Online Implementation of the Local Eigenvalue Modification Procedure for High-Rate Model Assimilation

High-rate structural health monitoring of active structures operating in high-rate dynamic environments empowers the execution of preventative behavior in response to structural degradation or external stimuli. Examples of structures operating in high-rate dynamic environments include hypersonic vehicles, space crafts, and ballistic packages. The effective selection of reactive actions to be taken in real time requires an up-to-date model of the structure’s state. Importantly, the short timescale of relevance to these structures means that the model must be continuously updated with a time step of 1 millisecond or less. However, traditional frequency-based methods for updating the finite element model online require solving the generalized eigenvalue problem, which becomes more complex as the number of nodes or FEA model increases, thereby increasing computational time. In this work, the local eigenvalue modification procedure is put forward to accelerate the extraction of natural frequencies from finite element models updated online. The local eigenvalue modification procedure works by precomputing the eigenvalue solution to a reference state of the system and then computes the single (i.e., local) change in the modal domain from the reference state to the current state online. The modal domain update in the local eigenvalue modification procedure bypasses the general eigenvalue problem, which is the most expensive computational step. For the online implementation of the state estimation, the Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research testbed is used. The testbed allows for the controlled movement of a pinned condition attached to an otherwise free cantilever beam. In previous studies, the testbed has been used with the generalized eigenvalue solver in a frequency-based model assimilation approach to infer the most likely position of the pinned condition (i.e., state of the structure). This work reports the effectivity of the local eigenvalue modification procedure compared to the generalized eigenvalue solution of the system for inference accuracy while varying the nodes dedicated to the analysis. The optimal efficiency of the system’s approach is explored for the testbed-based health assessments. Timing results and effects of sensor noise on the system are discussed in detail.