A nonlinear coherence function and its application to machine diagnostics

Abstract

The harmonic content in dynamic measurements from rotating machinery contains much subtle information concerning equipment operational condition and component degradation. For this reason, the power density spectrum (PSD) has long been employed to assess the relative magnitude of fault-related spectral contributions. Measurements on high-performance rocket engine turbomachinery suffer from severe noise contamination from numerous extraneous sources, which impedes rotating element diagnostic evaluation. It is thus difficult to determine whether an apparent high-level harmonic contribution is indeed related to the fundamental rotational frequency, f1, or possibly due to an independent source. The ordinary PSD, being an absolute value, is of no assistance to this problem. In an effort to relate synchronous speed characteristics with an arbitrary harmonic component, an unique coherence spectrum was devised which we call the hyper-coherence function. The hyper-coherence function, Hn(f1), defines the nonlinear correlation between waves at the fundamental frequency and harmonics at nf1, n = 1,2…. The computation is straightforward by FFT methods, and results in a line spectrum of correlation coefficients as a function of harmonic number. This paper presents the hyper-coherence as a multiple-ordered correlation function and illustrates its utility through application to several idealized signals, and the assessment of an apparent high-amplitude harmonic signature in rocket engine vibration measurements.