Uncertainty Laws of Free-Vibration Modal Identification

Free vibration test is a commonly used method in structural condition assessment to acquire vibration data from which modal parameters (e.g., natural frequencies, damping ratios, and mode shapes) can be extracted. This naturally leads to a fundamental question: how a field test can be planned optimally? Focusing on modal identification under free vibration, the paper addresses this question by proposing uncertainty laws, which give closed-form asymptotic formulas for coefficients of variation of modal parameters. These laws characterize the relationship between the identification uncertainties of modal parameters and the test configuration (e.g., location, number and noise level of sensors). With the assumptions of long data and small damping, the derivation involves the Fisher information matrix evaluation. Theoretical results and assumptions are validated using synthetic data. According to the derived uncertainty laws, the key factors governing identification uncertainty include the damping ratio, the bandwidth factor, the modal signal-to-noise ratio, and the effective data length. The developed uncertainty laws provide a scientific basis for managing identification uncertainties in free vibration tests.