An improved Bayesian model updating framework using an enriched spring-based finite element model for structural health monitoring

Classical finite‐element model updating (FEMU) requires iterative updates of the structural model. Alternative approaches are often computationally expensive or oversimplify the actual physical behavior of the structures. This paper introduces a novel approach, an enriched spring-based Bayesian finite element model updating (ES-BFEMU) method, which reduces computational cost while preserving high fidelity. In the proposed model, each structural element is divided into two beam-like sub-elements and a rotational spring. The stiffness matrix is derived by enriching the strain energy of both the sub-elements and the spring. This formulation enhances the physical interpretability of local stiffness degradation by explicitly representing rotational flexibility in potential damage zones. The enriched stiffness matrix is updated to provide a more realistic finite element model by detecting stiffness reductions within a Bayesian FEMU framework that considers the uncertainties. The computational efficiency is improved by adopting an adaptive transitional Markov chain Monte Carlo (TMCMC) algorithm to obtain the posterior probability of parameters. The proposed model is applied to the Salar Bridge, a six-span structure instrumented with accelerometers, displacement transducers, and strain gauges. Structural damage is simulated by introducing stiffness reduction coefficients into the elastic modulus of selected elements, with scenarios defined at reduction levels of 2%, 5%, 10%, and 15%. The introduced damages were successfully detected with a deviation of <2%. The proposed ES-BFEMU was also compared with surrogate and reduced-order FEMU approaches, demonstrating improved computational efficiency and higher accuracy in damage identification. The proposed model serves as a bridge between the surrogate and reduced-order FEMU. It reduces the computational cost associated with the reduced-order FEMU by a factor of 3.57 and enhances the accuracy of the surrogate method by 33%. The stress-time results of ES-BFEMU show a prediction error of <6.15% when compared to experimental results. These results demonstrate that ES-BFEMU provides a computationally efficient, physically interpretable, and reliable framework for structural health monitoring and damage identification.