Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8

10 Stochastic Wavenumber Estimation: Damage Detection Through Simulated Guided Lamb Waves 125 quantify material properties without requiring a baseline “healthy” structure for calibration. Furthermore, calibration of the transverse wave velocity rather than specific material properties eliminates the possibility of compensating effects that occur when considering elastic modulus and density. Due to its deterministic nature, current AWS methodology is also poorly suited to operate in conditions containing experimental uncertainty resulting from measurement tools commonly used in practice. The approach presented herein is shown to improve thickness estimates from wavenumber data exhibiting spurious peaks by considering expert judgment in prior distributions. Most importantly, the new method is shown to result in less false positives of damage than the existing deterministic approach and provides a means of quantifying uncertainty remaining in the predictions. While the calibration framework presented herein is shown to improve the damage detection and quantification of current state of the art methods, assumptions and limitations remain which should be addressed in future studies, as summarized below. • Consideration of uncertainties simultaneously. This paper assumes that parametric and experimental uncertainties can be analyzed independently. In realistic field applications, both types of uncertainties will likely be present simultaneously. Considering multiple uncertainties simultaneously within the framework presented is possible, but further work should be done to verify this approach. • Additional sources of uncertainty should also be considered. Particularly, experimental uncertainty has been presented herein as spurious peaks in data due to the quality of equipment available for testing. Another problem commonly occurring in practice is the inability to set up experiments such that scans are conducted perfectly perpendicular to the structure, especially for curved surfaces. The nature of experimental noise introduced by this operational condition may vary from that which we have presented and thus, requires further investigation. • Applications with increased complexity in the structure. Structures composed of composite materials, which are produced by bonding different materials, may have differences in the manner that guided Lamb waves propagate. If the layering of materials were to alter the wave propagation, the numerical model used to develop training data would likely exhibit some form of model form error. Thus, future studies including composite structures may potentially require more influence from the discrepancy function to account for this model form error. • Structures having less severe damage than that presented herein. For example, corrosion of pipes will likely occur as gradual damage where there is not a dramatic change from one thickness to another. While AWS has been proven capable of detecting gradual damage [38], the new method implementing Bayesian inference should also be evaluated for this application. References 1. Farrar, C.R., Worden, K.: An introduction to structural health monitoring. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 365(1851), 303–315 (2007) 2. Rytter, A.: Vibration based inspection of civil engineering structures. Ph.D., Aalborg University, Denmark (1993) 3. Atamturktur, H.S., Gilligan, C.R., Salyards, K.A.: Detection of internal defects in concrete members using global vibration characteristics. ACI Mater. J. 110(5), (2013) 4. Doebling, S.W., Farrar, C.R., Prime, M.B., Shevitz, D.W.: Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. 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