Structural Damage Detection under Uncertain Parameters Using Non-Probabilistic Meta-Model and Interval Mathematics

Rapid progress in the field of sensor technology has led to acquisition of massive amounts of measured data from structures being monitored. The data, however, contain inevitable measurement errors which often cause quantitative damage assessment to be ill conditioned. Attempts to incorporate a probabilistic method into a model have provided promising solutions to this problem by treating the uncertainties as random variables usually modeled with Gaussian distribution. However, the success enjoyed by the probabilistic method is limited by the lack of adequate information to obtain an unbiased probabilistic distribution of uncertainties. In addition, the probabilistic surrogate models involve complex and expensive computations, especially when generating output data. In this study, a non-probabilistic surrogate model based on wavelet weighted least squares support vector machine (WWLS-SVM) is proposed to address the problem of uncertainty in vibration based damage detection. The input data for WWLS-SVM consists of selected wavelet packet decomposition (WPD) features of the structural response signals, and the output is the Young’s modulus of structural elements. This method calculates the lower and upper boundaries of the changes in the Young’s modulus based on an interval analysis method. Considering the uncertainties in the input parameters, the surrogate model is used to predict the output of this interval bound. The proposed approach is applied to detect simulated damage in the four-story benchmark structure of IASC-ASCE SHM group. The results show that the proposed method can perform well in uncertainty-based damage detection of structures with less computational efforts compared to direct finite element model.