Bayesian model updating of blade structures based on a dual-layer adaptive dimension-reduced chebyshev surrogate

This study addresses the high-fidelity uncertainty quantification and model updating for blades under limited data conditions. An integrated framework combining the interval-based uncertainty modeling, surrogate modeling, and Bayesian updating is developed to investigate blade dynamic characteristics and improve model accuracy. In the surrogate construction stage, uncertainties in material properties, geometric parameters, and boundary-related parameters are first described by admissible intervals based on engineering knowledge and parameter tolerances. These intervals define the feasible parameter domain for the proposed adaptive Chebyshev surrogate model with dimension-wise interaction screening surrogate model and subsequently serve as the support of weakly informative uniform priors in the Bayesian updating stage. A dual-layer adaptive dimension-reduction Chebyshev surrogate model is constructed to reduce computational cost while maintaining high accuracy. Unlike Gaussian-process/Kriging-type probabilistic surrogates, the proposed surrogate model is a deterministic Chebyshev-based approximation framework that adaptively selects univariate polynomial orders and screens significant bivariate interaction terms. Based on the established surrogate model, the effects of uncertainties on the natural frequencies can be analyzed. In this study, the validation is performed using the first three natural frequencies of a simplified clamped single-blade model. A Bayesian model updating framework is further introduced, where key parameters are calibrated through the posterior inference using experimental modal data. By coupling the surrogate model with the Markov Chain Monte Carlo sampling, efficient and robust parameter estimations are achieved. The updated model demonstrates good agreement with experimental results, with prediction errors substantially reduced. The findings can provide an efficient methodology and guidance for the uncertainty quantification and model updating of blades. While the current validation is limited to a simplified single-blade model using the first three natural frequencies, the proposed framework demonstrates its feasibility for extension to more complex blade structures.