Structural Damage Detection by Integrating Non-Negative Matrix Factorization and Relevance Vector Machines

Abstract

This paper proposes a structural damage detection method based on wavelet packet decomposition, non-negative matrix factorization (NMF) and a relevance vector machine (RVM). First, vibration data at multiple points are used to calculate the wavelet packet node energies and construct a non-negative damage feature matrix. Second, to increase the damage detection accuracy, the NMF technique is employed to obtain the reduced dimensional representation of the non-negative damage feature matrix and extract the underlying features. Last, the RVM, a powerful tool for classification and regression, that can obtain the probability estimation for classification, is used to determine the relationship between features extracted with NMF and the corresponding damage patterns by considering the measurement noise. The trained RVMs are then used to perform damage pattern identification and classification of an unknown state structure. Numerical study on the Binzhou Yellow River Highway Bridge is carried out to validate the ability of the proposed method in damage detection. The results show that the RVM can achieve a high accuracy in damage pattern identification accuracy using the features extracted by NMF.