For the first time worldwide, innovative techniques, generic non-linear higher-order unnormalized cross-correlations of spectral moduli, for the diagnosis of complex assets, are proposed. The normalization of the proposed techniques is based on the absolute central moments, that have been proposed and widely investigated in mathematical works. The existing higher-order, cross-covariances of complex spectral components are not sufficiently effective. The novel technology is comprehensively experimentally validated for induction motor bearing diagnosis via motor current signals. Experimental results, provided by the proposed technique, confirmed high overall probabilities of correct diagnoses for bearings at early stages of damage development. The proposed diagnosis technology is compared with existing diagnosis technology, based on the triple cross-covariance of complex spectral components.