A numerical procedure based on cross-entropy method for stiffness identification
Résumé
The identification of physical parameters in a computational model is a crucial task so that it can be used as a prediction tool. Particularly, in structural dynamics, the identification process often seeks to determine the elastic properties of the system, materialized in the form of a stiffness coefficient. Depending on certain characteristics of the structural system (geometry complexity, vibration regime, material nature, etc.), the optimization problem underlying the identification process becomes nonlinear and non-convex, and its solution becomes an extremely challenging task, which requires the use of extremely robust numerical methods. In this context, this work deals with the problem of identifying the stiffness coefficient of a torsional spring coupled to an Euler-Bernoulli beam with an inertial element along its axis. A mechanical-mathematical model for the physical system is presented and the underlying natural frequencies are calculated through the solution of an eigenvalue problem. The identification problem is formulated in terms of the minimization of a discrepancy function, which measures the mismatch between natural frequencies calculated by the mathematical model and reference values obtained in laboratory experiments. A numerical strategy based on the Cross-Entropy method, a stochastic metaheuristic used in simulation of rare events and combinatorial optimization, is used to solve the minimization problem. Numerical results demonstrate the robustness and accuracy of the proposed numerical procedure. The method is compared with results from a Genetic Algorithm to appreciate the reduction in number of required function evaluations brought by the cross-entropy strategy.
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