Forward vs. Bayesian Inference Parameter Calibration: Two Approaches for Non-deterministic Parameter Calibration of a Beam-Column Model

Mathematical models are commonly used to predict the dynamic behavior of mechanical structures or to synthesize controllers for active systems. Calibrating the model parameters to experimental data is crucial to achieve reliable and adequate model predictions. However, the experimental dynamic behavior is uncertain due to variations in component properties, assembly and mounting. Therefore, uncertainty in the model parameters can be considered in a non-deterministic calibration. In this paper, we compare two approaches for a non-deterministic parameter calibration, which both consider uncertainty in the parameters of a beam-column model. The goal is to improve the model prediction of the axial load-dependent lateral dynamic behavior. The investigation is based on a beam-column system subjected to compressive axial loads used for active buckling control. A representative sample of 30 nominally identical beam-column systems characterizes the variations in the experimental lateral axial load-dependent dynamic behavior. First, in a forward parameter calibration approach, the parameters of the beam-column model are calibrated separately for all 30 investigated beam-column systems using a least squares optimization. The uncertainty in the parameters is obtained by assuming normal distributions of the separately calibrated parameters. Second, in a Bayesian inference parameter calibration approach, the parameters are calibrated using the complete sample of experimental data. Posterior distributions of the parameters characterize the uncertain dynamic behavior of the beam-column model. For both non-deterministic parameter calibration approaches, the predicted uncertainty ranges of the axial load-dependent lateral dynamic behavior are compared to the uncertain experimental behavior and the most accurate results are identified.