Title: On quantifying the uncertainty of stochastic process power spectrum estimates subject to missing data

Authors: Liam Comerford; Ioannis A. Kougioumtzoglou; Michael Beer

Addresses: Institute for Computer Science in Civil Engineering, Leibniz University Hannover, Germany ' Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA ' Institute for Computer Science in Civil Engineering, Leibniz University Hannover, Germany; Institute for Risk and Uncertainty, University of Liverpool, Liverpool, L69 3GH, UK; School of Civil Engineering, Shanghai Institute of Disaster Prevention and Relief, Tongji University, China

Abstract: The issue of quantifying the uncertainty in stochastic process power spectrum estimates based on realisations with missing data is addressed. In this regard, relying on relatively relaxed assumptions for the missing data, utilising fundamental concepts from probability theory, and resorting to Fourier and harmonic wavelets based representations of stationary and non-stationary stochastic processes, respectively, a closed-form expression is derived for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency. The significance of the derived PDF relates to cases where incomplete process realisations are available for power spectrum estimation applications. In this setting, standard power spectrum estimation techniques subject to missing data typically provide with a deterministic estimate for the power spectrum. Thus, no information is provided concerning the uncertainty in the estimates. Numerical examples herein demonstrate the large extent to which any given single estimate may be unrepresentative of the target spectrum.

Keywords: stochastic processes; power spectrum estimation; missing data; non-stationary; evolutionary; uncertainty; time-frequency; wavelets; probability density function; PDF.

DOI: 10.1504/IJSMSS.2015.078358

International Journal of Sustainable Materials and Structural Systems, 2015 Vol.2 No.1/2, pp.185 - 206

Received: 06 Aug 2015
Accepted: 28 Feb 2016

Published online: 15 Aug 2016 *

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