Committee neural networks for porosity and permeability prediction from well logs

Neural computing has moved beyond simple demonstration to more significant applications. Encouraged by recent developments in artificial neural network (ANN) modelling techniques, we have developed committee machine (CM) networks for converting well logs to porosity and permeability, and have applied the networks to real well data from the North Sea. Simple three‐layer back‐propagation ANNs constitute the blocks of a modular system where the porosity ANN uses sonic, density and resistivity logs for input. The permeability ANN is slightly more complex, with four inputs (density, gamma ray, neutron porosity and sonic). The optimum size of the hidden layer, the number of training data required, and alternative training techniques have been investigated using synthetic logs. For both networks an optimal number of neurons in the hidden layer is in the range 8–10. With a lower number of hidden units the network fails to represent the problem, and for higher complexity overfitting becomes a problem when data are noisy. A sufficient number of training samples for the porosity ANN is around 150, while the permeability ANN requires twice as many in order to keep network errors well below the errors in core data. For the porosity ANN the overtraining strategy is the suitable technique for bias reduction and an unconstrained optimal linear combination (OLC) is the best method of combining the CM output. For permeability, on the other hand, the combination of overtraining and OLC does not work. Error reduction by validation, simple averaging combined with range‐splitting provides the required accuracy. The accuracy of the resulting CM is restricted only by the accuracy of the real data. The ANN approach is shown to be superior to multiple linear regression techniques even with minor non‐linearity in the background model.     

Identification of physical processes inherent in artificial neural network rainfall runoff models

The emergence of artificial neural network (ANN) technology has provided many promising results in the field of hydrology and water resources simulation. However, one of the major criticisms of ANN hydrologic models is that they do not consider/explain the underlying physical processes in a watershed, resulting in them being labelled as black‐box models. This paper discusses a research study conducted in order to examine whether or not the physical processes in a watershed are inherent in a trained ANN rainfall‐runoff model. The investigation is based on analysing definite statistical measures of strength of relationship between the disintegrated hidden neuron responses of an ANN model and its input variables, as well as various deterministic components of a conceptual rainfall‐runoff model. The approach is illustrated by presenting a case study for the Kentucky River watershed. The results suggest that the distributed structure of the ANN is able to capture certain physical behaviour of the rainfall‐runoff process. The results demonstrate that the hidden neurons in the ANN rainfall‐runoff model approximate various components of the hydrologic system, such as infiltration, base flow, and delayed and quick surface flow, etc., and represent the rising limb and different portions of the falling limb of a flow hydrograph. Copyright © 2004 John Wiley & Sons, Ltd.     

The Utilization and Modeling of Photo-Fenton Process as a Single Unit in Textile Wastewater Treatment

Studies on the direct application of the photo-Fenton process (PFOP) to disinfect and decontaminate textile wastewater are rare. The output of the artificial neural network (ANN) models applied to the wastewater of a textile factory producing woven fabrics, which is used to assess the efficiency of the PFOP process, are investigated and compared with each other in this study. The highest PFOP efficiency is obtained at a pH of 3. Chemical oxygen demand (COD), suspended solids (SS) and color removal rates are 94%, 90%, and 96%, respectively. The data are modeled with ANNs and nonlinear external input autoregressive ANNs (NARX-ANN) using the MATLAB R2020a software program. Both Levenberg–Marquardt (trainlm) and scaled conjugate gradient (trainscg) algorithms are employed in the ANN and NARX-ANN models, whereas hyperbolic tangent sigmoid (Tansig) and logistic sigmoid (Logsig) functions are superimposed on the hidden layer in the ANN model, and Tansig functions are superimposed on the NARX-ANN model. It is determined that the developed ANN models are more effective in estimating the PFOP efficiency. The mean squared error is 0.000 953, and the coefficient of determination (R²) is 0.96 661.     

Short term streamflow forecasting using artificial neural networks

The research described in this article investigates the utility of Artificial Neural Networks (ANNs) for short term forecasting of streamflow. The work explores the capabilities of ANNs and compares the performance of this tool to conventional approaches used to forecast streamflow. Several issues associated with the use of an ANN are examined including the type of input data and the number, and the size of hidden layer(s) to be included in the network. Perceived strengths of ANNs are the capability for representing complex, non-linear relationships as well as being able to model interaction effects. The application of the ANN approach is to a portion of the Winnipeg River system in Northwest Ontario, Canada. Forecasting was conducted on a catchment area of approximately 20 000 km². using quarter monthly time intervals. The results were most promising. A very close fit was obtained during the calibration (training) phase and the ANNs developed consistently outperformed a conventional model during the verification (testing) phase for all of the four forecast lead-times. The average improvement in the root mean squared error (RMSE) for the 8 years of test data varied from 5 cms in the four time step ahead forecasts to 12.1 cms in the two time step ahead forecasts.     

Rainfall‐runoff modelling using artificial neural networks: comparison of network types

Growing interest in the use of artificial neural networks (ANNs) in rainfall‐runoff modelling has suggested certain issues that are still not addressed properly. One such concern is the use of network type, as theoretical studies on a multi‐layer perceptron (MLP) with a sigmoid transfer function enlightens certain limitations for its use. Alternatively, there is a strong belief in the general ANN user community that a radial basis function (RBF) network performs better than an MLP, as the former bases its nonlinearities on the training data set. This argument is not yet substantiated by applications in hydrology. This paper presents a comprehensive evaluation of the performance of MLP‐ and RBF‐type neural network models developed for rainfall‐runoff modelling of two Indian river basins. The performance of both the MLP and RBF network models were comprehensively evaluated in terms of their generalization properties, predicted hydrograph characteristics, and predictive uncertainty. The results of the study indicate that the choice of the network type certainly has an impact on the model prediction accuracy. The study suggests that both the networks have merits and limitations. For instance, the MLP requires a long trial‐and‐error procedure to fix the optimal number of hidden nodes, whereas for an RBF the structure of the network can be fixed using an appropriate training algorithm. However, a judgment on which is superior is not clearly possible from this study. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling suspended sediment concentration using artificial neural networks for Gangotri glacier

The dynamics of suspended sediment involves inherent non‐linearity and complexity because of existence of both spatial variability of the basin characteristics and temporal climatic patterns. This complexity, therefore, leads to inaccurate prediction by the conventional sediment rating curve (SRC) and other empirical methods. Over past few decades, artificial neural networks (ANNs) have emerged as one of the advanced modelling techniques capable of addressing inherent non‐linearity in the hydrological processes. In the present study, feed‐forward back propagation (FFBP) algorithm of ANNs is used to model stage–discharge–suspended sediment relationship for ablation season (May–September) for melt runoff released from Gangotri glacier, one of the largest glaciers in Himalaya. The simulations have been carried out on primary data of suspended sediment concentration (SSC) discharge and stage for ablation season of 11‐year period (1999–2009). Combinations of different input vectors (viz. stage, discharge and SSC) for present and previous days are considered for development of the ANN models and examining the effects of input vectors. Further, based on model performance indices for training and testing phase, a suitable modelling approach with appropriate model input structure is suggested. The conventional SRC method is also used for modelling discharge–sediment relationship and performance of developed models is evaluated by statistical indices, namely; root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²). Statistically, the performance of ANN‐based models is found to be superior as compared to SRC method in terms of the selected performance indices in simulating the daily SSC. The study reveals suitability of ANN approach for simulation and estimation of daily SSC in glacier melt runoff and, therefore, opens new avenues of research for application of hybrid soft computing models in glacier hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation and forecasting of daily groundwater outflow in a small chalky watershed

The purpose of this research is to include expert knowledge as one part of the modelling system and therefore offer the chance to create a productive interaction system between expert, mathematical model (MMO8) and artificial neural networks (ANNs). In the present project, the first objective is to determine some parameters by the MMO8 model, introduced as ANN input parameters to forecast spring outflow. The second objective is first to investigate the effect of temporal information by taking current and past data sets and then to forecast spring outflow. The good results obtained reveal the merit of the ANNs–MMO8 combination, and specifically multilayer perceptron (MLP) models. This methodology, for a network with lower, lag and number hidden layer, consistently produced better performance. Copyright © 2003 John Wiley & Sons, Ltd.     

Stream temperature modelling using artificial neural networks: application on Catamaran Brook,New Brunswick,Canada

Fish habitat and aquatic life in rivers are highly dependent on water temperature. Therefore, it is important to understand andto be able to predict river water temperatures using models. Such models can increase our knowledge of river thermal regimes as well as provide tools for environmental impact assessments. In this study, artificial neural networks (ANNs) will be used to develop models for predicting both the mean and maximum daily water temperature. The study was conducted within Catamaran Brook, a small drainage basin tributary to the Miramichi River (New Brunswick, Canada). In total, eight ANN models were investigated using a variety of input parameters. Of these models, four predicted mean daily water temperature and four predicted maximum daily water temperature. The best model for mean daily temperature had eight input parameters: minimum, maximum and mean air temperatures of the current day and those of the preceding day, the day of year and the water level. This model had an overall root‐mean‐square error (RMSE) of 0·96 °C, a bias of 0·26 °C and a coefficient of determination R² = 0·971. The model that best predicted maximum daily water temperature was similar to the first model but excluded mean daily air temperature. Good results were obtained for maximum water temperatures with an overall RMSE of 1·18 °C, a bias of 0·15 °C and R² = 0·961. The results of ANN models were similar to and/or better than those observed from the literature. The advantages of artificial neural networks models in modelling river water temperature lie in their simplicity of use, their low data requirement and their good performance, as well as their flexibility in allowing many input and output parameters. Copyright © 2008 Crown in the right of Canada and John Wiley & Sons, Ltd.     

Artificial neural networks as an alternative approach to groundwater numerical modelling and environmental design

Classical optimization methodologies based on mathematical theories have been developed for the solution of various constrained environmental design problems. Numerical models have been widely used to represent an environmental system accurately. The use of methodologies such as artificial neural networks (ANNs), which approximate the complicated behaviour and response of physical systems, allows the optimization of a large number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical model would be prohibitive. In this paper, a combination of an ANN with a differential evolution algorithm is proposed to replace the classical finite‐element numerical model in water resources management problems. The objective of the optimization problem is to determine the optimal operational strategy for the productive pumping wells located in the northern part of Rhodes Island in Greece, to cover the water demand and maintain the water table at certain levels. The conclusions of this study show that the use of ANN as an approximation model could (a) significantly reduce the computational burden associated with the accurate simulation of complex physical systems and (b) provide solutions very close to the optimal ones for various constrained environmental design problems. Copyright © 2008 John Wiley & Sons, Ltd.     

A systematic approach to the input determination for neural network rainfall–runoff models

Input determination has a great influence on the performance of artificial neural network (ANN) rainfall–runoff models. To improve the performance of ANN models, a systematic approach to the input determination for ANN models is proposed. In the proposed approach, the irrelevant inputs are removed. Then an adequate ANN model, which only includes highly relevant inputs, is constructed. Unlike the trial‐and‐error procedure, the proposed approach is more systematic and avoids unnecessary trials. To demonstrate the effectiveness of the proposed approach, an application to actual typhoon events is presented. The results show that the proposed ANN model, which is constructed by the proposed approach, has advantages over those obtained by the trial‐and‐error procedure. The proposed ANN model has a simpler architecture, needs less training time, and performs better. The proposed ANN model is recommended as an alternative to existing rainfall–runoff ANN models. Copyright © 2007 John Wiley & Sons, Ltd.     

Artificial neural network simulation for prediction of suspended sediment concentration in the River Ramganga,Ganges Basin,India

The relation between the water discharge (Q) and suspended sediment concentration (SSC) of the River Ramganga at Bareilly, Uttar Pradesh, in the Himalayas, has been modeled using Artificial Neural Networks (ANNs). The current study validates the practical capability and usefulness of this tool for simulating complex nonlinear, real world, river system processes in the Himalayan scenario. The modeling approach is based on the time series data collected from January to December (2008-2010) for Q and SSC. Three ANNs (T1-T3) with different network configurations have been developed and trained using the Levenberg Marquardt Back Propagation Algorithm in the Matlab routines. Networks were optimized using the enumeration technique, and, finally, the best network is used to predict the SSC values for the year 2011. The values thus obtained through the ANN model are compared with the observed values of SSC. The coefficient of determination (R2), for the optimal network was found to be 0.99. The study not only provides insight into ANN modeling in the Himalayan river scenario, but it also focuses on the importance of understanding a river basin and the factors that affect the SSC, before attempting to model it. Despite the temporal variations in the study area, it is possible to model and successfully predict the SSC values with very simplistic ANN models.     

The development of a regional geomagnetic daily variation model using neural networks

Global and regional geomagnetic field models give the components of the geomagnetic field as functions of position and epoch; most utilise a polynomial or Fourier series to map the input variables to the geomagnetic field values. The only temporal variation generally catered for in these models is the long term secular variation. However, there is an increasing need amongst certain users for models able to provide shorter term temporal variations, such as the geomagnetic daily variation. In this study, for the first time, artificial neural networks (ANNs) are utilised to develop a geomagnetic daily variation model. The model developed is for the southern African region; however, the method used could be applied to any other region or even globally. Besides local time and latitude, input variables considered in the daily variation model are season, sunspot number, and degree of geomagnetic activity. The ANN modelling of the geomagnetic daily variation is found to give results very similar to those obtained by the synthesis of harmonic coefficients which have been computed by the more traditional harmonic analysis of the daily variation.     

Improving generalization of artificial neural networks in rainfall–runoff modelling / Amélioration de la généralisation de réseaux de neurones artificiels pour la modélisation pluie-débit

Abstract

Artificial neural networks (ANNs) are general-purpose techniques that can be used for nonlinear data-driven rainfall–runoff modelling. The key issue to construct a good model by means of ANNs is to understand their structural features and the problems related to their construction. Indeed, the quantity and quality of data, the type of noise and the mathematical properties of the algorithm for estimating the usual large number of parameters (weights) are crucial for the generalization performances of ANNs. However, it is well known that ANNs may suffer from poor generalization properties due to the high number of parameters and non-Gaussian data noise. Therefore, in the first part of this paper, the features and problems of ANNs are discussed. Eight Avoiding Overfitting Techniques are then presented, considering that these are methods for improving the generalization of ANNs. For this reason, they have been tested on two case studies—rainfall–runoff data from two drainage basins in the south of Italy—in order to gain insight into their properties and to investigate if there is one that absolutely gives the best performance.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Porosity and permeability prediction from wireline logs using artificial neural networks: a North Sea case study

Estimations of porosity and permeability from well logs are important yet difficult tasks encountered in geophysical formation evaluation and reservoir engineering. Motivated by recent results of artificial neural network (ANN) modelling offshore eastern Canada, we have developed neural nets for converting well logs in the North Sea to porosity and permeability. We use two separate back-propagation ANNs (BP-ANNs) to model porosity and permeability. The porosity ANN is a simple three-layer network using sonic, density and resistivity logs for input. The permeability ANN is slightly more complex with four inputs (density, gamma ray, neutron porosity and sonic) and more neurons in the hidden layer to account for the increased complexity in the relationships. The networks, initially developed for basin-scale problems, perform sufficiently accurately to meet normal requirements in reservoir engineering when applied to Jurassic reservoirs in the Viking Graben area. The mean difference between the predicted porosity and helium porosity from core plugs is less than 0.01 fractional units. For the permeability network a mean difference of approximately 400 mD is mainly due to minor core-log depth mismatch in the heterogeneous parts of the reservoir and lack of adequate overburden corrections to the core permeability. A major advantage is that no a priori knowledge of the rock material and pore fluids is required. Real-time conversion based on measurements while drilling (MWD) is thus an obvious application.     

Modelling evaporation using an artificial neural network algorithm

This paper investigates the prediction of Class A pan evaporation using the artificial neural network (ANN) technique. The ANN back propagation algorithm has been evaluated for its applicability for predicting evaporation from minimum climatic data. Four combinations of input data were considered and the resulting values of evaporation were analysed and compared with those of existing models. The results from this study suggest that the neural computing technique could be employed successfully in modelling the evaporation process from the available climatic data set. However, an analysis of the residuals from the ANN models developed revealed that the models showed significant error in predictions during the validation, implying loss of generalization properties of ANN models unless trained carefully. The study indicated that evaporation values could be reasonably estimated using temperature data only through the ANN technique. This would be of much use in instances where data availability is limited. Copyright © 2002 John Wiley & Sons, Ltd.     

A fusion-based neural network methodology for monthly reservoir inflow prediction using MODIS products

ABSTRACT

A model fusion approach was developed based on five artificial neural networks (ANNs) and MODIS products. Static and dynamic ANNs – the multi-layer perceptron (MLP) with one and two hidden layers, general regression neural network (GRNN), radial basis function (RBF) and nonlinear autoregressive network with exogenous inputs (NARX) – were used to predict the monthly reservoir inflow in Mollasadra Dam, Fars Province, Iran. Leaf area index and snow cover from MODIS, and rainfall and runoff data were used to identify eight different combinations to train the models. Statistical error indices and the Borda count method were used to verify and rank the identified combinations. The best results for individual ANNs were combined with MODIS products in a fusion model. The results show that using MODIS products increased the accuracy of predictions, with the MLP with two hidden layers giving the best performance. Also, the fusion model was found to be superior to the best individual ANNs.     

Uncertainties in real‐time flood forecasting with neural networks

Although artificial neural networks (ANNs) have been applied in rainfall runoff modelling for many years, there are still many important issues unsolved that have prevented this powerful non‐linear tool from wide applications in operational flood forecasting activities. This paper describes three ANN configurations and it is found that a dedicated ANN for each lead‐time step has the best performance and a multiple output form has the worst result. The most popular form with multiple inputs and single output has the average performance. In comparison with a linear transfer function (TF) model, it is found that ANN models are uncompetitive against the TF model in short‐range predictions and should not be used in operational flood forecasting owing to their complicated calibration process. For longer range predictions, ANN models have an improved chance to perform better than the TF model; however, this is highly dependent on the training data arrangement and there are undesirable uncertainties involved, as demonstrated by bootstrap analysis in the study. To tackle the uncertainty issue, two novel approaches are proposed: distance analysis and response analysis. Instead of discarding the training data after the model's calibration, the data should be retained as an integral part of the model during its prediction stage and the uncertainty for each prediction could be judged in real time by measuring the distances against the training data. The response analysis is based on an extension of the traditional unit hydrograph concept and has a very useful potential to reveal the hydrological characteristics of ANN models, hence improving user confidence in using them in real time. Copyright © 2006 John Wiley & Sons, Ltd.     

Wave data assimilation using a hybrid approach in the Persian Gulf

The main goal of this study is to develop an efficient approach for the assimilation of the hindcasted wave parameters in the Persian Gulf. Hence, the third generation SWAN model was employed for wave modeling forced by the 6-h ECMWF wind data with a resolution of 0.5°. In situ wave measurements at two stations were utilized to evaluate the assimilation approaches. It was found that since the model errors are not the same for wave height and period, adaptation of model parameter does not result in simultaneous and comprehensive improvement of them. Therefore, an approach based on the error prediction and updating of output variables was employed to modify wave height and period. In this approach, artificial neural networks (ANNs) were used to estimate the deviations between the simulated and measured wave parameters. The results showed that updating of output variables leads to significant improvement in a wide range of the predicted wave characteristics. It was revealed that the best input parameters for error prediction networks are mean wind speed, mean wind direction, wind duration, and the wave parameters. In addition, combination of the ANN estimated error with numerically modeled wave parameters leads to further improvement in the predicted wave parameters in contrast to direct estimation of the parameters by ANN.     

Instance‐based learning compared to other data‐driven methods in hydrological forecasting

Data‐driven techniques based on machine learning algorithms are becoming popular in hydrological modelling, in particular for forecasting. Artificial neural networks (ANNs) are often the first choice. The so‐called instance‐based learning (IBL) has received relatively little attention, and the present paper explores the applicability of these methods in the field of hydrological forecasting. Their performance is compared with that of ANNs, M5 model trees and conceptual hydrological models. Four short‐term flow forecasting problems were solved for two catchments. Results showed that the IBL methods often produce better results than ANNs and M5 model trees, especially if used with the Gaussian kernel function. The study showed that IBL is an effective data‐driven method that can be successfully used in hydrological forecasting. Copyright © 2007 John Wiley & Sons, Ltd.