An Ensemble Modeling Approach to Forecast Daily Reservoir Inflow Using Bidirectional Long- and Short-Term Memory (Bi-LSTM), Variational Mode Decomposition (VMD), and Energy Entropy Method

Daily inflow forecasts provide important decision support for the operations and management of reservoirs. Accurate and reliable forecasting plays an important role in the optimal management of water resources. Numerous studies have shown that decomposition integration models have good prediction capacity. Considering the nonlinearity and unsteady state of daily incoming flow data, a hybrid model of adaptive variational mode decomposition (VMD) and bidirectional long- and short-term memory (Bi-LSTM) based on energy entropy was developed for daily inflow forecast. The model was analyzed using the mean absolute error (MAE), the root means square error (RMSE), Nash–Sutcliffe efficiency coefficient (NSE), and correlation coefficient (r). A historical daily inflow series of the Baozhusi Hydropower Station, China, is investigated by the proposed VMD-BiLSTM with hybrid models. For comparison, BP, GRNN, ELMAN, SVR, LSTM, Bi-LSTM, EMD-LSTM, and VMD-LSTM, were adopted and analyzed for evaluation and analyzed. We found that the proposed model, with MAE?=?38.965, RMSE?=?64.783, and NSE?=?95.7%, was superior to the other models. Therefore, the hybrid model is robust and efficient for forecasting highly nonstationary and nonlinear streamflow. It can be used as the preferred data-driven tool to predict the daily inflow flow, which can ensure the safe operation of hydropower stations in reservoirs. As an interdisciplinary field spanning both machine learning and hydrology, daily inflow forecasting can become an important breakthrough in the application of deep learning to hydrology.

     

基于集成学习模型的非平稳月径流预报

针对变化环境下月径流序列的非平稳性日益加剧,传统径流预报模型采用普通学习算法的局限性,基于Bagging和Boosting集成学习算法,构建了随机森林(RF)、梯度提升决策树(GBDT)和轻梯度提升机(LightGBM)3种集成学习模型,融合弹性网(EN)和变分模态分解(VMD),建立VMD-EN-RF、VMD-EN-GBDT和VMD-EN-LightGBM非平稳月径流组合预报模型,并以黄河流域实测月径流为研究对象,评估预报结果的不确定性。结果表明：单一集成学习模型能够提供可靠的预报结果,适用于非平稳月径流预报;融合VMD和EN的集成学习模型预报性能较单一集成学习模型有了显著提高,纳什效率系数提升了15%～20%,均方根误差降低了30%～40%;基于Boosting集成方法构建的集成学习模型优于Bagging集成方法,其中VMD-EN-LightGBM预见期3月内的预报效果优于VMD-EN-RF和VMD-EN-GBDT,在90%置信度的区间预报覆盖率高于90%,表现出良好的性能。     

A Novel Hybrid Decompose-Ensemble Strategy with a VMD-BPNN Approach for Daily Streamflow Estimating

Streamflow estimation is highly significant for water resource management. In this work, we improve the accuracy and stability of streamflow estimation through a novel hybrid decompose-ensemble model that employs variational mode decomposition (VMD) and back-propagation neural networks (BPNN). First, the latest decomposition algorithm, namely, VMD, was used to extract multiscale features that were subsequently learned and ensembled by the BPNN model to obtain the final estimate streamflow results. The historical daily streamflow series of Laoyukou and Wushan hydrological stations in China were analysed by VMD-BPNN, by a single GBRT and BPNN model, ensemble empirical mode decomposition (EEMD) models. The results confirmed that the VMD outperformed a single-estimation model without any decomposition and EEMD-based models; moreover, ensemble estimations using the BPNN model development technique were consistently better than a general summation method. The VMD-BPNN model’s estimation performance was superior to that of five other models at the Wushan station (GBRT, BPNN, EEMD-BPNN-SUM, VMD-BPNN-SUM, and EEMD-BPNN) using evaluation criteria of the root-mean-square error (RMSE?=?2.62 m³/s), the Nash–Sutcliffe efficiency coefficient (NSE?=?0. 9792) and the mean absolute error (MAE?=?1.38 m³/s). The proposed model also had a better performance in estimating higher-magnitude flows with a low criterion for MAE. Therefore, the hybrid VMD-BPNN model could be applied as a promising approach for short-term streamflow estimating.

     

An Ensemble Hybrid Forecasting Model for Annual Runoff Based on Sample Entropy,Secondary Decomposition,and Long Short-Term Memory Neural Network

Accurate and consistent annual runoff prediction in a region is a hot topic in management, optimization, and monitoring of water resources. A novel prediction model (ESMD-SE-WPD-LSTM) is presented in this study. Firstly, extreme-point symmetric mode decomposition (ESMD) is used to produce several intrinsic mode functions (IMF) and a residual (Res) by decomposing the original runoff series. Secondly, sample entropy (SE) method is employed to measure the complexity of each IMF. Thirdly, wavelet packet decomposition (WPD) is adopted to further decompose the IMF with the maximum SE into several appropriate components. Then long short-term memory (LSTM) model, a deep learning algorithm based recurrent approach, is employed to predict all components. Finally, forecasting results of all components are aggregated to generate the final prediction. The proposed model, which is applied to seven annual series from different areas in China, is evaluated based on four evaluation indexes (R, MAE, MAPE and RMSE). Results indicate that ESMD-SE-WPD-LSTM outperforms other benchmark models in terms of four evaluation indexes. Hence the proposed model can provide higher accuracy and consistency for annual runoff prediction, rendering it an efficient instrument for scientific management and planning of water resources.

     

风光水互补系统时间序列变量概率预报框架

风光水互补系统实时调度受风速、太阳辐射强度、径流和电力负荷等时间序列变量的不确定性影响,如何准确预报这些变量并量化预报的不确定性是风光水互补系统面临的关键难题。为此,本研究提出一种基于深度学习模型的时间序列变量概率预报框架。首先,从时间序列数据中挖掘特征输入并采用相关系数对生成的特征进行初选;其次,基于深度学习模型和高斯过程回归构建时间序列变量概率预报模型,同时分别通过0-1规划思想和贝叶斯优化算法实现特征组合优化和超参数优选;进而,从确定性预报、概率预报和可靠性3个方面对预报模型进行全面评价;最后,以雅砻江流域风光水互补先期试点示范基地作为研究对象,分别在径流、风速、光伏和负荷4个数据集上与目前7个不同的时间序列变量预报模型进行全面对比,验证本研究提出预报框架的精度和概率综合性能。     

Multivariable Time Series Forecasting for Urban Water Demand Based on Temporal Convolutional Network Combining Random Forest Feature Selection and Discrete Wavelet Transform

Urban water demand forecasting is crucial to reduce the waste of water resources and environmental protection. However, the non-stationarity and non-linearity of the water demand series under the influence of multivariate makes water demand prediction one of the long-standing challenges. This paper proposes a new hybrid forecasting model for urban water demand forecasting, which includes temporal convolution neural network (TCN), discrete wavelet transform (DWT) and random forest (RF). In order to improve the model’s forecasting abilities, the RF method is used to rank the factors and remove the less important factors. The dimension of raw data is reduced to improve calculating efficiency and accuracy. Then, the original water demand series is decomposed into different characteristic sub-series of multiple variables with better-behavior by DWT to weaken the fluctuation of original series. At the core of the proposed model, TCN is utilized to establish appropriate prediction models. Finally, to test and validate the proposed model, a real-world multivariate dataset from a water plant in Suzhou, China, is used for comparison experiments with the most recent state-of-the-art models. The results show that the mean absolute percentage error (MAPE) of the proposed model is 1.22% which is smaller than the other benchmark models. The proposed model indicates the only 2.2% of the prediction results have a relative error of more than 5%. It shows that the reliable results of the proposed model can be a superior tool for urban water demand forecasting.

     

基于多种混合模型的径流预测研究

变化环境下径流的波动不断加大,给径流的精准预报带来新的挑战。基于"分解-合成"策略的混合径流预报模型来提高预报精度是当前研究的热点之一。以往研究聚焦在单一的混合预报模型而忽视了它们的适用性研究。基于此,以渭河流域为例,在优选多元线性回归(MLR)、人工神经网络(ANN)和支持向量机(SVM)单一预报模型的基础上,分别基于经验模态分解(EMD)、集合经验模态分解(EEMD)和小波分解(WD)构建了多种混合模型,并融合了大气环流异常因子的信息。结果表明:(1)SVM模型预测精度高于ANN和MLR;(2)混合预测模型预测精度均高于单一模型,混合模型中WD-SVM的预测精度优于EMD-SVM和EEMD-SVM;(3)融合大气环流异常因子后WD-SVM模型预测精度最高,对极值预报精度的提高较为明显。     

BP 网络日径流序列预测的NLP 适用条件研究

对非线性预处理在人工神经网络日径流预测中的适应过程进行了仿真和模拟．提出了非线性预处理（NLP）适用条件的解算思路，通过实测数据和模拟数据，研究了NLP的适用条件。推导出NLP在神经网络SISO系统中适合于日径流预测，不适用于周平均流量序列、旬平均流量序列和月平均流量序列的预测，提出了判断NLP神经网络SISO系统进行日径流预测的有效性标准——多年日径流拐点14百分位．并通过广西平乐水文站和四川宝珠寺水文站1973～2001年的日径流量进行对比预测，验证了该标准是合理的。     

Deep Feature Learning Architectures for Daily Reservoir Inflow Forecasting

Inflow forecasting applies data supports for the operations and managements of reservoirs. To better accommodate the sophisticated characteristics of the daily reservoir inflow, two deep feature learning architectures, i.e., deep restricted Boltzmann machine (DRBM) and stack Autoencoder (SAE), respectively, are introduced in this paper. This study sheds light on the application of deep learning architectures for daily reservoir inflow forecasting, which has been attracting much attention in various areas for its ability to extract and learn useful features from a large number of data. Evaluations are made comparing the basic feed forward neural network (FFNN), the autoregressive integrated moving average (ARIMA), and two categories deep neural networks (DNNs) constructed by the integrations the FFNN with two deep feature learning architectures, named DRBM-based NN and stack SAE-based NN, respectively. Two daily inflow series of the Three Gorges reservoir (1/1/2000–31/12/2014) and the Gezhouba reservoir (1/1/1992–31/12/2014), China, are applied for four modeling exercises, respectively. The results show that, the two DNN models overwhelm the FFNN and the ARIMA models in terms of mean absolute percentage error, normalized root-mean-square error, and threshold statistic criteria.     

基于自适应变分模态分解和长短期记忆网络的月径流预报

准确可靠的月径流预报是流域水旱灾害防治及水资源合理配置的重要依据。原始径流时间序列包含多种频率成分，将时间序列数据分解预处理技术和机器学习模型相结合的混合模型已被用于捕捉径流动态过程。然而，将数据分解技术直接应用于整个时间序列是一种不切实际的方法，会导致部分信息从测试阶段传输到模型的训练过程中。为此，设计了一个用观测数据更新历史样本的自适应动态分解策略，提出基于自适应变分模态分解和长短期记忆网络的分解-预测-集成月径流预测混合模型。首先，采用自适应分解策略对径流时序数据进行变分模态分解，得到不同频率成分的子序列；其次，为每个分解子序列构建长短期记忆神经网络径流预测模型，并采用贝叶斯优化算法优选模型超参数；然后，将子序列的预测结果集成得到径流的最终预测结果；最后，以金沙江上游石鼓水文站月径流预报为研究实例，对比传统的分解策略(“捆绑分解”)和分解方法(离散小波变换和集成经验模态分解),验证所提混合模型的有效性和可行性。结果表明，所提混合模型在数据分解预处理中避免了引入未来信息，并能够进一步提升径流预报精度。     

基于优化VMD与GRU的混凝土坝变形预测模型

为提高大坝变形预测精度,基于“分解-重构”思想,采用变形信号处理技术对实测变形加以时频分解,并结合深度学习网络对分解信号分项预测再重构,提出一种基于优化变分模态分解(VMD)与门控循环单元(GRU)的混凝土坝变形预测模型。该模型使用灰狼优化算法(GWO)优化的VMD把原始数据分解为一组最优本征模态分量(IMF),利用GWO优化的GRU网络对每个IMF分量进行滚动预测,通过叠加各个分量的预测结果得到位移序列预测结果,解决了VMD人工选择参数导致分解效果差及GRU人工选择参数影响训练速度、使用效果及鲁棒性等问题。工程实例预测结果表明,该模型的预测误差小,具有良好的预测精度与稳健性。     

ARIMA与ANN组合预测模型在中长期径流预报中的应用

基于时间序列预测模型及BP神经网络,提出了新的组合预测方法.该方法采用三层结构的BP神经网络来构造组合预测模型,运用时间序列模型预测方法得出的预测结果,采用历史滚动法将前5年的预测结果数据作为BP网络的输入,以当前年份的预测结果为网络期望输入,建立了ARIMA-ANN组合预报模型.利用Matlab7神经网络工具箱对塔里木河上游源流卡群水文站的年径流量进行了预报及验证.结果表明:组合模型的预报结果精度高,容错能力强,是中长期径流预报的有效方法.     

Multiple Random Forests Modelling for Urban Water Consumption Forecasting

The precise forecasting of water consumption is the basis in water resources planning and management. However, predicting water consumption fluctuations is complicated, given their non-stationary and non-linear characteristics. In this paper, a multiple random forests model, integrated wavelet transform and random forests regression (W-RFR), is proposed for the prediction of daily urban water consumption in southwest of China. Raw time series were first decomposed into low- and high-frequency parts with discrete wavelet transformation (DWT). The random forests regression (RFR) method was then used for prediction using each subseries. In the process, the input and output constructions of the RFR model were proposed for each subseries on the basis of the delay times and the embedding dimension of the attractor reconstruction computed by the C-C method, respectively. The forecasting values of each subseries were summarized as the final results. Four performance criteria, i.e., correlation coefficient (R), mean absolute percentage error (MAPE), normalized root mean square error (NRMSE) and threshold static (TS), were used to evaluate the forecasting capacity of the W-RFR. The results indicated that the W-RFR can capture the basic dynamics of the daily urban water consumption. The forecasted performance of the proposed approach was also compared with those of models, i.e., the RFR and forward feed neural network (FFNN) models. The results indicated that among the models, the precision of the predictions of the proposed model was greater, which is attributed to good feature extractions from the multi-scale perspective and favorable feature learning performance using the decision trees.     

Improving Annual Streamflow Prediction by Extracting Information from High-frequency Components of Streamflow

Annual streamflow prediction is of great significance to the sustainable utilization of water resources, and predicting it accurately is challenging due to changes in streamflow have strong nonlinearity and uncertainty. To improve the prediction accuracy of annual streamflow, this study proposes a new hybrid prediction model based on extracting information from high-frequency components of streamflow. In the proposed model, the original streamflow data is decomposed by ensemble empirical mode decomposition (EEMD) into several intrinsic mode functions (IMFs) with different frequencies. Then, the dominant component and residual component are identified from the high-frequency components IMF1 and IMF2 using singular spectrum analysis (SSA), and the residual components are accumulated as a new component. Finally, all the components, including the new component that is not noise, are modelled by support vector machine (SVM), and the SVM is optimized by grey wolf optimizer (GWO). To analyse and verify the proposed model, the annual streamflow data are collected from the Liyuan River and Taolai River in the Heihe River Basin, and six models, autoregressive integrated moving average (ARIMA), cross validation (CV)-SVM, GWO-SVM, EEMD-ARIMA, EEMD-GWO-SVM and modified EEMD-GWO-SVM are considered as comparison models. The results indicate that the prediction performance of the proposed model is obviously better than that of other reference models, and extracting valuable information from high-frequency components can effectively improve annual streamflow prediction. Thus, the high-frequency components contained in the original streamflow series have an important impact on obtaining accurate streamflow prediction, and the proposed model makes full use of the high-frequency components and provides a reliable method for streamflow prediction.

     

Singular Spectrum Analysis and ARIMA Hybrid Model for Annual Runoff Forecasting

High accuracy forecasting of medium and long-term hydrological runoff is beneficial to reservoir operation and management. A hybrid model is proposed for medium and long-term hydrological forecasting in this paper. The hybrid model consists of two methods, Singular Spectrum Analysis (SSA) and Auto Regressive Integrated Moving Average (ARIMA). In this model, the time series of annual runoff are first decomposed into several sub-series corresponding to some tendentious and periodic motions by using SSA and then each sub-series is predicted, respectively, through an appropriate ARIMA model, and lastly a correction procedure is conducted for the sum of the prediction results to ensure the superposed residual to be a pure random series. The annual runoff data of two reservoirs in China are analyzed as case studies. The results have been compared with the predictions made by ARIMA and Singular Spectrum Analysis-Linear Recurrent Formulae (SSA-LRF). It is shown that hybrid model has the best performance.     

基于变分模态分解的分频径流预测模型

准确的径流预测对于流域防洪减灾、农业灌溉、水库调度等具有重要意义。针对径流序列具有较强的非线性和非平稳性特征,提出一种月径流预测混合模型VMD-(CNN-LSTM, ELMAN)。首先运用VMD将径流序列分解为多个模态分量,并计算各个模态分量的样本熵值(SE),将其划分为高频和中低频分量;然后运用CNN-LSTM模型预测高频分量,运用ELMAN模型预测中低频分量;最后将预测结果相加得到最终预测结果。将模型应用于黄河流域中下游段白马寺和黑石关水文站的月径流预测,并与CNN-LSTM、ELMAN、VMD-CNN-LSTM模型的预测结果进行对比与评价。研究结果表明：本文模型预测结果的NSE值均大于0.99,优于其他模型,表明VMD-(CNN-LSTM, ELMAN)模型具有较高的预测精度,可应用于实际研究区的径流预测。     

基于VMD-BP模型的河流流量预测方法

河流流量是水文监测和水资源管理的重要指标,流量预测对于水利建设、航运规划和水资源调度等方面具有重要的指导意义和参考价值。结合变分模态分解(VMD)处理非平稳序列的优势以及BP神经网络(BPNN)处理非线性拟合的能力,提出和构建了基于VMD-BP模型的河流流量预测方法。以长江宜昌水文站为实例,基于1998年和1999年的日水位和日流量数据,对方法模型进行了验证。结果表明:VMD-BP模型在一定程度上解决了水位和流量的多值关系,降低了数据的波动性,预测结果优于线性拟合的回归模型和BPNN模型,预测误差仅为1.61%,为河流流量预测提供了一种有效的方法。     

基于数值天气预报模式的流域中期径流预报

研究耦合天气预报模式的径流预报对提高预报预见期及流域防洪减灾具有重要意义。以金溪池潭水库流域为例,通过尺度转换和气象要素联结实现GEM和GFS两种数值天气模式与新安江模型的单向耦合,进行流域水文模拟以及中期径流预报。日径流过程和次洪过程模拟结果发现耦合数值天气预报模式的流域中期径流预报能够较好地预估一段时间内的径流总量,而对洪峰以及洪水过程预报能力稍有不足。预报误差来源有水文模型误差和降水预报误差两种,且降水预报的误差在水文模型中会有放大的效应,这增加了中期径流预报的不确定性。     

面向EMD分解的径流分量重构方法对比研究

水文序列非平稳与非线性的复杂变化导致水文序列中长期预测的准确性备受质疑。"分解-预测-重构"模式作为一种新的有效的预测思路近年来备受业界和学者关注。但受到高频分量预测误差大、趋势走向不确定等问题困扰,这种模式在发展过程中仍有诸多需要改进的地方。其中,径流分量的重构方法是控制高频分量误差,提高整体预测精度的关键性措施,其优劣对预测效果实现有着重要的意义。基于经验模态分解(EMD)和自回归模型(AR)建立"分解-预测"耦合模型,结合粒子群优化(PSO)算法,提出PSO重构系数优化法和高频分量剔除+重构系数优化法两种重构方法,结合前人提出的高频分量剔除法,以陕北丁家沟站、关中华县站、陕南白河站为算例,对不同重构方法的效果进行对比研究。研究结果表明:基于高频分量剔除法、PSO重构系数优化法、高频分量剔除+重构系数优化法三种重构方法的预测效果均较好,五项误差评价指标均优于标准重构法,三种重构方法均可不同程度地提高预测精度。对比研究发现:高频分量剔除法在重构过程中剔除了最不稳定且最难预测的高频分量,提高了预测精度,但提升效果有限;PSO重构系数优化法对所有径流分量赋予优化重构系数并重构,可最大程度地实现分量间的平差,有效提高了预测精度;高频分量剔除+重构系数优化法综合上述两种方法的优势,取得了比其他方法更好的预测效果。     

Monthly Rainfall Forecasting Using EEMD-SVR Based on Phase-Space Reconstruction

Rainfall links atmospheric and surficial processes and is one of the most important hydrologic variables. We apply support vector regression (SVR), which has a high generalization capability, to construct a rainfall forecasting model. Before construction of the model, a self-adaptive data analysis methodology called ensemble empirical mode decomposition (EEMD) is used to preprocess a rainfall data series. In addition, the phase-space reconstruction method is implemented to design input vectors for the forecasting model. The proposed hybrid model is applied to forecast the monthly rainfall at a weather station in Changchun, China as a case study. To demonstrate the capacity of the proposed hybrid model, a typical three-layer feed-forward artificial neural network model, an auto-regressive integrated moving average model, and a support vector regression model are constructed. Predictive performance of the models is evaluated based on normalized mean squared error (NMSE), mean absolute percent error (MAPE), Nash–Sutcliffe efficiency (NSE), and the coefficient of correlation (CC). Results indicate that the proposed hybrid model has the lowest NMSE and MAPE values of 0.10 and 14.90, respectively, and the highest NSE and CC values of 0.91 and 0.83, respectively, during the validation period. We conclude that the proposed hybrid model is feasible for monthly rainfall forecast and is better than the models currently in common use.