Keywords: scour depths, ANN, ANFIS, RBF, ski-jump buckets, spillway scour.

Artificial neural networks are associated with difficulties like the lack of success for a given problem and the unpredictable level of accuracy that can be achieved. In every new application it therefore becomes necessary to check their usefulness vis-á-vis the traditional methods and also to ascertain their performance by trying out different combinations of network architectures and learning schemes. The present study was directed in this direction and it involved the problem of scour depth prediction for ski-jump type of spillways. It differs from the previous works on hydraulic scour in that it pertains to the scour at the ski-jump bucket type of spillways and uses field measurements (rather than the controlled laboratory ones involved in most of the earlier studies) to train the networks and also evaluates performance of different network configurations and learning mechanisms. The network architectures considered are the regular feed forward back propagation trained network using the standard error back propagation (FFBP) as well as the cascade correlation (FFCC) training schemes, the relatively less used configurations of radial basis function (RBF) and adaptive neuro-fuzzy inference system (ANFIS).

Various investigators over a period of many decades in the past have given empirical formulae based on laboratory as well as prototype observations in order to predict the scour. However the problem of scour prediction has remained inconclusive, owing partly to the complexity of the phenomenon involved and partly to the limitation of the analysis tool used to synthesize the measured data, which is generally the statistical regression.

Considering the fact that direct prototype data would be more reliable than those belonging to hydraulic models, a survey of available works reporting such observations only was made. Considering that many traditional prediction formulae, including those due to Veronese [1], Wu [2], Martins [3], Incyth [4] are based only on q and H₁ neural networks with these two input nodes and one output node of the scour depth were developed. In total there were 91 input - output pairs formed from the published data. Eighty percent of the input - output patterns chosen randomly was used for network training while remaining ones were used for testing.

All developed networks were tested with the help of the testing pairs, not seen by the networks. The test results were qualitatively compared by drawing scatter plots and quantitatively assessed using the error measures of correlation coefficient (R), average errors (AE), and average absolute deviation (). Such testing was also performed in respect of a new regression equation derived by the authors on the basis of compiled data set.

It was found that if the prediction of scour downstream of a ski-jump buckets is made using only the regression formulae then the new equation derived by the authors based on compilation of past field data can be recommended in preference to the traditional equations by Veronese, Wu, Martinsa and Incyth. Among these prevailing formulae the Veronese one over-predicts the actual scour while the Incyth, Wu and Martins formulae under predict the same.

The usual feed forward networks of FFBP and FFCC showed a tendency to overestimate at lower values, unlike the radial basis function (RBF) and the adaptive neuro-fuzzy inference schemes (ANFIS) . The RBF and the ANFIS yielded more or less similar predictions with the ANFIS producing middle-ranged estimates in a slightly better way than the RBF.

A common application of four different error criteria confirmed the best performance of the ANFIS in this particular mapping problem. The treatment to non-linearities in the scour data meted out by the ANFIS approach worked much better than the other schemes. The scour data thus seem to be more amenable to fuzzy if then rules rather than crisp value processing in RBF or FFBP networks. The ANFIS ensures localized functioning of the transfer function as against the globalized one of a general FFBP resulting in smaller number of values participating in the mapping process, which in turn requires limited data for training. This could also be another reason for more acceptable performance of ANFIS in the present case.

This study thus showed that the traditional equation-based methods of predicting design scour downstream of a ski-jump bucket could better be replaced by the neural network and similar soft computing schemes.

1

A. Veronese, "Erosion de fond en aval d'une decharge", IAHR meeting for hydraulic works, Berlin, 1937

2

C.M. Wu, "Scour at downstream end of dams in Taiwan", International symposium on River Mechanics, Bangkok, Thailand, Vol. I, A13, 1-6, 1973.

3

R.B.F. Martins, "Scouring of rocky river beds by free jet spillways", International Water, Power and Dam Construction, 27(4), 152-153, 1975.

4

L. Incyth, "Estutio sobre modelo del aliviadero de la presa Casa de Piedra Informe Final", DOH-044-03-82, Ezeisa, Argentina, 1982.

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