Propagation of Systematic Sensor Uncertainty Into the Frequency Domain

Abstract

When it comes to the identification of dynamic system parameters, like stiffness and damping, the systematic measurement uncertainty is mostly ignored in the frequency domain because of its complicated and elaborate uncertainty propagation. Nevertheless, the uncertainty is far from being negligible. In order to examine the importance of the systematic measurement uncertainty in the frequency domain, the propagation of systematic uncertainty caused by four different sensor error types is investigated by using Monte Carlo simulations. It is shown that an uncertainty in the bias only affects static measurements, i.e., with an excitation frequency of the system being Ω=0. Furthermore, the uncertainty of the linearity and sensitivity only impacts the magnitude of the Fourier coefficient, whereas the uncertainty in the hysteresis results only in an uncertainty in the phase. Subsequently, it is shown that the linearity and hysteresis uncertainty are completely independent in the frequency domain. The results lead to simple propagation relations applicable to various engineering, science, and industry challenges without the need for the conduction of complex Monte Carlo simulations.