Bed load prediction in gravel-bed rivers using wavelet kernel extreme learning machine and meta-heuristic methods

  • K. RoushangarEmail author
  • S. Shahnazi
Original Paper


The present study aims at developing a wavelet kernel extreme learning machine (WKELM) and meta-heuristic method, known as particle swarm optimization (PSO). PSO algorithm is employed in order to provide a desirable modeling by optimal determination of parameters attributed to WKELM. In order to confirm the ability of employed PSO-WKELM approach in solving the problem, a well-known kernel-based support vector machine (SVM) is applied to compare the obtained results. 890 data points from 19 gravel-bed rivers located in the USA were used to feed the utilized heuristic models. Three different scenarios were proposed; in the scenario 1, different combinations of parameters based on hydraulic characteristics were prepared, scenario 2 was developed using both hydraulic and sediment properties as model inputs of bed load transport, and lastly, the performance of employed PSO-WKELM approach for prediction of bed load transport with different range of median particle size was investigated. The obtained results confirmed the higher predictive potential of PSO-WKELM in comparison with SVM. Also, it was found that prediction of bed load transport with median particles size ranging from 1 to 1.4 mm led to more valid outcome. Performing the sensitivity analysis demonstrated the remarkable impact of the ratio of average velocity (V) to shear velocity (U*) in modeling process.


Kernel-based methods Particle swarm optimization Prediction accuracy Support vector machine Sediment transport 



The authors would like to extend their appreciation to the US Forest Service and other agencies for providing extensive database to carry out this research.


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Copyright information

© Islamic Azad University (IAU) 2019

Authors and Affiliations

  1. 1.Department of Water Resources Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran

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