Engineering applications

Abstract

In this paper, we consider the fundamental problem of frequency estimation of multiple sinusoidal signals with stationary errors. We propose genetic algorithm and outlier-insensitive criterion function based technique for the frequency estimation problem. In the simulation studies and real life data analysis, it is observed that the proposed genetic algorithm based robust frequency estimators are able to resolve frequencies of the sinusoidal model with high degree of accuracy. Among the proposed methods, the genetic algorithm based least squares estimator, in the no-outlier scenario, provides efficient estimates, in the sense that their mean square errors attain the corresponding Cram er-Rao lower bounds. In the presence of outliers, the proposed robust methods perform quite well and seem to have a fairly high breakdown point with respect to level of outlier contamination. The proposed methods significantly do not depend on the initial guess values required for other iterative frequency estimation methods.

On the Existence and Uniqueness of an Rν-Generalized Solution to the Stokes Problem with Corner Singularity

“…Boundary value problems with singularity play an important role in fracture mechanics [1,2]. The singularity can be caused both by the degeneracy of the coefficients and the right-hand sides of the equation (see [3][4][5][6]) and by the presence of re-entrant corners on the boundary of a polygonal domain (see, [7][8][9][10]).…”