基于LSTM模型与加权最小二乘组合的日长变化预测方法

doi:10.11947/j.AGCS.2026.20250346

测绘学报 ›› 2026, Vol. 55 ›› Issue (3): 477-489.doi: 10.11947/j.AGCS.2026.20250346

基于LSTM模型与加权最小二乘组合的日长变化预测方法

刘婧璇¹(), 刘学习¹^,²(), 张克非¹, 杨超³, 吴素芹¹, 朱守庆¹, 郭福东¹

^1.中国矿业大学环境与测绘学院，江苏　徐州　221116
^2.湖北珞珈实验室，湖北　武汉　430079
^3.香港理工大学土地测量与地理信息学系，香港　999077

收稿日期:2025-08-26 修回日期:2026-03-17 出版日期:2026-04-16 发布日期:2026-04-16
通讯作者: 刘学习 E-mail:TS24160026A31@cumt.edu.cn;xuexiliu@cumt.edu.cn
作者简介:刘婧璇（2001—），女，硕士生，研究方向为地球定向参数解算及预报。E-mail：TS24160026A31@cumt.edu.cn
基金资助:
国家自然科学基金(42304015; 42274021; 42361134583);国家重点研发计划(2024YFB3910004);江苏省自然科学基金(BK20231087);中国博士后科学基金特别资助(2025T180062);湖北珞珈实验室开放基金(250100007);中国博士后科学基金面上项目(2024M753525);江苏省青年科技人才托举工程项目(JSTJ-2024-075);江苏省自然资源科技项目(JSZRKJ202510);中国矿业大学“双一流”建设提升自主创新能力项目(2022ZZCX06)

A prediction method for LOD based on combined LSTM and WLS

Jingxuan LIU¹(), Xuexi LIU¹^,²(), Kefei ZHANG¹, Chao YANG³, Suqin WU¹, Shouqing ZHU¹, Fudong GUO¹

^1.School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
^2.Hubei Luojia Laboratory, Wuhan 430079, China
^3.Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong 999077, China

Received:2025-08-26 Revised:2026-03-17 Online:2026-04-16 Published:2026-04-16
Contact: Xuexi LIU E-mail:TS24160026A31@cumt.edu.cn;xuexiliu@cumt.edu.cn
About author:LIU Jingxuan (2001—), female, postgraduate, majors in calculation and prediction of Earth orientation parameters. E-mail: TS24160026A31@cumt.edu.cn
Supported by:
The National Natural Science Foundation of China(42304015; 42274021; 42361134583);The National Key Research and Development Program of China(2024YFB3910004);The Natural Science Foundation of Jiangsu Province(BK20231087);Special Support form China Postdoctoral Science Foundation(2025T180062);The Project Supported by the Open Fund of Hubei Luojia Laboratory(250100007);General Project of China Postdoctoral Science Foundation(2024M753525);Jiangsu Province Youth Science and Technology Talent Support Project(JSTJ-2024-075);Jiangsu Provincial Natural Resources Science and Technology Project(JSZRKJ202510);Double First-Class Construction Project of China University of Mining and Technology(2022ZZCX06)

摘要/Abstract

摘要：

日长变化（LOD）是地球定向参数（EOP）的重要组成部分，由于地球自转速率受内外力作用而产生波动，表现为日长的增减，是直接影响昼夜更替周期的时间尺度。本文利用5种不同的方法对国际地球自转服务（IERS）发布的EOP 20 C04数据中2016年1月1日至2020年12月31日的LOD序列进行预测。方案一至方案五分别为：最小二乘自回归（LSAR）、加权最小二乘自回归（WLSAR）、长短期记忆网络（LSTM）+多项式曲线拟合（PCF）+最小二乘（LS）、长短期记忆网络与最小二乘组合模型（LSTM+LS）、长短期记忆网络与加权最小二乘组合模型（LSTM+WLS）。本文提出的方案五（LSTM+WLS）是对固体地球带谐潮汐改正后的LOD数据利用WLS方法得到残差项、拟合项和外推项，并对残差项利用LSTM模型引入有效角动量（EAM）数据进行预测，结合预测残差、外推项和固体地球带谐潮汐项得到LOD预测值。研究结果表明，相对于其他方案，本文提出的方案五在10天预测表现优异，平均绝对误差（MAE）为0.127 3 ms，相较于其他4个方案分别提升了5.7%、5.0%、2.6%、4.6%；在30天预测略优于方案一和二，与方案三和四几乎持平；90天预测MAE为0.1670 ms，相较于其他4个方案分别提升了8.0%、8.8%、15.3%、13.3%。总体而言，本文提出的LSTM+WLS模型在LOD中短期预报中表现优异。

关键词: 日长变化, LSTM, 最小二乘自回归, 地球定向参数, 有效角动量

Abstract:

The length of day (LOD), a crucial component of Earth orientation parameters (EOP), arises from fluctuations in Earth's rotation rate due to internal and external forces. These variations manifest as increases or decreases in LOD, directly influencing the timescale of the diurnal cycle. This study employs five distinct methods—least squares auto regressive (LSAR), weighted least squares auto-regressive (WLSAR), long short-term memory (LSTM) combined with polynomial curve fitting (PCF) extrapolation and least squares (LS) extrapolation, a hybrid LSTM and LS model (LSTM+LS), and a hybrid LSTM and weighted least squares model (LSTM+WLS), corresponding to schemes 1 to 5 in this study—to predict the LOD time series from January 1, 2016, to December 31, 2020, based on the EOP 20 C04 dataset released by the International Earth Rotation Service (IERS). The proposed scheme 5 (LSTM+WLS) in this study involves applying WLS method to the LOD data corrected for solid Earth zonal tidal effects to derive extrapolated, fitted, and residual terms. The residual term is then predicted using an LSTM model incorporating effective angular momentum (EAM) data. Finally, the LOD predictions are obtained by combining the predicted residuals, extrapolated terms, and solid Earth zonal tidal corrections. Compared to the other four schemes, scheme 5 demonstrates superior performance in 10-day predictions, achieving a mean absolute error (MAE) of 0.127 3 ms, representing improvements of 5.7%, 5.0%, 2.6%, and 4.6%, respectively. For 30-day predictions, it slightly outperforms schemes 1 and 2 while performing comparably to Schemes 3 and 4. In 90-day predictions, the MAE reaches 0.167 0 ms, with improvements of 8.0%, 8.8%, 15.3%, and 13.3% over the other schemes. Overall, the proposed LSTM+WLS model exhibits excellent performance in short-term LOD forecasting.

Key words: length of day, LSTM, LSAR, Earth orientation parameters, effective angular momentum

中图分类号:

P228

刘婧璇, 刘学习, 张克非, 杨超, 吴素芹, 朱守庆, 郭福东. 基于LSTM模型与加权最小二乘组合的日长变化预测方法[J]. 测绘学报, 2026, 55(3): 477-489.

Jingxuan LIU, Xuexi LIU, Kefei ZHANG, Chao YANG, Suqin WU, Shouqing ZHU, Fudong GUO. A prediction method for LOD based on combined LSTM and WLS[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(3): 477-489.

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外推天数	PCF+LS	LS	WLS
10天	0.010 2	0.012 3	0.013 0
30天	0.028 9	0.029 8	0.032 2
90天	0.073 2	0.071 3	0.065 2
180天	0.140 7	0.132 0	0.109 1
360天	0.292 2	0.251 3	0.188 7

参数	10天	30天	90天	180天	360天
编码器	10	10	512	256	256
				128	128
				256	256
解码器	14	14	256	128	128
解码器	7	7	256	64	64
全连接层数	无	无	无	Dense（128，ReLU）	Dense（128，ReLU）
全连接层数	无	无	无	Dense（128，ReLU）	Dense（128，ReLU）
优化器	Adam	Adam	Adam	Adam	Adam
损失函数	MSE	MSE	MSE	MSE	MSE

预测天数	公报A	方案一	方案二	方案三	方案四	方案五	方案五相对于其他方案预报精度的提升
预测天数	公报A	方案一	方案二	方案三	方案四	方案五	公报A	方案一	方案二	方案三	方案四
10天	0.128 4	0.134 5	0.133 7	0.130 6	0.133 1	0.127 3	0.9%	5.7%	5.0%	2.6%	4.6%
30天	0.204 7	0.160 7	0.160 6	0.155 3	0.155 8	0.156 7	30.6%	2.6%	2.5%	－0.9%	－0.6%
90天	0.240 7	0.180 4	0.181 7	0.192 6	0.189 2	0.167 0	44.1%	8.0%	8.8%	15.3%	13.3%
180天	0.302 5	0.184 5	0.176 8	0.257 4	0.239 0	0.212 3	42.5%	－13.1%	－16.7%	21.2%	12.6%
360天	0.537 5	0.242 2	0.208 2	0.364 7	0.316 7	0.262 8	104.5%	－7.8%	－20.8%	38.8%	20.5%

基于LSTM模型与加权最小二乘组合的日长变化预测方法

A prediction method for LOD based on combined LSTM and WLS

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