Reconstructing mode shapes with precision is essential for monitoring structural health, as it provides crucial insights into assessing system integrity. However, challenges like data loss, insufficient and non-collocated instrumentation, and reliance on Finite Element Method-based frameworks or static expansion techniques often lead to decreased accuracy in estimating dynamic characteristics. Some strategies attempt to address data sparsity through spatial virtual sensors—model-predicted responses at unmeasured points—but these reconstructed responses frequently fail to adequately replace real sensor data owing to having been contingent on the prior assumptions on the system's health state. To tackle these issues, this study presents an innovative method that improves the measurement model by incorporating time-lagged measurement layers, enhancing observability for the estimable system states. The model undergoes updates in the time domain via the Interacting Particle Kalman Filter (IPKF) algorithm by embedding time-delayed measurements. This results in more accurate system matrices and refined mode shapes, guaranteeing the accurate reconstruction of key dynamic properties. Numerical tests on a simply supported beam experiencing ambient vibration highlight the proposed method's greater accuracy and computational efficiency than traditional approaches.
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