The wavelet transform as a Gaussian process for damage detection

Abstract

This paper presents a novel statistical model for the wavelet transform of the acceleration response of a structure based on Gaussian process theory with applications to earthquake damage detection. The proposed model considers the wavelet coefficients at each time sample as a realization of a Gaussian process that depends solely on the damage state of the structure. Damage is then detected by identifying changes in the distribution of the model parameters. The model is purely data driven; it requires no prior knowledge of the structural properties, and all the parameters are learned directly from the measured data. The estimation of the model parameters is transformed to an optimization problem and the convexity of the objective function is investigated. An efficient algorithm for the parameter estimation is proposed and tested for accuracy. Finally, the statistical model is applied to the data obtained from a series of shake table experiments conducted at the University of Nevada, Reno. The results of the application of the proposed statistical model and implementation methodology are presented, and the validity of the model assumptions and damage detection capability are illustrated. A damage detection scheme based on the model parameters and statistical hypothesis testing is proposed and evaluated using the experimental dataset.