Learnable Wavelet Convolution and Sparsity-Enhanced Feature Extraction for Unsupervised Interpretable Fault Diagnosis in Mechanical Systems

Haitao Liu^1,*, Xuyang Wang¹, Shengcheng Quan¹, Qiaosheng Guo², Aichun Wang³, Lie Yang¹, Tingfang Zhang¹, Xiaojian Wu^1,*
1 School of Advanced Manufacturing, Nanchang University, Nanchang, China
2 Zhaoyang Gevotai (Xinfeng) Technology Co., Ltd., Ganzhou, China
3 Jiangling Motors Corporation, Ltd., Nanchang, China
* Corresponding Author: Haitao Liu. Email: email ; Xiaojian Wu. Email: email

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.085747

Received 17 May 2026; Accepted 29 June 2026; Published online 29 July 2026

Download PDF

Abstract

Rapid advances in information and automation technologies have accelerated the development of smart manufacturing, thereby heightening the importance of reliable fault diagnosis for mechanical equipment. Although neural network-based algorithms are widely adopted in industrial applications due to their strong feature extraction and classification capabilities, their deployment in safety-critical fields such as aerospace remains limited. This limitation mainly arises from poor model interpretability and a heavy reliance on large-scale labeled training data. To address these challenges, this paper proposes an interpretable neural network framework that integrates discrete wavelet transform (DWT) with neural networks. Specifically, discrete wavelet filters are embedded into convolutional kernels to construct a novel convolutional layer capable of performing time-frequency transformation, in which the filter coefficients are learnable and a learnable thresholding mechanism is introduced for adaptive denoising. For fault identification, both local and global features extracted from the wavelet decomposition layers are organized into an anomaly detection feature matrix and subsequently classified using a support vector machine. To further improve diagnostic performance under strong interference and complex operating conditions, a novel sparsity-based measurement method is incorporated during feature matrix construction, significantly enhancing the extraction of discriminative signal features from complex signals. The proposed method is validated on an open-source mechanical fault diagnosis dataset, demonstrating superior diagnostic accuracy as well as strong interpretability. Notably, the model is trained exclusively using normal operating data without any labeled fault samples, thereby enabling an unsupervised fault diagnosis framework and effectively alleviating the challenge of fault data scarcity.