Simplifications and theoretical assumptions are usually incorporated into the numerical modeling of structures. However, these assumptions may reduce the accuracy of the simulation results. This problem has led to the development of model-updating techniques to minimize the error between the experimental response and the modeled structure by updating its parameters based on the observed data. Structural numerical models are typically constructed using a deterministic approach, whereby a single best-estimated value of each structural parameter is obtained. However, structural models are often complex and involve many uncertain variables, where a unique solution that captures all the variability is not possible. Updating techniques using Bayesian Inference (BI) have been developed to quantify parametric uncertainty in analytical models. This paper presents the implementation of the BI in the parametric updating of a five-story building model and the quantification of its associated uncertainty. The Bayesian framework is implemented to update the model parameters and calculate the covariance matrix of the output parameters based on the experimental information provided by modal frequencies and mode shapes. The main advantage of this approach is that the uncertainty in the experimental data is considered by defining the likelihood function as a multivariate normal distribution, leading to a better representation of the actual building behavior. The results showed that this Bayesian model-updating approach effectively allows a statistically rigorous update of the model parameters, characterizing the uncertainty and increasing confidence in the model’s predictions, which is particularly useful in engineering applications where model accuracy is critical.

Fractional-order derivative (FD) models are widely used to describe the dynamic behavior of rubber-like materials. However, experiments have shown that FD models cannot reproduce the amplitude dependence and the slow stabilization phenomenon under harmonic excitation. To overcome these limitations, we introduce a modified FD Zener (MFDZ) model that incorporates a new parameter, average strain. The MFDZ model is shown to have good agreement with experimental data. Two illustrative examples are conducted to demonstrate the use of the MDFZ model for structural control. The results show that the MFDZ model can better describe rubber-like materials’ behavior and versatility when used in the dynamic analysis of structural systems.

Base isolation is a powerful technique to prevent damage in low- and medium-rise structures during an earthquake. Nowadays, the extensive use of high-damping viscoelastic (VE) materials in base isolators has motivated the necessity to model its mechanical behavior more accurately. Traditional approaches, such as Maxwell and Kelvin models, are often used to predict VE properties. However, these models cannot precisely represent the material’s frequency-dependent behavior. Mathematical models using fractional derivatives (FD) have been shown to have the features needed to capture and predict the salient VE characteristics. Despite the possibility of such accurate descriptions using FD models in VE material applications, their implementation has been limited because of the complex computations needed to obtain the mathematical solution. This is especially true in a base-isolated (BI) building, when the bearing-superstructure coupled system includes both fractional and integer differential equations. In this study, a novel framework is developed based on dynamic substructuring to analyze a hybrid BI system with both integer and fractional order differential equations. To demonstrate the framework, the seismic response of a multidegree of freedom building model coupled with a FD state space model governing the base isolators is obtained. The structural response of the asymmetric-plan 8-story benchmark building with 92 high-damping VE bearings, governed by the fractional derivative Zener (FDZ) model, is calculated and evaluated. Using this well-known benchmark structure, a numerical comparison is performed considering the seismic response of the building fixed to the ground, the BI building with traditional elastomeric bearings, and the BI building with FDZ bearings. The results demonstrate that the framework developed provides an effective and reliable approach to evaluate the hybrid base-isolated system equations.