In particular, the vessel kinematic information, including latitude (lat), longitude (lon), speed over ground (SOG), and course over ground (COG), plays a critical role in evaluating optimal navigation routes, and predicting the future path of a vessel over specific time-series data based on relevant historical data requires analyzing an array of AIS data [13]. It is denoted by equations (1), (2), (3) [14- 15]

Xt≜[lat,lon,SOG,COG]T(1)

The vessel's historical path (The original AIS data for the MMSI vessel, code of 525100764, expressed by Southern Vietnam Maritime Safety Corporation), which is expressed in Table 1, is represented by a sequence of observation points {Xt0,Xt1,…,XtT}, where ti < tj if i<j. Therefore, it is necessary to carry equally sampled observed data to obtain a series of T+1 as follows:

X0:T≜{Xt0,Xt0+Δt,Xt0+2*Δt…Xt0+T+Δt}(2)

The process of encoding complicated vessel motion data in this space feature poses a significant challenge. Therefore, the solution used is to expand the feature space by one higher dimension. The "four-hot" representation vector ht is used to separate lat, lon, SOG, and COG data into Nlat,Nlon,NSOG and NCOG bins [16], respectively. The vector ht is expressed by

ht≜[1tlat,1tlon,1tSOG,1tCOG]T(3)

Table 1 The original AIS data sample for the MMSI vessel code of 525100764

Tablica 1. Izvorni uzorak AIS podataka za MMSI brodski kod 525100764

Remark 2: Depending on the weather and traffic, different features of vessels traveling along the comparable route will be observed. In case of dealing with large inertia vessels, and complex propulsion systems, it is necessary to predict the safe routes.

Nowadays, vessels are becoming complex sensors concentrated as the maritime industry's digital revolution gathers increasing volume to support more energy-efficient marine and vessel operations and support handling the challenges of new legislation. The result of the combination of modern communication systems and advanced sensor technologies is significantly improved vessel connectivity, which allows for the collection and analysis of a large amount of operational data. Specifically, the synchronization and analysis of data from various sources will undoubtedly speed up decision-making for operators and improve vessel performance management in critical areas including energy and fuel management, emissions control, machinery and equipment monitoring [17], and route optimization. Thus, data mining will benefit the shipping sector by providing fresh insights and added value to support improved decision-making, asset tracking, predicting, and fleet-wide optimal application. The methodology used in this study focused on mining maritime traffic from historical vessel data, and consists of two stages: data collection and classification in the first stage, together with the required measurement metrics; analysis, and prediction of marine traffic states using tools or algorithms in the second stage.

The management system consists of four main components, namely the API server, the application, the computing server, and the database server, as shown in Fig. 3 below:

In the past ten years, concerns about maritime traffic safety and security have become evident due to the difficulties created by the increasing demand for additional vessels with greater capacity and velocity. To ensure the navigational safety, prevent collisions, and improve the effectiveness of vessel management, predicting the trajectory of vessels is essential. A relatively recent development for complex geographic applications is the addition of effective machine learning technologies to accurately predict trajectories. However, the complexity of the maritime environment and issues with data quality, particularly in the Vietnam Sea Port, which has a high density of vessels, hinder the reliable vessel trajectory predictions. On the other hand, with the system structure selected in Figure 3, the input data is processed and analyzed numerically, stored in Resource APIs, and then aggregated and filtered, with the data fields being separated. Subsequently, the 04 data fields (lat, lon, SOG, COG) selected for the prediction model are also the input data of the Maritime traffic state prediction model [25]. In addition, the MTSP model has not yet been implemented in any maritime management system in Vietnam, which motivates us to propose a solution based on the support of Deep Learning to provide the system with the following superior features. In this study, we suggest the MTSP model based on the LSTM network (LSTM is one of the deep learning algorithms as mentioned) to evaluate suitable paths for vessels along routes and experiments established on data collected from the AIS system through Resource APIs provided by Southern Vietnam Maritime Safety Corporation. The proposed model used for analyzing maritime traffic data has the following characteristics:

The LSTM network sequentially computes the input vessel path data string Xl with the hidden vector Η𝓁≜{ht}t=1𝓁, in which the memory cell corresponding to the input vector (at the current time step xt) and the hidden state (at the previous time step xt−1) update the hidden state inside ht expressed by [20]

it=σ(Uixt+Wiht−1+bi)ft=σ(Ufxt+Wfht−1+bf)ot=σ(Uoxt+Woht−1+bo)(4)

where ⊙ represents the element product, σ describes the sigmoid function, and tanh is the hyperbolic tangent function. Besides, i,f and o indicate the input gate, forget gate, and output gate, respectively. We get, c̃t and ct ϵ ℝq express the cell input activation vector and cell state, defined as follows:

c̃t=tanh(Ucxt+Wcht−1+bc)ct=ft⊙ct−1+it⊙c̃tht=ot⊙tanh(ct),(5)

The input weight matrices are represented by Ws(Wi,Wf,Wo,Uc)and Us(Wi,Wf,Wo,Wc), with bs(bi,bf,bo,bc) being the bias terms. The weight matrix subscript indicates the input-output connection. Wf is the implicit forgetting gate matrix, and Uf is the input-forgetting matrix. The encoder codes the vessel's kinematic state sequence X𝓁 one state at a time into a hidden state sequence. We employ an encoder-decoder architecture to solve the prediction problem of mapping one data sequence to another, specifically defining the mapping function F𝓁,h. The initial encoding function E is represented by [20]

H𝓁=E(X𝓁;θE)(6)

where H𝓁 is the neural network parametrized by θE that maps input sequence X𝓁 to an internal representation data sequence H𝓁={ht}t=1𝓁. Each hidden state ht∈R2q combines bidirectional recurrent neural network (RNN) with a state of size q.

The encoder layer computes the H𝓁 representation of the input sequence, which created the context representation by the aggregation function. The decoder repeatedly uses this context representation to generate the output prediction. We use the average pooling over time (AVG) to reduce the sequence H𝓁 to a single context vector as

z=col(zr)∈ℝ2q, r=1,…,2q(7)

for computing the mean value of each hidden unit. Each context feature zr is defined as

zr=1𝓁∑t=1𝓁(H𝓁)r,t,tϵ{1,…,𝓁}(8)

The symbol θD represents the parameterization of the autoregressive decoder function D to predict the future vessel path ŷj at each period j with the previous state ŷj−1 as follows [21]:

ŷj=D(ŷj−1,uj,zj,ψ,θD)(9)

where uj denotes the RNN hidden state with ψ being the planning descriptor and zj being the context vector. Finally, the output prediction response Ŷh of length h is given by

Ŷh=F𝓁,h(X𝓁,ψ), (10)

To evaluate the quality of the prediction model response, the authors employ the root-mean-square-error (RMSE) [22- 23] method to estimate the average error value of the squares between the predicted path Yĥ and the actual path Yi, which is defined as

R M S E = 1 n ∑ i = 1 n ( Y i − Y h ̂ ) 2 (11)

LSTMs initially tried to replicate human decision-making by utilizing machines to process large quantities of data. Advanced LSTM systems introduce autonomous vessels, which can operate independently without human intervention and have a lower mistake rate than human-operated vessels. Deep learning is gradually altering the maritime industry's traditional operational processes, especially in mining maritime traffic from vessel data as mentioned in this paper.

The optimal values including regression value attained 0.001075 in training, and the loss value reaches 0.0000039103. Besides, a set of historical vessel data from the AIS system is used as input data for the training prediction model to provide a safety path, as shown in Fig. 6. Thus, Fig. 6a illustrates the route taken by a vessel while departing from the wharf and moving towards the sea with the MMSI code 636018224 (indicated by the light-red line). Similarly, the blue line in the figure shows the path followed by the vessel while arriving from the sea to the wharf with the MMSI code 574999621. Finally, the dataset for the same type of vessel visualizing the maritime traffic conditions in VungTau port is indicated in Fig. 6b with vessels Type-1 (on the left side) and Type-3 (on the right side). Finally, the case study experimental results are shown in detail in Fig. 7, the predicted path of the vessel (red line) tracking follows the historical path (blue line) of this vessel.

In general, the system displays marine traffic data calculation and updating and indicates adequate reaction times with initial operation at Vungtau Port, Vietnam. Tests were carried out on using the proposed model from the collected and distributed traffic data as well as obtaining traffic information from the AIS system. The results (Figure 6 and Figure 7) outline the management integration system, which, once implemented, will enhance the operational efficiency of the region's specialist maritime management. The system serves the common benefit of the community and guarantees national security and defense in terms of financial efficiency. Therefore, determining its effectiveness is difficult. However, from a socioeconomic standpoint, the initiative has the following consequences: 

In the future, the model can develop new application features in ensuring maritime safety by predicting the possibility of collision, predicting the risk of running aground, determining the closest point of approach, monitoring cargo anchorage locations, monitoring and indicating current vessel status to reduce risks to vessel, property, and people, as well as environmental pollution hazards. The advanced and modern technologies in state management methods can be used to increase the attractiveness and competitiveness of the seaport system. In addition, it actively contributes to the gradual perfection of specialized management in the maritime sector through international conventions to which Vietnam is a signatory. To this end, the concerns highlighted in Remark 1 have been addressed and the issues thus resolved.