Statistical modeling of frequency response function estimation for uncertainty quantification

Abstract

Frequency response function (FRF) estimation is widely used for system identification and related applications, such as model updating and structural health monitoring. Whether estimated from data or from a finite element (FE) model, there is uncertainty involved that introduces variability in the FRF evaluation, which leads to misinterpretation of system identification results or false alarms (Type-I error) if used in hypothesis testing for damage detection. This paper aims to quantify the uncertainty of FRF estimated with randomly-excited experimental data using the H1 estimator, for both its magnitude and phase. A Gaussian bivariate statistical model is implemented, and probability density functions (PDF) of the magnitude and phase estimations are derived. The proposed statistical model is validated for both an ideal simulation test-bed and an experimental lab-scale structure. To further validate the model's robustness, artificial noise is added to contaminate the original data. The predicted PDFs show a very good match with histogram observations, where outlier percentage is selected as the comparison metric in this paper. For different significance levels, the outlier percentages all consistently agree with the pre-described uncertainty thresholds, indicating that the proposed statistical model suitably quantifies the uncertainty of FRF estimations using H1.