Simulation-enhanced Damage Detection

The use of Guided Waves (GWs) in Non-Destructive Evaluation (NDE) techniques has proven to be effective in localizing and characterizing damage at early stages of development, in locations often inaccessible by visual inspection, all while requiring only a sensor network of modest size. These capabilities, often deployed in the form of sporadic inspections, enable to complement more common vibration-based Structural Health Monitoring (SHM) installations, and are the recipient of substantial research interest. This procedure consists in using piezo-electric sensors to both, generate GWs in a structure, and record their propagation in terms of an electric signal. Among several data processing alternatives, model-based damage detection relies on repeated evaluation and update of an elastodynamic model of the damaged structure, which aims at matching the recorded signal with a simulated one.

The use of high frequencies, as well as the need for numerous evaluations of a model, lead to substantial computational cost, and call for automatized discretization of damage or other domain features. The Spectral Cell Method (SCM) is an effective strategy to tackle these challenges. It relies on deploying and combining three main components, namely: high order Ansatz spaces supported at Gauss-Lobatto-Legendre nodes, mesh-independent interface descriptions, and customized mass-lumping methods addressing elements intersected by these features. This leads to accurate, yet versatile, models, which can be efficiently solved via explicit time integration algorithms.
In this contribution, we propose a novel mass-lumping method for cut elements, which is aimed at minimizing lumping error. It consists in generating customized integration weights according to the cut configuration of an element, so that a diagonal mass matrix might be produced via the nodal quadrature technique. For this, linear moment fitting equations are relaxed into a quadratic programming problem, thus ensuring mass conservation and positiveness.

Compared to previous versions of the SCM, the approach put forth by Sergio Nicoli (SMM Group), Dr. Konstantinos Agathos Universit yof Exeter) and Prof. Eleni Chatzi (SMM group) enables to increase accuracy, albeit at the cost of reduced stability. We address this issue with a “leap-frog” time integration scheme, which we show to benefit multiple instances of the SCM. This delivers computation times that are competitive with state-of-the-art alternatives such as the spectral element method. With respect to this optimally convergent, mesh-conforming, method, the SCM trades some accuracy in favor of a broader applicability, and thus represents a powerful tool in the context of NDE procedures.

read more in the latest publication in external page Computer Methods in Applied Mechanics and Engineering