Probabilistic Vibration Analysis of Bladed disks: A Critical Review and Benchmark Evaluation of Random-Field Modeling and Uncertainty Quantification Methods

Bladed disks in modern turbomachinery are susceptible to mistuning from manufacturing tolerances and material inhomogeneity, leading to mode localization and amplified vibration responses that compromise fatigue life. This paper presents a comprehensive review of probabilistic vibration analysis methods for mistuned blisks, encompassing random field modeling techniques and uncertainty quantification frameworks, combined with an original benchmark study enabling evidence-based method selection. The theoretical foundations of spatially correlated random fields are developed, and a systematic survey of uncertainty propagation methods is provided, spanning Monte Carlo simulation, perturbation approaches, polynomial chaos expansion (PCE), Gaussian process regression, neural networks and reduced-order models. A benchmark study on a 20-blade titanium blisk compares three surrogate modeling approaches across four test cases with material uncertainty ranging from 2% to 15% coefficient of variation, including one case with combined material and load uncertainty. Results demonstrate that Kriging achieves coefficients of determination exceeding 0.98 with only 200 training samples, while sparse PCE requires approximately 2000 samples for comparable accuracy. PCE provides evaluation speeds one order of magnitude faster than Kriging, making it preferable for reliability analysis. PCE achieves superior extreme tail accuracy, with 99·9th percentile prediction errors of 0.038% compared to 0.143% for Kriging and 0.422% for neural networks. Sensitivity analysis reveals that loading uncertainty dominates material variability for disk-dominated configurations. This paper concludes with method selection guidelines and identifies directions for extending these frameworks to blade-dominated configurations, veering regions, and nonlinear phenomena.