基于Gaussian GRU与Copula函数的船舶交通流不确定性预测

doi:10.16411/j.cnki.issn1006-7736.2025.03.006

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大连海事大学学报 ›› 2025, Vol. 51 ›› Issue (3) : 54-63. DOI: 10.16411/j.cnki.issn1006-7736.2025.03.006

基于Gaussian GRU与Copula函数的船舶交通流不确定性预测

张栋，赵丽宁^*，潘明阳

作者信息 +

Uncertainty prediction of ship traffic flow based on Gaussian GRU and Copula function

ZHANG Dong，ZHAO Lining^*，PAN Mingyang

Author information +

文章历史 +

摘要

以船舶交通流为研究对象，提出一种基于高斯分布假设的门控循环单元（Gaussian GRU）模型预测船舶交通流参数的不确定性分布，并结合Copula函数建立交通流密度和速度的联合概率预测方法。首先，根据交通流的特征，设计一种残差GRU的结构，通过深度堆叠增强GRU的特征提取能力，并结合高斯似然函数估计交通流的概率密度分布。其次，为解决不确定性预测中预测的“滞后”问题，引入点值处理模块，以提高模型预测的稳定性和准确性。利用Gaussian Copula函数建立交通流密度和速度的联合概率模型，并通过采样方法对福姜沙水域中三个航道的状态进行估计。实验结果表明，相较现有模型，本文方法在点值预测和概率密度预测两方面均表现优异，能够更精确地量化船舶交通流的不确定性特征。

Abstract

Taking ship traffic flow as the research object, a Gaussiana gated recurrent unit (Gaussiana GRU) model based on the Gaussian distribution assumption was proposed to predict the uncertainty distribution of ship traffic flow parameters. Furthermore, a joint probability prediction method for traffic flow density and speed was established by combining with the Copula function. Firstly, based on the characteristics of traffic flow, a residual GRU structure was designed to enhance the feature extraction capability of GRU through deep stacking, and the Gaussian likelihood function was combined to estimate the probability density distribution of traffic flow. Secondly, in order to solve the "lag" problem of prediction in uncertainty prediction, a point value processing module was introduced to improve the stability and accuracy of model prediction. The joint probability model of traffic flow density and speed was established by using Gaussian Copula function, and the state of three waterways in the Fujiangsha water area were estimated by using sampling method. Experimental results show that compared with the existing models, this method performs well in both point value and probability density prediction, and can quantify the uncertainty characteristics of ship traffic flow more accurately.

导出引用

张栋, 赵丽宁, 潘明阳. 基于Gaussian GRU与Copula函数的船舶交通流不确定性预测[J]. 大连海事大学学报. 2025, 51(3): 54-63 https://doi.org/10.16411/j.cnki.issn1006-7736.2025.03.006

ZHANG Dong, ZHAO Lining, PAN Mingyang. Uncertainty prediction of ship traffic flow based on Gaussian GRU and Copula function[J]. Journal of Dalian Maritime University. 2025, 51(3): 54-63 https://doi.org/10.16411/j.cnki.issn1006-7736.2025.03.006

参考文献

[1] 吴莹莹，赵丽宁，袁志鑫，等. 基于注意力机制的CNN-GRU船舶交通流预测模型[J].大连海事大学学报, 2023, 49(1):75-84.

WU Y Y, ZHAO L N, YUAN Z X, et al. CNN-GRU ship traffic flow prediction model based on attention mechanism[J]. Journal of Dalian Maritime University, 2023, 49(1):75-84. (in Chinese)

[2] 张博中．基于船舶大数据的交通状态识别及可视化技术研究[D]. 大连:大连海事大学，2020．

ZHANG B Z. Research on traffic status recognition based on ship big data and visualization technology[D]. Dalian: Dalian Maritime University,2020. (in Chinese)

[3] LI L, PAN M Y, LIU Z Y, et al. Semi-dynamic spatial–temporal graph neural network for traffic state prediction in waterways[J]. Ocean Engineering, 2024, 293：116685.

[4] 廉清云,孙伟,李润生. 基于注意力机制的堆叠LSTM短时船舶交通流预测模型[J]. 大连海事大学学报， 2024, 50(1):57-65.

LIAN Q Y, SUN W, LI R S. Stacked LSTM short-term ship traffic flow prediction model based on attention mechanism[J]. Journal of Dalian Maritime University, 2024, 50(1):57-65. (in Chinese)

[5] TORBAT S, KHASHEI M, BIJARI M. A hybrid probabilistic fuzzy ARIMA model for consumption forecasting in commodity markets[J]. Economic Analysis and Policy, 2018, 58：22-31.

[6] YORDER M, HERING A S, NAVIDI W C, et al. Short‐term forecasting of categorical changes in wind power with Markov chain models[J]. Wind Energy, 2014, 17(9):1425-1439.

[7] PINSON P. Very-short-term probabilistic forecasting of wind power with generalized logit—normal distributions[J]. Journal of the Royal Statistical Society. Series C (Applied Statistics), 2012, 61(4):555-576.

[8] WEN R F, TORKKOLA K, NARAYANASWAMY B, et al. A multi-horizon quantile recurrent forecaster[J]. arXiv，2017:1711.11053.

[9] WANG Y Y, SMOLA A, MADDIX D C, et al. Deep Factors for forecasting[C]//Proceedings of Machine Learning Research.[S.l.:s.n.]:2019: 6607-6617.

[10] YU Y X, HAN X S, YANG M, et al. Probabilistic prediction of regional wind power based on spatiotemporal quantile regression[C]//IEEE Transactions on industry applications.[S.l.]:IEEE, 2020:56(6):6117-6127.

[11] SALINAS D, FFLUNKERT V, GASTHAUS J, et al. DeepAR: Probabilistic forecasting with autoregressive recurrent networks[J]. International Journal of Forecasting, 2020, 36(3):1181-1191.

[12] CHEN Y T, KANG Y F, CHEN Y X, et al. Probabilistic forecasting with temporal convolutional neural network[J]. Neurocomputing, 2020, 399: 491-501.

[13] LI Y Q, CHAI S J, WANG G B, et al. Quantifying the uncertainty in long-term traffic prediction based on PI-ConvLSTM network[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(11): 20429-20441.

[14] WANG B, VU H L, KIM I, et al. Distributional prediction of short-term traffic using neural networks[J]. Engineering Applications of Artificial Intelligence, 2023, 126: 107061.

[15] PACCHIARDI L, ADEWOYIN R A, DUEBEN P, et al. Probabilistic forecasting with generative networks via scoring rule minimization[J]. Journal of Machine Learning Research, 2024, 25(45): 1-64.

[16] ZHANG Z C, LI M, LIN X, et al. Multistep speed prediction on traffic networks: A deep learning approach considering spatio-temporal dependencies[J]. Transportation research part C: Emerging Technologies, 2019, 105: 297-322.

[17] DURANTE F, SEMPI C. Copula theory: an introduction[C]//Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw.Heidelberg: Springer Berlin Heidelberg, 2010: 3-31.

[18] YANG Y, LI D S, LI H B, et al. Joint probability distribution of weather factors: a neural network approach for environmental science[J]. Stochastic Environmental Research and Risk Assessment, 2023, 37(11): 4385-4397.

[19] LEE U J, CHO H Y, LEE B W, et al. Joint probability distribution of significant wave height and peak wave period using gaussian copula method[J]. Journal of Coastal Research, 2024, 116(SI): 96-100.

[20] ZHAO Y L, DONG S. Multivariate probability analysis of wind-wave actions on offshore wind turbine via copula-based analysis[J]. Ocean Engineering, 2023, 288:116071.

[21] SKLAR M. Fonctions de répartition à n dimensions et leurs marges[C]//Annales de l'ISUP. 1959, 8(3): 229-231.