数据分解技术与若干智能算法优化的高斯过程回归总氮预测

Gaussian Process Regression Total Nitrogen Prediction Based on Data Decomposition Technology and Several Intelligent Algorithms

总氮(TN)是反映水体污染程度和衡量湖库营养化状态的重要指标之一。为提高TN预测精度,基于经验小波变换(EWT)、小波包变换(WPT)分解技术,分别提出鱼鹰优化算法(OOA)、雾凇优化算法(ROA)、秃鹰搜索(BES)算法、黑寡妇优化算法(BWOA)优化的高斯过程回归(GPR)预测模型。首先分别利用EWT、WPT将TN时间序列分解为若干更具规律的子序列分量;然后简要介绍OOA、ROA、BES、BWOA算法原理,利用OOA、ROA、BES、BWOA优化GPR超参数;最后利用优化获得的最佳超参数建立EWT-OOA-GPR、EWT-ROA-GPR、EWT-BES-GPR、EWT-BWOA-GPR、WPT-OOA-GPR、WPT-ROA-GPR、WPT-BES-GPR、WPT-BWOA-GPR模型(简称EWT-OOA-GPR等8种模型)对TN各分量进行预测,重构后得到最终预测结果,并构建基于小波变换(WT)的WT-OOA-GPR、WT-ROA-GPR、WT-BES-GPR、WT-BWOA-GPR模型,基于支持向量机(SVM)的EWT-OOA-SVM等8种模型,未经优化的EWT-GPR、WPT-GPR模型和未经分解的OOA-GPR、ROA-GPR、BES-GPR、BWOA-GPR模型作对比分析,通过全国重要饮用水水源地暮底河水库2008—2022年月监测TN浓度时序数据对各模型进行验证。结果表明:①EWT-OOA-GPR等8种模型对TN预测的平均绝对百分比误差在0.161%~0.219%,决定系数均为0.9999,优于其他对比模型,具有更高的预测精度和更好的泛化能力;②EWT兼顾WT、EMD优势,WPT能同时分解低频、高频信号,二者均可将TN时序数据分解为更具规律的模态分量,显著提高模型预测精度,分解效果均优于WT方法;③OOA、ROA、BES、BWOA能有效优化GPR超参数,提高GPR预测性能。

Total nitrogen(TN)is one of the important indicators to reflect the degree of water pollution and measure the eutrophication status of lakes and reservoirs.To improve the accuracy of TN prediction,based on the empirical wavelet transform(EWT)and wavelet packet transform(WPT)decomposition technology,this paper proposes a Gaussian process regression(GPR)prediction model optimized by osprey optimization algorithm(OOA),rime optimization algorithm(ROA),bald eagle search(BES)and black widow optimization algorithm(BWOA)respectively.Firstly,the TN time series is decomposed into several more regular subsequence components by EWT and WPT respectively.Then,the paper briefly introduces the principles of OOA,ROA,BES,and BWOA algorithms and applies OOA,ROA,BES,and BWOA to optimize GPR hyperparameters.Finally,EWT-OOA-GPR,EWT-ROA-GPR,EWT-BES-GPR,EWT-BWOA-GPR,WPT-OOA-GPR,WPT-ROA-GPR,WPT-BES-GPR,WPT-BWOA-GPR models(EWT-OOA-GPR and other eight models for short)are established to predict the components of TN by the optimized super-parameters.The final prediction results are obtained after reconstruction,and WT-OOA-GPR,WT-ROA-GPR,WT-BES-GPR and WT-BWOA-GPR models based on wavelet transform(WT)are built.Eight models,including EWT-OOA-SVM based on support vector machine(SVM),the paper compares the unoptimized EWT-GPR,WPT-GPR models,and the uncomposed OOA-GPR,ROA-GPR,BES-GPR,and BWOA-GPR models.The models were verified by the monitoring TN concentration time series data of Mudihe Reservoir,an important drinking water source in China,from 2008 to 2022.The results are as follows.①The average absolute percentage error of eight models such as EWT-OOA-GPR for TN prediction is between 0.161%and 0.219%,and the coefficient of determination is 0.9999,which is superior to other comparison models,with higher prediction accuracy and better generalization ability.②EWT takes into account the advantages of WT and EMD.WPT can decompose low-frequency and high-frequency signals at the same time.Both of them can decompose TN time series data into more regular modal components,significantly improving the accuracy of model prediction,and the decomposition effect is better than that of the WT method.③OOA,ROA,BES,and BWOA can effectively optimize GPR hyperparameters and improve GPR prediction performance.