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.

     

基于EMD-LSTM耦合模型的趵突泉岩溶地下水水位预测应用

由于岩溶地下水具有强烈的非线性及非平稳波动特征,水位预测结果容易产生较大误差。针对岩溶地下水水位预测精度较差的问题,提出一种EMD-LSTM耦合模型,首先采用经验模态分解（EMD）将趵突泉岩溶地下水水位分解为5个分量（4个本征模函数项和1个残余项）,以此消除水位数据的非平稳波动性;同时构建长短期记忆（LSTM）神经网络模型,并将与地下水水位动态变化密切相关的降水量（表征含水层补给项）和月平均气温值、月最高气温值、月最低气温值、水汽压值（表征含水层排泄项）作为输入项分别对5个分量进行预测,最终将分量预测结果累加获得地下水水位预测值。结果表明：EMD能够显著消除岩溶地下水水位的非平稳波动特征;EMD-LSTM耦合模型可有效提高岩溶地下水水位的预测精度,其均方根误差相比于LSTM神经网络模型、ARIMA模型分别减小了27.86%和59.94%。总体来说,本文所提出的EMD-LSTM耦合模型具有较强的可靠性和稳定性,可为岩溶地下水水位的精确预测提供借鉴。     

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.

     

基于EEMD-PCA-ARIMA模型的大坝变形预测

针对大坝观测数据中存在的噪声容易掩盖实际变形曲线走势的问题,提出一种基于集合经验模态分解(EEMD)、主成分分析(PCA)和自回归移动平均模型(ARIMA)的大坝变形预测方法。通过对观测数据进行EEMD和PCA,从而构建映射矩阵,然后利用映射矩阵对原始数据构建的样本矩阵进行转换,实现消噪效果,进而对处理后的观测数据进行ARIMA建模预测,据此构建EEMD-PCA-ARIMA模型。依据所提出的模型对实际大坝坝顶水平位移观测数据进行预测分析,并与实测数据和经直接去掉高频分量消噪后的ARIMA预测模型、ARIMA预测模型、BP神经网络模型预测模型进行对比分析。结果表明:此方法能够更好地获取大坝的实际变形曲线,对于大坝变形预测而言是一种有效的方法。     

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。     

基于小波包分解的 LS-SVM-ARIMA 组合降水预测

针对降水量影响因素众多, 是一种复杂的非平稳、非线性且存在噪声问题的时间序列的特点, 提出一种基于小波包分解的 LS-SVM 与 ARIMA 组合模型的年降水量预测方法。利用小波包将降水序列分解成低频趋势序列和高频细节序列; 应用 LS-SVM 模型预测低频趋势序列, ARIMA 模型预测高频细节序列; 将两个模型的预测结果叠加, 得到年降水量的预测值。实例验证表明: 小波包对时间序列的分解比小波分解更精细, 组合模型预测能够全面的提取降水序列中所包含的信息, 更好地反映年降水量随时间变化规律, 提高了年降水量预测的精准度, 为降水量预测提供一种新方法。     

基于EEMD-LSTM-ARIMA的土石坝渗压预测模型研究

渗压监测是土石坝渗流安全评价的重要内容之一。由于渗压受到诸多外界因素的影响,测点的渗压值时间序列往往存在非平稳性、局部突变等特点,为此基于“分解-重构-组合”的思想构建了土石坝渗压预测的EEMD-LSTM-ARIMA模型。首先采用集合经验模态分解（EEMD）对时间序列特征进行提取,根据长短期记忆神经网络（LSTM）对提取出的特征分量进行预测,同时结合差分自回归移动平均方法（ARIMA）进行残差修正,组合LSTM和ARIMA的预测结果,重构得到改进预测模型。以某深厚覆盖层上的土石坝工程为例,选取主河床坝体防渗墙后2个典型测点的实测渗压值序列为研究对象进行应用验证。结果表明：相较于单一的LSTM模型和ARIMA模型,改进模型的平均绝对误差MAE、均方误差MSE、均方根误差RMSE均为3种模型中的最小值,预测精度明显优于另外2种模型,该模型为土石坝渗压的精确预测分析提供了新途径。     

Daily Runoff Forecasting Using a Hybrid Model Based on Variational Mode Decomposition and Deep Neural Networks

Accurate and reliable runoff forecasting plays an increasingly important role in the optimal management of water resources. To improve the prediction accuracy, a hybrid model based on variational mode decomposition (VMD) and deep neural networks (DNN), referred to as VMD-DNN, is proposed to perform daily runoff forecasting. First, VMD is applied to decompose the original runoff series into multiple intrinsic mode functions (IMFs), each with a relatively local frequency range. Second, predicted models of decomposed IMFs are established by learning the deep feature values of the DNN. Finally, the ensemble forecasting result is formulated by summing the prediction sub-results of the modelled IMFs. The proposed model is demonstrated using daily runoff series data from the Zhangjiashan Hydrological Station in Jing River, China. To fully illustrate the feasibility and superiority of this approach, the VMD-DNN hybrid model was compared with EMD-DNN, EEMD-DNN, and multi-scale feature extraction -based VMD-DNN, EMD-DNN and EEMD-DNN. The results reveal that the proposed hybrid VMD-DNN model produces the best performance based on the Nash-Sutcliffe efficiency (NSE?=?0.95), root mean square error (RMSE?=?9.92) and mean absolute error (MAE?=?3.82) values. Thus the proposed hybrid VMD-DNN model is a promising new method for daily runoff forecasting.

     

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.     

The Research of Monthly Discharge Predictor-corrector Model Based on Wavelet Decomposition

Based on wavelet analysis theory, a wavelet predictor-corrector model is developed for the simulation and prediction of monthly discharge time series. In this model, the non-stationary time series of monthly discharge is decomposed into an approximated time series and several stationary detail time series according to the principle of wavelet decomposition. Each one of the decomposed time series is predicted, respectively, through the ARMA model for stationary time series. Then the correction procedure is conducted for the sum of the prediction results. Taking the monthly discharge at Yichang station of Yangtse River as an example, the monthly discharge is simulated by using ARMA model, seasonal ARIMA model, BP artificial neural network model and the wavelet predictor-corrector model proposed in this article, respectively. And the effect of decomposition scale for the wavelet predictor-corrector model is also discussed. It is shown that the wavelet predictor-corrector model has higher prediction accuracy than the some other models and the decomposition scale has no obvious effect on the prediction for monthly discharge time series in the example.     

基于小波分析的月径流ARIMA预测方法

将一种基于小波分析的自回归滑动平均求和（ARIMA）模型用于月径流的预测。首先利用小波变换良好的局部化特性，将月径流序列分解成不同时间尺度上的子序列；然后对各个子序列利用ARIMA模型进行预测。将采用基于小波分析的ARIMA模型的预测结果与直接使用ARIMA模型的预测结果进行比较，结果表明引入小波变换提高了月径流预报精度。     

基于CEEMDAN-BA-SVR-Adaboost模型的白水河滑坡位移预测

为提高白水河滑坡位移预测精度,提出一种新的预测模型,即基于自适应噪声完全集合经验模态分解(CEEMDAN)-蝙蝠算法(BA)-支持向量回归机(SVR)-自适应提升算法(Adaboost)的模型。以该滑坡为研究对象,利用CEEMDAN将滑坡位移分解为趋势项以及由IMF分项构成的波动项。首先采用BP神经网络对趋势项位移进行预测,随后利用CEEMDAN-BA-SVR-Adaboost模型对波动项进行预测,并将预测结果与CEEMDAN-PSO-SVR-Adaboost、CEEMDAN-BA-BP-Adaboost、CEEMADAN-BA-SVR、BA-SVR-Adaboost模型预测结果进行对比分析,验证本模型在位移预测方面的优越性。此外,利用CEEMDAN-BA-SVR-Adaboost模型对ZG118波动项位移进行预测,同时计算ZG93监测点最终累计预测位移。结果表明,对白水河滑坡位移进行预测时,CEEMDAN-BA-SVR-Adaboost模型具有较高的准确性和适用性。     

混凝土坝变形Wavelet-EGM-PE-ARIMA组合预测模型

混凝土坝的总变形可以归结为由水压和温度变化引起的变形以及随时间发展的变形。其中,水压变形和温度变形体现为总变形中的周期性分量,而时效变形体现为总变形中的趋势性分量。借助复合建模思想,提出一种混凝土坝变形Wavelet-EGM-PE-ARIMA组合预测模型。首先利用小波多分辨分析功能,分解出大坝变形时间序列中的趋势性项、周期性项;其次,运用EGM模型实现对趋势性项的有效预测,采用周期外延模型实现对周期性项的有效预测,在此基础上,利用ARIMA模型实现对EGM模型和周期外延模型残差项的有效预测;最后通过某工程实例,检验所提出模型的有效性。计算结果表明:该组合模型充分考虑大坝各变形分量的变化规律,并基于此,实现对大坝变形时间序列有效的拟合和预测,且其拟合和预测精度均明显优于传统统计模型。     

基于互补式集合经验模态分解和SSA-ELM的短期风电功率预测

根据实际风电功率信号的波动性和非线性,提出了一种基于互补式集合经验模态分解(CEEMD)和樽海鞘群算法极限学习机(SSA-ELM)的短期风电功率预测模型。首先利用CEEMD将风电功率原始信号分解为一系列模态分量和剩余分量,以减小风电功率的非平稳性;其次采用樽海鞘群算法优化极限学习机对不同分量进行预测;最后将不同分量的预测值叠加得到最终的风电功率预测结果。通过实例仿真验证,并与其他方法进行对比,结果表明该预测模型可提供较高精度的预测结果,具有一定的实用价值。     

Probabilistic Assessment of Monthly River Discharge using Copula and OSVR Approaches

In this study, two efficient approaches for bivariate simulation are presented, which include meteorological and hydrological variables. For this purpose, the applicability of support vector regression (SVR) model optimized by Ant colony and Copula-GARCH (Generalized Autoregressive Conditional Heteroscedasticity) algorithms were investigated and compared in simulating the river discharge based on total monthly rainfall in Talezang Basin, Iran. Entropy theory was used to select a suitable meteorological station corresponding to a hydrometric station. The vector autoregressive model was also used as the base model in Copula-GARCH simulations. According to the 99% confidence intervals of the simulations, the accuracy of both models was confirmed. The simulation results showed that the Copula-GARCH model was more accurate than the optimized SVR (OSVR) model. Considering the 90% efficiency (NSE=0.90) of the Copula-GARCH approach, the results show a 36% improvement of RMSE statistics by the Copula-GARCH model compared to the OSVR model in simulating the river discharge on a monthly scale. The results also showed that by combining nonlinear ARCH models with the copula-based simulations, the reliability of the simulation results increases, which was also confirmed using the violin plot. The results also showed an increase in the accuracy of the Copula-GARCH model at the minimum and maximum values of the data.

     

Hybrid SSA-ARIMA-ANN Model for Forecasting Daily Rainfall

Rainfall, which is one of the most important hydrologic processes, is influenced by many meteorological factors like climatic change, atmospheric temperature, and atmospheric pressure. Even though there are several stochastic and data driven hydrologic models, accurate forecasting of rainfall, especially smaller time step rainfall forecasting, still remains a challenging task. Effective modelling of rainfall is puzzling due to its inherent erratic nature. This calls for an efficient model for accurately forecasting daily rainfall. Singular Spectrum Analysis (SSA) is a time series analysis tool, which is found to be a very successful data pre-processing algorithm. SSA decomposes a given time series into a finite number of simpler and decipherable components. This study proposes integration of Singular Spectrum Analysis (SSA), Auto Regressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) into a hybrid model (SSA-ARIMA-ANN), which can yield reliable daily rainfall forecasts in a river catchment. In the present study, spatially averaged daily rainfall data over Koyna catchment, Maharashtra has been used. In this study SSA is proposed as a data pre-processing tool to separate stationary and non-stationary components from the rainfall data. Correlogram and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test has been used to validate the stationary and non-stationary components. In the developed hybrid model, the stationary components of rainfall data are modelled using ARIMA method and non-stationary components are modelled using ANN. The study of statistical performance of the model shows that the hybrid SSA-ARIMA-ANN model could forecast the daily rainfall of the catchment with reliable accuracy.

     

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。     

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VMD的抽水蓄能机组振动参数演化预测

提出了一种基于移动最小二乘响应面和变分模态分解（Variational mode decomposition,VMD）的抽水蓄能机组振动参数演化预测方法。首先利用移动最小二乘响应面建立抽水蓄能机组振动参数实时评估模型。然后利用VMD将复杂非线性的机组振动参数时间序列分解若干个平稳分量时间序列。其次对每个分量进行特性识别,根据其不同属性,分别采用LS-SVM或GM（1,1）对每个分量进行预测。最后重构每个分量的预测值获得原始时间序列最终的预测结果。实例分析表明,该方法能较准确地预测机组振动参数演化趋势。     

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.