Unsupervised Noise-adaptive Unrolled Matching Pursuit Denoising Network for Bearing Fault Diagnosis

doi:10.3901/JME.2025.12.026

Abstract

Abstract: Rolling bearings are important support components that are prone to failures, thus it is an urgent need for their fault diagnosis. However, the interference from noise in the collected bearing vibration signals restricts the improvement of diagnostic accuracy. Aiming at the problems of poor adaptability, low interpretability and supervised training of the denoising methods based on signal processing, deep learning and sparse algorithm unrolling, a DCT-Laplace dictionary is firstly designed to represent the harmonic and impulse components; secondly, a removing impulse range wavelet transform noise estimation method is proposed to determine the standard deviation of the noise; thirdly, the unrolling number of the sparse algorithm unrolling network is adaptively determined by comparing the power of the noise and the reconstructed residuals, then an unsupervised noise-adaptive unrolled matching pursuit unsupervised denoising network based on the sparse algorithm unrolling is proposed; finally, the denoising results are then fed into the multi-layer iterative soft-thresholding algorithm network to realize the fault diagnosis of bearings. The proposed method is applied to two rolling bearing fault diagnosis experiments, and compared with other typical denoising methods. Experiment results show that the proposed method can effectively remove the noise from the signal and retain the fault features, hence improving the accuracy of fault diagnosis under noise.

Key words: sparse representation, algorithm unrolling, signal denoising, explainable network, fault diagnosis

CLC Number:

TH39

QIN Yi, YANG Rui, ZHAO Lijuan, MAO Yongfang. Unsupervised Noise-adaptive Unrolled Matching Pursuit Denoising Network for Bearing Fault Diagnosis[J]. Journal of Mechanical Engineering, 2025, 61(12): 26-38.

References

[1] HE B，QIN Y，Zhang A. Rolling bearing fault diagnosis by using a new index：The compound weighted characteristic energy ratio[J]. IEEE Transactions on Instrumentation and Measurement，2021，70：1-9.
[2] 李秋泽，谌亮，徐建新，等. 高速动车组用滚动轴承失效模式及对策展望[J]. 轴承，2024(3)：1-8. LI Qiuze，CHEN Liang，XU Jiangxin，et al. Failure modes and countermeasures of rolling bearings for high-speed EMUs[J]. Bearing，2024(3)：1-8.
[3] 孙灿飞，黄林然，沈勇. 复杂工况下的直升机行星传动轮系故障诊断[J]. 航空学报，2022，43(8)：103-111. SUN Canfei，HUANG Linran，SHENG Yong. Fault diagnosis of helicopter planetary drive gear train under complex working conditions[J]. Journal of Aeronautics and Astronautics，2022，43(8)：103-111.
[4] 邓林峰，王琦，郑玉巧. 基于改进残差网络的风电轴承故障迁移诊断方法[J]. 振动工程学报，2024，37(2)：356-364. DENG Linfeng，WANG Qi，ZHENG Yuqiao. Fault migration diagnosis method for wind power bearings based on improved residual network[J]. Journal of Vibration Engineering，2024，37(2)：356-364.
[5] 邵海东，肖一鸣，颜深. 仿真数据驱动的改进无监督域适应轴承故障诊断[J]. 机械工程学报，2023，59(3)：76-85. SHAO Haidong，XIAO Yiming，YAN Shen. Simulation data-driven enhanced unsupervised domain adaptation for bearing fault diagnosis[J]. Journal of Mechanical Engineering，2023，59(3)：76-85.
[6] Iunusova E，Gonzalez M K，Szipka K，et al. Early fault diagnosis in rolling element bearings：Comparative analysis of a knowledge-based and a data-driven approach[J]. Journal of Intelligent Manufacturing，2024，35：2327-2347.
[7] Wu H，Li J，Zhang Q，et al. Intelligent fault diagnosis of rolling bearings under varying operating conditions based on domain-adversarial neural network and attention mechanism[J]. ISA Transactions，2022，130：477-489.
[8] Zhou J，Wang S，Tong C，et al. Weighted basis pursuit denoising algorithm and its application in gear fault diagnosis[C]// Measurement & Data Analytics in the era of Artificial Intelligence (ICSMD)，proceedings of the 2021 International Conference on Sensing，Oct 21-23，2021，Nanjing，China：IEEE，2021：1-5.
[9] Ismail M T，Mamat S S，Hamzah F M，et al. Forecasting performance of denoising signal by wavelet and fourier transforms using SARIMA model[J]. AlP Conference Proceedings，2014，1605(1)：961-966.
[10] Song D，Baek A M C，Kim N. Forecasting stock market indices using padding-based fourier transform denoising and time series deep learning models[J]. IEEE Access，2021，9：83786-83796.
[11] Liu C，Zhang L. A novel denoising algorithm based on wavelet and non-local moment mean filtering[J]. Pattern Recognition，2023，122：108363.
[12] Nigam H K，Srivastava H M. Filtering of audio signals using discrete wavelet transforms[J]. Mathematics，2023，11(19)：4117.
[13] Mohguen W，Bekka R E. EMD-based denoising by customized thresholding[C]// Automation and Diagnosis (ICCAD)，proceedings of the 2017 International Conference on Control，Jan 19-21，2017，Hammamet，Tunisia：IEEE，2017：19-23.
[14] Koppolu P K，Chemmangat K. Automatic selection of IMFs to denoise the sEMG signals using EMD[J]. Journal of Electromyography and Kinesiology，2023，73：102834.
[15] Liu R，Shu M，Chen C. ECG signal denoising and reconstruction based on basis pursuit[J] Applied Sciences，2021，11(4)：1591.
[16] Han H，Wang H，Liu Z，et al. Intelligent vibration signal denoising method based on non-local fully convolutional neural network for rolling bearings[J]. ISA Transactions，2022，122：13-23.
[17] Ai T，Liu Z，Wang H，et al. Robust vibration signal denoising and diagnosis using encoder-decoder networks with cross-layer residual connection[C]// Proceedings of the 2021 Global Reliability and Prognostics and Health Management (PHM-Nanjing)，Oct 15-17，2021，Nanjing，China：IEEE，2021：1-5.
[18] 董绍江，裴雪武，吴文亮，等. 基于多层降噪技术及改进卷积神经网络的滚动轴承故障诊断方法[J]. 机械工程学报，2021，57(1)：148-156. DONG Shaojiang，PEI Xuewu，WU Wenliang，et al. Fault diagnosis method for rolling bearings based on multilayer noise reduction technology and improved convolutional neural network[J]. Journal of Mechanical Engineering，2021，57(1)：148-156.
[19] Buhrmester V，Munch D，Arens M. Analysis of explainers of black box deep neural networks for computer vision：A survey[J]. Machine Learning and Knowledge Extraction，2021，3(4)：966-989.
[20] Khatib R，Simon D，Elad M. Learned greedy method (LGM)：A novel neural architecture for sparse coding and beyond[J]. Journal of Visual Communication and Image Representation，2021，77：103095.
[21] Simon D，Elad M. Rethinking the CSC model for natural images[C]// Proceedings of the 33rd International Conference on Neural Information Processing Systems，Dec 8-14，2019，Vancouver，Canada：Curran Associates Inc，2019：2274-2284.
[22] Janjušević N，Khalilian-Gourtani A，Wang Y. CDLNet：noise-adaptive convolutional dictionary learning network for blind denoising and demosaicing[J]. IEEE Open Journal of Signal Processing，2022，3：196-211.
[23] Qin Y，Yang R，He B，et al. Multi-layer convolutional dictionary learning network for signal denoising and its application to explainable rolling bearing fault diagnosis[J]. ISA Transactions，2024，147：55-70.
[24] Ahmed N，Natarajan T，Rao K R. Discrete cosine transform[J]. IEEE Transactions on Computers，1974，C-23(1)：90-93.
[25] Deng F，Qiang Y，Yang S，et al. Sparse representation of parametric dictionary based on fault impact matching for wheelset bearing fault diagnosis[J]. ISA Transactions，2021，110：368-378.
[26] Donoho D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory，1995，41(3)：613-627.
[27] Donoho D L，JOHNSTONE I M. Adapting to unknown smoothness via wavelet shrinkage[J]. Journal of the American Statistical Association，1995，90：1200-1224.
[28] Ding F，Cao T. Application of daubechies wavelet transform in the estimation of standard deviation of white noise[C]// Proceedings of the 2011 Second International Conference on Digital Manufacturing & Automation，Aug 5-7，2011，Zhangjiajie，China：IEEE，2011：212-215.
[29] Jeong B G，Kim B C，Moon Y H，et al. Simplified noise model parameter estimation for signal-dependent noise[J]. Signal Processing，2014，96：266-73.
[30] Zhang Z，Ye Y，Luo B，et al. Investigation of microseismic signal denoising using an improved wavelet adaptive thresholding method[J]. Scientific Reports，2022，12(1)：22186.
[31] Li X，Jin J，Shen Y，et al. Noise level estimation method with application to EMD-based signal denoising[J]. Journal of Systems Engineering and Electronics，2016，27(4)：763-771.
[32] Mallat S G，Zhifeng Z. Matching pursuits with time-frequency dictionaries[J]. IEEE Transactions on Signal Processing，1993，41(12)：3397-3415.
[33] Cui L，Wang J，Lee S. Matching pursuit of an adaptive impulse dictionary for bearing fault diagnosis[J]. Journal of Sound and Vibration，2014，333(10)：2840-2862.
[34] Cui L，Gong X，Zhang J，et al. Double-dictionary matching pursuit for fault extent evaluation of rolling bearing based on the Lempel-Ziv complexity[J]. Journal of Sound and Vibration，2016，385：372-388.
[35] Li K，Ping X L，Wang H Q，et al. Sequential fuzzy diagnosis method for motor roller bearing in variable operating conditions based on vibration analysis[J]. Sensors，2013，13(6)：8013-8041.
[36] Qin Y，Yang R，Shi H，et al. Adaptive fast chirplet transform and its application into rolling bearing fault diagnosis under time-varying speed condition[J]. IEEE Transactions on Instrumentation and Measurement，2023，72：1-12.