Abstract Feature extraction based on sparse representation is widely applied in the field of mechanical fault diagnosis. L1 norm regularization is a classical sparse regularization method, but this method has sparse underestimation for large-value features. A signal sparse representation method based on generalized multivariate logarithmic regularization is proposed in this paper. First, the sparse penalty term in the proposed method is designed according to the minimum convolution and logarithmic function, namely the generalized logarithmic non-convex penalty function. Then, the convexity condition of the objective function is studied to verify the feasibility of the method. The applicability of the method is also improved by analyzing the parameter constraint relation in the objective function. Finally, the sparse optimal solution is obtained by the forward-back splitting algorithm. Experiments show that compared with other non-convex sparse models, the proposed method can solve the problem of sparse underestimation more effectively and improve the reliability of gearbox fault diagnosis.

Na Yin

Dengyun Sun

Zong Meng

Jimeng Li

Lixiao Cao

Fengjie Fan

Measurement Science and Technology

测量科学与技术发表关于新测量技术和相关仪器的文章。描述实验的论文必须代表测量科学或测量技术的进步，而不是已建立的实验技术的应用。考虑到期刊的多学科性质，作者必须对其工作进行介绍，以明确其工作在测量环境中的新颖性、重要性、更广泛的相关性以及与测量科学与技术读者群的相关性。所有提交的文章都应考虑所提供的测量的不确定性、精度和/或准确性。主题范围包括从开始到商业开发的物理、化学、工程以及环境和生命科学中测量的理论、实践和应用。期刊中的出版物应强调报告方法的新颖性，对其进行表征并使用示例或应用程序展示其性能。

The journal "Measurement Science and Technology" publishes research articles on new measurement technologies and related instruments. All experimental papers must demonstrate advancements in measurement science or technology, rather than merely applying established experimental techniques. Given the multidisciplinary nature of the journal, authors are required to clearly articulate the novelty, significance, broader relevance, and connection of their work to the readership of "Measurement Science and Technology". All submitted articles should consider the uncertainty, precision, and/or accuracy of the measurements provided. The scope of the journal includes the theory, practice, and application of measurements in physics, chemistry, engineering, environmental, and life sciences, ranging from fundamental research to commercial development. Publications in the journal should emphasize the novelty of the reported methods and demonstrate their performance through examples or applications.

《Measurement Science and Technology》期刊发表关于新测量技术及相关仪器的研究文章。所有描述实验的论文必须展示测量科学或测量技术的进步，而不仅仅是已建立实验技术的应用。考虑到期刊的多学科性质，作者需清晰阐述其研究在测量领域中的新颖性、重要性及广泛相关性，以及与《Measurement Science and Technology》读者群的关联性。所有提交的文章都应关注所提供测量的不确定性、精度和/或准确性。期刊涵盖的主题范围包括从基础研究到商业开发的物理、化学、工程、环境及生命科学中的测量理论、实践与应用。期刊中的出版物应强调方法的新颖性，并通过示例或应用展示其性能。

Gearbox fault diagnosis based on generalized multivariate logarithmic regularization

Experiments show that compared with other non-convex sparse models, the proposed method can solve the problem of sparse underestimation more effectively and improve the reliability of gearbox fault diagnosis.

Category	Quartile
工程技术	3
工程技术, 工程综合	3
工程技术, 仪器仪表	3

Gearbox fault diagnosis based on generalized multivariate logarithmic regularization

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Category	Quartile
INSTRUMENTS & INSTRUMENTATION	2