Non-probabilistic wavelet method to consider uncertainties in structural damage detection

In vibration-based damage detection studies, researchers have shown that wavelet transform (WT) is an effective tool for detecting damage. However, structural damage detection is hindered by uncertainties in structural models and measurement data. Various attempts have been made to address this problem by incorporating a probabilistic WT method. The success enjoyed by the probabilistic method is limited by lack of adequate information to obtain an unbiased probabilistic distribution of uncertainties. In addition, the probabilistic method involves complex and expensive computations. In this study, a non-probabilistic wavelet transform method is proposed that resolves the problem of uncertainties in vibration-based damage detection. The mode shapes of the damaged and undamaged structure are decomposed to obtain the wavelet transform coefficient values (m). With the interval analysis method, the uncertainties in the obtained mode shapes are taken to be coupled rather than statistically distributed. In this way, the interval bounds (upper and lower bounds) of the changes in the wavelet transform coefficient values are calculated. A coefficient increment factor (CIF) based on the wavelet transform coefficient value is established, and the elemental possibility of damage existence (PoDE) is defined. Numerical and experimental models of a four-side-fixed square steel plate are applied to demonstrate the efficiency of the proposed method. Furthermore, the effect of different damage severities and the impact of different noise levels on damage identification are presented. The proposed method effectively identified damage.