Fifth-order cumulants based higher order coupling feature extraction algorithm

Quadratic frequency coupling feature radiated by actual nonlinear vibration system can be extracted using third-order cumulants (TOC). Cubic frequency coupling feature and pairing frequency coupling one may be extracted using fourth order cumulants (FOC). Much higher order frequency coupling feature extraction isn´t studied now. In the paper, quadrtic frequency coupling and quadratic-to-cubic frequency coupling are firstly defined. The direct estimation formula of fifth-order cumulants (FFOC) is derived and two type different definitions of stationary complex random process FFOC are obtained. FFOC feature and relation between recursive estimation of FFOC and its computational load are analyzed. FFOC diagonal slice based adaptive line enhancer (FFOC-DSBALE) are developed. The FFOCDSBALE can recover or extract higher frequency coupling feature in Gaussian noise. Theoretic analysis and simulation result prove the validity of the proposed algorithm.