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Mathematics
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Statistical Machine Learning with Applications
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Statistical Machine Learning with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 11776

Special Issue Editors

Dr. Li Yang

E-Mail Website
Guest Editor
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: intelligent maintenance; decision optimization; power system reliability
Special Issues, Collections and Topics in MDPI journals
Dr. Yuchen Li

E-Mail Website
Guest Editor
School of Economics and Management, Beijing University of Technology, Beijing 100124, China
Interests: combinatorial optimization; stochastic programming; intelligent algorithm
Special Issues, Collections and Topics in MDPI journals
Dr. Mukund Nilakantan Janardhanan

E-Mail Website
Guest Editor
School of Engineering, University of Leicester, Leicester LE1 7RH, UK
Interests: evolutionary computation; intelligent algorithms; modelling and optimization of manufacturing systems; robotic assembly line balancing

Special Issue Information

Dear Colleagues,

Recent decades have witnessed the explosive growth of machine learning methodologies powered by continuous advancements in fundamental statistical theories and frontier data science, including big data, cloud computing, and the Internet of Things. Statistical machine learning, as a typical data-driven multidisciplinary technology, focuses mainly on the processing, analysis, and prediction of multi-source data through the formulation and optimization of probabilistic statistical models. To date, such technology has been extensively applied to diverse critical science domains, such as data mining, signal processing, pattern recognition, computer vision, natural language processing, biometrics, quality process control, risk analysis, lifetime diagnosis and prognosis, DNA sequencing, speech/handwriting recognition, and robotics, with tremendous, well-justified achievements.

This Special Issue is devoted to a collection of the latest theoretical advancements and industrial applications with regard to statistical machine learning, covering but not limited to the research topics outlined below:

  • Statistical modeling and inference
  • Analysis and optimization of probabilistic models
  • Processing and analysis of big data
  • Deep learning and its applications
  • Transfer learning and its applications
  • Reinforcement learning and its applications
  • Data-driven uncertainty quantification
  • Evolutionary computation and intelligent algorithms
  • Modeling and monitoring of smart manufacturing systems
  • The Bayesian approach and Bayesian networks
  • The fusion of machine learning and domain knowledge

Dr. Li Yang
Dr. Yuchen Li
Dr. Mukund Nilakantan Janardhanan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • statistical inference
  • probabilistic model
  • deep learning
  • neural network
  • reinforcement learning
  • Bayesian approach
  • intelligent optimization

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Published Papers (5 papers)

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Research

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22 pages, 2204 KiB  
Article
Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle
by Lijun Shang, Xiguang Yu, Liying Wang and Yongjun Du
Mathematics 2022, 10(20), 3723; https://doi.org/10.3390/math10203723 - 11 Oct 2022
Cited by 2 | Viewed by 1458
Abstract
Driven by digital technologies, it is possible that high-tech equipment management personnel use monitored job cycles to ensure products’ operation and maintenance over their life cycle. By means of monitored job cycles, this paper designs two categories of random maintenance policies: a two-stage [...] Read more.
Driven by digital technologies, it is possible that high-tech equipment management personnel use monitored job cycles to ensure products’ operation and maintenance over their life cycle. By means of monitored job cycles, this paper designs two categories of random maintenance policies: a two-stage two-dimensional free repair warranty (2DFRW) policy and a random hybrid periodic replacement (RHPR) policy. The 2DFRW policy is performed to ensure the product’s operation and maintenance over the warranty stage. Under such a policy, a product is minimally repaired at each failure, and regions of the second-stage warranty are set to be diverse to remove all inequities produced by limitations of the first-stage warranty. The warranty cost of two-stage 2DFRW is built and discussed. The RHPR policy is modeled to ensure the product’s operation and maintenance over the post-warranty stage. Under this policy, depending on the final expiry of the two-stage 2DFRW, a bivariate random periodic replacement (BRPR) policy and a univariate random periodic replacement (URPR) policy are skillfully used to reduce the maintenance cost over the post-warranty stage and maximally extend the residual useful time of the product through the warranty. The expected cost rate over the product’s operation and maintenance cycle is derived on the basis of renewal rewarded theorem. The optimal RHPR policy is analyzed by minimizing the cost rate. The presented models are numerically analyzed to explore hidden characteristics. Full article
(This article belongs to the Special Issue Statistical Machine Learning with Applications)
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19 pages, 2109 KiB  
Article
An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge
by Lijun Shang, Xiguang Yu, Yongjun Du, Anquan Zou and Qingan Qiu
Mathematics 2022, 10(18), 3229; https://doi.org/10.3390/math10183229 - 6 Sep 2022
Cited by 5 | Viewed by 1418
Abstract
Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random [...] Read more.
Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random working cycle, rebate and charge into warranty theory, a random free repair warranty with rebate and charge (RFRW-RC) is devised to ensure system reliability during the warranty stage. Under RFRW-RC, the rebate removes manufacturers’ responsibility for continuing to ensure system reliability, while the charge is a support where manufacturers continue to ensure system reliability. The warranty cost of RFRW-RC is derived, and a random discrete free repair warranty (RDFRW) is presented by simplifying RFRW-RC. By mixing random age replacement last (RARL) and classic age replacement (CAR), a random hybrid age replacement (RHAR) is designed in order to ensure system reliability during the post-warranty stage. In such an RHAR, RARL is applied to extend the replacement time during the post-warranty stage in order to maximize the remaining life of the system through warranty, and CAR is used to lower the maintenance cost of the system through warranty. The cost rate of RHAR is modeled, and the cost rate of RDFRW is offered as well by discussing parameter values. The decision variable is optimized by minimizing the cost rate model. The properties of the presented models are explored from numerical perspectives. Full article
(This article belongs to the Special Issue Statistical Machine Learning with Applications)
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18 pages, 2213 KiB  
Article
A Bivariate Post-Warranty Maintenance Model for the Product under a 2D Warranty
by Lijun Shang, Guojun Shang and Qingan Qiu
Mathematics 2022, 10(12), 1957; https://doi.org/10.3390/math10121957 - 7 Jun 2022
Cited by 2 | Viewed by 1834
Abstract
In this study, by integrating preventive maintenance (PM) into a two-dimensional warranty region, a two-dimensional warranty with customized PM (2D warranty with customized PM) is proposed from the manufacturer’s perspective to reduce the warranty cost. The warranty cost of a 2D warranty with [...] Read more.
In this study, by integrating preventive maintenance (PM) into a two-dimensional warranty region, a two-dimensional warranty with customized PM (2D warranty with customized PM) is proposed from the manufacturer’s perspective to reduce the warranty cost. The warranty cost of a 2D warranty with customized PM is derived. The manufacturer’s tradeoff between PM cost and minimal repair cost saving is obtained by choosing the proper reliability threshold and the number of customized PMs, and the advantage of a 2D warranty with customized PM is illustrated. Second, by integrating PM into the post-warranty period, a bivariate post-warranty maintenance (BPWM) policy is proposed from the consumer’s perspective to ensure the reliability of the product through the 2D warranty with customized PM. The expected cost rate model of BPWM is derived. Optimal BPWM is obtained in the numerical experiments. It is shown that a 2D warranty with customized PM is beneficial for both the manufacturer and the consumer, since both the manufacturer’s warranty cost and the consumer’s total cost are reduced. Full article
(This article belongs to the Special Issue Statistical Machine Learning with Applications)
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18 pages, 1625 KiB  
Article
Post-Warranty Replacement Models for the Product under a Hybrid Warranty
by Lijun Shang, Guojun Shang, Yongjun Du, Qingan Qiu, Li Yang and Qinglai Dong
Mathematics 2022, 10(10), 1644; https://doi.org/10.3390/math10101644 - 11 May 2022
Cited by 3 | Viewed by 1734
Abstract
In this article, by considering both a limited number of failure replacements and a limited number of random working cycles as warranty terms, a hybrid warranty (HW) is designed from the manufacturer’s point of view to warrant the product that does successive projects [...] Read more.
In this article, by considering both a limited number of failure replacements and a limited number of random working cycles as warranty terms, a hybrid warranty (HW) is designed from the manufacturer’s point of view to warrant the product that does successive projects at random working cycles. The warranty cost produced by HW is derived and analyzed. By defining that HW warrants the product, two types of post-warranty replacement models are investigated from the consumer’s point of view to ensure the reliability of the product through HW, i.e., customized post-warranty replacement and uniform post-warranty replacement. Depreciation expense is integrated into each post-warranty replacement. The expected cost rate model is presented for each post-warranty replacement and some special cases are obtained by setting parameters in the expected cost rate. Finally, sensitivities on both HW and post-warranty replacements are analyzed in numerical experiments. It is shown that when a limited number of failure replacements or/and a limited number of random working cycles are introduced to a warranty, the warranty cost can be reduced; and the performance of the uniform post-warranty replacement is superior to the customized post-warranty replacement. Full article
(This article belongs to the Special Issue Statistical Machine Learning with Applications)
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Review

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30 pages, 4429 KiB  
Review
A Review of Optimization for System Reliability of Microgrid
by Bingyin Lei, Yue Ren, Huiyu Luan, Ruonan Dong, Xiuyuan Wang, Junli Liao, Shu Fang and Kaiye Gao
Mathematics 2023, 11(4), 822; https://doi.org/10.3390/math11040822 - 6 Feb 2023
Cited by 16 | Viewed by 3817
Abstract
Clean and renewable energy is the only way to achieve sustainable energy development, with considerable social and economic benefits. As a key technology for clean and renewable energy, it is very important to research the reliability optimization of microgrids. This paper reviews the [...] Read more.
Clean and renewable energy is the only way to achieve sustainable energy development, with considerable social and economic benefits. As a key technology for clean and renewable energy, it is very important to research the reliability optimization of microgrids. This paper reviews the research progress in microgrid reliability optimization. This paper first classifies and summarizes the existing research on microgrid control strategies and reliability assessment. Then, the system reliability optimization framework is summarized in terms of both microgrid systems and optimization objectives. Next, we summarize the most commonly used optimization algorithms for microgrid reliability for different microgrid systems. Finally, we provide a bibliometric analysis of the literature on the reliability research of microgrids. In addition, we propose some research challenges in the future for the reliability of microgrids. Full article
(This article belongs to the Special Issue Statistical Machine Learning with Applications)
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