## 3 Results and Discussion  
[PERSON] [21] proved that for any mapping G from closed unit cube in \(n\)-dimensional Euclidean space [0,1]\({}^{n}\) to \(m\)-dimensional Euclidean space \(R^{m}\) in \(L_{2}\) (we say a function belongs to L2 if each of its coordinate functions is square-integrable on the unit cube), there exists a three-layer BP neural network, which is capable of approaching \(G\) with arbitrary precision. [PERSON] _et al._[22] believed that the Multiple Layer Perception (MLP) with only one hidden layer is sufficient in theory, and, compared to three layers, ANN with four layers is more likely to fall into local optima and harder to train, both of them are similar in other aspects. Hence, BP-ANN model with three layers is selected in this study. In the application of ANN, it is difficult but crucial to determine an appropriate number of neurons in hidden layer. If the number is too small, the accuracy of the ANN cannot be guaranteed; while if the number is too large, not only the number of connection weights in the network increases, but also the generalization performance of the network is likely to drop. Hence, in this study, the number of neurons in hidden layer is set to be 10. Input parameters are firstly normalized to fall into [0,1], as shown in Equation (23):  
\[\overline{x_{i}}=\frac{x_{i}-x_{min,i}}{x_{max,i}-x_{min,i}}. \tag{23}\]To prevent supersaturation of the neurons, only a certain range \(r\) of the \(S\)-type activation transfer function with larger curvature is used for mapping, as illustrated in Figure 3.  
Thus, Equation (23) is converted as:  
\[\overline{x_{i}}=\frac{x_{i}-x_{min,i}(1+d_{1})}{x_{max,i}\left(1+d_{2}\right)- x_{min,i}\left(1+d_{1}\right)}. \tag{24}\]  
After several testing trials of calculation, \(d_{1}=40\%\) and \(d_{2}=20\%\) in this study. The four types of observed data (\(\overrightarrow{Q_{in}},\overrightarrow{Q_{out}},\overrightarrow{L}, \overrightarrow{S}\)) and the observed sediment flushing efficiency of the TGR from the year 2003 to 2010 are used to train the BP-ANN model, and the data of the year 2011 is used to test it. The simulation and prediction results of the model are shown in Figure 4.  
Figure 4: **(a)** simulation result and (b) prediction result of the BP-ANN model. Figure 3: S-type activation transfer function and its adopted range. It can be seen from Figure 4 that the trained BP-ANN model can simulate the reservoir sediment flushing process with a high accuracy. When it comes to prediction, the BP-ANN model is able to reflect the relational characteristics of the reservoir sediment flushing. However, since the TGR has only been in operation for about 10 years, and the monthly data is available from 2003 to 2011, the samples used to train the BP-ANN are quite limited, and some deviations still exist. In addition, the sediment delivery from reservoir is an extremely complex process relevant to multiple influencing factors. The reservoir sediment flushing model itself is approximate with many empirical parameters. The four factors selected in this study are necessary and dominated but not sufficient. Last but not least, the majority of the sediment flows into the reservoir in flood season, and very little sediment comes in non-flood season. The difference between the sediment inflow can be several orders of magnitude in different seasons. The observed errors of sediment in the non-flood season itself is not as small as that in flood season. Synthesizing all the reasons above, the BP-ANN model established in this study is believed to be able to characterize the relationship between reservoir flushing sediment and its major influencing factors, especially in flood season, when most of the sediment comes. Figure 5 shows the goodness of fit between the model output and the observed data. A satisfying fitting degree can be achieved using only the trained data. For the test, the actual data distributes on both sides of the fit line.