基于差分回归模型和可迁移长短期记忆网络集成的三沙湾水温预测

赖晓倩; 余镒琦; 梁中耀; 陈火荣; 陈能汪

doi:10.12284/hyxb2023027

基于差分回归模型和可迁移长短期记忆网络集成的三沙湾水温预测

doi: 10.12284/hyxb2023027

赖晓倩^1,,
余镒琦²,
梁中耀²,
陈火荣³,
陈能汪^{1, 2, ,}

1.
厦门大学近海海洋环境科学国家重点实验室，福建厦门 361102
2.
厦门大学福建省海陆界面生态环境重点实验室，福建厦门 361102
3.
福建省渔业资源监测中心，福建福州 350003

基金项目: 福建省海洋经济发展补助资金项目（ZHHY-2019-1）；国家重点研发计划（2016YFC0502901）

详细信息

作者简介:
赖晓倩（1998-），女，福建省龙岩市人，助理工程师，主要从事大数据建模研究。E-mail：xiaoqianl1_2020@163.com

通讯作者:
陈能汪（1976-），男，教授，主要从事海陆界面生态环境研究。E-mail：nwchen@xmu.edu.cn

中图分类号: P731.11
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出版历程
- 收稿日期: 2022-07-06
- 修回日期: 2022-09-26
- 网络出版日期: 2023-04-10
- 刊出日期: 2023-03-31

Water temperature prediction in the Sansha Bay based on the integration of differential regression model and transportable long short-term memory network

1.
State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen 361102, China
2.
Fujian Provincial Key Laboratory for Coastal Ecology and Environmental Studies, Xiamen University, Xiamen 361102, China
3.
Fishery Resources Monitoring Center of Fujian Province, Fuzhou 350003, China

摘要

摘要: 水温预测是保障近海渔业生产和环境安全的关键技术。现有的数值模型开发成本大，业务化应用不足。本文提出了一种集成差分回归（Differential Regression, DR）和可迁移长短期记忆网络（Transferable Long Short-Term Memory, TLSTM）的水温预测方法。以厦门湾（源域，数据多）和三沙湾（目标域，数据少）水温为研究对象，根据三沙湾在线监测水温和预报气温数据建立了DR模型，根据厦门湾长时间监测水温数据建立了TLSTM模型，采用变权算法将纯差分回归模型、混差分回归模型和TLSTM模型集成为三沙湾DR-TLSTM模型，对模型性能进行了评估，并与仅根据三沙湾少量监测数据建立的LSTM模型效果进行了对比。结果表明：（1） TLSTM模型的预测精度优于基于目标域少量数据建立的LSTM模型；（2） DR-TLSTM集成模型具有较高的预测精度，未来1～7 d预测的均方根误差为0.13～0.77℃，未来1～3 d预测的均方根误差小于0.4℃；（3） DR-TLSTM集成模型可有效预测水温骤升或骤降趋势，对水温突变点的预测均方根误差为0.29～1.09℃。基于本文建立的DR-TLSTM集成模型，实现了三沙湾渔业水域的水温预警预报业务化信息服务。
- 水温预测 /
- 回归模型 /
- LSTM模型 /
- 迁移学习 /
- 变权集成
Abstract: Water temperature prediction is a key technology to ensure the production of coastal fisheries and environmental safety. The existing numerical models have high development costs with insufficient business applications. This study develops a prediction method of water temperature through integrating differential regression (DR) and transferable long short-term memory (TLSTM). Taking the water temperature of Xiamen Bay (source domain, with a large number of data) and Sansha Bay (target domain, with less data) as the research object, the DR model is established based on the data of monitoring water temperature and forecast temperature in the Sansha Bay, and the TLSTM model is established based on the long-term monitoring data of water temperature in the Xiamen Bay. The pure differential regression model, mixed differential regression model and TLSTM model are integrated into the DR-TLSTM model of Sansha Bay by using variable weight algorithm, and the performance of the model is evaluated, the results are compared with the LSTM model based on only a small amount of monitoring data in the Sansha Bay. The results show that: (1) the prediction accuracy of TLSTM model is better than that of LSTM model based on a small amount of data in the target domain; (2) the DR-TLSTM model has high prediction accuracy, and the root mean square error of prediction in the next 1−7 days is 0.13−0.77℃, and the root mean square error of prediction in the next 1−3 days is less than 0.4℃; (3) the DR-TLSTM model can effectively predict the sudden rise or fall trend of water temperature, and the root mean square error of predicting the sudden change point of water temperature is 0.29−1.09℃. Based on the DR-TLSTM model, the operational information service of water temperature early warning and forecast in the Sansha Bay is realized.
- water temperature prediction /
- regression model /
- LSTM model /
- transfer learning /
- variable weight integration

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图 1 基于差分回归（DR）与可迁移长短期记忆网络（TLSTM）集成的三沙湾DR-TLSTM模型建模流程

Fig. 1 Modeling process of DR-TLSTM model of Sansha Bay based on differential regression (DR) and transferable long short-term memory (TLSTM)

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图 2 迁移学习对模型预测三沙湾未来1~7 d水温的影响

a, c, e. 最高温100次重复测试的均方根误差（RMSE）、平均绝对误差（MAE）、拟合优度（R²）的平均值和标准差；b, d, f. 最低温100次重复测试的均方根误差（RMSE）、平均绝对误差（MAE）、拟合优度（R²）的平均值和标准差

Fig. 2 The influence of transfer learning on the prediction of water temperature for the next 1−7 days in the Sansha Bay

a, c, e. Means and standard deviations of root mean square error (RMSE), mean absolute error (MAE), goodness of fit （R²） of 100 replicates at the maximum temperature; b, d, f. means and standard deviations of root mean square error (RMSE), mean absolute error (MAE), goodness of fit （R²） of 100 replicates at the minimum temperature

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图 3 变权组合对模型预测三沙湾未来1~7 d水温的影响

Fig. 3 Influence of variable-weight combination on the predicted water temperature for the next 1− 7 days in the Sansha Bay

a, c, e. Means and standard deviations of root mean square error (RMSE), mean absolute error (MAE), goodness of fit (R²) of 100 replicates at the maximum temperature; b, d, f. means and standard deviations of root mean square error (RMSE), mean absolute error (MAE), goodness of fit (R²) of 100 replicates at the minimum temperature

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图 4 变权组合对模型预测三沙湾未来1~7 d水温突变点的影响

Fig. 4 Influence of variable-weight combination on the prediction of water temperature sudden change point for the next 1−7 days in the Sansha Bay

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图 5 三沙湾未来1~7 d水温实测值和模型预测值对比（2021−2022年）

a, b. 第1天对比结果；c, d. 第2天对比结果；e, f. 第3天对比结果；g, h. 第4天对比结果；i, j. 第5天对比结果；k, l. 第6天对比结果；m, n. 第7天对比结果

Fig. 5 Comparison of observed and predicted water temperature for the next 1−7 days in the Sansha Bay (2021−2022)

a, b. Comparison results on day 1; c, d. comparison results on day 2; e, f. comparison results on day 3; g, h. comparison results on day 4; i, j. comparison results on day 5; k, l. comparison results on day 6; m, n. comparison results on day 7

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图 6 基于差分回归（DR）与可迁移长短期记忆网络（TLSTM）集成的DR-TLSTM模型应用于三沙湾水温预警预报业务化的信息系统界面

Fig. 6 Operational information system interface based on water temperature early warning and forecast in the Sansha Bay by DR-TLSTM model based on differential regression (DR) and transferable long short-term memory (TLSTM)

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表 1 长短期记忆网络（LSTM）模型结构和数学表达式

Tab. 1 Structures and mathematical expressions of long short-term memory (LSTM) model

结构	数学表达式
输入门	$ {i}_{t}=\sigma \left({W}_{i}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{i}\right) $
遗忘门	$ {f}_{t}=\sigma \left({W}_{f}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{f}\right) $
输出门	$ {o}_{t}=\sigma \left({W}_{o}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{o}\right) $
临时记忆单元	${\widehat{C} }_{t}=\mathrm{tanh}\left({W}_{c}\cdot \left[{h}_{t-1},{x}_{t}\right]+{b}_{c}\right)$
记忆单元	$ {C}_{t}={f}_{t}\odot {C}_{t-1}+{i}_{t}\odot {\widehat{C}}_{t} $
隐藏单元	$ {h}_{t}={o}_{t}\odot \mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left({C}_{t}\right) $
注：式中，$ {i}_{t} $为输入门；$ {f}_{t} $为遗忘门；$ {o}_{t} $为输出门；$ {\widehat{C}}_{t} $为t时刻临时记忆单元的输出；$ {C}_{t} $为t时刻记忆单元的输出；$ {h}_{t} $为t时刻隐藏单元的输出；$ {x}_{t} $为t时刻的输入数据；$ \sigma $为Sigmoid激活函数；$ \mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h} $为双曲正切激活函数；$ {W}_{i} $、$ {W}_{f} $、$ {W}_{c} $、$ {W}_{o} $为权重矩阵；$ {b}_{i} $、$ {b}_{f} $、$ {b}_{c} $、$ {b}_{o} $为偏置向量；$ \odot $为逐元素点积运算。

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表 2 长短期记忆网络（LSTM）模型主要参数和设定值

Tab. 2 Main parameters and set values of long short-term memory (LSTM) model

主要参数	设定值
LSTM层1神经元个数	48
正则化层1正则化系数	0.2
LSTM层2神经元个数	32
正则化层2正则化系数	0.2
损失函数	MSE
优化器	Adam
批处理大小	32
迭代轮次	150
注：MSE为均方误差，Adam为基于适应性低阶矩估计的一阶梯度优化算法结果。

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表 3 三沙湾水温预警等级的划分

Tab. 3 Classification of water temperature warning levels in the Sansha Bay

温度	T＜10℃	10℃≤T＜12℃	12℃≤T＜14℃	14℃≤T≤28℃	28℃＜T≤30℃	30℃＜T≤32℃	T＞32℃
等级	红色低温	橙色低温	黄色低温	正常	黄色高温	橙色高温	红色高温

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表 4 迁移学习测试时100次重复实验的平均值统计

Tab. 4 Statistics of the means of 100 replicates in transfer learning test

预测天数	评价指标	目标域LSTM模型		TLSTM模型（未微调）		TLSTM模型
预测天数	评价指标	最高温	最低温	最高温	最低温	最高温	最低温
第1天	RMSE/℃	5.42	5.69	0.42	0.31	0.38	0.28
	MAE/℃	5.30	5.54	0.36	0.28	0.35	0.25
	R²	0.823	0.858	0.990	0.994	0.991	0.995
第2天	RMSE/℃	5.57	5.89	0.52	0.39	0.47	0.34
	MAE/℃	5.45	5.72	0.43	0.33	0.43	0.30
	R²	0.837	0.833	0.968	0.986	0.968	0.987
第3天	RMSE/℃	5.74	6.02	0.62	0.47	0.57	0.43
	MAE/℃	5.61	5.87	0.52	0.40	0.51	0.37
	R²	0.795	0.812	0.931	0.971	0.931	0.971
第4天	RMSE/℃	5.96	6.17	0.75	0.57	0.68	0.52
	MAE/℃	5.84	6.02	0.61	0.46	0.61	0.44
	R²	0.740	0.805	0.884	0.950	0.886	0.951
第5天	RMSE/℃	6.22	6.37	0.84	0.64	0.76	0.59
	MAE/℃	6.09	6.22	0.69	0.52	0.68	0.50
	R²	0.671	0.795	0.834	0.932	0.839	0.933
第6天	RMSE/℃	6.42	6.53	0.91	0.71	0.83	0.65
	MAE/℃	6.30	6.38	0.75	0.58	0.75	0.56
	R²	0.665	0.760	0.783	0.913	0.794	0.914
第7天	RMSE/℃	6.61	6.70	0.97	0.79	0.88	0.73
	MAE/℃	6.49	6.54	0.80	0.65	0.81	0.64
	R²	0.653	0.749	0.737	0.882	0.759	0.884

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表 5 变权组合测试时100次重复实验的平均值统计

Tab. 5 Statistics of the means of 100 replicates in variable-weight combination test

预测天数	评价指标	TLSTM模型		纯差分回归模型		混差分回归模型		DR-TLSTM集成模型
预测天数	评价指标	最高温	最低温	最高温	最低温	最高温	最低温	最高温	最低温
第1天	RMSE/℃	0.38	0.28	0.16	0.14	0.15	0.15	0.13	0.13
	MAE/℃	0.35	0.25	0.12	0.11	0.11	0.11	0.11	0.11
	R²	0.991	0.995	0.994	0.996	0.995	0.995	0.995	0.996
第2天	RMSE/℃	0.47	0.34	0.30	0.25	0.31	0.25	0.26	0.22
	MAE/℃	0.43	0.30	0.23	0.30	0.22	0.17	0.22	0.18
	R²	0.968	0.987	0.978	0.989	0.978	0.989	0.978	0.989
第3天	RMSE/℃	0.57	0.43	0.45	0.37	0.48	0.37	0.39	0.33
	MAE/℃	0.51	0.37	0.34	0.29	0.33	0.26	0.33	0.27
	R²	0.931	0.971	0.946	0.975	0.947	0.975	0.947	0.975
第4天	RMSE/℃	0.68	0.52	0.60	0.48	0.63	0.48	0.51	0.44
	MAE/℃	0.61	0.44	0.46	0.38	0.43	0.35	0.43	0.36
	R²	0.886	0.951	0.902	0.956	0.906	0.956	0.905	0.956
第5天	RMSE/℃	0.76	0.59	0.71	0.57	0.74	0.57	0.60	0.51
	MAE/℃	0.68	0.50	0.55	0.47	0.53	0.44	0.52	0.43
	R²	0.839	0.933	0.863	0.939	0.870	0.941	0.867	0.940
第6天	RMSE/℃	0.83	0.65	0.81	0.67	0.83	0.67	0.68	0.59
	MAE/℃	0.75	0.56	0.66	0.58	0.63	0.54	0.62	0.52
	R²	0.794	0.914	0.822	0.917	0.834	0.922	0.831	0.921
第7天	RMSE/℃	0.88	0.73	0.93	0.79	0.95	0.79	0.77	0.69
	MAE/℃	0.81	0.64	0.77	0.68	0.74	0.65	0.71	0.63
	R²	0.759	0.884	0.775	0.884	0.793	0.889	0.791	0.890

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表 6 突变点测试时100次重复实验的平均值统计

Tab. 6 Statistics of the means of 100 replicates in sudden change point prediction test

预测天数	评价指标	TLSTM模型		纯差分回归模型		混差分回归模型		DR-TLSTM集成模型
预测天数	评价指标	最高温	最低温	最高温	最低温	最高温	最低温	最高温	最低温
第1天	RMSE/℃	0.44	0.29	0.42	0.32	0.40	0.34	0.35	0.29
	MAE/℃	0.40	0.39	0.36	0.30	0.33	0.29	0.33	0.29
	R²	0.992	0.992	0.995	0.993	0.996	0.993	0.996	0.994
第2天	RMSE/℃	0.71	0.61	0.75	0.63	0.78	0.63	0.65	0.57
	MAE/℃	0.66	0.60	0.58	0.60	0.56	0.52	0.57	0.56
	R²	0.940	0.935	0.954	0.951	0.954	0.951	0.954	0.951
第3天	RMSE/℃	1.07	0.77	1.02	0.67	1.08	0.67	0.89	0.61
	MAE/℃	0.95	0.72	0.80	0.75	0.76	0.69	0.76	0.71
	R²	0.798	0.705	0.806	0.747	0.808	0.747	0.807	0.747
第4天	RMSE/℃	1.31	0.95	1.01	0.81	1.06	0.81	0.87	0.74
	MAE/℃	1.13	0.95	0.85	0.92	0.80	0.85	0.80	0.87
	R²	0.729	0.693	0.782	0.780	0.785	0.781	0.784	0.781
第5天	RMSE/℃	1.32	0.95	1.18	0.99	1.23	0.99	1.01	0.90
	MAE/℃	1.04	0.94	0.89	0.95	0.85	0.88	0.84	0.88
	R²	0.666	0.672	0.788	0.729	0.794	0.731	0.792	0.730
第6天	RMSE/℃	1.33	1.00	1.19	1.07	1.23	1.07	1.01	0.95
	MAE/℃	1.03	1.05	1.00	1.07	0.94	1.00	0.94	0.98
	R²	0.693	0.691	0.712	0.694	0.722	0.698	0.720	0.698
第7天	RMSE/℃	1.23	1.03	1.31	1.11	1.34	1.12	1.09	0.98
	MAE/℃	1.07	1.06	1.02	1.02	0.97	0.97	0.95	0.95
	R²	0.630	0.450	0.636	0.526	0.651	0.529	0.649	0.530

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表 7 基于差分回归（DR）与可迁移长短期记忆网络（TLSTM）集成的DR-TLSTM模型对三沙湾水温预警准确率的统计结果

Tab. 7 Statistical results of DR-TLSTM model based on differential regression (DR) and transferable long short-term memory (TLSTM) for water temperature early warning accuracy in the Sansha Bay

设备编号	第1天	第2天	第3天	第4天	第5天	第6天	第7天
1#渔排基	96.27%	94.03%	91.04%	88.06%	84.33%	82.84%	82.09%
2#渔排基	95.52%	94.03%	91.04%	88.06%	85.82%	83.58%	80.60%
3#渔排基	97.76%	95.52%	91.79%	91.79%	88.06%	87.31%	79.10%

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