Improving the performance of Artificial Neural Network using wavelet transform in the stream flow simulation (Case study: Gamasiyab river)

River's flow prediction and its flood are the important subjects related to the flood projects, hydroelectric power production and water allocation for agricultural, industry and drinking uses. In the present study, wavelet analysis combined with Artificial Neural Network (ANN) was performed to simulate Gamasiyab River flow, located in Nahavand.The analysis was done in daily and monthly scale. For this purpose, the original time series, using wavelet theory, decomposed to multi time sub-signals. Then, these sub-signals were used as input data to the ANN to simulate flow and then the outputs compared with the ANN’s results. In this study, we used the precipitation, temperature, evaporation and flow data of Varayeneh station during the period of 1969 to 2011.Then, 75% of the data was used for training and 25% was considered for simulating data.
In this research, the amount of N and, L were determined 516 and 2 recpectivly. Also, 1 to 4 decomposition degrees were examined to be more precise. The number of neurons in the first layer depends on the degree of wavelet decomposition. The number of input neurons to the network is “m*(j )” in which “j” is the wavelet decomposition degree and “m” is the number of input parameters. For example, for j=1, according to the input parameters which in this study is 4 (precipitation, flow, temperature and evaporation), the number of input neurons is equal to 8. The output layer also has one neuron. The number of the middle layer neurons is variable and is obtained by trial and error. However, in this study, the number of neurons analyzed in the middle layer was varied from 3 to 20. In this case, modeling was done using different training functions and transfer functions for different neurons of the hidden layers. For daily period, input parameters were also decomposed with wavelet function with the levels of 5 to 9 and used as the input data of ANN. Also, the results concluded that 5 architectures had the best performance and it was also observed that the number of neurons of the middle layer was less than 10 in the superior structures. This means that the optimal solution can be reached with a lower number of neurons. Different training functions were examined, but useing all training functions is not suggested because it is time-consuming. Therefore, as proposed in this article, the three models of “Levenberg-Marquardt”, “BFGS Quasi-Newton” and “Bayesian Regularization” due to their better performance are recommended for future studies. After examining different stimulus functions, it is concluded that four types of “Tansig”, “Logsig”, “Satlin” and “Poslin” stimulus functions are suggested to be used for future studies.
Signal decomposition with wavelet increased correlation between observation and simulation data compared to Artificial Neural Network model, so the R2 was increased by 3 percent during the daily period and 24 percent during the monthly period. Two Artificial Neural Network and Wavelet – Artificial Neural Network (WANN) models in the daily period had almost similar performance but Wavelet – Artificial Neural Network model had a better performance in predicting minimum points. Moreover, after examining different structures, is the results determined that 5 architectures, functioned better in the various models and in the daily and monthly periods of the architecture. It means that using the data of evaporation and temperature makes the performance of the models better than the architecture in which these data are not used. Accordingly, the use of temperature and evaporation parameters is suggested in further studies in addition to flow and precipitation parameters.
The results showed that hybrid model of Wavelet-Artificial Neural Network (WANN) outperformed the Artificial Neural Network model. The reason of this preference of the WANN hybrid model is that the separation affects the time series inputs before interring to the network and primary signal decomposed to the various sub-signals. By doing this, we can use the analysis that contain short term and long term effects.
Besides, wavelet function of “Db4” has a better performance than other wavelet functions in each time period. It has the best performance in the daily period in the 5 level and in the monthly period in the second level. Also, the results showed hybrid model outperformed to estimate extent points than artificial neural network model.