Proportional flexibility-based damage detection for buildings in unknown mass scenarios: The case of severely truncated modal spaces

Modal flexibility-based methods are recognized in the literature as effective methods for detecting damage in structures using vibration measurements. However, the application of such methods with output-only data (as is the case of civil structures tested under ambient excitations) is challenging, because the mass normalization factors required for assembling the modal flexibility matrix cannot be estimated directly from the data. To address this issue, a method for output-only damage detection and localization in building structures that can be applied with minimal or no a-priori information about the structural masses has been proposed in a previous work by the authors. In the method, to estimate the mass distribution and to assemble the proportional flexibility matrices, the modal orthogonality relationships that involve the mode shapes and the structural masses are used to form a system of equations, and through that system of equations, an inverse problem is solved for the estimation of the mass distribution. Reducing the number of available modes, however, reduces the number of available equations, while the number of unknowns (i.e., the number of degrees of freedom) stay the same; hence, the approach cannot be applied when the modal space is severely truncated. This paper proposes a technique for estimating the mass distribution and assembling proportional flexibility matrices from output-only vibration data that overcomes the mentioned limitations and that can be applied for any number of identified modes, including the case in which the modal space is severely truncated. The proposed technique is then integrated into the above-mentioned method for output-only damage detection in building structures, to verify the applicability of the whole procedure when considering the case of severely truncated modal spaces. Numerical simulations and experimental vibration tests were used to demonstrate the validity and effectiveness of the approaches proposed in this paper.