{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T17:29:17Z","timestamp":1764350957492,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T00:00:00Z","timestamp":1713484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52275085","2024GX-YBXM-265","300102252201"],"award-info":[{"award-number":["52275085","2024GX-YBXM-265","300102252201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015401","name":"Key Research and Development Program of Shaanxi","doi-asserted-by":"publisher","award":["52275085","2024GX-YBXM-265","300102252201"],"award-info":[{"award-number":["52275085","2024GX-YBXM-265","300102252201"]}],"id":[{"id":"10.13039\/501100015401","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["52275085","2024GX-YBXM-265","300102252201"],"award-info":[{"award-number":["52275085","2024GX-YBXM-265","300102252201"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Impulsive blind deconvolution (IBD) is a popular method to recover impulsive sources for bearing fault diagnosis. Its underpinnings are in the design of objective functions based on prior knowledge of impulsive sources and a transfer function to describe transmission path influences. However, popular objective functions cannot retain waveform impulsiveness and periodicity cyclostationarity simultaneously, and the single convolution operation of IBD methods is insufficient to describe transmission paths composed of multiple linear and nonlinear units. Inspired by the MaxPooling period modulation intensity (MPMI) and convolutional sparse learning (CSL), an adaptive multi-D-norm-driven sparse unfolding deconvolution network (AMD-SUDN) is proposed in this paper. The core strategy is that one target vector with simultaneous impulsiveness and cyclostationarity is constructed automatically through the MPMI; then, this vector is substituted into the multi D-norm to design objective functions. Moreover, an iterative soft threshold algorithm (ISTA) for the CSL model is derived, and its iterative steps are unfolded into one deconvolution network. The algorithm\u2019s performance and the hyperparameter configuration are investigated by a set of numerical simulations. Finally, the proposed AMD-SUDN is applied to detect the impulsive features of bearing faults. All comparative results verify that the proposed AMD-SUDN achieves a better deconvolution accuracy than state-of-the-art IBD methods.<\/jats:p>","DOI":"10.3390\/s24082624","type":"journal-article","created":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T10:53:17Z","timestamp":1713523997000},"page":"2624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Adaptive Multi-D-Norm-Driven Sparse Unfolding Deconvolutional Network for Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"24","author":[{"given":"Jianbo","family":"Lin","sequence":"first","affiliation":[{"name":"School of Construction Machinery, Chang\u2019an University, Xi\u2019an 710064, China"},{"name":"Key Laboratory of Road Construction Technology and Equipment of MOE, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2253-8605","authenticated-orcid":false,"given":"Han","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Construction Machinery, Chang\u2019an University, Xi\u2019an 710064, China"},{"name":"Key Laboratory of Road Construction Technology and Equipment of MOE, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Construction Machinery, Chang\u2019an University, Xi\u2019an 710064, China"},{"name":"Key Laboratory of Road Construction Technology and Equipment of MOE, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaohui","family":"Du","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108202","DOI":"10.1016\/j.ymssp.2021.108202","article-title":"A review on the application of blind deconvolution in machinery fault diagnosis","volume":"163","author":"Miao","year":"2022","journal-title":"Mech. 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