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On the Use of Metaheuristic Algorithms for Solving Conductivity-to-Mechanics Inverse Problems in Structural Health Monitoring of Self-Sensing Composites
thesisposted on 07.05.2021, 12:22 by Hashim Hassan
Structural health monitoring (SHM) has immense potential to improve the safety of aerospace, mechanical, and civil structures because it allows for continuous, real-time damage prognostication. However, conventional SHM methodologies are limited by factors such as the need for extensive external sensor arrays, inadequate sensitivity to small-sized damage, and poor spatial damage localization. As such, widespread implementation of SHM in engineering structures has been severely restricted. These limitations can be overcome through the use of multi-functional materials with intrinsic self-sensing capabilities. In this area, composite materials with nanofiller-modified polymer matrices have received considerable research interest. The electrical conductivity of these materials is affected by mechanical stimuli such as strain and damage. This is known as the piezoresistive effect and it has been leveraged extensively for SHM in self-sensing materials. However, prevailing conductivity-based SHM modalities suffer from two critical limitations. The first limitation is that the mechanical state of the structure must be indirectly inferred from conductivity changes. Since conductivity is not a structurally relevant property, it would be much more beneficial to know the displacements, strains, and stresses as these can be used to predict the onset of damage and failure. The second limitation is that the precise shape and size of damage cannot be accurately determined from conductivity changes. From a SHM point of view, knowing the precise shape and size of damage would greatly aid in-service inspection and nondestructive evaluation (NDE) of safety-critical structures. The underlying cause of these limitations is that recovering precise mechanics from conductivity presents an under determined and multi-modal inverse problem. Therefore, commonly used inversion schemes such as gradient-based optimization methods fail to produce physically meaningful solutions. Instead, metaheuristic search algorithms must be used in conjunction with physics-based damage models and realistic constraints on the solution search space. To that end, the overarching goal of this research is to address the limitations of conductivity-based SHM by developing metaheuristic algorithm-enabled methodologies for recovering precise mechanics from conductivity changes in self-sensing composites.
Three major scholarly contributions are made in this thesis. First, a piezoresistive inversion methodology is developed for recovering displacements, strains, and stresses in an elastically deformed self-sensing composite based on observed conductivity changes. For this, a genetic algorithm (GA) is integrated with an analytical piezoresistivity model and physics-based constraints on the search space. Using a simple stress based failure criterion, it is demonstrated that this approach can be used to accurately predict material failure. Second, the feasibility of using other widely used metaheuristic algorithms for piezoresistive inversion is explored. Specifically, simulated annealing (SA) and particle swarm optimization (PSO) are used and their performances are compared to the performance of the GA. It is concluded that while SA and PSO can certainly be used to solve the piezoresistive inversion problem, the GA is the best algorithm based on solution accuracy, consistency, and efficiency. Third, a novel methodology is developed for precisely determining damage shape and size from observed conductivity changes in self-sensing composites. For this, a GA is integrated with physics-based geometric models for damage and suitable constraints on the search space. By considering two specific damage modes —through-holes and delaminations —it is shown that this method can be used to precisely reconstruct the shape and size of damage.
In achieving these goals, this thesis advances the state of the art by addressing critical limitations of conductivity-based SHM. The methodologies developed herein can enable unprecedented NDE capabilities by providing real-time information about the precise mechanical state (displacements, strains, and stresses) and damage shape in self-sensing composites. This has incredible potential to improve the safety of structures in a myriad of engineering venues.