Treffer: Compensating Low Instrumentation for Mode Shape Estimation in Bayesian Filtering with Time-Delayed Data Embedding

Reconstructing mode shapes with precision is essential for monitoring structural health, as it providescrucial insights into assessing system integrity. However, challenges like data loss, insufficient and noncollocatedinstrumentation, and reliance on Finite Element Method-based frameworks or static expansiontechniques often lead to decreased accuracy in estimating dynamic characteristics. Some strategies attemptto address data sparsity through spatial virtual sensors—model-predicted responses at unmeasuredpoints—but these reconstructed responses frequently fail to adequately replace real sensor data owingto 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 incorporatingtime-lagged measurement layers, enhancing observability for the estimable system states. The modelundergoes updates in the time domain via the Interacting Particle Kalman Filter (IPKF) algorithm byembedding time-delayed measurements. This results in more accurate system matrices and refined modeshapes, guaranteeing the accurate reconstruction of key dynamic properties. Numerical tests on a simplysupported beam experiencing ambient vibration highlight the proposed method’s greater accuracy andcomputational efficiency than traditional approaches.