Mitigating Window-Induced Distortions in Modal Identification of Non-Proportionally Damped Systems using Sensitivity-Based Model Updating
摘要
Accurate estimation of damping parameters is crucial for predicting the dynamic response of structural systems. This study aims to investigate, quantify and correct the distortions introduced into complex mode shapes of non-proportionally damped systems due to the application of exponential window functions which are typically applied with a specified decay rate to suppress spectral leakage and enforce periodicity during the Fourier transformation of time-domain responses in experimental modal testing.
MethodsThe study quantifies the effects of window-induced distortions on complex modes using established damping non-proportionality indices. To address these challenges, a hybrid methodology combining the First-Order Perturbation Theory of damping along with the Inverse Eigen-Sensitivity Method for model updating is adopted.
ResultsThe study finds that exponential window application introduces artificial numerical damping which distorts the complex mode of the system. Increasing window decay rates progressively suppresses the true non-proportional damping characteristics and modal complexities of the system. This suppression reduces off-diagonal coupling in the modal damping matrix, leading to inaccurate representations of the system’s inherent non-proportional damping. The currently adopted hybrid approach iteratively minimises the discrepancies between the windowed and unwindowed complex modal data to recover accurate estimates of non-proportional damping parameters through model updating.
ConclusionWindow-induced artificial numerical damping significantly distorts complex mode shapes, obscuring the true non-proportional damping characteristics. The proposed hybrid methodology effectively corrects these distortions, enabling more accurate estimation of non-proportional damping parameters. Such corrections are vital for reliable health monitoring of existing structures, as they eliminate window-induced biases, leading to more accurate predictions of dynamic responses.