Keywords

1 Introduction

In recent years, great oceanic powers have proposed future maritime strategy objectives. The next generation of intelligent maritime transports has already triggered a new upsurge in research. For example, Japan has proposed an E-navigation strategy. Hasegawa et al. [1] have specifically described intelligent ship-navigation systems for the future. Europe has unmanned ship research organizations based on smart networks, e.g., the European-Union-funded Maritime Unmanned Navigation through Intelligence in Networks (MUNIN) project. Rødseth and Burmeister [2] discuss some of the key challenges for unmanned ships in existing navigational-aid conditions. Intelligent ship designs have been envisioned by large companies, e.g., autonomous navigation research from Rolls-Royce PLC in the merchant ship field.

Objectively speaking, in the ancient merchant-shipping industry, the speed of automation research and development, even the unmanned process of maritime transportation systems (MTS), is very slow, compared with Google and other Internet and automotive companies. However, considering the risk of maritime transport and the monotony of the crew’s work, intellectualization and automation should have greater development prospects in the MTS field. A research approach that draws on road transportation systems is necessary, especially in maritime transport safety and other important areas.

Trucco [3] used a Bayesian belief network—a specific extended application—for marine-traffic risk assessment. In his discussion, Trucco integrated human and organizational factors, using a Bayesian network to support hazard identification and assessment. This model had good risk-assessment support for a human involved in the situation, but it did not integrate a decision support system. When a ship encounters a dangerous situation, this model cannot play the role of decision support. This study intends to further use the Bayesian network approach to construct decision-support systems for handling complicated hazards in a sea environment.

In other areas, e.g., medical care quality, Ltifi [4] used Dynamic Decision Support Systems in the healthcare domain (MDDSS). Ltifi used the Knowledge Discovery from Databases (KDD) process technique in Dynamic Bayesian Networks (DBN), and proved that it can be used in a complex system when the situations are dubious and/or the raw data are complex structures. Lepreux [5] described a methodological process for the design and evaluation of a Human-Machine interactive system in an industrial railway context. In the maritime transportation field, Abu-Tair [6] presented a practical solution for obstacle (e.g., target ship) detection and collision avoidance, mainly for Unmanned Surface Vehicles (USVs). Perera [7] used a fuzzy-logic-based parallel decision-making (PDM) module and a Bayesian-network-based module to present a collision-avoidance system (CAS) at sea. It could handle multiple parallel collision-avoidance decisions, regarding several target-ship collisions. The decisions are executed as continuous handling actions to avoid complex collision situations at sea.

Seafarers at sea have their own unique traditions. To develop the features of this work, the same content was repeated extensively, which has been proved to be an appropriate and simple approach to automation. However, the complete ship navigation operation must have sufficient experience to deal with unexpected accidents or emergency situations. Before an accident, the officer of the watch (OOW) must have the ability to cut off the line caused by the accident. Therefore, based on experience and collected data, using Bayesian methods to make predictions, we can construct a decision-support system to help the OOW judge the danger and make decisions, before the accident, to achieve the safe navigation of the ship.

2 Reliable Decision Support System

Since “Preventing Collisions at Sea” was added to the International Maritime Organization (IMO) regulations, the proportion of accidents caused by human factors has increased year by year. For many accidents, an in-depth analysis has always found a human-factor impact. When conducting a comprehensive assessment on the safe navigation of a ship, Furusho [8] summarized four factors of safe ship navigation, according to the MTS characteristics: Man, machines, media, and management. Human factors are an important part of ship safety. The authors of this article also pointed out in a previous paper [9] that when constructing the basis for next-generation ship-navigation safety, a human (OOW) should be at the core position and at the top decision-making layer in collision avoidance. Therefore, when constructing a reliable decision-support system, the presupposition is to achieve autonomous ship-collision avoidance with automatic navigation.

2.1 Decision Pyramid

Safe ship navigation requires an operating system composed of two departments: the bridge and the engine room. (This is also called a conventional or traditional operating system). This operating system needs an automatic identification system (AIS), electronic chart display and information system (ECDIS), global positioning system (GPS), and a series of sensors to receive the navigation-environment information, estimate and operate the ship according to the OOW’s experience and skills, and avoid collisions or other difficulties. According to the previous discussion, it is necessary to design a next-generation reliable and compatible artificial-intelligence decision-making pyramid system. Figure 1 shows the Bayesian methods of artificial intelligence decision-support systems, which comprise the decision-making pyramid: OOW, Bayesian network method (BN Process), Operating System, Physical Environment, and Navigation Environments.

Fig. 1.
figure 1

Decision pyramid for safe navigation

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2.2 Safe Ship Navigation Process

For safe ship navigation using the decision-making process of the pyramid, the structure needs all aspects of technology research support, e.g., sensors collecting the ship’s environmental information, turbine reliability, ship maneuverability, steering stability, training of the Bayesian network nodes and structures, etc.

The physical environment of the ship includes the ship’s structure, anti-shear properties, stability, pressure stability, balance stability, etc. Another part is the performance of various sensors, including the AIS, ECDIS, GPS, depth sounder, etc. The navigation environment information is received by sensors; environment information can include the performance data of the ship itself, sea-state information, and the target-ship information. The specific classifications are shown in Table 1.

Table 1. Navigation environment information
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Navigation-related data can be automatically calculated by the operating system, according to the relevant IMO navigation regulations. For security, the information can be submitted to the operating system to select the steering operation. Guo et al. [10] compared the cerebellar model arithmetic computer (CMAC) neural network, the fuzzified CMAC, the bang-bang CMAC, and several of the more common methods of ship steering. The proposed multiple-fuzzy CMAC (MFCMAC) algorithm adopts the advantages of each mode and yields better control performance than each algorithm by itself. Under difficult circumstances, if the normal collision-avoidance operation cannot be completed, the navigation environment is extreme, or there is no trained data support, a Bayesian network (BN) can help avoid the collision based on the collected information of the past. When the available data do not allow the Bayesian network to make a complete decision, or past data on encountering the current situation is too sparse, the decision cannot be made. The OOW must complete the operation before the hazard occurs. Many complex situations are encountered at sea. The main objective of this paper is focused on how to make a collision-avoidance decision when one’s own ship and the target ship constitute the hazard-encounter situation.

With the data and structure trained by the BN, the system will support more conditions for automatic hazard prediction and decision-making. Finally, approaching the top of the decision pyramid, there will be less need for human participation in the decision-making. In the end, the human (OOW) could be replaced, and the necessary decision support and ship manipulation could be done remotely. This is an inevitable trend for the automated safe navigation of ships and autonomous decision-making processes.

3 Using Bayesian Networks to Support Decision-Making

On February 7, 2006, the Japanese body of maritime safety submitted a document to the Maritime Safety Committee of the International Maritime Organization (IMO) [11]. This document (MSC/81/18-1) presented how to use Bayesian network modeling in a formal safety assessment. The Bayesian network uses the past data as well as human factors. (The human (OOW) involved in the ship handling will generate a new data node, which will directly influence the exactness of the system prediction.) A Bayesian prediction, using a method that combines the objective and subjective information, can handle abnormal situations, recognize unknown conditions, or reasonably predict an unexpected emergency situation, by monitoring and then supporting the appropriate decision.

3.1 Definition of a Bayesian Network

A Bayesian network is a mathematical graphical prediction model based on probabilistic reasoning (a type of statistical model) that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). The Bayesian network provides statistical predictions, not only with reference to the objective data, but also to subjective information. At present, the Bayesian network does not have a universally accepted definition. In 2001, “Jensen” stated that a network with conditional independence and d-separation that satisfies the following four conditions is called a Bayesian network:

  1. I.

    There is a set of variables V={Xi}, i=1,2,…,n, that correspond to nodes; between the nodes is a set of directed edges E;

  2. II.

    Each variable takes a finite number of discrete values;

  3. III.

    Using the nodes and the variables corresponding to the directed edges between the nodes, construct a directed acyclic graph G = (V, E);

  4. IV.

    Each stage of Xi and its parent node set \( \prod\nolimits_{i} {} \), corresponds to a conditional probability distribution table p(xi|πi, G), and satisfies p(x1,x2,…,xn) = \( \prod\nolimits_{i = 1}^{n} {p(x_{i} |\pi_{i} ,G)} \).

3.2 Bayesian Probability and Prediction

Good predictions can help decision makers make reliable decisions. A Bayesian probability is derived from Bayesian statistics. If a hazard occurs, depending on the extent the OOW is trusted (this is usually a subjective probability), the OOW (or system), based on prior knowledge and existing observational data (trained data), uses probabilistic methods to predict the risk and make decisions. Note D = {x1 = x1, X2 = x2,…, Xn = xn} of the observed sample, in which X is an event variable, and x is the variable state or variable weights. Parameter θ is the prior probability of the occurrence of event X [θ = P (x | ξ)] and P (θ | ξ) is a probability function, in which ξ is the prior experience of the OOW.

The Bayesian probability can be stated as follows: Given a prior probability θ = P (x | ξ) and an observed sample D, seeking an operation step of n + 1 times, the probability of occurrence of event Xn + 1 is P (Xn + 1 = xn + 1 | D, ξ). According to the stated Collision Regulations of the International Convention and the Predetermined Decision-Making System Ship Collision-Avoidance model, Bayesian methods can be used to construct a basic prediction sample; the process is shown in Fig. 2.

Fig. 2.
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Part of a sample flowchart for collision avoidance

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Here, Rt (Xn) represents the probability of collision risk encountered in ship navigation, and corresponds to P (θ | D, ξ); Rt-1 (Xn) represents the prior probability of Rt (Xn), and corresponds to p (θ | ξ). According to the Bayesian formula, the posterior probability of formula p (θ | D, ξ) can be calculated by a prior probability p (θ |ξ):

$$ P\left( {\theta \,|\, D, \xi } \right) = \frac{P(\theta |\xi )P(D|\theta ,\xi )}{{P\left( {D|\xi } \right)}} = \frac{P(\theta |\xi )P(D|\theta ,\xi )}{{\int {P(\theta |\xi )P(D|\theta ,\xi )d\theta } }}. $$

In the prior probability (θ | ξ), a known sample D is conditionally independent of each event X. According to the ship sailing conditions and conforming to the international regulations for preventing collisions, the operation of variable X is only considered as a binary distribution. p (θ | D, ξ) = θh (1 − θ)t, in which h is the number of occurrences of the event in a sample D, and h + t = n.

Hypothesis

If a prior probability satisfies a β distribution, according to the distribution of the conjugate-distribution principle, the posterior probability is also a β distribution.

$$ P(\theta |\xi) = \beta (\theta |r_{h} ,r_{t}) = \frac{{\Gamma(r)}}{{{\Gamma(r_{h})} {\Gamma}(r_{t})}}\theta^{{r_{h} - 1}} (1 - \theta )^{{r_{t} - 1}}, $$

where \( {\text{r}}_{h} \)  > 0, \( {\text{r}}_{t} \)  > 0 is a β-distribution parameter, and prior experience is determined by nature itself. \( R\; = \;r_{h} \; + \;r_{t} \). Gamma Function Г (x + 1) = xГ (x), Г (1) = 1.

Then, the posterior distribution

$$ \text{p}(\uptheta | \text{D},\xi) =\upbeta (\uptheta | r_{h} + h,r_{t} + t) = \frac{\Gamma \text{(r +n)}}{{\Gamma (r_{h} + h, r_{t} + t)}}\uptheta^{{r_{h} + h - 1}} (1 -\uptheta)^{{r_{t} + t - 1}}. $$

The expected β distribution is known by the prior distribution:

$$ \int {\uptheta \upbeta (\uptheta| r_{h} ,r_{t} ){\text{d}}\uptheta} = \frac{{r_{h} }}{r} $$

Then, the predicted probability of the Bayesian formula:

$$ P\left( {X_{n + 1} = x_{n + 1} |\,D,\xi } \right) = \int {\uptheta\,P\left( {\theta \;|\;D,\xi } \right){\text{d}}\uptheta} = \int {\uptheta \upbeta (\uptheta|r_{h} + h,r_{t} + t){\text{d}}\uptheta} = \frac{{r_{h} + h}}{r + n}. $$

3.3 Case Study: Decision Analysis Before a Cargo Ship Collision

In specific cases, a particular feature is the key to causing an accident. This section selects a representative collision case study. According to the relevant experience of the OOW and fully estimating the sea conditions at the time, we use the previous discussion of Bayesian methods to help the OOW make navigation decisions before the collision.

This accident occurred 930 km off the east coast of Kinkazan Island, Ishinomaki City, Miyagiken. The source of this accident is the Japan Transport Safety Board [12]. Ship A—cargo ship NIKKEI TIGER—and ship B—fishing ship Hori Sakae Maru—collided, caused a serious accident leading to 13 people missing from the fishing ship. Figure 3 shows the three-minute relative position before the two ships collided, and a schematic diagram of their relative course. (Appendix A shows the two ships’ navigation tracks before and after the collision.) The OOW of ship A lacked navigation experience and was not familiar with the international navigation regulations. In the process of collision avoidance, as ship B’s green light (starboard lights) became visible, he incorrectly steered to port (left); then, he sharpened the angle of his turn (by 10°, twice). This is the direct reason for the collision.

Fig. 3.
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Relative positions before collision

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Hypothesis: The probability that the OOW saw the green light is \( P_{(G)} \). Upon seeing a green light, the ship should maintain its speed and course. The probability of keeping watch is \( P_{(K|G)} \) and the probability of a safe pass is \( P_{{(S|{\text{K}},G)}} \). The probability of a turn to port is \( P_{(T|G)} \) and the probability of a collision is \( P_{{(C|{\text{K}},{\text{T}},G)}} \). The specific structure is shown in Fig. 4. According to the hypothesis and using the Bayesian prediction method, the following conditional probability table can be obtained. K = 0 indicates that the OOW of ship A saw the green light and did not keep watch. T = 0 indicates that he saw the green light and did not turn to port. \( {\text{P}}_{{\left( {C = 0} \right)}} = 0.9 \) indicates a “strong” likelihood of a ship collision; \( {\text{P}}_{{\left( {C = 0} \right)}} = 0.1 \) indicates a “weak” likelihood of a ship collision.

Fig. 4.
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Examples of BN probability

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3.4 Application of a BN to a Human-in-the-Loop Decision-Support System

Academic research applying Bayesian methods to practical applications is extensive; e.g., macro-economic trends, financial risk management, intelligent user interfaces, information filtering, automatic vehicle navigation, medical care, economic prediction, speech-recognition text classification, etc. Depending on the different areas, there are different interpretations of the Bayesian network; e.g., Bayesian belief networks and dynamic Bayesian networks.

The core idea is to use the prior distribution and add sample information to infer the posterior distribution. The prior portion may be according to long-term experience in terms of human activity. It also can be judged by the decision-makers’ past common sense. It can also be applied to the OOW. Because of the experience, knowledge structure, individual differences in quality, and other reasons, the OOW would construct his own judgments and predictions in a certain kind of situation. A general prediction will always contain uncertain elements, as in the definition of information theory. In this paper, entropy is borrowed to describe the uncertainty prediction factors. This study uses Bayesian methods and Bayesian networks to construct an autonomous human-in-the-loop decision-support system. Prediction and assessment may encounter various problems when the ship sails, including human involvement in ship manipulation, the conditional probability of the OOW making decisions, etc.

4 Constructing the Decision-Support System

The Bayesian network is the core of the decision-support system for the ship’s safety navigation. Therefore, constructing a reasonable and reliable Bayesian network is the most significant work of this article. It can be approached from the definition of Bayesian networks. A Bayesian network consists of two parts: the structure (directed acyclic graph) and the parameters (conditional probability distribution table). To establish a Bayesian network model, first, the model must be given an index to predict, and collected examples of the corresponding data. Then, a predictive model is built based on the index and example data. The predictive model can be used to predict the new situation.

4.1 Index System for Risk Prediction

According to the actual ship-navigation conditions, the risk index is divided into four levels: decision-making risk D [t], the factor index, the direction index, and the basic event index. The first three indexes are defined as random discrete variables; the last stage can be discrete or continuous. The specific classifications are presented in Table 2.

Table 2. Decision-making risk index
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4.2 Process of Training the Structure and Parameters

Constructing a Bayesian network consists of two parts: (1) Defining the variables; (2) training the structure and parameters. Generally, these two tasks are executed sequentially; then, during construction, the following two aspects must be compromised.

On the one hand, to achieve sufficient accuracy, a sufficiently large and rich Bayesian network model must be constructed; on the other hand, the maintenance costs and the complexity of the probabilistic reasoning should be considered. For a complex model structure, the complexity of the probabilistic reasoning is also higher, which often affects the efficiency of the Bayesian network. In fact, the establishment of a Bayesian network often involves running the two processes iteratively, with repeated interaction.

The first main task is under the guidance of domain experts: Selecting the appropriate variables for the research questions field. In some cases, it also requires a certain strategy: Selecting an important factor from the variable provided by the expert. The second task is to construct the key node of the Bayesian network. The main objective is to build a directed acyclic graph and provide the distribution parameters for each node, where each node corresponds to a conditional probability-distribution table (CPT). Under normal circumstances, there are two different ways to construct a Bayesian network:

  1. 1.

    The completed study. In this approach, the structure and parameters of the Bayesian network are subjectively defined by people. Experts in the field determine the Bayesian network variables, the structure, and specify the distribution parameters. This Bayesian network is constructed entirely under the guidance of experts. Due to the limitations of the experts’ knowledge, the data from the constructed Bayesian network may greatly deviate from what occurs in practice.

  2. 2.

    Partial learning. In this approach, the node variables of the Bayesian network are subjectively defined by people. The Bayesian network structure and parameters are learned through extensive training with the data. This is a completely data-driven approach, with strong adaptability. The evolution of artificial intelligence, data mining, and machine learning makes this approach possible. Learning the structure and parameters of a Bayesian network from the data, is a direction for future research.

4.3 Construction of the Bayesian Network Prediction

Figure 5 shows the Bayesian network prediction model for decision support used for safe ship navigation, according to the characteristics of decision-making and risk assessment. The index system is optimized, with participation and abundance from expert knowledge.

Fig. 5.
figure 5

Vertical view of the Bayesian network model for risk prediction

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5 Conclusion

Bayesian networks can fully utilize the dependency information between variables to make predictions. The purpose of this paper was to draw experience from Bayesian networks successfully applied in other science fields, and utilize them to do risk prediction of ship navigation, and build a navigation decision-support system. This paper, with the OOW at the center and the top layer of decision-making, elaborated on the advantage of Bayesian methods to quantify in terms of human factors, the importance of added experience and past relevant knowledge to the prior information. We constructed a decision-support pyramid system based on Bayesian network prediction, to enhance the safe navigation of ships at sea.

The core of the decision-making pyramid system was a Bayesian network process. Bayesian networks are constituted by the defined variables and the training composition of the structure parameters. From Bayes’ theorem, this paper discussed in detail a variety of situations that could be encountered in ship navigation. To define these nodes for different risk conditions, a directed acyclic graph is given for each parameter position based on a Bayesian network for each stage of the corresponding conditional probability-distribution table. Finally, we displayed the fundamental vertical view of the Bayesian network model for risk prediction.