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Journal of Advanced Transportation
, Volume 2023 – May 20, 2023

/lp/hindawi-publishing-corporation/prediction-of-ship-traffic-flow-and-congestion-based-on-extreme-MZ0IkHpcwD

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- Publisher
- Hindawi Publishing Corporation
- ISSN
- 0197-6729
- eISSN
- 2042-3195
- DOI
- 10.1155/2023/7175863
- Publisher site
- See Article on Publisher Site

Hindawi Journal of Advanced Transportation Volume 2023, Article ID 7175863, 12 pages https://doi.org/10.1155/2023/7175863 Research Article Prediction of Ship Traffic Flow and Congestion Based on Extreme Learning Machine with Whale Optimization Algorithm and Fuzzy c-Means Clustering 1 2,3,4 1 4 Yongjun Chen, Ming Huang , Kaixuan Song, and Tengfei Wang Airport College, Binzhou University, Binzhou 256600, China Intelligent Transportation Systems Research Center, Wuhan University of Technology, Wuhan 430063, China National Engineering Research Center for Water Transport Safety (WTSC), Wuhan 430063, China School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China Correspondence should be addressed to Ming Huang; hm@whut.edu.cn Received 20 June 2022; Revised 30 October 2022; Accepted 26 November 2022; Published 20 May 2023 Academic Editor: Jing Zhao Copyright © 2023 Yongjun Chen et al. Tis is anopen access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Accurately predicting short-term congestions in ship trafc fow is important for water trafc safety and intelligent shipping. We propose a method for predicting the trafc fow of ships by applying the whale optimization algorithm to an extreme learning machine. Te method considers external environmental uncertainty and complexity of ships navigating in trafc-intensive waters. First, the parameters of ship trafc fow are divided into multiple modal components using variational mode decomposition and extreme learning machine. Te machine and the whale optimization algorithm constitute a hybrid modelling approach for predicting individual modal components and integrating the results of individual components. Considering a map between ship trafc fow parameters and congestion, fuzzy c-means clustering is used to predict the level of ship trafc congestion. To verify the efectiveness of the proposed method, ship trafc fow data of the Yangtze River estuary were selected for evaluation. Results from the proposed method for predicting ship trafc fow parameters are consistent with measurements. Specifcally, the prediction accuracy of the ship trafc congestion reaches 76.04%, which is reasonable and practical for predicting ship trafc congestion. practitioners, and government managers to develop an 1. Introduction approach for predicting ship trafc fow. Te status of ex- Te booming growth in trade has led to the development of pected ship trafc fow can be used to identify congestion the waterway transportation sector, and ship trafc fow early, improve canal trafc, and prevent accident. prediction has become extremely important with the ever- Methods for predicting trafc fow, which were frst only increasing waterway transport demand. Te Yangtze River, employed for predicting automobile trafc fow, have found as the largest river that runs through the east and west of widespread use now. Xiao et al. [1] proposed and built China, is the main channel to the sea for 11 inland provinces diferential information from the car-following inertia gray and autonomous regions of China and the main trans- model and gray system based on the classic car-following portation artery connecting the three economic zones in model and trafc status to establish diferential equations. southwest, central, and east part of China. Te Yangtze River Yan et al. [2] constructed a comprehensive trafc fow in- plays a pivotal role in the country’s economic and social dication system based on the robust L1 model minimum development because of its superior navigable conditions two-multiplier twin support vector regression. Based on and huge transit capacity. Once the ships in the Yangtze a recurrent neural network, Cui et al. [3] used a two-way/ River are blocked, the cost loss and environmental pollution one-way stacked long short-term memory (LSTM) network will be a great loss. Terefore, it is a goal of researchers, for trafc prediction. Tey combined a recurrent neural 2 Journal of Advanced Transportation vehicle path problem and designed a local search second network and its variants into a trafc prediction method. Li et al. [4] used the dense geometric correspondence network algorithm for a particular terrain. Mei [23] applied an ef- fcient clustering algorithm for the k-core decomposition of for multistep trafc prediction. By applying dynamic re- lations between trafc stations in space and time, Peng [5] large networks. Guo [24] applied a method for early warning proposed a prediction framework based on a neural network of trafc congestion areas based on dynamic identifcation, to dynamically map urban trafc fow. Cai et al. [6] derived which can efectively track the target and detect congestion the posttest estimation of the maximum correlation in the warning areas throughout the congestion evolution. Gao fxed embedding algorithm update such that a Kalman flter [25] applied a method to quantify the degree of trafc provides suitable trafc fow prediction. Wang et al. [7] congestion, constructed an image-based trafc congestion assessment framework, and integrated a trafc parameter combined trafc fow data and considered weather condi- tions to build a short-term trafc fow prediction model layer into a basic convolutional neural network that accel- erates processing and avoids complex postprocessing. Zhou based on an attention mechanism and a one-dimensional convolutional neural network with LSTM. Fang et al. [8] [26] proposed a clustering integration method based on structured hypermap learning to improve the clustering found that a typical LSTM network is prone to small fuc- tuations and can achieve high-accuracy trafc fow pre- efciency, stability, and robustness. diction. Shen et al. [9] performed trafc fow prediction Nguyen [27] used clustering to automatically label data, considering multi-intersection perception. Lu et al. [10] qualitatively assess the signifcance of the labels, and performed isolated-point short-term trafc fow prediction quantify the efect of label separation results in the feature based on a time-aware convolutional context block LSTM space. Costa [28] proposed an unsupervised approach for network and a novel loss switching mechanism. Li et al. [11] relating topic modelling and document clustering, seam- lessly unifying and jointly performing both tasks using performed deep feature learning by applying an advanced multitarget particle group optimization algorithm to the Bayesian generative modelling and post-ambiguous rea- soning. As a result, a method was derived to estimate the parameters of a deep belief network and by applying su- pervised learning to predict short-term trafc fow. Zhang congestion index using a speed transfer matrix and the corresponding center of mass. Te congestion index is es- et al. [12–14] proposed convolutional neural networks based on dynamic feature coding. Considering the selection of timated using fuzzy reasoning optimized by genetic algo- historical data, Zhang [13] proposed a selection method to rithms. Te index is evaluated using data from a receiver of collect appropriate historical data for daily trafc fow global satellite navigation system, and trafc status estimates prediction. can be obtained for most evaluated roads. Peixoto [29] Salamanis [14] proposed an efcient large-scale multi- devised clustering analysis for reducing trafc information at step trafc prediction model with fast inference. Almeida the edge of a vehicle network. Peter [30] applied the RSRU_TM method for improving trafc management. [15] used statistical algorithms and neural networks to de- scribe and predict trafc fow. Lee and Rhee [16] identifed Based on mobile crowd sensing for dynamic trafc efciency estimation, Ali [31] applied an algorithm for trafc con- two basic spatial dependencies in trafc, used distance, direction, and location diagram convolution networks, and gestion control. Huertas [32] combined an unsupervised transformed the three spatial relations into deep neural clustering algorithm with a predictive model based on networks for trafc speed prediction. Pavlyuk [17, 18] ap- multiple logistic regression for scalable prediction and plied integrated learning techniques in space-time structure analysis of trafc accidents. Chiabaut [33] proposed learning and applied them to predict short-term trafc fow a method for real-time assessment of trafc conditions. in cities. In addition, the researcher proposed a spatiotem- Bhatia [34] applied a data-driven approach to build artifcial poral cross-validation method to evaluate the model per- intelligence models for vehicle trafc behavior prediction. formance. Alves and Cordeiro [19] developed an adaptive Te aforementioned research fndings ofer a solid foundation for the study of the congestion risk of ship trafc algorithm to accurately predict trafc fow and monitor highways connected to a complex network using local trafc fow, but given the state of the research, there is no com- prehensive research on the variables afecting ship trafc measurements. Carpio [20] confrmed that LSTM-based trafc prediction can efectively reduce the complexity of fow and congestion risk [35]. Wang et al. [36] designed trafc prediction. To overcome the limitation of trafc a ship trafc fow model based on a multiple hexagon-based prediction on a specifc road, Jin [21] adapted the bi- convolutional neural network (mh-CNN) method. How- directional encoder representations from transformers to ever, the large spatial resolution of the method makes it trafc modelling, suitably predicting trafc fow in various difcult to be used in inland waterway navigation studies. Xu routes. and Zhang [37] proposed a RNN-based method to predict the ship trafc fow of Yangtze River. Te method is simple With the rapid growth in transport demand worldwide, trafc congestion is gradually increasing owing to natural and efective; however, the spatiotemporal dependence of ship trafc fow was not considered in the method. Ship and artifcial factors. Trafc congestion not only causes unnecessary waste of time and human and fnancial re- trafc fow statistics, on the other hand, are highly spatially articulated and temporally correlated and are infuenced by sources for those afected but also causes delays and lags in world trade [12]. Terefore, it is critical to study and mitigate a range of factors. From the standpoint of water trafc spatial trafc congestion. To solve trafc congestion in specifc correlation [38, 39], adjacent sections or channels are im- scenarios, Jin [22] formulated a dual-target cash transport pacted by nearby vessel trafc fow. Ship trafc fow exhibits Journal of Advanced Transportation 3 n+1 a particular time correlation in the close time distance [40]. Te update of u and, according to the alternating n+1 n+1 So, it makes sense to look at how to create a suitable con- direction method of multipliers, the update of ω and λ k k gestion risk model for ship trafc fow. can be expressed as Considering the advantages and drawbacks of the f(ω) − u (ω) + 0.5λ(ω) i≠k i n+1 abovementioned developments, we use variational mode u (ω) � , (4) k 2 decomposition (VMD), an extreme learning machine 1 + 2α ω + ω (ELM), the whale optimization algorithm (WOA), and fuzzy ∞ 2 c-means (FCM) clustering to accurately predict ship trafc ωu (ω) dω n+1 ⎛ ⎝ ⎞ ⎠ fow and congestion. In this paper, the VMD-ELM-WOA ω � , (5) k ∞ 2 u (ω) dω method is applied to predict ship trafc fow, which is convenient for planning in water areas and time periods prone to blockage and reduces the queuing time. Te three n+1 n n+1 ⎡ ⎣ ⎤ ⎦ λ (ω) � λ (ω) + τ f(ω) − u (ω) . (6) parts of VMD-ELM-WOA are innovatively combined to k reduce the time of trafc volume prediction and further improve the calculation accuracy. Finally, convergence is established for constant e >0 as Te remainder of this paper is organized as follows. Te follows: trafc fow prediction model using VMD-ELM-WOA is � � � � n+1 n � � introduced in Section 2. Section 3 details the prediction u − u � � k k < e. (7) � � model for ship trafc congestion. In Section 4, a case study � n� � � u � � k�1 based on measured ship trafc data is reported along with its results in diferent scenarios. Finally, we draw conclusions in Te steps for VMD are summarized as follows: Section 5. 1 1 (1) Set initialization parameters u , ω , λ and k k n+1 n+1 u , ω , λ . 2. VMD-ELM-WOA Method for Predicting Ship k k (2) Update equation (6) based on the results of equations Traffic Flow (3)–(5). 2.1. VMD Method of Ship Trafc Flow Analysis. VMD was (3) Update until the convergence condition in equation proposed in 2014 as a nonrecursive method. Since then, this (6) is satisfed. decomposition method has been widely used to treat (4) Return the corresponding modal component based nonlinear problems, being suitable for processing trafc fow on the number of modes. time series that have strong nonlinearity and high com- plexity. In fact, accurate prediction of ship trafc fow re- quires the decomposition of the corresponding time series. 2.2. ELM Method of Ship Trafc Flow Prediction. A con- VMD establishes a variable problem that is constantly ventional neural network shows a slow convergence and updated by constructing a constrained model center and high computation burden, impeding accurate predictions bandwidth to fnd the optimal solution. Suppose that a signal over a time series. Huang et al. proposed the ELM, which is is set to be band-decomposed into k intrinsic mode function basically a feedforward neural network, whose input weights components by a variable fractional modality. Ten, and thresholds can be randomly initialized to improve the � � training efciency for use in many cases. A diagram of the � �2 ⎧ ⎨ ⎫ ⎬ � j � − jω t � � ELM structure is shown in Figure 1. � � min z δ(t) + uk(t)e . (1) � t � ⎩ ⎭ � � πt u , ω 2 { } { } Consider N samples (X , X ) that describe the fow and k k i j density of ship trafc. Te input layer is mapped by the active Te corresponding constrained model can be expressed function as follows: as s.t. β fω X + b � o , (8) u � f, i i j i j (2) i�1 where L is the number of hidden layer nodes, where u � u , . . . , u and ω � ω , . . . ,ω are the k 1 k k 1 k x , x , . . . , x ,ω is the input weight, β is the output weight, modal numbers and center frequencies, respectively. 1 2 i i i and b is the bias of the hidden node. Equation (1) can be solved by introducing Lagrangian op- After network training achieves learning with zero error, erator λ and secondary penalty factor α, which are translated into the following unconstrained problem: � � � � � � � � � � � �2 o − t � 0, (9) � j j� � j � −jω t � � � � L u , ω ,λ � α z δ(t) + uk(t)e . j�1 k k � t � � � πt , β , and b that make the following condition and there are w i i (3) hold: 4 Journal of Advanced Transportation Input traffic flow parameters x Input Layer x x n-1 Output the traffic flow parameters of the segment Output Layer Hidden Layer Figure 1: ELM diagram. N 2.3.1. Surrounding Prey β fω X + b � t , (10) i i j j j ∗ → →→ → i�1 ⎧ ⎪ D � C X (t) − X(t) , (13) where β is the output weight, b is the threshold between ⎩→ → → �→ X(t + 1) � X (t) − A · D, implicit layers, and t is the output value. Equation (9) can be written in the following matrix form: where the vectors for the whale’s current position and optimal position are used while the whale constantly updates Hβ � T, its position during foraging. Vectors A and C are defned as f ω X + b · · · f ω X + b 1 1 1 N 1 L → → → → ⎢ ⎥ ⎡ ⎤ ⎥ (11) ⎢ ⎥ ⎧ ⎨ ⎢ A � 2 a × r − a, ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ H � ⎢ ⋮ ⋱ ⋮ ⎥. (14) ⎢ ⎥ ⎢ ⎥ → ⎢ ⎥ ⎩ ⎣ ⎦ C � 2 × r . f ω X + b · · · f ω X + b 1 N 1 L N L Considering the ELM principle, the weights and 2.3.2. Bubble Net Attack thresholds of the input can be randomly assigned, whereas the weights between the hidden layer and output layer can be (1) Shrink surroundings: the bubble net is shrunk by obtained using the solution to the system of equations: adjusting the die value of vector a, which drops linearly from 2 to 0 throughout the bubble net attack. ∗ ∗ β � H .T, (12) (2) Update spiral: Te humpback whales can also switch positions in a spiral during hunting. In addition to where ∗ denotes the Moore–Penrose pseudoinverse of the the shrinking surroundings to enclose the prey, the corresponding matrix. following update is defned: �→ � �→ 2.3. WOA of Parameter Determination. Owing to the ran- ⎧ ⎪ ′ bl ∗ X(t + 1) � D · e · cos(2πl) + X (t), domness of ELM weights and thresholds, the predictions (15) �→ ⎪ � �→ ′ ∗ may be biased. Terefore, we apply the WOA to the internal ⎩ D � X (t) − X(t) , parameters of the ship trafc fow model based on ELM. Te WOA is a heuristic algorithm that resembles the behavior of where l is a random value afecting the distance humpback whales. In brief, foraging is described by a spiral between the current and optimal positions. bubble net for catching a prey, eventually leading to food (3) Search for prey: In addition to tracking individual swallowing. Tis behavior is expressed in a target model as whales in optimal locations, humpback whales also detailed in the following. Journal of Advanced Transportation 5 use random searches to track their prey. Tis process FCM clustering is applied to the test set containing ship can be described as follows: trafc fow information. As a result, the test set is divided into diferent clusters, and the interaction between clustering → → → → D � C · X − X , rand and a test sample can be used to quickly identify the k- (16) → → → → nearest neighbors for classifcation. Ten, the congestion X(t + 1) � X − A · D . rand level is determined according to the weight of the ship trafc fow and density sample by weighting the neighborhood. Te update of population locations depends on the die Te calculation based on FCM clustering proceeds as value of A, which is randomly set for a value greater than 1. follows: When the die value is less than 1, the population searches (1) Apply FCM clustering to divide the test set into N along the direction of the optimal individual location. clusters: X , X , . . . , X , with cluster collection centers 1 2 N u , u , ..., u . Use any cluster X (1 ≤ k ≤ N) to create 1 2 N k a sample of the ship trafc fow and density of 2.4. Te Hybrid Method of VMD-ELM-WOA. In view of the m , m , . . . , m (1 ≤ c ≤ l). Defne cluster radius R for 1 2 c complexity and strong stochasticity of ship trafc fow, thetestsample.Temaximumdistancebetweenthetest a combinatorial approach is proposed to perform time series sample and cluster center contained in X is given by of ship trafc fow prediction, as shown in the structure in Figure 2. Te time series is frst decomposed into multiple R � max dist m , uk ,dist m , u , . . . ,dist m , u . k 1 2 k c k intrinsic mode function components using VMD. Ten, (17) prediction on every component is performed to fnally superimpose all the predictions. (2) Defne the predicted sample for randomly selected (1) Reduce the randomness and complexity of the cluster X (1 ≤ k ≤ N) and the target sample for original trafc signal by splitting it into multiple prediction. Te distance between the sample and intrinsic mode function components cluster X is d with the following boundary distance: through VMD. k k (2) Build a combined prediction method. Te weights d � dist m, u ‒R . (18) k k k and thresholds of the ELM for prediction are ran- domly initialized. Ten, the WOA is applied to If d >0, the sample of ship trafc fow parameters to optimize the internal ship trafc fow parameters of be predicted does not fall within the clustering level. the network, forming the hybrid ELM-WOA model. If d � 0, the sample is at the clustering boundary. (3) Build a composite method based on the components (3) Set distance d between the predicted ship trafc KNN obtained from step 1 to obtain multiple predictions fow parameter sample and training set of nearest and combine them for the fnal prediction. adjacent samples (1, 2, . . ., z). Te weight corre- sponding to the sample of the nearest adjacent ship trafc fow parameters for k is given by 3. Prediction of Ship Traffic Congestion d − d k�1 KNN KNN Predicting ship trafc fow relies on determining its main K K w � . (19) parameters. In addition, ship trafc congestion is refected (l − 1) d k�1 KNN according to the corresponding ship trafc fow parameter. However, ships are often afected by external environmental disturbances, and their fow is complex and uncertain. 4. Experimental Case Study Hence, we use FCM clustering to divide the ship trafc fow into diferent parameter mappings and then classify con- 4.1. Data and Evaluated Methods. Te data for this study gestion in segments. Given the lack of quantitative criteria to were obtained from 4-month ship trafc fow recordings classify ship trafc congestion, we analyze the classifcation from September to December 2020. Data were collected of road vehicle congestion, comprehensively assess the every 15min, 30min, and 1h for segments B, A, and C, characteristics of ship trafc fow in the waters of the respectively. Te dynamic data from September 6 to De- Yangtze estuary, and fnally classify ship congestion in cember 29, 2020, were used as the training set with a pre- navigable waters into four levels according to the congestion diction part from segment B. Te data from December 30, levels listed in Table 1. 2020, were used for prediction. Te samples for training Te fow diagram for predicting ship trafc congestion is were 11,256, 5768, and 2904, and those for prediction were shown in Figure 3. Using the ship automatic identifcation 96, 48, and 24, respectively. system to build a base station, we can obtain dynamic data To verify the efectiveness of the proposed VMD- from ships navigating in the channel, reject invalid and WOA-ELM method to predict ship trafc fow, we com- abnormal data, determine the ship trafc fow and density, pared our complete method with combinations WOA-ELM and predict ship trafc fow based on the VMD-ELM-WOA and EMD (empirical mode decomposition)-WOA-ELM and method. Ten, FCM clustering is applied to obtain the level prediction models ELM and backpropagation (BP). To fully of ship trafc congestion. evaluate the proposed VMD-WOA-ELM method, the 6 Journal of Advanced Transportation ELM- ELM- WO WOA A IMF IMF 3n 3n IMF IMF 2n 2n IMF 1n IMF 1n I Inp npu ut: S t: Sh hip ip tra trafc fo fc fow da w dat ta a A Ab bno nor rm mal al D Da at ta E a Elimina liminat tio ion n Predicted Value VMD Results VMD Calculation Figure 2: Diagram of VMD-ELM-WOA method for predicting ship trafc fow (IMF, intrinsic mode function). Table 1: Classifcation of ship congestion adopted in this study. Congestion level I II III IV Description Smooth fow Mild congestion Moderate congestion Severe congestion Congestion index range (0, 0.3] (0.3, 0.6] (0.6, 0.8] (0.8, 1] Severe Congestion Mild Congestion General Congestion Basically Congestion Input: Ship trafc fow data Input: Ship traf c fow data Abnormal Data Elimination Abnormal Data Elimination ELM-WOA prediction VMD Calculation model Figure 3: Flow diagram for predicting ship trafc congestion. training set and sample set of the same trafc fow and time is shown in Figure 4 for intervals of 15min, 30min, and density were selected as inputs, and the prediction was 1h, and the corresponding MAE, RMSE, and MAPE are compared with the corresponding measurement. Te listed in Table 2. computational platform used in this study was MathWorks Figure 5 and Table 3 show the corresponding prediction MATLAB 2017. results for ship trafc density. 4.4. Trafc Congestion Level. Using FCM clustering, trafc 4.2. Evaluation Indicators. To evaluate the accuracy of the fow and density measurements for the frst 3months of prediction methods for ship trafc fow parameters, we used segment B were collected and combined with trafc fow and the mean absolute error (MAE), root-mean-square error density measurements for December 30. Depending on the (RMSE), and mean absolute percentage error (MAPE): trafc fow parameters, trafc congestion is defned into four d � dist m, u ‒R , k k k levels according to the navigation conditions, as shown in ������������ � Figure 6. Te prediction in segment B considering 15min intervals and the measurements for December 31 are shown RMSE � y − y , t t (20) in Figure 7. Te predicted trafc congestion is similar to the measurements, with the prediction accuracy reaching n 1 y − y t t 76.04%, which indicates a suitable prediction of ship trafc MAPE � , n y congestion. i�1 where y is the measured value, y is the predicted value, and 4.5. Discussion. In order to quantitatively verify the appli- n is the number of samples. cability of the model, this paper uses fve models to calculate the values of MAE, RMSE, and MAPE for all 15min, 30min, 4.3. Spatiotemporal Evaluation. Using the proposed and and 60min in December 2018, as shown in Tables 2 and 3. comparison methods for ship trafc fow prediction, we From the tables, it can be seen that VMD-WOA-ELM obtained the trafc fow and density of segment B with data maintains a lower value in diferent time periods, as well as from December 30, 2018. Te trafc fow prediction over ship trafc fow and density, and on 3D colormap surface Journal of Advanced Transportation 7 0 20 40 60 80 100 0 10 20 30 40 50 Time Slice (15 min) Time Slice (30 min) Actual Value WOA-ELM Actual Value WOA-ELM BP EMD-WOA-ELM BP EMD-WOA-ELM ELM VMD-WOA-ELM ELM VMD-WOA-ELM (a) (b) 0 5 10152025 Time Slice (1 h) Actual Value WOA-ELM BP EMD-WOA-ELM ELM VMD-WOA-ELM (c) Figure 4: Results from proposed and comparison methods for prediction of ship trafc fow. (a) Trafc fow forecast of section B in 15min on December 30, 2018. (b) Trafc fow forecast for section B in 30minutes on December 30, 2018. (c) 1-hour trafc fow forecast for section B on December 30, 2018. Table 2: Comparison of prediction of ship trafc fow between proposed and comparison methods. Time 15min 30min 1h slice MAPE MAPE MAPE Method MAE RMSE MAE RMSE MAE RMSE (%) (%) (%) WOA-ELM 6.988 0 9.111 0 6.994 0 8.974 8 10.931 4 7.103 5 11.833 14.735 5 8.044 8 EMD-WOA-ELM 4.560 8 5.898 2 4.558 3 5.509 0 6.632 2 4.324 9 6.634 1 8.239 7 4.481 5 VMD-WOA-ELM 2.099 4 2.640 4 2.114 0 3.393 2 4.236 5 2.810 9 3.143 5 4.112 0 2.135 6 ELM 7.570 2 9.840 5 7.523 8 9.842 7 11.695 2 8.091 5 12.751 9 15.351 8.555 6 BP 7.420 5 9.869 5 7.402 1 9.288 6 11.922 2 7.733 5 12.454 1 15.909 8.493 3 Time Slice Ship Trafc Flow (Vel/15 min) Ship Trafc Flow (Vel/1 h) Ship Trafc Flow (Vel/30 min) 8 Journal of Advanced Transportation 10 11 9 10 8 9 7 8 6 7 5 6 4 5 0 20 40 60 80 100 0 10 20 30 40 50 Time Slice (15 min) Time Slice (30 min) Actual Value WOA-ELM Actual Value WOA-ELM BP EMD-WOA-ELM BP EMD-WOA-ELM ELM VMD-WOA-ELM ELM VMD-WOA-ELM (a) (b) 0 5 10152025 Time Slice (1 h) Actual Value WOA-ELM BP EMD-WOA-ELM ELM VMD-WOA-ELM (c) Figure 5: (a) Trafc fow prediction and error results of trafc fow prediction model for 15min in section B on December 30, 2018. (b) Trafc fow prediction and error results of trafc fow prediction model for 30min in section B on December 30, 2018. (c) Trafc fow prediction and error results of the 1-hour trafc fow prediction model in section B on December 30, 2018. plot with projection, the mapping value is lower than that of membership, thus performing a quantitative analysis of the the comparison model. ship trafc fow parameters. Te prediction trend in the characteristic parameters of Te MAE, RMSE, and MAPE values of the VMD-WOA- ship trafc fow is similar to the trend in the corresponding ELM-based ship trafc fow prediction method proposed in measurements, and FCM clustering allows to determine the this work are smaller and more stable generally, as illustrated level of ship trafc congestion over time and space, refecting in Figures 8–10. Tis demonstrates that the proposed spatiotemporal heterogeneity. In addition, the proposed method has a higher prediction accuracy since the pre- prediction method outperforms the comparison methods, as diction values achieved by using this method are closer to the indicated by its lowest prediction errors. FCM clustering measured values and can depict the application of ship trafc defnes the congestion level according to the degree of fow in terms of spatiotemporal variability. Te technique Ship Trafc Flow Density (Vel/n mile) Ship Trafc Flow Density (Vel/n mile) Ship Trafc Flow Density (Vel/n mile) Time (min) WOA-ELM ELM BP EMD-WOA-ELM VMD-WOA-ELM Journal of Advanced Transportation 9 Table 3: Comparison of prediction of ship trafc density between proposed and comparison methods. Time 15min 30min 1h slice MAPE MAPE MAPE Method MAE RMSE MAE RMSE MAE RMSE (%) (%) (%) WOA-ELM 3.427 1 0.563 6 7.0071 0.529 8 0.656 7 7.156 7 0.617 9 0.786 8 7.444 3 EMD-WOA-ELM 0.263 1 0.343 9 4.446 0 0.342 1 0.408 7 4.468 6 0.400 6 0.473 1 4.518 8 VMD-WOA-ELM 0.126 5 0.158 9 2.132 2 0.196 2 0.248 4 2.744 1 0.174 5 0.234 0 2.002 3 ELM 0.447 3 0.585 4 7.460 1 0.532 7 0.677 1 7.321 7 0.705 9 0.9109 8.054 8 BP 0.4346 0.586 6 7.308 5 0.557 1 0.683 5 8.071 8 0.687 6 0.832 2 7.861 6 Cluster Map 50 100 150 200 250 300 350 400 Segment Flow (Vel/15 min) Figure 6: Cluster of ship trafc fow parameters and prediction parameters for frst 3months of segment B. Grade Chart 3.5 2.5 1.5 0 10 20 30 40 50 60 70 80 90 100 Time Interval (15 min) Actual grade Prediction Level Figure 7: Measured and predicted levels of ship trafc congestion. MAE 12.80 11.73 10.65 9.575 8.500 7.425 6.350 5.275 4.200 3.125 2 2.050 Figure 8: MAE of ship trafc fow. Method MAE Ship Congestion Level of Flight Segment Flight Segment Density (Vel/mile) Time (min) Time (min) WOA-ELM WOA-ELM ELM ELM BP BP EMD-WOA-ELM EMD-WOA-ELM VMD-WOA-ELM VMD-WOA-ELM 10 Journal of Advanced Transportation RMSE proposed method does not consider the complexity of the 0.9120 network formed by the navigating ships. In future work, we 0.8366 1.0 will explore complex network theory to study the complexity 0.7612 0.9 of the waterway navigation network and improve the gen- 0.6858 0.8 eralization ability of the proposed prediction method. 0.6104 0.7 It should be noted that the studied areas in this paper are 0.5350 0.6 somewhat regional in nature. Although the Yangtze River 0.4596 0.5 0.3842 estuary is highly representative of the dense trafc fow 0.3088 0.4 waters, in order to make the corresponding methodological 0.2334 0.3 model applicable to all dense trafc fow waters, the sub- 0.1580 0.2 sequent research work should be extended to other water- 0.1 sheds based on the expansion of dense trafc fow waters. At the same time, this paper does not further deepen the re- search on the prediction and control of ship congestion before the occurrence of congestion based on the judgment of congestion risk level, and this research has extremely important theoretical and application values. Figure 9: RMSE of ship trafc fow. Data Availability MAPE (%) 8.620 Te data used in this paper were obtained from the collection 7.958 of AIS data of ships in the Yangtze estuary from the maritime 7.296 regulatory authority website (https://www.shipxy.com/). 6.634 5.972 Conflicts of Interest 5.310 4.648 Te authors declare that there are no conficts of interest 3.986 regarding the publication of this paper. 3.324 2.662 3 2.000 Acknowledgments Tis research was funded by the National Key R&D Program of China (grant no. 2021YFB1600400) and the National Natural Science Foundation of China (grant no. 52101403). References Figure 10: MAPE of ship trafc fow. [1] X. Xiao, H. Duan, and J.Wen, “A novel car-followinginertia gray model and its application in forecasting short-term trafc fow,” efciently addresses the issue of redundant ship trafc fow Applied Mathematical Modelling, vol. 87, pp. 546–570, 2020. data in areas with high ship trafc and lays the groundwork [2] H. Yan, T. Zhang, Y. Qi, and D.-J. 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Journal of Advanced Transportation – Hindawi Publishing Corporation

**Published: ** May 20, 2023

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