Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox

• Theoretical framework is introduced for development of HI. • Comparison of proposed HI is done with existing statistical HI. • Proposed HI has high sensitivity to gearbox degradation progression. • Proposed methodology effectively predicts RUL with limited data. Gears are one of the critical components in industrial machinery and operate under high loads for most of their Life. Health indicators (HI) such as root mean square (RMS), kurtosis, etc., often fail to reflect degradation consistently and, therefore, erroneously predict remaining useful Life (RUL). To address this gap, an HI is developed based on symmetric directed divergence (SDD) to quantify divergence between defect-free and defect conditions. This work establishes a signal-processing framework to compute the HI and estimate the RUL. First, a continuous wavelet transform (CWT) with a morlet wavelet is applied to decompose raw vibration signals, followed by the computation of CWT coefficients. Then, the divergence between the probability density function (PDF) of coefficients is computed for defect-free and defect conditions, resulting in a robust HI with a monotonic degradation trend. A Long Short-Term Memory (LSTM) model with a log1p squared error (LSE) is developed from the proposed HI to capture temporal dependencies in HI sequences for accurate RUL predictions. A performance comparison between existing HIs and the proposed measure shows that the proposed measure outperforms the existing ones. The study also highlights that using LSE improves performance, making it effective for non-linear degradation. A performance comparison between mean square error (MSE) and the proposed (LSE) functions shows that LSE yields superior results. A performance comparison of various models developed using the proposed health indicator has been conducted. Among them, the attention-based LSTM achieves the lowest loss and highest stability, and the standard LSTM shows the weakest performance.