An Optimization Method to Find the Initial Catenary Configuration by Using a Gradient-Based Algorithm

— In this study, an optimization method is proposed to obtain an initial configuration of the catenary. To this end, a gradient-based algorithm is employed, and the sensitivity analysis is performed by introducing an alternative finite difference method (FDM). Unlike the original FDM, a proposed method can dramatically reduce the computation cost due to its simplified format. The form-finding problem is formulated as the unconstrained optimization problem with an objective function defined by half mean squared error. In the optimization process, static analysis for the catenary constructed by the 2-node beam elements is performed at each iteration calculation using commercial software. A well-defined unconstrained optimization problem is solved successfully, and the validity of the suggested optimization method is supported by the numerical results obtained for specific design conditions.