Short term flood forecasting using RBF static neural network modeling a comparative study
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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, 2010 Short term flood forecasting using RBF static neural network modeling a comparative study Rahul P. Deshmukh A. A. Ghatol Indian Institute of Technology, Bombay Former Vice-Chancellor Powai, Mumbai Dr. Babasaheb Ambedkar Technological University, India Lonere, Raigad, India firstname.lastname@example.org email@example.com Abstract—The artificial neural networks (ANNs) have been essential and plays a vital role in planning for flood regulation applied to various hydrologic problems recently. This research and protection measures. demonstrates static neural approach by applying Radial basis The total runoff from catchment area depends upon function neural network to rainfall-runoff modeling for the various unknown parameters like Rainfall intensity, Duration upper area of Wardha River in India. The model is developed of rainfall, Frequency of intense rainfall, Evaporation, by processing online data over time using static modeling. Interception, Infiltration, Surface storage, Surface detention, Methodologies and techniques by applying different learning Channel detention, Geological characteristics of drainage rule and activation function are presented in this paper and a basin, Meteorological characteristics of basin, Geographical comparison for the short term runoff prediction results features of basin etc. Thus it is very difficult to predict runoff between them is also conducted. The prediction results of the at the dam due to the nonlinear and unknown parameters. Radial basis function neural network with Levenberg In this context, the power of ANNs arises from the Marquardt learning rule and Tanh activation function indicate capability for constructing complicated indicators (non-linear a satisfactory performance in the three hours ahead of time models). Among several artificial intelligence methods prediction. The conclusions also indicate that Radial basis artificial neural networks (ANN) holds a vital role and even function neural network with Levenberg Marquardt learning ASCE Task Committee Reports have accepted ANNs as an rule and Tanh activation function is more versatile than other efficient forecasting and modeling tool of complex hydrologic combinations for RBF neural network and can be considered systems. as an alternate and practical tool for predicting short term Neural networks are widely regarded as a potentially flood flow. effective approach for handling large amounts of dynamic, non-linear and noisy data, especially in situations where the underlying physical relationships are not fully understood. Keywords-component; Artificial neural network; Forecasting; Neural networks are also particularly well suited to modeling Rainfall; Runoff; systems on a real-time basis, and this could greatly benefit operational flood forecasting systems which aim to predict the I. INTRODUCTION flood hydrograph for purposes of flood warning and The main focus of this research is development of control. Artificial Neural Network (ANN) models for short term flood A subset of historical rainfall data from the Wardha forecasting, determining the characteristics of different neural River catchment in India was used to build neural network network models. Comparisons are made between the models for real time prediction. Telematic automatic rain performances of different parameters for Radial basis function gauging stations are deployed at eight identified strategic artificial neural network models. locations which transmit the real time rainfall data on hourly The field engineers face the danger of very heavy flow basis. At the dam site the ANN model is developed to predict of water through the gates to control the reservoir level by the runoff three hours ahead of time. proper operation of gates to achieve the amount of water In this paper, we demonstrate the use of Radial basis flowing over the spillway. This can be limited to maximum function neural network (RBF) model for real time prediction allowable flood and control flood downstream restricting river of runoff at the dam and compare the effectiveness of different channel capacity so as to have safe florid levels in the river learning rules and activation function. Radial basis function within the city limits on the downstream. neural network is having a feed-forward structure consisting of By keeping the water level in the dam at the optimum hidden layer for a given number of locally tuned units which level in the monsoon the post monsoon replenishment can be are fully interconnected to an output layer of linear units. conveniently stored between the full reservoir level and the At a time when global climatic change would seem to permissible maximum water level. Flood estimation is very be increasing the risk of historically unprecedented changes in 93 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, 2010 river regimes, it would appear to be appropriate that MSE (Mean Square Error): alternative representations for flood forecasting should be considered. The formula for the mean square error is: d yij P N 2 II. METHODOLOGY ij j 0 i 0 In this study different parameters like learning rule and MSE NP activation function are employed for rainfall-runoff modeling … (1) using Radial basis function neural network model of artificial Where neural network. P = number of output PEs, Radial basis functions networks have a very strong N = number of exemplars in the data set, mathematical foundation rooted in regularization theory for yij solving ill-conditioned problems. = network output for exemplar i at PE j, The mapping function of a radial basis function dij = desired output for exemplar i at PE j. network, is built up of Gaussians rather than sigmoids as in MLP networks. Learning in RBF network is carried out in two phases: first for the hidden layer, and then for the output layer. NMSE (Normalized Mean Square Error): The hidden layer is self-organising; its parameters depend on the distribution of the inputs, not on the mapping from the input The normalized mean squared error is defined by to the output. The output layer, on the other hand, uses the following formula: supervised learning (gradient or linear regression) to set its P N MSE parameters. NMSE 2 N N N dij 2 dij i 0 N i 0 P j 0 … (2) Where P = number of output processing elements, N = number of exemplars in the data set, MSE = mean square error, dij = desired output for exemplar i at processing element j. r (correlation coefficient): The size of the mean square error (MSE) can be used to determine how well the network output fits the desired output, but it doesn't necessarily reflect whether the two sets of data move in the same direction. For instance, by simply Figure 1. The Radial basis function neural network scaling the network output, the MSE can be changed without changing the directionality of the data. The correlation In this study we applied different learning rules to the coefficient (r) solves this problem. By definition, the RBF neural network and studied the optimum performance correlation coefficient between a network output x and a with different activation function. We applied Momentum, desired output d is: Deltabar Delta, Levenberg Marquardt , Conjugate Gradient, Quick prop learning rule with activation function Tanh, Linear _ x x d _ Tanh, Sigmoid and Linear Sigmoid. i i d i r N 2 2 _ _ Performance Measures: di d i xi x i The learning and generalization ability of the estimated N N … (3) NN model is assessed on the basis of important performance measures such as MSE (Mean Square Error), NMSE (Normalized Mean Square Error) and r (Correlation 1 N _ 1 N x d _ coefficient) x i d i where N i 1 and N i 1 94 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, 2010 The correlation coefficient is confined to the range [-1, 1]. Data: Rainfall runoff data for this study is taken from the When r = 1 there is a perfect positive linear correlation between Wardha river catchment area which contains a mix of urban x and d, that is, they co-vary, which means that they vary by and rural land. The catchments is evenly distributed in eight the same amount. zones based on the amount of rainfall and geographical survey. The model is developed using historical rainfall runoff data , III. STUDY AREA AND DATA SET provided by Upper Wardha Dam Division Amravati, The Upper Wardha catchment area lies directly in the path department of irrigation Govt. of Maharashtra. Network is of depression movements which originates in the Bay of trained by rainfall information gathered from eight telemetric Bengal. When the low pressure area is formed in the Bay of rain-gauge stations distributed evenly throughout the catchment Bengal and cyclone moves in North West directions, many area and runoff at the dam site. times this catchment receives very heavy intense cyclonic The data is received at the central control room online through precipitation for a day or two. Occurrence of such events have this system on hourly basis. The Upper Wardha dam reservoir been observed in the months of August and September. operations are also fully automated. The amount of inflow, Rainfall is so intense that immediately flash runoff, causing amount of discharge is also recorded on hourly basis. From the heavy flood has been very common feature in this catchment. inflow and discharge data the cumulative inflow is calculated. For such flashy type of catchment and wide variety in The following features are identified for the modeling the topography, runoff at dam is still complicated to predict. The neural network . conventional methods also display chaotic result. Thus ANN TABLE I - THE PARAMETERS USED FOR TRAINING THE NETWORK based model is built to predict the total runoff from rainfall in Upper Wardha catchment area for controlling water level of the Month RG1 RG2 RG3 RG4 RG5 RG6 RG7 RG8 CIF dam. In the initial reaches, near its origin catchment area is hilly • Month – The month of rainfall and covered with forest. The latter portion of the river lies • Rain1 to Rain8 – Eight rain gauging stations. almost in plain with wide valleys. • Cum Inflow – Cumulative inflow in dam The catchment area up to dam site is 4302 sq. km. At Seven years of data on hourly basis from 2001 to 2007 is dam site the river has wide fan shaped catchment area which used. It has been found that major rain fall (90%) occurs in the has large variation with respect to slope, soil and vegetation month of June to October Mostly all other months are dry cover. hence data from five months. June to October is used to train the network IV. RESULT The different structures of neural network are employed to learn the unknown characterization of the system from the dataset presented to it. The dataset is partitioned into three categories, namely training, cross validation and test. The idea behind this is that the estimated NN model should be tested against the dataset that was never presented to it before. This is necessary to ensure the generalization. An experiment is performed at least twenty five times with different random initializations of the connection weights in order to improve generalization. Figure 2- Location of Upper Wardha dam on Indian map The data set is divided in to training , testing and cross validation data and the network is trained for all models of Radial basis function neural network for 5000 epochs. The performance results obtain on parameters by applying learning rules Momentum, Deltabar Delta, Levenberg Marquardt , Conjugate Gradient, Quick prop with activation function Tanh, Linear Tanh, Sigmoid, Linear Sigmoid are listed in Table II through Table VI. Figure 3- The Wardha river catchment 95 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, 2010 TABLE II - RBF NETWORK PERFORMANCE WITH MOMENTUM LEARNING RULE TABLE V - RBF NETWORK PERFORMANCE WITH CONJUGATE GRADIENT LEARNING RULE Param MSE N Min Max eter MSE Abs Abs r Param MSE N Min Max 1 error error eter MSE Abs Abs r 4 error error Tanh 0.106 0.124 0.034 0.465 0.534 Tanh 0.094 0.165 0.051 0.312 0.646 Linear 0.097 0.105 0.024 0.212 0.639 Tanh Linear 0.089 0.094 0.059 0.215 0.633 Sigmo 0.089 0.093 0.047 0.421 0.678 Tanh id Sigmo 0.092 0.134 0.041 0.474 0.701 Linear 0.094 0.132 0.041 0.381 0.689 id Sigmo Linear 0.094 0.124 0.064 0.541 0.732 id Sigmo id TABLE VI - RBF NETWORK PERFORMANCE WITH QUICK PROP. LEARNING TABLE III - RBF NETWORK PERFORMANCE WITH DELTABAR DELTA RULE LEARNING RULE Param MSE N Min Max Param MSE N Min Max MSE Abs Abs r MSE Abs Abs r eter eter 5 error error 2 error error Tanh 0.133 0.245 0.042 0.465 0.584 Tanh 0.093 0.141 0.051 0.564 0.651 Linear 0.169 0.212 0.054 0.514 0.601 Linear 0.190 0.241 0.041 0.412 0.591 Tanh Tanh Sigmo 0.106 0.256 0.059 0.329 0.563 Sigmo 0.143 0.215 0.032 0.495 0.543 id id Linear 0.098 0.112 0.046 0.311 0.609 Linear 0.086 0.095 0.067 0.315 0.603 Sigmo Sigmo id id The parameters and performance for RBF model with different learning rule and activation function are compared on TABLE IV - RBF NETWORK PERFORMANCE WITH L. M. LEARNING RULE the performance scale and are listed in the Table VII shown below. The comparative analysis of the MSE and r (the Param MSE N Min Max correlation coefficient) is done. eter MSE Abs Abs r 3 error error TABLE VII – COMPARISON OF PERFORMANCE PARAMETERS Tanh 0.076 0.064 0.018 0.143 0.854 Linear 0.086 0.094 0.028 0.298 0.732 Tanh Sigmo 0.083 0.094 0.020 0.228 0.634 id Linear 0.089 0.095 0.034 0.469 0.758 Sigmo id After training the network the optimum performance is studied and it is found that Levenberg Marquardt learning rule and Tanh activation function produce optimal result. In the Table- VIII the parameters and the best performances for Radial basis function neural network are listed. 96 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, 2010 TABLE VIII- RBF NETWORK PARAMETERS have fewer weights, these networks train extremely fast and require fewer training samples. Parameter Performance MSE 0.07629 V. CONCLUSION NMSE 0.06431 An ANN-based short-term runoff forecasting system is Min Abs Error 0.01943 developed in this work. A comparison between five different Max Abs Error 0.14387 learning rules with four activation function for optimal r 0.85437 performance for Radial basis function neural network model is made. We find that Radial basis function neural network with Levenberg Marquardt learning rule and Tanh activation Fig 4 shows the plot of actual Vs predicted optimum values for function is more versatile than other approaches studied. Radial Radial basis function neural network found with Levenberg basis function neural network with Levenberg Marquardt Marquardt learning rule and Tanh activation function. learning rule and Tanh activation function is performing better as compare to other approaches studied as far as the overall performance is concerned for forecasting runoff for 3 hrs lead time. Other approaches studied are also performing optimally. Which means that static model of Radial basis function neural Actual Vs Predicted Runoff by RBF NN Model network with Levenberg Marquardt learning rule and Tanh 10 activation function is powerful tool for short term runoff 8 forecasting for Wardha River basin. Runoff 6 4 ACKNOWLEDGMENT 2 0 This study is supported by Upper Wardha Dam Division 1 3 5 7 9 11 13 15 17 19 21 23 25 Amravati, department of irrigation Govt. of Maharashtra, India Exemplar Actual Runoff Predicted Runoff REFERENCES Figure 4.– Actual Vs. Predicted runoff by RBF for L.M. and Tanh The error found in the actual and predicted runoff at the  P. Srivastava, J. N. McVair, and T. E. Johnson, "Comparison of process- based and artificial neural network approaches for streamflow modeling dam site is plotted for RBF network as shown in the Figure 5. in an agricultural watershed," Journal of the American Water Resources Association, vol. 42, pp. 545563, Jun 2006. Error in prediction for RBF NN Model  K. Hornik, M. 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His area of reserch are artificial intelligence and neural networks. A. A. Ghatol received the B.E. from Nagpur university foallowed by M. Tech and P.hd. from IIT Bombay. He is best teacher award recipient of government of Maharastra state. He has worked as director of College of Engineering Poona and Vice-Chancellor, Dr. Babasaheb Ambedkar Technological University, Lonere, Raigad, India. His area of research is artificial intelligence, neural networks and semiconductors. 98 http://sites.google.com/site/ijcsis/ ISSN 1947-5500