Unknown input uncertainty calculation using virtual input shaping and interval analysis

A triaxial accelerometer has been developed to measure and determine the uncertainty associated with unknown vibrations disturbing a small force metrology experiment. However, methodological shortcomings remain regarding the calculation of uncertainty for dynamic measurements. Therefore, this paper proposes an alternative framework to estimate the uncertainty of specific dynamic quantities of interest with a nonlinear and uncertain measuring system. The novelty of the proposed methodology lies in the use of an accurate and equivalent representation of the physical system based on a linear model, combined with an additive virtual input describing all the unknown unmodeled dynamics. Measurement models are defined considering measurement biases, and uncertainty is calculated using interval analysis tools. Such tools allow determining the feasible values of the quantities of interest to be estimated. The innovative aspects of the proposed approach are fully illustrated in simulation on the triaxial accelerometer, comparing linear and nonlinear measurement models in passive mode. • Equivalent representation of a nonlinear system by a linear model with a virtual input. • Virtual input shaping to distinguish quantities of interest from measurement biases. • Uncertainty propagation by solving inverse problem using interval analysis. • Simulation of a passive triaxial pendulum accelerometer in different scenarios.