Research On The Two-dimensional Shallow Water Wave Equation Inversion Of Roughness With Cuckoo Algorithm

The application of shallow water equations covers a lot of areas, such as river flow, flood forecasting, flood plain and coastal storm surges. Recently, research on the solving, modification and parameter calculation of shallow water wave equation has drawn a lot of concern. The coefficients of roughness and eddy viscosity are sensitive and important parameters of 2-D shallow water wave equation. Thus the accuracy of parameters is the key to the successful application of the model.Cuckoo search algorithm(CS) is an emerging meta heuristic algorithm. It is a new stochastic global optimization algorithm based on swarm intelligence. The algorithm has the advantages of less control parameters, optimal search path and strong global optimization ability etc. Compared with other algorithms, cuckoo search algorithm has more advantages in solving the parameter inversion of the 2-D shallow water equation.Firstly, we apply CS in multi modal functions optimization process, and compare the results of CS with niche particle swarm algorithm(NPSO) and basic particle swarm algorithm(PSO). It turns out that, whether the accuracy of the solutions, or the time of computation, cuckoo search algorithm is proved superior, which can verify the advantage of CS. Secondly, we invert the coefficients of roughness and eddy viscosity of the 2-D shallow water equation with CS. It shows that, the algorithm has not only high precision, but also rapid computing speed, and the inversing value perfectly matched the real value. However, the anti-noise property of CS is weak. Finally, based on two parameters—number of the nest and the probability of being discovered of the cuckoo eggs, we do a sensitivity analysis on CS. Find that with the increasing of the nest and decreasing of the probability, the accuracy of optimal solution is becoming higher and the trend of absolute error and relative error is getting smaller. Accordingly, the running time of program is proved to be longer. The inversion results show the feasibility and effectiveness of CS. Therefore, the algorithm discussed in this article has quite high practical value in the parameter inversion problem of 2-D shallow water equation and is expected to be widely used.