<b>Computational Studies on the Self-Sensing Inverse Problem Enhanced with Sensor Data Fusion</b>

<p dir="ltr">Many equipment operators and inspectors today make use of time-based maintenance strategies to ensure proper working order of engineering systems and structures. This approach can be costly and inefficient because inspections and maintenance are not targeted, and equipment downtime can be lengthy during this process. Condition-based maintenance, on the other hand, involves monitoring the condition of critical components or structures so that targeted maintenance is performed only when the parts being monitored exhibit signs indicating the end of its operational life. Shifting toward more efficient condition-based maintenance strategies for mechanical systems requires material state awareness (MSA) of the critical components and structures the system is comprised of. MSA of a structure involves attaining a thorough understanding of the structure's material properties, current mechanical state, and damage modes in order to estimate its remaining lifetime. Currently, many non-destructive evaluation (NDE) sensors and techniques are currently being developed and fielded for embedded sensing and condition monitoring applications, including in civil and aerospace structures. Among them, the self-sensing inverse problem (SSIP) is an emerging method that possesses great potential for providing MSA for piezoresistive materials.</p><p><br></p><p dir="ltr">Piezoresistive materials exhibit a change in electrical conductivity when subject to strain, making them a prime candidate for manufacturing structures that have the innate ability to transduce its mechanical state. The SSIP is a mathematical method that recovers the continuous displacement and strain field of the deformed piezoresistive material from measured resistivity (or conductivity) changes. Being able to obtain the full-field displacements and strains of a component or structure is a key insight into its mechanical state, enabling accurate stress and failure analyses that can prove invaluable for condition-based maintenance. Computational and experimental demonstrations of the SSIP to date have yielded good results on simple shapes and experimental test specimen. However, the accuracy of the SSIP recovered displacement field is not guaranteed because the SSIP is an ill-posed and undetermined inverse problem. Furthermore, present work on the SSIP has focused on simple shapes and loads, and the applicability of the SSIP on more complex geometries has not yet been explored.</p><p><br></p><p dir="ltr">In this work, sensor data fusion (SDF) of the electrical data the SSIP utilizes for displacement field recovery with discrete displacement and strain data is explored as a way to increase the accuracy of the reconstructed displacement field and to improve the reliability of the SSIP when the resistivity data contains noise and outliers. Through a series of computational experiments, it was found that by supplementing resistivity data with sensors providing displacement data, the SSIP was able to recover the displacement field of a complex shape resembling real world structural components with good accuracy. Recovery of the displacement field was not possible without the use of additional sensor data. Furthermore, the displacement sensors made the SSIP more robust to increases in resistivity data noise. When resistivity data were supplemented with sensors providing strain data, while not as accurate as reconstructions enhanced with displacement data, there was still a significant improvement in the displacement reconstruction accuracy, even with a moderate increase in resistivity data noise. </p>