Assessing soft calculation methods in river suspended sediment estimation (Hassan Abad station of Tirah river)

Introduction
Rivers are always faced with erosion and sediment transport. Sediment transport in rivers is one of the most complex topics in river engineering and is always the focus of experts and water engineers. This phenomenon is one of the important hydrodynamic processes that affect many hydraulic systems and water facilities and is considered one of the basic problems in the exploiting surface water resources globally. Estimating the sediment load of rivers is one of the important and practical issues in the studies and design of water engineering projects, such as the design and development of irrigation and drainage networks, water extraction from rivers, etc. Sediment concentration can be calculated by direct or indirect methods, which are usually expensive and time-consuming direct methods. Various factors affect this phenomenon, which makes their analysis difficult. Therefore, they cannot model the sedimentation phenomenon with acceptable accuracy. Hydraulic models cannot always be trusted due to the need for a lot of data, unavailability of the required data, and the inaccuracy of the data due to human error for simulating sediments. Nowadays, fuzzy and neural intelligent conductor systems, due to their ability to solve complex and nonlinear phenomena, have found many applications in various water engineering problems, including sedimentation. The purpose of this research is to evaluate and compare adaptive neural fuzzy models (ANFIS), support vector machine (SVM), gene expression programming (GEP), and group model of data handling (GMDH) in estimating the sediment load of Tirah River, Markazi Province.
 
Materials and Methods
In this research, first, the long-term daily statistics of temperature, rainfall, average flow rate, and sediment concentration of Hasan Abad hydrometric and sediment measuring station located on the main branch of the Tirah River were collected. Then, the data sufficiency test for analysis, checking the correlation between parameters of river discharge, precipitation, temperature with sediment discharge, and determining the long-term average of suspended sediment in the studied stations were performed. In the next step, a suitable combination of input variables was selected. The design of the input parameter pattern can be based on the relationship between flow and sediment flow parameters, rainfall, temperature, flow, and sediment flow. Of course, considering that the mentioned parameters have a historical course, therefore, the design of the input patterns of soft computing models should be done based on time delays (like what is discussed in the analysis and forecasting of time series). Determining the most appropriate time delay of the input parameters in the modeling of discharge, sediment, temperature, and rainfall, then the appropriate design of the structure of the used soft calculation models was done. In the next step, the estimation of sediment discharge using an SVM, GEP, and ANFIS group method of GMDH data control and comparison of three data mining methods, and also with the sediment rating curve and observational data. About 70 % of the research data was used as training and between 20 to 30 % for validation and testing.
 
Results and Discussion
Based on the statistical indicators of optimal model selection, the best performance of the SVR model has been obtained for model number one. In this model, the R² and RMSE obtained from the model are 0.96 and 0.0047, respectively. Besides, the R² and the RMSE error of the models in predicting suspended sediment values in the test stage are 0.95 and 0.014, respectively for the ANFIS model, and 0.50 and 4.97, respectively for the GEP model. The best performance of the ANFIS model has been obtained for model number one. In this model, the R² and the RMSE obtained from the model are 0.95 and 0.014. The R² and RMSE of the models in predicting suspended sediment values in the test stage are 0.96, 0.0047 for the SVR model, and 0.50, 4.97 for the GEP model, respectively. The best performance of the GEP model has been obtained for pattern number nine. In this model, the R² and RMSE obtained from the model are 0.99 and 0.010, respectively. The R² and the RMSE of the models in predicting the amount of suspended sediment in the test stage are respectively equal to 0.70, 0.015 for the ANFIS model and 0.78, 0.0185 tons respectively for the SVR model.
 
Conclusion
It can be seen that the performance of the GEP model was better compared to other models. SVR and ANFIS models are ranked second and third. In the next step, the best-selected pattern of ANFIS, SVM, and GEP models was used as the input of the GMDH model. First, input pattern one, which was selected as the best pattern for ANFIS and SVM models, was introduced as the input of the GMDH model. In the training and test, the values of R² statistical indices are 0.94 and 0.99, respectively, the RMSE error value is 0.0079 and 0.0038, respectively, the MSE value is 0.000062 and 0.000015, respectively, and the MAPE values are respectively 0.007 and 0.003. In the next step, input pattern nine, which was selected as the best pattern for the GEP model, is introduced as GMDH input. In the training and test steps, the value of R² is equal to 0.95 and 0.98 respectively, the RMSE error value is equal to 0.0077 and 0.0045 respectively, and the MSE value is equal to 0.0006 and 0.00002 respectively, and MAPE value is equal to 363 and 502. The results showed the acceptable performance of the GMDH model with the highest R² equal to 0.99 and 0.98 and the lowest RMSE equal to 0.0038 and 0.0045, respectively.