Chapter 5 Impact Load Identification for the DROPBEAR Setup Using a Finite Input Covariance (FIC) Estimator Peter Lander, Yang Wang, and Jacob Dodson Abstract Various applications in structural dynamics may require the real-time estimation of unknown input. A recently developed joint input-state estimator for linear systems treats the unknown input as white Gaussian noise with finite covariance. The performance of this finite input covariance (FIC) estimator is validated using simulated data from a finite element model of the Air Force Research Laboratory’s experimental testbed called the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research). The estimator performance is compared with a few wellknown estimators, including the augmented Kalman filter (AKF) and the weighted least squares (WLS) estimators. The results show that the FIC estimator is capable of accurately estimating an impact load applied to the beam when acceleration is measured at a small number of locations. Additionally, the results show that the FIC estimator eliminates the low-frequency drift error that other well-known estimators are susceptible to. Keywords Input estimation · Dynamic testing · Linear stochastic system · Impact load identification 5.1 Introduction The objective of this research is to assess the performance of an input and state estimation framework for structures undergoing high-speed dynamic events. In such scenarios, oftentimes the structure is subject to an unknown and unmeasurable impact load that needs to be identified/estimated. The proposed joint input-state estimator is validated with a test setup named DROPBEAR (Dynamic Reproduction Of Projectiles in Ballistic Environments for Advanced Research) at the Air Force Research Laboratory Munitions Directorate, located at Eglin Air Force Base [1]. The technical approach focuses on the input and state estimation from acceleration response data using a finite input covariance (FIC) estimator. The performance of the FIC estimator is compared to two other estimators, one using an augmented Kalman filter (AKF) and another using weighted least squares (WLS) estimation. 5.2 Background The simulations performed for this research are based on the DROPBEAR testbed [1]. The testbed consists of a cantilever steel beam with an actuated roller that serves as either a moving or stationary pin support along the length of the beam. Additionally, an electromagnet can be attached to the beam and programmed to fall at a certain time, acting as a changing P. Lander ( ) School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA e-mail: Peter.Lander@gatech.edu Y.Wang School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA e-mail: yang.wang@ce.gatech.ed J. Dodson Air Force Research Laboratory, Munitions Directorate, Eglin AFB, FL, USA e-mail: jacob.dodson.2@us.af.mil © The Society for Experimental Mechanics, Inc. 2020 Z. Mao (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47638-0_5 51
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