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Mathematics
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Mathematical Modelling and Computational Methods in Reliability Engineering
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Mathematical Modelling and Computational Methods in Reliability Engineering

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

Deadline for manuscript submissions: closed (30 June 2024) | Viewed by 4332

Special Issue Editors

Dr. Sinan Xiao

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
Interests: uncertainty quantification; reliability analysis; sensitivity analysis; Bayesian inference; machine learning
Dr. Pan Wang

E-Mail Website
Guest Editor
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
Interests: reliability; uncertainty-based optimization; surrogate models; uncertainty quantification

Special Issue Information

Dear Colleagues,

Complex engineering systems, such as aerospace and transportation systems, nuclear power plants, mechanical structures, and constructed infrastructures, can be impacted by various types of uncertainties. These uncertainties can affect the system's performance, resulting in inadequate fulfilment of its intended function. Thus, reliability has become an important issue. To design a reliable engineering system, it is important to understand its failure mechanism, estimate the reliability (or failure probability), analyze the effects of different uncertain factors on system failure.

This Special Issue titled "Mathematical Modelling and Computational Methods in Reliability Engineering" aims to present recent research about theoretical and numerical studies in reliability engineering. Potential topics include but are not limited to: (1) modelling of failure mechanism, (2) computational methods for failure probability estimation, (3) reliability sensitivity analysis, (4) reliability-based design and optimization, (5) Bayesian statistics in reliability engineering, (6) applications with reliability engineering problems. Original research articles and comprehensive reviews are highly welcome.

Dr. Sinan Xiao
Dr. Pan Wang
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

  • complex systems
  • failure mechanism
  • mathematical modeling
  • reliability models
  • failure probability
  • sensitivity analysis
  • uncertainty quantification
  • reliability design
  • optimization
  • statistical methods
  • machine learning

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Published Papers (4 papers)

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Research

26 pages, 1785 KiB  
Article
Development of a Mathematical Model of Operation Reliability of Mine Hoisting Plants
by Pavel V. Shishkin, Boris V. Malozyomov, Nikita V. Martyushev, Svetlana N. Sorokova, Egor A. Efremenkov, Denis V. Valuev and Mengxu Qi
Mathematics 2024, 12(12), 1843; https://doi.org/10.3390/math12121843 - 13 Jun 2024
Viewed by 811
Abstract
The work analyzes the performance assurance of mine hoisting machines, including the problem of the quality of performance of the functions. The quality of functioning allows evaluation of a set of properties of the process of lifting loads, designed to meet the given [...] Read more.
The work analyzes the performance assurance of mine hoisting machines, including the problem of the quality of performance of the functions. The quality of functioning allows evaluation of a set of properties of the process of lifting loads, designed to meet the given requirements in accordance with the purpose and evaluated performance indicators. In this case, the quality of the function depends not only on the elements that worked properly or failed during system functioning but also on the moments involving certain changes in the states of the system. The considered system of power supply of mine hoisting installations is rather complex with respect to reliability. The proposed approach allows this rather complex system to lead in terms of the form of a serial connection of elements, allowing for determining the influence of the functioning of its subsystems and electrical equipment on the technological process of cargo lifting in a coal mine. The presented mathematical concept of increasing the reliability and failure-free operation of mine hoisting plants with the help of the developed mathematical model of the mine hoisting plant allowed studying the reliability indicators of the hoisting plant operation and reserving the equipment most effectively to increase reliability. The determination of coupling coefficients in this study made it possible to analyze the impact of the reliability of electrical equipment and power supply systems on the operation of technological machines to improve the reliability of mining equipment and the efficiency of technical systems of mining equipment. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Reliability Engineering)
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22 pages, 4309 KiB  
Article
Reliability and Residual Life of Cold Standby Systems
by Longlong Liu, Xiaochuan Ai and Jun Wu
Mathematics 2024, 12(10), 1540; https://doi.org/10.3390/math12101540 - 15 May 2024
Viewed by 1216
Abstract
In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study [...] Read more.
In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Reliability Engineering)
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27 pages, 9704 KiB  
Article
RUL Prediction for Piezoelectric Vibration Sensors Based on Digital-Twin and LSTM Network
by Chengcheng Fu, Cheng Gao and Weifang Zhang
Mathematics 2024, 12(8), 1229; https://doi.org/10.3390/math12081229 - 19 Apr 2024
Cited by 1 | Viewed by 868
Abstract
Piezoelectric vibration sensors (PVSs) are widely used in high-temperature environments, such as vibration measurements in aero-engines, because of their high accuracy, small size, and high temperature resistance. Accurate prediction of its RUL (Remaining Useful Life) is essential for applying and maintaining PVSs. Based [...] Read more.
Piezoelectric vibration sensors (PVSs) are widely used in high-temperature environments, such as vibration measurements in aero-engines, because of their high accuracy, small size, and high temperature resistance. Accurate prediction of its RUL (Remaining Useful Life) is essential for applying and maintaining PVSs. Based on PVSs’ characteristics and main failure modes, this work combines the Digital-Twin (DT) and Long Short-Term Memory (LSTM) networks to predict the RUL of PVSs. In this framework, DT can provide rich data collection, analysis, and simulation capabilities, which have advantages in RUL prediction, and LSTM network has good results in predicting time sequence data. The proposed method exploits the advantages of those techniques in feature data collection, sample optimization, and RUL multiclassification. To verify the prediction of this method, a DT platform is established to conduct PVS degradation tests, which generates sample datasets, then the LSTM network is trained and validated. It has been proved that prediction accuracy is more than 99.7%, and training time is within 94 s. Based on this network, the RUL of PVSs is predicted using different test samples. The results show that the method performed well in prediction accuracy, sample data utilization, and compatibility. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Reliability Engineering)
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19 pages, 2855 KiB  
Article
Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling
by Marie Chiron, Jérôme Morio and Sylvain Dubreuil
Mathematics 2023, 11(20), 4357; https://doi.org/10.3390/math11204357 - 20 Oct 2023
Cited by 2 | Viewed by 863
Abstract
Evaluating the failure probability of a system is essential in order to assess its reliability. This probability may significantly depend on deterministic parameters such as distribution parameters or design parameters. The sensitivity of the failure probability with regard to these parameters is then [...] Read more.
Evaluating the failure probability of a system is essential in order to assess its reliability. This probability may significantly depend on deterministic parameters such as distribution parameters or design parameters. The sensitivity of the failure probability with regard to these parameters is then critical for the reliability analysis of the system or in reliability-based design optimization. Here, we introduce a new approach to estimate the failure probability derivatives with respect to deterministic inputs, where the bias can be controlled and the simulation budget is kept low. The sensitivity estimate is obtained as a byproduct of a heteroscedastic polynomial regression with a database built with simulation methods. The polynomial comes from a Taylor series expansion of the approximated sensitivity domain integral obtained with the Weak approach. This new methodology is applied to two engineering use cases with the importance sampling strategy. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computational Methods in Reliability Engineering)
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