Identifying frequency-domain operating deflection shapes and internal damage in structures using geometric vision method

Operating deflection shape (ODS) analysis characterizes structural vibration in the frequency domain without requiring prior knowledge of excitation, offering an automatic means to assess dynamic behavior and detect damage in service. Building on this, we present a geometric vision–based sensing method for ODS identification under a depth-parameterization framework, enabling direct recovery of full-field vibration responses from spatiotemporal image motion captured by a stereo imaging system. To ensure accurate ODS reconstruction, a random sample consensus–based calibration algorithm is developed to rectify stereo geometry and establish a depth-parameterized projective system. Within this framework, we formulate a linear model that maps measured image motion of object points to their ODS responses in the frequency domain. In addition, a wavelet-based algorithm is proposed to extract damage parameters from defective structures using the reconstructed ODS fields. Experimental validations confirm that the proposed vision-based sensing method and damage identification approach are both effective and robust, providing a promising pathway for structural vibration monitoring and health assessment in complex operational environments.