Applying the Concept of Complexity to Structural Health Monitoring

Abstract

Structural Health Monitoring (SHM) is the process of implementing an online and automated damage detection strategy for aerospace, civil and mechanical engineering infrastructure. Since 2000, the authors have addressed SHM as essentially a problem in statistical pattern recognition, and they continue to believe that this framework is the most appropriate way to develop SHM solutions. The detailed approach is based on a four-step paradigm that includes: (1) Operational evaluation, (2) Data acquisition, (3) Feature selection/extraction, and (4) Statistical model development for feature classification. A current shortcoming of this paradigm is that almost all feature selection is done in an ad hoc manner and is often based solely on engineering judgement and experience of the people developing the SHM system. Furthermore, very little effort has been made to demonstrate that these features are consistent with experimental observations of material damage evolution or the current physical models of damage initiation and evolution. Partly to address this shortcoming, the authors reintroduce previously-proposed ‘fundamental axioms’ of SHM to show how solutions might be organized and informed in their light. In fact, the discussion is focused on the most recently-added ‘axiom’: damage increases the complexity of a system, and what is meant by the term complexity. Often entropy measures - either thermodynamic or information entropy, are used to quantify complexity. However, there are many measures of entropy extant in the literature. This paper will show the application of several measures of information entropy to a numerical example of a system with increasing levels of damage present. A simple proof that damage leads to an increase in entropy is presented.