Hierarchical parameter sensitivity analysis for finite element model updating

To address the challenge of high-dimensional parameter spaces in the update of finite element (FE) model for structural damage detection, this study introduces a hierarchical parameter sensitivity evaluation (GSA) approach aimed at key parameter selection and interaction effect quantification. This method serves as an effective pre-processing step for Bayesian model updating. A steel bridge is used as the case study, for which an FE model is developed using design specifications and includes 40 bearing stiffness parameters, covering translational rigidity in the X, Y, Z and rotational stiffness about the Z axis. Environmental vibration data are collected using MEMS sensors and are processed through fast Fourier transform (FFT), decomposition of the frequency domain (FDD) and identification of the stochastic subspazio (SSID). These techniques produce the first four natural frequencies ranging from 2.60 to 12.55 Hz, and the corresponding mode shapes. Modal data is used to construct likelihood functions based on modal correlation. The fundamental effect (EE) method is first applied to filter uncertain parameters by evaluating their average effect on the objective function, which is represented by the μ* statistic. This analysis identified 20 significant translation stiffness parameters in the X and Y directions, while parameters related to the Z direction and rotation had minimal effect. Thereafter, the data-driven SOBOL variance method was used to quantify the first-order effect and the total interaction effect. Gaussian process regression is employed to utilize the previously generated EE data. The results indicate that stiffness parameters in the Y direction have first-order effects ranging from 0.09 to 0.14 and total effects between 0.38 and 0.51, which are substantially greater than those observed in the X direction, where values remain below 0.001. This highlights the dominant influence of parameter interactions in the Y direction. Overall, the proposed method provides a computationally efficient tool for parameter prioritization and interaction analysis in damage detection, contributing to the reduction of model complexity in FE model calibration within structural health monitoring frameworks.