UC San Diego

Many different industrial sectors such as aerospace, civil, mechanical, and automotive rely on complex systems that have evolved beyond their original design due to, among other things, damage, aging, upgrades, or degradation. The mismatch between the original design life and the current state of these systems motivates the need for an improved representation of their as-built, as-deployed state to monitor their structural health. Furthermore, as these systems continue to evolve beyond their original design, this virtual representation needs to adapt as well. To help ensure the reliability of these systems, a structural health monitoring (SHM) system that relies on an accurate representation of the system it monitors is desired. This dissertation presents the development of a workflow for integration of physics-constrained and structure-preserving machine learning (ML) models that can function as digital twins of a system with the purpose of enabling response forecasting to future states, as well as provide a basis for damage detection based on domain shifts observed in the data from the monitored system. The proposed approach leverages the well-established foundations of computational mechanics theory to constrain the parameter space of the ML models. This dissertation presents a series of extensions and variations of the basic principles of structure preservation in nonlinear dynamics to increase efficiency by reducing the data needs (through a sparse measurement requirement), reducing the computational burden through order reduction, and leveraging prior knowledge of the ideal system before it deviated from its nominal condition. Furthermore, this work proposes a strategy to deal with observational uncertainty (e.g., from measurement error) and epistemic uncertainty (e.g., from model limitations). Lastly, the digital twin model is used in combination with detection theory to establish a probabilistic reasoner that enables risk- and cost-informed decision-making. The entire workflow establishes a strategy for physically-interpretable ML models that can be interrogated to infer health states and to forecast their structural health state under future operational loads with increased accuracy.