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Summary Identifying structural damage can usually be modeled as a problem with the use of linear equations. Due to measurement noise and spatial incompleteness of the measured mode shapes, these linear equations are usually ill conditioned, which will significantly reduce the accuracy of subsequent damage assessment. This study develops an iterative total least squares (TLS) based estimation method, which can effectively mitigate such ill conditioning and avoid propagating noise into estimates of structural damage severity. In particular, a procedure, called the δ–p curve method, is proposed to choose the effective rank of a TLS estimation. Further, an iterative approach of TLS‐based estimation is proposed to eliminate spurious damage estimates due to modal expansion and measurement noise. To investigate the effectiveness of the proposed iterative TLS‐based estimation method, detailed numerical studies of damage assessment are first conducted on a simulated 3D frame structure, in which both noise pollution and spatial incompleteness of the mode shapes are considered. Additionally, experimental tests with a laboratory structure are performed to validate the proposed method. Results indicate that the proposed iterative TLS‐based method can accurately identify the structural damage, even with noise‐polluted and spatially incomplete modes.

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