Online parameter estimation under non-persistent excitations for high-rate dynamic systems

Abstract

High-rate dynamic systems are defined as systems experiencing dynamic events of typical amplitudes higher than 100 g n for a duration of less than 100 ms. They are characterized by 1) large uncertainties on the external loads; 2) high levels of nonstationarity and heavy disturbance; and 3) generation of unmodeled dynamics from changes in mechanical configuration. To fully enable these systems, feedback capabilities must be developed. This includes computationally fast software and low latency hardware. This paper presents a pure time-based online parameter estimation algorithm for high-rate dynamic systems with real-time applicability. The algorithm is based on a model reference adaptive system architecture consisting of a reference system and an adaptive model. The adaptive model is built on a reduced order physical representation of the system and uncertainties are linearized. Uncertain coefficients are adapted leveraging instantaneous measurements and historical input-output data sets, termed history stack data, based on concurrent learning theory for coping with the lack of persistent excitation. The history stack is sequentially modified based on a singular value maximizing algorithm to accelerate convergence. The algorithm is numerically verified and experimentally validated on a testbed consisting of a cantilever beam with a moving cart. Numerical verifications show that the algorithm provides fast and accurate convergence when concurrent learning is used. Experimental validations show that the algorithm can successfully identify static positions of the cart, and can also track its movement relatively well, with large chattering and overshoots during travel time. The average computation speed of the algorithm per sample step, implemented in MATLAB, is 93 ls. It is envisioned that the implementation of the algorithm on an FPGA, along with refined coding, will greatly reduce computation time.

Generated datasets from dynamic reproduction of projectiles in ballistic environments for advanced research (DROPBEAR) testbed

“…Yan et al [8] selected various frequency extraction techniques for DROPBEAR data and examined their applicability to HR-SHM. Yan et al [9] conducted real-time state estimation using a sliding mode observer (SMO) and showed computation time of 95 μs. Nelson et al [10] combined Yan's SMO with an ensemble of recurrent neural networks (RNNs) to construct a hybrid predictive algorithm with zero timing deadline.…”

Real-time state estimation using recurrent neural network and topological data analysis

“…Physics-based techniques have been proposed to conduct high-rate structural health monitoring, including a sliding mode observer-based algorithm for real-time state estimation based on a physical representation, 5 and a model reference adaptive system-based algorithm that can achieve computation speed in the sub-millisecond time-frame. 6 Data-based techniques have also been explored. A key challenge in data-based formulations is in data scarcity arising, because high-rate experiments are expensive to conduct and may only include limited dynamic responses.…”

Hybrid algorithm for zero timing deadline overshoot state estimation of high-rate dynamic systems

“…This paper investigates a physics-informed machine learning architecture for HRSHM applications by integrating the data-driven ensemble of RNNs previously developed by the authors Barzegar et al (2022) with the physics-based MRAS also previously developed by the authors Yan et al (2021). The LSTM provides the MRAS with multi-step ahead predictions, thus allowing the MRAS to pre-compute the system's dynamic state and thus eliminate timing deadline overshoot caused by the MRAS computation time.…”

“…The MRAS architecture is described in detail in Yan et al (2021) and illustrated in Figure 2.3. Briefly, the MRAS is an adaptive observer that constructs a representation ('adaptive model') of the unknown ('reference model') system.…”

“…can be shown to be stable using Lyapunov stability Yan et al (2021), where P can be a user-defined positive definite matrix or by solving the Riccati equation…”