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Inchoate fault detection for machine health monitoring (MHM) demands high level of fault classification accuracy under poor signal-to-noise ratio (SNR) which persists in most industrial environment. Vibration signals are extensively used in signature matching for abnormality detection and diagnosis. In order to guarantee improved performance under poor SNR, feature extraction based on statistical parameters which are immune to Gaussian noise becomes inevitable. This paper proposes a novel framework for adaptive feature extraction based on higher order cumulants (HOCs) and wavelet transform (WT) (AFHCW) for MHM. Features extracted based on HOCs have the tendency to mitigate the impact of Gaussian noise. WT provides better time and frequency domain analysis for the nonstationary signals such as vibration in which spectral contents vary with respect to time. In AFHCW, stationary WT is used to ensure linear processing on the vibration data prior to feature extraction, and it helps in mitigating the impact of poor SNR. K-nearest neighbor classifier is used to categorize the type of the fault. Simulation studies show that the proposed scheme outperforms the existing techniques in terms of classification accuracy under poor SNR.