长期Transformer和自适应傅里叶变换的动态图卷积交通流预测研究

张红; 伊敏; 张玺君; 李扬; 张鹏程

doi:10.11999/JEIT241076

长期Transformer和自适应傅里叶变换的动态图卷积交通流预测研究

doi: 10.11999/JEIT241076 cstr: 32379.14.JEIT241076

兰州理工大学计算机与通信学院兰州 730050

基金项目: 甘肃省重点研发项目(23YFGA0063)，国家自然科学基金(62363022, 61663021)，甘肃省自然科学基金(22JR5RA226, 23JRRA886)，甘肃省教育厅产业支撑计划(2023CYZC-35)

详细信息

作者简介:
张红：女，博士，副教授，研究方向为机器学习、大数据分析、智能交通

伊敏：女，硕士生，研究方向为智能交通

张玺君：男，博士，副教授，研究方向为大数据处理、数据挖掘分析、嵌入式系统、机器学习、智能交通

李扬：男，硕士生，研究方向为智能交通

张鹏程：男，硕士生，研究方向为智能交通

通讯作者:
张红　zhanghong@lut.edu.cn

中图分类号: TN911.7
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出版历程
- 收稿日期: 2024-12-05
- 修回日期: 2025-05-25
- 网络出版日期: 2025-06-07
- 刊出日期: 2025-07-22

Long-term Transformer and Adaptive Fourier Transform for Dynamic Graph Convolutional Traffic Flow Prediction Study

School of Computer & Communication, Lanzhou University of Technology, LanZhou 730050, China

Funds: The Key R&D Program of Gansu Province (23YFGA0063), The National Natural Science Foundation of China (62363022,61663021),The Natural Science Foundation of Gansu Province(22JR5RA226, 23JRRA886), Gansu Provincial Department of Education: Industrial Support Plan Project (2023CYZC-35)

摘要

摘要: 针对交通流长期趋势性与非平稳性不易有效建模，以及交通流的隐藏动态时空特征难以捕捉的问题，该文提出一种基于长期Transformer和自适应傅里叶变换的动态图卷积交通流预测模型(ADGformer)。其中，长期门控卷积层通过掩码子序列Transformer从长历史序列中学习压缩的、上下文信息丰富的子序列表示，并利用膨胀门控卷积从子序列的时间表示中有效捕捉交通流的长期趋势特征。并设计一种动态图构造器生成动态可学习图，并利用可学习动态图卷积对节点间潜在的和时变的空间依赖关系进行建模以有效捕获交通流的动态隐藏空间特征。其次，自适应频谱块利用傅里叶变换来增强特征表示并捕获长短期的交互作用，同时通过自适应阈值处理来降低交通流的非平稳性。实验结果表明，所提ADGformer模型具有较好的预测性能。
- 交通流预测 /
- 动态图卷积 /
- 长期Transformer /
- 傅里叶变换 /
- 非平稳性
Abstract: Objective The rapid development of Intelligent Transportation Systems (ITS), combined with population growth and increasing vehicle ownership, has intensified traffic congestion and road capacity limitations. Accurate and timely traffic flow prediction supports traffic control centers in road management and assists travelers in avoiding congestion and improving travel efficiency, thereby relieving traffic pressure and enhancing road network utilization. However, current models struggle to capture the complex, non-stationary, and long-term dependent characteristics of traffic systems, limiting prediction accuracy. To address these limitations, deep learning approaches—such as dynamic graph convolution and Transformer architectures—have gained prominence in traffic prediction. This study proposes a dynamic graph convolutional traffic flow prediction model (ADGformer) that integrates a long-term Transformer with an adaptive Fourier transform. The model is designed to more effectively capture long-term temporal dependencies, handle non-stationary patterns, and extract latent dynamic spatiotemporal features from traffic flow data. Methods The ADGformer model, based on a Long-Term Transformer and Adaptive Fourier Transform, comprises three primary components:a stacked Long-term Gated Convolutional (LGConv) layer, a spatial convolutional layer, and a Multifaceted Fusion Module. The LGConv layer integrates a Masked Sub-series Transformer and dilated gated convolution to extract long-term trend features from temporally segmented traffic flow series, thereby enhancing long-term prediction performance. The Masked Sub-series Transformer—comprising the Subsequent Temporal Representation Learner (STRL) and a self-supervised task head—learns compact and context-rich representations from extended time series sub-segments. The spatial convolutional layer incorporates a dynamic graph constructor that generates learnable graphs based on the hidden states of spatially related nodes. These dynamic graphs are then processed using learnable dynamic graph convolution to extract latent spatial features that evolve over time. To address the non-stationarity of traffic flow sequences, an adaptive spectral block based on Fourier transform is introduced. Results and Discussions The ADGformer model adaptively models inter-node relationships through a dynamic graph constructor, effectively capturing spatial dependencies within traffic networks and the evolving spatial characteristics of traffic flows. It also learns compressed, context-rich subsequence representations and long-term temporal patterns from extended input sequences. The adaptive spectral block, based on the Fourier transform, reduces the non-stationarity of traffic flow data. To evaluate model performance, this study conducts comparison and ablation experiments on three benchmark datasets. On the PEMSD4 dataset, the ADGformer model reduces MAE under Horizon 3 by approximately 21.57% and 16.72% compared with traditional models such as VAR and LR, respectively. Under Horizon 12 on the England dataset, ADGformer reduces RMSE by 3.35% and 2.44% compared with GWNet and MTGNN, respectively. ADGformer achieves the highest prediction accuracy across all three datasets (Table 2). Visualization comparisons with XGBoost, ASTGCN, and DCRNN on PEMSD4 and England datasets further confirm its superior long-term predictive performance (Fig. 5). The model maintains robust performance as the prediction horizon increases. To assess the contributions of individual components, ablation experiments are performed for Horizons 3, 6, and 12. On Horizon 12 of the PEMSD4 dataset, ADGformer improves MAE by approximately 3.69%, 5.09%, 0.92%, and 7.59% relative to the variant models NMS-Trans, NLGConv, NASB, and NDGConv, respectively. On the England dataset, MAPE is reduced by 3.56%, 18.53%, 2.98%, and 4.87%, respectively (Table 3). Visual results of the ablation study (Fig. 6) show that ADGformer consistently outperforms its variants as the forecast step increases, confirming the effectiveness of each module in the proposed model. Conclusions To address the limitations of existing traffic flow prediction models—namely, (1) failure to capture hidden dynamic spatio-temporal correlations among road network nodes, (2) insufficient learning of key temporal information and long-term trend features from extended historical sequences, and (3) limited ability to reduce the non-stationarity of traffic data—this study proposes a combinatorial traffic flow prediction model, ADGformer, which enables accurate long-term traffic flow prediction. ADGformer employs a Masked Sub-series Transformer to pre-train long historical sequences and extract compact, information-rich subsequence representations. A gated mechanism combined with one-dimensional dilated convolution is then applied to capture long-term trend features and enhance temporal modeling capacity. The model also integrates a spatial convolutional layer constructed from dynamic traffic patterns. Through learnable dynamic graph convolution, it effectively captures evolving spatial dependencies across the network. Furthermore, an adaptive spectral block based on Fourier transform is designed to enhance feature representation and reduce non-stationarity by applying adaptive thresholding to suppress noise, while preserving both long- and short-term interactions. Given the complex and variable nature of traffic flow, future work will consider integrating additional features such as periodicity to further improve prediction performance.
- Traffic flow prediction /
- Dynamic graph convolution /
- Long-term transformer /
- Fourier transform /
- Non-stationarity

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图 1 模型框架图

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图 2 Masked Sub-series Transformer的结构组成

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图 3 动态图的构造

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图 4 可学习动态图卷积

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图 5 PEMSD4和England数据集上不同模型性能比较

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图 6 PEMSD8和England数据集上与变体模型性能对比

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表 1 数据集详细信息

数据集	节点	边	时间步长(min)	时间跨度(月)
PEMSD4	307	16 969	5	2
PEMSD8	170	17 833	5	2
England	314	17 353	15	6

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表 2 各种模型在3个数据集上的预测结果

数据集	模型	Horizon 3			Horizon 6			Horizon 12
数据集	模型	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
PEMSD4	HA	3.567 9	6.778 7	0.080 3	3.568 9	6.779 7	0.080 4	3.570 7	6.781 5	0.080 4
	VAR	1.662 4	3.0882	0.032 7	2.125 0	4.015 6	0.043 3	2.568 7	4.834 7	0.053 6
	XGBoost	1.447 1	2.973 2	0.028 8	1.915 9	4.095 5	0.041 3	2.532 7	5.323 9	0.058 5
	LR	1.565 5	3.138 4	0.030 9	2.075 8	4.291 8	0.043 9	2.795 1	5.597 8	0.062 7
	ASTGCN	1.542 8	3.142 8	0.032 3	1.937 4	4.106 2	0.042 5	2.442 4	5.139 2	0.055 2
	GMAN	1.376 0	2.980 3	0.027 9	1.621 3	3.790 6	0.034 8	1.865 0	4.479 1	0.041 6
	DCRNN	1.429 5	2.880 5	0.028 1	1.853 1	3.873 1	0.039 1	2.366 6	4.899 1	0.052 7
	MTGNN	1.348 5	2.851 7	0.026 8	1.645 4	3.752 3	0.034 8	1.930 6	4.497 2	0.042 6
	GWNet	1.326 6	2.815 9	0.026 6	1.645 6	3.764 0	0.035 6	1.955 0	4.556 0	0.044 6
	ADGformer	1.303 8	2.728 6	0.025 6	1.606 0	3.684 3	0.032 7	1.862 9	4.367 6	0.041 1
PEMSD8	HA	2.811 9	5.676 3	0.063 1	2.809 9	5.673 0	0.063 0	2.804 7	5.664 7	0.062 7
	VAR	1.132 7	2.071 2	0.022 4	1.716 6	3.305 3	0.035 6	2.166 1	4.250 0	0.046 7
	XGBoost	1.199 7	2.569 8	0.024 1	1.560 4	3.503 0	0.033 8	2.000 8	4.484 0	0.045 8
	LR	1.271 1	2.633 5	0.024 4	1.661 4	3.560 6	0.033 5	2.168 1	4.579 4	0.045 9
	ASTGCN	1.379 4	2.993 4	0.029 7	1.644 6	3.619 4	0.035 8	1.994 5	4.288 0	0.043 6
	GMAN	1.137 4	2.675 2	0.023 4	1.323 7	3.395 0	0.029 2	1.512 0	4.0524	0.035 5
	DCRNN	1.195 7	2.467 9	0.023 6	1.534 7	3.303 4	0.032 5	1.905 1	4.145 1	0.042 7
	MTGNN	1.140 2	2.573 8	0.023 4	1.397 7	3.491 3	0.031 4	1.632 3	4.249 0	0.039 4
	GWNet	1.118 4	0.023 3	2.553 3	1.384 9	3.532 7	0.031 9	1.604 3	4.242 4	0.039 1
	ADGformer	1.046 9	2.451 6	0.019 1	1.318 5	3.282 0	0.028 5	1.505 8	4.051 4	0.035 3
England	HA	7.047 3	12.213 3	0.099 3	7.044 1	12.210 6	0.099 3	7.034 1	12.200 5	0.099 2
	VAR	3.213 5	5.725 4	0.041 9	4.101 9	7.576 4	0.056 3	4.837 2	8.948 7	0.069 3
	XGBoost	3.192 4	6.717 7	0.044 0	4.298 8	8.667 3	0.063 1	5.523 7	10.475 6	0.082 9
	LR	3.773 2	7.433 1	0.050 5	5.281 6	9.704 5	0.073 7	6.566 4	11.599 1	0.094 3
	ASTGCN	3.214 1	6.540 4	0.043 9	3.926 2	7.917 7	0.055 6	4.601 0	9.079 3	0.066 4
	GMAN	2.611 7	6.287 4	0.036 2	2.955 8	7.333 9	0.043 1	3.306 6	8.140 4	0.049 3
	DCRNN	2.836 3	6.106 2	0.038 1	3.491 3	7.447 3	0.048 7	4.281 3	8.721 7	0.061 0
	MTGNN	2.535 2	5.978 9	0.035 4	2.921 6	7.088 9	0.043 0	3.335 9	7.993 6	0.050 7
	GWNet	2.521 6	5.961 0	0.034 8	2.961 0	7.128 4	0.043 6	3.446 1	8.068 7	0.051 3
	ADGformer	2.519 0	5.943 5	0.034 8	2.907 9	7.045 0	0.042 8	3.243 4	7.798 8	0.048 8

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表 3 ADGformer模型与变体模型在不同时间步长的预测性能

数据集	模型	Horizon 3			Horizon 6			Horizon 12
数据集	模型	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
PEMSD4	NMS-Trans	1.330 3	2.810 3	0.026 2	1.643 3	3.727 1	0.035 1	1.934 3	4.493 5	0.043 2
	NLGConv	1.353 8	2.828 6	0.027 6	1.656 0	3.784 3	0.036 7	1.962 9	4.567 6	0.044 1
	NASB	1.303 2	2.772 3	0.025 8	1.611 1	3.694 7	0.033 9	1.880 2	4.399 0	0.041 9
	NDGConv	1.345 2	2.828 4	0.026 4	1.684 3	3.782 7	0.035 7	2.016 0	4.625 8	0.045 1
	ADGformer	1.303 8	2.728 6	0.025 6	1.606 0	3.684 3	0.032 7	1.862 9	4.367 6	0.041 1
PEMSD8	NMS-Trans	1.103 9	2.483 2	0.021 9	1.360 0	3.332 8	0.029 1	1.607 1	4.076 5	0.036 3
	NLGConv	1.111 4	2.500 5	0.022 2	1.389 6	3.447 0	0.030 4	1.666 7	4.263 7	0.038 5
	NASB	1.121 8	2.566 9	0.022 9	1.398 2	3.533 4	0.031 0	1.631 3	4.232 8	0.037 9
	NDGConv	1.149 5	2.563 2	0.023 9	1.442 5	3.497 0	0.031 9	1.724 6	4.263 1	0.039 7
	ADGformer	1.046 9	2.451 6	0.019 1	1.318 5	3.282 0	0.028 5	1.505 8	4.051 4	0.035 3
England	NMS-Trans	2.528 2	5.994 9	0.035 3	2.889 0	7.109 5	0.043 3	3.288 5	7.900 6	0.050 6
	NLGConv	2.513 2	6.271 1	0.037 3	2.988 9	7.178 7	0.044 2	3.297 7	7.993 7	0.059 9
	NASB	2.524 7	5.984 7	0.035 3	2.911 9	7.092 5	0.044 3	3.267 8	7.917 2	0.050 3
	NDGConv	2.555 7	6.088 4	0.036 2	2.957 3	7.258 3	0.044 2	3.339 8	7.997 9	0.051 3
	ADGformer	2.519 0	5.943 5	0.034 8	2.907 9	7.045 0	0.042 8	3.243 4	7.798 8	0.048 8

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