Parametric and Non-parametric Stochastic Damage Detection Based on Bayesian Model Updating Framework with Hybrid Uncertainties

Structural health monitoring (SHM) is the process of detecting, differentiating, and localizing damages of in-service structures and has been regarded as a critical technique for aerospace, civil and mechanical engineering infrastructures. The damage is always considered as a reduction of the structure's inherent characteristics, e.g., stiffness, or any changes that have a negative impact on the structure. Due to the natural connection with system identification and the ability to link experimental measurement and numerical simulation of structures, model updating becomes an efficient method for damage detection. With the inevitable uncertainties in modelling and measurement under consideration, this paper processes a stochastic damage detection method based on the Bayesian model updating framework. The transitional Markov Chain Monte Carlo (TMCMC) algorithm is employed to solve the model updating problem. The Bhattacharyya distance-based likelihood function is established to quantify the discrepancy between results from numerical simulation and experimental measurement. The Bayesian updating framework with the Bhattacharyya distance quantification metric makes it possible to provide a stochastic measure of the damage probability. In the sense of model updating, damage detection is realized by identifying reductions in the stiffness of the model compared to the initial model. Both parametric and non-parametric methods are carried out to implement stochastic damage detection. In the parametric method, a stiffness factor is introduced as a random variable to parameterize the stiffness by multiplying it to the nominal stiffness. In the non-parametric method, the stiffness itself is assumed as a random variable following a pre-determined distribution with unknown mean and variance. This stochastic damage detection framework is implemented into a classic 3-degree-of-freedom spring-mass system. In this study, the probability of damage is defined and calculated to quantify the probability of different scales of damage to various structural components. The results from both the parametric method and non-parametric method are discussed to explore the feasibility and performance of this stochastic damage detection framework.