Iterative Correction Method for Structural Damping Ratios via Frequency Response Function Leakage Error Compensation

Abstract The damping ratio serves as a direct indicator of a structure’s ability to dissipate energy and is crucial for structural safety evaluation, dynamic response forecasting, vibration mitigation, and finite-element model updating. However, accurate damping-ratio identification relies heavily on the shape of a resonance curve in spectrum, which are often distorted due to spectral leakage in measured frequency response functions (FRFs). These distortions typically appear as reduced peak amplitudes, broadened peak widths, and the emergence of sidelobes. Spectral leakage typically results from the truncation of time-domain signals by window functions, particularly in free decay signals during experimental modal testing. As a result, spectral leakage has long posed a bottleneck in the precise identification of structural damping ratios. This study proposes a parameter identification framework that compensates for spectral leakage errors during the damping-ratio estimation process. First, analytical formulations are established to quantify spectral leakage errors in both displacement and acceleration FRFs, and the relationship between the theoretical FRF and the measured FRF with leakage error is derived. Subsequently, an iterative compensation method is introduced to reduce the impact of spectral leakage and enhance the accuracy of damping-ratio identification. Furthermore, the iterative method is extended to provide compensation formulas for six types of window functions, including rectangular, triangular, Hanning, Hamming, Blackman, and exponential windows. The proposed iterative framework enables accurate damping identification across all these windowing schemes. Finally, the effectiveness of the proposed methodology is validated through numerical case studies, benchmark model simulations, and frame experiments. Results confirm that the approach can effectively compensate for spectral leakage errors and achieve accurate damping-ratio identification.