A Comparison of Metaheuristic Algorithms for Solving the Piezoresistive Inverse Problem in Self-Sensing Materials

Nanofiller-modified materials have been widely explored for self-sensing in diverse venues spanning civil, aerospace, robotic, and even biomedical applications. Key to self-sensing is the fact that these materials are piezoresistive - their electrical conductivity is influenced by deformation and damage. Considerable research has aimed at leveraging this for intrinsic self-sensing. However, prevailing techniques provide no information about the underlying mechanical state of the material. Instead, damage and strain must be indirectly inferred from conductivity changes. The cause of this limitation is that recovering mechanics from electrical measurements is an ill-posed, under-determined, and multi-modal inverse problem. As such, global search algorithms coupled with physically motivated constraints must be used to obtain a solution. Previously, it was demonstrated that genetic algorithms (GAs) provide a suitable means of solving the displacement-from-conductivity problem. These algorithms, while undoubtedly powerful, suffer from artifacts in the strain solutions and variability in the solutions between successive searches. The goal of this work is to explore other commonly used global search algorithms which can be used to solve the displacement-from-conductivity inverse problem. In addition to GAs, we focus on two prevailing types of metaheuristic global search algorithms: simulated annealing and particle swarm optimization. Each algorithm is tested on experimental data where a self-sensing nanocomposite was deformed and electrical impedance tomography was used to image the conductivity change. The results for each algorithm are compared to standard finite element simulations and experimental observations via digital image correlation. A comparison is then drawn between the three algorithms in terms of solution quality, variability, accuracy, and computational efficiency.