**Jin Yan 1,\*, Simon Laflamme 1, Premjeet Singh 2, Ayan Sadhu <sup>2</sup> and Jacob Dodson <sup>3</sup>**


Received: 24 July 2020; Accepted: 21 August 2020; Published: 24 August 2020

**Abstract:** High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 g*n* for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and even be critical to their deployment. However, these systems are characterized by large uncertainties, high non-stationarities, and unmodeled dynamics, and it follows that the design of real-time state-estimators for such purpose is difficult. In this paper, we compare the promise of five time-frequency representation (TFR) methods at conducting real-time state estimation for high-rate systems, with the objective of providing a path to designing implementable algorithms. In particular, we examine the performance of the short-time Fourier transform (STFT), wavelet transformation (WT), Wigner–Ville distribution (WVD), synchrosqueezed transform (SST), and multi-synchrosqueezed transform (MSST) methods. This study is conducted using experimental data from the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research) testbed, consisting of a rapidly moving cart on a cantilever beam that acts as a moving boundary condition. The capability of each method at extracting the beam's fundamental frequency is evaluated in terms of precision, spectral energy concentration, computation speed, and convergence speed. It is found that both the STFT and WT methods are promising methods due to their fast computation speed, with the WT showing particular promise due to its faster convergence, but at the cost of lower precision on the estimation depending on circumstances.

**Keywords:** high-rate dynamics; structural health monitoring; time-frequency analysis; synchrosqueezing transform (SST)
