ISSN 1733-8670
ZESZYTY NAUKOWE NR 11(83)
AKADEMII MORSKIEJ
W SZCZECINIE
IV MIĘDZYNARODOWA KONFERENCJA NAUKOWO-TECHNICZNA E X P L O - S H I P 2 0 0 6
Andrzej Drozd
Ship’s Fuzzy Speed Curve
Key words: ship’s weather routeing, voyage planning, applications of fuzzy set theory
In this paper an example of speed down curve construction for one ship type is pre-sented. The relationship between ship’s speed changes and environmental factors is defined on the basis of observational data. The artificial neural network was used for a regression analysis. Taking into account the fact that input data imprecision can hardly be avoided, which consequently makes the predicted ship speed approximate, the proposed notation of ship speed in given conditions has the form of fuzzy number.
Rozmyta charakterystyka prędkościowa statku
Słowa kluczowe: nawigacja pogodowa, planowanie podróży statku, zastosowania teorii zbiorów rozmytych
W artykule zaprezentowano przykład konstrukcji charakterystyki prędkościowej dla wybranego typu statku. Zależność zmian prędkości statku w funkcji wpływu czynników środowiska zewnętrznego określono na podstawie danych obserwacyjnych, a do celów analizy regresji zastosowano sztuczną sieć neuronową. Biorąc pod uwagę fakt trudnych do uniknięcia w praktyce niedokładności danych wejściowych, co w konsekwencji upo-ważnia do opisu przewidywanej prędkości statku w postaci 'około', zaproponowano do tego celu zapis w postaci liczby rozmytej.
Introduction
The definition of ship’s characteristics is one of the key problems in weath-er-optimum route selection. Among others, the prediction of ship’s speed in given wind and wave conditions is particularly essential. Despite of the fact that numerical models exist, analysis of observational data remains a significant method for solving the problem or model verification [1, 5]. Moreover, some Onboard Routing Systems demand user data input, and in this case observed ship speeds analyses are necessary [9]. This paper is to introduce the method used by this author for the determination of wind and wave parameters influence on the ship’s speed on the basis of ship’s observed positions and archive weath-er/ocean dataset.
1. Research material
1.1. Ships voyages data
This part of the data used comes from voyages of five ships of the same type, owned by the Polish Steamship Company. These bulk-carriers, built in Japan, intended mainly for steel carriage, came into service in the years 1999 – 2000. The speed curve is based on the data from 63 voyages of vessels carrying steel prod-ucts from Ijmuiden to the Great Lakes in the years 1999 – 2004. Although in this case the ships are always partly loaded due to draft limitations for the Seaway locks entrance, their loading conditions may be regarded as similar in all cases. The selection was deliberate to minimize an additional error resulting from differ-ent loading conditions, while ship’s behaviour depends on that. Observed posi-tions were noted at average 4 hours intervals on the basis of Log Books and addi-tional data were collected from Sea Passage Reports and Port Logs, all accessible due to the shipowner courtesy. Vessel particulars and her picture are presented below. Ships voyages data used are presented in Figures 2 and 3.
Vessel particulars: LPP: 199.9 m Beam: 23.60 m
Depth Mid-Ship: 15.3 m (from keel to deck); Design draft: 10.67 m SDWT: 34 939 mt Lakes: 22 982 mt (8.02 m) Main Engine Power: 6370 KW Calm sea speed: 14.5 knots (at design draft)
1.2. Environmental data and their compound with ships voyages data
Due to the fact that environmental factors recorded in ships Log Books (particularly wave parameters) have in general little credibility and usefulness, for the task of constructing the speed curve , archive data wereused. Wind and wave data come from Weathernews Inc. archive dataset and current data comes from Prof. Arthur Mariano, the University of Miami. All data have one degree by Latitude and one degree by Longitude resolution. The relevant North Atlantic Ocean area was taken into account. The compound of environmental and ships voyages data is presented in Table 2.
Fig. 2. Sketch of real 63 voyages of ISA-type ships carried out in years 1999-2004 from Ijmuiden (IJM) to Escoumains (ESC) with cargo of steel products
Rys. 2. Szkic 63 rzeczywiście zrealizowanych podróży statków typu ISA w latach 1999 – 2004 z Ijmuiden (IJM) do Escoumains (ESC) z ładunkiem stali
Iceberg limit
Gulfstream location
Fig. 3. Compilation of example voyage with observed ship’s positions marked, limit of icebergs and Gulfstream location. Numbered positions corresponds with positions and dates marked
in table 2 (LP column)
Rys. 3. Opracowanie przykładowej podróży z zaznaczonymi pozycjami statku, granicą gór lodo-wych i położeniem Golfsztromu. Ponumerowane pozycje statku odpowiadają pozycjom i datom
zaznaczonym w tabeli 2 (kolumna LP)
Table 1 Basic statistics of ISA-type voyages
Podstawowe statystyki podróży statków typu ISA
Minimum Average Maximum Standard deviation Distance [NM]: 2 855.90 3 033.86 3 296.30 119.92 Time [hrs]: 201.00 223.69 266.50 16.88 Average speed [kn]: 11.26 13.61 14.83 0.75 DWT [mt]: 19 227.91 22 795.15 23 467.17 684.41 Draft FWD [m]: 6.55 7.69 7.95 0.23 Draft AFT [m]: 7.25 7.93 8.26 0.14
Table 2 Example of compounded ship’s voyage and environmental factors data
Przykład złożenia danych o stanie środowiska zewnętrznego i danych o podróży statku
Abbreviations used:
YY, MM, DD, UTC – year, month, day and UTC time;
LAT, LON – geographical coordinates (degree.minutes.tenths_
of_minutes);
OQ – observed wind angle [deg], computed on the basis of recorded in
Log Book observed wind direction and ship’s course;
OV – observed wind speed [kn], converted from Beaufort scale
nota-tion;
CR – ship’s course make goodcomputed on the basis of noted ship’s
positions;
VS – ship’s speed computed on the basis of noted ship’s positions and
times. In this case VS represents average speed for a given stretch of time where speed losses result both from natural (environmental) factors as well as voluntary speed reduction to fulfil seakeeping criteria as it is required [7];
cells for RG (ship’s rolling), PT (ship’s pitching), WS (water spray) and GW (green water) are darkened if relevant phenomenon is noted in
LP OQ OV CR VS RG PT WS GW VV VQ PH PQ PP SH SQ SP 01 024 17-21 249 12.0 16 003 01.2 002 06.5 00.5 097 06.8 -0.2 02 003 11-16 222 15.8 07 047 01.0 079 09.1 --- ----03 023 07-10 248 15.7 04 011 00.7 105 02.3 ---- --- ---- +0.5 04 VAR 01-03 251 13.4 01 052 01.0 030 09.5 --- ----05 VAR 01-03 262 14.9 01 079 01.8 009 11.8 --- ----06 104 07-10 261 10.2 15 038 02.9 015 11.3 ---- --- ---- +0.1 07 125 17-21 260 14.2 15 043 03.4 020 10.5 ---- --- ---- -0.4 08 079 22-27 259 13.5 30 058 02.9 011 09.1 00.8 078 06.6 -0.4 09 075 34-47 255 10.2 33 069 02.7 071 04.6 01.5 017 12.2 +0.1 10 013 41-47 260 07.9 37 052 04.6 062 06.4 00.4 035 10.0 -0.2 11 030 41-55 277 04.6 39 069 06.2 039 08.3 00.3 025 06.8 -0.2 12 010 48-55 280 03.7 40 015 07.6 030 09.7 01.0 021 10.8 -0.2 13 049 34-47 221 07.9 31 035 08.0 036 10.8 01.6 034 07.6 -0.3 14 004 41-47 266 07.7 26 009 07.7 000 11.5 01.3 023 07.8 -0.3 15 001 34-40 269 09.5 27 041 07.1 001 11.7 01.2 036 08.0 -0.4 16 052 28-33 277 09.4 34 059 06.4 013 11.3 02.3 054 09.0 -0.3 17 068 34-47 270 07.3 39 051 06.3 047 10.2 02.3 039 11.1 -0.2 18 033 41-47 258 07.5 38 051 06.5 043 09.5 02.1 045 11.5 -0.1 19 039 34-40 264 09.2 27 042 06.4 051 09.6 01.3 016 12.1 ----20 025 28-33 272 10.8 23 050 06.1 048 09.6 01.0 068 14.2 -0.3 21 023 28-40 270 11.4 24 017 05.2 024 09.3 02.5 077 14.8 -0.5 22 038 28-40 254 11.1 25 009 04.2 079 10.7 03.0 088 12.4 -0.1 23 042 34-40 250 11.0 27 014 03.9 062 09.4 02.9 006 12.5 -0.2 24 033 34-40 259 11.6 26 024 04.1 027 06.9 03.0 002 14.3 -0.2 25 010 28-33 257 11.1 25 027 03.8 044 08.4 02.8 000 13.5 -0.3 26 009 28-33 256 11.7 28 037 04.0 007 06.8 01.9 048 15.1 -0.2 27 034 22-33 259 11.3 35 016 04.5 000 06.9 01.2 158 14.2 -0.2 28 038 22-33 263 10.4 38 020 05.5 033 07.7 00.5 100 14.8 +0.2 29 032 34-40 257 08.1 36 010 06.4 032 08.6 00.2 002 13.4 ----30 036 34-47 261 07.8 26 042 06.6 039 09.6 00.8 033 07.4 -0.2 31 004 22-33 266 10.2 23 046 06.6 034 10.2 01.0 024 06.5 ----32 031 28-33 261 10.9 27 055 06.5 004 10.4 01.0 029 06.9 -0.2 33 026 28-33 266 10.5 32 067 06.3 018 10.0 01.0 038 07.2 -0.3 34 050 34-40 265 10.1 33 069 06.0 037 09.5 01.0 047 07.0 -0.4 35 99 045 34-40 270 10.7 30 040 05.6 043 09.0 00.9 045 07.0 -0.5 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 99 +001.13.1 10 28 2230 +50.01.0 -002.36.0 10 28 1900 +50.16.1 -001.27.0 -028.32.6 10 28 0600 +52.08.1 +002.55.0 10 28 1200 +50.57.3 11 02 0500 +47.09.5 +47.30.7 11 11 0500 +48.22.6 -026.21.6 11 11 02 0100 +47.20.9 -027.25.7 11 01 2100 -023.11.4 -022.07.3 01 1700 +47.39.7 -025.14.3 01 0900 +48.10.0 01 -019.54.0 11 01 0100 +48.22.8 -020.58.8 10 31 2100 +48.21.1 -018.00.5 10 31 1600 +48.25.9 -018.44.9 10 31 1200 +48.31.9 -016.19.7 10 31 0800 +48.32.1 -017.16.3 10 31 0400 +48.27.5 -014.36.0 10 31 0000 +48.28.0 -015.22.5 10 30 2000 +48.30.0 -013.42.6 10 30 1600 +48.54.0 -014.04.8 10 30 1200 +48.51.3 30 0800 +48.48.9 -013.14.6 -011.27.4 10 30 0400 +48.54.2 -012.27.4 -006.52.5 10 29 2000 +49.15.1 -010.06.3 +46.26.1 -036.21.6 +46.29.7 11 03 0200 11 03 1400 -030.38.2 -031.24.4 +46.49.0 +46.56.4 02 2200 -032.20.4 +46.32.8 -033.19.7 +46.39.7 +46.42.6 -034.22.3 -035.23.1 11 02 1700 29 0700 10 29 10 1100 10 11 11 03 0600 11 03 1000 UTC MM DD LAT -029.37.9 28 0110 10 LON 99 99 +49.44.2 -005.50.3 0900 +47.01.2 YY +49.37.6 30 0000 +49.04.7 10 11 02 02 1300 11 +52.29.0 +004.23.4 WIND
LP / DATE / HOURS SHIP'S POSITION OBS WIND SPEED- AND SEA-KEEPING PRI WAVE SEC WAVE
a Log Book. While it is assumed that such records indicate worsened but still acceptable seakeeping conditions (no additional speed reduction or course changes actions), these cases are normally taken into account for speed curve creation;
VV – wind speed [kn]; VQ – wind angle [deg];
PH – primary wave height [m]; PP – primary wave period [s]; PQ –
primary wave angle [deg];
SH – secondary wave height [m]; SP – secondary wave period [s]; SQ –
secondary wave angle [deg];
CF – current factor [kn].
1.3. Data qualification and assimilation
As a result of vessel and environmental data collection, 3717 observations were obtained. While ship’s speed depends on independent factors, the neural network was used for the extraction of each parameter influence . Only the pa-rameters of the current, as this factor influence is known, were taken into con-sideration before using the network. Thus the new variable VC (observed speed corrected to current effect, simply ship’s speed through water) was introduced: VC = VS – CF. As the quality of neural network responses depends mainly on the quality of training dataset [6], the collected observations were for various reasons limited as follows:
– due to strong tidal currents influence on ship’s speed in English Channel / North Sea area, observations made eastward of 00730’ W were elimi-nated;
– due to the fact that a simple linear grid interpolation was used, to avoid errors while ship position is close to land (zero-inputs for adjoining cor-ners), observations made westward of 05230’ W were eliminated; – data with other than wind/wave influence speed reductions (drills,
en-gine tests etc.) were eliminated.
Moreover, due to lack of observations with zero-inputs for environmental factors and for proper function approximation, the following data was assimilat-ed (calm sea speassimilat-ed assumassimilat-ed as about 14.5 with 0.5 knot for the term ‘about’):
– for VC = 14.0 to VC = 15.0 with step 0.2 and for VV = 0 to VV = 4 with step 2 and for VQ = 000 to 180 with step 10, other parameters set as zero;
– for VC = 14.0 to VC = 15.0 with step 0.2 and for PH = 0 to PH = 0.5 with step 0.5 and for PQ = 000 to 180 with step 10, other parameters set as zero;
– for VC = 14.0 to VC = 15.0 with step 0.2 and for SH = 0 to SH = 0.5 with step 0.5 and for SQ = 000 to 180 with step 10, other parameters set as zero.
Example cluster graphs for input data (2888 cases in all) are presented be-low. The qualified VC data cases are marked as ″″, assimilated VC as ″ ″.
H i s t o g r a m f o r V C ( a l l c a s e s ) a r e a l s o a d d e d .
Graph 1. VC scatter for VV and VQ Wykres 1. Rozrzut VC dla VV i VQ
Graph 2. VC scatter for PH and PQ Wykres 2. Rozrzut VC dla PH i PQ
Graph 3. VC scatter for PH and PP Wykres 3. Rozrzut VC dla PH i PP
Graph 4. VC histogram Wykres 4. Histogram VC 0 10 20 30 40 50 60 70 V V [kn] 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 V Q [d e g ] 0 1 2 3 4 5 6 7 8 9 10 PH [m] 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 P Q [d e g ] 0 1 2 3 4 5 6 7 8 9 10 PH [m ] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 P P [s ] 3 4 5 6 7 8 9 10 11 12 13 14 15 16 V C [k n] 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 N U M B E R O F V C
2. The research tool description and results
2.1. Data division and network optimization
For the network optimization Statistica Neural Network (SNN) software was used. Before that, all the cases were divided as follows:
– 1444 cases for network training;
– 722 cases for verification set, (which enables checking whether the net-work, estimated on the basis of training set, has the ability to general-ize);
– 722 cases for network tests.
Fig. 4. Statistica Neural Network windows Rys. 4. Okna programu Statistica Neural Network
The chosen network has eight input neurons, which represent respective environmental factors, eight neurons in one hidden layer and one output VC. This multilayer perceptron represents one of the most common network archi-tectures used in regression problems. This particular network was trained with back propagation and conjugate gradient descent algorithms. Correlations ob-tained for each set (training, verification and test), which are all close to 0.9, show a good recognition of the problem by the tool used. For zero-value input parameters the network returns value of calm sea speed 14.7 kn.
Fig. 5. Neural network illustration Rys. 5. Schemat sieci
2.2. Results for the influence of environmental factors on ship’s speed
The following graphs present the influence of consecutive factors on ship’s speed VC. Despite the fact that graphs should not be used for ship prediction due to the fact that while presenting a chosen pair of parameters the rest of the parameters are not zero-value but averaged, the general impact is visible.
Graph 5. Predicted VC for VV and VQ Wykres 5. Predykcja VC w funkcji VV i VQ
Graph 6. Predicted VC for PH and PQ Wykres 6. Predykcja VC w funkcji PH i PQ
3. Fuzziness of the results
Graphs 7 – 10 were constructed for certain speed ranges and the present number of observations for real ship’s speeds for consecutive VC predictions. As it can be seen from the graph, a bigger dispersion of real VC is for a smaller predicted VC. The reason for that seems to be caused by different Captain’s behaviour in heavier wind/wave conditions (different voluntary speed reduc-tions).
3 4 5 6 7 8 9 10 11 12 13 14 15 VC REAL 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 N U M B E R O F O B S E R V A T IO N S 3 4 5 6 7 8 9 10 11 12 13 14 15 VC REAL 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 N U M B E R O F O B S E R V A T IO N S
Graph 7. Number of real ship speeds for VC predicted from range 13.5 – 15.0 kn Wykres 7. Liczba obserwowanych rzeczywistych
prędkości statku dla VC prognozowanej z przedziału 13,5 – 15,0 w
Graph 8. Number of real ship speeds for VC predicted from range 12.5 – 13.5 kn Wykres 8. Liczba obserwowanych rzeczywi-stych prędkości statku dla VC prognozowanej
z przedziału 12,5 – 13,5 w 3 4 5 6 7 8 9 10 11 12 13 14 15 VC REAL 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 N U M B E R O F O B S E R V A T IO N S 3 4 5 6 7 8 9 10 11 12 13 14 15 VC REAL 0 1 2 3 4 5 6 7 8 9 10 11 12 N U M B E R O F O B S E R V A T IO N S
Graph 9. Number of real ship speeds for VC predicted from range 10.5 – 11.5 kn Wykres 9. Liczba obserwowanych rzeczywistych
prędkości statku dla VC prognozowanej z przedziału 10,5 – 11,5 w
Graph 10. Number of real ship speeds for VC predicted from range 09.5 – 10.5 kn Wykres 10. Liczba obserwowanych rzeczywi-stych prędkości statku dla VC prognozowanej
z przedziału 09,5 – 10,5 w
The fuzzy set theory allows us to express the figures in 'about' form. One of the membership functions used is the symmetric Gauss function [4], where the degree of membership in our case can be described as:
2 predicted ) ( a VC VC e VC
where e is the base of the natural logarithm, and a parameter describes the func-tion curve (see graph 11).
Values for a parameter for this example were found to be: – a = 0.50 for VC predicted = 14.5 or higher;
– a = 0.75 for VC predicted = 14.0;
– a = 1.00 for VC predicted = 13.0 and for VC predicted = 12.0; – a = 2.00 for VC predicted = 11.0 or smaller.
Graph 11. General Gauss-type membership function Wykres 11. Funkcja przynależności typu Gaussa
Fig. 6. Aplication for fuzzy ship’s speed prediction Rys. 6. Aplikacja predykcji rozmytej prędkości statku
Conclusion
This paper presents an example of speed down curve construction for one ship type. An artificial neural network, which was found to be a good tool for regression analysis of such type task, returns the predicted ship’s speed in ordi-nary case. While it is reasonable to note predicted ship’s speed in 'about' form, the notation as fuzzy numbers was proposed. The obtained results seem to be
quite firmly 'fuzzy', but in the presented example the imprecision of input infor-mation is hardly avoidable in practice. It seems that uppermost errors come from current information, while this data is seasonal only in nature [2] and from the fact that wind/wave conditions are averaged for noted ship’s positions. What is interesting, 'fuzziness' doesn’t increase while predicted ship’s speed drops below the value of 11 knots.
Literature
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Wpłynęło do redakcji w lutym 2006 r.
Recenzent
dr hab. inż. Michał Holec, prof. AM w Gdyni
Adres Autora
mgr inż. Andrzej Drozd
Akademia Morska w Szczecinie, Instytut Nawigacji Morskiej Wały Chrobrego 1-2, 70-500 Szczecin
