Multi-step ahead state estimation with hybrid algorithm for high-rate dynamic systems

High-rate systems are defined as engineering systems that undergo accelerations of amplitudes typically greater than 100 gn over less than 100 ms. Examples include adaptive airbag deploy-ment systems, hypersonic vehicles, and active blast mitigation systems. The use of feedback mechanisms in these high-rate applications is often critical in ensuring their continuous operations and safety. Of interest to this paper are algorithms needed to support high-rate structural health monitoring (HRSHM) to empower sub-millisecond decision systems. HRSHM is a complex task because high-rate systems are uniquely 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 that necessitate careful crafting of adaptive strategies. This paper studies benefits of integrating a data-driven predictive model with a physics-based state observer to reduce latency and convergence time estimating actionable information. The predictive model, constructed with long short-term memory (LSTM) cells, performs multi-step ahead signal prediction acting as the input to the physical model, a model reference adaptive system (MRAS). The MRAS then performs state estimation of the predicted signal rather than the true signal. A comparison study was done between the proposed hybrid algorithm and a physics-based MRAS on a testbed involving a fast-moving boundary condition. Results showed that the hybrid algorithm could perform state estimations with zero timing deadline overshoot and with up to 50% faster convergence time when compared to the MRAS under constant boundary conditions. However, the hybrid generally underperformed the MRAS algorithm in terms of convergence accuracy during motion of the boundary condition by increasing convergence time by 20%, attributable to the lag in learning the new dynamics used in predicting. The performance of the NSE algorithm was also examined on a true high-rate system, where it was shown to be capable of qualitatively tracking actionable information.