Estimation of Suspended Sediment Yield in Natural Rivers Using Machine-coded Linear Genetic Programming

Estimation of suspended sediment yield is subject to uncertainty and bias. Many methods have been developed for estimating sediment yield but they still lack accuracy and robustness. This paper investigates the use of a machine-coded linear genetic programming (LGP) in daily suspended sediment estimation. The accuracy of LGP is compared with those of the Gene-expression programming (GEP), which is another branch of GP, and artificial neural network (ANN) technique. Daily streamflow and suspended sediment data from two stations on the Tongue River in Montana, USA, are used as case studies. Root mean square error (RMSE) and determination coefficient (R²) statistics are used for evaluating the accuracy of the models. Based on the comparison of the results, it is found that the LGP performs better than the GEP and ANN techniques. The GEP was also found to be better than the ANN. For the upstream and downstream stations, it is found that the LGP models with RMSE = 175 ton/day, R² = 0.941 and RMSE = 254 ton/day, R² = 0.959 in test period is superior in estimating daily suspended sediments than the best accurate GEP model with RMSE = 231 ton/day, R² = 0.941 and RMSE = 331 ton/day, R² = 0.934, respectively.     

Gene-Expression Programming for the Development of a Stage-Discharge Curve of the Pahang River

This study presents Gene-Expression Programming (GEP), an extension of Genetic Programming (GP), as an alternative approach to modeling the stage-discharge relationship for the Pahang River. The results are compared to those obtained by more conventional methods, i.e., the stage rating curve (SRC) and regression techniques. Additionally, the explicit formulations of the developed GEP models are presented. The performance of the GEP model was found to be substantially superior to both GP and the conventional models.     

Development of a Predictive Equation for Modelling the Infiltration Process Using Gene Expression Programming

In this study, the soft computing technique of Gene expression programming (GEP) has been employed to generate a predictive equation of infiltration rate (f_p). Infiltration experiments were conducted at 124 different sites and soil samples were collected to assess various soil properties throughout the Himalayan lake catchment. Parameters determined from observed data using nonlinear-Levenberg Marquardt algorithm were substituted in Horton, Kostiakov and Philip infiltration models and f_p were predicted. Using soil data generated by laboratory investigation of soil samples, the GEP model was developed. Training and testing of the GEP model was performed using 70% and 30% of data respectively. Performance of GEP developed functional relationship was evaluated by comparing predictions from it and aforementioned infiltration models with field observed f_p, and by applying overall performance index (OPI) computed using Coefficient of Determination (R²), Nash–Sutcliffe Efficiency (E_NS), Willmott’s Index of Agreement (W), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Expression developed using GEP indicated feasibility of developed equation with E_NS, R², W, RMSE and MAE of 0.84, 0.84, 0.96, 1.9, and 0.8, respectively for training data-set and 0.84, 0.85, 0.95, 1.2, and 0.95, respectively for testing data-set. Comparative analysis revealed that though with a slightly higher OPI value (0.7–0.8), the performance of conventional models is better compared to the GEP model (0.66) but the GEP model having satisfactory performance may be used for f_p prediction particularly in absence of observed data.

     

Daily Mean Streamflow Prediction in Perennial and Non-Perennial Rivers Using Four Data Driven Techniques

This study examines and compares the performance of four new attractive artificial intelligence techniques including artificial neural network (ANN), hybrid wavelet-artificial neural network (WANN), Genetic expression programming (GEP), and hybrid wavelet-genetic expression programming (WGEP) for daily mean streamflow prediction of perennial and non-perennial rivers located in semi-arid region of Zagros mountains in Iran. For this purpose, data of daily mean streamflow of the Behesht-Abad (perennial) and Joneghan (non-perennial) rivers as well as precipitation information of 17 meteorological stations for the period 1999–2008 were used. Coefficient of determination (R²) and root mean square error (RMSE) were used for evaluating the applicability of developed models. This study showed that although the GEP model was the most accurate in predicting peak flows, but in overall among the four mentioned models in both perennial and non-perennial rivers, WANN had the best performance. Among input patterns, flow based and coupled precipitation-flow based patterns with negligible difference to each other were determined to be the best patterns. Also this study confirmed that combining wavelet method with ANN and GEP and developing WANN and WGEP methods results in improving the performance of ANN and GEP models.     

Regional-Specific Numerical Models of Evapotranspiration Using Gene-Expression Programming Interface in Sahel

An accurate and simple Reference Evapotranspiration (ETo) numerical model eases to use for supporting irrigation planning and its effective management is highly desired in Sahelian regions. This paper investigates the performance ability of the Gene-expression Programming (GEP) for modeling ETo using decadal climatic data from a Sahelian country; Burkina Faso. For the study; important data are collected from six synoptic meteorological stations located in different regions; Gaoua, P?, Boromo, Ouahigouya, Bogandé and Dori. The climatic data combinations are used as inputs to develop the GEP models at regional-specific data basis for estimating ETo. GEP performances are evaluated with the root mean square error (RMSE), and coefficient of correlation (R) between estimated and targeted Penman-Monteith FAO56 set as the true reference values. Obviously; from the statistical viewpoint; GEP computing technique has showed a good ability for providing numerical models on a regional data basis. The performances of GEP based on temperatures data are quite good able to substitute empirical equations at regional level to some extent. It is found that the models with wind velocity yield high accuracies by causing radical improve of the performances with R² (0.925-0.961) and RMSE (0.131-0.272?mm?day^-1); while relative humidity may cause only (R²?=?0.801-0.933 and RMSE?=?0.370-0.578?mm?day^-1). Statistically; GEP is an effectual modeling tool for computing successfully evapotranspiration in Sahel.     

Precipitation Estimation Using Support Vector Machine with Discrete Wavelet Transform

Precipitation prediction is of dispensable importance in many hydrological applications. In this study, monthly precipitation data sets from Serbia for the period 1946–2012 were used to estimate precipitation. To fulfil this objective, three mathematical techniques named artificial neural network (ANN), genetic programming (GP) and support vector machine with wavelet transform algorithm (WT-SVM) were applied. The mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), Pearson correlation coefficient (r) and coefficient of determination (R²) were used to evaluate the performance of the WT-SVM, GP and ANN models. The achieved results demonstrate that the WT-SVM outperforms the GP and ANN models for estimating monthly precipitation.     

Pipe Break Rate Assessment While Considering Physical and Operational Factors: A Methodology based on Global Positioning System and Data-Driven Techniques

An accurate prediction of pipes failure rate plays a substantial role in the management of Water Distribution Networks (WDNs). In this study, a field study was conducted to register pipes break and relevant causes in the WDN of Yazd City, Iran. In this way, 851 water pipes were incepted and localized by the Global Positioning System (GPS) apparatus. Then, 1033 failure cases were reported in the eight zones of understudy WDN during March-December 2014. Pipes break rate (BR_P) was calculated using the depth of pipe installation (h_P), number of failures (N_P), the pressure of water pipes in operation (P), and age of pipe (A_P). After completing a pipe break database, robust Artificial Intelligence models, namely Multivariate Adaptive Regression Spline (MARS), Gene-Expression Programming (GEP), and M5 Model Tree were employed to extract precise formulation for the pipes break rate estimation. Results of the proposed relationships demonstrated that the MARS model with Coefficient of Correlation (R) of 0.981 and Root Mean Square Error (RMSE) of 0.544 provided more satisfying efficiency than the M5 model (R?=?0.888 and RMSE?=?1.096). Furthermore, statistical results indicated that MARS and GEP models had comparatively at the same accuracy level. Explicit equations by Artificial Intelligence (AI) models were satisfactorily comparable with those obtained by literature review in terms of various conditions: physical, operational, and environmental factors and complexity of AI models. Through a probabilistic framework for the pipes break rate, the results of first-order reliability analysis indicated that the MARS technique had a highly satisfying performance when MARS-extracted-equation was assigned as a limit state function.

     

Estimation of Peak Flood Discharges at Ungauged Sites Across Turkey

The reliable forecasting of the peak flood discharge at river basins is a common problem, and it becomes more complicated when there is inadequate recorded data. The statistical methods commonly used for the estimation of peak flood discharges are generally considered to be inadequate because of the complexity of this problem. Recently, genetic programming (GP) which is a branch of soft computing methods has attracted the attention of the hydrologists. In this study, gene-expression programming (GEP) and linear genetic programming (LGP), which are extensions to GP, in addition to logistic regression (LR) were employed in order to forecast peak flood discharges. The study covered 543 ungauged sites across Turkey. Drainage area, elevation, latitude, longitude, and return period were used as the inputs while the peak flood discharge was the output. Model comparison results revealed that GEP predicted the peak flood discharges with R ²?=?57.4?% correlation, LGP with 56?% and LR model with 42.3?%, respectively. The peak flood discharges in all river basins can now be determined using the single equation provided by the GEP model.     

New Approaches for Estimation of Monthly Rainfall Based on GEP-ARCH and ANN-ARCH Hybrid Models

Accurate estimation of rainfall has an important role in the optimal water resources management, as well as hydrological and climatological studies. In the present study, two novel types of hybrid models, namely gene expression programming-autoregressive conditional heteroscedasticity (GEP-ARCH) and artificial neural networks-autoregressive conditional heteroscedasticity (ANN-ARCH) are introduced to estimate monthly rainfall time series. To fulfill this purpose, five stations with various climatic conditions were selected in Iran. The lagged monthly rainfall data was utilized to develop the different GEP and ANN scenarios. The performance of proposed hybrid models was compared to the GEP and ANN models using root mean square error (RMSE) and coefficient of determination (R²). The results show that the proposed GEP-ARCH and ANN-ARCH models give a much better performance than the GEP and ANN in all of the studied stations with various climates. Furthermore, the ANN-ARCH model generally presents better performance in comparison with the GEP-ARCH model.     

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.     

利用Hyperion图像估算森林覆盖度

植被覆盖度是评价土地荒漠化最有效的指标,遥感是获取区域尺度植被覆盖度参数的一个重要手段。针对EO-1 Hyperion高光谱遥感图像成像的特点,探讨了高光谱Hyperion图像的预处理和森林覆盖度遥感估算的方法,研究中采用几何光学模型和混合像元模型等方法从高光谱EO-1 Hyperion图像估算植被覆盖度,进一步将2种方法估算的植被覆盖度进行了对比,并利用实测数据对估算结果进行验证。研究结果表明:利用几何光学模型反演的植被覆盖度(决定系数R²=0.76;均方根误差RMSE=0.06)优于混合像元模型法(R²=0.71; RMSE=0.07)。     

Gene-Expression Programming for Short-Term Forecasting of Daily Reference Evapotranspiration Using Public Weather Forecast Information

This study aimed to forecast the daily reference evapotranspiration (ETo) using a gene-expression programming (GEP) algorithm with limited public weather forecast information over Gaoyou station, located in Jiangsu province, China. To calibrate and validate the gene-expression code, important meteorological data and weather forecast information were collected from the local meteorological station and public weather media, respectively. The GEP algebraic formulation was successfully constructed based only on daily minimum and maximum air temperature using the true FAO56 Penman-Monteith (PM) set as reference values. The performance of the models was then assessed using the correlation coefficient (R), root mean squared error (RMSE), root relative squared error (RRSE) and mean absolute error (MAE). The study demonstrated that GEP is able to calibrate ETo (all errors ≤0.990 mm/day, R = 0.832–0.866) and forecast the daily ETo with good accuracy (RMSE = 1.207 mm/day, MAE = 0.902 mm/day, RRSE = 0.629 mm/day, R = 0.777). The model accuracies slightly decreased over a 7-day forecast lead-time. These results suggest that the GEP algorithm can be considered as a deployable tool for ETo forecast to anticipate decision on short-term irrigation schedule in the study zone.     

An expert system for predicting shear stress distribution in circular open channels using gene expression programming

The shear stress distribution in circular channels was modeled in this study using gene expression programming (GEP). 173 sets of reliable data were collected under four flow conditions for use in the training and testing stages. The effect of input variables on GEP modeling was studied and 15 different GEP models with individual, binary, ternary, and quaternary input combinations were investigated. The sensitivity analysis results demonstrate that dimensionless parameter y/P, where y is the transverse coordinate, and P is the wetted perimeter, is the most influential parameter with regard to the shear stress distribution in circular channels. GEP model 10, with the parameter y/P and Reynolds number (Re) as inputs, outperformed the other GEP models, with a coefficient of determination of 0.7814 for the testing data set. An equation was derived from the best GEP model and its results were compared with an artificial neural network (ANN) model and an equation based on the Shannon entropy proposed by other researchers. The GEP model, with an average RMSE of 0.0301, exhibits superior performance over the Shannon entropy-based equation, with an average RMSE of 0.1049, and the ANN model, with an average RMSE of 0.2815 for all flow depths.     

Genetic Programming for Predicting Longitudinal Dispersion Coefficients in Streams

This paper presents a genetic programming (GP) approach to predict the longitudinal dispersion coefficients in natural streams. Published data were compiled from the literature for the dispersion coefficient for a wide range of flow conditions, and they were used for the development and testing of the proposed method. The proposed GP approach produced excellent results (R²  = 0.98 and RMSE = 0.085) compared to the existing predictors (Rajeev and Dutta, Hydrol Res 40(6):544–552, 2009, R² = 0.345 and RMSE = 1778.6) for dispersion coefficient.     

Season Algorithm-Multigene Genetic Programming: A New Approach for Rainfall-Runoff Modelling

Genetic programming (GP) is recognized as a robust machine learning method for rainfall-runoff modelling. However, it may produce lagged forecasts if autocorrelation feature of runoff series is not taken carefully into account. To enhance timing accuracy of GP-based rainfall-runoff models, the paper proposes a new rainfall-runoff model that integrates season algorithm (SA) with multigene-GP (MGGP). The proposed SA-MGGP model was trained and validated for single- and two- and three-day ahead streamflow forecasts at Haldizen Catchment, Trabzon, Turkey. Timing and prediction accuracy of the proposed model were assessed in terms of different efficiency criteria. In addition, the efficiency results were compared to those of monolithic GP, MGGP, and SA-GP forecasting models developed in the present study as the benchmarks. The outcomes indicated that SA augments timing accuracy of GP-based models in the range 250% to 500%. It is also found that MGGP may identify underlying structure of the rainfall-runoff process slightly better than monolithic GP at the study catchment.     

Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming

Artificial neural networks (ANNs) and genetic programming (GP) have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hydraulic jumps, such as the free surface location and energy dissipation. The dimensionless hydraulic parameters, including jump depth, jump length, and energy dissipation, were determined as functions of the Froude number and the height and length of corrugations. The estimations of the ANN and GP models were found to be in good agreement with the measured data. The results of the ANN model were compared with those of the GP model, showing that the proposed ANN models are much more accurate than the GP models.     

基于遗传规划的径流预测新方法

应用遗传规划方法进行中长期径流预测,将预测模型视为遗传规划中的个体加以处理,依据生物界“优胜劣汰”的原则,运用复制、交叉和变异等遗传操作算子;根据历史样本数据自动生成最佳的径流预测模型,包括模型的函数形式以及模型参数;最后运用得到的预测模型对某水文站的年径流进行预测。仿真结果表明,基于遗传规划的径流预测模型可以明显提高径流预测精度,为解决中长期径流预测问题提供了一种行之有效的新方法。     

Development and Implementation of Support Vector Machine Regression Surrogate Models for Predicting Groundwater Pumping-Induced Saltwater Intrusion into Coastal Aquifers

Predicting the extent of saltwater intrusion (SWI) into coastal aquifers in response to changing pumping patterns is a prerequisite of any groundwater management framework. This study investigates the feasibility of using support vector machine regression (SVMr), an innovative artificial intelligence-based machine learning algorithm for predicting salinity concentrations at selected monitoring wells in an illustrative aquifer under variable groundwater pumping conditions. For evaluation purpose, the prediction results of SVMr are compared with well-established genetic programming (GP) based surrogate models. SVMr and GP models are trained and validated using identical sets of input (pumping) and output (salinity concentration) datasets. The trained and validated models are then used to predict salinity concentrations at specified monitoring wells in response to new pumping datasets. Prediction capabilities of the two learning machines are evaluated using different proficiency measures to ensure their practicality and generalisation ability. The performance evaluation results suggest that the prediction capability of SVMr is superior to GP models. Also, a sensitivity analysis methodology is proposed for assessing the impact of pumping rates on salt concentrations at monitoring locations. This sensitivity analysis provides a subset of most influential pumping rates, which is used to construct new SVMr surrogate models with improved predictive capabilities. The improved prediction capability and the generalisation ability of the SVMr models together with the ability to improve the accuracy of prediction by refining the input set for training makes the use of proposed SVMr models more attractive. Prediction models with more accurate prediction capability makes it potentially very useful for designing large scale coastal aquifer management strategies.     

Use of Gene-Expression Programming to Estimate Manning’s Roughness Coefficient for High Gradient Streams

Manning’s roughness coefficient (n) has been widely used in the estimation of flood discharges or depths of flow in natural channels. Therefore, the selection of appropriate Manning’s n values is of paramount importance for hydraulic engineers and hydrologists and requires considerable experience, although extensive guidelines are available. Generally, the largest source of error in post-flood estimates (termed indirect measurements) is due to estimates of Manning’s n values, particularly when there has been minimal field verification of flow resistance. This emphasizes the need to improve methods for estimating n values. The objective of this study was to develop a soft computing model in the estimation of the Manning’s n values using 75 discharge measurements on 21 high gradient streams in Colorado, USA. The data are from high gradient (S?>?0.002 m/m), cobble- and boulder-bed streams for within bank flows. This study presents Gene-Expression Programming (GEP), an extension of Genetic Programming (GP), as an improved approach to estimate Manning’s roughness coefficient for high gradient streams. This study uses field data and assessed the potential of gene-expression programming (GEP) to estimate Manning’s n values. GEP is a search technique that automatically simplifies genetic programs during an evolutionary processes (or evolves) to obtain the most robust computer program (e.g., simplify mathematical expressions, decision trees, polynomial constructs, and logical expressions). Field measurements collected by Jarrett (J Hydraulic Eng ASCE 110: 1519–1539, 1984) were used to train the GEP network and evolve programs. The developed network and evolved programs were validated by using observations that were not involved in training. GEP and ANN-RBF (artificial neural network-radial basis function) models were found to be substantially more effective (e.g., R² for testing/validation of GEP and RBF-ANN is 0.745 and 0.65, respectively) than Jarrett’s (J Hydraulic Eng ASCE 110: 1519–1539, 1984) equation (R² for testing/validation equals 0.58) in predicting the Manning’s n.     

Precipitation Forecasting Using Wavelet-Genetic Programming and Wavelet-Neuro-Fuzzy Conjunction Models

Forecasting precipitation as a major component of the hydrological cycle is of primary importance in water resources engineering, planning and management as well as in scheduling irrigation practices. In the present study the abilities of hybrid wavelet-genetic programming [i.e. wavelet-gene-expression programming, WGEP] and wavelet-neuro-fuzzy (WNF) models for daily precipitation forecasting are investigated. In the first step, the single genetic programming (GEP) and neuro-fuzzy (NF) models are applied to forecast daily precipitation amounts based on previously recorded values, but the results are very weak. In the next step the hybrid WGEP and WNF models are used by introducing the wavelet coefficients as GEP and NF inputs, but no satisfactory results are produced, even though the accuracies increased to a great extent. In the third step, the new WGEP and WNF models are built; by merging the best single and hybrid models’ inputs and introducing them as the models inputs. The results show the new hybrid WGEP models are effective in forecasting daily precipitation, while the new WNF models are unable to learn the non linear process of precipitation very well.