Combined Weighted Envelope Spectrum: An enhanced demodulation framework for extracting characteristic frequency of rotating machinery

Abstract

Envelope spectrum plays a pivotal role in the surveillance and diagnostics of rotating machinery. Two prevailing techniques for constructing this spectral quantity are narrowband demodulation and cyclostationary analysis. However, the former is susceptible to failure under low Signal-to-Noise Ratio (SNR) conditions or in the presence of non-Gaussian noise, while the latter exhibits sensitivity to cyclostationary noise, such as electromagnetic interferences. Notably, specific tasks determine the characteristic frequencies expected to be detected. More precisely, the determination of target component and noise interference depends on the mechanical part under scrutiny. Consequently, the envelope spectra provided by classical methods often manifest deficiencies when confronted with intricate monitoring signals from rotating machinery. To address this challenge, this paper proposes an enhanced demodulation framework—Combined Weighted Envelope Spectrum (CWES), tailored for extracting specific characteristic frequencies. First, a cyclostationary model for rotating machinery is presented, demarcating the target component as solely the cyclostationary signal caused by the mechanical element of concern. Second, the weighting functions with/without prior knowledge of characteristic frequency are elaborately designed, and the Adaptive Combined Weighted Envelope Spectrum (ACWES) and the Optimal Combined Weighted Envelope Spectrum (OCWES) are constructed correspondingly. Moreover, the indicator Characteristic peak-to-Noise peak Ratio (CNR) is proposed to evaluate the demodulation performance of different envelope spectra. Ultimately, the effectiveness of ACWES and OCWES is validated by simulation signals and experimental data from rolling bearing, centrifugal pump, and Francis turbine, and the comparison with the state-of-the-art demodulation methods verifies the superiority of the proposed enhanced demodulation framework.