Hydrological time‐series modelling using an adaptive neuro‐fuzzy inference system

Accurate forecasting of hydrological time‐series is a quite important issue for a wise and sustainable use of water resources. In this study, an adaptive neuro‐fuzzy inference system (ANFIS) approach is used to construct a time‐series forecasting system. In particular, the applicability of an ANFIS to the forecasting of the time‐series is investigated. To illustrate the applicability and capability of an ANFIS, the River Great Menderes, located in western Turkey, is chosen as a case study area. The advantage of this method is that it uses the input–output data sets. A total of 5844 daily data sets collected from 1985 to 2000 are used for the time‐series forecasting. Models having various input structures were constructed and the best structure was investigated. In addition, four various training/testing data sets were built by cross‐validation methods and the best data set was obtained. The performance of the ANFIS models in training and testing sets was compared with observations and also evaluated. In order to get an accurate and reliable comparison, the best‐fit model structure was also trained and tested by artificial neural networks and traditional time‐series analysis techniques and the results compared. The results indicate that the ANFIS can be applied successfully and provide high accuracy and reliability for time‐series modelling. Copyright © 2007 John Wiley & Sons, Ltd.     

A fuzzy dynamic flood routing model for natural channels

A fuzzy dynamic flood routing model (FDFRM) for natural channels is presented, wherein the flood wave can be approximated to a monoclinal wave. This study is based on modification of an earlier published work by the same authors, where the nature of the wave was of gravity type. Momentum equation of the dynamic wave model is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. Hence, the FDFRM gets rid of the assumptions associated with the momentum equation. Also, it overcomes the necessity of calculating friction slope (S_f) in flood routing and hence the associated uncertainties are eliminated. The fuzzy rule based model is developed on an equation for wave velocity, which is obtained in terms of discontinuities in the gradient of flow parameters. The channel reach is divided into a number of approximately uniform sub‐reaches. Training set required for development of the fuzzy rule based model for each sub‐reach is obtained from discharge‐area relationship at its mean section. For highly heterogeneous sub‐reaches, optimized fuzzy rule based models are obtained by means of a neuro‐fuzzy algorithm. For demonstration, the FDFRM is applied to flood routing problems in a fictitious channel with single uniform reach, in a fictitious channel with two uniform sub‐reaches and also in a natural channel with a number of approximately uniform sub‐reaches. It is observed that in cases of the fictitious channels, the FDFRM outputs match well with those of an implicit numerical model (INM), which solves the dynamic wave equations using an implicit numerical scheme. For the natural channel, the FDFRM outputs are comparable to those of the HEC‐RAS model. Copyright © 2009 John Wiley & Sons, Ltd.     

The data‐driven approach as an operational real‐time flood forecasting model

Accurate water level forecasts are essential for flood warning. This study adopts a data‐driven approach based on the adaptive network–based fuzzy inference system (ANFIS) to forecast the daily water levels of the Lower Mekong River at Pakse, Lao People's Democratic Republic. ANFIS is a hybrid system combining fuzzy inference system and artificial neural networks. Five ANFIS models were developed to provide water level forecasts from 1 to 5 days ahead, respectively. The results show that although ANFIS forecasts of water levels up to three lead days satisfied the benchmark, four‐ and five‐lead‐day forecasts were only slightly better in performance compared with the currently adopted operational model. This limitation is imposed by the auto‐ and cross‐correlations of the water level time series. Output updating procedures based on the autoregressive (AR) and recursive AR (RAR) models were used to enhance ANFIS model outputs. The RAR model performed better than the AR model. In addition, a partial recursive procedure that reduced the number of recursive steps when applying the AR or the RAR model for multi‐step‐ahead error prediction was superior to the fully recursive procedure. The RAR‐based partial recursive updating procedure significantly improved three‐, four‐ and five‐lead‐day forecasts. Our study further shows that for long lead times, ANFIS model errors are dominated by lag time errors. Although the ANFIS model with the RAR‐based partial recursive updating procedure provided the best results, this method was able to reduce the lag time errors significantly for the falling limbs only. Improvements for the rising limbs were modest. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of integrated back‐propagation network and self organizing map for flood forecasting

Much of the nonlinearity and uncertainty regarding the flood process is because hydrologic data required for estimation are often tremendously difficult to obtain. This study employed a back‐propagation network (BPN) as the main structure in flood forecasting to learn and to demonstrate the sophisticated nonlinear mapping relationship. However, a deterministic BPN model implies high uncertainty and poor consistency for verification work even when the learning performance is satisfactory for flood forecasting. Therefore, a novel procedure was proposed in this investigation which integrates linear transfer function (LTF) and self‐organizing map (SOM) to efficiently determine the intervals of weights and biases of a flood forecasting neural network to avoid the above problems. A SOM network with classification ability was applied to the solutions and parameters of the BPN model in the learning stage, to classify the network parameter rules and to obtain the winning parameters. The outcomes from the previous stage were then used as the ranges of the parameters in the recall stage. Finally, a case study was carried out in Wu‐Shi basin to demonstrate the effectiveness of the proposal. Copyright © 2009 John Wiley & Sons, Ltd.     

Efficient estimation of flood forecast prediction intervals via single‐ and multi‐objective versions of the LUBE method

Prediction intervals (PIs) are commonly used to quantify the accuracy and precision of a forecast. However, traditional ways to construct PIs typically require strong assumptions about data distribution and involve a large computational burden. Here, we improve upon the recent proposed Lower Upper Bound Estimation method and extend it to a multi‐objective framework. The proposed methods are demonstrated using a real‐world flood forecasting case study for the upper Yangtze River Watershed. Results indicate that the proposed methods are able to efficiently construct appropriate PIs, while outperforming other methods including the widely used Generalized Likelihood Uncertainty Estimation approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Conceptual fuzzy neural network model for water quality simulation

Artificial neural networks (ANNs) have been applied successfully in various fields. However, ANN models depend on large sets of historical data, and are of limited use when only vague and uncertain information is available, which leads to difficulties in defining the model architecture and a low reliability of results. A conceptual fuzzy neural network (CFNN) is proposed and applied in a water quality model to simulate the Barra Bonita reservoir system, located in the southeast region of Brazil. The CFNN model consists of a rationally‐defined architecture based on accumulated expert knowledge about variables and processes included in the model. A genetic algorithm is used as the training method for finding the parameters of fuzzy inference and the connection weights. The proposed model may handle the uncertainties related to the system itself, model parameterization, complexity of concepts involved and scarcity and inaccuracy of data. The CFNN showed greater robustness and reliability when dealing with systems for which data are considered to be vague, uncertain or incomplete. The CFNN model structure is easier to understand and to define than other ANN‐based models. Moreover, it can help to understand the basic behaviour of the system as a whole, being a successful example of cooperation between human and machine. Copyright © 2006 John Wiley & Sons, Ltd.     

Developing a hybrid multi‐model for peak flood forecasting

The present study aims to develop a hybrid multi‐model using the soft computing approach. The model is a combination of a fuzzy logic, artificial neural network (ANN) and genetic algorithm (GA). While neural networks are low‐level computational structures that perform well dealing with raw data, fuzzy logic deal with reasoning on a higher level by using linguistic information acquired from domain experts. However, fuzzy systems lack the ability to learn and cannot adjust themselves to a new environment. Moreover, experts occasionally make mistakes and thus some rules used in a system may be false. A network type structure of the present hybrid model is a multi‐layer feed‐forward network, the main part is a fuzzy system based on the first‐order Sugeno fuzzy model with a fuzzification and a defuzzification processes. The consequent parameters are determined by least square method. The back‐propagation is applied to adjust weights of network. Then, the antecedent parameters of the membership function are updated accordingly by the gradient descent method. The GA was applied to select the fuzzy rule. The hybrid multi‐model was used to forecast the flood level at Chiang Mai (under the big flood 2005) and the Koriyama flood (2003) in Japan. The forecasting results are evaluated using standard global goodness of fit statistic, efficient index (EI), the root mean square error (RMSE) and the peak flood error. Moreover, the results are compared to the results of a neuro‐genetic model (NGO) and ANFIS model using the same input and output variables. It was found that the hybrid multi‐model can be used successfully with an efficiency index (EI) more than 0·95 (for Chiang Mai flood up to 12 h ahead forecasting) and more than 0·90 (for Koriyama flood up to 8 h ahead forecasting). In general, all of three models can predict the water level with satisfactory results. However, the hybrid model gave the best flood peak estimation among the three models. Therefore, the use of fuzzy rule base, which is selected by GA in the hybrid multi‐model helps to improve the accuracy of flood peak. Copyright © 2009 John Wiley & Sons, Ltd.     

Enforced self‐organizing map neural networks for river flood forecasting

Self‐organizing maps (SOMs) have been successfully accepted widely in science and engineering problems; not only are their results unbiased, but they can also be visualized. In this study, we propose an enforced SOM (ESOM) coupled with a linear regression output layer for flood forecasting. The ESOM re‐executes a few extra training patterns, e.g. the peak flow, as recycling input data increases the mapping space of peak flow in the topological structure of SOM, and the weighted sum of the extended output layer of the network improves the accuracy of forecasting peak flow. We have investigated an ESOM neural network by using the flood data of the Da‐Chia River, Taiwan, and evaluated its performance based on the results obtained from a commonly used back‐propagation neural network. The results demonstrate that the ESOM neural network has great efficiency for clustering, especially for the peak flow, and super capability of modelling the flood forecast. The topology maps created from the ESOM are interesting and informative. Copyright © 2007 John Wiley & Sons, Ltd.     

Prediction of coarse particle movement with adaptive neuro‐fuzzy inference systems

The use of a neuro‐fuzzy approach is proposed to model the dynamics of entrainment of a coarse particle by rolling. It is hypothesized that near‐bed turbulent flow structures of different magnitude and duration or frequency and energy content are responsible for the particle displacement. A number of Adaptive Neuro‐Fuzzy Inference System (ANFIS) architectures are proposed and developed to link the hydrodynamic forcing exerted on a solid particle to its response, and model the underlying nonlinear dynamics of the system. ANFIS combines the advantages of fuzzy inference (If‐Then) rules with the power of learning and adaptation of the neural networks. The model components and forecasting procedure are discussed in detail. To demonstrate the model's applicability for near‐threshold flow conditions an example is provided, where flow velocity and particle displacement data from flume experiments are used as input and output for the training and testing of the ANFIS models. In particular, a Laser Doppler velocimeter (LDV) is employed to obtain long records of local streamwise velocity components upstream of a mobile exposed particle. These measurements are acquired synchronously with the time history of the particle's position detected by a setup including a He‐Ne laser and a photodetector. The representation of the input signal in the time and frequency domain is implemented and the best performing models are found capable of reproducing the complex dynamics of particle response. Following a trial and error approach the different models are compared in terms of their efficiency and forecast accuracy using a number of performance indices. Copyright © 2011 John Wiley & Sons, Ltd.     

An evaluation of a traditional and a neural net modelling approach to flood forecasting for an upland catchment

This study evaluates two (of the many) modelling approaches to flood forecasting for an upland catchment (the River South Tyne at Haydon Bridge, England). The first modelling approach utilizes ‘traditional’ hydrological models. It consists of a rainfall–runoff model (the probability distributed model, or PDM) for flow simulation in the upper catchment. Those flows are then routed to the lower catchment using two kinematic wave (KW) routing models. When run in forecast‐mode, the PDM and KW models utilize model updating procedures. The second modelling approach uses neural network models, which use a ‘pattern‐matching’ process to produce model forecasts.Following calibration, the models are evaluated in terms of their fit to continuous stage data and flood event magnitudes and timings within a validation period. Forecast times of 1 h, 2 h and 4 h are selected (the catchment has a response time of approximately 4 h). The ‘traditional’ models generally perform adequately at all three forecast times. The neural networks produce reasonable forecasts of small‐ to medium‐sized flood events but have difficulty in forecasting the magnitude of the larger flood events in the validation period. Possible modifications to the latter approach are discussed. © Crown copyright 2002. Reproduced with the permission of Her Majesty's stationery office. Published by John Wiley & Sons, Ltd.     

淮河具有行蓄洪区河系洪水预报水力学模型研究

针对淮河流域河系特点,建立淮河具有行蓄洪区河系洪水预报模型.干流河道洪水演进采用一维水动力学模型,钐岗分流量利用分流曲线法推求,利用虚拟线性水库法解决大洪水时支流洪水受干流顶托作用,临淮岗闸作为水力学模型的内边界条件进行处理,利用分流比法概化行洪过程,行洪区内只有蓄满时,才会有出流,行洪区内的洪水利用Muskingum...     

A self‐organization algorithm for real‐time flood forecast

The group method of data handling (GMDH) algorithm presented by A. C. Ivakhnenko and colleagues is an heuristic self‐organization method. It establishes the input–output relationship of a complex system using a multilayered perception‐type structure that is similar to a feed‐forward multilayer neural network. This study provides a step towards understanding and evaluating a role for GMDH in the investigation of the complex rainfall–runoff processes in a heterogeneous watershed in Taiwan. Two versions of the revised GMDH model are implemented: a stepwise regression procedure and a recursive formula. Eleven typhoon events in the Shen‐cei Creek watershed, Taiwan, are used to build the model and verify its usefulness. The prediction results of the revised GMDH models and the instantaneous unit hydrograph (IUH) model are compared. Based on the criteria of forecasting precision and the rate and time of peak error, a much better performance is obtained with the revised GMDH models. Copyright © 1999 John Wiley & Sons, Ltd.     

Short‐term inflow forecasting using an artificial neural network model

The primary objective of this study is to investigate the possibility of including more temporal and spatial information on short‐term inflow forecasting, which is not easily attained in the traditional time‐series models or conceptual hydrological models. In order to achieve this objective, an artificial neural network (ANN) model for short‐term inflow forecasting is developed and several issues associated with the use of an ANN model are examined in this study. The formulated ANN model is used to forecast 1‐ to 7‐h ahead inflows into a hydropower reservoir. The root‐mean‐squared error (RMSE), the Nash–Sutcliffe coefficient (NSC), the A information criterion (AIC), B information criterion (BIC) of the 1‐ to 7‐h ahead forecasts, and the cross‐correlation coefficient between the forecast and observed inflows are estimated. Model performance is analysed and some quantitative analysis is presented. The results obtained are satisfactory. Perceived strengths of the ANN model are the capability for representing complex and non‐linear relationships as well as being able to include more information in the model easily. Although the results obtained may not be universal, they are expected to reveal some possible problems in ANN models and provide some helpful insights in the development and application of ANN models in the field of hydrology and water resources. Copyright © 2002 John Wiley & Sons, Ltd.     

Intelligent control for modeling of real‐time reservoir operation,part II: artificial neural network with operating rule curves

To bridge the gap between academic research and actual operation, we propose an intelligent control system for reservoir operation. The methodology includes two major processes, the knowledge acquired and implemented, and the inference system. In this study, a genetic algorithm (GA) and a fuzzy rule base (FRB) are used to extract knowledge based on the historical inflow data with a design objective function and on the operating rule curves respectively. The adaptive network‐based fuzzy inference system (ANFIS) is then used to implement the knowledge, to create the fuzzy inference system, and then to estimate the optimal reservoir operation. To investigate its applicability and practicability, the Shihmen reservoir, Taiwan, is used as a case study. For the purpose of comparison, a simulation of the currently used M‐5 operating rule curve is also performed. The results demonstrate that (1) the GA is an efficient way to search the optimal input–output patterns, (2) the FRB can extract the knowledge from the operating rule curves, and (3) the ANFIS models built on different types of knowledge can produce much better performance than the traditional M‐5 curves in real‐time reservoir operation. Moreover, we show that the model can be more intelligent for reservoir operation if more information (or knowledge) is involved. Copyright © 2004 John Wiley & Sons, Ltd.     

The FAM(Fuzzy Asociative Memory)neural network model and its application in earthquake prediction

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Confidence interval of real‐time forecast stages provided by the STAFOM‐RCM model: the case study of the Tiber River (Italy)

This study proposes a statistically based procedure to quantify the confidence interval (CI) to be associated to the stages forecast by a simple model called STAge FOrecasting Model‐Rating Curve Model (STAFOM‐RCM). This model can be used for single river reaches characterized by different intermediate drainage areas and mean wave travel times when real‐time stage records, cross section surveys and rating curves are available at both ends. The model requires, at each time of forecast, an estimate of the lateral contribution q_for between the two sections delimiting the reach. The CI of the stage is provided by analyzing the statistical properties of model output in terms of lateral flow, and it is derived from the CI of the lateral contribution q_for which, in turn, is set up by associating to each q_for the q_opt which allows STAFOM‐RCM to reproduce the exact observed stage. From an operative point of view, the q_for values are ranked in order of magnitude and subdivided in classes where the q_opt values can be represented through normal distributions of proper mean and variance from which an interval of selected confidence level for q_for is computed and transferred to the stage. Three river reaches of the Tiber river, in central Italy, are used as case study. A sensitivity analysis is also performed in order to identify the minimum calibration set of flood events. The CIs obtained are consistent with the level of confidence selected and have practical utility. An interesting aspect is that different CI widths can be produced for the same forecast stage since they depend on the estimate of q_for made at the time of forecast. Overall, the proposed procedure for CI estimate is simple and can be conveniently adapted for other forecasting models provided that they have physically based parameters which need to be updated during the forecast. Copyright © 2012 John Wiley & Sons, Ltd.     

Applying ANN emulators in uncertainty assessment of flood inundation modelling: a comparison of two surrogate schemes

Abstract

A generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis.     

Counterpropagation fuzzy–neural network for streamflow reconstruction

This study combines neural networks and fuzzy arithmetic to present a counterpropagation fuzzy–neural network (CFNN) for streamflow reconstruction. The CFNN has a rule‐based control, a modified self‐organizing counterpropagation network, and a fuzzy control predictor. It can generate rules automatically by increasing the training data to improve the accuracy of streamflow reconstruction. The CFNN establishes the input and output relationship of a watershed without set‐up parameters. The parameters are estimated systematically by the approach converging to an optimal solution. One sequence of data generated by the Monte Carlo method is used to demonstrate the accuracy of the CFNN. The streamflow data of the Da‐chia River, in central Taiwan, is also used to evaluate the performances of the CFNN. The results indicate the reliability and accuracy of the CFNN for streamflow reconstruction. Copyright © 2001 John Wiley & Sons, Ltd.