Joint Instantaneous Amplitude-Frequency Analysis of Vibration Signals for Vibration-Based Condition Monitoring of Rolling Bearings

TL;DR

This paper tackles vibration-based condition monitoring of rolling bearings by exploiting the instantaneous amplitude and frequency of vibration signals. It introduces three novel envelope representations—Instantaneous Amplitude-Frequency Mapping (IAFM), Instantaneous Amplitude-Frequency Correlation (IAFC), and Instantaneous Energy-Frequency Distribution (IEFD)—derived from the Hilbert Transform, and builds six discriminative features that capture energy-frequency dynamics over time. On the PU bearing dataset, the method achieves 99.60% accuracy and ROC-AUC of 1.00, with moderate computational demands suitable for real-time monitoring, outperforming STFT- and HHT-based baselines and approaching the efficiency of DL methods with far fewer features. The work provides a practical, reproducible framework for rapid fault detection in rolling bearings, supported by publicly available Python code.

Abstract

Vibrations of damaged bearings are manifested as modulations in the amplitude of the generated vibration signal, making envelope analysis an effective approach for discriminating between healthy and abnormal vibration patterns. Motivated by this, we introduce a low-complexity method for vibration-based condition monitoring (VBCM) of rolling bearings based on envelope analysis. In the proposed method, the instantaneous amplitude (envelope) and instantaneous frequency of the vibration signal are jointly utilized to facilitate three novel envelope representations: instantaneous amplitude-frequency mapping (IAFM), instantaneous amplitude-frequency correlation (IAFC), and instantaneous energy-frequency distribution (IEFD). Maintaining temporal information, these representations effectively capture energy-frequency variations that are unique to the condition of the bearing, thereby enabling the extraction of discriminative features with high sensitivity to variations in operational conditions. Accordingly, six new highly discriminative features are engineered from these representations, capturing and characterizing their shapes. The experimental results show outstanding performance in detecting and diagnosing various fault types, demonstrating the effectiveness of the proposed method in capturing unique variations in energy and frequency between healthy and faulty bearings. Moreover, the proposed method has moderate computational complexity, meeting the requirements of real-time applications. Further, the Python code of the proposed method is made public to support collaborative research efforts and ensure the reproducibility of the presented work

Figures (8)

• Figure 1: Instantaneous amplitude (IA) and Instantaneous frequency (IF) of a rolling bearing vibration signal, $v_h(t)$.
• Figure 2: Instantaneous amplitude-frequency mapping (IAFM), Envelope PSD, and envelope spectrum of the healthy vibration pattern, $v_h(t)$.
• Figure 3: IAFC of the healthy vibration pattern, $v_h(t)$
• Figure 4: Joint time-energy-frequency representation of the healthy vibration pattern, $v_h(t)$
• Figure 5: IEFD along with the joint time-energy-frequency visualization of the healthy vibration pattern, $v_h(t)$.