a growing a growing attention attention in theoretical in theoretical and practical and applications.practical applications. Decision supportDecision systems support [13systems] are vital [13] inare collision vital in situationscollision situations at sea and at theysea and are provedthey usefulare proved for collision useful avoidancefor collision and avoidance safety intervention and safety intervention [14] or extended [14] or to extended intelligent to routeintelligent planning route [15 ] planning [15] and autonomous navigation algorithms. These methods need to perceive all risky and autonomous navigation algorithms. These methods need to perceive all risky situations in their first situations in their first stage which is very important for navigation safety. Risk identification was stage which is very important for navigation safety. Risk identification was considered in Reference [16] considered in Reference [16] based on Automatic Identification System (AIS) data and the Closest based on Automatic Identification System (AIS) data and the Closest Point of Approach (CPA) [17] Point of Approach (CPA) [17] as well as distance at CPA and time to CPA parameters. These are as well as distance at CPA and time to CPA parameters. These are typically based on assumptions typically based on assumptions of linear tracks, constant speed and course and neglect vessel of linear tracks, constant speed and course and neglect vessel dimensions and maneuverability. dimensions and maneuverability. Another method for ship collision candidate detection was Another method for ship collision candidate detection was proposed in Reference [18] based on a proposed in Reference [18] based on a velocity obstacle approach. AIS information was also used for velocityrisk identification obstacle approach. for vessel AIScontact information with fixed was offshore also used platforms for risk [19]. identification Full reviews for on vessel individual contact withship fixed-ship ocollisionffshore platformsrisk analysis [19 and]. Full assessment reviews onare individual respectively ship-ship given in collision Reference risk [20] analysis and [21] and assessmentwhere a considerable are respectively number given of in research Reference items [20 addressed,21] where individual a considerable collision number risk of detection research and items addressedcollision avoidan individualce methods collision designed risk detection and validated and collision using avoidance AIS data. methods designed and validated using AIS data.

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A critical shortcoming in the existing maritime navigation risk identification and evaluation methods is the neglection of vessel maneuverability which is a key factor that varies across different vessels and determines the risk in case of close-quarters situations. Moreover, the existing methods in the literature focus on individual risk while ignoring combinations of multiple collisions and ground situations and their interactions which limits the set of possible evasive actions and increase navigational complexity and confliction with navigation rules. In this work, a vessel maneuverability-based safety domain is designed within an adaptive framework based on navigation situations to identify both collision and grounding risk situations in a fast and computation-efficient approach. This algorithm is designed and validated through extensive amounts of AIS data (as it is the only sufficiently available data), hence the method is not considered as the basic risk identification tool. This was a worth-mentioning aspect for most AIS-based anti-collision methods published so far and it is supported by resolution A.1106(29) [22] issued by IMO including guidelines on potential use of AIS but also its limits in this regard. Those guidelines recognize and recommend the use of AIS for anti-collision assistance but advise cautions that all safety-relevant information must be used and that AIS does not replace other systems. However, the implementation of this algorithm, with sufficient computational resources and access to online AIS information over a large monitored area, does not only detect but also identify navigation risk when available and yields a powerful tool for warnings and decision support, especially when multiple collisions and groundings situations starts developing. In addition, the implementation of this algorithm onboard vessels with access to information from all navigational systems will grant it an increased effectiveness. Compared to the existing methods in the literature, the actual navigation risk is introduced as a combination of interactions of multiple collision and/or grounding candidates. This work considers all types of navigation risk and their combinations over a large monitored area, the objective is to design and validate a computationally efficient algorithm for accurate and automatic risk identification from big historical AIS data. The successful identification of risky situations plays a leading role for decision support and smart navigation to assist the crew and avoid navigational hazards. Moreover, the analysis of huge historical data allows the extraction of a large set of risky situations with their probability of occurrence, this set is invaluable for simulating and verifying the trustworthiness of remote control and autonomous navigation functions. The rest of this article is organized as follows, Section2 introduces the proposed method, starting from basic maneuverability aspects involved in the construction of a polygonal safety domain and its efficient approximation, followed by the designed collision and grounding spatial risk functions and the overall risk evaluation methods. Section3 then describes some data samples used for this application and the main results with a few examples and their discussions. This paper is then concluded in Section4 where important conclusions are drawn in addition to a summary of the major findings and potential applications of the presented method and suggestions for future work.

2. Risk Identification Methodology The minimum distance to avoid accidents in a navigation scenario depends on the maneuverability and real navigation conditions and configuration of the involved vessels in addition to the situation complexity. Maritime navigation is dominated by the Convention on the International Regulations for Preventing Collisions at Sea (COLREG) [23]. Different COLREG rules apply for different close quarter situations and therefore the safe navigation distance is generalized to the concept of blocking areas which together define a vessel safety domain with varying parameters based on vessel maneuverability and encounter situation. The simplified polygonal maneuverability-dependent adaptive safety domain outperforms state-of-the-art approaches in terms of risk identification effectiveness and computation efficiency and extends to large temporal and spatial scales in realistic applications. Individual vessel-to-vessel collision risk and vessel grounding risk are evaluated based on a spatial risk function over the region of safety domain violations. The overall risk is a combination of several collision and grounding candidate situations all faced at the same time for one or several interacting vessels. J. Mar. Sci. Eng. 2020, 8, 5 5 of 19 J. Mar. Sci. Eng. 2020, 8, 5 5 of 19

2.1.2.1. Vessel Vessel Maneuverability Maneuverability TheThe vessel vessel maneuverability maneuverability measures measures the the vessel’s vessel’s ability ability of stopping,of stopping, accelerating, accelerating, varying varying its its coursecourse and and maintaining maintaining a desired a desired trajectory. trajectory. There There are are therefore therefore various various types types of maneuversof maneuvers a ship a ship needsneeds to executeto execute to satisfyto satisfy navigation navigation safety safety conditions. conditions. The The vessel vessel stopping stopping ability, ability, for for example, example, measuresmeasures its capacityits capacity to stopto stop within within a certain a certain distance distance (the (the track track reach) reach) when when full full engine engine astern astern is is appliedapplied for for a vessel a vessel sailing sailing at at its its full full test test speed. speed. The The maneuverability maneuverability aspects aspects areare thereforetherefore testedtested to to ensureensure that the vessel vessel can can safely safely navigate navigate under under worst worst case case scenarios. scenarios. Full Full-scale-scale tests tests are then are thenused to usedevaluate to evaluate the ship’s the ship’s maneuvering maneuvering performance, performance, which which must must satisfy satisfy IMO IMO standards standards [24 []24 for] for ship shipmaneuverability. maneuverability. In full-scale trials, the test speed Vtest corresponds to at least 90% of the speed at 85% of the In full-scale trials, the test speed 푉푡푒푠푡 corresponds to at least 90% of the speed at 85% of the maximummaximum engine engine output. output. At At the the test test speed, speed, the the turning turning circle circle maneuver maneuver test test measures measures the the turning turning abilityability and and it is it performed is performed with with 35◦ 35°rudder rudder angle angle (or (or maximum maximum permissible permissible angle) angle) to bothto both starboard starboard andand port port sides sides following followi ang steady a steady approach approach with with zero zero yaw yaw rate rate as demonstrated as demonstrated in Figure in Figure3a. 3a.

(a) (b)

Figure 3. International Maritime Organization (IMO) full-scale tests: (a) IMO full-circle turning Figure 3. International Maritime Organization (IMO) full-scale tests: (a) IMO full-circle turning maneuver test; (b) IMO full-astern stopping maneuver test. maneuver test; (b) IMO full-astern stopping maneuver test. In this trial, the turning ability is measured in terms of tactical diameter, advance (and maximum In this trial, the turning ability is measured in terms of tactical diameter, advance (and maximum advance) and time to change heading 90 degrees and 180 degrees. In addition, the zig-zag test evaluates advance) and time to change heading 90 degrees and 180 degrees. In addition, the zig-zag test the ship performance for maintaining a trajectory and the full astern stopping test determines the track evaluates the ship performance for maintaining a trajectory and the full astern stopping test reach until a ship is stopped dead in the water after a full astern is given as depicted in Figure3b. determines the track reach until a ship is stopped dead in the water after a full astern is given as According to IMO resolution MSC.137(76) [23], the advance (A ) in a turning circle maneuver depicted in Figure 3b. D must not exceed 4.5 ship lengths (L) AD 4.5 L and the track reach (ST) should not exceed 15 ship According to IMO resolution MSC.137(76)≤ [23], the advance (퐴퐷) in a turning circle maneuver lengths in a full astern stopping test ST 15 L (20 ship lengths in other situations). The maneuverability must not exceed 4.5 ship lengths (L)≤ 퐴 ≤ 4.5퐿 and the track reach (푆 ) should not exceed 15 ship aspects determine the ability of a vessel to avoid퐷 accidents, however, the maneuverability푇 parameters lengths in a full astern stopping test 푆 ≤ 15퐿 (20 ship lengths in other situations). The are speed-dependent and need to be estimated푇 for the prevailing navigation conditions which are maneuverability aspects determine the ability of a vessel to avoid accidents, however, the diﬀerent from those in the full-scale trials. The authors of Reference [25] derived a mathematical model maneuverability parameters are speed-dependent and need to be estimated for the prevailing to estimate the stopping ability of vessels ﬁtted with a screw propulsion or a waterjet propulsion navigation conditions which are different from those in the full-scale trials. The authors of Reference system. Assuming a straight contour track and a thrust changing linearly in time from forward thrust [25] derived a mathematical model to estimate the stopping ability of vessels fitted with a screw T to aft-ward thrust T during time t to reverse the thrust, the motion equation for the displacement F propulsion or a waterjetA propulsionr system. Assuming a straight contour track and a thrust changing

linearly in time from forward thrust 푇퐹 to aft-ward thrust 푇퐴 during time 푡푟 to reverse the thrust, the motion equation for the displacement ∆ for a vessel moving at speed 푈 is split into two parts:

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∆ for a vessel moving at speed U is split into two parts: time since the full astern order is applied (t = 0) until the time the thrust is fully reversed (t = tr) as given by Equation (1) and time after that, t > tr, until the vessel is stopped dead-in-water as given in Equation (2). Hence from Reference [25] we have

!2 ∆(1 + k1) dU t U U = (TA + TF) R f or 0 < t tr, (1) g ds − tr − U0 ≤

!2 ∆(1 + k1) dU U U = TA R f or t > tr, (2) g ds − − U0 where k1 is the longitudinal added mass coeﬃcient, s is the travelled distance along the track and g is the gravity acceleration. R is the ahead vessel resistance at speed U and R0 is the resistance at approach speed U0. Solving the previous equations, the track reach ST is presented as

" 2 !# ∆(1 + k1)U0 R0 ST = ln 1 + + 0.5U0tr. (3) 2gR0 TA

The authors of Reference [26] demonstrated that the track reach depends on the propeller diameter, vessel resistance coefficient, ratio of the astern to the ahead power, quasi-propulsive coefficient and many other parameters. Their results indicate that the track reach is within 4 to 16 ship lengths L for different thrust reverse time tr and astern to ahead power ratio. In the same context, a free-running model is presented in Reference [27] for the estimation of full-scale stopping ability in which the experimental validation results are in accordance with those obtained by Reference [26].

2.2. Vessel Safety Domains In a close quarter situation, actions taken by only one vessel will not be enough to avoid risk of collision. The safe passing distance hence depends on the approach rate and directions as well as the speed and maneuverability of both vessels. According to the type of encounter between two approaching vessels, four blocking areas are deﬁned as safety regions that must not be violated by one another. The areas are modelled in Reference [28] as a combination of ellipses having the following radii   r   2   2 kDT   R f = 1 + 1.34 kAD + L   2     r    2  =  + 2 + kDT  , (4)  Ra 1 0.67 kAD 2 L      = ( + )  Rs 0.2 kDT L   Rp = (0.2 + 0.75kDT)L where R f and Ra are respectively the longitudinal radii in fore and aft directions; Rs and Rp are the lateral radii in starboard and port sides, respectively as shown in Figure4. These parameters are estimated based on the vessel speed V and the previously explained vessel maneuverability aspects of advance AD and tactical diameters DT as well as their respective gains kAD and kDT which are estimated according to the vessel’s speed over ground (SOG) as

 A  D 0.3591log10(SOG)+0.0952  kAD = L = 10 D . (5)  T 0.5441log10(SOG) 0.0795  kDT = L = 10 −

These dimensions are adopted by many researchers to identify close quarter situations and hence collision risk [29–31] based on a maneuverability-dependent safety domain. J. Mar. Sci. Eng. 2020, 8, 5 7 of 19

J. Mar. Mar. Sci. Sci. Eng. Eng. 20202020,, 88,, 5 5 77 of of 19

Figure 4. Safety domains: (a) Blocking area versus fixed domains (b), (c), (d) and (e) with dimensions proposed by [32–35], respectively ((b), (c), (d) and (e) are reproduced respectively from [32–35] with permissions from Cambridge University Press 2009, Cambridge University Press 2013, Elsevier 2016, and Elsevier 2018, respectively).

It is worth mentioning that this type of domain combines the dimension, maneuverability and real speed-over-ground for each vessel. These extensions present a remarkable advantage over the conventional safety domains [32–35] which are only length-dependent as shown in Figure 5. The domains presented by References [32], [34] and [35] correspond respectively to major axes of 10 퐿, Figure 4. SafetySafety domains: domains: (a ()a Blocking) Blocking area area versus versus fixed ﬁxed domains domains (b), (b (–ce),) ( withd) and dimensions (e) with dimensions proposed 20 퐿 and 16 퐿, such dimensions are inappropriate at low speed and those domains need to be proposedby [32–35 ],by respectively[32–35], respectively ((b–e) are ((b reproduced), (c), (d) and respectively (e) are reproduced from [ 32respectively–35] with permissionsfrom [32–35] fromwith adapted for particular situations and for practical applications [33]. permissionsCambridge Universityfrom Cambridge Press University 2009, Cambridge Press 2009, University Cambridge Press University 2013, Elsevier Press 2013, 2016, Elsevier and Elsevier 2016, and2018, Elsevier respectively). 2018, respectively). 2.3. Corrected Efficient Polygonal Domain It is worth mentioning that this type of domain combines the dimension, maneuverability and ItA isstatistical worth mentioning analysis of thatAIS datathis typein Reference of domain [36 combines] has shown the that dimension, around 10% maneuverability of all normal andsafe real speed-over-ground for each vessel. These extensions present a remarkable advantage over realsituations speed -wereover -performedground for with each a vessel. ship-ship These passing extensions distance present of less a thanremarkable 2 퐿. Considering advantage only over near the the conventional safety domains [32–35] which are only length-dependent as shown in Figure5. conventionalcollision situations, safety thisdomains rate is[32 much–35] whichhigher. are This only implies length that-dependent the fixed as 10 sh 퐿own, 20 퐿in andFigure 16 퐿5. shipThe The domains presented by References [32,34,35] correspond respectively to major axes of 10 L, 20 L domains presentedare oversized, by References especially for[32 ],large [34] vesselsand [3 5and] correspond cases of low respectively speed. In tothis major work, axes a 5 -ofvertices 10 퐿, and 16 L, such dimensions are inappropriate at low speed and those domains need to be adapted for 20polygonal 퐿 and 16domain 퐿, such is proposed dimensions as demonstrated are inappropriate in Figure at low 5 for speed accurate and thoseapproximation domains of need blocking to be particular situations and for practical applications [33]. adaptedareas and for for particular cost-efficient situations computations and for practicalin regard applications of large area [3 analysis3]. and big AIS data.

2.3. Corrected Efficient Polygonal Domain A statistical analysis of AIS data in Reference [36] has shown that around 10% of all normal safe situations were performed with a ship-ship passing distance of less than 2 퐿. Considering only near collision situations, this rate is much higher. This implies that the fixed 10 퐿, 20 퐿 and 16 퐿 ship domains are oversized, especially for large vessels and cases of low speed. In this work, a 5-vertices polygonal domain is proposed as demonstrated in Figure 5 for accurate approximation of blocking areas and for cost-efficient computations in regard of large area analysis and big AIS data.

Figure 5. IllustrationIllustration of of the the proposed proposed vessel vessel domain for a vessel at low speed o overver ground (SOG).(SOG). 2.3. Corrected Eﬃcient Polygonal Domain

A statistical analysis of AIS data in Reference [36] has shown that around 10% of all normal safe situations were performed with a ship-ship passing distance of less than 2 L. Considering only near collision situations, this rate is much higher. This implies that the ﬁxed 10 L, 20 L and 16 L ship domains are oversized, especially for large vessels and cases of low speed. In this work, a 5-vertices polygonal domain is proposed as demonstrated in Figure5 for accurate approximation of blocking areas and for cost-eﬃcient computations in regard of large area analysis and big AIS data. Figure 5. Illustration of the proposed vessel domain for a vessel at low speed over ground (SOG).

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J. Mar. Sci. Eng. 2020, 8, 5 8 of 19 To measure the collision and/or grounding risk associated with an individual close quarter To measure the collision and/or grounding risk associated with an individual close quarter situation, grounding and collision risk factors are added to the presented domain for each vessel situation, grounding and collision risk factors are added to the presented domain for each vessel throughthrough a a special special riskrisk evaluationevaluation functionfunction asas FigureFigure6 6 demonstrates. demonstrates.

(a) (b)

Figure 6. Safety domain for a vessel at 10 knots: (a) Comparison with a quaternion domain and an Figure 6. Safety domain for a vessel at 10 knots: (a) Comparison with a quaternion domain and an elliptic domain based on blocking areas; (b) domain with spatial CR function. elliptic domain based on blocking areas; (b) domain with spatial CR function. Figure6 also presents some comparisons with the quaternion domain [ 29] and an elliptic domain Figure 6 also presents some comparisons with the quaternion domain [29] and an elliptic domain defined by the blocking area radii [28]. The detailed derivation and correction of the domain and the defined by the blocking area radii [28]. The detailed derivation and correction of the domain and the special risk functions are presented below. In the following, the index/subscript i refers to any vessel at special risk functions are presented below. In the following, the index/subscript 푖 refers to any vessel a particular time t, both indices are sometimes dropped for simplicity. The domain is defined for any at a particular time 푡, both indices are sometimes dropped for simplicity. The domain is defined for vesselany vessel at a particular at a particular time thoughtime though its maneuverability, its maneuverability, speed speed over ground over ground (SOG), (SOG), course course over ground over (COG)ground angle (COG) in degreesangle in in degrees clockwise in clock directionwise direction with respect with to respect the north to the pole north and {A,pole B, and C, D,{A, L B,= AC, +D,B} dimensions,L= A + B} dimensions, (see Figure (see5). NoticeFigure 5). in EquationNotice in (4)Equation that the (4) vessel’s that the breadth vessel’s isbreadth approximated is approximated by 0.4 L , the domain size is 2 L 0.4 L at very low speed (SOG 0) which it is not correct and position errors in by 0.4퐿, the domain size× is 2퐿 × 0.4퐿 at very low speed≈ (푆푂퐺 ≈ 0) which it is not correct and position dataerrors are in not data considered. are not First,considered. the blocking First, area the blockingradii in Equation area radii (4) arein Equation corrected (4)in Equationare corrected (6) based in onEquation the accurate (6) based vessel on dimensions the accurate (shown vessel indimensions Figure5) so(shown that the in constructedFigure 5) so domainthat the appliesconstructed with accuracydomain applies to low speedwith accuracy situations to low and speed tolerate situations inaccuracies and tolerate of measured inaccuracies position of measured as well. Compared position toas the well. traditional Compared concepts to the traditional of Figure4 concepts, the proposed of Figure fore 4, andthe proposed aft direction fore radii and ofaft Equationdirection (6)radii vary of respectivelyEquation (6) in vary [A, 8respectivelyL] and [B, 4.23 in [A,L] 8 for L] the and whole [B, 4.23 range L] for of the practical whole speed range [0, of 40practical knots]. speed This reflects[0, 40 thatknots]. the mentionedThis reflects theoretical that the mentioned proposals theoretical do not suit proposals real applications, do not suit especially real applications, at low speed. especially at low speed.   r   2   2 kDT   Ri, f = A + 1.34 kAD + 푘 2L + ∆er  푅 = 퐴 +(1.34 √푘 2 + ( 2퐷푇) ) 퐿 + ∆  푖,푓 퐴퐷 2 푒푟   r    k 2 R = B + 0.67 k 2 + DT 2L + ∆ , (6)  i,a  AD 2 2푘퐷푇  er  푅푖,푎 = 퐵 + (0.67 √푘퐴퐷 + ( ) ) 퐿 + ∆푒푟 , (6)  2  R = C + (0.2 + k )L + ∆  i,s DT er  푅푖,푠 = 퐶 + (0.2 + 푘퐷푇) 퐿 + ∆푒푟  Ri,p = D + (0.2 + 0.75kDT)L + ∆er {푅푖,푝 = 퐷 + (0.2 + 0.75푘퐷푇) 퐿 + ∆푒푟 where ∆er is the combined error due to the limited resolution of GPS location accuracy and the precision where ∆푒푟 is the combined error due to the limited resolution of GPS location accuracy and the ofprecision which format of which the AIS format (longitude, the AIS latitude) (longitude, location latitude) is transferred location is and transferred stored: it isand generally stored: in it the is generally in the level of 10−4 in decimal degrees. This error is constant in time but its meters- equivalent (converted) value is varying according to the latitude 푒푟 ∆ = 푐표푠(퐿푎푡) × 2휋 × 6378137 × . 푒푟 360 (7)

J. Mar. Sci. Eng. 2020, 8, 5 9 of 19

4 level of 10− in decimal degrees. This error is constant in time but its meters-equivalent (converted) value is varying according to the latitude er ∆er = cos(Lat) 2π 6378137 . (7) × × × 360 As shown in Figure5, the proposed vessel safety domain is characterized by its 5 dimensions   D1 = 0.9Ri,s   =  D2 0.9Ri,p  −  D3 = 0.9Ri,a , (8)  −  D = 0.75R 0.25R  4 i, f i,a  − D5 = 1.1Ri, f which makes a better approximation to the blocking areas [28] compared to the quaternion domain [29], as indicated in Figure4. A vessel i at time t located at longitude x = Lon and latitude y = Lat sailing at speed SOG and course COG has a safety domain Pi(t) deﬁned by its ﬁve vertices (points) n o P (t) P (t), P (t), P (t), P (t), P (t) , (9) i ≡ i,1 i,2 i,3 i,4 i,5 in which their (x, y) coordinates are obtained as   Pi,1 = p1x, p1y    Pi,2 = p2x, p2y   P = p3 , p3 , (10)  i,3 x y   P = p4x, p4y  i,4   Pi,5 = p5x, p5y such that

 p1 p1   D D   x yi   x y   1 3   i       ( ) ( )     p2x p2y   D1 D4   cos COG sin COG   xi yi           p3x p3y  =  0 D    +  x yi  (11)    5     i      ×      p4x p4y   D2 D4  sin(COG) cos(COG)  xi yi      −   p5x p5y D2 D3 xi yi

Given a particular AIS data set, where N vessels are present at the same time over a given location, N(N 1) there could be up to 2− vessel to vessel close quarter situations and N vessels in grounding situations to be veriﬁed for safety domain violation. The key advantage of the proposed approach compared to the oversized domains and the considered uncertainties will be highlighted in the discussion of results from realistic data and application.

2.4. Risk Evaluation Functions Instead of binary evaluation of risky and risk-free situations, the proposed vessel safety domain is further combined with a risk scoring function that scores the risky situations depending on the type of encounter (crossing, head-on, overtaking), amount of domain violation (intersection of two domains or domain with land shapes) and more importantly, how unsafe is the encounter as indicated in Figure6. An exponential risk function is adopted which evaluates to a relative risk factor r = 1 at the actual vessel region and decays exponentially to a relatively small risk factor r0 = 0.1 at the borders of the vessel’s domain as illustrated in Figure7. The risk functions are not symmetrical and decay at di ﬀerent rates in diﬀerent directions. Risk functions are therefore tuned with the parameter r0 (given in α in Equation (12)) and controlled with the four blocking area radii given by Equation (6) and shown in J. Mar. Sci. Eng. 2020, 8, 5 10 of 19

Figure4a. Risk functions depend on the encounter type deﬁned by positive or negative projections xp, yp shown in Figure5, Section 2.5 will introduce how to calculate the projections and how to evaluate the risk functions, this section only describes the selected longitudinal/lateral/spatial risk functions for collision/grounding at positive/negative sides. The so many combinations are reduced J. Mar. Sci. Eng. 2020, 8, 5 10 of 19 with the sign function.

GR (x ) GR (y ) Lat p Lon p CR (x ) 0.8 CR (y ) 0.8 Lat p Lon p

0.6 0.6

0.4 0.4

0.2 0.2

-2 -1 012345 -2 -1 0123 x [L] y [L] p p

(a) (b)

Figure 7. Risk evaluation functions: (a), Longitudinal collision and grounding functions (b), lateral Figure 7. Risk evaluation functions: (a), Longitudinal collision and grounding functions (b), lateral collision and grounding functions (c), spatial collision function (d) spatial grounding function. collision and grounding functions (c), spatial collision function (d) spatial grounding function. Collision and grounding risk functions are then deﬁned in longitudinal and lateral directions of Collision and grounding risk functions are then defined in longitudinal and lateral directions of the vessel as well as the overall spatial risk functions. The longitudinal collision risk function CRLon yp the vessel as well as the overall spatial risk functions. The longitudinal collision risk function is deﬁned through the parameter α as 퐶푅퐿표푛(푦푝) is defined through the parameter 훼 as !! 1 1 3 α = ln ,1 (12) 1 훼 = (푙푛r(0 ))3, (12) 푟0 2y α 3 ( p ) − (1+sign(yp))Ri, f (1 sign(yp))Ri,a 3 CRLon yp = e − − , (13) 2푦푝 훼 −( ) (13) (1+푠푖푔푛(푦푝)) 푅푖,푓−(1−푠푖푔푛(푦푝)) 푅푖,푎 퐶푅퐿표푛(푦푝) = 푒 , where 푦푝 is the projection on the longitudinal direction of the vessel track defined by its 퐶푂퐺 and reference point as indicated in Figure 5 and 푠푖푔푛(푥) is the sign function 1 푖푓 푥 ≥ 0 푠푖푔푛(푥) = { , −1 푖푓 푥 < 0 (14)

Hence the longitudinal risk function 퐶푅퐿표푛(푦푝) of Equation (13) is asymmetrical, it will pass with fore radii 푅푖,푓 in case of a front encounter 푦푝 ≥ 0; and with the aft radii 푅푖,푎 in case of an encounter from the back 푦푝 < 0. 푅푖,푓 or 푅푖,푎 is the parameter that controls the decaying rate of 퐶푅퐿표푛(푦푝).

J. Mar. Sci. Eng. 2020, 8, 5 11 of 19

where yp is the projection on the longitudinal direction of the vessel track deﬁned by its COG and reference point as indicated in Figure5 and sign(x) is the sign function ( 1 i f x 0 sign(x) = ≥ , (14) 1 i f x < 0 − Hence the longitudinal risk function CRLon yp of Equation (13) is asymmetrical, it will pass with fore radii Ri, f in case of a front encounter yp 0; and with the aft radii Ri,a in case of an encounter from ≥ the back yp < 0. Ri, f or Ri,a is the parameter that controls the decaying rate of CRLon yp .

1 3 1 3 1 3 1 yp(ln( r )) yp(ln( )) 3 0 r0 ( R ) ( ) − i, f Ri,a CRLon yp = e f or yp 0; and CRLon yp = e f or yp < 0. (15) ≥ Recall Figure5 where xp, yp are projections on the vessel track and xp, yp = (0, 0) is the reference point onboard the ship. The longitudinal risk function CRLon yp is shown in the top-left of Figure7. The function evaluates to relative risk r = 1 at the reference point and at the physical ship around yp 0 (due to the power ˆ3). The function decays at diﬀerent rates in front of and behind the ≈ ship to a smaller risk factor r = 0.1 at yp = R 5 L and at yp = R 3 L, respectively. Notice that 0 i, f ≈ − i,a ≈ CRLon(2 L) > 0.8 but CRLon( 2 L) < 0.4, this is logical because the same critical passing distance (e.g., − 2 L) between a target ship and own ship implies more danger in case of front passing than in case of passing behind. In the same manner, the lateral collision risk function is deﬁned as

2x α 3 ( p ) − (1+sign(xp))Ri,s (1 sign(xp))Ri,p CRLat xp = e − − , (16) where xp is the lateral projection on the vessel track as shown in Figure5. The spatial collision risk function for a vessel i is then given over the deﬁned domain as CRsi xp, yp = CRLon yp CRLat xp 2y α 3 × 2x α 3 (( p ) +( p ) ) (17) (1+sign(yp))R (1 sign(yp))R (1+sign(xp))R (1 sign(xp))R = e− i, f − − i,a i,s− − i,p . The grounding risk function GRi xp, yp for the ith vessel is deﬁned through the same manner of CRsi, as depicted in Figure8, in which the risk factor decays at the same rate in the forward direction but at twice the rate in the remaining three directions

2y α 3 x α 3 (( p ) +( p ) ) − (1+sign(yp))Ri, f 2(1 sign(yp))Ri,a (1+sign(xp))Ri,s (1 sign(xp))Ri,p GRsi xp, yp = e − − − − . (18)

The longitudinal, lateral and spatial risk functions for collision and grounding, respectively, are shown in Figure7. Notice that the same vessel domain (Figure5) and risk evaluation parameters Equation (6) are used for collision and grounding risk evaluation, however, with different spatial functions (Equations (16) and (17) and Figure7). The main advantage here is to ensure memory-e fficiency such that each AIS message in combination with vessel dimensions is mapped into 14 single-precision floating-point numbers (vertices’ x-y coordinates defined by Equation (11) and four parameters of Equation (6)). J. Mar. Sci. Eng. 2020, 8, 5 12 of 19

퐶푅푖,푗 = ∯ 퐶푅푠푖(푥푝푖, 푦푝푖) × 퐶푅푠푗(푥푝푗, 푦푝푗) 푑푥 푑푦, 퐶푖∩푗 (20)

where 푥푝푖, 푥푝푗, 푦푝푖 and 푦푝푗 are the lateral and longitudinal projections on the tracks of vessel 푖 and 푗 respectively. This computation is not feasible and it is approximated based on the area 퐴푝푖,푗 and the centroid (퐶푥, 퐶푦) of the intersection region 푃푖,푗 (assumed small) as

퐴푐푖,푗 = 퐴푟푒푎 (퐶푖∩푗 ) { , (21) (퐶푥, 퐶푦) = 퐶푒푛푡푟표푖푑(퐶푖∩푗)

퐶푅푖,푗 = 퐶푅푗,푖 = 퐴푐푖,푗 × 퐶푅푠푖(퐶푥푝푖, 퐶푦푝푖) × 퐶푅푠푗(퐶푥푝푗, 퐶푦푝푗), (22) where

퐶푥푝푖 푐표푠 (퐶푂퐺 ) −푠푖푛 (퐶푂퐺 ) 퐶푥 푥푖 [ ] = [ 푖 푖 ] ([ ] − [ ]), (23) 퐶푦푝푖 푠푖푛 (퐶푂퐺푖) 푐표푠 (퐶푂퐺푖) 퐶푦 푦푖

퐶푥푝푗 푐표푠 (퐶푂퐺푗) −푠푖푛 (퐶푂퐺푗) 퐶푥 푥푗 J. Mar. Sci. Eng. 2020, 8, 5 [ ] = [ ] ([ ] − [푦 ]). 12 of(2 194) 퐶푦푝푗 푠푖푛 (퐶푂퐺푗) 푐표푠 (퐶푂퐺푗) 퐶푦 푗

Figure 8. Demonstration of collision and grounding risk regions for different vessels in a selected area Figure 8. Demonstration of collision and grounding risk regions for different vessels in a selected area at one time instance. at one time instance. 2.5. Collision and Grounding Risk Evaluation The overall risk of immediate collision for a vessel 푖 is identified as the cumulative risk for multipleThe collisionclose quarter risk (CR) situations in a vessel (see for to vesselexample encounter Figure situation8) in which is definedthe vessel through is involved, the violation hence of the safety domains and the spatial collision risk functions of both vessels. Consider two vessels i and j, the two vessels have different maneuverability,퐶푅푖 = ∑푗 퐶푅푖, dimensions푗 , ∀ 푗 푠. 푡. 퐶푅 and푖,푗 > SOG0, and therefore different safety(25) domainsTheP groundingi(t) and Pj risk(t) respectively. of vessel 푖 is The calculated close quarter based situation on the intersection is in different of the perspectives vessel safety for thedomain two vessels;with land First, shapes the region represented in which by the a possibly two domains large intersectset of shoreline is defined polygons as 푺푷 . This intersection

would result in multiple nonempty grounding risk regions 푮풊 Ci j(t) = Pi(t) Pj(t) = Cj i(t). (19) ∩ ∩ ∩ 푮풊 = 푃푖(푡) ∩ 푺푷 = {퐺푖,1, 퐺푖,2, … , 퐺푖,푛}. (26) This intersection zone can easily be obtained for the two 5-vertices polygonal shapes and this The area and the centroid’s coordinates of the 푘푡ℎ grounding risk region of the 푖푡ℎ vessel are operation is computationally advantageous compared to elliptical domains. The resulting intersection region is also a polygonal shape in which퐴퐺 the푖,푘 calculation= 퐴푟푒푎 (퐺푖, of푘) collision risk is feasible. The collision risk { . (27) is non-zero if this region is not empty( and퐺푥푖, the푘, 퐺푦 risk푖,푘) is= evaluated퐶푒푛푡푟표푖푑( as퐺푖,푘 the) integration of the multiplication of the two projected CR functions over the region of intersect for 푘 = 1, … , 푛. The grounding risk for the 푖푡ℎ vessel is then evaluated as = 푛 CRi,j 퐺푅C푖i =j CRs ∑푘=i 1x퐴퐺pi, 푖y,푘pi× 퐺푅푠CRs푖(j퐺푥푝xpj푖,,푘y, pj퐺푦푝dx푖,푘 dy). , (20)(28) ∩ × where 퐺푥푝 and 퐺푦푝 are respectively the projection of 푘푡ℎ grounding-risky region on the track where xpi, x푖pj,푘, ypi and y푖pj,푘 are the lateral and longitudinal projections on the tracks of vessel i and j of the 푖푡ℎ vessel respectively. This computation is not feasible and it is approximated based on the area Api,j and the centroid (Cx, Cy) of the intersection퐺푥푝푖,푘 region푐표푠 (퐶푂퐺Pi,j)(assumed−푠푖푛 (퐶푂퐺 small)) as퐺푥푖,푘 푥푖 [ ] = [ 푖 푖 ] ([ ] − [ ]). (29) 퐺푦푝 푠푖푛 (퐶푂퐺 ) 푐표푠 (퐶푂퐺 ) 퐺푦 푦푖 푖,푘  푖 푖 푖,푘   Aci,j = Area Ci j  ∩ , (21)  (Cx, Cy) = Centroid Ci j ∩ CR = CR = Ac CRs Cx , Cy CRs Cx , Cy , (22) i,j j,i i,j × i pi pi × j pj pj where " # " # " # " #! Cx cos(COG ) sin(COG ) Cx x pi = i − i i , (23) Cypi sin(COGi) cos(COGi) Cy − yi " #   " # " #! Cx  cos COGj sin COGj  Cx x pj =  −  j   . (24) Cypj sin COGj cos COGj Cy − yj The overall risk of immediate collision for a vessel i is identiﬁed as the cumulative risk for multiple close quarter situations (see for example Figure8) in which the vessel is involved, hence X CR = CR , j s.t. CR > 0, (25) i i,j ∀ i,j j J. Mar. Sci. Eng. 2020, 8, 5 13 of 19

The grounding risk of vessel i is calculated based on the intersection of the vessel safety domain with land shapes represented by a possibly large set of shoreline polygons SP. This intersection would result in multiple nonempty grounding risk regions Gi n o G = P (t) SP = G , G , ... , G . (26) i i ∩ i,1 i,2 i,n The area and the centroid’s coordinates of the kth grounding risk region of the ith vessel are    AGi,k = Area Gi, k  . (27)  Gxi, k, Gyi,k = Centroid Gi, k for k = 1, ... , n. The grounding risk for the ith vessel is then evaluated as

Xn GR = AG GRs Gxp , Gyp . (28) i i,k × i i, k i,k k=1 where Gxpi, k and Gypi,k are respectively the projection of kth grounding-risky region on the track of the ith vessel " # " # " # " #! Gxp cos(COG ) sin(COG ) Gx x i, k = i − i i, k i . (29) Gypi,k sin(COGi) cos(COGi) Gyi,k − yi The relative risk score of the immediate danger of a navigation accident (collision or grounding) for a certain navigation scenario depends on all the near risky situations and unsafe maneuvers, it is given as X R = CRi + βGRi, (30) i where β is a constant that can be set to specify the relative importance of collisions compared to grounding accidents. When the algorithm outlined above is applied to a large dataset of AIS data, it will identify and extract critical navigational scenarios based on the value of the risk score; situations with a high value will typically be navigationally complex and can be used to deﬁne risky navigational scenarios.

3. Applications and Discussion The algorithms for identifying risky navigational situations outlined above have been applied to a large set of AIS data and have identiﬁed a number of challenging navigational situations accordingly. Some of the extracted situations will be described in the following examples.

3.1. Data Description and Set-up The experimental validation data in this paper consists of two large sets of AIS data over a continuous full year as indicated in Table1.

Table 1. Description of raw 8.3 107 automatic identiﬁcation system (AIS) data records for validation. × Time Space Vessels Lo. La. Time Period Resolution Resolution Length Breadth Number Speed Range Range

03-Jan-2018 to 0 to 270 sMAYDAYMedian 3.942◦ 2.5◦ 4 15 m to 2 m to 10− ◦ 17836 0 to 53.1 02-Jan-2019 = 225s 1.072◦ 0.669◦ 400 m 61.9 m

AIS information from all vessels is interpolated and synchronized to 1 min in this work and all service vessels are ignored for risk identification. These include: Crew boats, pilot vessels, supply tenders, work and repair vessels, search and rescue vessels and salvage ships as well as J. Mar. Sci. Eng. 2020, 8, 5 14 of 19 mooring/towing/pushing/tugging vessels. These vessels are generally small and agile and are intended to perform their operations in contact with other bigger vessels so they are assumed neutral in this work. Notice that, for simplicity, the time parameter t was dropped in the previous risk functions as well as the actual collision, grounding and overall risk of each situation. In real applications, AIS data is first synchronized to similar time points at which the blocking area radii are updated as given by Equations (6) and (7) for each vessel (i) and their safety domains as in Equations (8)–(11) at each time t. All safety domain violations are then identified for all relevant vessel to vessel (Equation (19)) and vessel to ground (Equation (26)) combinations. Collision risk CR is determined through Equations (21)–(25) and similarly the grounding risk (Equations (27)–(29)) and the situation risk by Equation (30). The AIS data is interpolated and synchronized in this work to 1 min intervals

t to zi(t) = zi(to) + zi t f zi(to) − , (31) − t to f − for t = 0, 1, 2, , where to is the most recent time vessel i sent AIS records before t and t is the ﬁrst ··· f time after that. This equation applies to all dynamic navigation parameters in which zi stands for either of { Loni, Lati, SOGi, COGi} for each vessel i. Information about the vessel, such as its type and actual dimensions, are obtained from vessel registry. High-resolution digital maps are also used in the identiﬁcation of grounding risk.

3.2. Obtained Results and Discussion A navigation risk example is demonstrated in Figure8 in which all vessels are indicated in black surface, their safety domains in blue lines, collision regions in red and grounding regions in yellow. The vessel domain is updated based on the vessel length and maneuverability depending on its speed for which static vessels have a small domain that accounts only for GPS inaccuracy and imprecision, this is a remarkable advantage compared to theoretical fixed L-dependent domains of Figure4 which are oversized. Since moored vessels usually transmit inaccurate COG records, they are ignored for grounding risk identification without the loss of generality. In this illustration example, vessel 2 n o encounters four grounding obstacles that need to be avoided G2 = G2, 1, G2,2, G2,3, G2,4 and vessel 3 is navigating under two potential collision candidates C2 3 and C3 2 Figure8 reflects some types of ∩ ∩ position uncertainties which have been introduced in Section 2.3 as well as unreliable COG for moored vessels and negligible interpolation errors. Indeed, introducing time to Figure8 and verifying the situation over a few successive instances reflects many vessels were just about one minute to collision for many times. In the next timestamp (after one minute), vessels 1 and 2 will be in a close quarter situation of head on collision and both vessels must alter their course to starboard side according to COLREG rule 14 to avoid accident. This cannot be achieved easily since both vessels are in risk of grounding on their starboard side and both vessels must proceed carefully at safe speed to avoid collision or grounding. Vessel 3 on the other hands cannot overtake vessel 2 on the right side due to limited maneuvering area and the danger of grounding for which it must decrease its speed. However, vessel 3 in this case will impede the route of vessel 4, this action is not allowed by COLREG rule 13. Hence, this situation is navigationally complex and associated with considerable navigational risk and can be identified from a large set of AIS data. Given the one-year AIS data for the two sample areas described in Table1, results of all the identified risky situations are demonstrated in Figures9–11. Figures9a and 10a describe the spatial locations of the identified vessel to vessel collision risks for two different areas and their respective risk distributions are demonstrated in Figures9b and 10b. Variations of both collision and grounding risk over the two areas are both shown in Figure 11 for the year 2018. J. Mar. Sci. Eng. 2020, 8, 5 14 of 19

A navigation risk example is demonstrated in Figure 8 in which all vessels are indicated in black surface, their safety domains in blue lines, collision regions in red and grounding regions in yellow. The vessel domain is updated based on the vessel length and maneuverability depending on its speed for which static vessels have a small domain that accounts only for GPS inaccuracy and imprecision, this is a remarkable advantage compared to theoretical fixed L-dependent domains of Figure 4 which are oversized. Since moored vessels usually transmit inaccurate 퐶푂퐺 records, they are ignored for grounding risk identification without the loss of generality. In this illustration example, vessel 2

encounters four grounding obstacles that need to be avoided 푮ퟐ = {퐺2,1, 퐺2,2, 퐺2,3, 퐺2,4} and vessel 3 is navigating under two potential collision candidates 퐶2∩3 and 퐶3∩2 Figure 8 reflects some types of position uncertainties which have been introduced in Section 2.3 as well as unreliable COG for moored vessels and negligible interpolation errors. Indeed, introducing time to Figure 8 and verifying the situation over a few successive instances reflects many vessels were just about one minute to collision for many times. In the next timestamp (after one minute), vessels 1 and 2 will be in a close quarter situation of head on collision and both vessels must alter their course to starboard side according to COLREG rule 14 to avoid accident. This cannot be achieved easily since both vessels are in risk of grounding on their starboard side and both vessels must proceed carefully at safe speed to avoid collision or grounding. Vessel 3 on the other hands cannot overtake vessel 2 on the right side due to limited maneuvering area and the danger of grounding for which it must decrease its speed. However, vessel 3 in this case will impede the route of vessel 4, this action is not allowed by COLREG rule 13. Hence, this situation is navigationally complex and associated with considerable navigational risk and can be identified from a large set of AIS data. Given the one-year AIS data for the two sample areas described in Table 1, results of all the identified risky situations are demonstrated in Figures 9–11. Figures 9a and 10a describe the spatial locations of the identified vessel to vessel collision risks for two different areas and their respective J.risk Mar. distribut Sci. Eng.ions2020 ,are8, 5 demonstrated in Figures 9b and 10b. Variations of both collision and grounding 15 of 19 risk over the two areas are both shown in Figure 11 for the year 2018.

(a) (b) J. Mar. Sci. Eng. 2020, 8, 5 15 of 19 Figure 9. Identiﬁed collision risk over sample data from area 1 for a year: (a) Spatial distribution; (b) Figure 9. Identified collision risk over sample data from area 1 for a year: (a) Spatial distribution; (b) J. Mar. Sci. Eng. 2020, 8, 5 15 of 19 Risk distribution.

(a) (b) (a) (b) Figure 10. Identified collision risk over sample data from area 2 for a year: (a) Spatial distribution; (b) Figure 10. Identiﬁed collision risk over sample data from area 2 for a year: (a) Spatial distribution; (b) FigureRisk 10. distribution. Identified collision risk over sample data from area 2 for a year: (a) Spatial distribution; (b) RiskRisk distribution. distribution.

(a) (a) (b) (b) Figure 11. Variation over time of overall collision and grounding risk: (a) Sample data of area 1; FigureFigure 11. Variation11. Variation over over time timeof overall of overall collision collision and grounding and grounding risk: ( arisk:) Sample (a) Sample data of data area of1; (areab) 1; (b) (b) Sample data of area 2. SampleSample data data of area of area 2. 2. Examples of some risky situations are also illustrated in Figures 12–14. Figure 12 represent a ExamplesExamples of someof some risky risky situations situations are alsoare illustratedalso illustrated in Figures in Figures 12–14. 12 Figure–14. Figure 12 represent 12 represent a a collision-risky situation due to a combination of conﬂicting overtaking and head-on encounter COLREG collisioncollision-risky-risky situation situation due due to a to combination a combination of conflicting of conflicting overtaking overtaking and head and- on head encounter-on encounter COLREGCOLREG rules, rules, the the largest largest vessel vessel is involved is involved in three in three possible possible collision collision situations situations in which in which the the avoidanceavoidance of head of head-on - collisionon collision (alter (alter course course to starboard to starboard according according to rule to 14) rule would 14) would result inresult a in a collisioncollision with with the theother other two twovessels vessels for which for which this vessel this vessel must mustnot impede not impede their routes. their routes. This situation This situation cancan be solvedbe solved if all if theall thevessels vessels keep keep their their track track and speedand speed except except the vessel the vessel moving moving northwa northward that rd that mustmust take take actions actions alone alone to avoid to avoid collision. collision. These These actions actions highly highly depend depend on its maneuverability.on its maneuverability. Figure Figure 13 13also also describes describes another another situation situation involving involving a combination a combination of head of headon, overtaking on, overtaking and grounding and grounding wherewhere the theavoidance avoidance of one of oneaccident accident may mayresult result in another in another accident. accident.

J. Mar. Sci. Eng. 2020, 8, 5 16 of 19

J. Mar. Sci. Eng. 2020, 8, 5 16 of 19 rules, the largest vessel is involved in three possible collision situations in which the avoidance of head-on collision (alter course to starboard according to rule 14) would result in a collision with the other two vessels for which this vessel must not impede their routes. This situation can be solved if all the vessels keep their track and speed except the vessel moving northward that must take actions J.alone Mar. Sci. to avoidEng. 2020 collision., 8, 5 These actions highly depend on its maneuverability. Figure 13 also describes16 of 19 another situation involving a combination of head on, overtaking and grounding where the avoidance J. Mar. Sci. Eng. 2020, 8, 5 16 of 19 of one accident may result in another accident.

Figure 12. Risky navigation situation with conflicting head-on and overtaking maneuvers.

Figure 12. Risky navigation situation with conflicting head-on and overtaking maneuvers. Figure 12. Risky navigation situation with conﬂicting head-on and overtaking maneuvers. Figure 12. Risky navigation situation with conflicting head-on and overtaking maneuvers.

Figure 13. A critical navigation situation due to limited maneuvering area and risk of grounding.

A combination of conflicting navigation maneuvers (crossing and overtaking) is demonstrated in Figure 14 in which one vessel is in immediate danger of collision with a crossing vessel and an overtaking vessel. This vessel must give way to the vessel crossing on its starboard side according to COLREG rule 15, the later vessel has right of way and is in stand-on maneuver but may take action to avoid collision (rule 17). The first vessel must take substantial action (rule 16) and must not pass in from of the crossing vessel, however, this may result in collision with the overtaking vessel (rule 13). Figure 13. A critical navigation situation due to limited maneuvering area and risk of grounding. Figure 13. A critical navigation situation due to limited maneuvering area and risk of grounding.

Figure 13. A critical navigation situation due to limited maneuvering area and risk of grounding. A combination of conflicting navigation maneuvers (crossing and overtaking) is demonstrated in Figure 14 in which one vessel is in immediate danger of collision with a crossing vessel and an A combination of conflicting navigation maneuvers (crossing and overtaking) is demonstrated overtaking vessel. This vessel must give way to the vessel crossing on its starboard side according to in Figure 14 in which one vessel is in immediate danger of collision with a crossing vessel and an COLREG rule 15, the later vessel has right of way and is in stand-on maneuver but may take action overtaking vessel. This vessel must give way to the vessel crossing on its starboard side according to to avoid collision (rule 17). The first vessel must take substantial action (rule 16) and must not pass COLREG rule 15, the later vessel has right of way and is in stand-on maneuver but may take action in from of the crossing vessel, however, this may result in collision with the overtaking vessel (rule to avoid collision (rule 17). The first vessel must take substantial action (rule 16) and must not pass 13). in from of the crossing vessel, however, this may result in collision with the overtaking vessel (rule 13).

Figure 14. Collision risk due to conflicting crossing and overtaking maneuvers. Figure 14. Collision risk due to conflicting crossing and overtaking maneuvers. A combination of conflicting navigation maneuvers (crossing and overtaking) is demonstrated in4. Conclusions Figure 14 in which one vessel is in immediate danger of collision with a crossing vessel and an overtakingA practical vessel. method This vessel was mustpresented give wayin this to thearticle vessel for crossingthe automatic on its starboardidentification side accordingof maritime to COLREGnavigation rule risk 15, in the realistic later vessel and has large right-scale of way applications. and is in stand-on The proposed maneuver solution but may has take paramount action to avoidadvantages collision in terms(rule 17). of effectivenessThe first vessel and must computational take substantial efficiency action and(rule plays 16) and a crucialmust not role pass as in a from of the crossing vessel, however, this may result in collision with the overtaking vessel (rule 13).

Figure 14. Collision risk due to conflicting crossing and overtaking maneuvers.

Figure 14. Collision risk due to conflicting crossing and overtaking maneuvers. 4. Conclusions 4. ConclusionsA practical method was presented in this article for the automatic identification of maritime navigation risk in realistic and large-scale applications. The proposed solution has paramount A practical method was presented in this article for the automatic identification of maritime advantages in terms of effectiveness and computational efficiency and plays a crucial role as a navigation risk in realistic and large-scale applications. The proposed solution has paramount advantages in terms of effectiveness and computational efficiency and plays a crucial role as a

J. Mar. Sci. Eng. 2020, 8, 5 17 of 19

4. Conclusions A practical method was presented in this article for the automatic identification of maritime navigation risk in realistic and large-scale applications. The proposed solution has paramount advantages in terms of effectiveness and computational efficiency and plays a crucial role as a warning input for smart navigation and decision support tools as well as in remote control and autonomous navigation technologies. Individual grounding and collision risks were evaluated through an accurate adaptive vessel safety domain that considers the actual navigation parameters as well as vessel dimensions and maneuverability. This approach is based on a correction of blocking area radii in which close quarter situations are addressed through a five-vertices polygonal safety domain. Depending on the type of encounter and danger of collision and/or grounding situations, individual risk was evaluated through a spatial risk function. In this paper, real navigational risk is identified through the combination of multiple candidates of groundings and collisions for a set of interacting vessels over any area and period of time. The overall method is fast and computation-efficient and exhibits a remarkable possibility to address large-scale navigation monitoring and risk identification. The presented algorithm is supported by a thorough analysis of two large sets of AIS data, each spans one year and covers a large geographical area and are combined with vessel registry and high-resolution digital maps. In addition to high efficiency, the obtained results demonstrate potential applications and illustrate the reliability of the developed methods to identify accurately various aspects of navigation risk. The presented procedure also supports significant future extensions to non-immediate navigation risk identification and prediction to determine safe situations that my cause navigation risk in a while. Another important feature that may be investigated in the future is a deeper analysis of complexity in navigation scenarios regarding COLREGs and special rules while considering weather conditions, visibility, wind, sea state, water depth and tides. The main limitation of the presented work is in fact a data limitation with the utilization of AIS data only, which limits the applications to decision support rather than the basic tool for collision avoidance. However, the main advantages of the algorithm are its effectiveness and computation-efficiency to analyze big amounts of data for anti-collision support over a large area in a finite time and resources. The algorithm can easily integrate with other navigational systems and access data from more sources for enhanced performance.

Author Contributions: Conceptualization, Ø.E.; methodology, A.B.; software, A.B.; validation, I.K.G. and E.V.; formal analysis, A.B. and I.K.G.; investigation, Ø.E.; resources, E.V. and Ø.E.; data curation, E.V. and A.B.; writing—original draft preparation, A.B.; writing—review and editing, I.K.G. and E.V.; visualization, A.B.; project administration, I.K.G. All authors have read and agreed to the published version of the manuscript. Funding: This research is funded by the Norwegian Research Council research-based innovation center BigInsight, project no 237718. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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