基于数据分解与十种“植物”算法优化的RELM地下水位预测

Groundwater level prediction based on data decomposition and ten “plant” algorithm optimization using RELM

摘要

【目的】提高地下水位时间序列预测精度对于科学预判地下水位变化趋势、合理开发和利用地下水资源具有重要意义。为提高地下水位时间序列预测精度，解决数据分解组合时间序列预测模型计算规模大、复杂程度高等问题【方法】基于小波包分解(WPT)、入侵杂草优化(IWO)算法/花授粉算法(FPA)/树木生长算法(TGA)/向日葵优化(SFO)算法/食肉植物算法(CPA)/蒲公英优化(DO)算法/常春藤算法(IVYA)/青蒿素优化(AO)算法/苔藓生长优化(MGO)算法/莲花效应优化算法(LEA)共十种“植物”算法和正则化极限学习机(RELM),提出基于WPT分解处理的IWO/FPA/TGA/SFO/CPA/DO/IVYA/AO/MGO/LEA-RELM预测模型，并通过云南省西城、南庄、临安、文澜、者林寨、植物园6个地下水位时间序列预测实例对各模型进行验证。首先，利用1层WPT将实例地下水位时间序列分解为趋势项和波动项，并基于趋势项和波动项训练集构建RELM超参数优化实例目标函数；其次，利用十种“植物”算法对实例目标函数进行极值寻优，获得各算法最优超参数；最后，利用最优超参数构建IWO/FPA/TGA/SFO/CPA/DO/IVYA/AO/MGO/LEA-RELM模型对实例地下水位时间序列趋势项和波动项进行预测和重构。【结果】结果显示：IVYA、CPA、FPA寻优性能优于IWO、AO、SFO、DO,远优于LEA、MGO、TGA;IVYA-RELM、CPA-RELM、FPA-RELM模型预测的平均绝对百分比误差(MAPE)在0.003 0%~0.000 4%之间，平均绝对误差(MAE)在0.038 9~0.006 3 m之间，决定系数(DC)在0.997 7~0.999 8之间，预测精度优于其他对比模型，具有较好的预测效果。【结论】结果表明：十种“植物”算法的寻优性能排名与十种组合模型的拟合精度、预测精度排名具有高度的一致性。总体上，算法寻优能力越强，组合模型的拟合、预测精度越高，性能越好；WPT分解分量少、分量规律性强，是一种简介高效的分解方法。

Abstract

[Objective] Improving the accuracy of groundwater level time series prediction is of great significance for scientifically predicting the change trends of groundwater levels and ensuring the rational development and utilization of groundwater resources. The aim is to improve the accuracy of groundwater level time series prediction and address the issues of large computational scale and high complexity in data decomposition-based combination time series prediction models. [Methods] A WPT-decomposed IWO/FPA/TGA/SFO/CPA/DO/IVYA/AO/MGO/LEA-RELM prediction model was proposed, combining Regularized Extreme Learning Machine(RELM) with ten “plant” optimization algorithms, including Wavelet Packet Decomposition(WPT), Invasive Weed Optimization(IWO), Flower Pollination Algorithm(FPA), Tree Growth Algorithm(TGA), Sunflower Optimization(SFO), Carnivorous Plant Algorithm(CPA), Dandelion Optimization(DO), Ivy Algorithm(IVYA), Artemisinin Optimization(AO), Moss Growth Optimization(MGO), and Lotus Effect Optimization Algorithm(LEA). This model was validated using groundwater level time series prediction examples from six locations in Yunnan Province, including Xicheng, Nanzhuang, Lin'an, Wenlan, Zhelinzhai, and Botanical Garden. First, the example's groundwater level time series were decomposed into trend and fluctuation components using one-level WPT. Based on these components, a RELM hyperparameter optimization objective function for the example was established. Then, the ten “plant” algorithms were used to optimize the objective function to determine the best hyperparameters. Finally, the optimal hyperparameters were used to establish IWO/FPA/TGA/SFO/CPA/DO/IVYA/AO/MGO/LEA-RELM models to predict and reconstruct the trend and fluctuation components of the example's groundwater level time series. [Results] The result showed that IVYA, CPA, and FPA outperformed IWO, AO, SFO, DO in optimization performance, and significantly outperformed LEA, MGO, and TGA. The IVYA-RELM, CPA-RELM, and FPA-RELM models achieved a MEAn absolute percentage error(MAPE) of 0.003 0% to 0.000 4%, a MEA absolute error(MAE) of 0.038 9 m to 0.006 3 m, and a coefficient of determination(DC) of 0.997 7 to 0.999 8, which outperformed other comparison models and demonstrated excellent prediction performance. [Conclusion] The result indicate that the optimization performance of the ten “plant” algorithms is highly consistent with the fitting and prediction accuracy rankings of the ten combined models. Overall, the stronger the optimization ability of the algorithms, the higher the fitting and prediction accuracy, and the better the performance of the combined models. The WPT decomposition, with fewer components and strong regularity, is a simple and efficient decomposition method.

关键词

地下水位预测 / 小波包分解 / 十种“植物”算法 / 正则化极限学习机 / 实例目标函数 / 超参数优化 / 影响因素

Key words

groundwater level prediction / wavelet packet decomposition / ten “plant” algorithms / regularized extreme learning machine / example objective function / hyperparameter optimization / influencing factors

基金资助

国家重点研发计划项目(2021YFC300205-06)