Application of heuristic methods to the identification of the parameters of discrete-continuous models

Abstract

The article presents the process of identifying discrete-continuous models with the use of heuristic algorithms. A stepped cantilever beam was used as an example of a discrete-continuous model. The theoretical model was developed based on the formalism of Lagrange multipliers and the Timoshenko theory. Based on experimental research, the theoretical model was validated and the optimization problem was formulated. Optimizations were made for two algorithms: genetic (GA) and particle swarm (PSO). The minimization of the relative error of the obtained experimental and numerical results was used as the objective function. The performed process of identifying the theoretical model can be used to determine the eigenfrequencies of models without the need to conduct experimental tests. The presented methodology regarding the parameter identification of the beams with the variable cross-sectional area (according to the Timosheno theory) with additional discrete components allows us to solve similar problems without the need to exit complex patterns.