System identification in the frequency domain plays a fundamental role in many aspects of mechanical and structural engineering. Frequency domain approaches typically involve estimation of a transfer function, whether it is the usual frequency response function (FRF) or an output-to-output transfer model (transmissibility). The field of structural health monitoring, which involves extracting and classifying features mined from in-sit structural performance data for the purposes of damage condition assessment, has exploited many features for this purpose that inherently are derived from estimations of frequency domain models such as the FRF or transmissibility. Structural health monitoring inevitably involves a hypothesis test at the classification stage such as the (common) binary question: are the features mined from data derived from a reference condition or from data derived from a different (test) condition? Inevitably, this decision involves stochastic data, as any such candidate feature is compromised by error, which we categorize as (i) operational and environmental, (ii) measurement, and (iii) computational/estimation. Regardless of source, this noise leads to the propagation of error, resulting in possible false positive (Type I) errors in the classification. As such, the quantification of uncertainty in the estimation of such features is tantamount to making informed decisions based on a hypothesis test. This paper will demonstrate several statistical models that describe the uncertainty in FRF estimation and will compare their performance to features derived from them for the purposes of detecting damage, with ultimate performance evaluated by receiver operating characteristics (ROCs). A simulation and a plate subject to single-input/single-output vibration testing will serve as the comparison testbeds.
Structural health monitoring: Frequency domain analysis of beam with breathing crack
