Modelng perceved collson rsk n port water navgaton Hoong Chor Chn Assocate Professor, Department of Cvl Engneerng, Natonal Unversty of Sngapore, Engneerng Drve, EA #07-03, Sngapore 7576 Emal: cvechc@nus.edu.sg Tel: +65 656550 Ashm Kumar Debnath* Research Scholar, Department of Cvl Engneerng, Natonal Unversty of Sngapore, Engneerng Drve, EW #0-0B, Sngapore 7576 Emal: ashm@nus.edu.sg Tel: +65 65655 * Correspondng Author Abstract An ncrease n the lkelhood of navgatonal collsons n port waters has put focus on the collson avodance process n port traffc safety. The most wdely used on-board collson avodance system s the automatc radar plottng ad whch s a passve warnng system that trggers an alert based on the plot s pre-defned ndcators of dstance and tme proxmtes at the closest pont of approaches n encounters wth nearby vessels. To better help plot n decson makng n close quarter stuatons, collson rsk should be consdered as a contnuous monotonc functon of the proxmtes and rsk percepton should be consdered probablstcally. Ths paper derves an ordered probt regresson model to study perceved collson rsks. To llustrate the procedure, the rsks perceved by Sngapore port plots were obtaned to calbrate the regresson model. The results demonstrate that a framework based on the probablstc rsk assessment model can be used to gve a better understandng of collson rsk and to defne a more approprate level of evasve actons. Keywords: Ordered regresson model; Rsk percepton; Collson rsk; Port navgaton safety; Automatc Radar Plottng Ad; Harbor plot. Please cte ths artcle as: Chn, H.C. and Debnath, A.K. (009) Modelng Perceved Collson Rsk n Port Water Navgaton. Safety Scence, 7(0), pp. 0-6.
. Introducton Navgatonal collsons are a major safety concern n many seaports. The growth of shppng traffc over the past decades has ntensfed collson lkelhood n busy and congested port waters (Darbra and Casal, 00; Sato and Ish, 998; Yp, 007). Consequently, the collson avodance process has come nto focus n port navgaton safety. In general, harbor plots assess and mtgate collson rsk by combnng data obtaned from collson avodance systems (CAS) wth nformaton obtaned by vsual watch-keepng. The most wdely CAS used on most merchant vessels s the Automatc Radar Plottng Ad (ARPA) (Statheros et al., 008). It allows plots to track a number of target vessels wthn the radar detecton range. Apart from provdng a graphcal dsplay of the surroundng vessel traffc, ARPA provdes forecasted values of two proxmty measures for selected target vessels Dstance at Closest Pont of Approach (DCPA) and Tme to Closest Pont of Approach (TCPA). The two ndcators are respectvely the probable dstance and tme requred between the subject vessel and a target vessel at ther Closest Pont of Approach (CPA), gven that the course and speed of both vessels reman unchanged. Plots make use of these proxmty ndcators as a bass of rsk assessment to determne ther own necessary course of acton to avod a collson. ARPA also possesses a warnng system (e.g., aural alarm or flashng symbol) to alert the plots of collson rsk. Plots may set some crtcal values (DCPAlmt and TCPAlmt) to trgger the warnng system. Snce the crtcal values are defned by plots, ARPA s a passve system based on the ntutve perceved rsks of the plots. Ths warnng system s useful to draw attenton of plots who needed remnder when they have temporarly lost stuatonal awareness. Several researchers, such as Grech et al. (00) and Wagenaar and Groeneweg (987) have shown that the lack of stuatonal awareness s responsble for about 70% of human errors n navgaton. Further, Hetherngton et al. (006) and Rothblum (000) have also shown that human errors contrbute to more than 90% of collsons. Employng ths arrangement of alertness, rsk of collson s expressed as a unt step functon nvolvng two possble states: potental collson rsk and no rsk, the former state when both the proxmty ndcators are below the crtcal lmts whle the latter for any other condton. An mprovement to the bnary state of rsk assessment s the three-level warnng system proposed by Lu, Q. et al. (006). Usng preset crtcal values of DCPA and TCPA, they defne the stuaton as safe, potental collson rsk and drect collson rsk. It should be noted that collson rsk s strctly a contnuous monotonc functon of the proxmty ndcators based on the vessel nteracton wth nfluence from the performance capablty and experence of the plots n handlng close quarter stuatons. Both the bnary and three-state systems may not fully represent the range of rsks nvolved and the approprate actons needed of plots. Other researches on CAS have focused on dfferent aspects of collson avodance, such as mprovement on plottng performance of ARPA (Sato and Ish, 998; Pedersen et al., 999), development of cone-shaped danger regons (Leanrt, 983), evaluaton of dsplay technques (Pedersen et al., 00a), and evaluaton of ant-collson maneuvers n CAS (Pedersen and Jacobsen, 00; Pedersen et al., 00b; Pedersen et al., 003). In all cases collson rsk s treated as a dscrete varable rather than a contnuous varable. Furthermore, as the performance and judgment n close encounter vary from one plot to another, t s also necessary to consder the probablstc aspects of defnng rsk. Moreover, other factors such
as vessel sze and the envronment play an mportant role n nfluencng navgatonal rsk. These factors are not consdered n the system of rsk assessment and collson avodance. Ths paper develops a probablstc model of collson rsk derved from percepton of the plots. Ordered Probt Regresson modelng s employed to examne rsk for navgaton n dfferent vessel classes under both day and nght condtons. To llustrate the dervaton of the model, perceved rsks are obtaned from a rsk percepton survey on Sngapore port plots. The followng sectons descrbe the methodology of the study consstng of the formulaton, assessment and modelng consderatons of the ordered probt regresson model, followed by development of safety margns and descrpton of a rsk percepton survey. Estmaton results and model ftness are then dscussed along wth the nterpretatons of the perceved safety margns. A framework of probablstc rsk assessment n CAS s fnally proposed.. Methodology. Ordered Probt Regresson Model To develop a probablstc model of collson rsk an ordered probt regresson model s formulated, whch s calbrated by usng perceved rsk data. Intensty of the rsk can be expressed by a scale categorzng rsk nto fve levels (see Table ). The regresson model s formulated to sut the categorcal response varable... Model formulaton Snce the rsk levels used n the scale are subjectve but ordered n nature, an ordered categorcal analyss wll be most approprate to treat such data. Two possble regresson models may be employed: the ordered probt or ordered logt models. The models dffer n the assumpton of the dstrbutons of regresson errors. The probt model assumes a normal dstrbuton of errors wth mean 0 and varance, whereas the logt model assumes a standard logstc dstrbuton wth mean 0 and varanceπ 3. The ordered probt model s selected for ths study though the choce matters lttle as both models produce very smlar results. The ordered probt model s usually formulated as a latent (.e., unobserved) varable framework. The structural model specfcaton s: y = βx + ε () where y s a contnuous latent varable measurng perceved collson rsk for the th set of X ; X s the vector of ndependent varables; β s the vector of regresson coeffcents; ε s ~ N 0,. the random error term ( ) The measurement model, n whch the latent varable ordnal varable y, s specfed as: y s mapped on to an observed y = m f y < ; for m = to J () m m 3
where J s number of ordnal categores n y and the threshold values ( ) are unknown parameters descrbng the boundares of rsk levels. Therefore, the observed dscrete rsk levels are ted to the contnuous latent varable as follows: y = 3 5 f f f f f y < y < y < 3 3 y < y < [ Very Hgh Rsk (VHR)] [ Hgh Rsk (HR)] [ Moderate Rsk (MR)] [ Low Rsk (LR)] [ Safe] (3) where the threshold values,, 3, and are unknown parameters to be estmated. Based on the normalty assumpton of the error term, the probablty of rsk level m for gven X can be predcted as: Pˆr ( y m X ) = F( ˆ βx ˆ ) F( ˆ βˆ X ) ; Pˆr ( = m ) = = m m J m= where F s the cumulatve dstrbuton functon forε. y X () Once the probabltes of each rsk level are predcted from the model estmates, assocated collson rsks can be computed. To do so, rsk scores (RSm) are assgned to each rsk level based on the thresholds, as shown n Fgure. The RSm represents the probablty of collson for rsk level m. Usng the proposed rsk scale as shown n Table, rsk scores for VHR and Safe levels are assgned values of and 0 respectvely. The VHR level refers to vessel nteractons where collson cannot be avoded, whch represents the probablty of collson as. On the other hand where no acton s requred under the Safe level, the probablty of collson s zero. As seen from equaton (3), the Safe level exsts f y. The values may be normalzed to a probablty value wth the range [0,]. (Insert Table here) (Insert Fgure here) The collson rsk for gven c J m= m ( y = m X ) X can then be computed as: P X = RS Pˆ r ; 0 P (5) c.. Model assessment In order to examne the sgnfcance of Xs ncluded n model the z-test s employed and to evaluate f the model have suffcent explanatory and predctve power several goodness-of-ft (gof) measures found n Long and Freese (006) are used. The lkelhood rato statstcs, G = ( LL( β ) LL(0)), s used to examne the overall gof of the model by testng the global
null hypothess that all coeffcents except the ntercept are zero, where LL (β ) and LL (0) are the log-lkelhoods of the ftted model and the null model respectvely. The McKelvey and Zavona s R, M & Z R = Var ( y ) /( Var( y ) + Var( ε )), s also used to measure the predctve power of the model...3 Modelng consderatons The rsk of collson n any vessel nteracton may vary wth the sze of vessels nvolved. Perez and Clemente (007) have shown that maneuverablty and ease n speed adjustments dmnshes as vessel sze ncreases and for ths reason, vessels of dfferent szes would produce dfferent levels of rsk n an nteracton. Consequently, the perceved rsks by the plots may also vary. In order to consder the effects of vessel szes n the study of perceved rsks, vessels may be clustered nto four vessel classes (VC) accordng to the vessel gross tonnage (GT). The classfcaton based on the Sngapore port regulatons s used n ths study (see Table ). (Insert TABLE here) As the perceved rsk s nfluenced by the plot s experence n a partcular vessel class, both experence and VC need to be consdered together n the percepton survey. In general, plots wth more experence are authorzed to operate VC wth hgher GT, a postve assocaton between experence and VC wll exst. Hence, modelng perceved rsks separately for each VC s necessary. Furthermore, navgaton s affected by the envronment, and n partcular, n day and nght settngs. Therefore, perceved rsks would also be dfferent for day and nght condtons. Hence, perceved rsks need to be modeled separately for day and nght condtons.. Development of safety margns The ordered probt model dstngushes dfferent rsk levels by generatng a set of thresholds, whch represent the boundares of the rsk levels on the latent varable scale, as shown n equaton (3). Snce the values of are on the scale of y, the structural model (equaton ) can be modfed as: ˆ ˆ β DCPA + ˆ β TCPA ; for m = to J- (6) m = where ˆ m, ˆβ and ˆβ are known parameters from regresson estmates. Therefore, for each rsk level two boundary ponts on DCPA and TCPA scale,.e., ( DCPA TCPA= 0 ) and ( TCPA DCPA= 0 ) respectvely, can be obtaned by settng TCPA = 0 and DCPA = 0 respectvely n equaton (6). DCPA TCPA= 0 s the dstance safety margn (DSM) that plots accept for the respectve rsk levels. For a gven rsk level, ths would be the maxmum passng dstance between two shps that the plots would allow. TCPA DCPA= 0 s the tme safety margn (TSM) whch represents the margnal tme remanng before a collson. To examne the adequacy of the perceved safety margns n navgaton, the margns can be compared aganst some exstng standards. The margns are examned at two levels n a collson process; frstly, at the level requrng mmedate evasve actons to prevent a 5
collson and secondly, at shp doman level where plots start to perceve that a collson rsk exsts. The standards used for comparson are those related to shp maneuverablty (IMO, 00) and shp doman (Fuj and Tanaka, 97)... Safety margns at mmedate evasve acton level The margns are compared aganst the IMO standards for shp maneuverablty (IMO, 00). The standards are used to evaluate maneuverng performance of shps n desgn, constructon, repar and operaton of vessels. Accordng to the standards, a vessel s ntal turnng ablty (ITA) s measured by a 0 /0 zgzag test. The executon of the test ncludes applcaton of a 0 rudder angle to an ntally straght approach, whch s termed as frst execute. When the headng changes to 0 off the orgnal headng, another 0 rudder angle s appled n the drecton opposte to prevous rudder angle applcaton, whch s termed as second execute (SE). The standard of ITA s that a vessel should not travel more than.5 tmes of her length by the tme of SE applcaton from the orgnal headng. The ITA standard can be employed to examne f the perceved safety margns at HR level are adequate enough for safe navgaton. As seen from Table, the HR level refers to vessel nteractons where mmedate actons are necessary to avod a potental collson. It means that f any actons are not taken mmedately (.e., TCPA = 0) the rsk level wll rse to the VHR level, whch refers to nteractons resultng n certan collson. Safety margns hgher than the ITA standard mply that a plot s ahead of the vessel (Bowdtch, 976),.e., there s a suffcent safety margn to avod a collson. Snce the ITA standard ncludes the term, shp length, n ts consderaton, t s necessary to obtan representatve lengths of all VCs. From observatons of the vessels GT and lengthoverall (LOA), the summary statstcs of the LOAs of the VCs are presented n Table 3. The 50 th percentles are used as representatves of the LOAs of VCs, because n the survey the plots were asked to rate ther perceved collson rsk for an average vessel sze that they operate frequently. (Insert Table 3 here) Although the ITA standard sets a requrement of maneuverablty n terms of space, t does not set any drect requrement n terms of tme. Therefore, a surrogate measure of maneuverablty n terms of tme requrement s derved. Ths s computed based on the lmtng dstance separaton when the vessel s operatng at the maxmum regulated speed In ths study, the maxmum speed of navgaton adopted s knots accordng to the Sngapore port regulatons (MPA, 006). Ths results n the surrogate measure, tme to second execute (TSE), whch s the tme to reach the SE n a 0 /0 zgzag test at a speed of knots... Safety margns at shp doman level The perceved safety margns at LR level can be compared aganst the standard of shp doman (Fuj and Tanaka, 97) n order to examne the adequacy of the margns. The shp doman s the surroundng effectve waters around a vessel that a plot requres to keep clear of other vessels. Accordng to ths standard, a plot s requred to mantan a dstance of at least tmes the shp length, from the center of hs vessel to that of other vessels. If a vessel penetrates the crcular doman crcumference, plots are requred to montor the vessel movement contnuously to assess collson rsk. Usng ths concept, ths wll concde wth the transton from the Safe level to LR level n the proposed rsk scale. The standards for DSM 6
and TSM at LR level would be the doman radus (DR) and the tme to doman crcumference (TDC) respectvely..3 Rsk percepton survey To llustrate the method developed, perceptons of collson rsks under dfferent vessel nteracton stuatons need to be obtaned from the plots. Perceved rsk data can be collected by employng two expermental methods: smulaton or survey. The former s an exercse whch can be carred out usng shp-handlng smulators, where plots are asked to navgate vessels n a specfed navgatonal envronment and to judge collson rsks at varous stages of the navgaton. The dffculty n a smulaton exercse s the amount of resources needed for a suffcently large number of plots to ensure a sound statstcal analyss. On the other hand, the survey method nvolves conductng questonnares among plots by generatng a sutable platform for them to judge collson rsk. In ths case, DCPA and TCPA values would be used to defne the navgatonal condtons, and plots would specfy the level of ther perceved rsk under varous condtons of DCPA and TCPA. The survey method allows a hgh amount of respondents to be obtaned easly for a proper statstcal analyss. The survey method s employed n ths study..3. Survey desgn To collect perceved rsk data, t s necessary to develop a two-way rsk matrx, defned by dfferent values of DCPA and TCPA. The approprate values of DCPA and TCPA used n classfyng the dfferent navgatonal stuaton were determned based on the expert nput of several experenced plots n a prelmnary survey. Based on the outcome of the prelmnary survey, a 5x5 rsk matrx s formulated, representng 5 threshold values of TCPA (,3,5,0,0) mnutes and 5 values of DCPA (,,5,7,0) cables length. Plots are asked to ndcate ther level of perceved rsk of collson n terms of Safe, Low Rsk, Moderate Rsk, Hgh Rsk and Very Hgh Rsk, for each of the 5 combnatons of DCPA and TCPA. The perceved rsk were assessed separately for the day and nght condtons..3. Data collecton A total of 60 plots were gven the survey forms. Partcpaton was voluntary and the response s anonymous. A total of 70 respondents completed the survey gvng a return rate of %. The age of the respondents ranges from 8 to 6 years wth a mean and standard devaton of 3.0 years and 9.8 years respectvely. The experence of the respondents as harbor plot exhbts a mean and standard devaton of.3 years and 0.9 years respectvely, rangng from 3 months to 0 years. The wde range of age and experence n the sample gave qute a good representatve pcture of the populaton. 3. Results and dscusson 3. Estmaton results of the ordered probt model The ordered probt models were calbrated usng the maxmum lkelhood method for each of the vessel class and separately for day and nght condtons. Table shows the estmated parameters and goodness-of ft statstcs of all models. The lkelhood rato statstcs of all models (e.g., 3. and 87.8 for VC-Day and VC-Nght models respectvely) are well above the crtcal value for sgnfcance at % level of sgnfcance, whch mples that the cable length = 0. nautcal mle 7
models have reasonable good ft. The McKelvey and Zavona s R values (e.g., 0.58 and 0.7 for VC-Day and VC-Nght models respectvely) also ndcate suffcent predctve power for all models. Both DCPA and TCPA show sgnfcant postve assocaton wth the latent varable n all models (e.g., for VC-Day model: β DCPA = 0.7, p < 0.00; β TCPA = 0., p < 0.00). Ths ndcates that collson rsk decreases f DCPA and TCPA ncrease (see equaton 3). The method for estmatng collson rsk from the regresson estmates s llustrated for DCPA = cable length and TCPA = mnutes, as shown n Table 5. A comparson of the rsks wth the scores of the rsk levels (presented n Table 6) of all models shows that the rsks fall n the HR range (e.g., for VC-Day model: rsk = 0.86 < RSHR = 0.9), whch s expected for such small values of DCPA and TCPA. Rsks n nght condtons are also found to be hgher than those n the day, e.g., the rsk n nght ncreases by.3% for VC. The trends observed n perceptons of the plots are dscussed n the followng secton. (Insert TABLE 5 here) (Insert TABLE 6 here) 3. Dstance and tme safety margns 3.. Safety margns at mmedate evasve acton level Ratos of safety margns to the maneuverablty standards are employed to examne adequacy of the margns. Ratos greater than or equal to unty ndcate that the margns are adequate. The hgher the ratos are from unty, the hgher the safety buffers beyond the standards. The computed ratos (presented n Table 7) show that the margns are adequate (.e., greater than one) for all vessel classes n both day and nght condtons. (Insert Table 7 here) A comparson of the results wth the ratos of DSM to ITA standard shows that plots of VC hold hghest ratos (3.6 and 5. n day and nght respectvely). It means that ths plot group mantans hgher space buffer beyond the standard, compared to other plots. For all plots, the ratos n nght condtons are found to be hgher than those n the day. Among all, the hghest ncrement n the ratos n nght from those n the day (equals.8) s observed for the plots of VC. It means that these plots mantan hgher safety margns n nght, thus are more careful than the other plots n nght condtons. Smlar results are found n comparng the results wth the ratos of TSM to TSE. Plots of VC attrbute hghest ratos n both day and nght navgaton (6. and 6.3 respectvely). Among all, ths plot group s found to be nfluenced mostly by a change from day to nght condton, so that the rato n nght ncreases by 9.9. Interestngly, t s noted that the ratos of TSM to TSE are hgher than those of DSM to ITA standard for all plots. It ndcates that plots are keen to mantan hgher safety margns n tme than n space. 3.. Safety margns at shp doman level Ratos of DSM to DR and TSM to TDC (shown n Table 8) are also found greater than unty for all vessel classes, whch mply that the margns are adequate. The fndngs at shp doman level are smlar to those n the mmedate evasve acton level. 8
(Insert Table 8 here) A comparson of results wth the ratos of DSM to DR show that plots of VC hold the hghest ratos n both day and nght condtons and the hghest ncrement n ratos from day to nght. Ths plot group mantans DSM of 6.8 tmes the DR n day condton, whereas n nght t ncreases to 7.9 tmes the DR. Whle all plots mantan hgher margns n nght condtons, the hghest ncrement n ths (equals.) s observed for the plots of VC. The ratos of TSM to TDC also show that the plots of VC mantan the hghest safety buffers (ratos of 30.9 and 38. n day and nght condtons respectvely) and are most senstve to a change from day to nght condton (the rato n nght ncreases by 7.3). The other plots are also found to mantan hgher margns n nght condtons. 3..3 Dscusson on results Analyses of the safety margns have dentfed several fndngs. Frstly, the margns n nght condtons are hgher than those n the day. Ths fndng s consstent wth that n Debnath and Chn (009) who reported that plots perceve hgher collson rsks at nght,.e., hgher margns are necessary to mtgate the rsks. Mantanng hgher margns at nght s logcal because durng the day the speeds and dstances between vessels and even any change of courses can be judged readly because of better vsblty. At nght plots need to rely on navgatonal ads (e.g., radar, navgatonal lghts etc.). Ths may mply that n assessng rsks, plots place a hgher value on ther own vsual judgment than on nstruments. Furthermore, effectveness of navgatonal lghts can be reduced n nght due to brght background lghts on shore and from nearby slands (see Akten, 00; Lu, C. et al., 006). Naturally vsblty deterorates at nght whch could further hnder the watchkeepng process leadng to possble confuson n navgaton. Secondly, there s a clear trend of percevng hgher tme safety margns than the dstance margns. Ths could be because the plots are more able to perceve rsk based on the vsual mage of a vessel and hence the dstance between vessels. Snce the plots are less senstve to tme change when vessels are n relatve moton, they wll become more careful and hence provde a hgher safety margn. Fnally, plots of low GT vessels (.e., VC) mantan hgher safety buffers and are more senstve to a change from day to nght condtons than the plots of larger vessels. The plots of VC are generally less experenced wth less knowledge of the port water characterstcs and traffc envronment. Lutzhoft and Nyce (006) have argued that new plots prepare a database n memory by combnng statc nformaton from course books and navgatonal experences, and use the database for future navgaton. Therefore, these less experenced plots reman n a learnng stage and are more conservatve n rsk percepton. Also such plots may requre more reacton tme to decde and take evasve actons n a close encounter.. Proposed framework of probablstc rsk assessment n CAS The foregong shows that the proposed models have reasonable predctve power and that the perceved safety margns are adequate. Ths mples that the regresson estmates can be used effectvely to develop a CAS. A framework of rsk assessment n CAS that utlzes the estmates to predct collson rsk s now proposed. A block dagram showng confguratons of the CAS s presented n Fgure. 9
(Insert Fgure here) The CAS requres the courses and speeds of own vessel and target vessels as nput nformaton and these can be obtaned from on-board radar, global postonng system (GPS) and automatc dentfcaton system (AIS) of own vessel. By utlzng the nput data, DCPA and TCPA are calculated to assess the rsk of collson n vessel nteractons. Interactons wth non-negatve TCPA values mply there s a rsk of collson. For such nteractons, t s necessary to predct and assess the rsk and ths s accomplshed by employng the probablstc model developed n ths paper. Takng n consderaton the vessel classes and navgaton tme (.e., day or nght), the model predcts the level of collson rsk based on the values of DCPA and TCPA. From the level of rsk present, the assocated alarm to alert the plots can be ncorporated. By assessng the collson rsk wth all nteractng vessels wthn the of detecton range of the radar of own vessel, t s possble to rank the nteractng vessels n descendng order of collson rsk and the assocated level of alarm. Wth contnuous trackng of other vessels, a real-tme system wth mult-level alarm alerts can be developed that wll enable plots to make approprate correctve actons, prortzed accordng to the level of rsk nvolved. Ths s partcularly mportant when there are more than one nearby vessels that contrbute to the exstng rsk n navgaton. Plots wll be able to better manage the rsk n a more systematc manner under such complex navgatonal envronment. Even under less complex envronment where nteracton s only wth one nearby vessel, the mult-ter system allows earler warnng wth less serous evasve acton compared to the two-state system. Ths should alert plots who have temporarly lost stuatonal awareness and help them to avod enterng unknowngly nto a close encounter stuaton. Furthermore, the mult-level system wll allow plots wth dfferent experence and capablty to better adapt ther own judgment and courses of acton to match the dfferent levels of danger and alert produced by the system. Ths adaptaton arsng from the dfferent perceved nterpretaton of danger and customzed level of acton s partcularly mportant for the system to gan greater credblty. 5. Concluson An ordered probt regresson model was derved for probablstc modelng of perceved collson rsk n port water navgaton. To llustrate the method, perceved rsks were obtaned from a rsk percepton survey on Sngapore port plots and are used to calbrate the models for dfferent vessel classes under both day and nght condtons. Estmaton results show all the calbrated modules have reasonable goodness-of ft and predctve powers. Perceved dstance and tme safety margns were analyzed to examne ther adequacy wth standards of shp maneuverablty and shp doman. Results ndcate that the judgment of the plots s reasonably reflectve of the varous safety margns. Several nterestng fndngs were derved from the analyses. Frstly, plots gve a larger safety margns at nght than n the day. Secondly, plots tend to gve a hgher allowance of safety for tme separaton and ths s largely because they judge tme separaton less precsely. Fnally, plots of low GT vessels, representng the less experenced ones, mantan hgher safety buffers and are more careful than ther more experenced counterparts n nght condtons. 0
A framework to develop a collson avodance system based on probablstc rsk assessment usng the regresson estmates to predct collson rsk s proposed. It s possble to ntroduce an nteracton component wth mult-level alarm system to alerts plots of the dfferent levels of navgatonal rsk. There are several mportant benefts of a mult-level system. It wll help plots to make an earler evasve acton. In more complex stuatons nvolvng more than one nteractng vessel, a more systematc and prortzed plan of acton can be produced. Fnally a more customzed and adaptable system s possble based on the ndvdual plot experence and capablty. Whle Sngapore port plots have been surveyed to develop the model n ths paper, the modelng technque should be generally applcable. Ths research provdes valuable nsghts nto modelng percepton of collson rsk of plots n navgaton. The use of a probablstc model to predct rsks perceved by plots s unque and robust. The developed models can be readly appled n developng a mult-level alert collson avodance system. Acknowledgements The authors would lke to thank Mr. Wllam Seow, Mr. Er Chor Meng and Mr. Tan Teck Kheng of PSA Marne (Pte) Ltd Sngapore for ther nvaluable help n conductng ths survey. Specal thanks also go to all the harbor plots of PSA Marne (Pte) Ltd who partcpated n ths survey. References Akten, N., 00. Analyss of shppng casualtes n the Bosphorus. Journal of Navgaton 57, 35-356. Bowdtch, N., 976. Bowdtch for Yachtsmen: Plotng. Davd McKay Company, Inc., NY. Darbra, R.M., Casal, J., 00. Hstorcal analyss of accdents n seaports. Safety Scence, 85-98. Debnath, A.K., Chn, H.C., 009. Herarchcal modelng of perceved collson rsks n port farways. Transportaton Research Record, n press. Fuj, Y., Tanaka, K., 97. Traffc capacty. Journal of Navgaton, 53-55. Grech, M., Horberry, T., Smth, A., 00. Human error n martme operatons: Analyses of accdent reports usng the lexmancer tool. In: Proceedngs of the th Annual Meetng of the Human Factors and Ergonomcs Socety, September 30-October, Baltmore, U.S. Hetherngton, C., Fln, R., Mearns, K., 006. Safety n shppng: The human element. Journal of Safety Research 37, 0-. IMO, 00. Standards for shp maneuverablty. Resoluton MSC.37(76), Annex 6, Internatonal Martme Organzaton. Lenart, A.S., 983. Collson threat parameters for a new radar dsplay and plot technque. Journal of Navgaton 36, 0-0. Lu, Q., Pedersen, E., Okazak, T., Fukuto, J., Tanaka, K. 006. Drect percepton nterface for shp-shp collson avodance. In: Proceedngs of the 006 IEEE nternatonal conference on systems, man and cybernetcs, October 8-, Tape, Tawan. Lu, C.-P., Lang, G-S., Su, Y., Chu, C-W., 006. Navgaton safety analyss n Tawanese ports. Journal of Navgaton 59, 0-. Long, J.S., Freese, J., 006. Regresson models for categorcal dependent varables usng Stata. Second Edton, Stata Press, Texas, USA.
Lutzhoft, M.H., Nyce, J.M., 006. Plotng by heart and by chart. Journal of Navgaton 59, -37. MPA, 006. Sngapore port nformaton. The 006/007 edton, Martme and Port Authorty of Sngapore. Pedersen, E., Ara, Y., Sato, N., 999. On the effect of plottng performance by the errors of pontng targets n the ARPA system. Journal of Navgaton 5, 9-5. Pedersen, E., Inoue, K., Tsugane, M., 00a. Evaluaton of a radar plot and dsplay technque for ant-collson assessment of multple targets n true vector presentaton by applcaton of a envronmental stress model. Journal of Japan Insttute of Navgaton 06, -. Pedersen, E., Inoue, K., Tsugane, M., 00b. On decson makng n connecton wth optmal ant-collson maneuvers by hgh speed craft n waters congested by conventonal speed vessels. Journal of Japan Insttute of Navgaton 07, 77-83. Pedersen, E., Inoue, K., Tsugane, M., 003. Smulator studes on a collson avodance dsplay that facltates effcent and precse assessment of evasve maneuvers n congested waterways. Journal of Navgaton 56, -7. Pedersen, E., Jacobsen, A., 00. On a radar plot and dsplay technque for judgng antcollson manoeuvers from the vewpont of acqured targets. Sngapore Martme and Port Journal 00, 67-73. Perez, F.L., Clemente, J.A., 007. The nfluence of some shp parameters on manoeuvrablty studed at the desgn stage. Ocean Engneerng 3(3-), 58-55. Rothblum, A.R., 000. Human error and martme safety. Paper presented at the Natonal Safety Councl Congress and Expo, October 3-0, Orlando, FL. Sato, Y., Ish, H., 998. Study of a collson-avodance system for shps. Control Engneerng Practce 6, -9. Statheros, T., Howells, G., McDonald-Maer, K., 008. Autonomous shp collson avodance navgaton concepts, technologes and technques. Journal of Navgaton 6, 9-. Wagenaar, W.A., Groeneweg, J., 987. Accdents at sea: Multple causes and mpossble consequences. Internatonal Journal of Man-Machne Studes 7, 587-598. Yp, T.L., 007. Port traffc rsks A study of accdents n Hong Kong waters. Transportaton Research Part E, do: 0.06/j.tre.006.09.00.
Table Navgatonal collson rsk scale Rsk level Safe Low Moderate Hgh Very hgh Level of actons necessary to avod collson No actons necessary Keep safe navgatonal watch Take precautonary actons, communcate wth other shp Immedate actons needed Collson mmnent, cannot be avoded Table Vessel categores accordng to gross tonnage Vessel class Descrpton VC If 300 GT 000 VC If 000 < GT 0000 VC 3 If 0000 < GT 75000 VC If GT > 75000 Table 3 Summary statstcs of vessel lengths n meters Vessel class No of Observatons Medan Mn Max VC 383 8 6 6 VC 6 68 0 97 VC3 37 09 6 305 VC 3 3.5 50 35 3
Table Ordered probt estmates for perceved collson rsk Ordered probt regresson models VC VC VC 3 VC Day Nght Day Nght Day Nght Day Nght Regresson estmates of covarates DCPA (cables length) Coef. 0.660 0.79 0.56 0.650 0.6 0.70 0.3 0.088 Std. Err. 0.0 0.00 0.087 0.053 0.08 0.08 0.03 0.07 Z-stat.0* 0.77*.5*.* 0.65* 0.93* 9.8* 7.85* TCPA (mnutes) Coef. 0.68 0.090 0.378 0.637 0.5 0.8 0.03 0.089 Std. Err. 0.008 0.0096 0.088 0.030 0.09 0.07 0.0058 0.0056 Z-stat 0.80* 9.35*.39*.8* 9.70* 0.07* 7.* 6.0* Thresholds ˆ 0.76 0.37 0.7505.30 0.3 0.5363 0.373 0.57 Std. Err. 0.89 0.0 0.578 0.36 0.67 0.659 0.0833 0.0808 ˆ.068.96.53 3.393.53.86.35.59 Std. Err. 0.50 0.86 0.73 0.3088 0.805 0.857 0.089 0.0898 3 ˆ 3.088.997.6098 5.9758.358.7565.36.59 Std. Err. 0.738 0.67 0.03 0.776 0.039 0.7 0.09 0.07 ˆ 3.59 3.0 6.938 8.5806 3.08 3.937 3.3680 3.375 Std. Err. 0.058 0.9 0.5655 0.676 0.390 0.60 0.00 0.5 Summary statstcs # of Obs 35 35 5 5 50 50 950 950 LL (0) -500.5-58. -33.0-33.3-395.0-395.0-50.9-505.6 LL (β ) -378.8 -.5-53.9-50.7-300.0-9. -93.9 -.7 G ( dof) 3. 87.8 360. 385.0 90. 0. 63.0 55.7 M&Z R 0.583 0.7 0.89 0.887 0.578 0.59 0.57 0.56 * sgnfcant at 99% sgnfcance level; LL (0) : log-lkelhood at zero; LL (β ) : log-lkelhood at convergence; G : lkelhood rato statstcs; M&Z R : McKelvey and Zavona s R. Table 5 Estmated rsk level probabltes and collson rsks (at DCPA = cable length, TCPA = mnutes) Day Tme Nght Tme Predcted probablty from model estmates Collson Predcted probablty from model estmates Collson VHR HR MR LR SAFE rsk VHR HR MR LR SAFE rsk VC 0.099 0.98 0.383 0.098 0.000 0.858 0.76 0.333 0.98 0.0507 0.005 0.869 VC 0.305 0.5857 0.0935 0.0003 0.0000 0.90 0.595 0.37 0.033 0.0000 0.0000 0.98 VC3 0.33 0.6 0.59 0.096 0.006 0.887 0.56 0.395 0.0836 0.00 0.0003 0.900 VC 0.7 0.363 0.379 0.069 0.007 0.88 0.533 0.38 0.070 0.09 0.00 0.90 Vessel class
Table 6 Rsk scores for rsk levels Vessel Day Nght class RS HR RS MR RS LR RS HR RS MR RS LR VC 0.938 0.6679 0.3309 0.89 0.570 0.3376 VC 0.898 0.636 0.3353 0.883 0.60 0.3036 VC3 0.9066 0.555 0.37 0.860 0.50 0.300 VC 0.889 0.5803 0.3033 0.863 0.599 0.538 Table 7 Safety margns and maneuverablty standards at mmedate acton level Vessel class Rato of DSM to ITA Rato of TSM to TSE Day Nght Increase at nght Day Nght Increase at nght VC 3.60 5.3.83 6.0 6.7 9.87 VC.99.30 0.3 6.8.35.53 VC3.07.37 0.30 9.5 0.88.37 VC.3.67 0.3 6. 7.8.3 Table 8 Safety margns and maneuverablty standards at shp doman level Vessel class Rato of DSM to DR Rato of TSM to TDC Day Nght Increase at nght Day Nght Increase at nght VC 6.77 7.90. 30.86 38.8 7.33 VC 3. 3.6 0.3.66 7.93 6.7 VC3.89 3. 0.3 3.5.79.5 VC.99.3 0. 9.5 0. 0.87 5
Fgure Rsk scores for subjectve rsk levels VHR HR MR LR SAFE 0 3 3 y Rsk Score RS m Fgure Block dagram of collson avodance system Radar, GPS, AIS Obtan course and speed of own vessel Obtan course and speed of target vessel Calculate DCPA, TCPA To next target vessel TCPA 0 NO YES Estmate collson rsk, P c Pc > RS HR NO Pc > RS MR NO Pc > RS LR NO Pc > RS safe YES YES YES YES NO Dsplay DCPA, TCPA, P c Alarm: VHR Alarm: HR Alarm: MR Alarm: LR 6