Closure to 'Improved Particle Swarm Optimization-Based Artificial Neural Network for Rainfall-Runoff Modeling' by Mohsen Asadnia, Lloyd H. C. Chua, X. S. Qin, and Amin Talei

摘要

The writers wish to thank the discusser for comments and discussion. The aim of the original paper as highlighted in the Abstract and Introduction was to introduce a new technique in improving particle swarm optimization (PSO) for training an artificial neural network (ANN). Three well-known learning algorithms, namely (1) conjugate gradient (CG), (2) gradient decsent (GD), and (3) Levenberg-Marquardt (LM), were adopted and the best performing one on the data was then compared with conventional PSO-neural network (NN) and improved PSO-NN. The response to the points raised by the discusser is as follows: The general thrust of the discusser's question focuses on the selection of inputs. This is indeed pertinent for the ANN and other data-driven models such as neurofuzzy systems (NFSs) and several publications have addressed this issue (Maier and Dandy 1997; Coulibaly et al. 2000; Sudheer et al. 2002; Nayak et al. 2007; Talei and Chua 2012). In the original paper however, the focus was on the comparison across ANN models adopting different training methods. Therefore, a less-than-rigorous approach was used in the selection of inputs and adopted correlation analysis to select a common set of inputs for the models. It is the writers' view that deficiency in the less-than-optimal selection of inputs is not significant to the results, since this will be common to all the models considered. In Fig. 3 of the original paper, the cross-correlation analysis between rainfall lags and water level. As can be seen from t-6 onwards the correlation coefficient is almost similar. The initial analyses showed that considering rainfall lags up to t-7 would be sufficient and considering more lags could not improve the models practically. To response to the issue raised by discusser on using H(t-1) as the only water level lag, the decision was made based on the autocorrelation analysis between H(t) and its lags up to H(t-10). In this analysis, the correlation coefficient (CC) values between H(t-1), H(t-2), and H(t-3) with H(t)) were 0.867, 0.734, and 0.658, respectively. The CC value was below 0.6 from H(t-4) onwards. Initial results showed that adding more water level lags will not improve model performance. This was attributed to the fact that the mutual information between highly correlated inputs can deteriorate the performance in data-driven models such as ANN and NFS (Talei and Chua 2012; Talei et al. 2013). Therefore, using H(t-1) was found to be sufficient for the models of the original paper. Moreover, it was revealed that using water level lags alone as input is not sufficient and adding rainfall lags will improve model performance.