Structural Damage Localization and Quantification Based on Additional Virtual Masses and Bayesian Theory

In vibration-based damage identification, a common problem is that modal information is not enough and insensitive to local damage. To solve this problem, an effective method is to increase the amount of modal information and enhance the sensitivity of the experimental data to the local damage. In this paper, a damage identification method based on additional virtual masses and Bayesian theory is proposed. First, the virtual structure with optimal additional mass and high sensitivity to local damage is determined through sensitivity analysis, and then a large number of virtual structures can be obtained by adding virtual masses; thus, a lot of modal and statistical information of virtual structures can be obtained. Second, the Bayesian theory is used to obtain the posterior probability distribution of the damage factor when structural a priori information is considered. Third, by finding the extreme value of the probability density function, the damage factor is derived based on the a priori information and the statistical information of virtual structures. Finally, the effectiveness of the proposed method is verified by numerical simulations and experiments of a 3-story frame structure. Experimental and numerical results show that the proposed method can be used to identify the damage severity of each substructure and thus damaged substructures can be localized and quantified; the error in damage factor is basically within 5%, which shows the accuracy of the proposed method. The proposed method can not only provide the structural damage localization and quantification result (i.e.,the damage factor), but also the probability distribution of the damage factor; moreover, it has high sensitivity to damage and high accuracy and efficiency.