Real-time structural model updating using local eigenvalue modification procedure for applications in high-rate dynamic events

Abstract

Estimating the state of structures that experience high-rate dynamics requires real-time model updating capabilities. High-rate dynamic events are characterized by (1) large uncertainties in the external loads, (2) high levels of non-stationarities and heavy disturbances, and (3) unmodeled dynamics generated from changes in system configurations. In order to achieve real-time model updating for high-rate dynamics, an algorithm should be able to update the structure’s state on a timescale of 1 ms or less while circumventing pre-calculations to enable its operation over un-modeled event. This work formulates an algorithm to meet the stringent latency requirements using the local eigenvalue modification procedure (LEMP). In doing so, the model is transformed from the physical domain into the modal space which numerically simplifies the calculations needed to determine the state of a complex structure. To track the system through time, the structure’s state is continuously updated by adjusting the associated model through online modal analysis. Its future states are estimated using a Bayesian search algorithm to compare the measured signals with selected modal models. New modal models are built based on the enhanced estimate of the structure’s state and used for subsequent state estimations. The methodology is applied to an experimental testbed experiencing varying dynamics to update a surrogate model. Results show that the LEMP algorithm could update the state of the high-rate dynamics system within 1 ms for up to 250 nodes, a speed up of 125 times when compared to solving for the systems state using the generalized eigenvalue approach. The timing, accuracy, and computational resources are discussed in this paper and compared to the baseline generalized eigenvalue approach. An example problem and code are provided in a public repository.