Microsecond Model Updating for 2D Structural Systems Using the Local Eigenvalue Modification Procedure

Abstract

Systems that experience high-rate dynamics, such as blast or impact, are susceptible to rapid alterations that could result in loss of life and financial investments. These systems are characterized by a high dynamic response with a high-rate (< 100 ms) and high amplitude (> 100 g³). A system exposed to high-rate dynamic environments is frequently prone to rapid plastic deformation, which can cause structural, electrical, and sensor damage. A feedback loop of fast-acting actuators empowered with rapid state estimates can be utilized to stop further harm. The state estimator must be quick and resilient to the significant uncertainties, non-stationarities, and strong disturbances associated with high-rate dynamic systems. A model for 2Dimensional systems is developed to demonstrate high-rate tracking or estimation of a structure where a change in stiffness at locations on the system represents damage. The Local Eigenvalue Modification Procedure (LEMP) algorithm is applied to solve the system’s equation quickly and efficiently within a set latency for state estimation. LEMP utilizes a single generalized eigenvalue solution for the initial system and simplifies altered state equations by transforming them into modal space, isolating the DOFs that contribute to the changes between states, and defining equations in terms of the initial state, thereby reducing computational time. This preliminary work develops a 2D finite element model using classical plate theory. A 2D model simulation of the plate’s initial state is carried out on Abaqus and compared to the analytical model formulated solved using the generalized eigenvalue approach to test the formulated model. The changes made to the plate are then solved using LEMP to avoid solving the time-consuming eigenvalue solution. In this work, the change in the system is demonstrated by change in stiffness at different locations on the plate. Results report the performance metrics for the considered case. The approach’s applicability to deployment on edge computing systems for real-time model updating of structures operating in high-rate dynamic environments is discussed.