Modeling Human Encounter Situation Awareness Results Using Support Vector Machine Models

Abstract

This study constructs a support vector machine model based on supervised learning to model the results of situation awareness for ship collision avoidance. To explain the model, collision risk situations were defined, and human situation recognition results were collected in the specified cases. Moreover, it was used to build predictors and outcome variables. Finally, the constructed variable was applied to the classification model. This model provides insight into the results of the navigator’s encounter situation awareness when collision avoidance is required. The results indicate that the proposed model can be used to predict human situation awareness outcomes in given cases.

1. Introduction

The results of the navigator’s perception of the encounter situation are crucial for the safety of navigation. When the risk of collision is suspected, humans perform a four-step information-processing process [1]. It is information acquisition, situation analysis, decision-making, and action. Several methods have been reported for determining the risk of collision. The navigator uses indicators such as distance at the close point of approach (DCPA), time to DCPA (TCPA), and changes in relative bearing to determine the risk of collision [2]. This method, applied to navigation equipment such as ARPA (automatic radar plotting aid), provides numerical information to the navigator through simple calculations. In addition, some numerical models have been reported to assess the risk of collision. Ren et al. [3] reported a numerical model that combines membership functions that calculate collision risk based on fuzzy logic using AIS data. Li and Fang [4] built a collision risk evaluation model using a multi-radar network based on the Dempster–Shafer theory to overcome the shortcomings of the existing collision risk model. Xu and Wang [5] reviewed the basic concept of collision risk and the numerical model for calculating collision risk. Xie et al. [6] introduced a simplified three-way guided ship dynamics model, and the model’s control prediction and real-time collision avoidance model were constructed. In addition, Shaobo et al. [7] established a collision avoidance model for autonomous ships that reflects the interaction of the obstacles during the collision avoidance operation.

The navigator, who felt the risk of a collision through various means, analyzes the encounter situation to escape the dangerous situation [8]. The International Regulations for Preventing Collisions at Sea (COLREGs) is a principle when a navigator analyzes a situation. According to the COLREGs, an encounter situation is categorized as head-on, crossing, or overtaking [9]. Here, crossing is divided again into a give-away and stand-on. Give-away is the situation when the OS (own ship) should avoid the TS (target ship). Stand-on is the situation when the TS should avoid the OS. However, the COLREGs define only the basic concepts and principles and do not provide specific numerical figures [10]. Furthermore, the navigator’s judgment is sometimes respected, and exceptions are recognized [11]. Therefore, the navigator analyzes the encounter situation and determines the action by applying his experience and judgment in the field. Moreover, at this time, the operator’s decision is subjective and likely to include errors [12,13]. This error has been reported to account for most collision accidents [14,15]. There have been interesting reports to reduce these errors and build algorithms to determine quantitative collision risk. Tam and Bucknall [16] classified the type of collision risk encounters with obstacles as an area-based method to develop an evaluation method. Hasegawa et al. [17] and Namgung [18] divided the areas facing obstacles into six based on the relative bearing of the OS in order to build the algorithm. Yoo and Lee [19] numerically classified encounter situations based on the COLREGs to verify the environmental stress model, one of the collision risk indexes. Zhang et al. [20] classified encounter situations based on areas and angles to develop a collision avoidance decision-making system. However, it was discovered that the figures for the relative bearings used to distinguish the head-on and the crossing are different in each study.

Through a review of previous studies, we confirmed the flow of decision-making regarding collision avoidance by navigators. Here, the navigator’s decision is reported to be subjective and contains errors. Interesting contributions have been reported to compensate for the errors and help with safe navigation. The goal of these reports is to develop a decision-making system for collision avoidance that reduces errors. Although many results have been reported, there are still some drawbacks to existing methods for determining encounter situations:

(1)

COLREGs use somewhat ambiguous words to distinguish between encounters and do not provide figures for specific angles.

(2)

Various reports are numerically distinguishing encounters based on the COLREGs. However, we found that the COLREGs do not report specific figures and that the figures are applied differently for each study. As a result, there can be a significant difference in the encounters classified when performing actual collision avoidance.

(3)

The navigator who learns the regulations and operates the actual ship is a presence that includes errors. There have been few reports of how they judge encounter situations. It can affect collision avoidance behavior.

The purpose of this study is to model the results of the encounter situation recognition by the navigator who detected the risk of collision by the COLREGs. Our contribution is focused on modeling the human situation awareness results that distinguish between crossing and head-on. According to the rules of the COLREGs, the overtake could be determined using the angle of the stern light. To explain this process, human situation awareness results were collected in the presence of a collision risk. The variables required for the model were constructed using the collected data. Subsequently, a classifier model that predicts human situation awareness results was established, and its performance was verified.

The remainder of this paper is as follows. Section 2 defines the risks and situations of collisions and describes the interview scenarios, variable construction, and pre-processing processes used to collect data. Subsequently, we describe a methodology including constructing and evaluating a support vector machine to explain the relationship between the obtainable variables and the context-aware results in the face of a collision. Section 3 presents the analysis of the acquired data and the results of the estimated model. Section 4 discusses the study’s results, and Section 5 summarizes the results.

2. Materials and Methods

Figure 1 shows the flow of studies. To illustrate the proposed model, we define the risk of collision. The reason for defining the risk of collision is that if humans are judged at the risk of collision, situation awareness and information processing are carried out to avoid the collision. However, the risk of collision is a subjective emotion. Therefore, a figure called the collision risk index (CRI) was used to quantify the risk of collision. In general, it has been reported that there is a crisis of conflict if the CRI is above 0.5 [21]. Then, scenarios for obtaining the navigator’s situation recognition results from the defined risk of collision are constructed as a matrix. After that, a questionnaire was prepared based on the obtained scenario. Finally, data collection, pre-processing, model construction, and verification methods are described.

2.1. Rules of Collision Avoidance

Vessels shall comply with specific rules when carrying out collision avoidance. That is, the COLREGs. The regulations are divided into six categories from Part A to F and include 41 regulations. This chapter describes encounter situations and collision avoidance customs classified by the COLREGs:

• Head-on: This is the situation that shall be deemed to exist when a vessel sees the other ahead or nearly ahead. In this case, the vessels shall alter their course to starboard so that each shall pass on the port to port.
• Crossing: This is the situation that shall be deemed to exist when a vessel crosses the others. In this case, the vessel with the other on her own starboard side shall keep out of the way.
• Overtaking: This is the situation that shall be deemed to exist when a vessel shall be overtaking when coming up toward the other from a direction more than 22.5° abaft her beam. In this case, any vessel overtaking any other should keep out of the way of the vessel being overtaken.

Some reports numerically determine the three types of encounters. Table 1 is a table that summarizes the variables used to determine encounter situations in previous studies and their values. The definitions of terms used in Table 1 are as follows:

• The term “Relative Bearing” refers to the measurement of the azimuth between the heading of both ships clockwise from the heading of the OS to the heading of the TS [22].
• The term “Heading” refers to the direction in which a vessel is pointed at any given moment, expressed as the angular distance from 000 degrees clockwise through 360 degrees [22].
• The term “Encounter angle” refers to the angle measured by transposing the heading of the TS to the starting point of the heading vector of the OS [23].

Table 1. Variables and parameters used in the classification of encounter situations.

	Relative Bearing	Heading (OS)	Heading (TS)	Encounter Angle	Range of Head-on (°)
[16]	✓	✓	✓		337.5~022.5
[17]	✓	✓	✓	✓	348.75~011.25
[19]	✓	✓	✓		345~015
[20]	✓	✓	✓	✓	355~005
[18]	✓	✓	✓	✓	348.75~011.25

where the Range of Head-on refers to the area value determined as a Head-on situation if TS exists in the range based on the relative bearing of the OS.

Table 1. Variables and parameters used in the classification of encounter situations.

	Relative Bearing	Heading (OS)	Heading (TS)	Encounter Angle	Range of Head-on (°)
[16]	✓	✓	✓		337.5~022.5
[17]	✓	✓	✓	✓	348.75~011.25
[19]	✓	✓	✓		345~015
[20]	✓	✓	✓	✓	355~005
[18]	✓	✓	✓	✓	348.75~011.25

where the Range of Head-on refers to the area value determined as a Head-on situation if TS exists in the range based on the relative bearing of the OS.

The characteristic of the Tam and Bucknall [16] criterion is that the angle classified as the head-on is the largest, and a safe zone is set according to the angle of the meeting. Unlike other models, the Hasegawa et al. [17] model and Namgung [18] model are characterized by numerically distinguishing between overtaking and overtaken. In addition, the two models added the quarter-lee situation in the crossing situation. Zhang et al. [20] have the smallest angle classified as a head-on. By introducing the concept of safe distance, logic was added not to classify it as an encounter situation if there is no risk of collision. In this study aspect, the angle at which the relative bearing and OS look at the TS was used to determine encounter situations. The aspect is the relative bearing in which the TS looks at the OS. The aspect is positive if the OS is on the starboard side of the TS and vice versa.

2.2. Risk of Collision

This section describes the numerical calculation method for the risk of collision when two ships encounter each other. After that, the flow of the interview scenario to collect the results of the navigator’s situation perception is explained.

2.2.1. Collision Risk Index

In this study, an index was used to calculate the risk of collision. Several indicators have been reported for calculating the risk of collision, but we used the index reported in the study of Shaobo et al. [7]. It is because collision risk indexes reported in other studies define head-on and crossing using different values, and weights are applied accordingly. Therefore, it was judged inappropriate for our study. The parameters required for calculating indexes applied in our study are DCPA, TCPA, distance ($d$), relative bearing (${\psi }_r$), and speed ratio ($K$).

The variables of the two ships, OS and TS, are described to define the parameters encountered in the collision situation. The two ships in Figure 2 are assumed to move on the Earth-fixed coordinate system. Here, the coordinates of the OS are $P_o\left(x_o,y_o\right)$, the velocity is $V_o$, the course is ${\psi }_o$, the coordinates of the TS are $P_t\left(x_t,y_t\right)$, the velocity is $V_t$, and the course is ${\psi }_t$. Moreover, Az is the azimuth of the OS and TS. When the OS navigates in its course ${\psi }_o$, its relative velocity components are on the X axis, Y axis ($∆X,∆Y$), respectively, and its relationship with the TS is calculated as follows [24].

$$\begin{array}{c}∆X=V_t\mathit{sin}{\psi }_t-V_o\mathit{sin}{\psi }_o\\ ∆Y=V_t\mathit{cos}{\psi }_t-V_o\mathit{cos}{\psi }_o\end{array}$$

(1)

$$V_r=\sqrt{∆X^2+∆Y^2}$$

(2)

$${\psi }_r=\arctan \frac{∆X}{∆Y}$$

(3)

Here, $V_r$ means relative speed, and ${\psi }_r$ means relative direction.

When knowing the three parameters (OS’s coordinates converted into radians (${\phi }_o$, ${\lambda }_o$), distance to the TS ($d$), and bearing to the TS ($Az$)), the coordinates of the TS (${\phi }_t$, ${\lambda }_t$) were obtained using rhumb line calculation [25,26]. The latitude of the TS converted into radians (${\phi }_t$) is described in Equation (5), where the angular distance ($\varphi$) is calculated from Equation (4).

$$\varphi =d/R$$

(4)

$${\phi }_t={\phi }_o+\varphi ·\cos Az$$

(5)

The longitude of the TS converted into radians (${\lambda }_t$) is obtained by adding the longitudinal difference between the OS and the TS ($∆\lambda$). The calculation of $∆\lambda$ uses the projected latitude difference described in Equations (6) and (7). The constant $\delta$ is derived using the inverse Gudermannian function, which provides the height of the Mercator projection of a given latitude.

$$\delta =\mathit{ln}\left(\mathit{tan}(\pi /4+{\phi }_t/2\right)/\mathit{tan}(\pi /4+{\phi }_o/2\left)\right)$$

(6)

As for the projected latitude difference ($q$), different values were used when there was a latitude difference and when there was no latitude difference using the constant $\delta$. For the computations, $10e^{-12}$ was used as a number close to zero.

$${\phi }_t={\phi }_o+\varphi ·\cos Az$$

(7)

$$∆\lambda =\varphi ·\sin Az/q$$

(8)

The longitude of the TS converted into radians (${\lambda }_t$) is derived by adding a longitudinal difference to the ${\lambda }_o$.

$${\lambda }_t={\lambda }_o+\mathsf{\Delta }\lambda$$

(9)

where $R$ is the radius of the Earth (3440 nautical miles).

Using this variable, DCPA and TCPA, which navigators use as criteria for judgment during collision avoidance, are derived using Equations (10) and (11).

$$\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}=d\times \left|\sin ({\psi }_r-Az+\pi )\right|$$

(10)

$$\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}=d\times \cos ({\psi }_r-Az+\pi )/V_r$$

(11)

In the above process, parameters necessary for calculating the CRI were obtained. The CRI is calculated by converting the acquired parameters into utility functions. Equation (12) defines the crash risk indicators. It is calculated by multiplying each parameter’s function ($U\left(x\right)$) by weight. The figures in

Table 2. Weight values for utility function of CRI.

Weights	${\mathit{w}}_1$	${\mathit{w}}_2$	${\mathit{w}}_3$	${\mathit{w}}_4$	${\mathit{w}}_5$
	0.4	0.367	0.167	0.033	0.033

are the weights multiplied by the utility function. If the CRI is over 0.5, there is a risk of collision between the OS and TS, and the OS shall take appropriate action to avoid the collision.

$$\mathrm{C}\mathrm{R}\mathrm{I}=w_1\mathrm{U}\left(\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}\right)+w_2\mathrm{U}\left(\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right)+{\mathrm{w}}_3\mathrm{U}\left(d\right)+w_4\mathrm{U}\left({\psi }_r\right)+w_5\mathrm{U}\left(K\right)$$

(12)

Equation (13) describes a utility function ($\mathrm{U}\left(\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}\right)$) of the CRI related to the DCPA. This function converts the DCPA to a number between 0 and 1 based on the minimum passing distance ($d_s$) and the safe passing distance ($d_p$). Equation (14) describes calculating $d_s$ according to the relative bearing (${\psi }_r$).

$$\mathrm{U}\left(\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}\right)=\left\{\begin{array}{ll}1& \mathrm{DCPA}\le d_s\\ \sin \left[\frac{\pi }{d_p-d_s}\left(\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}-\frac{d_p+d_s}{2}\right)\right]& d_s<\mathrm{DCPA}\le d_p\\ 0& d_p\le \mathrm{DCPA}\end{array}\right.$$

(13)

Here, $d_p$ is twice $d_s$ [7].

$$d_s=\left\{\begin{array}{ll}1.1-\frac{{\psi }_r}{\pi }\times 0.2& 0\le {\psi }_r<\frac{5\pi }{8}\\ 1.0-\frac{{\psi }_r}{\pi }\times 0.4& \frac{5\pi }{8}\le {\psi }_r<\pi \\ 1.0-\frac{2\pi -{\psi }_r}{\pi }\times 0.4& \pi \le {\psi }_r<\frac{11\pi }{8}\\ 1.1-\frac{2\pi -{\psi }_r}{\pi }\times 0.4& \frac{11\pi }{8}\le {\psi }_r<2\pi \end{array}\right.$$

(14)

Equation (15) describes a utility function ($\mathrm{U}\left(\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right)$) of a CRI related to the TCPA. This function converts the TCPA under certain conditions.

$$\mathrm{U}\left(\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right)=\left\{\begin{array}{ll}1& 0\le \left|\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right|\le t_1\\ {\left(\frac{t_2-\left|\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right|}{t_2-t_1}\right)}^2& t_1<\left|TCPA\right|\le t_2\\ 0& t_2\le \left|\mathrm{T}\mathrm{C}\mathrm{P}\mathrm{A}\right|\end{array}\right.$$

(15)

Here, $t_1$ and $t_2$ are calculated as Equations (16) and (17).

$$t_1=\left\{\begin{array}{ll}\frac{\sqrt{d_s^2-\mathrm{D}\mathrm{C}\mathrm{P}{\mathrm{A}}^2}}{V_r}& \mathrm{DCPA}\le d_s\\ \frac{d_s-\mathrm{D}\mathrm{C}\mathrm{P}\mathrm{A}}{V_r}& \mathrm{DCPA}>d_s\end{array}\right.$$

(16)

$$t_2=\frac{\sqrt{d_p^2-\mathrm{D}\mathrm{C}\mathrm{P}{\mathrm{A}}^2}}{V_r}$$

(17)

Subsequently, the utility functions of the CRI related to the distance, direction, and speed ratio are calculated as Equations (18)–(20).

$$\mathrm{U}\left(d\right)=\left\{\begin{array}{ll}1& 0\le d\le d_s\\ \left(\frac{d_p-d}{d_p-d_s}\right)& d_s<d\le d_p\\ 0& d_p<d\end{array}\right.$$

(18)

$$\mathrm{U}\left({\psi }_r\right)=\frac{1}{2}\left[\cos \left({\psi }_r-\frac{19\pi }{180}\right)+\sqrt{\frac{440}{289}+{\cos }^2\left({\psi }_r-\frac{19\pi }{180}\right)}\right]-\frac{5}{17}$$

(19)

$$\mathrm{U}\left(K\right)={\left(1+\frac{2}{K\sqrt{K^2+1+2K\sin {\psi }_o}}\right)}^{-1}$$

(20)

2.2.2. Collision Scenario

In order to obtain data, it is necessary to develop a scenario with a risk of collision. To develop this scenario, we constructed the CRI values as matrices by entering numerical conditions to find situations where the risk of collision exists. The matrix’s horizontal axis used the TS’s relative bearing based on the OS. Here, the relative bearing was based on the head of the OS, with a value of −27 degrees to 27 degrees. Moreover, the longitudinal axis of the matrix was the aspect. Here, the aspect is the angle at which the TS looks at the OS, and a value from −25 degrees to 25 degrees was used. The scenario for the questionnaire was constructed by calculating the CRI of 0.5 or more at randomly designated values of the above two variables at regular intervals. The figures are reported in Table S1. The distance between the OS and the TS was set at 6 miles reported to commence the collision avoidance operation [27,28]. The collision risk matrix was constructed using the collision risk index described in Section 2.2.1. for three cases when the OS is faster than TS, the speed of the OS and TS are the same, and the OS is slower than the TS based on the relative bearing, aspect, and fixed distance of 6 miles.

2.3. Experimental Data Acquisition

In this section, a method for collecting data for model construction and a method for processing the collected data are described.

2.3.1. Surveying

In order to conduct the survey, the encounter scenario with a CRI of 0.5 or higher was constructed, which was considered at risk of collision. The survey was conducted using the constructed scenario as follows:

• Survey period: November 2022 to December 2022.
• Question: What kind of encounter situation (head-on, stand-on, give-away, safe situation) is considered in the given picture?
• Method: online.
• Interviewees: qualified navigators in practice.
• Figure 3 shows some of the questionnaires given to interviewees. In Figure 3, the OS is the center of the half-circle, and the TS is visualized as a red triangle.

2.3.2. Data Processing

The collected data were processed through a three-step procedure:

• Step 1 (merging variables and surveyed data): The data required for the experiment were constructed by combining the scenarios provided in the interview with the interviewers’ response results. The provided scenario is used as a predictor, and the response result is used as an outcome variable.
• Step 2 (variable construction): The relative orientation of the OS to the TS, aspect to the TS to the OS, and speed ratio were selected as explanatory variables. Moreover, the result variable was labeled as a categorical variable. The response result was labeled 0 for head-on, 1 for give-away, and 2 for stand-on. Finally, the data that responded as a safe situation were not used to build the model.
• Step 3 (data pre-processing): Processed data are pre-processed to suit model construction. It is crucial because pre-processing affects the model’s performance [29]. Each data point used in this study was divided into training, validation, and test data. First, the entire data are divided into training–validation data and test data. After that, the data are again divided into training and validation data. The division ratio is 7:3. Subsequently, the predictors were standardized. Standardization was performed using only the training data. At this time, the validation data and test data did not affect standardization.

2.4. Classification Model

The support vector machine model is formulated to estimate the relationship between the acquired predictor and the encounter situation resulting from the survey response. The model’s input is a variable obtained through the process described in Section 2.2.2. The output is a situation awareness result predicted using a trained model. The input and output data pairs were divided into training–validation data and test data. At this time, the division ratio of the data was 7:3. After that, the training–validation data were again divided into training data and validation data at the same rate. It is because the optimal hyperparameter is obtained using the grid search (yellow box of Figure 1). Finally, we constructed the final model using the optimal hyperparameters obtained through the grid search. In this section, a support vector model applied to the model is described, and the hyperparameters are described. Finally, the validation method for the model is described.

2.4.1. Support Vector Machine

The support vector machine is a model that finds hyperplanes that efficiently classify a given data [30]. Support vector machines have been reported to perform well in generalization because they aim to minimize training errors [31]. The method for selecting a hyperplane in a support vector machine is to find the hyperplane as the optimal solution, where the margin of the distance of the class data is maximized. The definitions of data input into the model are $D=\{\left(x_1,y_1\right),\left(x_2,y_2\right),\cdots \left(x_i,y_i\right),y_i\in \{-1,1\}$. The equation defining the hyperplane classifying classes according to the label is $w·x_i+b=0$. Here, $w$ is the gradient of the hyperplane, $x$ is the location of the data on the hyperplane, and $b$ is the bias. The separation hyperplane of the two classes of data is defined as $w·x_i+b\ge +1$ (for $y_i=+1$) and $w·x_i+b\le -1$(for $y_i=-1$). Equation (21) is derived by combining the two equations as constraint terms.

$$y_i\left(w·x_i+b\right)\ge 1$$

(21)

The data points on the separation hyperplane of each class are called support vectors. They are defined as $w·x_i+b=\pm 1$. The margin is the distance ($2/{‖w‖}_2$) between the two support vectors. The support vector machine model is guided to Equation (22), which minimizes the reciprocal of the distance, in that it is a model that maximizes the margin.

$$\mathit{max} Margin=\mathit{min}\frac{1}{2}{‖w‖}_2$$

(22)

Equations (21) and (22) are only available when they are entirely linearly separable. Therefore, Equations (23) and (24) are derived by adding terms that allow errors (${\xi }_i$).

$$\mathit{max} Margin=\mathrm{minimize}\frac{1}{2}{‖w‖}_2^2+C\sum _{i=1}^n{\xi }_i$$

(23)

$$y_i\left(w{·x}_i+b\right)\ge 1-{\xi }_i,i=\mathrm{1,2},\dots ,n$$

(24)

Here, ${\xi }_i$ is an error, and $C$ is a regulatory term that regulates the error. The lower the regulation, the more training errors are allowed so that underfitting can occur. In contrast, the higher the regulation, the more overfitting can occur because training errors are not allowed.

Kernel transformations that map predictors to higher dimensions are used to model boundaries that can be constructed non-linearly. The kernel includes linear, polynomial ($d^{th},d\ge 2$), and Gaussian kernel. Equations (25)–(27) define linear, polynomial, and Gaussian kernels.

$$K⟨x_1,x_2⟩=⟨x_1,x_2⟩$$

(25)

$$K⟨x_1,x_2⟩={\left(a⟨x_1,x_2⟩+b\right)}^d$$

(26)

$$K⟨x_1,x_2⟩=\exp \left(\frac{-{‖x_1-x_2‖}_2^2}{2{\sigma }^2}\right)$$

(27)

2.4.2. Hyperparameters

The classification model used in this study is linear, polynomial(2nd, 3rd), and Gaussian kernel support vector machine. Each model is designed to find an optimization model through the regulation of hyperparameters:

• Hyperparameters of the linear and polynomial models (2d, 3d): The value of regulation terms C has adjusted. C was 0.001, 0.01, 0.1, 1, 10, 100, and 1000.
• Hyperparameters of the Gaussian kernel model: The values of regulation terms C and gamma were adjusted. Gamma is a parameter that regulates the dispersion of the Gaussian kernel. C was adjusted to 0.001, 0.01, 0.1, 1, 10, and 100. Gamma was adjusted to auto, 0.001, 0.01, 0.1, 1, 10, and 100. Here, if gamma is set to auto, the reciprocal of the number of predictors is the input.
• Grid search: Grid search methods were used to find the optimal numerical value among adjustable hyperparameters efficiently. Grid search performs pre-learning for all cases for a group of hyperparameter candidates and derives optimal hyperparameters through cross-validation. Here, the test data should not be involved in the grid search. Therefore, the entire data were divided into three types of data: training, validation, and test.

2.4.3. Model Validation

Several metrics have been used to evaluate the performance of the built support vector machine models. It has been validated via the F1 score, and receiver operating characteristic (ROC) and area under the ROC curve (AUC) metrics. These metrics are calculated based on a confusion matrix [32]. It is a matrix of the predicted label values based on the true label. Figure 4a explains the confusion matrix of the binary classification. Here, precision is the probability that the result of the true label is positive when the result of the prediction label is positive. Precision does not guarantee the model’s reliability when the prediction results are negative. On the other hand, recall is the probability that the result of the predictive label is positive when the result of the true label is positive. Here, the recall does not provide information on predictions made when the true label is negative. In this study, a multi-classification model was used. Figure 4b describes the confusion matrix of multi-class classification. When evaluating multiple categories, metrics are calculated in two ways. One of those is macro-averaging. Using the example in Figure 4b, the precision and recall are calculated independently for each class as follows. The precision for classes 1, 2, and 3 is (2/7, 3/4, and 4/5), and the recall for classes 1, 2, and 3 is (5/5, 3/6, and 4/5), respectively. The precision and recall using macro-averaging are the sum average of each class value calculated independently, where the values are 0.61 and 0.77, respectively. Micro-averaging, on the other hand, is a method for calculating metrics using the overall positive and negative figures by developing a confusion matrix for each class and summing up the developed confusion matrix. Figure 5 describes developing a confusion matrix for each class using micro-averaging using the figures in Figure 4b. The precision and recall using micro-averaging are 0.75.

The F1 score is an evaluation metric considering the recall and precision, calculated as Equation (28).

$$\mathrm{F}1\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}=\frac{2\times Precision\times Recall}{Precision+Recall}$$

(28)

The ROC curve is an evaluation index built by combining the true positive rate (TPR) and the false positive rate (FPR). Here, the TPR is the same indicator as the recall. The FPR is calculated as $1-\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}$. Specificity is the probability that the prediction result is negative when the true label is negative. As opposed to the recall, this indicator does not provide information on predictions made when the true label is positive. The AUC with the TPR as the y-axis and the FPR as the x-axis is shown in Equation (29).

$$\mathrm{A}\mathrm{U}\mathrm{C}={\int }_0^{1}TPR\left(FP{R}^{-1}\left(x\right)\right)dx$$

(29)

Python 3.7 and libraries were used to build and validate the model [33,34,35,36].

3. Results

In this section, data acquisition and modeling results are reported.

3.1. Results of Data

In this section, the results of the construction of the collision risk matrix required for the survey and survey results are reported.

3.1.1. Calculation Results of Collision Risk Matrices

The situation in which there is a risk of collision was constructed as a matrix using the CRI. In constructing the matrix, the values reported in Section 2.2.1. were used. The matrix was constructed in three cases ($V_t<V_o$, $V_t=V_o$, and $V_t>V_o$). Figure 6 is a visualization of the constructed matrix as a heat map. In order to conduct interviews efficiently, we used some of the three scenarios as the final collision risk scenario.

3.1.2. Results of Data Acquisition

The predictors and outcome variables used in the model construction were acquired through data acquisition and pre-processing through surveys.

Interview data: Interviews were collected from 36 officers (12 chief officers, 19 2nd officers, and 5 3rd officers) and 4 captains. In particular, 4767 data points were collected.

Table 3. Data description and statistical metrics.

Variable	Type	Unit	Count	Mean	Std	Min	Max
$\mathrm{Relative}\mathrm{bearing}({\psi }_r$)	Continuous	Degree	4767	0.22	14.31	−27	27
Aspect	Continuous	Degree	4767	−0.03	11.98	−25	25
$\mathrm{Speed}\mathrm{rate}(K$)	Continuous	-	4767	1.00	0.17	0.75	1.25
Y	Categorical	-	4767	-	-	-	-

summarizes the characteristics and statistics of the variables used in the model. Figure 7 shows the distribution of predictors.

Table 4. Correlation matrix between the predictors.

	$\mathbf{Relative}\mathbf{Bearing}\left({\mathit{\psi }}_{\mathit{r}}\right)$	Aspect	$\mathbf{Speed}\mathbf{Rate}\left(\mathit{K}\right)$
Relative bearing (${\psi }_r$)	1
Aspect	−0.63	1
Speed rate ($K$)	0.04	−0.01	1

shows the correlation matrix between variables.

3.2. Classification Modeling

The classification model was constructed using the support vector machine model. In this section, the results of the model’s construction are described, and then the verification results are reported.

3.2.1. Estimation Results of the Classification Model

Each classification model was based on a support vector machine trained by adjusting the kernel and hyperparameters. Hyperparameters were searched based on a high F1 score. The adjusted hyperparameters were kernels, regulatory terms C, and gamma controlling the bias of the Gaussian distribution for the Gaussian kernels.

Table 5. Estimation of the optimal hyperparameters of the model.

Model	Kernel	C	Gamma	Acc.	Precision	Recall	F1 Score
					Macro	Macro	Macro	Micro
SVM	Linear	0.001	-	0.86	0.86	0.86	0.86	0.86
	Polynomial (2d)	10	-	0.62	0.61	0.63	0.61	0.62
	Polynomial (3d)	10	-	0.86	0.87	0.87	0.87	0.86
	Gaussian (RBF)	100	0.01	0.86	0.86	0.86	0.86	0.86

where, C is the regulation terms, gamma is the parameter that regulates the dispersion of the Gaussian kernel, and Acc. is the Accuracy.

shows the parameters of the optimized classification model. In learning, cross-validation was performed to prevent overfitting (5-fold).

3.2.2. Validation Results of the Model

The confusion matrix for each model is shown in

Table 6. Confusion matrices for high-performance SVM kernels.

Linear				Polynomial (2d)				Polynomial (3d)				Gaussian (RBF)
True	Predicted			True	Predicted			True	Predicted			True	Predicted
	0	1	2		0	1	2		0	1	2		0	1	2
0	320	35	21	0	343	20	13	0	335	20	21	0	302	41	33
1	43	366	0	1	49	243	117	1	47	362	0	1	33	376	0
2	70	0	337	2	81	174	152	2	74	0	333	2	60	0	347

where 0, 1, and 2 mean Head-on, Give-away, and Stand-on, respectively.

.

In addition, the AUC scores were calculated, and the ROC curves were obtained (Figure 8). The AUC scores obtained of models except the polynomial (2d) model were over 0.9.

The polynomial (3d) model obtained the highest accuracy and performance (F1 score) among the constructed models. In addition, it is not overfitted because it has a training score of 0.88. In addition, the ROC and AUC metric also secured a high performance of 0.9 or higher. Therefore, the polynomial (3d) model performed best among the compared models.

4. Discussion

This study used a support vector machine to build the encounter situation recognized by the navigator as a classification model. The main contribution of this study was to develop a model that predicts encounters recognized by navigators in situations with a risk of collision. This section describes the data, models, and results used in the study. As described in Section 2, three numerical predictors were applied: relative bearing, aspect, and speed ratio. As reported in previous studies, these variables can be obtained from the relative relationship between the OS and TS. This study shows a difference in that the distance between the OS and TS is designated as 6 miles, which is known to initiate collision avoidance action. The variables used in the model are data obtained from surveys based on scenarios estimated based on the CRI that there is a collision risk in the relative relationship between the OS and TS. The CRI figures are generally accepted as having a risk of collision [21]. Therefore, the question that answered that it was safe to a given question was not used to build the model. The survey was conducted on 40 navigators. However, we judged that model construction is sufficiently possible because there are 4767 data points used for model construction and verification.

For the model in this study to be used for situation prediction, a high-performance model must be built using the results of human situation awareness in situations with a risk of collision. As mentioned in Section 3.2, a model was established to label the results of situation recognition as head-on, give-away, and stand-on and predict the recognition results.

As a result of the results mentioned in Section 3.2.1 and the verification through the ROC and AUC metrics and confusion matrix in Section 3.2.2, the model proposed in this study obtained a high performance. In particular, it is inferred that the classifier’s performance is good, given that the ROC and AUC metrics score was 0.9 or higher [37].

Table 7. Example of prediction results of the proposed model and other methods.

Relative Bearing	Aspect	Proposed Model	Method 1	Method 2	Method 3	Method 4
0	0	Head-on	Head-on	Head-on	Head-on	Head-on
0	5	Head-on	Head-on	Head-on	Head-on	Head-on
0	10	Head-on	Head-on	Head-on	Head-on	Head-on
0	−3	Head-on	Head-on	Head-on	Head-on	Head-on
0	3	Head-on	Head-on	Head-on	Head-on	Head-on
0	7	Head-on	Head-on	Head-on	Head-on	Head-on
3	−13	Head-on	Head-on	Give-away	Head-on	Head-on
3	−8	Head-on	Head-on	Head-on	Head-on	Head-on
3	−3	Head-on	Head-on	Head-on	Head-on	Head-on
3	0	Head-on	Head-on	Head-on	Head-on	Head-on
5	−15	Give-away	Head-on	Give-away	Head-on	Give-away
5	−10	Head-on	Head-on	Give-away	Head-on	Give-away
5	−5	Head-on	Head-on	Head-on	Head-on	Give-away
5	0	Head-on	Head-on	Head-on	Head-on	Give-away
7	−17	Give-away	Head-on	Give-away	Head-on	Give-away
7	−7	Head-on	Head-on	Give-away	Head-on	Give-away
10	−20	Give-away	Head-on	Give-away	Head-on	Give-away
10	−10	Give-away	Head-on	Give-away	Head-on	Give-away
10	−5	Give-away	Head-on	Give-away	Head-on	Give-away
15	−15	Give-away	Head-on	Give-away	Give-away	Give-away
17	−12	Give-away	Head-on	Give-away	Give-away	Give-away
20	−25	Give-away	Head-on	Give-away	Give-away	Give-away
20	−20	Give-away	Head-on	Give-away	Give-away	Give-away
20	−15	Give-away	Head-on	Give-away	Give-away	Give-away
22	−17	Give-away	Head-on	Give-away	Give-away	Give-away
23	−13	Give-away	Head-on	Give-away	Give-away	Give-away

shows some examples of the results predicted using the polynomial (3d) model and the previous methods. In Table 7, the proposed model gives the prediction results of the polynomial (3d) model. Method 1 gives the criteria of Tam and Bucknall [16], Method 2 gives the criteria of Hasegawa et al. [17] and Namgung [18], Method 3 gives the criteria of Yoo and Lee [19], and Method 4 gives the criteria of Zhang et al. [20]. At this time, Method 1 classified most cases into a head-on situation. It is because the standard of classification is 22.5 degrees, which has the most extensive range. Meanwhile, there was a section in which the awareness results of the navigator were collected as a sample, and the reported methods were calculated differently. The reason is that humans contain errors and are influenced by situational awareness based on skills and technical knowledge, so these effects are presumed to have been reflected.

On the other hand, the limitations of this study are as follows. First, the data were collected through a survey. Surveys are reported in a non-experimental way in data collection. It also has the advantage of acquiring data relatively simply. However, errors in the collected survey data and problems with the representability of the population have been reported [38]. Second, the model built in this study is a model that predicts only situation recognition results. Therefore, it is not easy to analyze in detail the factors that affect the results of each explanatory variable. Third, situational awareness and decision-making are influenced by human skills, rules, and knowledge [39]. The effect of these three factors has yet to be specifically analyzed in this study. These have been discovered as challenges to be solved in future works.

5. Conclusions

The support vector machine was constructed to model the results of the navigator’s situation awareness in encounters considered at risk of collision. To build this model, a situation considered at risk of collision was defined, and an interview was conducted by constructing the defined situation as a scenario. Predictors were obtained from the interviews, and we trained a model for the navigator’s situation-aware prediction. The construction results showed that the proposed model could accurately predict the context-aware results. This study provides the results of modeling the results of the navigator’s recognition of the situation in the face of a collision. The resulting model is expected to be applied to future system development combined with collision avoidance algorithms. Finally, as reported in the discussion of this study, a future work is to report on the impact of human skills, skills, and knowledge in determining the human decision of encounter situations based on experiments using real-vessel or ship maneuvering simulation data.