Boundary Transformation Vectors: A Geometric Method of Quantifying Attractor Deformation for Structural Health Monitoring

Abstract

Chaotic signals have long held promise as a means of excitation in structural health monitoring applications, but methods to process the structural response and infer damage are limited in number and effectiveness. Here, an alternative geometric methodology is presented that is based on measuring the boundary deformation of a system attractor as parameters change. This technique involves sampling the boundaries of two system attractors: one with nominal parameters and one with varied parameters, and then computing boundary transformation vectors (BTVs) between them. These vectors encode information about how the system has changed. This method allows damage level as well as type/location to be simultaneously quantified in simulated structures, and represents a major step toward making chaotic excitation a more practical choice for structural health monitoring.