Abstract
With increased cross-border shipping, ships’ traffic flow in various port waters also significantly increases. This will in turn increase the numbers of ship collisions. The traditional research methods for ship collision risk are mostly based on statistical analysis or empirical models. These methods have certain limitations when dealing with complex and ever-changing port water environments. To address these issues, a risk predicting model for port waters based on grey relational analysis and backpropagation neural network was proposed. The study first used fuzzy grey correlation to analyse collision risk data, and then combined it with backpropagation neural network to enhance predicting efficiency, and constructed a risk prediction model. In the results, the relative error and root mean square error of this predicting means in the data processing process were 0.26% and 80.62%, respectively. The fitness value and data analysis accuracy of this model were 0.92 and 93.29%, respectively. These indicators were obviously better than other methods. This confirms that this model has higher accuracy and stability. It can provide a scientific and reasonable decision-making basis for port management departments, thereby reducing the occurrence of ship collision accidents.
1. Introduction
As global trade continues to grow, the flow of ship traffic in port waters continues to rise, leading to an increase in ship collision risk (SCR). Ship collisions not only cause huge economic losses but may also threaten the safety of crew members and the marine environment. Therefore, accurate evaluation and prediction of SCR in port waters is a problem that needs to be addressed in the shipping industry [1−2]. Due to the current use of a single prediction model for predicting water traffic accidents, there are certain limitations, and existing SCR assessment techniques lack modelling of nonlinear and dynamic relationships, resulting in poor accuracy of assessment [3]. Therefore, a port water SCR prediction model based on grey relational analysis (GRA) and back propagation neural network (BPNN) was proposed in this study. GRA cannot effectively handle nonlinear problems in collision risk prediction and is also influenced by subjective factors [4−5]. Therefore, the study utilized fuzzification to optimize GRA and constructed a collision risk prediction model using BPNN after being optimized [6−7]. A model that combines two methods can not only avoid local optima but also improve the training efficiency and risk predicting accuracy by utilizing the setting of initial weights in incomplete information. This study aims to integrate the advantages of GRA and BPNN to construct a more efficient and accurate SCR assessment model for port waters. The innovation of the research lies in the use of fuzzification to optimize the GRA algorithm, and in order to further improve the performance of the prediction model, entropy weights are added to the model. This model can comprehensively consider dynamic environmental factors, extract effective information from each individual prediction model and fill the gap of existing SCR assessment techniques in port waters that cannot comprehensively consider the characteristics of water traffic systems and the influencing factors of water traffic accidents.
The following sections are arranged as follows. Section 3 incorporates the concept of fuzzification in the processing of ship collision data in port waters using GRA to obtain fuzzy membership relationships. After obtaining collision data processing results, Section 3 integrates GRA and BPNN to construct a port water area SCR prediction model. Section 4 verifies the predictive and avoidance performance of the SCR prediction model through simulation experiments. Section 5 summarizes the results and analyses the advantages and disadvantages of these research methods used.
2. Related work
With the development of maritime transportation, the traffic volume of ships in port waters is constantly increasing, and SCR in port waters has become an increasingly prominent problem. To effectively predict and reduce SCR, many scholars have conducted relevant research. Shi et al. [8] proposed a fuzzy logic modelling method for regional multi-ship collision risk assessment based on considering the influence of ship intersection angle and navigation environment to study the impact of ship intersection angle on SCR. This method used fuzzy logic to fuzzify factors, such as Distance of Closest Point of Approach (DCPA) and Time to Closest Point of Approach (TCPA), when multiple ships encountered each other. Then an analytical hierarchy process was used to obtain weights for collisions between ships, thereby obtaining the collision risk value. This method achieved multi-SCR early warning within the region. Jenkin et al. [9] aimed to improve their collision risk prediction ability. A comparative verification was conducted using GPS satellite and Beidou satellite systems. This study utilized the initial semi-major axis range and position evaluation of the disposal track to determine the collision probability. When the initial eccentricity was 0.0003, the available initial SMA range was 363 km. When the initial eccentricity was 0.001, its range was only 3 km, covering the worst-case scenario of eccentricity growth. Ha et al. [10] proposed a method based on ship domain and nearest point to evaluate SCR to avoid ship collisions. Due to the limitations of quantitative calculation that can affect collision risk calculation, this study combined collision risk and nearest point calculation methods for quantitative calculation. This method was suitable for various examples in simulation experiments and effectively quantitatively analysed ship collisions. Zhen et al. [11] proposed a regional SCR evaluation method based on encountering ship clusters and aggregation density to improve the SCR evaluation of restricted water areas with multiple ships. Ship clusters and cluster density, as important indicators, could reflect the distribution of ships and the likelihood of collisions, thereby improving the accuracy and reliability of predictions. This method could quantify collision risk's spatiotemporal distribution.
Zheng et al. [12] proposed an interactive multi-criteria decision-making method to apply grey correlation coefficients to different weight assignments in their research. This method used profit loss and favourability advantage to rank decision options for weight allocation. This method significantly improved the determinacy and correlation of complex problems. Liu et al. [13] proposed a spatial modelling and analysing means for ship encounters in the spatial domain using a geographic information system and other technologies to effectively study intelligent navigation. Firstly, this study utilized various collected parameters to establish ships’ dynamic spatiotemporal model. Then, a spatiotemporal model was used to determine whether a ship was encountered. If there was an encounter, spatial analysis could be provided. This method significantly reduced spatial ambiguity when encountering risks, greatly improving the accuracy and superiority of predictions [13]. To effectively analyse the factors that cause ship collision accidents, Lang et al. [14] extracted 98 causes from 300 ship collision accidents and constructed a network of accident causes and causal triggering chains. This network contained six hidden root causes. By fully considering these six reasons, the causal relationship between them and ship collision accidents was analysed. This network significantly improved the prediction ability of collision accidents, greatly reducing the occurrence of collision accidents.
In summary, applying artificial intelligence methods such as machine learning to predict port SCR has significant research value in preventing ship collision accidents. However, previous studies often lacked comprehensive consideration of various environmental factors, which was insufficient to comprehensively evaluate collision risks. Therefore, the study aims to construct a more efficient and accurate risk assessment model for ship collisions in port waters by effectively combining GRA with neural networks. The research aims to establish an SCR prediction model that can comprehensively consider environmental factors and provide scientific decision-making support for ship drivers and port management departments, thereby reducing SCR and ensuring the safety and smoothness of port waters.
3. Port ship collision risk prediction combining GRA and BPNN
To effectively prevent and reduce ship collisions, a new port SCR prediction model is constructed by combining GRA and BPNN. By fully leveraging the advantages of GRA in handling uncertainty and incomplete information and the ability of BPNN in nonlinear mapping and adaptive learning, accurate prediction of port SCR can be achieved.
3.1. Ship port collision risk analysis based on fuzzy GRA
The International Regulations for Preventing Collisions at Sea aims to regulate how ships can avoid collisions when travelling and encountering intersections at sea and to establish codes of conduct for ships in different situations and how to respond in case of distress. But as the number of ships increases, the navigation environment becomes more complex, posing challenges for ship collision avoidance and increasing the risk of collision accidents. Therefore, the study will build a collision risk prediction model for port ships to prevent ship collision accidents and ensure the safe navigation of ships. The risk analysing of ship port collision is an important research content for shipping safety. Due to various factors affecting the occurrence of ship port collision accidents, and the complex relationship between these factors, this study applies GRA to the risk analysis of ship collision in ports. There are many risk factors that can cause ship collisions in port waters. To determine the primary and secondary relationships between ship collision factors in port waters, this study compares the correlation values between collision risk and influencing factors using GRA [15, 16]. When the correlation value is high, it indicates that this factor is the main factor causing collisions. When the correlation value is low, it is a secondary factor. The study utilizes GRA to analyse the values between eight predetermined factors and the impact of collision risk. Firstly, the comparison sequence for comparing the eight factors used for analysis is determined. Then, the sample data are processed using the mean method. The grey correlation coefficient value can be calculated again, and the correlation degree value can be finally calculated through the above three steps. The mean method is represented by Equation (1) for processing sample data.
where k represents a certain moment in the sequence of the sample data, and i represents the number of items in the sequence. The value of the grey correlation coefficient can be calculated by Equation (2).
In Equation (2), ∆(min) represents the two-level minimum value in the sample data, ρ represents the resolution coefficient value, ∆(max) represents the maximum value of two levels in the sample data and |${{\Delta }_{0i}}(k)$| represents the relationship value of time in the sample data. The correlation value can be represented by Equation (3).
In Equation (3), ri represents the correlation, and ri approaching 1 indicates a better correlation between the two. Based on the above analysis, this study takes the speed, distance, encounter angle and weight of ships in the port, as well as the visibility, wind level, wave level and ship density of the port, as the main factors for research. These factors cover the characteristics of the ship itself, environmental factors and the condition of other ships, which are of great significance for evaluating the risk of ship collisions in port waters. Therefore, selecting these factors as the main factors helps to establish a comprehensive collision risk assessment model. SCR values are used as reference sequences, and eight influencing factors are used as comparison sequences. Table 1 shows the correlation between collision risk and influencing factors.
Correlation values between collision risk and influencing factors.
| Project | Ship speed | Ship distance | Ship encounter angle | Ship weight | Port visibility | Port wind power | Port wave | Port vessel density |
|---|---|---|---|---|---|---|---|---|
| Collision risk | 0.895 | 0.916 | 0.758 | 0.771 | 0.796 | 0.718 | 0.725 | 0.812 |
| Project | Ship speed | Ship distance | Ship encounter angle | Ship weight | Port visibility | Port wind power | Port wave | Port vessel density |
|---|---|---|---|---|---|---|---|---|
| Collision risk | 0.895 | 0.916 | 0.758 | 0.771 | 0.796 | 0.718 | 0.725 | 0.812 |
Correlation values between collision risk and influencing factors.
| Project | Ship speed | Ship distance | Ship encounter angle | Ship weight | Port visibility | Port wind power | Port wave | Port vessel density |
|---|---|---|---|---|---|---|---|---|
| Collision risk | 0.895 | 0.916 | 0.758 | 0.771 | 0.796 | 0.718 | 0.725 | 0.812 |
| Project | Ship speed | Ship distance | Ship encounter angle | Ship weight | Port visibility | Port wind power | Port wave | Port vessel density |
|---|---|---|---|---|---|---|---|---|
| Collision risk | 0.895 | 0.916 | 0.758 | 0.771 | 0.796 | 0.718 | 0.725 | 0.812 |
In Table 1, ship speed and distance affect collision risk greatly, and the influence of other factors cannot be ignored. This indicates that the eight factors selected in this study related to collision risk can be used for studying the risk of ship collisions in ports. After determining the influencing factors, this study introduces fuzzy evaluation into the assessment of port collision risk. This can convert the factors that affect port SCR into membership functions, thereby obtaining the risk of collision between port vessels under different influences [17−18]. Firstly, the parameters of the target vessel were determined. The study sets the influencing factors as a set, then establishes an evaluation set for the target ship and finally uses the constructed set to establish an evaluation matrix. At this point, Equation (4) can be used to represent the set.
where uk represents the influencing factors in the set. The target ship evaluation set can be represented by Equation (5).
In Equation (5), r1 represents the danger of ships in the port, and r2 represents the ships' safety in the port. To ensure accuracy in calculation, the study also assigns weights to the factors affecting collision risk, thereby normalizing the weights of all factors. An SCR evaluation matrix is constructed through the above research, which can be represented by Equation (6).
In Equation (6), ruk represents the membership degree of each influencing factor in the set. At this point, the port SCR can be represented by Equation (7).
In summary, the study utilizes GRA and fuzzy evaluation to obtain the calculated SCR values for the port. Fig. 1 shows the relationship between the safe distance and collision distance of port vessels.
Diagram of the relationship between the safe distance and collision distance of port ships.
In Fig. 1, in the calculation of port SCR, the first step is to collect the ship's own data and to use fuzzy GRA to process the membership values of different influencing factors. The eight main factors obtained from the study are taken as a set, and the membership values of each influencing factor are utilized to calculate ship collision's risk value.
3.2. Construction of a ship collision risk prediction model integrating GRA and BPNN
There is still a problem of slow convergence speed in the calculation of port collision risk using fuzzy GRA. To solve the slow convergence speed, BPNN is introduced into port SCR research. BPNN can learn from a large amount of data, thereby improving the computational efficiency of risk calculation and improving the prediction training results. Meanwhile, it can improve the convergence speed of calculations, quickly calculate collision risk values and provide guarantees for ship navigation [19−20]. Therefore, based on the fuzzification of GRA processing, BPNN is integrated to construct a collision risk prediction model. BPNN effectively reflects the role of various collision data in port SCR by increasing the weight values and thresholds in network's each layer. Fig. 2 shows the network topology of BPNN.
The network structure topology diagram of BPNN.
In Fig. 2, this study adds a linearly weighted signal to BPNN and uses it as a method to calculate neuron input, which can be calculated using Equation (8).
In Equation (8), wi means the i-th node input's value by the neuron and xi means the neuron's input connection weight. When a threshold is added to a neuron and compared with the input value, it indicates that the neuron has been activated, and the neuron is able to transmit the signal to the next neuron. When the activation function performs operations, it can utilize the input of neurons to obtain outputs. The activation function utilized in this study is the Sigmoid function, which can be represented by Equation (9).
After activating the function, when the input value of the hidden layer reaches the set threshold, the study uses the input value as the independent variable for risk prediction. Then the output values of each unit in the hidden layer are calculated using a function, and the output values can be calculated using Equation (10).
In Equation (10), wij represents the connection weight, θ1j represents the threshold and j represents the quantity of neurons contained in the hidden layer. After calculating the output value, the BPNN training can be completed. Fig. 3 shows the training diagram that combines GRA and BPNN.
Training flowchart of the collision risk prediction model combining the GRA algorithm and BPNN.
In Fig. 3, when the training error of the collision prediction model is less than the set error, the prediction model will stop training. To validate this collision prediction model's feasibility, risk prediction experiments are conducted. However, this collision prediction risk model has a non-linear gradient optimization problem, which can lead to local optima. Therefore, to further improve the prediction model's performance, entropy weights are added to the model. Entropy weight can effectively measure the uncertainty of ship collisions in ports and can better generalize unknown data in collision risk. When the collision risk data is chaotic, the entropy value will be very high. When it is not, the entropy value is small. This is because the calculation of entropy weights utilizes objective weights, which significantly reduce the interference of human factors [21−23]. The calculation of entropy weight in collision risk prediction models first requires processing the output values of collision risk training to form a data matrix. Then standardization is implemented, and the entropy and entropy weight of the risk assessment indicators are obtained. The data matrix of entropy weight can be represented by Equation (11).
where xnm represents the number of influencing factors of the n-th evaluation object in the training output value of the prediction model, which is m. Standardization can be represented by Equation (12).
In Equation (12), yij represents the output indicator value. The higher its value, the greater the likelihood of collision risk. The entropy weight of evaluation indicators can be expressed by Equation (13).
In Equation (13), Hj represents the entropy weight of the j-th indicator. After obtaining the entropy weight, it can effectively compute the port collision risk's weight and obtain accurate port SCR values. Fig. 4 shows the flowchart of the port SCR prediction model.
Flowchart of the port vessel collision risk prediction model.
To verify the performance of the model, statistical analysis was conducted on the error between the predicted results and the true values. At a confidence level of 1−a for the overall mean μ, the confidence interval was calculated as shown in Equation (14).
where |$\bar{X}$| represents the mean, S represents the standard deviation and n represents the number of samples.
4. Performance analysis of a ship collision risk prediction model integrating GRA and BPNN
The study collected collision risk data from a certain port to validate the port SCR prediction model's performance. Ship speed, ship distance, ship encounter angle, ship weight, port visibility, port wind power, port wave and port ship density were utilized as the model's inputs. The collision risk prediction was used as the output value. Too little learning can lead to the model not being able to fully learn the features of the data, resulting in poor accuracy of the prediction model. However, excessive learning times can also lead to overfitting of the model, increasing its uncertainty. Therefore, the study set the learning frequency to 200. A larger learning rate may cause oscillations during the training process, increasing its uncertainty, while a smaller learning rate may lead to a slow convergence speed. Therefore, the study sets the learning rate to 0.1 to ensure the convergence speed of the model while avoiding oscillations. MATLAB software was used to compare the automatic identification system (AIS), long short term memory (LSTM) network and prediction model to verify the collision risk prediction performance.
4.1. Risk data processing capability analysing of ship collision risk prediction model in port waters
To verify the risk data processing ability of the SCR prediction model, the study obtained real data on port ship collision events from port management agencies, including ship collision events that occurred in different seasons and types of ports. This was divided into training and testing sets in a 4:1 ratio. The study compared LSTM and AIS with the prediction model. Fig. 5 shows the comparison results of relative error (RE) and root mean square error (RMSE) of three methods in port SCR data processing.
Comparison results of relative error (a) and root mean square error (b) in data processing of port vessel collision risk.
In Fig. 5(a), SCR data processing's RE had differences among all methods, with a prediction model of 0.26%, AIS of 0.31% and LSTM of 0.43%. In Fig. 5(b), there were also certain differences in the RMSE of the three methods in SCR data processing, with a prediction model of 80.62, AIS of 87.29 and LSTM of 92.08. In addition, at a 95% confidence level, the error between the predicted results of the proposed model and the true values is within the allowable error range of [0, 0.03%] in the confidence interval, indicating a high level of reliability of the results. This indicated that the risk prediction model constructed had significantly better accuracy and stability in data processing compared to comparative methods and had higher performance. To further verify the predictive model's ability to process SCR data, data analysing accuracy and fitness were selected as validating indicators. Fig. 6 shows the comparison results.
Comparison of accuracy and fitness of data analysis using three methods.
In Fig. 6, there were certain differences in the fitness and analysis accuracy of these three methods in port SCR prediction. The fitness and data analysis accuracy of the predictive model, AIS and LSTM methods were 0.92, 0.83 and 0.76, as well as 93.29%, 85.69% and 79.29%, respectively. This indicated that the collision risk prediction model constructed had higher predictive ability in risk prediction and stronger screening ability in parameter combinations. This is because BP neural networks have powerful data processing and learning abilities, which can learn complex relationships between data from a large amount of data and provide more accurate prediction results. AIS is mainly used to obtain real-time basic information of ships, while LSTM has certain limitations in its performance in complex prediction tasks that comprehensively consider multiple factors. To verify the collision risk prediction performance, three methods were applied in two obstacle avoidance modes, as shown in Fig. 7.
Comparison results of two obstacle avoidance modes using three methods: (a) mode 1; (b) mode 2.
In Fig. 7(a), in obstacle avoidance mode 1, there was a significant difference in obstacle avoidance ambiguity between these three methods over time. The average ambiguity value of the prediction model was 0.46, while the average ambiguity values of AIS and LSTM were 0.63 and 0.81, respectively. In Fig. 7(b), in obstacle avoidance mode 2, the fuzziness of the prediction model, AIS and LSTM all showed a decreasing trend, with average fuzziness values of 0.21, 0.59 and 0.62, respectively. This indicated that the constructed collision risk prediction model had a more reliable performance in handling uncertain data. This may be because the optimization of the GRA algorithm by fuzzification combines the flexibility of fuzzy logic and the advantages of the GRA algorithm in data correlation, further enhancing the model's ability to handle complex and variable factors. To verify the positioning ability of the prediction model in the position, speed and direction of port ships, the study used ship vectors as validation indicators. Fig. 8 shows the simulation results of ship vectors before and after applying the prediction model. The vector's direction is the ship's navigation direction. The length of a vector represents a ship's sailing speed. The vector's starting point is the position of the ship at this time.
Comparison results of ship vectors before and after applying prediction models: (a) ship vector map before applying prediction model; (b) ship vector map after applying prediction model.
Comparing Figs. 8(a) and (b), the distance between port ships before applying the prediction model was very close, which greatly increased ship collisions. After applying this prediction model, ships’ distance in the entire port significantly increased. Meanwhile, in the prediction model, the ships in the entire port became more orderly. This not only reduced SCR but also improved the operational efficiency of the port. This indicated that the port collision risk prediction model had better performance in ship scheduling and collision avoidance.
4.2. Application performance analysis of the ship collision risk prediction model
To validate the port SCR prediction model's specific application effect, simulation experiments were conducted using MATLAB software. In the simulation experiment, the true and predicted values of collision risk were used as validation indicators. Fig. 9 shows the comparison between the predicted collision risk values of three methods and the actual collision risk values.
Comparison of collision risk prediction and actual collision risk values using three methods.
In Fig. 9, the average indicator of the true collision risk value was 0.36, and the average indicators of the collision risk prediction values for the prediction model, AIS and LSTM were 0.32, 0.39 and 0.41, respectively. The predicted collision risk of the prediction model followed a similar trend to the actual value. This indicated that the collision risk prediction model constructed had higher practicality and was more suitable for predicting port SCR. To further verify this SCR prediction model's performance, AIS and LSTM were used as comparison methods to compare with the prediction model, and the SCR prediction time was used as a validation indicator. Fig. 10 shows a comparison of the time consumption of three methods in SCR prediction.
Comparison of time consumption results of three methods in the ship collision risk prediction process.
In Fig. 10, all three methods had lower time consumption in SCR prediction. The risk prediction time of the prediction model was 1.16 seconds. The risk prediction time for AIS and LSTM was 1.46 s and 1.62 s, respectively. This indicated that the prediction speed of the SCR prediction model constructed was significantly better than the other two methods. This showed that the prediction model issued collision risk warnings and took corresponding collision avoidance measures in a timely manner. According to the International Rules for Preventing Collisions at Sea, stand-on vessels were designated as research vessels, and four classic ship encounter situations were used as research objects to verify algorithmic performance. Fig. 11 shows the avoidance effect of the risk prediction model under four typical encounter situations.
Schematic diagram of the avoidance effect of risk prediction models under four typical encounter situations: (a) the first type of avoidance effect; (b) the second type of avoidance effect; (c) the third type of avoidance effect; (d) the fourth type of avoidance effect.
In Fig. 11(a), the target ship was located in front of the direct ship, and these two ships took the most effective measures to avoid collision through collision risk prediction models. The situation in Figs. 11(b), (c) and (d) was the same, with the target ship located on the port side, starboard side and channel of the direct ship. By using collision risk prediction models for early warning, both the target vessel and the stand-on vessel took correct decisions to avoid collisions simultaneously. In port SCR research, when conducting risk warning, it should avoid the minimum collision distance. If the collision distance is less than the minimum collision distance, it is impossible to avoid the occurrence of ship collisions.
5. Conclusions
With the developing maritime shipping, the risk of collisions between ships in port waters is also increasing, which is related to the normal operation of ports and the safety of ships. To effectively improve the predictive ability of SCR in port waters, a fuzzy GRA and BPNN were effectively combined to construct a ship collision analysis and prediction model in port waters. The average ambiguity value of the prediction model was 0.46, and the average indicator of the collision risk prediction value was 0.32. Its risk prediction time was 1.16 s, which was 0.3 s and 0.46 s less than the risk prediction time of AIS and LSTM, respectively. The performance indicators of the SCR prediction model constructed were better than those of the comparative methods, indicating that the prediction model had higher prediction accuracy and stability. This can provide more scientific and accurate SCR assessment results for port management departments, which helps to improve the safety level of port waters. Although this study has achieved good research results, there are still certain shortcomings. There are many factors that affect ship navigation safety in port waters. This study only selects eight factors, which may have certain limitations. The next step of research can consider more influencing factors to improve the reliability and comprehensiveness of the port SCR prediction model.
Acknowledgements
We thank Beibu Gulf University for all the necessary support.
Author contributions
Dan Wang collected the samples. Yan Jing analysed the data. Dan Wang and Yan Jing conducted the experiments and analysed the results. Both authors discussed the results and wrote the manuscript.
Funding
The research is supported by the Guangxi Science and Technology Program, (Grant No. AB23026132); and the Project for Enhancing Young and Middle-aged Teacher's Research Basis Ability in Colleges of Guangxi (Grant No. 2023KY0438).
Conflict of interest statement. None declared.
