A Bayesian Method for Simultaneous Identification of Structural Mass and Stiffness Using Static–Dynamic Measurements

Abstract

This paper presents a Bayesian-based finite element model updating method that integrates static displacement measurements and dynamic modal data to simultaneously identify structural mass and stiffness parameters. By leveraging Bayesian inference, a posterior probability density function (PDF) is constructed by integrating static displacement and modal parameters, thereby effectively decoupling the identification of structural mass and stiffness. The Delayed Rejection Adaptive Metropolis (DRAM) Markov Chain Monte Carlo (MCMC) sampling algorithm is utilized to derive the posterior distributions of the updated parameters. To mitigate the computational burden associated with repetitive finite element (FE) analyses during large-scale MCMC sampling, a Kriging surrogate model is employed to efficiently approximate the time-consuming FE simulations. Numerical examples involving a cantilever beam and an actual concrete three-span single-box girder bridge illustrate that the proposed method accurately identifies simultaneous variations in mass and stiffness at multiple structural locations, effectively addressing parameter coupling and misidentification issues encountered when using either static or dynamic data alone. Moreover, the Kriging surrogate significantly improves computational efficiency. Experimental validation on an aluminum alloy cantilever beam further corroborates the effectiveness and practical applicability of the proposed method.

Keywords

• model updating
• Kriging
• Bayesian inference
• mass identification
• stiffness identification