Inference method for congestion propagation between ports based on granger causality and reservoir computing

Abstract

The present application relates to the technical field of port logistics intelligent analysis, and is a congestion propagation inference method among ports based on Granger causality and reserve pool calculation, comprising: based on an L space modeling method, a multiple directed container ship transportation network is constructed according to AIS ship trajectory data; the average waiting time of a port is used as a core index to quantify the congestion degree of the port; the network characteristics of the container ship transportation network are calculated; an initial candidate port set is constructed; a machine learning prediction model based on congestion propagation relationship and reserve pool calculation among ports is constructed to predict the congestion degree of each port at the next time step; a greedy iteration algorithm is designed based on the Granger causality idea, and the congestion propagation relationship inference result of each port is optimized based on the congestion prediction error; a congestion degree prediction model is constructed, the congestion propagation relationship is taken as the input, and the prediction of the congestion degree of the port is realized. The present application can accurately infer the congestion propagation among ports.

Description

A Port Congestion Propagation Inference Method Based on Granger Causality and Reservoir Calculation Technical Field

[0001] This invention relates to the field of intelligent analysis technology for port logistics, and in particular to a method for inferring the propagation of congestion between ports based on Granger causality and reserve pool calculation. Background Technology

[0002] Maritime transport handles over 80% of global freight volume and over 95% of my country's import and export freight volume, holding an irreplaceable position in modern freight transportation. In recent years, influenced by various factors, port disruptions have become frequent, often triggering larger-scale port congestion propagation, leading to supply chain disruptions and posing significant difficulties and challenges to the global shipping industry. Therefore, studying the mechanisms of congestion propagation between ports is of great importance.

[0003] Current research on port congestion propagation in maritime networks can be mainly divided into two categories: research on congestion propagation mechanisms based on cascading failure models and data-driven research on inferring congestion propagation relationships between ports.

[0004] Research on congestion propagation mechanisms based on cascading failure models aims to simulate the dynamic propagation of congestion in a port network triggered by an initial port outage by constructing a cascading failure model of the maritime network. Existing work mainly relies on the classic "capacity-load" model framework to construct cascading failure models of maritime networks. When the load of a port exceeds its capacity limit, it is considered a congestion outage, which may trigger successive failures of neighboring or related ports. Although significant progress has been made in this area, much of it is limited to the theoretical level, relying on idealized assumptions to simulate the port congestion propagation process. It has not yet incorporated high-precision, fine-grained AIS vessel trajectory data, thus making it difficult to provide a more detailed and realistic characterization of the congestion propagation mechanism.

[0005] Data-driven inference of congestion propagation relationships between ports is still in its exploratory stage. Existing research mainly relies on machine learning prediction models to learn complex spatiotemporal correlation patterns from historical port congestion data to enhance their performance in short-term prediction tasks (such as port congestion status or ship traffic). While these machine learning prediction models can uncover spatiotemporal correlation features closely related to port congestion propagation mechanisms, their inherent lack of interpretability makes it difficult to explicitly characterize congestion propagation relationships between ports in maritime networks. Li et al. (Li J, Zhang S, Xu B. Containership delaypropagation risk analysis based on effective multivariate transfer entropy. Ocean Engineering, 2024a, 298: 117077.) used a machine learning causal model based on effective multivariate transfer entropy to infer the propagation relationship of container ship delay risks between some ports globally, in East Asia, and Southeast Asia. However, this method did not incorporate domain knowledge of maritime networks (such as network topology and the role of hub ports) during feature reduction and causal inference, ignoring several variables that play a crucial role in the maritime system, which may lead to misjudgments of causal relationships. Furthermore, its effectiveness has only been verified on synthetic data generated based on preset equations, and the inferred congestion propagation relationship has not yet been empirically tested in real maritime networks in conjunction with practical tasks such as port congestion prediction.

[0006] Currently, research on machine learning methods based on causal inference to reveal the transmission relationships of congestion between ports is still scarce. Therefore, there is a need to provide a method for inferring congestion transmission relationships based on Granger causality. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method for inferring congestion propagation among ports based on Granger causality and a reserve pool calculation. This invention combines globally covered AIS trajectory data to study a data-driven method for inferring congestion propagation relationships among ports, inferring the congestion propagation relationship for each port (i.e., which other ports influence a port's congestion status). First, the average waiting time for ships at berths is used to characterize the congestion level of each port at each time step, while simultaneously modeling the global container shipping network. Next, a machine learning method based on congestion propagation relationships among ports and a reserve pool calculation is constructed. Then, considering factors such as route connectivity and geographical proximity between ports, a candidate port set for congestion propagation relationships is selected for each port. Furthermore, a greedy iterative algorithm based on Granger causality is proposed, aiming to minimize the prediction error of the congestion level in the next time step, to infer the optimal congestion propagation relationship for each port from the candidate port set.

[0008] The technical means employed in this invention are as follows:

[0009] A method for inferring congestion propagation between ports based on Granger causality and a reserve pool calculation includes: constructing a multi-directed container ship transportation network based on AIS ship trajectory data using the L-space modeling method; quantifying port congestion level using the average berthing time of the port as a core indicator; calculating the network characteristics of the container ship transportation network; constructing an initial set of candidate ports; constructing a machine learning prediction model based on congestion propagation relationships and a reserve pool calculation to predict the congestion level of each port in the next time step; designing a greedy iterative algorithm based on Granger causality to optimize the congestion propagation relationship inference results for each port based on the congestion prediction error; and constructing a congestion level prediction model that uses the congestion propagation relationship as input to predict the port congestion level.

[0010] Furthermore, the L-space modeling method abstracts ports in the maritime network as nodes; directed edges correspond to the continuous calling-in behavior of ships between two ports; and the container ship transportation network is constructed. ,in, This represents a set of port nodes, where each node represents a port. Let represent the set of directed edges, where each directed edge corresponds to a ship's observed continuous berthing behavior between two ports. If, within the study interval, the same ship has multiple records matching a directed edge, then at the port node... and A corresponding number of multiple edges are formed between them.

[0011] Furthermore, the feature is that the average waiting time represents the average waiting time of container ships waiting at the port anchorage within a certain hour at a certain port since their arrival at the port.

[0012] Furthermore, the feature is that the calculation of the network characteristics of the container ship transportation network specifically includes:

[0013] After constructing a global container shipping network, basic statistics are used to characterize the importance of nodes and the strength of the connections between nodes. These basic statistics include: node degree, frequency of ship passage between ports, and distance between ports.

[0014] The node degree represents the navigation route connecting a port to other ports, used to measure the importance of a node in the network; the inter-port vessel traffic frequency represents the navigation record of consecutive calls at two specific ports within the study period, reflecting the closeness of maritime trade between ports; the inter-port distance is calculated using latitude and longitude, characterizing the feasibility of the two ports as alternative ports.

[0015] Furthermore, the method of constructing the initial candidate port set specifically includes:

[0016] Representing the set of all port nodes as Locate the target port The start time of the congestion is Other ports The start time of the congestion is Extract the upstream port set of the shipping route topology. Collection of neighboring ports within the congestion zone by geographical distance ; Filter the upstream port set of the shipping route topology and nearby ports China satisfies The nodes are used to generate an initial set of candidate ports. .

[0017] Furthermore, the feature is that the construction of the machine learning prediction model based on the congestion propagation relationship between ports and the calculation of the reserve pool specifically includes:

[0018] Let the input sequence be The input sequence is represented as:

[0019]

[0020] in, Indicates that the system is in Moment Dimensional state, For the corresponding 3D nonlinear vector field, Represents the state vector The time derivative, whose evolution is determined by an unknown nonlinear function. dominated.

[0021] The input sequence Mapped to higher levels through the input layer In 3D space, the state sequence of the reservoir is obtained. The state sequence of the reservoir is mapped to the desired output space through the output layer. The output sequence is obtained from the following equation:

[0022]

[0023]

[0024] in, It's the leakage rate. For bias terms, It is the hyperbolic tangent function. , These are the input weight matrix and the output weight matrix, respectively. For the sparse weighted adjacency matrix of the reservoir, The model represents the The prediction results.

[0025] The loss function of the reserve pool can be expressed as:

[0026]

[0027] in, The coefficient of the regularization penalty term is . Represent a suitable matrix norm;

[0028] The congestion propagation relationship is obtained through the input matrix. and adjacency matrix Encoding to the reserve pool calculation:

[0029]

[0030]

[0031] in, This is the floor function. It is The matrix, Set all elements in column A to random values, and set all elements in the remaining columns to 0. It consists of multiple A matrix formed by stacking matrices row by row in order; It is A random sparse matrix, This represents the block diagonal matrix construction operation, which converts a series of submatrices... Arranged along the main diagonal, with zeros filling the off-diagonal positions, thus forming the internal connection matrix of the reservoir. .

[0032] Furthermore, it is characterized in that, for each port The inference results regarding congestion propagation relationships were optimized, specifically including:

[0033] Initial candidate port set By embedding the predictions into the reservoir calculation, the corresponding predicted values ​​are obtained, and the mean absolute error (MAE) is used as the average absolute error between the predicted and actual values, i.e., the initial prediction error. At this point, the candidate port set Prediction error ;

[0034] A port influence evaluation system is constructed based on the aforementioned container shipping network. :

[0035]

[0036] in, Indicates influence score. This represents the ranking of ports sorted in descending order of node degree. This indicates the ranking of ports in descending order of ship traffic frequency. This indicates the ranking of ports in ascending order of geographical distance;

[0037] The candidate port set is calculated using the aforementioned port influence evaluation system. Influence score of each port ;

[0038] From the current set of candidate ports Remove the port that is unmarked and has the lowest influence score. to form a port cluster ,Will Embedding machine learning prediction models to calculate prediction errors Combining Granger causality principles, a greedy iterative algorithm is designed if the following conditions are met: Then determine If a node has a congestion propagation relationship with the target port, it is marked as an irremovable node; otherwise, removal is permitted, and updates are performed. ,in, The significance threshold, Indicates the set of candidate ports Port-based prediction models embedded in machine learning The prediction error.

[0039] Repeat the node removal operation until the prediction error converges to a stable lower bound, the port set tends to stabilize, and the iteration terminates; then utilize the port set after the iteration. The optimal congestion propagation relationships for the target port are determined, and an adjacency matrix is ​​generated. .

[0040] Furthermore, the congestion prediction model includes a graph convolution module and a temporal convolution module, which are used alternately to capture spatial and temporal dependencies, respectively.

[0041] The graph convolution module propagates the congestion status of a port to adjacent ports step by step through a congestion propagation relationship structure, representing the time series of congestion levels of all ports as follows: , Represents the model parameter matrix. To represent the structure of congestion propagation, the forward transition matrix and the backward transition matrix are expressed as follows:

[0042]

[0043]

[0044] The diffusion map convolutional layer representation is written as:

[0045]

[0046] in, Indicates the output. This represents the finite number of steps that the diffusion process takes.

[0047] The temporal convolution module comprises a first dilated causal convolution and a second dilated causal convolution. The first dilated causal convolution is followed by a hyperbolic tangent activation function as a filter to capture local dynamic changes in port congestion from the input time series. The second dilated causal convolution is followed by a sigmoid activation function as a gating unit to weightedly modulate the features extracted by the filter. Given a one-dimensional sequence input... and a filter , will input and exist The dilated causal convolution operation of step is represented as:

[0048]

[0049] in, It is an expansion factor used to control the jump distance and capture congestion changes at different time scales.

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] This invention provides a method for inferring congestion propagation between ports based on Granger causality and reservoir calculation. It proposes an improved reservoir calculation method, encoding the congestion propagation relationship between ports into an input matrix and an adjacency matrix, and embedding them into the reservoir calculation process. Compared to the traditional reservoir model, the new method can better capture the internal relationships of the dynamic system. Then, based on the constructed reservoir calculation model, a greedy iterative algorithm is designed using Granger causality to infer the congestion propagation relationship between ports. In testing, the inference performance of this study is good in real-world tasks, and its prediction performance is superior to existing methods. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 is a framework diagram of the port congestion propagation inference method based on Granger causality and reserve pool calculation in this invention.

[0054] Figure 2 is a comparison of the adjacency matrix constructed based on Topology-A and the adjacency matrix inferred by the congestion propagation inference model in this embodiment of the invention. Detailed Implementation

[0055] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0058] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0059] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0060] As shown in Figure 1, this invention provides a method for inferring congestion propagation between ports based on Granger causality and reserve pool calculations, including: constructing a multi-directed container ship transportation network based on AIS ship trajectory data using the L-space modeling method; in a preferred embodiment of this invention, the L-space modeling method abstracts ports in the maritime network as nodes; directed edges correspond to the continuous call-in behavior of ships between two ports; and the container ship transportation network is constructed. ,in, This represents a set of port nodes, where each node represents a port. Let represent the set of directed edges, where each directed edge corresponds to a ship's observed continuous berthing behavior between two ports. If, within the study interval, the same ship has multiple records matching a directed edge, then at the port node... and A corresponding number of multiple edges are formed between them.

[0061] In practice, the container shipping network is constructed as a multi-directed graph that accurately reflects the complex connections between different ports based on specific vessel call-in behaviors, including repeated sailing routes and frequencies. This modeling approach not only captures directionality but also reflects the activity intensity on specific routes through the presence of multiple edges.

[0062] The average waiting time at a port is used as a core indicator to quantify the degree of port congestion. In a preferred embodiment of the present invention, the average waiting time represents the average waiting time of container ships waiting at the port anchorage within a certain hour at a certain port since their arrival.

[0063] During implementation, within the target hour interval, for all container ships waiting to berth at anchor, the accumulated waiting time from their arrival at the port to the end of that hour is calculated, and the arithmetic mean of the accumulated waiting times for all ships is taken. The formula is as follows:

[0064]

[0065] in, It is a port In the The level of congestion per hour, It is the first Hours waiting at the port The number of container ships at the anchorage, It is up to the number Hourly container ships At the port The cumulative waiting time at the anchorage. Then the port... Time period Historical congestion data is .

[0066] Calculate the network characteristics of the container shipping network; in a preferred embodiment of the present invention, after constructing the global container shipping network, basic statistics are used to characterize the importance of nodes and the strength of the association between nodes. The basic statistics include: node degree, frequency of ship passage between ports and distance between ports.

[0067] Node degree represents the navigation routes connecting a port to other ports, used to measure the importance of a node in the network; inter-port vessel traffic frequency represents the navigation records of consecutive calls at two specific ports within the study period, reflecting the closeness of maritime trade between ports; inter-port distance is calculated using latitude and longitude, characterizing the feasibility of two ports as alternative ports. When a port experiences congestion, shipping companies typically assess whether to divert vessels to nearby ports, taking into account factors such as geographical distance. Therefore, ports that are closer together are more likely to be alternative ports for each other.

[0068] On the one hand, port congestion triggers a chain reaction, with congestion at upstream ports spreading to downstream ports after a certain time delay. On the other hand, to avoid port congestion, shipping companies typically prefer geographically proximate ports as alternative port of call. Therefore, an initial candidate port set is constructed; specifically, in a preferred embodiment of this invention, the set of all port nodes is represented as... Locate the target port The start time of the congestion is Other ports The start time of the congestion is Extract the upstream port set of the shipping route topology. Collection of nearby ports within a congestion zone (1200 km) ; Filter the upstream port set of the shipping route topology and nearby ports China satisfies The nodes are used to generate an initial set of candidate ports. By combining the dual spatial constraints of route topology and geographical proximity with time constraints, we can effectively avoid introducing unreasonable nodes in the process of learning the congestion propagation structure, and thus more accurately infer the propagation structure of port congestion.

[0069] A machine learning prediction model based on the congestion propagation relationship between ports and reserve pool calculation is constructed to predict the congestion level of each port in the next time step. Specifically, as a preferred embodiment of this invention, reserve pool calculation (RC) is a machine learning paradigm particularly suitable for dynamic system learning, exhibiting excellent performance in time series prediction. Let the input sequence be... The input sequence is represented as:

[0070]

[0071] in, Indicates that the system is in Moment Dimensional state, For the corresponding A nonlinear vector field; this vector field (equivalent to each component function) ) and this The underlying complex interaction mechanisms among the variables are completely unknown beforehand (i.e., neither partially known nor completely known). The only known information about this underlying system is the time series observed at discrete time steps. . Represents the state vector The time derivative, whose evolution is determined by an unknown nonlinear function. dominated.

[0072] Reserve pool computation maps inputs to a high-dimensional latent space through a high-dimensional dynamic system (reservoir), and then maps from the latent space to the desired output space. However, traditional reserve pool computation randomly assigns input layer and reserve pool link weights, making it difficult to capture the internal relationships of the dynamic system, resulting in poor prediction performance. Therefore, this paper proposes a machine learning model based on inter-port congestion propagation relationships and reserve pool computation to further improve upon traditional reserve pool computation. The inter-port congestion propagation relationships are encoded into the reserve pool computation through the input matrix and adjacency matrix, and the weights of the output layer are trained through ridge regression, thereby constructing a machine learning model based on inter-port congestion propagation relationships and reserve pool computation to predict the congestion level of each port in the next time step; the schematic diagram is shown in Figure 1. Compared with traditional RC, this machine learning model can more accurately predict the short-term congestion level of ports in the maritime network; conversely, a model with high prediction accuracy also implies its successful capture and accurate representation of inter-port congestion propagation relationships.

[0073] Input sequence Mapped to higher levels through the input layer In 3D space, the state sequence of the reservoir is obtained. The output layer maps the data to the desired output space; the state sequence of the reservoir. The output sequence is obtained from the following equation:

[0074]

[0075]

[0076] in, It's the leakage rate. For bias terms, It is the hyperbolic tangent function. , These are the input weight matrix and the output weight matrix, respectively. For the sparse weighted adjacency matrix of the reservoir, This represents the model's prediction result at t+1.

[0077] Minimize the predicted value and the true value The task of the loss function is to minimize the loss function, which can be expressed as:

[0078]

[0079] in, The coefficient of the regularization penalty term is . To represent a suitable matrix norm, the L2 norm is usually chosen.

[0080] The key to designing machine learning prediction models lies in how to effectively encode the congestion propagation relationships between ports into the reserve pool calculation through the combined action of the input matrix and the adjacency matrix. The input matrix determines how the input is mapped to the reserve pool, while the adjacency matrix describes the connectivity relationships between nodes in the reserve pool. The machine learning prediction model uses the input matrix to encode the congestion propagation relationships... and adjacency matrix Encoding into the reserve pool calculation:

[0081]

[0082]

[0083] in, This is the floor function. It is The matrix, Set all elements in column A to random values, and set all elements in the remaining columns to 0. It consists of multiple A matrix formed by stacking matrices row by row in order; It is A random sparse matrix, A matrix is ​​a combination of multiple A diagonal matrix is ​​formed by arranging matrices along their diagonals. This represents the block diagonal matrix construction operation, which involves constructing a series of submatrices. Arranged along the main diagonal, with the off-diagonal positions filled with zeros, thus forming an internal connection matrix of the reservoir. .

[0084] Based on Granger causality, a greedy iterative algorithm is designed to optimize the congestion propagation relationship inference results for each port based on congestion prediction errors. In a preferred implementation, a target port is selected based on factors such as inter-port shipping route connections and geographical proximity. Define a candidate port set for potential congestion propagation relationships and calculate the initial prediction error of the machine learning model embedded in this candidate port set. Construct an influence evaluation system to quantify the influence of each port node in the candidate port set on the target port. Generate a new candidate port set by prioritizing the removal of ports with low influence. Combining Granger causality, determine the congestion propagation relationship (i.e., causal relationship) through error feedback. If the model prediction error under the new candidate port set significantly increases, it indicates that the historical information of the previously removed ports has a significant impact on the prediction of the target port. Therefore, the removed ports are restored and marked as irremovable; otherwise, retain the optimization result. Repeat this iterative process until all ports in the candidate port set are marked and the prediction error tends to stabilize. The final port set obtained is the optimal congestion propagation relationship for the target port.

[0085] Initial candidate port set By embedding the data into the reserve pool calculation, the corresponding predicted values ​​are obtained, and the mean absolute error (MAE) of the initial prediction is used as the average absolute error between the predicted and actual values. At this point, the candidate port set Prediction error ;

[0086] Constructing a Port Influence Evaluation System Based on Container Shipping Networks :

[0087]

[0088] in, Indicates influence score. This represents the ranking of ports sorted in descending order of node degree. This indicates the ranking of ports in descending order of ship traffic frequency. This indicates the ranking of ports in ascending order of geographical distance (i.e., from highest to lowest geographical proximity).

[0089] Calculate the candidate port set using a port influence evaluation system Influence score of each port ;

[0090] Remove the unmarked port with the lowest influence score from the current candidate port set S. to form a port cluster , will set Embedding machine learning prediction models to calculate prediction errors Combining Granger causality principles, a greedy iterative algorithm is designed if the following conditions are met: Then determine If a congestion propagation relationship exists with the target port, mark it as an irremovable node; otherwise, accept the removal operation and update S= , = ,in, The significance threshold is set to 0.1. Indicates the set of candidate ports Targeted ports under embedded machine learning prediction models The prediction error.

[0091] Repeat the node removal operation until the prediction error converges to a stable lower bound, the port set tends to stabilize, and the iteration terminates; then utilize the port set after the iteration. The optimal congestion propagation relationships for the target port are determined, and an adjacency matrix is ​​generated. .

[0092] In the field of urban road traffic flow prediction, machine learning methods have matured, and urban road networks are relatively simple, enabling effective integration of spatiotemporal dependencies for accurate modeling. However, research on port congestion prediction remains relatively scarce: existing work is mostly limited to using temporal neural networks such as LSTM to model historical data of individual ports, generally neglecting the spatial correlation between ports, especially failing to fully incorporate the congestion propagation mechanism between ports, thus limiting the predictive ability of the model under complex maritime networks. Therefore, this invention uses a port congestion state prediction task to verify the effectiveness of the proposed inference congestion propagation relationship structure framework. A multi-step congestion degree prediction model is constructed, consisting of a graph convolution module and a temporal convolution module. The congestion propagation relationship structure serves as the input to the graph convolution module, which is used alternately with the temporal convolution module to capture spatial and temporal dependencies respectively.

[0093] The graph convolution module propagates the congestion status of a port to neighboring ports through a congestion propagation structure, representing the time series of congestion levels for all ports as follows: , Represents the model parameter matrix. To represent the structure of congestion propagation, the forward transition matrix and the backward transition matrix are expressed as follows:

[0094]

[0095]

[0096] The diffusion map convolutional layer representation is written as:

[0097]

[0098] in, Indicates the output. This represents the finite number of steps that the diffusion process takes.

[0099] The top layer of the diffusion graph convolution, by aggregating information from multi-hop propagation paths, can capture the impact of congestion at distant ports on the current port. The bottom layer of the diffusion graph convolution, however, primarily focuses on the congestion propagation relationships between directly adjacent ports, reflecting the local direct impact. This layered design allows the model to both model the complex propagation effects formed by the superposition of multiple direct propagation relationships and retain sensitivity to local propagation relationships.

[0100] The temporal convolution module consists of a first dilated causal convolution and a second dilated causal convolution. The first dilated causal convolution is followed by a hyperbolic tangent activation function as a filter to capture local dynamic changes in port congestion from the input time series. The second dilated causal convolution is followed by a sigmoid activation function as a gating unit to weight and modulate the features extracted by the filter. Given a one-dimensional sequence input... and a filter , will input and exist The dilated causal convolution operation of step is represented as:

[0101]

[0102] in, The dilation factor controls the jump distance, capturing congestion changes across different time scales. By stacking multiple dilated causal convolutions in ascending order of dilation factor, the model's receptive field can grow exponentially. This design allows the model to better capture long-term dependencies and trend changes in port congestion. Furthermore, by increasing network depth, the model can not only cover a larger time range but also effectively mitigate the gradient explosion problem, thereby improving training stability and prediction performance.

[0103] Example

[0104] To evaluate the effectiveness of the proposed algorithm, a multi-step prediction task for port congestion was designed based on a real maritime dynamic network, and systematic verification was conducted through comparative experiments. AIS data of global container ships within a certain time period was selected as the dataset; the top 50 pairs of ports ranked by distance in ascending order and the top 50 pairs of ports ranked by ship passage frequency in descending order were selected as the observation objects to predict congestion status. The model training used the mean absolute error between the actual and predicted values ​​as the loss function, and the Adam optimizer was used for parameter updates, with an initial learning rate set to 1e. -3The training cycle is 100 epochs. Regarding data partitioning, 60% of the data is divided into a training set, 20% into a validation set, and 20% into a test set, ensuring no overlap in the time dimension. The model selection strategy dynamically saves the optimal checkpoint based on the validation set performance. The evaluation metric system includes mean absolute error and root mean square error, used to quantify the degree of deviation between predicted and true values. In the multi-step prediction experiments of this invention, the presented experimental data are the arithmetic mean of the results obtained from five independent repeated experiments.

[0105] Experiments were conducted by constructing graph adjacency matrices in different ways, i.e., using different methods to characterize the congestion propagation relationship between ports. The specific comparison results are shown in Table 1.

[0106] Table 1. Validation of the effectiveness of the congestion propagation relationship structure.

[0107]

[0108] Where Pre-defined-A indicates that N is generated randomly. N-dimensional adjacency matrix To predict the congestion propagation relationships between ports, including... The congestion propagation relationship between ports (consistent with the number of ports in the congestion propagation relationship structure inferred in this invention) can be expressed by the following formula: Directed-A indicates that an adaptive adjacency matrix is ​​used to characterize the congestion propagation relationship between ports for prediction. The adjacency matrix is ​​calculated using the similarity score of node embeddings. It can be expressed as the following formula: ,in Topology-A uses the route network topology E as the adjacency matrix. To predict congestion propagation between ports, i.e. ;GRCGNN(ours) is the adjacency matrix obtained using this invention. To predict the spread of congestion between ports.

[0109] Experimental results show that the proposed method (GRCGCN) outperforms other adjacency matrix construction methods in short-term, medium-term, and long-term congestion prediction tasks. Notably, the adjacency matrix constructed based on Topology-A slightly outperforms this method in long-term prediction, but its performance is slightly inferior in short-term and medium-term prediction, though it is still superior to the other two methods overall. To further analyze Topology-A and the congestion propagation matrix inferred by this invention, the adjacency matrix A (congestion propagation matrix) inferred by this invention is visualized and compared with the adjacency matrix (route topology matrix) constructed based on Topology-A, as shown in Figure 2. Analysis reveals that 91.6% of the congestion propagation matrix also appears in the route topology (overlapping parts are marked in red), indicating that route topology is a major factor in congestion propagation. However, compared to route topology, the congestion propagation matrix removes redundant connections and retains key congestion propagation relationships.

[0110] In addition, this study compared its predictive performance with the current mainstream port congestion prediction model, namely the LSTM model, and also compared it with the graph neural network model Graph WaveNet. Graph WaveNet innovatively constructs an adaptive adjacency matrix to dynamically capture potential spatial dependencies. The specific comparison results are shown in Table 2.

[0111] Table 2 Comparison of Port Congestion Prediction Performance

[0112]

[0113] The results show that the GRCGNN model significantly outperforms other models across all metrics. Furthermore, GRCGNN demonstrates superior performance in short-, medium-, and long-term predictions.

[0114] The above results fully demonstrate that the method proposed in this invention has good effectiveness and practicality in actual port congestion prediction tasks; the route topology is one of the key factors affecting the port congestion propagation process.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inferring the propagation of congestion between ports based on Granger causality and reserve pool calculations, characterized in that, include: Based on the L-space modeling method, a multi-directional container ship transportation network is constructed using AIS ship trajectory data; The average waiting time at ports is used as the core indicator to quantify port congestion; the network characteristics of the container ship transportation network are calculated; an initial set of candidate ports is constructed; and a machine learning prediction model based on the congestion propagation relationship between ports and the calculation of the reserve pool is constructed to predict the congestion level of each port in the next time step. Based on the Granger causality concept, a greedy iterative algorithm is designed to optimize the inference results of congestion propagation relationships for each port based on the congestion prediction error. A congestion degree prediction model is constructed, and the effectiveness of the congestion propagation relationship structure is verified by taking the congestion propagation relationship as input.

2. The method for inferring inter-port congestion propagation based on Granger causality and reserve pool calculations according to claim 1, characterized in that, The L-space modeling method abstracts ports in the maritime network as nodes; directed edges correspond to the continuous calling-in behavior of ships between two ports; and the container ship transportation network is constructed. ,in, This represents a set of port nodes, where each node represents a port. Let represent the set of directed edges, where each directed edge corresponds to a ship's observed continuous berthing behavior between two ports. If, within the study interval, the same ship has multiple records matching a directed edge, then at the port node... A corresponding number of multiple edges are formed between v and v.

3. The method for inferring inter-port congestion propagation based on Granger causality and reserve pool calculations according to claim 1, characterized in that, The average waiting time refers to the average waiting time of container ships waiting at the port anchorage within a certain hour at a certain port since their arrival.

4. The method for inferring the propagation of congestion between ports based on Granger causality and reserve pool calculations according to claim 1, characterized in that, The calculation of the network characteristics of the container shipping network specifically includes: after constructing the container shipping network, using basic statistics to characterize the importance of nodes and the strength of association between nodes. The basic statistics include: node degree, inter-port vessel traffic frequency, and inter-port distance. The node degree represents the navigation routes connecting a port to other ports and is used to measure the importance of a node in the network. The inter-port vessel traffic frequency represents the navigation records of consecutive calls at two specific ports within the study period, reflecting the closeness of maritime trade between ports. The inter-port distance is calculated using latitude and longitude to characterize the feasibility of the two ports as alternative ports.

5. The method for inferring inter-port congestion propagation based on Granger causality and reserve pool calculations according to claim 1, characterized in that, The construction of the initial candidate port set specifically includes: representing the set of all port nodes as... Locate the target port The start time of the congestion is Other ports The start time of the congestion is Extract the upstream port set of the shipping route topology. Collection of neighboring ports within the congestion zone by geographical distance ; Filter the upstream port set of the shipping route topology and nearby ports China satisfies The nodes are used to generate an initial set of candidate ports. 。 6. The method for inferring inter-port congestion propagation based on Granger causality and reserve pool calculations according to claim 1, characterized in that, The construction of a machine learning prediction model based on the congestion propagation relationship between ports and the calculation of reserve pools specifically includes: assuming the input sequence is... The input sequence is represented as: in, Indicates that the system is in Moment Dimensional state, For the corresponding 3D nonlinear vector field, Represents the state vector The time derivative, whose evolution is determined by an unknown nonlinear function. Dominated; the input sequence Mapped to higher levels through the input layer In 3D space, the state sequence of the reservoir is obtained. The state sequence of the reservoir is mapped to the desired output space through the output layer. The output sequence is obtained from the following equation: in, It's the leakage rate. For bias terms, It is the hyperbolic tangent function. ， These are the input weight matrix and the output weight matrix, respectively. For the sparse weighted adjacency matrix of the reservoir, The model represents the The prediction results; the loss function of the reserve pool is expressed as: in, The coefficient of the regularization penalty term is . Representing a suitable matrix norm; the congestion propagation relationship is expressed through an input matrix. and adjacency matrix Encoding to the reserve pool calculation: in, This is the floor function. It is The matrix, Set all elements in column A to random values, and set all elements in the remaining columns to 0. It consists of multiple A matrix formed by stacking matrices row by row in order; It is A random sparse matrix, This represents the block diagonal matrix construction operation, which converts a series of submatrices... Arranged along the main diagonal, with zeros filling the off-diagonal positions, thus forming the internal connection matrix of the reservoir. 。 7. The method for inferring the propagation of congestion between ports based on Granger causality and reserve pool calculations according to claim 5, characterized in that, For each of the ports The congestion propagation relationship inference results are optimized, specifically including: refining the initial candidate port set. By embedding the predictions into the reserve pool calculation, the corresponding predicted values ​​are obtained, and the mean absolute error of the prediction, i.e., the initial prediction error, is used as the average absolute error of the prediction. At this point, the candidate port set Prediction error A port influence evaluation system is constructed based on the aforementioned container shipping network. ： in, Indicates influence score. This represents the ranking of ports sorted in descending order of node degree. This indicates the ranking of ports in descending order of ship traffic frequency. This represents the ranking of ports in ascending order of geographical distance; the candidate port set is calculated using the aforementioned port influence evaluation system. Influence score of each port From the current set of candidate ports Remove the port that is unmarked and has the lowest influence score. to form a port cluster ,Will Embedding machine learning prediction models to calculate prediction errors Combining Granger causality principles, a greedy iterative algorithm is designed if the following conditions are met: Then determine If a node has a congestion propagation relationship with the target port, it is marked as an irremovable node; otherwise, removal is permitted, and updates are performed. ,in, The significance threshold, Indicates the set of candidate ports Port-based prediction models embedded in machine learning The prediction error is calculated; the node removal operation is repeated until the prediction error converges to the stable lower bound, the port set tends to stabilize, and the iteration is terminated; the port set after the iteration is completed is used. constituting the target port The optimal congestion propagation relationship, adjacency matrix This indicates the structure of congestion propagation relationships.

8. The method for inferring inter-port congestion propagation based on Granger causality and reserve pool calculations according to claim 7, characterized in that, The congestion prediction model includes a graph convolution module and a temporal convolution module, which are used alternately to capture spatial and temporal dependencies, respectively. The graph convolution module propagates the congestion status of a port to adjacent ports step by step through a congestion propagation structure, representing the time series of congestion levels of all ports as follows: ， Represents the model parameter matrix. To represent the structure of congestion propagation, the forward transition matrix and the backward transition matrix are expressed as follows: The diffusion map convolutional layer representation is written as: in, Indicates the output. This represents the finite number of steps executed in the diffusion process; the temporal convolution module comprises a first dilated causal convolution and a second dilated causal convolution. The first dilated causal convolution is followed by a hyperbolic tangent activation function as a filter to capture local dynamic changes in port congestion from the input time series; the second dilated causal convolution is followed by a sigmoid activation function as a gating unit to weightedly modulate the features extracted by the filter; given a one-dimensional sequence input... and a filter , will input and exist The dilated causal convolution operation of step is represented as: in, It is an expansion factor used to control the jump distance and capture congestion changes at different time scales.

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