Analysis of a deformed three-dimensional culvert structure using neural networks

Applying dynamic backpropagation neural networks with energy function as minimization index, the deformed behaviors for culvert structure under a static loading are analyzed in this paper. The training process is avoided by using stiffness matrix and force vector of the structure instead of using weighting matrix and bias vector in the neural networks calculations. The ability of neural networks is verified by comparing the results with analytical solutions and finite element solutions. In order to improve the numerical accuracy, three grid systems are used to model the problem and to check the grid independence. From the concept of energy, the existence of an attractor for the three grid systems is proved and the solution is obtained accordingly. In addition, from the numerical experiments, the convergence rate can be accelerated significantly by introducing a relaxation factor in the calculation. Based on the displacement profile and the three-dimensional displacement plot, the results reasonably show that more downward deformations occur at the centerline of the whole culvert structure, particularly at the top surface of the centerline. The obtained information may provide a better understanding of typical structural problems frequently found in the field of civil engineering.