A physically motivated reduced-order modal energy technique for ARMA spectrum estimation
Eberle, Robert Raymond
Spanos, Pol D.
Doctor of Philosophy thesis
A reduced-order modal energy (ROME) technique for spectrum estimation is introduced. In this technique the transfer function of a higher-order autoregressive (AR) model of a power spectrum is decomposed into partial fractions. These individual fractions are examined from the perspective of relative significance to the total energy of the system. First, the technique is formulated for a scalar random process (the univariate case). In the derivation, two solution procedures are discussed. In one procedure, a system of equations is solved to determine the unknown numerator coefficients of the partial fraction expansion. In the second procedure, a unique approach is used which yields each numerator coefficient directly, avoids solving a system of equations, and greatly reduces the requisite computation time. Next, the reduced-order modal energy technique is formulated for a vector random process (the multivariate case); it provides a parsimonious estimate of the power spectral density by capturing frequencies associated with significant spectral values. Numerical examples involving short data sequences, Space Shuttle acceleration data, and sunspot and temperature measurements are presented which demonstrate the usefulness of the technique.
Mechanical engineering; Aerospace engineering; Electronics; Electrical engineering