Kernel Dependence Analysis for Structural Health Monitoring with High-dimensional, Small Size Datasets

Abstract

Health monitoring functionality is a key feature of smart and sustainable structures. The statistical inference problem for this functionality usually boils down to novelty detection which aims to distinguishing the intact and damaged states of structures. An important challenge in this unsupervised inference problem is the characterization of dependencies between structural responses at various locations. Failure in considering this phenomenon usually results in high false positive (FP) rates and hence, inaccurate damage localization. The existing methods, such as graphical models or conditional classifiers, mainly use density estimation for considering the dependencies of random variables (RV) in structural health monitoring (SHM); and as a result, these methods usually suffer from the curse of dimensionality which makes them unable to handle high-dimensional problems. In this study, we propose a new approach for novelty detection that uses kernel dependence techniques, instead of density estimations methods, for considering statistical dependencies of RVs. Thus, the proposed method can handle arbitrarily high-dimensional problems with no simplifying assumptions. The performance of the algorithm was tested by experimental data in a SHM application problem. The results show that the damage localization accuracy can be significantly improved by the proposed technique compared to its peer methods