Modeling of Ship Collision Risk Based on Cloud Model

Existing models for assessing ship collision risk involve complex calculations that complicate the simultaneous qualitative and quantitative analysis of the factors affecting ship navigation safety. Therefore, these models often exhibit slow generation of the risk index and evaluation results with reduced accuracy. To resolve these issues, we model the ship collision risk based on the cloud model theory. Specifically, we select “distance of closest point of approach (DCPA)” and “time to closest point of approach (TCPA)” as the main factors affecting the ship collision risk and analyze the data of DCPA, TCPA, and collision risk index (CRI) based on their cloud models. By combining these analyses with a double-condition-single-rule generator, we construct a cloud model for ship collision risk and finally develop a cloud model-based inference engine system to assess ship collision risk. This engine allows us to establish different ship collision risk analysis models according to the scenario encountered by the ship, which can be used to verify the feasibility of the proposed algorithm for ship collision risk modeling. Through comparisons with traditional ship collision risk models, the proposed ship collision risk model is found to be superior owing to its simple implementation, accurate results, and shorter time required to generate the risk model. The model established in this study enables the crew to determine the key objects to be avoided in case of potential collision with multiple ships. At last,analysis and research of cloud model ship collision risk based on global sensitivity and uncertainty are done to reduce the dimension of the risk parameters and show the main factors of unstable collision risk,therefore,the uncertain results in the calculation of the degree of danger are avoided, some reasonable suggestions are proposed for real navigation safety. the maritime pilot can make correct decisions promptly to reduce or avoid the occurrence of collision accidents.


I. INTRODUCTION
Fuzzy analysis, gray theory, comprehensive safety evaluation, and fuzzy comprehensive evaluation have been used extensively for safety assessment of ship navigation [1]- [3]. However, despite the many advances made in the field of ship navigation safety assessment, several issues are encountered during the assessment process [4]. Ship collision avoidance is a complex problem that requires a comprehensive analysis from many different perspectives. There are many influencing factors associated with ship collision risk as well as numerous indicators used in the system assessment of a ship collision risk model. Although traditional mathematical methods do The associate editor coordinating the review of this manuscript and approving it for publication was Xiwang Dong. account for the fuzziness of the relevant influencing factors, they fail to consider the randomness of these influencing factors and often rely excessively on subjective decisions made by humans during the evaluation process. Furthermore, considering the high complexity of the different factors affecting the safety of ship navigation, neither qualitative nor quantitative factors should be used alone to assess ship collision risk. When addressing problems with high uncertainty, the fuzzy comprehensive evaluation method is considered to be an oversimplification owing to the strong limitations of the algorithm itself. In contrast, the gray prediction model is very simple to implement, but it ignores the correlation among various factors [5] and relies heavily on historical data. Thus, the gray prediction model may also yield huge errors during risk assessment. In general, all the aforementioned methods have their own advantages and disadvantages for evaluating and analyzing the safety of ship navigation. However, these methods cannot combine qualitative and quantitative analyses of the factors affecting ship navigation safety, which reduces the accuracy of the evaluation results.
The cloud model theory, a method used for decisionmaking, was first proposed by Deyi Li, an academician at the Chinese Academy of Science, in 1995 [6]. The cloud model theory offers many novel strategies for solving more complex problems in the field of decision-making. It offers an elegant approach to combine the advantages of fuzzy mathematics and probability statistics while eliminating the traditional concepts of membership functions. In addition, the cloud model theory can adequately resolve the randomness of factors, which cannot be achieved in fuzzy comprehensive evaluation. In summary, the cloud model theory considers both the fuzziness and the randomness of targeting entities, which enables the combination and transformation of qualitative and quantitative descriptions [7]. Good quality must be ensured during the conversion process between the qualitative information and quantitative data to achieve a high degree of consistency between the subjective and objective assessments of the evaluation results.
The cloud model theory has been gradually applied to many aspects of society since its inception. First, under the influence of many intricate factors, the cloud model can enable conversion between the qualitative concepts and the quantitative data while simultaneously checking for loopholes in the traditional methods. Second, the cloud model resolves the data collection issue during the evaluation process. Specifically, by processing the data of a small sample in the cloud model based on stochastic simulation calculation, more accurate data support for the final evaluation results can be obtained. Finally, the evaluation method based on cloud model theory can transmit and retain the uncertainty present in the evaluation process. Additionally, because the number of calculations performed on cloud drops is directly proportional to the accuracy of the evaluation results obtained from the cloud model, the cloud model is superior to other methods for use in evaluation. Considering these merits, we propose a method to assess ship collision risk based on cloud model theory.

II. MULTI-CONDITION-SINGLE-RULE CLOUD GENERATOR AND ITS ALGORITHM
The cloud generator is the most important component for the cloud model-based inference as well as the model to realize conversion between quantitative values and qualitative concepts. There are three types of cloud generators; namely, forward, backward, and condition cloud generators. Condition cloud generators can be further divided into two categories: X-condition and Y-condition cloud generators. The multi-condition-single-rule generator is composed of multiple forward cloud generators and one backward cloud generator. Such a structure can be represented by ''If A 1 , A 2 , . . ., An, then B.'' According to the design requirements, two influencing factors are required for the inference in the model. Therefore, a double-condition-single-rule generator is described here. Fig. 1 shows the structure of the double-condition-single-rule generator comprising two forward cloud generators and one backward cloud generator. This can be represented by ''If A 1 and A 2 , then B.'' In the figure, (Ex A1 , En A1 , He A1 , Ex A2 , En A2 , He A2 ) represent the membership cloud eigenvalues of the two-dimensional qualitative concepts A 1 and A 2 , (Ex B , En B , He B ) are the membership cloud eigenvalues of the backward qualitative concept B, CG A is the X-condition cloud generator, and CG B is the Y-condition cloud generator. When the qualitative rule forward cloud generator CG A is stimulated by the inputs x A1 and x A2 , a random output (x A1 , x A2 , µ) will be generated and used as the input for CG B . Subsequently, a random cloud drop denoted as drop (x B , µ) will be generated by CG B .
In summary, the signal conversion process takes three input conditions and generates one output condition. The input conditions include the membership cloud eigenvalues (Ex A1 , Ex A2 , En A1 , En A2 , He A1 , He A2 ) and the quantitative value (x A1 , x A2 ) of the forward two-dimensional qualitative concepts A 1 and A 2 as well as the membership cloud eigenvalues (Ex B , En B , He B ) of the backward qualitative concept B. The output condition is the quantitative value x B of the backward qualitative concept that satisfies the degree of certainty µ [8].
1. Based on the input eigenvalue for the cloud drop, a random number En i is generated from the normal distribution with an expectation of En and a standard deviation of He: 2. Based on the input eigenvalue of the cloud drop, a random number En A2 is generated from the normal distribution with an expectation of En A2 and a standard deviation of He A2 : 3. The degree of certainty µ is calculated as follows: 4. Based on the input eigenvalue of the cloud drop, a random number En B is generated from the normal distribution with an expectation of En B and a standard deviation of He B : 5. If x A1 and x A2 each activate the rising edge of its corresponding cloud model, then the output value x B will also activate the rising edge of the cloud model B. This is expressed by the following equation: 6. If x A1 and x A2 each activate the falling edge of its corresponding cloud model, then the output value x B will also activate the falling edge of the cloud model B. This is expressed by the following equation: 7. If x A1 activates the rising edge of cloud model A 1 and generates a degree of certainty of µ 1 , While x A2 activates the falling edge of cloud model A 2 and generates a degree of certainty of µ 2 , then the output value x B will be related to both µ 1 and µ 2 , shown by the following equation: 8. If x A1 activates the rising edge of cloud model A 1 and generates a degree of certainty of µ 1 , While x A2 activates the falling edge of cloud model A 2 and generates a degree of certainty of µ 2 , then the output value x B will be related to both µ 1 and µ 2 , shown by the following equation: x B1 = Ex B + En B −2 ln µ 1 ,

III. CONSTRUCTION OF SHIP COLLISION RISK CLOUD MODEL
When a ship encounters multiple vessels in a complex marine environment, the maritime pilot must make a series of decisions instantaneously to determine whether the ship needs to avoid collisions, which ship should be the key collision avoidance target, and what is the correct operating sequence. However, owing to the uncertain and random nature of both the ship's navigation environment and human behavior, ship collision risk can vary with high uncertainty. Therefore, a two-dimensional mufti-rule cloud model is constructed based on distance of closest point of approach (DCPA) and time to the closest point of approach (TCPA) in this paper for determining the ship collision risk [9]. DCPA and TCPA can reflect the relative distance (d), azimuth (c), and speed ratio (k) of the two ships, which are commonly used in the calculation of ship collision risk [19]. DCPA is the distance of the closest point of approach between two vessels. In the relative motion radar, the size of the DCPA is the vertical dimension from the center of the circle to the relative movement line of the target ship, whose unit is the sea mile (n mile), in which the CAP is the closest point of the approach that represents the foot of a perpendicular [10]. The DCPA and TCPA models in Fig. 1 are built based on the known information, such as the location information, the navigation speed, and the heading. The implementation process of the DCPA and TCPA is shown in Fig. 2.
The process is as follows. Set own vessel at initial position (x 0 , y 0 ), speed V 0 , heading ϕ, and collision avoidance angle ϕ. Set the target ship at (x t , y t ), speed V t , and heading ϕ t . Subsequently, the following equations can be derived: 1) The heading cross angle of the target vessel and own ship is given by (9): 2) The components of the own vessel's speed in the x-axis and the y-axis directions are given by (10): 3) The components of the target vessel speed in the x-axis and the y-axis directions are given by (11): 4) The speeds at which the target vessel is moving in the x-axis and the y-axis directions of the own vessel is given by (12): 5) The size of the relative movement speed of the target vessel is given by (13): 6) The direction of the relative movement speed of the target vessel is given by (14): 7) The distance between the own vessel and the target vessel is given by (15): 8) The azimuth angle for the target vessel relative to the own vessel is given by (16): 9) The distance of the closest point of approach (DCPA) is as follows: 10) The time of closest point of approach (TCPA) is as follows: DCPA and TCPA are the main factors affecting the collision risk of cloud model ships, and TCPA is also determined by DCPA. Therefore, it can be stated that DCPA is the main sensitive factor and determines the magnitude of the collision risk.
The qualitative linguistic variables used to describe the ship collision risk can be transformed into quantitative knowledge expressed by the cloud object via the inference mechanism embedded in the cloud model. This quantitative knowledge can be further mapped to specific expressions by the preconstructed mufti-rule cloud generator. In other words, after processing the input variable by multiple forward cloud generators, a ship collision risk value will be output finally by the backward cloud generator. These mufti-rule cloud generators together form the inference engine system of the mufti-rule cloud model. By using the cloud model as the analysis tool, this inference engine can convert the qualitative concepts into quantitative values. In this study, two input variables are required for the cloud model of ship collision risk. However, different combinations of the two input variables would yield different ship collision risks. Therefore, we adapted the theories associated with the double-condition-multi-rule cloud generators and established the inference mechanism of the ship collision risk cloud model, as shown in Fig. 3. In the model, the DCPA is expressed by M , the TCPA is expressed by N , the collision risk index (CRI) is expressed by Q, CG-A represents the two-dimensional X-condition cloud generator associated with DCPA and TCPA with membership cloud eigenvalues of (Ex M , En M , He M , Ex N , En N , He N ), and CG-B represents the one-dimensional Y-condition cloud generator associated with CRI with membership cloud eigenvalues of Ex Q , En Q , He Q .
The input variables of the ship collision risk cloud model are DCPA M and TCPA N , whereas the output variable is the ship collision risk Q. After studying the ''rules,'' the thinking modes of the ship pilot, i.e., the concepts associated with natural language, will be classified by the cloud model based on the navigation density, closeness to the shore, and openness of the sea. These criteria are the three numeric input and output variables of the cloud model. Afterwards, we also classify the input and output variables of the CRI cloud model by using different concepts. Specifically, we construct m inference rules in the CRI cloud model and generate the uncertainty inference rule library. The collision risk inference mechanism of the CRI cloud model is given by where represents the inference mechanism of the cloud model, M and N are the input variables, and Q is the output variable. VOLUME 8, 2020 When a specific set of DCPA and TCPA (i.e., (M , N )) are input to the cloud model, the corresponding forward generators with different rules will be stimulated to yield a set of certainty values µ i randomly. These values will reflect the extent to which the relevant qualitative rules are activated. µ i will stimulate CG-B to generate a set of cloud drops drop (Q i , µ i ) randomly. These cloud drops indicate that the magnitude of the ship collision risk is Q i when the degree of certainty is µ i . Finally, these cloud drops will be merged together into a single cloud drop via geometric calculation as the output Q associated with this pair of (M , N ). This model reflects the relationship between the ship collision risk and DCPA as well as TCPA. It can accurately describe the uncertainty of the ship collision risk during the ship's navigation process. Therefore, under different potential collision conditions, the variation in the ship collision risk can be reflected by simply changing the heading parameters of our ship and the target ships input to the cloud model. This entire mechanism demonstrates the process of transferring the uncertainty from input variables to output variables and therefore enables the modeling of ship collision risk based on the uncertainty and fuzziness of cloud model theory.

IV. INFERENCE MODEL REALIZATION IN THE SHIP COLLISION RISK CLOUD MODEL A. CONCEPT CLASSIFICATION FOR PARAMETERS USED IN SHIP COLLISION RISK CLOUD MODEL
After examining the collision avoidance behavior and the international collision avoidance rules at sea, we classify DCPA, TCPA, and CRI into {small, relatively small, medium, relatively large, large} via natural language concepts according to the navigation density of the sea, as discussed in the literature [11], [12]. The subsets of the concepts associated with these three parameters are shown in Table 1. Assuming that the levels used to describe DCPA, TCPA, and CRI are N , M, and Q, respectively, the subsets of the aforementioned concepts and the numerical characteristics of the associated cloud models are as shown in Tables 2, 3, and 4. The cloud diagrams of the concepts associated with each parameter are shown in Figs. 4, 5, and 6.
Taking the concept of DCPA = M 3 (i.e., a medium DCPA) as an example, we first select all the data (i.e., the cloud drops) showing DCPA = M 3 in the cloud model database of DCPA to form the database of the thinking mode (i.e., natural language) of the ship pilot. Next, we determine the   number of data N (i = 1, 2, · · ·, N ) in the database with a medium DCPA and use the inverse cloud algorithm to calculate the cloud eigenvalues (Ex M 3 , En M 3 , He M 3 ) of concept M3 (medium DCPA) as (1.5, 0.25, 0.01). The concept of the membership cloud representing a medium DCPA is shown in Fig. 7. A DCPA of 1.5 n mile between the target ship and our ship is equivalent to the ''medium'' expectation by the ship pilot. The cloud models associated with other concept    sets can all be calculated using a similar method to the one discussed here.

B. ESTABLISHMENT OF RULE LIBRARY FOR SHIP COLLISION RISK CLOUD MODEL
The results are classified according to the concepts of the ship collision risk. The two input variables are DCPA and TCPA. The concepts associated with these two parameters are divided into five layers. Combining different layers of these two input variables yields 25 different qualitative rules associated with DCPA, TCPA, and CRI. These qualitative inference rules are presented in detail in Table 5. The shortest encounter time is medium or large, which will not affect the magnitude of the ship collision risk, in which case the collision risk is relatively small. In the calculation process of ship collision risk, TCPA can only affect the size of the ship collision risk if DCPA is less than a certain threshold. We use one example to clarify the CRI inference rule. The rule represented by ''if M 2 , N 2 , then Q 3 '' implies the following: if DCPA is ''relatively small'' and TCPA is ''relatively small,'' then CRI is ''medium.''

C. IMPLEMENTATION OF SHIP COLLISION RISK ASSESSMENT BASED ON THE CLOUD MODEL
The cloud model-based inference mechanism is established based on the concepts of DCPA, TCPA, and CRI. The qualitative concepts are obtained from the constructed ship collision risk database. The rule generators are constructed based on the X-condition and Y-condition cloud generators. These steps enable us to establish an inference rule library from the 25 qualitative rules discussed earlier. When a certain set of values is input to the model, the transitivity of the cloud model-based inference mechanism allows the uncertainty and fuzziness of the input variables to be transferred to the output variables. The cloud model-based inference diagram of ship collision risk is shown in Fig. 8.
Owing to the uncertainty involved in the inference process, the same set of data inputs may yield different outputs. As shown in Fig. 7, when given a set of precise input values (M , N ) for DCPA and TCPA, these input values can be used to activate the qualitative concepts of the corresponding forward cloud rule. An activation level of µ i corresponds to the clouds exhibiting the largest and the second largest degrees of certainty. Because we have two input variables, four clouds are generated during this process. Next, we calculate the joint degree of certainty based on these four clouds and select the largest and second largest joint degrees of certainty (µ 1 , µ 2 ). These values activate two qualitative rules and drive the backward cloud generators to produce four cloud drops. Next, we select the two outermost cloud drops, (Q 1 , µ 1 ) and (Q 2 , µ 2 ) , and calculate the ship collision risk Q via the geometric method. The expression for calculating the output Q is given by (20): The calculation process described above only yields a single calculation result. Because the cloud model-based inference process involves the generation of multiple random numbers, using the same input will yield a slightly different result for every new round of inference. This also represents the uncertainty of the cloud model. To resolve this, we can perform a finite number of iterative inferences in a practical calculation and use the average of the calculated results as the final CRI output for ship collision risk.

V. SIMULATION ANALYSIS OF SHIP COLLISION RISK BY THE CLOUD MODEL A. PROGRAM PERFORMANCE ANALYSIS
The actual scenario encountered by a ship is classified by the azimuth angle. Scenarios where multiple ships encounter each other in the sea can be classified into the following three circumstances by the ''rule'': head on situation, cross situation, and overtake situation. In a head on situation, the target ship is sailing toward our ship with an azimuth angle of 180 • . In a cross situation, the target ship is sailing toward our ship with an azimuth angle of 5 • to 112.5 • . In other words, the target ship is traveling on the left front side or the right front side of our ship. In an overtake situation, the target ship is sailing toward our ship with an azimuth angle in the range 112.5 • to 247.5 • , i.e., the target ship is following our ship from the rear with an angle exceeding 22.5 • [13], [14].
To validate the applicability of the program, different ship encounter scenarios are discussed in the following sections. Specifically, we simulate cases where the target ship encounters our ship at sea with the same navigation parameters but different azimuth angles B. The change in the ship collision risk is determined according to the output of the program. The navigation parameters of our ship and multiple target ships are given as follows. First, we assume that the velocities of our ship, ship No.1, ship No.2, ship No.3, and ship No.4 are 14, 7, 14, 21, and 28 kn, respectively. When analyzing the collision risks under different situations, the relationship between ship collision risk and distance is given by the following: (1) In a head on situation, the relationship between ship collision risk and distance is as shown in Table 6. Using the data shown in Table 6, we can plot the change in the ship collision risk as a function of the distance between the two ships with the relative distance D as the x-axis and the CRI as the y-axis, as shown in Fig. 9. (2) When the azimuth angle is 30 • , the change in the ship collision risk with increasing distance is as shown in Table 7.
Using the data shown in Table 7, we can plot the change in the ship collision risk as a function of the distance between the two ships with the relative distance D as the x-axis and the CRI as the y-axis, as shown in Fig. 10. (3) When the azimuth angle is 60 • , the change in the ship collision risk with increasing distance is as shown in Table 8. Using the data shown in Table 8, we can plot the change in the ship collision risk as a function of the distance between the two ships with the relative distance D as the x-axis and the CRI as the y-axis, as shown in Fig. 11. (4) When the azimuth angle is 330 • , the change in the ship collision risk with increasing distance as is shown in Table 9.
Using the data shown in Table 9, we can plot the change in the ship collision risk as a function of the distance between  the two ships with the relative distance D as the x-axis and the CRI as the y-axis, as shown in Table 10. Based on the above four data sets, we plotted the variation in the ship collision risk for varying inter-ship distances; the x-axis denotes the relative distance D, and the y-axis denotes the CRI under different encounter situations. From the ship collision risk model established based on the cloud model theory in this paper, we can infer that (1) the CRI model developed in this study can reflect the real situation where multiple ships encounter each other at sea. The model can also VOLUME 8, 2020 demonstrate the risk level of our ship with respect to different target ships; (2) when two ships are sailing with a constant relative distance D and azimuth angle B, the ship collision risk increases with the velocity of the target ship. This trend is in accordance with the actual navigation characteristic at sea. Therefore, the results confirm that the ship collision risk model developed in this study is applicable. In addition, the proposed model also provides a priority sequence of the target ships as well as the key target ship to be avoided during the navigation. This information will allow the pilot to make accurate collision avoidance decisions promptly.

B. SIMULATION RESULTS AND COMPARATIVE ANALYSIS
Case I: Assume that our ship is traveling with a velocity of c t = 240 • V = 10 kn and a course of C 0 = 0 • . Further, assume that the total number of target ships is five. A multiship encounter scenario is subsequently established in this case study that includes the velocity V , azimuth angle B, course angle C, and the relative distance with our ship D for all the target ships. The detailed modeling process and results are shown in Fig. 12. The traditional mathematical algorithm introduced in the previous section was also used to calculate the value of the ship collision risk. The results are summarized in Table 11. The values calculated by the traditional methods are used here as reference for the comparative analysis [15].  Because the collision risks of the simulated ships in this group are all smaller than the ship collision risk threshold of 0.6, but remain at the medium level, the pilot should remain cautious and be alert for potential dangers.
For the target ship with DCPA of 2.05 and TCPA of 17.17, the collision risk is 0.5613. For the target ship with DCPA of 3.21 and TCPA of 7.38 the collision risk is 0.5166, which is lower. As the DCPA plays an important role in the collision risk index, the distance between the two vessels puts them in a dangerous situation. Collision will occur with the own vessel when the DCPA is less than the safe distance, and the TCPA is used to express the urgency degree of the two vessels; therefore, the TCPA determines whether or not a collision risk exists when the DCPA is unchanged.
Two sets of multi-ship encountering scenarios were established in this study. We modeled and calculated the ship collision risk for each scenario using the cloud model theory and compared the results with the values obtained using the traditional mathematical models.
Case II: Assume that our ship is traveling with a velocity of c t = 240 • = 14 kn and a course of C 0 = 60 • . Assume that the total number of target ships is five. A multiship encountering scenario is subsequently established in this case study that includes velocity V , azimuth angle B, course angle C, and relative distance with our ship D for all the target ships. The detailed modeling process and results are shown in Table 12. The traditional mathematical algorithm introduced in the previous section was also used to calculate the ship collision risk. The results are summarized in Table 13. The values calculated by the fuzzy methods are used as reference for the comparative analysis. Table 12 also indicates that the results obtained using the cloud model theory are extremely close to the values calculated using the traditional mathematical methods. The order of ship collision risk of the five target ships calculated using the traditional mathematical method is CRI 1 < CRI 2 < CRI 3 < CRI 4 < CRI 5. However, the ship collision risks of the five target ships calculated based on the cloud model theory are 0.5025, 0.5448, 0.5473, 0.7447, and 0.7343; further, the order of ship collision risk follows CRI 1 < CRI 2 < CRI 3 < CRI 5 < CRI 4. Table 10 indicates that the  The comparison of the above two groups demonstrate that the results calculated based on the cloud model theory are extremely close to those calculated using the fuzzy mathematical method. Because the calculation process of the cloud model theory involves the generation of multiple random numbers, the fuzziness and uncertain nature of the input data are preserved during the calculation process and well transmitted to the output data. Repeating the calculation with a finite number of cycles and estimating the average value can improve the accuracy of the data. Therefore, the cloud model theory-based method can replace the fuzzy mathematical algorithm as it exhibits better accuracy.
In other words, the algorithm relies too heavily on the subjective decision of human beings that prevents using the results calculated using the traditional mathematical algorithm in a real scenario. Because the cloud model theory exhibits a certain level of randomness and fuzziness, it conforms to the human mindset and is easy to comprehend. After the qualitative and quantitative processing of the data based on the cloud model, a set of precise values can be input to the model to activate the largest and second largest degrees of certainty. The virtual cloud is then generated using the geometric relationship. Finally, the calculation process can be repeated for a finite number of cycles and the average output value can be used as the final CRI result. Because the value is calculated on the basis of the uncertainty transmission, the proposed method can more accurately reflect the collision risk when encountering other ships. Therefore, the results calculated based on the cloud model theory is more consistent with the actual scenario.
Because the ship collision risk model established based on the cloud model theory can calculate the exact value of ship collision risk, it is suitable for determining both the ship collision risk when the two ships meet and the priority sequence of the target ships to be avoided when multiple ships encounter each other. Because considering too many factors will yield logic issues, the uncertainty and fuzziness are incorporated in the model solely considering the two influencing factors including DCPA and TCPA. This strategy leads to a clear logic, light computation task, high calculation speed, and high accuracy of the proposed method.

VI. ANALYSIS AND RESEARCH OF SHIP COLLISION RISK BASED ON GLOBAL SENSITIVITY AND UNCERTAINTY
The establishment of ship collision risk is a crucial prerequisite for intelligent ship collision avoidance. To improve the effectiveness and superiority of the model, sensitivity analysis and uncertainty analysis are applied to the key links of ship collision prediction and avoidance. This can improve the accuracy and reliability of the calculation model of ship collision risk based on model of cloud, providing reasonable theoretical guidance for ship navigation safety in the future [16].

A. GLOBAL SENSITIVITY ANALYSIS OF SHIP COLLISION RISK BASED ON MORRIS SCREENING METHOD
Morris screening method is a widely used global sensitivity analysis method and belongs to the one-time one-variable method [17]. Specifically, a variable in the model is selected while the other parameters are fixed; Then, the variable randomly changes within its value range; Next, the value of the objective function is obtained by entering the variable and run the model; afterward, the influence value is used to judge the degree of influence of the parameter change on the output value. The process of global sensitivity analysis of the overall ship collision risk is described as follows. First, the various factors affecting the risk of ship collision and the parameter value range corresponding to each factor are determined; second, select any factor and divide the range of disturbance within its value range, such as 2 changes: +5% and −5%, respectively; on this basis, the corresponding value of the parameter is input into the model to obtain the corresponding model output value (the value of the collision risk (CRI) of the ship at this time); next, the parameter value after the disturbance change is input into the model calculation again to obtain the model output value result under the disturbance; afterward, the calculation of the sensitivity to the hazard of ship collision when the parameter changes is completed using the given calculation formula; then, the single parameter sensitivity calculation has been completed. Next, whether all the analysis processes of the required parameters are completed under the expected conditions is considered. If it is not completed, return to the foregoing process and re-use the same method to calculate the sensitivity of different parameters until all required parameters are calculated. Finally, theoretical analysis of the results is performed, such as the numerical division of the degree of influence of the judgment and the sensitivity ranking of different parameters. VOLUME 8, 2020 Global sensitivity analysis of ship collision risk is performed based on the Morris screening method for quantifiable and input able parameters. Five factors, DCPA, TCPA, the relative distance between the two ships D, the relative azimuth B, and the ship speed ratio K (the speed ratio of the target ship to our ship), are selected as the research objects. Combined with the established cloud model for calculating the collision risk of ships, the basic Morris screening method is used as a research method to identify the degree of influence of various parameters on the collision risk of ships.
The position of our ship is taken as the origin of the coordinate system, which is the reference position. The speed V of our ship is initially set to 10kn, and the heading angle C 0 of our ship is set to 0 • ; then, set the number of target ships and the motion parameters of the target ship: target ship speed V, azimuth angle B, heading angle C, and the distance D between own ship and target ship. Afterward, these parameters are input into the calculation model to acquire the output value. After changing the input parameters, the value of the ship collision risk after the change is obtained. The output results of case 1 are presented in Table . The corresponding curves of the data in the above table are exhibited in figures13. Among them, the abscissa is the degree of change of the variable; the change of different parameters reflects the different degree of change in the numerical calculation results of the ship collision risk. The abscissa is the degree of change of the variable; for example, 1 denotes +20%, 3 represents the reference value 0%, and 4 refers to -10%.
It is worth noting that the slope of the curve in the figure does not directly correspond to the rate of change of ship collision risk while it is obtained after dividing by the product of the reference parameter value and the percentage of change. The benchmark values of the five parameters are 1.000, 3.496, 10, 20, and 1, respectively, and each change of the parameter is 10%. Finally, through the calculation of the average rate of change of its various parameters, the values corresponding to the five parameters are 0.301, 0.145, 0.072, 0.040, 0.034. Therefore, the different sensitivity results With the help of cloud model related algorithms, a complete cloud model reasoning system is established. On this basis, the global sensitivity analysis by Morris screening method is used to obtain the sensitivity ranking corresponding to various influencing factors. This analysis result can be used to improve the cloud model establishment process to improve the emphasis of the cloud model on parameter variables.

C. UNCERTAINTY ANALYSIS OF SHIP COLLISION RISK BASED ON INFORMATION ENTROPY THEORY
Under the constraints of different ship environments and encounter situations, the uncertainty of specific conditions is expressed by transforming qualitative concepts into quantitative values based on the theoretical basis of information entropy. It provides a ready-made scientific foundation for the selection of collision avoidance decisions in the future navigation field. The choice of ship avoidance method is affected by the environment and the actor, and the concept of ''entropy'' can be used for quantitative analysis and research [18].
When analyzing ship avoidance actions, it is assumed that all possible states in the decision of ship avoidance actions are X = {X1, X2, X3, . . . , Xn}, and the corresponding probability of each state is p = {p1, p2, p3....pn}. Then, the corresponding relationship S of the information structure of the target ship can be obtained as: In the process of ship avoidance action, the uncertainty can be expressed by the value of the average amount of information ''entropy (E).'' The greater the calculated entropy value, the greater the uncertainty represented, and the greater the randomness of the choice of avoidance action. Studying the uncertainty of collision avoidance behavior is helpful for direct ships to understand the uncertainties of multiple collision avoidance behaviors when two ships are at different distances, different DCPA and TCPA. Therefore, collision avoidance actions can be taken calmly to avoid various collision accidents. The encounter situation in the confrontation situation is selected, and different action distance settings are set based on it, helping us understand the entropy value of the encounter in various situations and obtain scientific and reasonable analysis results. The entropy values corresponding to the various types of situation and distance encountered are listed as follows, as well as the different types of ship avoidance methods. Encounter situation: straight ahead, cross at a small angle ahead, cross straight, near the cross, chasing, and being chased; Action distance taken: 4-3, 3-2, 2-1, 1-0(n mile); The modes of ship avoidance actions are: turn left, turn right, slow down, turn left to slow down, turn right to slow down, and keep speed and direction. In the above statistical results, the avoidance method when the distance of action taken is about 2 n mile is selected separately, and the selection probability is provided as following.
Statistics obtained by the above form, corresponding to the same kind of encounter situation, different ways of collision avoidance makes the final calculation of the selection of probability entropy results vary, reflecting the different between the driver for the uncertainty of collision avoidance mode selection, high uncertainty, as a result of human factors we should take various measures to try to reduce or even avoid, so as to ensure the safety of ship sailing has higher degrees.
The selection probability of various collision avoidance modes is different at different operating distances. The relevant data of the incoming ship on the left side and the incoming ship on the right side are shown in the tables below. The entropy data is not completely symmetrical and has certain  deviation. We can compare the data of incoming ships on both sides.
The change rule of entropy value can be clearly observed, and the avoidance characteristics of different situations can be summarized accordingly, as well as the reasons for the difference of uncertainty. The curves are shown in Figure 14 below. The abscissa is divided into five values: 1, 2, 3, 4, and 5; they represent the distance between ships as 4-3 n mile, 3-2 n mile, 2-1 n mile, 1-0 n mile, and the mean entropy of different action distances in the same encounter situation, respectively; the ordinate represents the results of different entropy values. In the figures, different signs are used to distinguish different encounter situations.
It can be observed through the above analysis that in most cases, the decrease in the distance brings about an increase in entropy, reflecting the increase in the uncertainty of collision risk at different distances. Second, under different encounter situations, the uncertainties reflected by the entropy results are different from each other. For example, the front curve is quite different from other curves when the ship arrives on the left. Overall, there is less uncertainty in the encounter time directly ahead; the degree of uncertainty is roughly the same in other cases; the average uncertainty when the ship comes on the right is greater; the entropy value is higher; the curve is denser. Finally, in most cases, the degree of uncertainty increases as the distance decreases. This is because when the distance between ships is large, the ship's pilot is calmer about the situation. The selection of avoidance methods can be conducted according to the elements such as "Rules", and the decrease in the distance makes the driver's judgment and choice add more human factors. The short decision time brings about an increase in the possibility of avoiding options, leading to an increase in entropy. Nevertheless, the entropy value decreases when it approaches 1 n mile. According to the understanding of actual navigation conditions, when the ship is very close, the singularity of the situation results in the singularity of the driver's choice of avoidance methods, allowing most people to choose the same avoidance method, reducing the entropy value.
It can be observed through the above analysis that in most cases, the decrease in the distance brings about an increase in entropy, reflecting the increase in the uncertainty of collision risk at different distances. Second, under different encounter situations, the uncertainties reflected by the entropy results are different from each other. For example, the front curve is quite different from other curves when the ship arrives on the left. Overall, there is less uncertainty in the encounter time directly ahead; the degree of uncertainty is roughly the same in other cases; the average uncertainty when the ship comes on the right is greater; the entropy value is higher; the curve is denser. Finally, in most cases, the degree of uncertainty increases as the distance decreases. This is because when the distance between ships is large, the ship's pilot is calmer about the situation. The selection of avoidance methods can be conducted according to the elements such as "Rules", and the decrease in the distance makes the driver's judgment and choice add more human factors. The short decision time brings about an increase in the possibility of avoiding options, leading to an increase in entropy. Nevertheless, the entropy value decreases when it approaches 1 n mile. According to the understanding of actual navigation conditions, when the ship is very close, the singularity of the situation results in the singularity of the driver's choice of avoidance methods, allowing most people to choose the same avoidance method, reducing the entropy value.
Considering from the perspective of the uncertainty of avoidance actions, the workers should observe various information between ships and make scientific judgments as soon as possible, and then propose reasonable collision avoidance measures. This is the key to preventing or avoiding ship collision accidents and the best way to ensure the safety of people and property.

VII. CONCLUSION
In this paper, we combined the fuzziness and uncertainty feature of a cloud model to establish a ship collision risk model based on the cloud model theory. This model can provide a ship collision risk order when multiple ships are present at sea, which reduces the time required to determine the key ships to avoid during navigation as well as the collision avoidance sequence.
Sensitivity and uncertainty analysis for ship collision risk cloud model is progammed. It can reflect the importance of its influencing parameters, the emphasis on different parameters, and the advantages of the established cloud model in variable selection. Based on the content of the "Rules", the uncertain results in the calculation of the degree of danger are avoided, and some reasonable suggestions for real navigation safety are proposed.
Therefore, the proposed method can alleviate or prevent potential accidents from the source by helping the pilot of the ship make correct decisions promptly. The proposed design will effectively improve the ship collision avoidance system, reduce ship collision accidents caused by human factors, and further promote the development of a more intelligent and automated ship collision avoidance system. However, the errors of DCPA and TCPA are not currently considered in the cloud model, which decreases the accuracy of the collision risk. In further work, we will solve this problem. Furthermore, the simulation is a study of the risk analysis of ship collision under the condition of one encounter with multiple ships. However, after the ship completes a risk analysis of collision avoidance and takes the collision avoidance action, a new risk situation will be generated based on the action. Therefore, in the process of collision risk analysis, all risks should be predicted to obtain a total risk assessment. Therefore, it should involve the selection of all ship collision avoidance actions, on the basis of which the overall risk assessment is completed. This will be dealt with in follow-up research.