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

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)....

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Main Authors: Anil Kumar, Jianlong Wang, Chander Parkash, Vikas Sharma, Hesheng Tang
Format: Article
Language:English
Published: Elsevier 2025-09-01
Series:Results in Engineering
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Online Access:http://www.sciencedirect.com/science/article/pii/S2590123025024442
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author Anil Kumar
Jianlong Wang
Chander Parkash
Vikas Sharma
Hesheng Tang
author_facet Anil Kumar
Jianlong Wang
Chander Parkash
Vikas Sharma
Hesheng Tang
author_sort Anil Kumar
collection DOAJ
description 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.
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spelling doaj-art-cf88bb6351b64505aa9109227a3ad8d32025-08-20T03:02:36ZengElsevierResults in Engineering2590-12302025-09-012710637310.1016/j.rineng.2025.106373Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearboxAnil Kumar0Jianlong Wang1Chander Parkash2Vikas Sharma3Hesheng Tang4College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325 035, China; Corresponding authors.College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325 035, ChinaDepartment of Mathematics, Patel Memorial National College, Rajpura Punjab, 140 104, India; Corresponding authors.Experimental Stress and Vibration Laboratory, Department of Mechanical-Mechatronics Engineering, The LNM Institute of Information Technology, Jaipur, Rajasthan, 302 031, IndiaCollege of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325 035, ChinaGears 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.http://www.sciencedirect.com/science/article/pii/S2590123025024442Symmetric Directed Divergence (SDD)Wavelet Divergence: LSTMWavelet Transform
spellingShingle Anil Kumar
Jianlong Wang
Chander Parkash
Vikas Sharma
Hesheng Tang
Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
Results in Engineering
Symmetric Directed Divergence (SDD)
Wavelet Divergence: LSTM
Wavelet Transform
title Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
title_full Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
title_fullStr Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
title_full_unstemmed Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
title_short Development of a robust wavelet divergence-based framework for health monitoring and remaining useful life estimation of gearbox
title_sort development of a robust wavelet divergence based framework for health monitoring and remaining useful life estimation of gearbox
topic Symmetric Directed Divergence (SDD)
Wavelet Divergence: LSTM
Wavelet Transform
url http://www.sciencedirect.com/science/article/pii/S2590123025024442
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