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Optimal Structural Health Monitoring Feature Selection via Minimized Performance Uncertainty

Power spectral measurements are very ubiquitous for their utility in generating structural health monitoring (SHM) features, because of their clear physical interpretation and easy computation through Fourier transform. In most SHM applications, optimal features are always desired to perform whatever level of assessment is required. Optimal in this sense refers to a measure of performance capability to enhance decision-making, because structural health monitoring inevitably involves, at some level, a hypothesis test: in the binary case, the question becomes are the features extracted from data derived from a baseline condition (baseline can also mean linear, or any reference condition designated the null hypothesis) or ...from data derived from a different (test) condition. Inevitably, this decision involves stochastic data, as any such candidate feature is compromised by noise, which we may categorize as (i) operational and environmental, (ii) measurement, and (iii) computational/estimation. Regardless of source, this noise leads to the propagation of uncertainty from inception to final estimation of the feature; in all cases, the subsequent distribution of the features can lead to significant false positive (Type I) or false negative (Type II) errors in the classification of the features via the hypothesis test. Frequency domain approaches for SHM typically involve estimation of some form of transfer function, typically the usual frequency response function (FRF). Based upon the statistical modeling of the uncertainty of feature estimations, this paper evaluates the performance of two FRF-derived features, namely the dot-product difference (DPD) and Euclidian distance (ED), and statistical significance detection qualities are quantitatively compared. In each of the feature evaluations, the performance comparison is executed under the condition of best trade-off between sensitivity and specificity, adopting receiver operating characteristics as the performance indicator. Monte Carlo simulation and lab-scaled tests on plate-like structures are both implemented to validate the optimal feature selection process and demonstrate performance enhancement. The comparisons are facilitated through computation of receiver operating characteristics (ROCs), which are data-driven methods for comparing detection rates to error rates as a function of decision boundaries established between data distributions, independent of the actual underlying distribution.