Variable input observer for structural health monitoring of high-rate systems

The development of high-rate structural health monitoring methods is intended to provide damage detection on timescales of 10 µs -10ms where speed of detection is critical to maintain structural integrity. Here, a novel Variable Input Observer (VIO) coupled with an adaptive observer is proposed as a potential solution for complex high-rate problems. The VIO is designed to adapt its input space based on real-time identification of the system’s essential dynamics. By selecting appropriate time-delayed coordinates defined by both a time delay and an embedding dimension, the proper input space is chosen which allows more accurate estimations of the current state and a reduction of the convergence rate. The optimal time-delay is estimated based on mutual information, and the embedding dimension is based on false nearest neighbors. A simulation of the VIO is conducted on a two degree-of-freedom system with simulated damage. Results are compared with an adaptive Luenberger observer, a fixed time-delay observer, and a Kalman Filter. Under its preliminary design, the VIO converges significantly faster than the Luenberger and fixed observer. It performed similarly to the Kalman Filter in terms of convergence, but with greater accuracy.The development of high-rate structural health monitoring methods is intended to provide damage detection on timescales of 10 µs -10ms where speed of detection is critical to maintain structural integrity. Here, a novel Variable Input Observer (VIO) coupled with an adaptive observer is proposed as a potential solution for complex high-rate problems. The VIO is designed to adapt its input space based on real-time identification of the system’s essential dynamics. By selecting appropriate time-delayed coordinates defined by both a time delay and an embedding dimension, the proper input space is chosen which allows more accurate estimations of the current state and a reduction of the convergence rate. The optimal time-delay is estimated based on mutual information, and the embedding dimension is based on false nearest neighbors. A simulation of the VIO is conducted on a two degree-of-freedom system with simulated damage. Results are compared with an adaptive Luenberger observer, a fixed time-delay observer, ...