Modeling of stage–discharge relationship for Gharraf River, southern Iraq using backpropagation artificial neural networks, M5 decision trees, and Takagi–Sugeno inference system technique: a comparative study

Alaa M. Al-Abadi 0 0 A. M. Al-Abadi (&) Department of Geology, College of Sciences, University of Basra , Basra , Iraq The potential of using three different data-driven techniques namely, multilayer perceptron with backpropagation artificial neural network (MLP), M5 decision tree model, and Takagi-Sugeno (TS) inference system for mimic stage-discharge relationship at Gharraf River system, southern Iraq has been investigated and discussed in this study. The study used the available stage and discharge data for predicting discharge using different combinations of stage, antecedent stages, and antecedent discharge values. The models' results were compared using root mean squared error (RMSE) and coefficient of determination (R2) error statistics. The results of the comparison in testing stage reveal that M5 and Takagi-Sugeno techniques have certain advantages for setting up stage-discharge than multilayer perceptron artificial neural network. Although the performance of TS inference system was very close to that for M5 model in terms of R2, the M5 method has the lowest RMSE (8.10 m3/s). The study implies that both M5 and TS inference systems are promising tool for identifying stage-discharge relationship in the study area. - The reliable estimation of river flow rate (discharge) is a prerequisite and crucial component for hydrological applications and analyses. Because of the dynamic nature of hydrological system, direct measurements of discharge are typically time consuming, costly and even impossible, especially during flood. Therefore, most discharge records are derived from converting the measured water levels (stages) to discharges by a functional relationship that is expressed as a rating curve. A calibrated stagedischarge rating offers an easy, cheap, and fast technique to estimate discharge (World Meteorological Organization 1980; Kennedy 1984; Herschy 1999). Stagedischarge rating is generally treated as the following power curve (Herschy 1999): where Q is the discharge; H is the stage; a is an index exponent; a and b are constants (depending on the study area). Unfortunately, the functional relationship between stage and discharge is complex, time-varying, and cannot always captured by simple rating curve, even with the help of traditional modeling techniques such as polynomial regression or autoregressive integrated moving average ARIMA technique (Bhattacharya and Solomatine 2000). Many research attempts to establish this relation via data-driven techniques such as artificial neural networks ANNs (Tawfik et al. 1997; Bhattacharya and Solomatine 2000; Sudheer and Jain 2003; Bisht et al. 2010), decision trees (Bhattacharya and Solomatine 2003; Ghimire and Reddy 2010; Ajmera and Goyal 2012), support vector machine (Aggarwal et al. 2012), wavelet-regression model (Kisi 2011), TakagiSugeno fuzzy inference system (Lohani et al. 2006), and evolutionary-based data-driven models (Ghimire and Reddy 2010; Azamathulla et al. 2011). The results approve that these techniques are very efficient and reliable. The aim of this study is to investigate the potential of the different data-driven models (artificial neural networks, fuzzy inference system, and M5 decision trees) to emulate stagedischarge rating curve of the Gharraf River at Hay, south of Iraq. Daily records of the stage and discharge are available for this river at Hay station for the period from April 2005 to May 2006. The performance of these techniques was compared and the best one with smaller estimation error selected for future estimation of discharge from available data of previous discharge and stage values. Modeling techniques Artificial neural networks Artificial neural networks (ANNs) are massively parallel systems composed of many processing elements connected by links of variable weights. Given sufficient data and complexity, ANNs can be trained to model any relationship between a series of independent and dependent variables. For this reason, ANNs are considered to be universal approximates and have been successfully applied to a wide variety of problems that are difficult to understand, define and quantify. There are many different types of ANNs based on topology. One of the many ANN paradigms, the Multilayer Perceptron (MLP) network, is by far the most popular (Lippmann 1987). The MLP is layered feedforward network which is typically trained with static backpropagation (BP) algorithm. MLP is capable of approximating any measurable function from one finitedimensional space to another within a desired degree of accuracy (HornikK and White 1989). The MLP network consists of layers of parallel processing nodes. Each layer is fully connected to the preceding layer by interconnection strength, or weights, w. Figure 1 presents a three-layer Fig. 1 Architecture of multilayer perceptron with one hidden layer MLP neural network consisting of layers i, j, and k, with interconnection weights wij and wjk between layers of neurons. Each neuron in a layer receives and processes weighted input from a previous layer and transmits its output to nodes in the following layer through links. The connection between ith and jth neuron is characterized by the weight coefficient wij and the ith neuron by the threshold coefficient #i. The weight coefficient reflects the degree of importance of the given connection in the network. The output value of the ith neuron xi is computed as follows: (Haykin 1994) where f(ni) is the activation function. The threshold coefficient can be understood as a weight coefficient of the connection. With formally added neuron j, where xj = 1, sigmoid shape activation functions are normally defined as: The backpropagation algorithm works by computing the error between the network output and the corresponding target value and propagating this backward through the network to update the weights. The weight updates are calculated based on: Dwijt lDWijt Where g and l are the learning and momentum rates, respectively. E is the error, or objective function, and Dwij (t) and Dwij (t1) are the weight increments between nodes i and j for iterations t and t1. A detailed description of this algorithm can be found in Fausett (1994) and Haykin (1994). M5 decision tree A decision tree is a logical model represented as a binary (two-way split) tree that shows how the values of a target (dependent) variable can be predicted using the values of a set of predictor (independent) variables. There are basically two types of decision trees: (1) classification trees which are the msost commonly used to predict a symbolic attribute (class) (2) regression trees which are used to predict the value of a numeric attribute Witten and Frank (2005). If each leaf in the tree contains a linear regression model, which is used to predict the target variable at that leaf, then it is called a model tree. X1 & X2 inputs of system The M5 model tree algorithm was originally developed by Quinlan (1992). Detailed description of (...truncated)