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Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization

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

Deadline for manuscript submissions: 30 April 2024 | Viewed by 14318

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Special Issue Editors

Prof. Dr. Hongyan Dui

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Guest Editor

School of Management Engineering, Zhengzhou University, Zhengzhou 450001, China
Interests: system resilience; reliability optimization

Dr. Keke Wang

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Guest Editor

School of Management Engineering, Zhengzhou University, Zhengzhou, China
Interests: Energy and power forecasting, power market management, electricity price forecasting
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Prof. Dr. Qianqian Zhao

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School of Management Engineering, Zhengzhou University, Zhengzhou 450001, China
Interests: maintenance strategy; scheduling optimization; redundancy design

Special Issue Information

Dear Colleagues,

You are kindly invited to contribute to this Special Issue, entitled Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization, with an original research article or comprehensive review. Articles concerning theoretical research and applications of stochastic models in resilience management and reliability optimization are solicited. The reliability of critical engineering systems, such as transportation systems, environmental energy, infrastructure, equipment support, nuclear power plants, etc., has been among the top concerns of society. Recently, resilience problems have attracted increasing attention from both academia and industry, given that disruptive events are more frequent globally than ever before. Resilience quantifies the ability of the system to respond, absorb, and adapt to, and recover from, a disruptive event.

Prof. Dr. Hongyan Dui
Prof. Dr. Keke Wang
Prof. Dr. Qianqian 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

complex systems
resilience management
reliability models
transportation system
environmental energy
carbon emissions
electric vehicle
statistics forecasting models
hybrid models
equipment support, infrastructure
nuclear power plants
markov and semi-markov models

Published Papers (11 papers)

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Research

18 pages, 2715 KiB

Open AccessArticle

Start-Up Strategy-Based Resilience Optimization of Onsite Monitoring Systems Containing Multifunctional Sensors

by Jiangbin Zhao, Zaoyan Zhang, Mengtao Liang, Xiangang Cao and Zhiqiang Cai

Mathematics 2023, 11(19), 4023; https://doi.org/10.3390/math11194023 - 22 Sep 2023

Viewed by 660

Abstract

In nonrepairable multifunctional systems, the lost function of a component can be restored by the same function from another component; therefore, the activation mechanism of redundant functions illustrates that multifunctional systems have resilience features. This study evaluates the resilience of multifunctional systems and analyzes the properties of system resilience first. To determine the optimal start-up strategy, a resilience-oriented start-up strategy optimization model for onsite monitoring systems (OMSs) is established to maximize system resilience under a limited budget. In this study, real-time reliability is regarded as the system performance to evaluate the system resilience, and a two-stage local search based genetic algorithm (TLSGA) is proposed to solve the resilience optimization problem. The results of our numerical experiments show that the TLSGA can more effectively solve the problems for OMSs, with high function failure rates and low component failure rates compared with classical genetic algorithms under 48 systems. Moreover, the optimal combinations of unmanned aerial vehicles (UAVs) for an OMS under a limited budget shows that UAVs with a higher carrying capacity should be given priority for selection. Therefore, this study provides an effective solution for determining the optimal start-up strategy to maximize the resilience of OMSs, which is beneficial for OMS configuration. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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16 pages, 3333 KiB

Open AccessArticle

Redundancy-Based Resilience Optimization of Multi-Component Systems

by Hongyan Dui, Xinyue Wang and Haohao Zhou

Mathematics 2023, 11(14), 3151; https://doi.org/10.3390/math11143151 - 18 Jul 2023

Cited by 1 | Viewed by 843

Abstract

Systems are damaged due to various disturbances, and the reliability of the systems is reduced. Measures to improve system resilience need to be studied since many systems still need to operate normally after suffering damage. In this paper, the whole process of the disturbance and recovery of the system is considered, and a resilience optimization model of a multi-component system is proposed. Firstly, a system resilience assessment method is proposed based on system reliability, and the system resilience loss is used as the resilience assessment index. Secondly, two component importance indexes, loss importance and recovery importance, are proposed for the system disturbance phase and recovery phase, respectively. The two importance indexes are weighted to obtain the weighted importance so as to measure the change law of system resilience and determine the influence degrees of components on system reliability. Then, under the constraint of maintenance time, an optimization model is established to determine a redundancy strategy to maximize system resilience. Finally, through an example analysis of a wind turbine system with its main components, it is verified that the redundancy strategy proposed with this method can reduce the loss of system resilience and effectively improve system reliability. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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17 pages, 2014 KiB

Open AccessArticle

Recovery Model and Maintenance Optimization for Urban Road Networks with Congestion

by Hongyan Dui, Yulu Zhang, Songru Zhang and Yun-An Zhang

Mathematics 2023, 11(9), 2004; https://doi.org/10.3390/math11092004 - 23 Apr 2023

Viewed by 999

Abstract

Urban road networks have promoted high-quality travel for residents by increasing connectivity and intelligence. But road congestion has not been effectively alleviated, causing a loss of time and energy. At present, the recovery of urban road networks mainly considers removing the failed edges. Considering the recovery cost and time, it is important to take active maintenance behavior to restore these networks. One of the key problems is dispatching traffic workers reasonably to achieve timely maintenance. In this paper, a flow-distribution-based process and execution (FD-PE) model is established for solving congestion. The maintenance centers (MC) study the reasons for and spread of congestion by edge flow. Based on the genetic algorithm (GA), two models of maintenance for urban road networks are developed, which include a single MC-centered dispatching plan and the co-scheduling of MCs. Both models aim at minimizing recovery time and allocating maintenance resources. The road network in Zhengzhou is borrowed as a case to explain the feasibility of the proposed models. The results show that on the premise of dividing network regions, it is reasonable to take a single MC to recover congestion. Compared with a single MC, the co-scheduling of MCs may save more time. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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16 pages, 3032 KiB

Open AccessArticle

Reliability Analysis of the Multi-State k-out-of-n: F Systems with Multiple Operation Mechanisms

by Yanbo Song and Xiaoyue Wang

Mathematics 2022, 10(23), 4615; https://doi.org/10.3390/math10234615 - 05 Dec 2022

Cited by 10 | Viewed by 1291

Abstract

Modern engineering systems are designed and utilized to realize complicated functions, and their operation mechanisms are becoming more complex. Nevertheless, prior related research mainly focused on the reliability evaluations of the systems with a single operation mechanism, which are not appropriate to depict the operation process of systems with multiple operation mechanisms. Faced with the research gaps and practical needs, this paper establishes a new reliability model for the multi-state k-out-of-n: F system composed of n subsystems, which runs under multiple interactive operation mechanisms, including performance sharing, balanced requirement, and protection strategy. The units in each subsystem can share the performance via a common bus, with the purpose of regulating the performance of all equal units. A new triggering criterion of the protection device in each subsystem is proposed based on the total performance of the units. Due to the protection from the device, the degradation rate of the units between two adjacent states decreases to a lower rate. Each subsystem breaks down when the total performance of the units reaches a critical value. According to the number of failed subsystems, the state of the entire system can be divided into multiple states. The Markov process imbedding method combined with the finite Markov chain imbedding approach is developed to obtain the probabilistic indexes of each subsystem and the entire system. The applicability of the proposed model and the effectiveness of the method can be sufficiently demonstrated by illustrative examples and sensitivity analyses. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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15 pages, 1286 KiB

Open AccessArticle

Reliability Analysis and Redundancy Optimization of a Command Post Phased-Mission System

by Hongyan Dui, Huiting Xu and Yun-An Zhang

Mathematics 2022, 10(22), 4180; https://doi.org/10.3390/math10224180 - 09 Nov 2022

Cited by 3 | Viewed by 1091

Abstract

This paper divides the execution process of the command post system into four stages: information acquisition, information processing, decision control and response execution. It combines multilayer complex networks with a phased-mission system. Most studies have only evaluated the reliability of phased-mission systems. This paper evaluates and optimizes the reliability of a phased-mission system. In order to improve the mission success rate and maximize the reliability of a command post system, this paper provides a multitasking node criticality index, and the index is used to identify the key nodes in the command post’s four-stage network Then, the hot backup system of the node is selected to determine the redundant structure of the key node. Under the constraints of the operation and maintenance costs of key nodes, with the goal of maximizing the reliability of the information processing network layer, the multitask redundancy optimization model of each stage is established. Finally, the reliability of the missions before and after redundancy optimization is compared, using the case analysis of the four-layer network to verify the effectiveness of the proposed model. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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22 pages, 2214 KiB

Open AccessArticle

Resilience-Based Surrogate Robustness Measure and Optimization Method for Robust Job-Shop Scheduling

by Shichang Xiao, Zigao Wu and Hongyan Dui

Mathematics 2022, 10(21), 4048; https://doi.org/10.3390/math10214048 - 31 Oct 2022

Cited by 2 | Viewed by 1038

Abstract

This paper addresses the robust job-shop scheduling problems (RJSSP) with stochastic deteriorating processing times by considering the resilience of the production schedule. To deal with the disturbances caused by the processing time variations, the expected deviation between the realized makespan and the initial makespan is adopted to measure the robustness of a schedule. A surrogate model for robust scheduling is proposed, which can optimize both the schedule performance and robustness of RJSSP. Specifically, the computational burden of simulation is considered a deficiency for robustness evaluation under the disturbance of stochastic processing times. Therefore, a resilience-based surrogate robustness measure (SRM-R) is provided for the robustness estimation in the surrogate model. The proposed SRM-R considers the production resilience and can utilize the available information on stochastic deteriorating processing times and slack times in the schedule structure by analyzing the disturbance propagation of the correlated operations in the schedule. Finally, a multi-objective hybrid estimation of distribution algorithm is employed to obtain the Pareto optimal solutions of RJSSP. The simulation experiment results show that the presented SRM-R is effective and can provide the Pareto solutions with a lower computational burden. Furthermore, an RJSSP case derived from the manufacturing environment demonstrates that the proposed approach can generate satisfactory robust solutions with significantly improved computational efficiency. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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18 pages, 1898 KiB

Open AccessFeature PaperArticle

Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks

by Yaguang Wu and Qingan Qiu

Mathematics 2022, 10(15), 2732; https://doi.org/10.3390/math10152732 - 02 Aug 2022

Cited by 2 | Viewed by 940

Abstract

Safety-critical systems are commonly required to complete specific missions in shock environments, and their failures may lead to severe economic losses and significant safety hazards. To enhance system reliability, protective devices are commonly equipped to resist external shocks. The existing literature focuses mainly on the maintenance policy of safety-critical systems, ignoring the system reliability analysis considering the effect of protective devices and the self-exciting mechanism of shocks. This paper considers multi-state systems equipped with a protective device in shock environments where valid shocks and invalid shocks occur stochastically. The system state degenerates due to valid shocks or the self-exciting behavior of invalid shocks. The self-exciting mechanism is triggered when the number of cumulative or consecutive invalid shocks suffered by the system exceeds a certain threshold, leading the system to a worse state. The protective device can be triggered to protect the system from the damage of external shocks when the state is worse than a predetermined threshold. The protective effect is characterized by reducing the probability of valid shocks. A finite Markov chain embedding approach is used to evaluate the system reliability index. In addition, an optimization model is constructed to determine the optimal triggering threshold of the protective device. The numerical results indicate that protective devices can significantly improve the reliability of the system and incorporating the self-exciting mechanism of shocks into reliability modeling contributes to accurate reliability evaluation. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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19 pages, 1816 KiB

Open AccessArticle

Probabilistic Analysis of a Marine Ecological System with Intense Variability

by Yassine Sabbar, Asad Khan and Anwarud Din

Mathematics 2022, 10(13), 2262; https://doi.org/10.3390/math10132262 - 28 Jun 2022

Cited by 9 | Viewed by 1356

Abstract

This work seeks to simulate and examine the complex character of marine predation. By taking into account the interaction between phytoplankton and zooplankton, we present a sophisticated mathematical system with a general functional response describing the ecological competition. This system is disturbed by a novel category of perturbations in the hybrid form which simulates certain unstable climatic and environmental variations. We merge between the higher-order white noise and quadratic jumps to offer an excellent overview of the complexity induced in the ecosystem. Analytically, we offer a surrogate framework to get the sharp sill between stationarity and zooplankton eradication. Our analysis enriches and improves many works by proposing an unfamiliar form of perturbation and unifying the criteria of said asymptotic characteristics. Numerically, we probe the rigor of our sill in a non-standard case: cubic white noise and quadratic leaps. We demonstrate that the increased order of perturbation has a significant effect on the zooplankton living time. This result shows that the sources of intricate fluctuations carry out an active role in the transient dynamics of marine ecological systems. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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16 pages, 1026 KiB

Open AccessArticle

A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles

by Lijun Shang, Yongjun Du, Cang Wu and Chengye Ma

Mathematics 2022, 10(13), 2225; https://doi.org/10.3390/math10132225 - 25 Jun 2022

Cited by 5 | Viewed by 955

Abstract

A monitoring system (MS) has been used to monitor products’ job cycles. It is indicated that by incorporating the job cycle into the product’s life cycle, warrantors can devise novel warranty models and consumers can define and model random maintenances sustaining the reliability of the product through warranty. In this study, by incorporating limited job cycles and a refund into the traditional free repair warranty, a two-dimensional free repair warranty with a refund (2DFRW-R) is devised for guaranteeing the product reliability to consumers. Under the condition that 2DFRW-R is planned to guarantee product reliability, a bivariate random periodic replacement (BRPR) (i.e., a random periodic replacement where the accomplishment of the Nth job cycle and the replacement time T are designed as replacement limits) is modeled to sustain the post-warranty reliability from the point of view of the consumer. From the point of view of the warrantor, the warranty cost related to 2DFRW-R is derived, and the characteristics of 2DFRW-R are explored. From the point of view of consumers, the expected cost rate related to BRPR is constructed, and the existence and uniqueness of the optimal BRPR are summarized as well. By discussing parameters, several special cases are derived. The characteristics of the proposed models are analyzed in numerical examples. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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18 pages, 2691 KiB

Open AccessArticle

An Intelligent Fault Analysis and Diagnosis System for Electromagnet Manufacturing Process Based on Fuzzy Fault Tree and Evidence Theory

by Jihong Pang, Jinkun Dai and Yong Li

Mathematics 2022, 10(9), 1437; https://doi.org/10.3390/math10091437 - 24 Apr 2022

Cited by 6 | Viewed by 1581

Abstract

Because an electromagnet has a complex structure and manufacturing process, it is difficult to analyze the overall failure of the electromagnet. In order to solve this problem, a fault intelligent analysis and diagnosis system based on fuzzy fault tree and evidence theory is proposed in this paper. First, the failure structure and fuzzy fault tree are generated according to the experience. Second, the probability of failure caused by basic events is obtained based on the data statistics of the insufficient holding force of the electromagnet in the past. Then, the probability of the basic events is given by using the synthesis rules of evidence theory. Next, the belief interval of the basic event is set as the fuzzy number, and the intelligent analysis is completed by using the calculated fuzzy importance. Finally, the validity and feasibility of the proposed method is proved by using the failure of insufficient retention force in the electromagnet manufacturing process as an example. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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15 pages, 1496 KiB

Open AccessArticle

Performance Degradation Based on Importance Change and Application in Dissimilar Redundancy Actuation System

by Yadong Zhang, Chao Zhang, Shaoping Wang, Rentong Chen and Mileta M. Tomovic

Mathematics 2022, 10(5), 843; https://doi.org/10.3390/math10050843 - 07 Mar 2022

Cited by 5 | Viewed by 1914

Abstract

The importance measure is a crucial method to identify and evaluate the system weak link. It is widely used in the optimization design and maintenance decision of aviation, aerospace, nuclear energy and other systems. The dissimilar redundancy actuation system (DRAS) is a key aircraft control subsystem which performs aircraft attitude and flight trajectory control. Its performance and reliability directly affect the aircraft flight quality and flight safety. This paper considers the influence of the Birnbaum importance measure (BIM) and integrated importance measure (IIM) on the reliability changes of key components in DRAS. The differences of physical fault characteristics of different components due to performance degradation and power mismatch, are first considered. The reliability of each component in the system is then estimated by assuming that the stochastic degradation process of the DRAS components follows an inverse Gaussian (IG) process. Finally, the weak links of the system are identified using BIM and IIM, so that the resources can be reasonably allocated to the weak links during the maintenance period. The proposed method can provide a technical support for personnel maintenance, in order to improve the system reliability with a minimal lifecycle cost. Full article

(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)

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