Damage Identification at Off-Grid Locations on Plate-like Structures using Frequency-Coupled Group Lasso

Abstract

Localizing elastic wave scatterers is the working principle behind a family of model-based approaches to detect and localize damage in plate-like structures. These approaches take advantage of a physical model of propagation and scattering, which enables an efficient data-driven strategy to decompose the effect of damage on the structure. This strategy consists in measuring on the healthy structure the responses to excitations at predefined candidate damage locations, and then in building from these a dictionary that maps damage at candidate locations to changes in responses. At inspection time, inverse methods are used to identify damage, based on this dictionary and the responses measured on the structure under test. One such inverse method is Frequency-Coupled Group Lasso, which exploits the inherent sparsity of damage to reduce the number of required measurements. This paper examines the performance of the above-described approach in the “off-grid” case, that is, when the damage is not located at one of the predefined candidate locations. This is an important extension because real-world damage can occur at a large or infinite number of locations, but the number of candidate locations is limited by measurement and/or computing cost. Off-grid cases are simulated by removing from the dictionary the entries corresponding to the actual damage locations and then running Frequency-Coupled Group Lasso with this incomplete dictionary. The results are then compared to the on-grid case, when the actual damage locations are included in the dictionary. Damage identification is demonstrated on a 600mm by 600mm composite plate with up to 6 damage locations, using a single accelerometer and 7 hammer excitations. Off-grid performance is evaluated for 4 different accelerometer locations, for SNRs ranging from 30 to 10dB, and compared to on-grid performance. The proposed damage identification approach is shown to remain robust in the off-grid case, further proving its real-world applicability.