Probabilistic Approach for Damping Identification Considering Uncertainty in Experimental Modal Analysis

The system identification technology is essentially an inverse procedure, starting from the experimentally measured response, to construct mass, stiffness, and damping matrices of the structure. However, the measurement inevitably contains uncertainties, which significantly impact the identified system characteristics, especially for damping terms. In the presence of experimental uncertainty, the aim of damping identification in this paper is not a single deterministic solution with maximum fidelity to a single experiment, but rather a set of optimized solutions with acceptable robustness to multiple uncertain experiments. To achieve this objective, an integrated approach combining deterministic identification and probabilistic calibration techniques is proposed. This approach starts from the properness condition of modes in a deterministic identification. A probabilistic estimation technique is performed on the preliminary identified data so that an uncertainty boundary is available for the calibration procedure where the genetic algorithm and classical optimization techniques are used. A comprehensive comparison metric for two continuous quantities is proposed as the objective function in the calibration procedure. Finally, a probabilistic validation metric is proposed to assess the stability of the calibrated damping matrix. In both simulated and experimental examples, the finally obtained matrices exhibit their robustness with regard to the experimental uncertainty.