# Assessment of Soft Computing Techniques for the Prediction of Suspended Sediment Loads in Rivers
## 4 Model Application and Results
### The Suspended Sediment Load (SSL) Estimation through Local Linear Regression Models
Figure 12: Performance of the ANN model for the increasing number of hidden nodes. stations (Combination 2 and Nodes 11) were 0.95, 0.90, 233.48 (t/day) and 3.43%, and 0.91, 0.82, 335.71 (t/day) and 2.53%, respectively. Similarly, in Table 6, the above-mentioned parameters are 0.94, 0.89, 235.6 (t/day) and 8.78%, and 0.90, 0.82, 339.23 (t/day) and 3.17% for the LLR approach for the Pirna and Magdeburg-Strombrucke stations, respectively. The outcomes from Tables 6 and 7 reveal that the best ANN models are slightly superior to the best LLR models, but differences between the outputs of both techniques were not significant, and they could be taken as an alternate approach for modelling SSL. The observed and predicted SSL of the best ANN models during the test phase for the Pirna and Magdeburg-Strombrucke stations are presented in Figures 13 and 14, respectively. Therefore, the five selected input variables in combination 1 for the Pirna station and combination 2 for the Magdeburg-Strombrucke station were decomposed at level (_i_) 3 by applying the db4 mother wavelet. Furthermore, each of the selected input variables was decomposed at level 3, which generated 1 approximation (A3) and 3 details (D1, D2, D3), with a total of four sub-signals. Thus, the selected five input variables (i.e., \(Q_{l}\), \(Q_{l-1}\), \(Q_{l-2}\), \(S_{t-1}\) and \(S_{t-2}\)) generated 20 (5 \(\times\) 4) sub-signals. Then, from all these decomposed subseries, only the subseries with a significant correlation with the observed data were fed into an ANN model to develop a hybrid WANN model for the prediction of SSL. Consequently, different WANN models were developed to compute the SSL for all the best combinations of each station. The predictive capacity of different developed WANN models for both stations was assessed through different statistical parameters such as R, R\({}^{2}\), RMSE and PBIAS. The performance evaluation of different WANN models for the Pirna gauging station and Magdeburg-Strombrucke gauging station in the training and testing phase are presented in Table 8. It was revealed from Table 8 that R, R\({}^{2}\), RMSE and PBIAS for all the WANN models for the Pirna gauging station and Magdeburg-Strombrucke gauging station vary from 0.95 to 0.99 and 0.96 to 0.96, 0.91 to 0.97 and 0.92 to 0.92, 391.5 t/day to 695.51 t/day and 454.82 t/day to 481.09 t/day, and \(-\)1.29% to 0.39% and \(-\)0.54% to 0.21% during the training period, respectively. Similarly, it was observed that \(R\), \(R^{2}\), \(RMSE\) and \(PBIAS\) for all the WANN models for the Pirna gauging station and Magdeburg-Strombrucke gauging station vary from 0.91 to 0.97 and 0.94 to 0.95, 0.82 to 0.95 and 0.89 to 0.90, 160.26 t/day to 290.96 t/day and 248.26 t/day to 263.71 t/day, and \(-\)1.57% to 0.93% and \(-\)0.81% to 0.74% during the testing period, respectively. Table 8 shows that, among all the WANN models for both stations, the model that has input combination \(Q_{l}\), \(Q_{l-2}\), \(S_{t-1}\) and \(S_{t-2}\) had the least error and relatively higher accuracy. Further, the outcomes from Tables 7 and 8 revealed that the WANN models delivered a superior performance to the LLR and ANN models in suspended sediment load prediction. The best WANN models for the Pirna gauging station and Magdeburg-Strombrucke gauging station had a testing R, R\({}^{2}\), RMSE and PBIAS of 0.97 and 0.95, 0.95 and 0.90, 160.26 and 248.26 t/day, and \(-\)0.73% and \(-\)0.46%, respectively (Table 8) and were more accurate than the best ANN model, which had a testing R, R\({}^{2}\), RMSE and PBIAS of 0.95, 0.90, 233.48 t/day and 3.43% (Table 7) for the Pirna gauging station and 0.91, 0.82, 335.71 t/day and 2.53% (Table 7) for the Magdeburg-Strombrucke gauging station, respectively. We know that the combination of R\({}^{2}\) values closer to 1 (1 is the perfect fit value) coupled with the lower RMSE and PBIAS values (0 is the perfect fit value) pointed to the