Effect of Pruning and Smoothing while Using M5 Model Tree Technique for Reservoir Inflow Prediction

Abstract

This study reports the performance of an M5 model tree (MT) and the effects of pruning and smoothing applied to reservoir inflow prediction. The full year and seasonal monthly time step MT predictions were compared with conventional univariate autoregressive integrated moving average (stochastic) models. It was found that stochastic models could not predict the future inflows in a better way, because the observed series had not followed any particular distribution. However, it was found that the stochastic models showed better improvement using a logarithmic-transformed series, but the logarithmic-transformed MT results showed otherwise. The model validation was performed using the comparison of goodness of fit measures, standard statistics, time series, and scatter plots of predicted inflows with observed inflows. The effect of pruning each leaf in the MT model was also studied. Instead of pruning all the leaves, leading to lesser predictive accuracy, selective pruning was carried out based on the importance of the processes, for example, peak and low flow. The performance of both stochastic and MT models showed that seasonal monthly prediction was superior to full-year monthly prediction because of large zero values in latter data set. Encouraging results indicated that the seasonal nontransformed selective-pruned MT models performed better and produced reliable forecasts of high and low inflows than the stochastic models. A pruned and smoothed MT model (PSMT) performed 79% better than the stochastic models in terms of mean square error (MSE). On the other hand, MSE was 98% better than the stochastic model in an unpruned and unsmoothed MT (UPUSMT) model. Because of better peak prediction by UPUSMT model, the MSE was 90% better than the PSMT models. The other advantage of an MT was having a set of equations and if-then rules to predict the inflow as well as peak inflow into the Pawana reservoir.