Maritime University of Szczecin
Akademia Morska w Szczecinie
2011, 25(97) pp. 5–12 2011, 25(97) s. 5–12
The process of creating a knowledge base of the Bayesian
model of navigational situation assessment
Proces tworzenia bazy wiedzy bayesowskiego modelu oceny
sytuacji nawigacyjnej
Andrzej Bąk
Maritime University of Szczecin, Faculty of Navigation, Institut of Marine Navigation Akademia Morska w Szczecinie, Wydział Nawigacyjny, Instytut Nawigacji Morskiej 70-500 Szczecin, ul. Wały Chrobrego 1–2, e-mail: a.bak@am.szczecin.pl
Key words: navigation, Bayesian networks, inference Abstract
An attempt is made to build a knowledge data base to be used a basis for a navigational situation assessment system. The system is based on Bayesian networks. A research experiment will be described, in which simulation tests were carried out to define a relevant data base. This article also presents a model for manoeuvre identification and a simulator application created for simulation tests. It has been proved that automatic identification of ships manoeuvres is possible and, so is the navigational situation assessment in view of navigational safety.
Słowa kluczowe: nawigacja, sieci bayesowskie, wnioskowanie Abstrakt
Artykuł przedstawia próbę skonstruowania bazy wiedzy, służącej jako podstawa w systemie oceny sytuacji nawigacyjnej. System został oparty o sieci bayesowskie. Opisano eksperyment badawczy oraz wykonano szereg prób symulacyjnych, umożliwiających zdefiniowanie bazy danych. Przedstawiony został również model identyfikacji manewru oraz aplikacja symulatora powstała na potrzeby badań symulacyjnych. Wykazano, iż możliwa jest automatyczna identyfikacja manewrów wykonywanych przez statki, a co za tym idzie, ocena sytuacji nawigacyjnej pod kątem bezpieczeństwa żeglugi.
Introduction
Conducting a ship to its destination involves the use of position determination methods and continuous identification of a navigational situation. The navigator has to make numerous decisions taking into account changes in the ship-environment system. Decisions made by the navigator directly affect the safety of the ship, its crew and cargo. In the process of decision making the navigator makes use of information delivered by navigational devices, their knowledge and experience. Besides, they use various facilities of navigational assistance, such as VTS and reporting systems, and the entire infrastructure consisting of sea and land-based aids to navigation. Combining
all the available data, the navigator identifies and assesses a current navigational situation.
However, as research conducted by many authors shows, the human factor still remains a very frequent cause of marine accidents. This is also confirmed by the results of analysis of data from the Accident Register of Insurance and Accidents Department at the Polish Steamship Company for three periods of this shipowner’s operations: 1960– 1969 [1, 2], 1970–1978 [3] and 1980–1989 [4], where it becomes clear that the human error is the dominating cause of navigational accidents. In the years 1960–1969 ship’s personnel were responsible for 55.9% of all accidents of PSC ships, and respectively, for 56.8% and 68.7% in 1970–1978 and 1980–1989. The Dutch Shipping Council
reports that in 1982–1985 the human factor caused 345 accidents of the total 2250. At the same time it was found that in 96% of cases accidents could have been avoided if the participants had behaved appropriately [5]. Besides, 60% of the accidents caused by the humans occurred because the navigators conducting the ships concerned made false assumptions or exercised wrong habits. Research done by Kostilainen and Hyvaringa [6], resulting in statistics concerning the areas of accident occurrence, showed that about 70% took place in restricted areas, including 40% recorded in ports and approach channels. Only 16% of accidents happened in the open sea.
The above considerations lead to obvious conclusions that new solutions are needed to reduce the number of marine accidents. Most accidents are due to incorrect assessment of a navigational situation. Therefore, the natural trend is towards the construction of systems that will automatically identify and classify a navigational situation. Such systems, with their advisory function, gather, process and synthesize all available information. Often built as expert systems, they are able to generalize knowledge, which makes them useful in many situations that were not predicted in the process of learning. These systems utilize artificial intelligence (AI) tools, as these are capable of interpreting linguistic information, as well as ambiguous, incomplete, inconsistent or inaccurate data etc. The development of AI methods noted in recent years is strictly connected with now easy access to powerful computers. Systems using artificial intelligence tools prove perfect in situations of exccess information. The navigator, exposed to too much data, may sometimes wrongly assess a navigational situation as the essential information may be neglected. The final effect will be the same as in the case of insufficient data the navigator may have to assess a navigational situation and lead to an emergency situation. AI systems process available information, classify it into important and unimportant, and the outcome the nawigator obtains is an identification of the present navigational situation. It should be noted that the assessment is done on the basis of experts’ knowledge that has been implemented into these systems. AI systems find particular applications in areas where navigation is difficult, such as restricted areas. In marine traffic engineering restricted water areas are divided as follows [7]: 1) area restricted in the vertical plane,
2) area restricted in the horizontal plane.
There exists a certain probability of occurrence of an accident that may be of various type:
hull damage due to ship-shore contact,
grounding after the ship deviates from a deep-water route,
damage to a marine structure or aids to navi-gation,
collision with another ship after leaving the designated traffic lane.
Using expert services in restricted areas is highly recommended. It is impossible to carry a group of experts on board, but it is possible to use AI systems for navigational situation assessment, which may significantly enhance the navigation safety level in such areas. The most frequently used AI tools are:
expert systems,
artificial neural networks, fuzzy systems,
genetic algorithms.
Their implementation requires the use of adequate methods of aquistition, extraction and representation of navigator expert knowledge, applicable to navigational situation assessment. This article presents the method for creating and defining parameters of the Bayesian network used for the assessment of a navigational situation. Besides, it describes the process of defining the Bayesian network structure and the method of its learning based on the data gathered from simulation tests. Built by this author, a ship movement simulator is presented along with the method used in the tests.
The model for the determination of the probability that a given navigational situation will occur is based on Bayesian networks. The construction of this model consisted in:
formulating assumptions to be satisfied,
building a knowledge base reflecting the ship status (manoeuvres it is performing at a given moment),
developing the model structure, defining the Bayesian network.
Simulation research was done in two stages. The first stage included the identification of the relation between ship manoeuvres and its move-ment parameter changes. In the second stage the probability of collision of two ships during a passing manoeuvre performed in three different fairway configurations.
Assumptions for the construction of a shipboard system of navigational situation assessment in restricted areas System description
The system for the assessment of a navigational situation in restricted waters, involving two ships, should include a number of functional modules, the most important of them being as follows (Fig. 1): communication module; it gathers information
on the status of the ship and the environment, decision-inference module, which assesses a
na-vigational situation, konwledge base module, display module.
The system should gather available updated information on ship movement parameters, environmental data and actions taken by the ship navigator. Then, from these data and the knowledge gathered in the knowledge base the navigator should conclude whether the present situation is safe or dangerous by determining the probability of collision.
Fig. 1. A diagram of a ship’s navigational situation assessment system
Rys. 1. Schemat systemu oceny sytuacji nawigacyjnej statku
The dual division into safe and dangerous situations is not sufficient, as it is difficult to categorize each situation as definitely safe or dangerous. In this study a navigational situation will be evaluated by the system using 0 to 1 range, as is the case in [8]. The value 0 corresponds to a safe situation, where there is no danger of collision with another ship, while 1 stands for a dangerous situation, where a collision is imminent.
The knowledge base contains navigational situations descriptions, ship movement parameters, environmental parameters and actions taken by the navigator. Although it is obviously impossible to implement a complete set of detailed situations, the base should comprise as many of them as possible, because this directly translates into the reliability of situation assessment.
Preliminary tests indicated that the number of navigational situation descriptions in the knowledge base may initially be a two-digit figure (20–30), which for the inference algorithm based on Bayesian networks, that are capable of generalization and approximation, is quite satisfactory. As new observations appear, the knowledge base can be currently updated thanks to another property of Bayesian networks, i.e. learning ability.
Knowledge base
The knowledge database features data (facts) referring to the ship, its manoeuvring capabilities, method of steering and interrelations between ship movement parameters and the occurrence of a given navigational situation. The knowledge base content allows, by means of a Bayesian network, to determine the probability of occurrence of navigational situations defined in it. The base was created from simulation tests that resulted in unequivocal determination of the moment when a specific navigational situation occurs, on the basis of ship movement data. The external method of knowledge base recording enables a simple adjustment of the situation assessment system to be used on board other ships that have different manoeuvring characteristics. The construction and contents of the knowledge base determine the number of situations that can be recognized in the process of identification. The knowledge base contains:
names of recognized situations,
list of ship movement parameters corresponding to a given situation.
The following ship movement parameters were recorded:
true course,
course over ground, advance speed, transverse speed, rate of turn,
manoeuvre performed.
From the recorded ship movement parameters, where the sampling time being one second, additional quantities were computed:
change in true course,
change in course over ground, change in advance speed, change in transverse speed, change in rate of turn.
Decision inference module Input module Module of user interface present situation sen so rs Knowledge base module
The inference module of manoeuvre identification This module is tasked to analyze data inflowing from the input module, compare them with information contained in the database, and on this basis to identify the type of manoeuvre that is performed by own and target ships. Additionally, the module allows to define probability values of situation assessement, which enables filtering the obtained results to enhance the reliability of the assessment. The module itself consists of adequa-tely constructed and defined Bayesian network (Fig. 2) allowing to, on the basis of current data, assess the probability of each distinguished events. The network output only presents a situation that is most likely to happen at a given moment.
Fig. 2. Decision-inference module Rys. 2. Moduł decyzyjno-wnioskujący
Manoeuvre identification module
Construction of the ship status knowledge base The construction of the knowledge base relied on the results of simulation tests that aimed at the identification of relations between phenomena taking place in the process of navigation. These interrelations referred to movement parameters of ships and manoeuvres performed by those ships. It is necessary to define the relations between specific nodes of the network, because the future model of ship’s collision situation is to work using Bayesian networks. These relations are of cause-and-effect character, therefore all possible situations and their posssible development in time should be known. Due to the complex nature of the problem and practically indefinite number of situations that may occur, the task seems apparently impossible to solve. However, if we use the ability of Bayesian networks to generalize knowledge, it is sufficient to perform simulation tests of characteristic, most
common situations, and the remaining situations will be extrapolated from the data existing in the knowledge base. The BayesiaLab application was used for the construction of the base, featuring algorithms for network learning based on data provided. The application enables determining the relations between network nodes based on real data and those generated during simulation tests.
Construction of the simulation model
Simulation tests were carried out with the use of ship movement simulator (Fig. 3). The simulation program was created within a larger project aimed at the development of Pilot Navigation System (project No 6T12 2003C/06136) implemented by a research team of the Institute of Marine Traffic Engineering, Maritime University of Szczecin. This writer participated in the project as its co-author and creator of the major part of the application code of the pilot system. The module architecture of the application facilitates changes in the program and its adjustment to current needs of the researcher. The changes introduced by this author, as compared to the original PNS code, refer to the possibility of inclusion and use of a mathematical model of ship movement, as well as the implementation of the control of two ships proceeding within the same area. The module architecture of the application allows to build a ship movement simulator operating in a computer network and enables controlling one ship from a separate console. Another modification consisted in implementing the procedure identifying and indicating potential points of collision on the waterplanes of both ships for present ship movement parameters. It was necessary due to subsequent determination of impact energy that depends, inter alia, on the mutual location of the two ships at the moment of collision.
The mathematical model of ship movement incorporated in the said application was developed at the Institute of Marine Traffic Engineering, Maritime University of Szczecin [9]. The application itself, using that model, was built by this author. The program offers performance of simulation tests in freely designed area by any defined ship. Depending on the selected ship type, adequate control options are available.
One relevant feature of the program is that during the simulation tests all ships movement parameters can be recorded. In addition, a separate program was developed as an application for post
factum analysis of the movements and trajectories
of both ships. In pu t m od ule Decision-inference module User interface module
Kn owle dg e ba se m od ule Speed Manoeuvre
The ship movement simulator consists of the following modules:
mathematical model of ship movement, control,
electronic chart, computing, display.
One significant advantage of this application is its universality in the choice of areas and ships. This results directly from the module configuration of the program and a possibility of preparing the data on ships and areas outside the application by using other programs.
Fig. 3. Application of the ship movement simulator [author’s study]
Rys. 3. Aplikacja symulatora ruchu statku [opracowanie wła-sne]
Simulation research
In the initial phase of building the system of navigational situation assessment the test objects were identified and defined, taking into consideration requirements resulting from the algorithms that were to be used. The objects, that is ships that in the system are described as a number of ship movement parameters varying in time. For simplification, one type of ship sailing under ballast was examined. Neither channel effect nor hydrometeorological conditions were taken into account.
A series of tests made were based on the method used by Quint [10] in defining a model of an F-16 aircraft behaviour. The tests were expected to indicate the relations between the manoeuvres performed and corresponding ship movement parameters. To this end a series of manoeuvring tests was made, leading to a definition of ship model behaviour and the identification of its state.
The ship used in the research was a bulk carrier with the following parameters:
capacity 5,000 DWT,
length between perpendiculars Lpp = 92 m,
breadth B = 15 m, draft T = 6.35 m.
The ship was equipped with a conventional propeller.
The simulation tests consisted in a series of zigzag tests with various rudder deflection and different advance speeds of the ship. During the manoeuvres the speed decreased by about 0.5 kn relative to the setting, but it had no effect on the quality of generated data.
The following parameter values of ship movement were recorded during each test:
• change in true course – KR; • advance speed – Vx;
• transverse speed – Vy;
• changes in the above speeds – Vx,Vy; • rate of turn – ;
• change in rate of turn – .
The simulation tests and their parameters are shown in table 1.
Table 1. Parameters of simulation tests performed Tabela 1. Parametry wykonanych prób symulacyjnych
Initial speed rudder deflection 1 full ahead – 14 kn ±5°; ±10°; ±15°; ±20°; ±25°; ±30° 2 half ahead – 10 kn ±5°; ±10°; ±15°; ±20°; ±25°; ±30° 3 8 kn ±5°; ±10°; ±15°; ±20°; ±25°; ±30° 4 slow ahead – 6 kn ±5°; ±10°; ±15°; ±20°; ±25°; ±30° 5 dead slow ahead – 4 kn ±5°; ±10°; ±15°; ±20°; ±25°; ±30°
The data were recorded at one second intervals. Altogether 30 simulation tests were carried out for various speeds.
Test results
The obtained results of simulation tests served as a basis for the defining of the structure and conditional probabilities in the Bayesian network representing the ship and capable of inferring on the ship status in terms of manoeuvres being performed. Two programs were used for the purpose: BayesiaLab and BayesNetLearner.
In order to build and define the network proper, ship states and corresponding movement parame-ters had to be distinguished. As mentioned before, the network should perform inference concerning the manoeuvre carried out by the ship (turn to port or starboard, slowing down, acceleration). There-fore, the parameter “manoeuvre” is attributed the following values (Table 2):
The parameter “speed” has these values: constant,
fast acceleration, slowing down, fast slowing down.
The above values use one of Bayesian network properties, i.e. possibility of combining linguistic information with numerical data. The particular values of parameters “Manoeuvre” and “Speed” were assigned corresponding ship movement parameters. Example data, given in table 5, are the
Table 3. Parameters of ship movement and the values of “Manoeuvre” and “Speed” assigned by the Bayesian network Tabela 3. Parametry ruchu statku wraz z przypisanymi przez sieć bayesowską wartościami „Manewru” i „Prędkości”
KR [°] KR V [kn] V Vy [kn] Vy [1/s] Manoeuvre Speed
0 8 0 0 0 0 7.99 –0.01 0 0 0 0 yawing constant 0 0 7.99 0.00 0 0 0 0 yawing constant 0 0 7.98 –0.01 0 0 0 0 yawing constant 0 0 7.97 –0.01 0 0 0 0 yawing constant 0 0 7.97 0.00 0 0 0 0 yawing constant 0 0 7.96 –0.01 0 0 0 0 yawing constant 0 0 7.96 0.00 0 0 0 0 yawing constant 0 0 7.95 –0.01 0 0 0 0 yawing constant 0 0 7.94 –0.01 –0.01 –0.01 0.01 0.01 yawing constant
3.6 0.6 7.86 –0.01 –0.19 –0.01 0.42 0.04 turn to starboard constant 4.2 0.6 7.86 0.00 –0.21 –0.02 0.45 0.03 turn to starboard constant 5 0.8 7.85 –0.01 –0.23 –0.02 0.49 0.04 turn to starboard constant 5.7 0.7 7.84 –0.01 –0.21 0.02 0.49 0 starboard 10 constant 7.4 0.5 7.82 –0.01 –0.21 –0.01 0.49 0 starboard 10 constant
8.1 0.7 7.82 0.00 –0.2 0.01 0.49 0 starboard 10 constant
8.8 0.7 7.81 –0.01 –0.21 –0.01 0.47 –0.02 turn to port constant 9.5 0.7 7.8 –0.01 –0.2 0.01 0.48 0.01 starboard 10 constant 10.3 0.8 7.79 –0.01 –0.21 –0.01 0.48 0 starboard 10 constant 10.7 0.4 7.79 0.00 –0.22 -0.01 0.48 0 starboard 10 constant 11.4 0.7 7.78 –0.01 –0.17 0.05 0.43 –0.05 turn to port constant 13.5 0.3 7.74 –0.01 0.03 0.02 0.18 –0.06 turn to port constant 13.7 0.2 7.74 0.00 0.05 0.02 0.12 –0.06 turn to port constant 13.8 0.1 7.73 –0.01 0.07 0.02 0.05 –0.07 quick turn to port constant Table 4. Example results of manoeuvre identification by the Bayesian network
Tabela 4. Przykładowe wyniki identyfikacji manewru przez sieć bayesowską
deltaKR VxD[w] deltaV deltaVy omD[1/s] deltaOmega manoeuvre $manoeuvre $$manoeuvre 0.1 4.68 0 0 0.04 0.01 turn to starboard turn to starboard 0.927397256 0.1 4.67 0 0 0.05 0.01 turn to starboard turn to starboard 0.927397256 0.3 4.68 0 0 0.15 0.01 turn to starboard turn to starboard 0.927397256 0.1 4.66 –0.02 –0.01 0.15 0 starboard 5 turn to starboard 0.916560007 0.2 4.67 0.01 0 0.16 0.01 turn to starboard turn to starboard 0.348532234
0.2 4.69 0.02 0 0.16 0 starboard 5 starboard 5 0.647907882
0.2 4.69 0 0 0.16 0 starboard 5 turn to starboard 0.348532234 0.3 4.7 0.01 0 0.17 0.01 turn to starboard turn to starboard 0.348532234
0.3 4.7 0 0.02 0.17 0 starboard 5 starboard 5 0.913629131
0.2 4.7 0 0 0.18 0.01 turn to starboard starboard 5 0.651466982
0.2 4.69 –0.01 0 0.18 0 starboard 5 starboard 5 0.651466982
0.3 4.69 0 –0.01 0.19 0.01 turn to starboard starboard 5 0.651466982 Table 2. Values of the “Manoeuvre” parameter
Tabela 2. Wartości parametru „Manewr” Manoeuvre
yawing port 5 starboard 5
turn to port port 10 starboard 10 quick turn to port port 15 starboard 15 turn to starboard port 20 starboard 20 quick turn to starboard port 25 starboard 25 port 30 starboard 30
data recorded during one of the simulation tests. The parameters “manoeuvre” and “speed” were assigned linguistic terms describing the behaviour of the ship.
The Bayesian network structure was determined from the gathered data and using the Bayes Net Learner program (Fig. 4). The process of network learning based on the data generated during simulation tests took place in the BayesiaLab application. As a result, a complete network was obtained. The network is capable of performing inference on manoeuvres of the ship from its movement parameters.
Fig. 4. A Bayesian network representing one ship and performing inference on the manoeuvre being carried out [author’s study]
Rys. 4. Sieć bayesowska reprezentująca jeden statek i wnio-skująca o manewrze, jaki jest wykonywany [opracowanie własne]
Statistical analysis of simulation tests results
The created Bayesian network was tested for its reliability. First, learning sets were used for the purpose. Each set was subsequently analyzed by the created network. Information on the performed manoeuvre was not included in the sets that contained data defining ship movement parameters. Information provided at the output was on the probable manoeuvre performed by the ship. The results were later compared with the original values from the learning sets. The probability of assessment correctness of the ship’s manoeuvre depending on the set ranged from 85% to 90%, which was regarded as sufficient for further research. It is essential that the network, providing its assessment of ship’s status (manoeuvre), also gives the probability of such assessment.
Example results of the manoeuvre type assessment by the network is presented in table 4. The column “manoeuvre” in the table indicates the real manoeuvre done by the ship, the column “$manoeuvre” includes a manoeuvre estimated by
the Bayesian network, while the column “$$manoeuvre” includes the assessment probability. Initially, the network was tested using the learning sets, which was aimed at finding out the network effectiveness.
Fig. 5. Distribution of the probabilities of correct manoeuvre identification by the Bayesian network for a ship manoeuvring along the Szczecin–Świnoujście fairway
Rys. 5. Rozkład prawdopodobieństw identyfikacji manewru przez sieć bayesowską dla statku manewrującego na torze podejściowym Szczecin–Świnoujście
Fig. 6. Number of correct and incorrect manoeuvre identifications by the Bayesian network for a ship manoeuvring along the Szczecin–Świnoujście fairway
Rys. 6. Liczba ocen poprawnych i błędnych identyfikacji manewru przez sieć bayesowską dla statku manewrującego na torze podejściowym Szczecin–Świnoujście
Further in the research the network was tested using data other than those from the learning set. The tests consisted in several ship passages along the Szczecin–Świnoujście fairway, where all manoeuvre data were recorded along with actually performed manoeuvres. 15 passages were done from the entrance heads of Świnoujście to the grain silo Ewa abeam. The recorded results – ship movement parameters were examined by the previously defined Bayesian network. The results of network assessment were probable manoeuvres of the ship. Comparing the manoeuvres identified by the network with real manoeuvres performed by
Rozkład prawdopodobieństw identyfikacji manewru bayesowskiej Przedziały prawdopodobieństw Li cz ba ob s. 2.2% 3.8% 0.5% 1.4% 3.9% 4.4% 2.0% 2.1% 10.8% 68.8% 0 752 1504 2256 3008 3760 4512 5264 6016 6768 7520 8272 9024 9776 10528 11280 12032 (0;10] (10;20] (20;30] (30;40] (40;50] (50;60] (60;70] (70;80] (80;90] (90;100] 0 982 1964 2946 3928 4910 5892 6874 7856 8838 9820 10802 11784 12766 13748 14730 15712 Incorrect Correct 10.2% 89.8% Assessment Nu m be r of ob se rv ati on s Speed Manoeuvre Probability intervals 68.8% Nu m be r of ob se rv ati on s 10.8% 2.1% 2.0% 4.4% 3.9% 1.4% 0.5% 3.8% 2.2%
the ship allowed to evaluate the reliability of actual assessments. The 89.8% figure confirms that the network was correctly defined (Fig. 6). The probability distribution of assessment made by the defined Bayesian network is given in figure 5. The assessments were provided with a relatively high probability (as many as 68.8% of them with a probability ranging from 90% to 100%), which also proves that the structure definition and relations between network nodes were correct. Summary
A Bayesian network was created from simulation test results described in this article. The network uses the theorem formulated by Bayes on discovering the relations between network nodes. After the processes of network learning and verification using learning data sets, the correctness of network inference was examined by using data other than those contained in the learning sets.
The proper assessment of a navigational situation is one of the most important factors of safe navigation in a restricted area. The developed and defined Bayesian network herein presented allows to estimate the present navgational situation. Besides, the network is capable of indicating which manoeuvre the ship is currently performing. On this basis, and using data referring to the quantities involving both ships, such as:
CPA (Closest Point of Approach),
TCPA (Time to Closest Point of Approach), distance between ships,
relative bearing and aspect,
it is possible to perform inference on the present navigational situation of the ship. The developed mathematical model is based on a Bayesian network. It has abilities to acquire, represent, approximate and generalize knowledge and to interpret information in numerical as well as linguistic form. Besides, it is capable of updating its knowledge as new data become available. Importantly, such update network learning process may take place in real time during normal operation of the system.
The research has resulted in the following conclusions:
1. It is possible to automatically identify a ma-noeuvre being performed by the ship from its movement parameters and their changes.
2. A navigational situation in a restricted area can be automatically identified.
3. The degree of confidence in its own assessment given by the Bayesian network makes it possible to reject incorrect assessments, which makes the system resistant to errors of situation assessment – the system performs self-verification.
4. The correlation of assessment by the system and by experts ranged from 0.72 to 0.94.
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Recenzent: dr hab. inż. Krzysztof Czaplewski, prof. AMW Akademia Marynarki Wojennej w Gdyni
