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Inverse Estimation for Damage Assessment in SHM: Moving Beyond the Probability of Detection



SHM systems are built to detect and estimate damage. For such systems, the detection of damage should be, inevitable. It is no longer conceivable that the system will regularly fail to detect damage. Instead, researchers should focus on methods to predict the extent of damage and feasible ranges of the signals that correspond to such damage. We refer to the application of such methods as the reliability of detection. Specifically, this paper considers SHM systems monitoring a particular region of interest. We no longer estimate the probability of detection (POD), but instead, use aspects of the POD process in order to determine the range of signal values that are statistically associated with the damage of interest. That is, instead of using the two step process in MLHNBK-1823 which converts regression results into probability estimates for damage detection, we examine directly the relationship between the signals and the level of damage. Then, using inverse estimation techniques, we estimate the range of signal values associated with a particular level of damage. We maintain the notion of statistical confidence and compute only the range of signal values that correspond to the confidence level of interest. Because signal data structure varies, we demonstrate several methods to construct the inverse estimate and its confidence interval. We applied these techniques in order to estimate damage from experimental data. Our experiment consisted of an array of PZT sensors adhered to a wing spar which was then fatigued on a test bed until crack lengths of 0.7mm were observed. Crack lengths were measured directly by pausing the test bed after a fixed number of cycles. Features were extracted from the waveforms received by the PZT sensors and associated with crack length through the estimation of a functional form. For a particular crack length of interest, inverse estimation on the functional form between the signal features and the crack length allowed us to estimate the associated signal value and 95% confidence interval. The inverse estimation techniques prove useful in estimating the signal values associated with a particular crack length. Further development of this application includes adjustments for environmental conditions.

doi: 10.12783/SHM2015/331

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