Bayesian methodology for diagnosis uncertainty quantification and health monitoring

SUMMARY This paper develops a Bayesian approach for the continuous quantification and updating of uncertainty in structural health monitoring. The uncertainty in each of the three steps of damage diagnosis—detection, localization, and quantification—is considered. Bayesian hypothesis testing is used for damage detection, thus facilitating easy quantification and updating of the uncertainty in damage detection. Qualitative damage signatures derived from the model are used for rapid damage localization; when the damage signatures fail to localize the damage uniquely, the uncertainty in damage localization is quantified using the principle of likelihood. Damage quantification is done through the method of maximum likelihood, and the uncertainty in damage quantification is estimated through Bayesian inference. The uncertainty in each of the three steps is continuously updated with the acquisition of more measurements. The overall uncertainty in diagnosis is also calculated, using the concept of total probability. The proposed methods are illustrated using two types of example problems—structural frame and a hydraulic actuation system. Copyright © 2011 John Wiley & Sons, Ltd.