Structural Health Monitoring in the Context of Nonequilibrium Phase Transitions

Abstract

A statistical pattern recognition paradigm for a structural health monitoring (SHM) system can be defined as operational evaluation, data acquisition, feature selection and extraction, and statistical classification. Currently, feature selection is primarily based on physics-informed engineering judgment. The goal of this work is to develop a more principled approach for feature selection. This study begins with the concept of increased complexity of a system that results from structural degradation and identifies this change in complexity using previously proposed features related to entropy, acceleration distributions, holder exponent, and residual errors from auto-regressive models. The unique aspect of this study is the demonstration that these features are consistent with recent developments in statistical physics associated with fluctuation dynamics and nonequilibrium (NE) phase transformations (PT). In the context of SHM, a NEPT consists of an irreversible process (e.g., crack formation, yielding) characterized by an energy-absorbing transformation process. Recently, NE fluctuation theorems define expected behaviors of systems exhibiting NEPT related to entropy production, work and ground state energy, scaling characterization of intermittent NE fluctuations, and extreme statistics of these fluctuations. The theorems state that if there is a NEPT (damage) and associated energy dissipation, then there are corresponding changes in fluctuation response. The hypothesis of this study is that the selected damage-sensitive features exhibit properties defined by the fluctuation theorem. To generate data for the entropy production calculations and create a link to recent studies of NE fluctuation theorems, experimental and numerical tests are conducted on systems with NEPTs. Furthermore, based on other studies of NE fluctuations, the statistical physics community has shown that a variety of physical (e.g., biological) and nonphysical (e.g., economic) systems follow common trends leading to universal properties at the NEPTs and we investigate these properties to see if they can provide a more principled guide to damage-sensitive feature selection.