Uncertainty Laws of MIMO Modal Identification

Abstract

‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., number and location of shakers/sensors, noise level, data duration). Focusing on the case of experimental modal analysis with multiple-input and multiple-output, the uncertainty laws of modal parameters for wellseparated modes are proposed in the paper. Asymptotic expressions for the posterior coefficient of variation of modal parameters are derived via the Fisher information matrix for long data and small damping scenarios. Assumptions and theory are validated using synthetic test data. Governing factors motivated by the theory are investigated, including the equivalent modal signal-to-noise ratio and data duration. The developed uncertainty laws provide a scientific basis for planning and managing identification uncertainties in vibration tests with known multiple-inputs