Discharge forecasting using an Online Sequential Extreme Learning Machine (OS-ELM) model: A case study in Neckar River, Germany
Introduction
Flood forecasting plays a very significant role in planning and implementing the structural and non-structural measures required to protect human lives, properties and services from floods. Problems due to flooding intensify when they occur in areas of large-scale human settlement. Floods can cause extensive damage to human life and property and, as a consequence, lead to large economic losses. The damage caused by floods is more intense in underdeveloped and developing countries because of factors such as exponential growth of population, and fiscal restraints [20], [68], [44], [46], [50], [52], [75]. Hourly flood forecasting is useful since sufficient lead time allows for appropriate flood prevention measures, evacuation plans and rehabilitation actions. During an approaching flood event even a one hour advance warning can save many lives. To avoid or mitigate the losses caused by floods, accurate information of ‘flood peak’, and ‘time to peak’ in flood forecasting is of primary concern [81].
Flood forecasting models can be broadly classified as physically based or empirically (or black box) based approaches. A wide variety of rainfall–runoff models have been developed and applied for flood forecasting either based on a mechanistic approach or a systems theoretic approach. Spatially distributed modelling is a typical example of the mechanistic approach to construct a model that explicitly accounts for as much of the small-scale physics and the natural heterogeneity as computationally possible by considering variables such as groundwater, precipitation, evapotranspiration, initial soil moisture content and temperature [40]. A large number of studies have examined the phenomenon of flood wave movement in rivers and channels using physically based methods [51], [53], [41], [14], [57], [31], [81]. Although physical methods provide reasonable accuracy, their implementation and calibration typically present various difficulties [48]. Physical based methods which take into account the impact of hydrological and hydro-meteorological variables are useful but they have been criticized for being overly complex, leading to problems of over parameterization [10] which may manifest itself in large prediction uncertainty [70]. In river flow forecasting applications, data-based hydrological methods are becoming popular due to their rapid development times and minimum information requirements. Although they may lack the ability to provide physical interpretation and insight into catchment processes, they are nevertheless able to provide relatively accurate flow forecasts [3]. The lack of extensive data, cost of collection and inaccessibility of sites are a common reason to select models which can simulate river flow variability based on past recorded flow data [33], [61].
Black box models (i.e. data-driven approaches) which operate on the interrelationship between input-output data without capturing the complete dynamics of the system may therefore be preferable in certain cases (e.g., in contexts of limited data). With the advent of computers and the availability of high computational facilities many researchers have employed Artificial Intelligence (AI) techniques in flood forecasting (e.g., [17], [64], [62], [23], [7], [56], [32]). Much research has been carried out on the use of Artificial Neural Networks (ANN) since they are reliable and promising especially in flood forecasting [13], [77], [78], [62], [23], [7], [56], [8], [24], [32]. However, several researchers found that ANNs are highly sensitive to the trained data [79]. The performance of neural networks depend upon the number of hidden neurons, and the number and choice of training algorithms and transfer functions [29]. To overcome these limitations, some researchers have used hybrid models like ANN-GA (Genetic algorithm), or ANN-PSO (Particle swarm optimization) to improve the accuracy of ANNs [63]. It has also been found that ANNs employ gradient-based learning algorithms, and thus are subjected to over tuning which can result in substantial local computing time.
Genetic programing is similar to the Genetic Algorithm (GA) except it uses a parse tree structure to obtain a solution while GA uses bite strips. The technique is truly a ‘‘bottom up’’ process, as there is no assumption made regarding the structure of the relationship between the independent and dependent variables but an appropriate relationship is identified for any given time series. GP has been successfully used in many studies to solve problems in the field of water resources engineering. Drecourt [19], Whigham and Crapper [76], Babovic and Keijzer [6], Makkeasorn et al. [43], Kisi and Shiri [35], Sahay and Srivastava [58] applied GP to rainfall-runoff modelling.
The support vector machine (SVM), a kernel-based procedure, is a relatively new machine learning method based on the Vapnik–Chervonenkis (VC) theory [69]. The main advantage of SVM is that it not only possesses the strength of ANN but can overcome some of its major problems such as local minimum and network over fitting [4]. Although SVM has been used in many areas successfully [83], [39], [71], [72], [49], [25], its output depends on the selection of a suitable kernel function and parameters. The hyper parameters of SVM are heuristic and generally selected by a time-consuming trial and error process [18]. Huang et al. [30] proposed the Extreme Learning Machine (ELM) to overcome the disadvantages of ANN, SVM and other traditional data driven methods (back-propagation). The ELM algorithm has gained popularity in various scientific fields such as forecasting coal mine water inrush [84]; non stationary time series prediction [73]; estimation of monsoon rainfall [1]; estimation of wind speed distribution [60]; sales forecasting [66]; and rainfall-runoff modelling [67].
In general, ELM uses batch learning type algorithms for training. These algorithms are time-consuming and whenever new data is received a retraining is performed with past data. A new algorithm, OS-ELM, was proposed by Liang et al. [36] which allows for online sequential learning and uses data one-by-one (chunk-by-chunk) with variable chunk size. Lima et al. [38] have successfully used the OS-ELM method for daily, monthly and yearly flood forecasting; this is the only application of OS-ELM in the hydrological literature to date. The updating of weights on the basis of subsequent data and random selection of hidden node parameters makes this method fast and accurate [82] and hence suitable for short term flood forecasting where even small errors can cause extensive damage to life and property. The major objective of this study was to examine the pertinence of OS-ELM for short term flood forecasting, and to compare its predictive ability with ANN, SVM and Genetic Programming (GP). The usefulness of the OS-ELM approach in flood forecasting was evaluated using a case study for the Neckar River, Germany.
The paper is organized as follows: Section 2 introduces the Online Sequential Extreme Learning Machine algorithm. The overall characteristics of the catchment area are presented in Section 3. Section 4 describes the performance measures used in the analysis. In Section 5 the procedure to select the model structure and input data is explained. This section also provides a general overview of the contemporary soft computing techniques which are compared with OS-ELM in this study. In section 6 the results are analyzed and discussed. Finally, the conclusions are presented in section 7.
Section snippets
Online sequential extreme learning machine
Using the principles of ELM, OS-ELM was developed for SLFNs (Single-layer feedforward neural networks) including additive and RBF (Radial basis function) hidden nodes. Consider N arbitrary discrete samples . If with L hidden nodes an SLFN can approximate these N samples with minimum error, it then connotes that there exist and such that [36]:where and denote the learning parameters of the hidden nodes, is the output weight,
Characteristics of the catchment area
The Upper Neckar basin, selected as a case study, is located in south-western Germany in the state of Baden-Württemberg. It lies between the Black Forest on the west and the Schwäbische Alb in the southeast. The Neckar River originates in the ‘Schwenninger Moos’, which is a small moor at an altitude of 706 m a.s.l.
Analyses were conducted on the Neckar River between two observation stations, Rottweil and Oberndorf, separated by a distance of 24.2 km (Fig 2). The intermediate drainage area between
Performance measures used in the analysis
Model performances, in general, are evaluated by using several standard statistical techniques which are often referred to as ‘‘goodness of fit’’ statistics [47], [63], [54]. The criteria employed in this study were: the root mean square error (RMSE) between the observed and forecasted values; the Nash-Sutcliffe (NS) efficiency coefficient that measures the closeness with which the proposed method reproduces the observed or benchmark solution [45] and the coefficient of determination (R2). The
Methodology
ANN, SVM and Genetic Programming (GP) are commonly used methods and detailed descriptions are beyond the scope of this paper. Readers can obtain a thorough understanding of ANNs in water resource management from Bishop [11], Haykin [28], and Maier and Dandy [42]. For SVM readers are directed to Vapnik [69] and Deka [18], and for GP readers are directed to Banzhaf et al. [9] and Goldberg and Holland [26].
Forecast at one hour lead time
The case study in this paper analyzes the ability of artificial intelligence techniques in flood forecasting where a significant amount of lateral flow enters between the upstream and downstream gauging stations. Performance measures were calculated to evaluate the proposed OS-ELM, SVM, ANN and GP models at the 1 h lead forecast (Table 5). For the training phase, the NS efficiency was greater than 95% for OS-ELM and SVM but between 90% and 95% for GP and ANN. RMSE is lowest and R2 highest for
Conclusions
A comparative study was conducted to investigate the performance of contemporary AI techniques for flood forecasting at a downstream gauging station using hourly time series. We investigated the application of three widely used AI techniques (ANN, SVM and GP) and one newer method (OS-ELM). The methods utilized the relational structure or statistical properties of the data series with a certain amount of lagged input variables. Consideration of lateral flow by traditional methods using a
Acknowledgements
The authors are grateful to the Institut für Wasser- und Umweltsystemmodellierung, Stuttgart, Germany for providing the data used in this study. Partial funding for this study was provided by an NSERC Discovery Grant held by Jan Adamowski.
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