الفهرس 
Daily inflow forecastingOnly 14 pages are availabe for public view
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Abstract
Application of stochastic methods and data-driven models to time series analysis and reservoir operation has been a major focus of water resources planning and management. The aim of this study is to investigate the suitability of applying these models in water resources planning and management. Stochastic analysis and data-driven models are applied to the management and operation of reservoirs (case study, the Bigge, Henne, Möhne and Sorpe reservoirs in the Ruhr River basin). The ability of these models to accurately simulate water resources management problems is the first priority of this study. However, an operational application is not the main object. This thesis is focused on the following topics: 1. The stochastic properties of inflow processes The stochastic characteristics of the inflow processes of the reservoirs are examined. The inflow processes are investigated for seasonality, trend, long memory and stationarity. The results of the seasonality test of the daily, 10-days and monthly inflow time series show that: • The inflow time series have a clear seasonality in the mean and standard deviation. Seasons with high mean values have also high standard deviations. • The coefficient of variation has higher values in the dry periods. • The higher values of the skewness occur in seasons with low flow and vice versa. • The autocorrelation coefficients are low for high inflow seasons and high for seasons with low inflow for all inflow time series, except daily inflow time series at lag of one day. The results of the seasonal Mann-Kendall test at 5% significance level indicate that a downward trend is only detected for all tested inflow time series of the Sorpe reservoir. The Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests are used to test the stationarity of the log-transformed and standardized daily, 10-days, monthly, 3-months, 6-months and annual inflow time series at 5% significance level. The results show that all inflow time series appear to be stationary by applying log-transformation and standardization to them. 2. Forecasting of daily inflow The applicability of the backpropagation neural network (BPNN), adaptive neuro-fuzzy inference system (ANFIS), autoregressive moving average (ARMA) and the autoregressive fractional integrated moving average (ARFIMA) models are explored to one-step and two-steps ahead forecasting of the daily inflow into the Bigge, Henne, Möhne and Sorpe reservoirs. These models are divided into two groups according to the potential input variables: Univariate models (group M1-1 and group M1-2) • The simulation models are the BPNN, ANFIS, ARMA and ARFIMA. • The potential input variables are the average daily inflow. Multivariate models (group M2) • The simulation models are the BPNN and ANFIS. • The potential input variables are the average daily inflow and the daily rainfall. The training algorithm that is utilized for all the BPNN models in the dissertation is Levenberg-Marquardt algorithm and the used activation functions are tan-sigmoid and linear functions for the hidden layer neurons and for the output one respectively. The overfitting problem is suppressed in the BPNN and ANFIS models by applying the early stopping procedure. The BPNN models are trained using one hidden layer. The number of neurons in the hidden layer and the optimal input variables in the BPNN models are determined using a trial-and-error procedure. Starting with the input variables of the optimum BPNN models, another trial-and-error procedure is developed to find the ANFIS models which have the best performance. The orders of the autoregressive (AR) and moving average (MA) components in the ARMA and ARFIMA models are determined by trying different values between 0 and 5. The Akaike Information Criterion (AIC) is used to select the best ARMA and ARFIMA models (the models with minimum AIC). The diagnostic of the ARMA and ARFIMA models are tested by applying the Ljung-Box test at 5 % significance level and the results show that the null hypothesis of model adequacy is rejected only for the simulated daily inflow time series of the Henne and Möhne reservoirs using the ARFIMA model. Different efficiency criteria (correlation coefficient, root mean square error, average relative error percentage, index of agreement and Nash-Sutcliffe coefficient) are used to compare the performance of the models. The comparison shows that the performances of the models, group M1-1 and the models, group M1-2, don’t have significantly different performance except for the average relative error percentage (AREP). The BPNN and ANFIS models have the minimum values of the AREP for all daily inflow time series. The models, group M2, are found to outperform the models group M1-2, in respect of all used efficiency criteria. 3. Filling missing values in daily inflow time series The efficiency of the BPNN and ANFIS models and the generalized linear model (GLM) for filling the missing values in the daily inflow time series of the Bigge, Henne, Möhne and Sorpe reservoirs are explored. High correlation values between the daily inflow time series are detected. Therefore, the inflow of each reservoir is estimated using the inflow data of the other reservoirs as input variables. The BPNN models are trained using one hidden layer with three neurons. ANFIS models with three membership functions (Gaussian type) associated with each input variable are used. The link function and distribution of the response for GLM are selected using a trial-and-error procedure. In respect of the estimated values of the root mean square error (rmse), the BPNN models have better performances for filling the missing data. The BPNN model is employed to extend the time series of the monthly inflow into the Bigge reservoir in the period from 11/1960 to 10/1965. 4. Generation of the monthly inflow data The Thomas-Fiering (T-F), Gamma Thomas-Fiering (Gamma T-F), Monte Carlo (MC) and periodic hidden Markov (PHMM) models are applied to generate monthly inflow data into the Bigge, Henne, Möhne and Sorpe reservoirs. The inverse transform method is used to generate random numbers in the T-F and MC models. However, Wilson-Hilferty transformation is proposed to reproduce skewed noises in the Gamma T-F model. The Cholesky decomposition method is used to preserve month-to-month correlation in the generated monthly inflow data by the MC model. Three monthly inflow time series with lengths 100, 300 and 500 years are generated using T-F, Gamma T-F, MC and PHMM. The statistical parameters (mean, standard deviation, month-to-month correlation and skewness) of the generated monthly inflow are compared with those of the observed one. The results of the comparison show that the T-F, MC and PHMM models reproduce most of the statistical parameters very well. PHMM is a methodology newly developed within this thesis to generate monthly inflow. PHMM has the ability to reproduce all statistical parameters (except month-to-month correlation) very well. Finally, using the quantile-quantile (Q-Q) and the survivor function plots, the observed and the simulated monthly distributions are graphically compared. These plots indicate the ability of the MC and PHMM models to reproduce the statistical distribution of the observations, in particular the extreme values with superiority of the PHMM. More research is needed to improve the performance of PHMM in preserving month-to-month correlation. A procedure is developed to detect the expected consecutive 5 years that have minimum total inflow using the MC model. The generated monthly inflow time series during the 5 years can be adopted as an inflow scenario for optimization of the reservoir operation. 5. Prediction of the travel time of reservoirs’ releases along the Ruhr Historical flow data (15 minute time series) are used to estimate the travel time of the released flow from the Bigge, Sorpe, Möhne and Henne reservoirs to some downstream gauges. The estimated travel time values are used to build the nonlinear regression (NLR) models to detect the relation between travel time and the flow at each downstream gauge. These NLR models can be easily used to predict the travel time when knowing the flow at the downstream gauge. The estimated travel time values along the reach from gauge Ahausen to gauge Hagen-Hohenlimburg are simulated using the ANFIS, BPNN and multiple linear regression (MLR) models. Due to the limited amounts of the travel time data, k-fold cross validation (KFCV) and leave-one-out cross validation (LOOCV) are used to estimate the generalization errors in the ANFIS, BPNN and MLR models. The values of the generalization error show that the ANFIS model A5 outperforms the other models. The ANFIS model A5 has the following input variables: 1. The increase in the reservoir release (QR) with two membership functions (Gaussian type). 2. The discharge at the downstream gauge (QD) with three membership functions (Gaussian type). The upper and middle reaches of the Ruhr River are simulated using the Hydrologic Engineering Center River Analysis System (HEC-RAS) and the results are compared with those of the NLR model. The comparison shows a moderate agreement between the results of the two models. A graphical user interface (Fliesszeit GUI) is developed using Matlab (The MathWorks, Inc). For any 15 minutes historical flow data this GUI can be used to: 1. Determine the jump points in the flow at the release gauge and the corresponding downstream gauges. 2. Plot the hydrographs at each jump point. These hydrographs can be used to estimate the travel time. 3. The estimated travel time value can be manually entered to update the travel time values that have been estimated previously. 4. The simulation models can be trained using the updated travel time values.