Catenary Finite Element Model Initialization using Optimization

The contact quality between pantograph and catenary plays a critical role in providing the required energy to power the trains’ traction systems. The need to study and analyze the dynamic behavior of these coupled systems has led to the development of pantograph/catenary interaction simulation software. Despite the increasing interest in the dynamic analysis of the catenary and its interaction with the pantograph, the accurate analysis of its configuration at static equilibrium becomes of most interest where its correct initial undeformed shape and correspondent undeformed mesh must be found. The initialization of the catenary, that is, the setting of the initial positions of the catenary finite element nodes have different requirements due to the different methods used in the solution of their dynamics. Furthermore, as the static configuration of the catenary provides its initial conditions for dynamic analysis it is possible that these have a significant influence on the simulation results. This is even more critical when considering the contact wire sag correct deformed shape where contact with the pantograph occurs. The work, presented in this paper, proposes a catenary initialization procedure based on the definition of a fitness function to be minimized using classical gradient based optimization. The proposed methodology also opens the possibility to model catenary systems that have defects such as irregularities in its sag caused by damaged, poorly maintained or ill mounted overhead lines. Here, this irregularity can be imposed on the static equilibrium configuration of the model and the same minimization problem is set to find its corresponding undeformed shape.