Stochastic model updating of rotor support parameters using Bayesian approach

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Uncertainties due to assembling, installation, and operational conditions are extensively involved in rotating systems' parameters. Stochastic characteristics of these parameters may seriously affect rotating systems' vibrational characteristics, such as their critical speeds and vibration amplitudes. These effects make the variability of parameters in the modeling of rotary machines inevitable. In rotating machinery, material properties and geometric parameters of the rotor, bearing characteristics and supports stiffness determine the system's dynamic response. Stochastic model updating methods consider model response variability and allocate them to the model parameters; however, they are not commonly employed in rotor dynamics, and deterministic approaches are still prevalent in this field. Due to the cost and efforts needed to set up experiments and obtain outcomes that reflect the machine's actual characteristics, stochastic updating practices of industrial rotating systems are rarely reported in the literature. This paper adopts an appropriate parameter selection procedure and suitable sampling strategy for stochastic model updating to investigate variability in the dynamic behavior of a complex turbo compressor rotor-bearing-support system, leading to successful parameter identification results. The compressor rotor is mounted on hydrodynamic journal bearings with speed-dependent stiffness and damping. Due to the rotating system complex model, a variance-based global sensitivity method is employed for parameter selection to eliminate non-influential parameters in the model updating and to alleviate updating complexity and computational burden. The Bayesian approach in the stochastic model updating is applied to estimate parameter uncertainty in the rotor with speed-dependent characteristics. Advanced Markov chain Monte Carlo sampling method using delayed rejection adaptive Metropolis algorithm is employed in the stochastic model updating. The updating procedure obtains marginal posterior probabilities of parameters, and uncertain parameter distributions are evaluated using the maximum entropy criterion.