Variable input observer for nonstationary high-rate dynamic systems

Engineering systems experiencing events of amplitudes higher than 100 g n for a duration under 100 ms, here termed high-rate dynamics, can undergo rapid damaging effects. If the structural health of such systems could be accurately estimated in a timely manner, preventative measures could be employed to minimize adverse effects. For complex high-rate problems, adaptive observers have shown promise due to their capability to deal with nonstationary, noisy, and uncertain systems. However, adaptive observers have slow convergence rates, which impede their applicability to the high-rate problems. To improve on the convergence rate, we propose a variable input space concept for optimizing the use of data history of high-rate dynamics, with the objective to produce an optimal representation of the system of interest. Using the embedding theory, the algorithm sequentially selects and adapts a vector of inputs that preserves the essential dynamics of the high-rate system. In this paper, the variable input space is integrated in a wavelet neural network, which constitutes a variable input observer. The observer is simulated using experimental data from a high-rate system. Different input space adaptation methods are studied, and the performance is also compared against an optimized fixed input strategy. It is found that a smooth transition of the input space eliminates error spikes and yields faster convergence. The variable input observer is further studied in a hybrid model-/data-driven formulation, and results demonstrate significant improvement in performance gained from the added physical knowledge.