Examining Random Uncertainty Using a Newly Developed Power Spectrum Based Method

Abstract

During steady state measurements, erratic oscillations can often be observed in the measured signals. For example, when measuring the ship-model resistance in a towing tank, oscillations might originate from vortex shedding, carriage control, rail imperfections, etc. These oscillations contribute to the random uncertainty of the observed mean value. The total observed random uncertainty can be caused by rapidly or slowly evolving oscillations. Rapidly evolving means that the periodicity is typically within the time frame of measurement, e.g. vortex shedding. Slowly evolving means that the periodicity is typically not contained within the available time frame of measurement, e.g. creep in a force sensor. The random uncertainty of the mean of a single measurement can be evaluated accurately when the rapidly evolving effects are dominant. The observed autocovariance of the signal can be used to find an uncertainty estimate for the signal as a whole [1]. In this paper, a new methodology to quantify the individual contribution of various spectral components to the random uncertainty is presented. The new methodology is based on the power spectrum of a signal. The power spectrum only describes the energy content of all the rapidly evolving effects, while energy of slowly evolving effects is absent. For many stationary processes, individual spectral components of the power spectrum can be regarded uncorrelated or weakly correlated with each other. Each individual frequency component may be regarded as an uncorrelated band pass noise process. The uncertainty contribution of such processes to the mean value can be evaluated accurately, hence the spectral density of the process is directly correlated to the uncertainty of the mean; lowering the spectral density lowers the uncertainty. By quantifying the uncertainty contribution for each spectral component, various effects can be distinguished in the frequency domain and their individual contribution to the uncertainty of the mean can be determined. Using this information, sound decisions can be made to what effects should receive effort to lower the amplitude of oscillation and hence the random uncertainty. This paper presents the newly developed power spectrum based method, called uncertainty spectrum, to determine the spectral contribution to the uncertainty of the mean and demonstrates the application of this method to ship-model resistance measurement data.