自构建改进型鲸鱼优化BP神经网络的ET0模拟计算

doi:10.13229/j.cnki.jdxbgxb20200545

摘要/Abstract

摘要：

参考作物蒸发蒸腾量（ET₀）是影响现代水文研究的关键因素，本文建立了一种改进的鲸鱼优化算法（GWOA）和BP神经网络的ET₀模型。通过遗传算法中选择机制与自适应的变异因子代替了传统鲸鱼优化算法（WOA）的最佳搜索代理选择，优化了鲸鱼算法种群多样性与跳出局部最优的能力；借助改变鲸鱼算法收敛因子与权重因子的更新策略，明显提高了鲸鱼优化算法拟合精度和收敛速度。在陕西省北部地区5个站点ET₀模拟仿真中，将基础气象数据作为要素输入，利用FAO 56 Penman-Monteith（FAO P-M）模型运算结果作为参考值，同时将GWOA-BP模型模拟结果与其他算法模型的模拟结果进行评价参数的对比，在仅有气温数据时，GWOA-BP模型仍能较好反映气象因子与ET₀之间的非线性约束关系（平均R²为0.990，平均R_MSE为0.287 mm/d），完全可以代替传统模型Hargreavers模型（R²提升了5%，R_MSE下降了63%）；在不同气象因子输入下的模拟计算数据表明，陕西省北部地区ET₀的重要气象因子排序为日最高温度T_max、日最低温度T_min、逐日日照对数n、逐日空气相对湿度RH、逐日平均风速u₂；在相同气象因子输入下的模拟计算数据表明，GWOA-BP拟合精度均高于WOA-BP、BP模型。

关键词: 计算机应用, 植物营养学, 参考作物蒸发蒸腾量, 鲸鱼优化算法, Penman-Monteith模型

Abstract:

Reference evapotranspiration （ET₀） is a key factor affecting modern hydrological research， and is one of the core variables to be controlled in the process of crop transpiration. An improved genetic whale optimization algorithm （GWOA） and ET₀model of BP neural network were established. The traditional whale optimization algorithm was replaced by the selection mechanism and adaptive mutation factor in genetic algorithm， The results show that the optimal search agent selection of WOA optimizes the population diversity and the ability to jump out of the local optimum of the whale algorithm， likewise significantly improves the fitting accuracy and convergence speed of the whale optimization algorithm by changing the convergence factor and weight factor of the whale algorithm. In the ET₀ simulation of five stations in Northern Shaanxi Province， the basic meteorological data were input as elements， The calculation results of FAO P-M model were used as reference value， and the simulation results of GWOA-BP model were compared with those of other algorithm models. When there is only temperature data， GWOA-BP model can still reflect the nonlinear constraint relationship between meteorological factors and ET₀ （average R² is 0.990， average R_MSE is 0.287 mm/d）， which can completely replace the traditional model hargreavers model （R²increased by 5% and R_MSE decreased by 63%）；The simulation data under different meteorological factors input show that the important meteorological factors of ET₀ in Northern Shaanxi Province are T_max、T_min、n、RH and u₂； the simulation data under the same meteorological factor input show that the fitting accuracy of GWOA-BP is higher than that of WOA-BP and BP models.

Key words: computer application, plant nutrition, reference evapotranspiration, whale optimization algorithm, Penman-Monteith model

中图分类号:

TP391.9

姚引娣,贺军瑾,李杨莉,谢荡远,李英. 自构建改进型鲸鱼优化BP神经网络的ET₀模拟计算[J]. 吉林大学学报(工学版), 2021, 51(5): 1798-1807.

Yin-di YAO,Jun-jin HE,Yang-li LI,Dang-yuan XIE,Ying LI. ET₀ simulation of self⁃constructed improved whale optimized BP neural network[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(5): 1798-1807.

图/表 7

图1

表1

七个基准测试函数"

类型	表达式	WOA	GWOA
F₁	$∑ i = 1 n x 12$	2.10e-078	1.24e-309
F₂	$∑ i = 1 n \| x i \| + ∏ i = 1 n \| x i \|$	9.57e-056	5.4e-089
F₃	$m a x \| x i \|, 1 ≤ i ≤ n$	65.463	26.942
F₄	$∑ i = 1 n x i + 0.5 2$	0.903 2	0.330 6
F₅	$∑ i = 1 n - x i s i n \| x i \|$	-8 735	-11 910
F₆	$∑ i = 1 n i x i 4 + r a n d o m 0,1$	0.002 37	0.000 10
F₇	$∑ i = 1 n x i 2 - 10 c o s 2 π x i + 10$	1.13e-013	1.13e-013

表1

图2

表2

图3

图4

表3

三种算法拟合精度"

评价指标	GWOA-BP	WOA-BP	BP
R²	0.983	0.965	0.900
R_MSE/（ $m m ? d - 1$ ）	0.258	0.372	0.629

表3

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方案	输入因子	R²					R_MSE/（mm·d^-1）
方案	输入因子	神木	洛川	榆林	延长	定边	神木	洛川	榆林	延长	定边
GWOA-BP1	T_min、T_max	0.839	0.859	0.879	0.908	0.881	0.770	1.202	1.271	0.969	1.256
GWOA-BP2	T_min、T_max、RH	0.940	0.909	0.926	0.926	0.913	0.487	0.958	0.988	0.871	1.132
GWOA-BP3	T_min、T_max、u₂	0.909	0.863	0.898	0.911	0.898	0.615	1.192	1.183	0.952	1.111
GWOA-BP4	T_min、T_max、n	0.891	0.945	0.943	0.975	0.947	0.638	0.747	0.865	0.494	0.815
GWOA-BP5	T_min、T_max、RH、u₂	0.963	0.913	0.932	0.926	0.922	0.377	0.948	0.951	0.871	0.998
GWOA-BP6	T_min、T_max、u₂、n	0.948	0.953	0.957	0.976	0.959	0.462	0.687	0.753	0.486	0.708
GWOA-BP7	T_min、T_max、n、RH	0.967	0.970	0.970	0.981	0.966	0.388	0.553	0.631	0.429	0.680
GWOA-BP8	T_min、T_max、n、RH、u₂	0.977	0.976	0.978	0.982	0.975	0.294	0.491	0.532	0.423	0.549
GWOA-BP9	T_min、T_max、R_a	0.999	0.986	0.990	0.992	0.986	0.001	0.385	0.363	0.280	0.406
Har	T_min、T_max、R_a	0.939	0.940	0.943	0.946	0.939	0.482	0.742	0.889	0.800	0.740

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自构建改进型鲸鱼优化BP神经网络的ET₀模拟计算

ET₀ simulation of self⁃constructed improved whale optimized BP neural network

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