A Computational Geometry Approach to the Life-Cycle Modeling of Remotely-Sensed Defects

摘要

Remote sensing is gaining in popularity for structural condition assessment, and in current practice, engineers are collecting large amounts of data throughout a system's life-cycle. These data must be interpreted to characterize defects, and to help engineers estimate a structure's remaining life. The challenge is that remotely-sensed defects are not typically quantified in a manner that robustly conveys life-cycle dynamics. We propose that the geometric concept of the convex hull can help address this limitation. The convex hull is the smallest convex polygon that surrounds all points in a set, regardless of dimensionality, and is a unique representation of the set. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. Furthermore, the concept of the convex hull can be extended to high-dimensional spaces, supporting the fusion of multiple sensors and data types. In this study, 2D point clouds analogous to information derived from point clouds were generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via vectorized autoregression and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust the noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.