Monthly Streamflow Forecasting Using ELM-IPSO Based on Phase Space Reconstruction

We have developed a hybrid model that integrates chaos theory and an extreme learning machine with optimal parameters selected using an improved particle swarm optimization (ELM-IPSO) for monthly runoff analysis and prediction. Monthly streamflow data covering a period of 55 years from Daiying hydrological station in the Chaohe River basin in northern China were used for the study. The Lyapunov exponent, the correlation dimension method, and the nonlinear prediction method were used to characterize the streamflow data. With the time series of the reconstructed phase space matrix as input variables, an improved particle swarm optimization was used to improve the performance of the extreme learning machine. Finally, the optimal chaotic ensemble learning model for monthly streamflow prediction was obtained. The accuracy of the predictions of the streamflow series (linear correlation coefficient of about 0.89 and efficiency coefficient of about 0.78) indicate the validity of our approach for predicting streamflow dynamics. The developed method had a higher prediction accuracy compared with an auto-regression method, an artificial neural network, an extreme learning machine with genetic algorithm and with PSO algorithm, suggesting that ELM-IPSO is an efficient method for monthly streamflow prediction.

     

免疫粒子群算法与支持向量机在枯水期月径流预测中的应用

针对支持向量机(SVM)最佳算法参数难以确定以及基本粒子群算法(PSO)易陷入局部极值等不足,提出免疫粒子群算法(IAPSO),利用IAPSO算法搜寻SVM学习参数,构建IAPSO-SVM预测模型,并与PSO-SVM、GA-SVM模型作为对比,以云南省某水文站枯水期月径流预测为例进行实例研究,利用实例前43年和后10年资料对模型进行训练和预测。结果表明:IAPSO-SVM模型对实例后10年枯水期1-3月月均径流预测的平均相对误差绝对值分别为3.32%、6.52%和6.55%,精度优于PSO-SVM和GA-SVM模型,表明IAPSO-SVM模型具有较高的预测精度和泛化能力。IAPSO算法利用浓度选择机制及免疫接种原理,改进了基本粒子群优化算法的全局寻优能力和收敛速度,具有较强的全局寻优能力。利用IAPSO算法优化得到的SVM学习参数可有效提高SVM模型的预测精度和泛化能力。     

异构多种群粒子群优化算法在水位流量关系拟合中的应用

通过8个复杂函数对一种异构多种群粒子群优化算法进行仿真验证,并与传统单种群粒子群优化算法进行对比。针对水位流量关系拟合中相关参数难以确定的不足,利用异构多种群粒子群优化算法优化水位流量关系相关参数,以云南省龙潭站、西洋站水位流量关系拟合为例进行实例研究,并与粒子群优化算法、最小二乘法拟合结果进行对比。结果表明:异构多种群粒子群优化算法收敛精度远远优于粒子群优化算法,具有较好的计算鲁棒性和全局寻优能力。该算法对龙潭站和西洋站水位流量关系拟合的平均相对误差绝对值分别仅为0.27%和0.50%,拟合精度优于粒子群优化算法和最小二乘法。利用异构多种群粒子群优化算法优化水位流量关系可以获得更好的拟合效果。     

文化算法与投影寻踪融合模型在相似流域优选中的应用

研究文化算法(CA)与投影寻踪(PP)融合模型应用于相似流域优选中的可行性和有效性。以12个小河站控制流域优选为例,建立CA-PP相似流域优选模型,并构建差分进化(DE)算法-PP、和声搜索(HS)算法-PP和粒子群优化(PSO)算法-PP作为对比模型,将优选结果与随机分析法、集对分析法、模糊分析法、灰色分析法的优选结果进行比较。结果表明:CA寻优PP目标函数获得的最优值、最劣值、平均值和标准差均优于DE、HS和PSO算法,具有较好的全局极值寻优能力和收敛稳定性能。CAPP模型对相似流域的优选结果与DE-PP、HS-PP和PSO-PP模型,以及随机分析法、集对分析法、模糊分析法、灰色分析法的优选结果相同,但在优选顺序上存在差异。CA-PP模型用于相似流域优选是可行和有效的,可为同类优选提供新的途径和方法。     

改进WOA-指数幂乘积模型在基坑变形预测中的应用

为提高基坑变形预测精度,提出基于拉普拉斯交叉算子(LX)改进的鲸鱼优化算法(LXWOA)优化的指数幂乘积(EPP)基坑变形预测模型。选取4个标准测试函数对LXWOA进行仿真验证,并与基本鲸鱼优化算法(WOA)、灰狼优化(GWO)算法、正弦余弦算法(SCA)、粒子群优化(PSO)算法的仿真结果进行比较。利用LXWOA对EPP模型的指数参数进行优化,构建LXWOA-EPP变形预测模型,并构建WOA-EPP、GWO-EPP、SCA-EPP、PSO-EPP模型与LXWOA-SVM、LXWOA-BP模型作对比,以文献基坑监测数据为例进行实例研究,分别利用自相关函数法和虚假最邻近法确定实例延迟时间和嵌入维数,构建模型输入、输出向量,利用实例前15期和后3期监测数据对各模型进行训练和预测。结果表明:LXWOA搜索能力优于WOA、GWO、SCA和PSO算法,具有较好的寻优精度和全局搜索能力。LXWOA-EPP模型对实例预测的平均相对误差绝对值、平均绝对误差、均方根误差分别为0. 18%、0. 008 mm、0. 009 mm,均优于WOA-EPP等6种模型和文献预测精度,表明LXWOA能有效优化EPP模型参数,LXWOA-EPP模型用于变形预测是可行和有效的,模型及方法可为其他相关预测研究提供参考。     

A Hybrid VMD-SVM Model for Practical Streamflow Prediction Using an Innovative Input Selection Framework

Some previous studies have proved that prediction models using traditional overall decomposition sampling (ODS) strategy are unreasonable because the subseries obtained by the ODS strategy contain future information to be predicted. It is, therefore, necessary to put forward a new sampling strategy to fix this defect and also to improve the accuracy and reliability of decomposition-based models. In this paper, a stepwise decomposition sampling (SDS) strategy according to the practical prediction process is introduced. Moreover, an innovative input selection framework is proposed to build a strong decomposition-based monthly streamflow prediction model, in which sunspots and atmospheric circulation anomaly factors are employed as candidate input variables to enhance the prediction accuracy of monthly streamflow in addition to regular inputs such as precipitation and evaporation. Meanwhile, the partial correlation algorithm is employed to select optimal input variables from candidate input variables including precipitation, evaporation, sunspots, and atmospheric circulation anomaly factors. Four basins of the U.S. MOPEX project with various climate characteristics were selected as a case study. Results indicate that: (1) adding teleconnection factors into candidate input variables helps enhance the prediction accuracy of the support vector machine (SVM) model in predicting streamflow; (2) the innovative input selection framework helps to improve the prediction capacity of models whose candidate input variables interact with each other compared with traditional selection strategy; (3) the SDS strategy can effectively prevent future information from being included into input variables, which is an appropriate substitute of the ODS strategy in developing prediction models; (4) as for monthly streamflow, the hybrid variable model decomposition-support vector machine (VMD-SVM) models, using an innovative input selection framework and the SDS strategy, perform better than those which have not adopted this framework in all study areas. Generally, the findings of this study showed that the hybrid VMD-SVM model combining the SDS strategy and innovative input selection framework is a useful and powerful tool for practical hydrological prediction work in the context of climate change.

     

基于DPSO-ANFIS的大坝变形预测模型

变形预测模型是大坝结构安全性态分析的关键技术支撑。针对现有大坝变形预测模型在精确度、泛化性等方面的不足,将自适应模糊神经网络引入到大坝变形预测模型中,利用动态权重粒子群算法对自适应模糊神经网络中模糊层的适应度值进行参数寻优,形成可以寻找最优适应度值的自适应模糊神经网络,进而建立基于DPSO-ANFIS的大坝变形预测模型。根据大坝原型监测数据,代入训练好的模型得到输出值,并将其与实际监测数据进行对比分析。工程实例应用表明,基于DPSO-ANFIS的大坝变形预测模型输出值与实测值偏差最大为0.0516 mm,均方根误差为0.0351 mm,平均绝对误差为0.0320 mm,各项指标精度均优于基于PSO-ANFIS、ANFIS和BP神经网络的大坝变形预测模型。针对不同位置测点、预测时间段,基于DPSO-ANFIS的大坝变形预测模型输出值接近实测值,预测趋势符合真实值走向,整体预测性能稳定。该模型具有较高的精确度、良好的泛化性与可靠的稳定性,工程实用综合性能较优。     

A Comparative Study of Autoregressive,Autoregressive Moving Average,Gene Expression Programming and Bayesian Networks for Estimating Monthly Streamflow

In the recent years, artificial intelligence techniques have attracted much attention in hydrological studies, while time series models are rarely used in this field. The present study evaluates the performance of artificial intelligence techniques including gene expression programming (GEP), Bayesian networks (BN), as well as time series models, namely autoregressive (AR) and autoregressive moving average (ARMA) for estimation of monthly streamflow. In addition, simple multiple linear regression (MLR) was also used. To fulfill this objective, the monthly streamflow data of Ponel and Toolelat stations located on Shafarood and Polrood Rivers, respectively in Northern Iran were used for the period of October 1964 to September 2014. In order to investigate the models’ accuracy, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²) were employed as the error statistics. The obtained results demonstrated that the single AR and ARMA time series models had better performance in comparison with the single GEP, BN and MLR methods. Furthermore, in this study, six hybrid models known as GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR and MLR-ARMA were developed to enhance the estimation accuracy of the monthly streamflow. It was concluded that the developed hybrid models were more accurate than the corresponding single artificial intelligence and time series models. The obtained results confirmed that the integration of time series models and artificial intelligence techniques could be of use to improve the accuracy of single models in modeling purposes related to the hydrological studies.     

Using Optimized Deep Learning to Predict Daily Streamflow: A Comparison to Common Machine Learning Algorithms

From a watershed management perspective, streamflow need to be predicted accurately using simple, reliable, and cost-effective tools. Present study demonstrates the first applications of a novel optimized deep-learning algorithm of a convolutional neural network (CNN) using BAT metaheuristic algorithm (i.e., CNN-BAT). Using the prediction powers of 4 well-known algorithms as benchmarks – multilayer perceptron (MLP-BAT), adaptive neuro-fuzzy inference system (ANFIS-BAT), support vector regression (SVR-BAT) and random forest (RF-BAT), the CNN-BAT model is tested for daily streamflow (Q_t) prediction in the Korkorsar catchment in northern Iran. Fifteen years of daily rainfall (R_t) and streamflow data from 1997 to 2012 were collected and used for model development and evaluation. The dataset was divided into two groups for building and testing models. The correlation coefficient (r) between rainfall and streamflow with and without antecedent events (i.e., R_t-1, R_t-2, etc.) (as the input variables) and Q_t (as the output variable) served as the basis for constructing different input scenarios. Several quantitative and visually-based evaluation metrics were used to validate and compare the model’s performance. The results indicate that R_t was the most effective input variable on Q_t prediction and the integration of R_t, R_t-1, and Q_t-1 was the optimal input combination. The evaluation metrics show that the CNN-BAT algorithm outperforms the other algorithms. The Friedman and Wilcoxon signed-rank test indicates that the prediction power of CNN-BAT algorithm is significantly/statistically different from the other developed algorithms.

     

仿生算法优化BP神经网络在降雨空间插值中的应用

人工神经网络能够充分挖掘已知样本中的规律,从而对未观测数据进行预测,可应用于降雨量空间插值计算中。在BP神经网络进行降雨空间插值的基础上,引入遗传、粒子群和蚁群3种仿生算法对BP神经网络初始权值和阈值进行优化,将优化后的BP神经网络应用于三峡区间流域年、月和日3个时间尺度的降雨空间插值中。结果表明:仿生算法对BP神经网络初始权值和阈值优化求解后,降低了BP神经网络陷入局部最小以及过拟合的风险,在插值过程中表现出较好的稳定性,取得了理想的插值结果。     

基于GWO-LSTM的丹江口水库入库径流预测

入库径流预测对丹江口水库调度及水资源利用具有重要的指示意义。基于灰狼优化算法（GWO）构建不同的预测模型,开展丹江口水库月入库径流预测研究,并探讨网络结构超参数的选取及验证GWO全局遍历性、收敛快的特点。结果表明:灰狼优化的长短期记忆模型（GWO-LSTM）的预测精度和泛化性能优于灰狼优化的人工神经网络模型（GWO-BP）和逐步回归模型,其验证期的纳什效率系数平均达到0.969,整体趋势预测较好,峰值捕捉略有不足,可适用于丹江口水库月入库径流预测;模型超参数依据经验取值时,其预测结果不如GWO优化,验证期的纳什效率系数不足0.5,未达到可接受范围,而且带有一定的偶然性,建议选用具有全局优化特性的优化算法进行超参数选取;验证了GWO算法全局遍历性和收敛快的特点,平均在3次迭代后可达到收敛状态。     

基于系统微分响应的暴雨强度公式参数优化

暴雨强度公式参数的优化求解本质是一个高维非线性优化问题,目前常采用的优化求解方法是在以误差平方和为目标函数的基础上通过智能算法优化求解参数。为研究这类方法的合理性,通过随机抽样、参数空间网格化方法分析了常用暴雨强度公式参数求解方法的局限性,评价了常用智能算法的参数优化能力,进而提出了基于系统微分响应的暴雨强度公式参数优化方法。结果表明：以均方误差作为目标函数对非线性函数求解参数会增加额外参数解;在没有有效确定参数范围的情况下,随机抽样很难获得满足精度要求的参数样本,在有效确定参数范围后,目标函数的响应面上仍会存在无穷多个局部最优值,且很多局部最优的目标函数与全局最优近乎相同;以粒子群算法、SCE-UA算法为代表的随机搜索优化算法会因为参数初始取值范围过大、目标函数响应面局部最优参数解数量过多等问题而难以获得参数真值;提出的基于系统微分响应的暴雨强度公式参数优化方法能够快速寻找到参数真值,不仅效率高且能够避免陷入局部最优。     

基坑变形预测的改进供需优化算法-指数幂乘积模型

为提高基坑变形预测精度,提出改进供需优化算法-指数幂乘积基坑变形预测模型(ISDO-EPP模型)。通过6个标准测试函数和3个应用实例对ISDO算法的寻优能力进行验证,并与基本供需优化(SDO)算法、鲸鱼优化算法(WOA)、灰狼优化(GWO)算法、蛾群算法(MSA)、粒子群优化(PSO)算法的寻优结果进行比较。以3个基坑沉降预测为例,通过自相关函数法和虚假最邻近法确定各实例延迟时间和嵌入维数,构造输入、输出向量对各模型进行训练和预测。结果表明,ISDO算法搜索能力优于SDO等5种算法,具有较好的寻优精度、全局搜索能力和稳健性能。ISDO-EPP模型对3个实例预测的平均相对误差绝对值分别为0.73%、3.36%和1.33%,均优于ISDO-SVM、ISDO-BP模型,表明ISDO算法能有效优化EPP模型参数,ISDO-EPP模型用于变形预测是可行和有效的。     

SSO-BP模型在水资源可再生能力评价中的应用

为评价区域水资源可再生能力,提出了水资源可再生能力评价指标体系和分级标准,构建了基于BP神经网络的评价模型,并以云南省文山州水资源可再生能力评价为例进行实例研究。首先,遴选出单位面积水资源量等10个指标,构建水资源可再生能力评价指标体系和分级标准;其次,针对BP神经网络初始权值和阈值难以确定的不足,利用一种全新的仿生群体智能算法--群居蜘蛛优化（SSO）算法优化BP神经网络初始参数,提出了SSO-BP评价模型,并通过6个高维复杂函数对SSO算法进行验证,且与粒子群优化（PSO）算法进行对比;最后,利用SSO-BP模型对实例进行水资源可再生能力评价。结果表明：① SSO算法具有较好的收敛精度和全局寻优能力,可有效提高BP神经网络模型的预测精度和泛化能力。② 文山州各评价区域2014年水资源可再生能力处于最强与中等之间,符合区域现状。     

基于遗传算法的模糊优选BP网络模型及其应用

在模糊优选BP神经网络模型的基础上，引入遗传算法，提出融入遗传算法的模糊优选神经网络预测模型，是对模糊优选BP神经网络模型的进一步发展。其基本思路是：在BP算法训练网络出现收敛速度缓慢时启用遗传算法优化网络的运行参数，把优化的结果作为BP算法的初始值再用BP算法训练网络，这样交替运行BP算法和遗传算法，直到达到问题要求的精度。在新疆雅马渡站年径流量的预报中，预测模型在预报精度和算法的收敛速度方面都达到了较好的效果。     

基于多组群教学优化的随机森林预测模型及应用

为有效提高水文预测预报精度,提出了一种基于多组群教学优化(MGTLO)的随机森林(RF)预测方法,利用MGTLO算法对RF两个关键参数进行优化,构建MGTLO-RF预测模型,并与基于MGTLO算法优化的支持向量机(SVM)、BP神经网络两种常规预测模型作对比分析。以云南省龙潭站月径流和年径流预测为例进行实例研究,利用前44 a和后10 a资料对MGTLO-RF等3种模型进行训练和预测。结果表明:所提出的MGTLO-RF模型具有更好的预测精度和泛化能力,可作为水文预测预报和相关预测研究的一种有效工具。     

基于人工生态系统优化算法的组合生长需水预测模型

为提高需水预测精度,拓展生长模型在需水预测中的应用,提出基于人工生态系统优化(AEO)算法的组合生长需水预测模型。结合实例,选取6个标准测试函数在不同维度条件下对AEO算法进行仿真验证,并与鲸鱼优化算法(WOA)、灰狼优化(GWO)算法、教学优化(TLBO)算法和传统粒子群优化(PSO)算法的仿真结果进行比较。基于Weibull、Richards、Usher 3种单一生长模型构建Weibull-Richards-Usher、Weibull-Richards、Weibull-Usher、Richards-Usher 4种组合生长模型,利用AEO算法同时对组合模型参数和权重系数进行优化,提出AEO-Weibull-Richards-Usher、AEO-Weibull-Richards、AEO-Weibull-Usher、AEO-Richards-Usher需水预测模型,并构建AEO-Weibull、AEO-Richards、AEO-Usher、AEO-SVM、AEO-BP模型作对比,以上海市需水预测为例进行实例验证,利用实例前30组和后8组统计资料对各组合模型进行训练和预测。结果表明,在不同维度条件下,AEO算法寻优精度优于WOA、GWO、TLBO、PSO算法,具有较好的寻优精度和全局搜索能力。4种组合模型对实例预测的平均相对误差绝对值、平均绝对误差分别在0.94%~1.17%、0.30亿~0.37亿m³之间,预测精度优于AEO-Weibull等其他5种模型。4种组合模型均具有较好的预测精度和泛化能力,表明AEO算法能同时有效优化组合生长模型参数和权重系数,基于AEO算法的组合生长模型用于需水预测是可行和有效的。     

混沌粒子群优化算法在马斯京根模型参数优化中的应用

针对目前马斯京根模型参数率定中存在的求解复杂、精度不高等问题,本文将混沌搜索机制引入粒子群优化算法中,构建混沌粒子群优化算法对马斯京根模型参数进行率定。这种方法利用混沌运动的遍历性,改善了粒子群优化算法的全局寻优能力,避免算法陷入局部极值,使得粒子群体的进化速度加快,提高了算法的收敛速度和精度。通过实例应用表明,混沌粒子群优化算法可以有效地估算出马斯京根模型参数,优化效果明显优于粒子群优化算法及试错法,因此该算法具有很好的实用性。     

混沌粒子群优化算法在确定含水层参数中的应用

以泰斯公式为例,将混沌粒子群优化算法应用于求解分析抽水试验数据,解决含水层参数的函数优化问题.通过在粒子群算法的初始化粒子位置及后续的细搜索过程中加入混沌序列,提高了算法的收敛速度和精度.数值实验结果表明:混沌粒子群算法能够有效地应用于求解含水层参数计算问题;粒子数的增多对混沌粒子群算法收敛性的影响不明显;待估导水系数选取不同的倍数均体现出混沌粒子群算法的收敛性明显优于粒子群优化算法.混沌粒子群算法应用于确定含水层参数是可行的.     

Effect of calibration data series length on performance and optimal parameters of hydrological model

In order to assess the effects of calibration data series length on the performance and optimal parameter values of a hydrological model in ungauged or data-limited catchments (data are non-continuous and fragmental in some catchments), we used non-continuous calibration periods for more independent streamflow data for SIMHYD (simple hydrology) model calibration. Nash-Sutcliffe efficiency and percentage water balance error were used as performance measures. The particle swarm optimization (PSO) method was used to calibrate the rainfall-runoff models. Different lengths of data series ranging from one year to ten years, randomly sampled, were used to study the impact of calibration data series length. Fifty-five relatively unimpaired catchments located all over Australia with daily precipitation, potential evapotranspiration, and streamflow data were tested to obtain more general conclusions. The results show that longer calibration data series do not necessarily result in better model performance. In general, eight years of data are sufficient to obtain steady estimates of model performance and parameters for the SIMHYD model. It is also shown that most humid catchments require fewer calibration data to obtain a good performance and stable parameter values. The model performs better in humid and semi-humid catchments than in arid catchments. Our results may have useful and interesting implications for the efficiency of using limited observation data for hydrological model calibration in different climates.