Millisecond model updating for structures experiencing unmodeled high-rate dynamic events

Abstract

Real-time control of next-generation active structures that experience unmodeled high-rate dynamic events require an up-to-date numerical model of the structural system. Examples of active structures that experience unmodeled high-rate dynamic events include hypersonic vehicles, active blast mitigation, and ballistic packages. Due to the dynamic environments that these structures operate in it follows that a numerical model of the system be updated on the timescale of less than 10 ms. Furthermore, the requirement for the monitoring of unmodeled high-rate dynamic events means that the proposed model updating technique cannot rely on precalculated data sets or offline training, therefore, the real-time structural updating technique must be capable of learning the state of the structure on-the-fly. This work proposes and validates an algorithmic framework for a millisecond error minimization model updating technique that updates a finite element analysis model of the structural system by minimizing the error between the structure’s measured state and a series of parallelized models that are calculated in real-time with the structure as it moves through the high-rate dynamic event. The proposed algorithm is numerically and experimentally validated using an experimental testbed designed to simulate the dynamic events of projectiles in ballistic environments that consists of a cantilever beam and a movable roller support that introduces a continuously changing boundary condition to simulate a change in the structural system (i.e. damage). Experimental results demonstrate that the location of the roller on the testbed could be accurately tracked and updated every 4.04 ms with an accuracy of 2.9% (10.05 mm over a beam of 350 mm) for a standard test profile and that the algorithm could track roller movement through an impact loading. Furthermore, the proposed algorithm demonstrated it was capable of tracking stochastic roller movement with an accuracy of 3.73%. The delay in the estimated roller position caused by the time required to collect a sufficient quantity of vibration data, the need for constant excitation of the structure, and the robustness of the proposed algorithm are discussed.