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Mathematics
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Advances in Statistical Process Monitoring and Wavelet Analysis
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Advances in Statistical Process Monitoring and Wavelet Analysis

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 1501

Special Issue Editors

Dr. Achraf Cohen

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Hal Marcus College of Science and Engineering, The University of West Florida, Pensacola, FL, USA
Interests: statistical process monitoring; wavelets analysis; statistical modeling; predictive modeling; data-driven methods; quality engineering; machine learning applicaitons
Prof. Dr. Yichuan Zhao

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA
Interests: nonparametric statistics; survival analysis; empirical likelihood; biostatistics; Bayesian analysis

Special Issue Information

Dear Colleagues,

Applied mathematics and statistics methods have advanced considerably during the past decades, mainly as a result of the remarkable rise of computing and data abundance. Statistical process monitoring involves collecting data, learning from it, and developing data-driven models for monitoring purposes. Wavelet methods have become standard in applied mathematics and an effective tool for statistical monitoring, including dimension reduction, denoising, feature engineering for machine learning methods, time-frequency analysis, image processing, and signal processing. This Special Issue seeks new techniques and innovative applications in different statistical process monitoring settings, including in the fields of health monitoring, image monitoring, and profile monitoring, to name a few.

Dr. Achraf Cohen
Prof. Dr. Yichuan Zhao
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 process monitoring
  • wavelet analysis
  • control charts
  • machine learning methods

Published Papers (2 papers)

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Research

12 pages, 270 KiB  
Article
Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes
by Lei Qiao and Bing Wang
Mathematics 2024, 12(10), 1473; https://doi.org/10.3390/math12101473 - 9 May 2024
Viewed by 348
Abstract
In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic [...] Read more.
In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic to construct the nonparametric Multivariate Cumulative Sum multi-chart, under the assumption that there is prior information about the abrupt changes. Through theoretical and numerical analysis, we show that the proposed control chart is more effective compared to other existing control charts. The good monitoring effect of this method demonstrates a strong potential for application. Full article
(This article belongs to the Special Issue Advances in Statistical Process Monitoring and Wavelet Analysis)
16 pages, 1986 KiB  
Article
Unknown Health States Recognition with Collective-Decision-Based Deep Learning Networks in Predictive Maintenance Applications
by Chuyue Lou and Mohamed Amine Atoui
Mathematics 2024, 12(1), 89; https://doi.org/10.3390/math12010089 - 26 Dec 2023
Viewed by 847
Abstract
At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) [...] Read more.
At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) can learn effective representations of health states from industrial data. Many developed CNN-based schemes, such as advanced CNNs that introduce residual learning and multi-scale learning, have shown good performance in health states recognition tasks under the assumption that all the classes are known. However, these schemes have no ability to deal with new abnormal samples that belong to state classes not part of the training set. In this paper, a collective decision framework for different CNNs is proposed. It is based on a one-vs.-rest network (OVRN) to simultaneously achieve classification of known and unknown health states. OVRNs learn class-specific discriminative features and enhance the ability to reject new abnormal samples incorporated to different CNNs. According to the validation results on the public dataset of the Tennessee Eastman process (TEP), the proposed CNN-based decision schemes incorporating an OVRN have outstanding recognition ability for samples of unknown heath states while maintaining satisfactory accuracy on known states. The results show that the new DL framework outperforms state-of-the-art CNNs, and the one based on residual and multi-scale learning has the best overall performance. Full article
(This article belongs to the Special Issue Advances in Statistical Process Monitoring and Wavelet Analysis)
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