Multi-objective parameter identification of Euler–Bernoulli beams under axial load

Abstract

Identification of physical parameters of the partial differential equation describing transverse vibrations of an axially loaded Euler–Bernoulli beam (EBB) is proposed via a multi-objective optimization formulation and solved by a genetic algorithm. Conflicting objectives such as performance and stability are specifically formulated and optimized simultaneously. Stability is quantified in terms of the solution׳s time growth factor. Physical parameter sets in the resulting Pareto front approximation represent best trade-offs with respect to the multiple objectives. To compute output error performance objectives, the EBB equation is discretized via finite differences in space and time and reformulated to a state space system. Identifiability is verified by checking regularity of the so-called Fisher information matrix. The identification methodology is capable of determining material parameters, including damping, as well as the axial load from few, spatially concentrated measurements. Its features are demonstrated and successfully validated on specific simulation data and measurement data obtained from a laboratory testbed.