A Computational Method for Full-Field Mechanics Imaging via the Self-Sensing Inverse Problem Enhanced with Sensor Data Fusion

Achieving material state awareness (MSA) of a mechanical system, structure, or component empowers engineers to be able to perform accurate failure prognosis and estimate remaining operational lifetime. Piezoresistive materials exhibit a change in electrical conductivity (or resistivity) when subjected to mechanical strain and therefore have the potential to enable functional, self-sensing structures that can provide real-time insight into their mechanical state. While piezoresistive materials have been demonstrated to be able to detect and localize damage by imaging conductivity changes, conductivity changes alone do not directly translate to stresses, strains, or displacements, values that are more meaningful for stress and failure analyses. To this end, the self-sensing inverse problem (SSIP) is a method which reconstructs the strain state that gives rise to an observed conductivity distribution. The SSIP has to date been computationally and experimentally demonstrated to reconstruct the deformed displacement field of simple geometries under load with reasonable accuracy, but mathematical limitations can make obtaining an accurate reconstruction difficult. In this work, we seek to improve the ability of the SSIP to obtain accurate displacement field reconstructions on more complex geometries by incorporating sensor data fusion (SDF) techniques. We herein develop a computational inverse problem for two SDF methods, one fusing electrical resistivity with displacement data and another fusing resistivity with strain data, and demonstrate these methods computationally on shapes representing aircraft components. These results show that incorporating data from relatively few displacement sensors allows the SSIP to reconstruct the displacement field with high accuracy. The results also demonstrate that incorporating strain sensor data improves the accuracy of the displacement reconstruction, though to a lesser degree than displacement data.