Linearization of the eigenvalue problem has been widely used in vibration-based damage detection utilizing the change of natural frequencies. However, the linearization method introduces bias in the estimation of damage parameters. Moreover, the commonly employed regularization method may render the estimation different from the true underlying solution. These issues may cause wrong estimation in the damage severities and even wrong damage locations. Limited work has been done to address these issues. It is found that particular combinations of natural frequencies will result in less biased estimation using linearization approach. In this paper, we propose a measurement selection algorithm to select an optimal set of natural frequencies for vibration-based damage identification. The proposed algorithm adopts L1-norm regularization with iterative matrix randomization for estimation of damage parameters. The selection is based on the estimated bias using the least square method. Comprehensive case analyses are conducted to validate the effectiveness of the method.

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