Algorithms for spectrum background estimation of non-stationary signals

Abstract

The spectrum background, or in short, the background, is associated with the slow variations of the spectrum. The estimated background can be used to pre-whiten the spectrum and to identify significant variations in machine structure. However, the known background estimation techniques have been considered mainly in the context of stationary signals. Thus, the goal of this paper is to present new algorithms for background estimation of non-stationary signals. Based on the examination of available techniques for separating discrete frequencies and the background, we present two new algorithms for non-stationary signals: (i) time–frequency background estimation (TFBE), recommended when the rotation speed is unknown, and (ii) cycle-order background estimation (COBE), recommended when the rotation speed is known. The performance of these two new algorithms is demonstrated using a large data bank composed of simulated vibration signals of rotating components in different rotating speed profiles combined with realistic transfer functions measured on different rotating machines. These vibration signals were designed for a comprehensive investigation of the capabilities and limitations of the new algorithms. The accuracy of the new algorithms to estimate the background depends on the rotating speed variation. Good estimations of the backgrounds were achieved for rotating speed variations up to 10 Hz/s. Furthermore, the abilities of the algorithms are illustrated on real measured data.