Force localization and reconstruction based on a novel sparse Kalman filter

Abstract

Most of existing methods for force identification assume the force locations to be known a priori. In this paper, we propose a novel recursive algorithm, named sparse Kalman filter, to simultaneously localize and reconstruct forces in time domain. The spatial distribution of forces at each time step is estimated by Relevance Vector Machine. With its sparsity-inducing ability, sparse Kalman filter can monitor forces at a large number of potential locations with a limited number of sensors, at a speed much higher than traditional batch methods. We also present the application of sparse Kalman filter with a smoothing technique, namely allowing a time delay between the measurement and input estimation step. In this way, the computational dimension is increased in exchange for an improved estimation accuracy. The proposed algorithms are validated on numerical simulations of a fixed-end beam, a truss structure, and an engineering-scale support structure. In each simulation, different sampling frequencies, smoothing delays, measurement noise levels, and force locations are considered to comprehensively understand the performance of sparse Kalman filter and its smoothing version.