Collisions are one of the major accidents in the shipping industry, causing significant losses. In this work, a framework of marine collision risk identification strategy was developed to quantitatively analyse collision risks and provide an easy and convenient way to monitor traffic flow in relevant waters to mitigate the chances of collision. The model was verified by using automatic identification system data obtained from Tianjin Port. When compared to previous research, the proposed model can identify risks earlier and give people more time to analyse and take action. The results indicate that it also can provide a visual display to alert relevant personnel. The model can be used as a reference to identify potential collision risks or as an information source for future research.

Applying non-accident critical events (NACEs) as an alternative measuring method to assess ship collision risk has become popular in recent years. NACEs has shown temporal features in different waters. This study uses the quaternion ship domain method to identify NACEs around the Yangtze Estuary and adjacent coastal waters from the Automatic Identification System (AIS) data in October 2019. The results indicate that NACEs show different temporal features in estuaries and coastal waters. The relationship between tides, channel types and ships is discussed. In addition, we established a statistical method for the occurrence time of NACEs and the state of tides according to the half-tide level and the nearest time. The outcomes of this study provide a direction for exploring the relationship between NACEs and environmental conditions, which is also instructive for the study of the causes of ship accidents.

A ship's perception of risk is an important basis for collision avoidance. To improve such perception, several risk measurement parameters on the ship domain are determined, including the approach factor, the time to domain violation (TDV) and the possible collision domain. Then, a risk hierarchy prewarning (RHP) model based on the violation detection of a ship domain is proposed, in which a two-level alarm scheme is adopted accordingly. A low-intensity alarm will be activated by reaching the minimum approach factor and the TDV threshold, and a high-intensity alarm will be activated by the factor of the possible collision domain and the TDV threshold. Subsequently, a novel guard zone in ARPA radar utilising the RHP model has been developed to establish a ship's risk perception system for officers on watch at sea. The model proposed in this paper can not only enhance the veracity of risk assessment around our own ship, but also be used as a decision support system for collision avoidance.

The ship safety domain plays a significant role in collision risk assessment. However, few studies take the practical considerations of implementing this method in the vicinity of bridge-waters into account. Therefore, historical automatic identification system data is utilised to construct and analyse ship domains considering ship–ship and ship–bridge collisions. A method for determining the closest boundary is proposed, and the boundary of the ship domain is fitted by the least squares method. The ship domains near bridge-waters are constructed as ellipse models, the characteristics of which are discussed. Novel fuzzy quaternion ship domain models are established respectively for inland ships and bridge piers, which would assist in the construction of a risk quantification model and the calculation of a grid ship collision index. A case study is carried out on the multi-bridge waterway of the Yangtze River in Wuhan, China. The results show that the size of the ship domain is highly correlated with the ship's speed and length, and analysis of collision risk can reflect the real situation near bridge-waters, which is helpful to demonstrate the application of the ship domain in quantifying the collision risk and to characterise the collision risk distribution near bridge-waters.

Applying the existing domain model in ship domain research in a restricted area can be difficult owing to multiple factors that must be considered. This study presents a new domain model that can be applied in such environments. According to Endsley's theory of situation awareness, people have their own criteria in decision making based on factors such as individual and environmental factors. To investigate these factors, 125 seafarers were interviewed and threshold values based on their awareness were examined. The factors were evaluated as the closest points of approach. Domain modelling was performed based on these seafarer awareness values; then, the existing and awareness domains were compared, revealing that the awareness-based domain of seafarers is more affected by ship manoeuvrability than by ship size and speed, unlike the findings of existing domain research. Therefore, this study presents a new domain model that is both realistic and practical in a confined area, including various factors considered by seafarers based on the awareness values formed.

Using near miss data detected from non-accident information to analyse marine traffic risk can alleviate some of the limitations of accident-based methods. A model based on an arena for detecting scenes of near miss is proposed to detect comprehensively those ship encounters with potential collision risk. To eliminate the influence of data sampling frequency on the detection of scenes of near miss, a single near miss is defined as the whole progress of traffic state from the time the target ship sails into the arena of the subject ship to the time it leaves the arena of the subject ship. To research the geographical distribution characteristics of marine traffic risk, first, a statistical model for the scenes of near miss based on the water grid method is proposed, and then a macroscopic collision risk model based on near miss is developed. The geographical distribution characteristics of marine traffic risk in the Bohai Sea are analysed, and the water areas of high marine traffic risk are obtained. The findings can provide theoretical support for marine safety management.

Developing risk models to predict where collisions between vessels might occur is hindered by the relative sparsity of collisions. To address this, vessel encounters and near-misses have been used as a surrogate indicator of collision risk, referred to as ‘domain analysis’. When constructed empirically, using historical information, previous work is challenged by the multitude of factors which influence the passing distances between vessels. Within this paper, we conduct data mining of big vessel traffic datasets to determine the encounter characteristics across different waterways, vessel types and speeds, weather conditions and other exploratory variables. To achieve this, we utilise a novel approach of machine learning through a random forest algorithm to predict the critical passing distance between vessels in a multitude of conditions. We contribute a far greater range of influencing factors on domain size and shape than previous studies. Finally, we investigate the potential advantages of this approach to assess the spatial risk of collision across a large region. The results help to establish the factors that influence collision risk between navigating vessels and enable empirical maritime risk assessments.

Ship domain is an important theory in ship collision avoidance and an effective collision detection method. First, several classical ship domain models are used in experiments. The results show that the alarm rate is too high in busy waters, leading to greatly reduced practicality of the model. Potential collision risk cannot be detected effectively, especially for a ship with restricted manoeuvrability, which is usually regarded as an overtaken ship due to its navigation characteristics. Therefore, it is necessary to fully consider the interference of other ships to ships with limited manoeuvrability in an encounter situation. A novel ship domain model for ships with restricted manoeuvrability in busy waters is proposed. Considering the navigation characteristics of a ship with restricted manoeuvrability and the influence of the ship–ship effect, an algorithm to determine the boundary of the ship domain model is given by force and moment equations. AIS trajectory data of the North Channel of the Yangtze River Estuary are used to perform a comparative experiment, and four classical ship domain models are employed to perform comparative experiments. The results show that the alarm rates of the novel ship domain model are 7⋅608%, 15⋅131%, 55⋅785% and 7⋅608% lower than those of the other four classical models, and this outcome can effectively reduce the high false alarm rate produced by other models in this environment.

The objective of this study is to propose a methodology for assessing waterway traffic capacity in the Shanghai estuary of the Yangtze River. To achieve this objective, we first put forward the estimation method which utilises the minimum collision distance taking the dynamic ship domain into consideration. Considering possible effects caused by unknown external factors, the waterway traffic capacity is then represented by a probability distribution. Finally, we quantify the equivalent units of ships with various ship sizes as well as the effects of large-sized ships on the waterway traffic capacity. Results show that a large-sized ship is equivalent to more small-sized ships during the daytime period than at night. In addition, the deployment of large-sized ships could increase the waterway traffic capacity and such an increment highly depends on the increased proportion of large-sized ships in the waterway traffic.

A round of three celestial sights yields three lines of position along which the observer's true position could lie. Due to measurement errors, the lines of position do not intersect at a point but rather form a triangle called the “cocked hat”. The probability that this encloses the observer's true position is well known to be 25% which is the average over all possible cocked hats that could arise when the sights are made. It does not apply to any specific set of sights and in that case the probabilities depend on the statistical distribution of the measurement errors. With fixed azimuths for the observed celestial bodies and assuming a normal distribution for the errors in their measured altitudes, a closed form analytic expression is derived for the probability of the observer's position falling inside the cocked hat and this is related back to the global average. Probabilities for exterior regions bounded by the lines of position are also obtained. General results are given that apply for any number of lines of position.

When ships approach each other, they should keep a minimum area around them clear of other vessels in order to remain safe. The geometrical shape of this area has been studied since the early 1970s and is defined as the ship domain. The progress in computer capacity since then and the introduction of the Automatic Identification System (AIS) provides the potential to further investigate the size and the governing factors of the domain. This investigation revisits and proposes a method using data based on 600,000 ship encounters at 36 locations. It is concluded that the ship domain has the shape of an ellipse with half axis radii of 0.9 and 0.45 nautical miles. However, there are two factors that greatly affect the ship domain: how large the area is that is used to gather vessel intersections and whether they are constrained by water depth. In contradiction to some previous research, it is found that the ship domain is unrelated to the length of the ship.

Facilitated by recent establishment of terrestrial networks and satellite constellations of Automatic Identification System (AIS) receivers, ship trajectories are becoming increasingly available and the size of recorded trajectories is getting larger. Large sets of trajectories create problems of storing, transmitting and processing data. Using appropriate methods, an accurate representation of the original trajectories can be obtained by compressing redundant information, while maintaining the main characteristic elements. In this paper, a new scheme and the implementation of the Douglas-Peucker (DP) algorithm are presented, which can simplify AIS trajectories by extracting characteristic points. As for the simplification threshold, the solo parameter of the DP algorithm, a new AIS-based minimum ship domain evaluation method is proposed and acts as criteria for simplification threshold determination. Finally, a validation is made to examine the effectiveness of the DP simplification algorithm and the rationality of the simplification threshold. The result indicates that the DP algorithm can simplify AIS trajectories effectively; the simplification threshold is scientific and reasonable.

There are limited studies on the use of ship domain as the safety criterion for ship navigation within confined waters. In this paper, a free-form ship domain has been developed empirically for navigation in confined waters. Two individual domains of an asymmetrical polygonal shape have been assumed around the own ship and target ship, and the size of the ship domains is assumed to be dynamically enlarged with increased ship speeds. The required safe distance modelled using the proposed ship domain takes into account dynamic changes in relative bearing and heading. The model is calibrated using the data of vessel movements in Singapore Strait and Singapore Port. An innovative process has been adopted that iteratively adjusts the parameters in the basic ship domain of a stationary ship; a speed function as well as a weight function to maximise the usage of the dataset. The resulting ship domain model compares well with existing ship domains for typical encounters, such as those of Fujii and Coldwell but represents non-typical encounters more effectively than existing models.

In this paper, a novel ship domain model termed quaternion ship domain (QSD) is proposed. Unlike other ship domains, the proposed QSD is more dependable and more flexible for navigators to use to make decisions. The main characteristics are that: the domain size is determined by the quaternion including four radii, i.e. fore, aft, starboard and port, which sufficiently take factors affecting the domain (i.e. ship manoeuvring capability, speeds and courses, etc.) into account; and that the domain shape is modelled by another parameter which makes the QSD more flexible since the ship boundary could not only be linear or nonlinear, but also be thin or fat. In order to reasonably relate the proposed QSD to practical applications, i.e. collision risk assessment, collision avoidance and trajectory planning, etc., a fuzzy QSD (FQSD) has been developed by using fuzzy sets. As a result, fuzzy boundaries rather than crisp ones in the FQSD are more practical and more convenient for navigators to understand and judge since uncertainty and fuzzy information have been merged into the FQSD. Furthermore, concepts of longitudinal and lateral risk based on the FQSD have been introduced to estimate the spatial collision risk (SCR) for the ships encountered. Finally, several computer simulations have been conducted on various encounter situations and comparative studies with other ship domains have been comprehensively analyzed. Simulation results demonstrate that the proposed QSD is more effective and more flexible than other ship domains, and that the intelligent SCR based on the FQSD are reasonable and dependable.

Most of the existing typical ship domains have been comprehensively reviewed and classified. Most of these ship domains are described in a geometrical manner that is difficult to apply to practices and simulations in marine traffic engineering. According to different types of geometrical ship domains, we have proposed mathematical models, based on which a unified analytical framework has been established. It is feasible and practical for the analytical models to be applied to the assessment of navigational safety, collision avoidance and trajectory planning, etc. Finally, some computer simulations and comparative studies of the proposed domain model have been presented and the simulation results show that the uniform analytical framework for ship domains is effective and identical to the original geometrical ones. It should be noted that the analytical domain models could be directly applied in any collision risk, collision avoidance or VTS system while the geometrical ones would be more illustrative but less practical or analytical.

One of the basic tasks in shipping is to ensure safe navigation of vessels. The concept of the ship domain is of major importance in the assessment of a navigational situation and the avoidance of ship collisions. It is difficult to determine a ship domain as its shape and size depend on a number of factors. One question to be answered before the determination of the ship domain is which method to use: statistical, analytic, or expert method using artificial intelligence tools; other questions are connected with domain interpretation. The authors have analyzed the ship domain as a criterion for the assessment of ship navigational safety in an encounter situation in the open sea. The research results are used to answer some of the questions.

Part 2 includes definitions of the ship domain and ship fuzzy domain. Part 3, in turn, presents methods of their determination as well as relevant questions. The results of the authors' research, described in Part 4, make up a basis for the determination of the domain and ship fuzzy domain. These have been determined with the so-called dynamic domains as a point of departure. The criteria of ship domain and closest point of approach are compared and discussed. Encounters of various size ships are considered in Part 5. The research and its results are described. Both ship domains and ship fuzzy domains of encountering ships are analyzed. Then, conclusions have been formulated in relation to the effect of the sizes of encountering ships on the shapes and sizes of their domains. Final conclusions are given in Part 6.

The paper introduces a new measure of collision risk derived from the concept of a ship domain. Its simplicity and the fact that it takes into account the courses of both ships, makes it a good alternative to the commonly used term of the distance at the closest point of approach (DCPA). The measure being presented is flexible enough to be applied in combination with any given ship domain. Derivations of all the necessary equations for the Fuji domain have been presented in detail. Additionally, the paper contains numerical algorithms that are capable of determining value of the measure for any other ship domain. Based on these algorithms a generic method for determination of the necessary course alteration is developed. Also, an example of an already known formula for risk assessment, that may benefit from the measure, is provided. All of the algorithms, formulas and their derivations in the text are presented explicitly, so that they could be directly applied in any collision avoidance or VTS system.