A Bayesian Probabilistic Approach for Crack Characterization in Plate Structures

This article explores the possibility of using a Bayesian probabilistic approach for the detection of cracks in thin plate structures, utilizing measured dynamic responses at only a few points on the plate. Existing laser scanning or shearography based crack detection methods are applicable only when measurement at the region near the defect is possible. These types of techniques are important in providing information, in addition to that obtained through visual inspection, for the purpose of structural health monitoring. Because of the global nature of the vibration characteristics of structural systems, this article puts forward a crack detection approach that can be applicable with only a few sensors and when the sensor locations are not close to the crack. This kind of method is particularly valuable as it can be applied when visual inspection is not possible (e.g., part of the plate is obstructed and is not assessable by inspectors). Owing to the problems of measurement noise and incomplete measurement (i.e., only a limited number of measurement points are employed and high-mode information is lost because of the digitization of the signal and measurement noise), the results of crack detection as an inverse problem contain uncertainties. To explicitly handle such uncertainty, the proposed crack detection method follows the Bayesian statistical system identification framework. Rather than pinpointing the crack parameters (i.e., the crack location, length, and depth), the posterior probability density function (PDF) of the crack parameters is calculated to quantify the confidence level of the identified results, which is extremely important for engineers when they make judgments about remedial works. This article reports the theoretical development of the modeling of a cracked plate and a crack detection method together with numerical verification of the proposed method. The case study results are very encouraging, and indicate that the proposed method is feasible.