Output-only damage detection in buildings using proportional modal flexibility-based deflections in unknown mass scenarios

Methods based on the evaluation of structural deflections from experimental modal flexibility matrices are important tools in vibration-based damage detection, especially for building structures. Modal flexibility matrices, however, can not be directly estimated when dealing with output-only vibration data (e.g. in the important case of structures tested under ambient vibrations). One can use an a-priori estimate of the mass matrix of the structure or the added mass method to obtain the modal normalization constants needed to assemble the flexibility matrix, but these operations can be challenging for real-life civil structures. To address this problem, a modal flexibility-based approach for output-only damage detection and localization in building structures that can be applied with minimal or no a-priori information on the structural masses is proposed in this paper. This approach is also able to deal with the general case in which mass modifications, e.g. due to operational variability in structures, are present before and after damage. The approach is based on the estimation (directly from output-only data) of modal flexibility-based deflections of building structures that are proportional with respect to the corresponding true deflections. From analytical investigations it was found that the missing scaling factor between the two deflections can be made theoretically equal to the total mass of the structure, as proposed in the paper. Then, interstory drifts evaluated from the proportional deflections are used for damage detection and localization according to two proposed strategies. The first strategy can be applied with minimal a-priori information on the masses (i.e. using a parameter that quantifies an eventual relative modification of the total mass of the structure before and after damage). The second one is a more advantageous strategy that can be applied from output-only data without any a-priori information on the masses, even in the case in which the masses are varied before and after damage. The effectiveness of the proposed approach was demonstrated using both numerical simulations and experimental vibration tests on frame building structures.