Uncertainty Quantification of Power Spectrum and Spectral Moments Estimates Subject to Missing Data

Abstract

In this paper, the challenge of quantifying the uncertainty in stochastic process spectral estimates based on realizations with missing data is addressed. Specifically, relying on relatively relaxed assumptions for the missing data and on a kriging modeling scheme, utilizing fundamental concepts from probability theory, and resorting to a Fourier-based representation of stationary stochastic processes, a closed-form expression for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency is derived. Next, the approach is extended for also determining the PDF of spectral moments estimates. Clearly, this is of significant importance to various reliability assessment methodologies that rely on knowledge of the system response spectral moments for evaluating its survival probability. Further, utilizing a Cholesky decomposition for the PDF-related integrals kept the computational cost at a minimal level. Several numerical examples are included and compared against pertinent Monte Carlo simulations for demonstrating the validity of the approach.