Reduction of the model prediction error in vibration-based SHM applications

Abstract

The accuracy of an SHM scheme is partly controlled by the accuracy of the predictive models involved within the design process of the detector that associates sensor data with a corresponding health state. On the other hand, the accuracy of the predictive model, which is quantified by the error between predictions and observations, is partly controlled by its parameter magnitudes. This work provides a unified framework that allows for reducing the model prediction error by updating the model parameters in the light of experimental observations. The problem is cast in a probabilistic setting and tackled through inferential statistics. Forward and inverse uncertainty quantification approaches are employed in a sequential manner. The framework is able to yield point estimates in accordance to a Maximum Likelihood Estimator (MLE) and is also able to construct credible intervals through computational Bayesian updating. The former is treated by genetic algorithms whereas the later through Markov Chain Monte Carlo computational statistics. The framework is showcased on a vibration problem of the simplified benchmark case named as “Jim Beam”. The first ten modal parameters are considered as the discriminant features of interest . A surrogate of the finite element model of the considered specimen serves as the predictive model and the eigenfrequencies are extracted from a linear modal analysis. The parameters of inferential interest are the Young’s modulus and an artificial stiffness related parameter that is introduced so as to model the flexural rigidity of the specimen’s bolted connections. Experimental Modal Analysis and Operational Modal Analysis are the two approaches that were employed for experimentally identifying the modes and their corresponding frequencies. Results are provided from both the MLE and the Bayesian updating process and the effectiveness of each approach is discussed.