Date of Award
Summer 2025
Document Type
Open Access Dissertation
Department
Mechanical Engineering
First Advisor
Austin Downey
Abstract
Real-time model updating is crucial for active structures and electronic assemblies subjected to high-rate dynamic events. High-rate dynamic events refer to events that occur at high speeds and with rapid changes in the forces and energy involved. These events can include explosions, impacts, and crashes. These systems are characterized by a high dynamic response with a high rate (< 100 ms), high amplitude (> 100 gn), highly nonlinear, meaning that the response is not proportional to the applied force, and involve complex interactions between multiple objects or materials. A system exposed to high-rate dynamic environments is frequently prone to rapid plastic deformation, involving violent and destructive effects, such as shockwaves, fragmentation, and deformation of structures, which can cause structural, electrical, and sensor damage. Understanding these characteristics is crucial for predicting and mitigating high-rate dynamic events’ effects and designing materials and structures that can withstand these extreme conditions. Challenges associated with estimating and updating the state of high-rate dynamic events in real-time include (1) adequate sensing,(2) lack of system knowledge, (3) high variability in loads, and (4) limited resources for algorithm implementation. The state estimator must be quick and resilient to the significant uncertainties, non-stationarities, and strong disturbances associated with high-rate dynamic systems.
This work proposes and implements the Local Eigenvalue Modification Procedure (LEMP) as an efficient method for updating real-time structural models to address these challenges. LEMP simplifies the computational process by using a single generalized eigenvalue solution from the system’s baseline state and reducing subsequent computations into a set of second-order secular equations. These equations isolate only the degrees of freedom associated with structural changes, transforming the updating problem into a localized one that avoids re-solving the full eigenvalue problem. A divide-and-conquer algorithm is introduced to solve these secular equations efficiently, achieving state update times well below the 1 ms threshold required for real-time performance. The methodology is validated first on 1D beam structures using the DROPBEAR experimental testbed and later extended to 2D plate models and complex PCBs undergoing damage. Across all tested configurations, LEMP consistently achieved sub-millisecond state update times and high accuracy, with signal-to-noise ratios exceeding 30 dB in most modes and mean absolute errors under 1 Hz for lower modes.
Furthermore, this work advances LEMP’s applicability to reduced-order models (ROMs) and more complex 2D systems. An optimized 25-node cantilever plate configuration was developed and validated as the optimal reduced mesh for capturing local stiffness changes. A single and four-state perturbation was introduced, and the corresponding frequency responses were evaluated. Results show that LEMP maintained less than 10% error compared to full generalized eigenvalue (GE) computations while being 20 to 22 times faster for state changes. For instance, a four-state local stiffness change took only 1.62 ms to compute using LEMP versus 36.04 ms with GE, confirming its real-time viability. These contributions are supported by robust parametric studies involving mode selection, nodal reduction, and error profiling, all of which informed the development of a practical, deployable framework for high-rate environments.
This work advances the field of structural health monitoring by delivering a computationally efficient, accurate, and scalable model updating strategy capable of tracking high-rate structural dynamics in real-time. Modal reduction, algorithmic optimization, and application-specific modeling offer a powerful tool for adaptive system control, especially in mission-critical domains. Through the LEMP framework, this dissertation lays the foundation for smarter, faster, and more resilient structural monitoring and response systems under extreme dynamic conditions.
Rights
© 2025, Emmanuel Abiodun Ogunniyi
Recommended Citation
Ogunniyi, E. A.(2025). Reduced Order Model-Based Framework for Microsecond Model Updating of Two-Dimensional Structural Systems Using the Local Eigenvalue Modification Procedure. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8383