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Entropy
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Entropy for Characterization of Uncertainty in Risk and Reliability
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Entropy for Characterization of Uncertainty in Risk and Reliability

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (15 December 2017) | Viewed by 27077

Special Issue Editors

Prof. Dr. Mohammad Modarres

E-Mail
Guest Editor
Center for Risk and Reliability, Clark School of Engineering, University of Maryland, College Park, MD 20742-7531 USA
Interests: probabilistic risk assessment; reliability modeling of complex systems; probabilistic physics of failure; uncertainty analysis; structural integrity and reliability assessment; entropic aging; degradation and damage
Prof. Enrique López Droguett

E-Mail Website
Guest Editor
University of Maryland, College Park, USA;
Mechanical Engineering Department, University of Chile, Santiago, Chile
Interests: reliability of complex systems; deep learning methods in fault diagnosis and prognosis; big data analytics in predictive maintenance; uncertainty analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

When performing a risk or reliability analysis, fundamentally, one is interested in identifying, at some level of confidence, the range of possible and probable values of the unknown of interest, such as the probability of an event or amount of damage and degradation. Usually, the system or process under analysis cannot be characterized completely due to the lack of knowledge concerning the underlying phenomena, which results in epistemic uncertainty.

In the past, uncertainty characterization in risk and reliability has been addressed based on different approaches, such as the frequentist principles, Bayesian thinking, possibilistic theory, and fuzzy logic. In this context, entropy has emerged as a promising approach due to its flexibility in representing uncertainty based on a multitude of evidence types as well as on different domains of application. In particular, information entropy, maximum entropy and thermodynamic entropy have been the focus of recent and current research clearly indicating the enormous scope and potential of entropy based uncertainty characterization and applications to several fields, such as structural integrity, prognostics and health management, reliability and maintenance engineering in the light of big data, and Internet of Things based system health monitoring and management.

This Special Issue invites contributions in the field of "Entropy Based Uncertainty Characterization in Risk and Reliability". The Guest Editors seek submissions with an original perspective and advanced thinking on this topic and related issues. Novel and original papers on theoretical development and their applications should include, but not be limited to, the following:

  • Probabilistic Physics of Failure

  • Structural Integrity

  • Prognostics and Health Management

  • Degradation and Damage Modeling

  • Risk, Reliability and Maintenance Modeling

  • Entropy Theory of Aging

Prof. Dr. Mohammad Modarres
Prof. Enrique López Droguett
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. Entropy is an international peer-reviewed open access monthly 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

  • Entropy, Uncertainty

  • Information Entropy

  • Maximum Entropy

  • Thermodynamic Entropy

  • Damage

  • Degradation

  • Aging

Published Papers (6 papers)

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Research

16 pages, 3845 KiB  
Article
An Entropy Based Bayesian Network Framework for System Health Monitoring
by Tarannom Parhizkar, Samaneh Balali and Ali Mosleh
Entropy 2018, 20(6), 416; https://0-doi-org.brum.beds.ac.uk/10.3390/e20060416 - 30 May 2018
Cited by 19 | Viewed by 3641
Abstract
Oil pipeline network system health monitoring is important primarily due to the high cost of failure consequences. Optimal sensor selection helps provide more effective system health information from the perspective of economic and technical constraints. Optimization models confront different issues. For instance, many [...] Read more.
Oil pipeline network system health monitoring is important primarily due to the high cost of failure consequences. Optimal sensor selection helps provide more effective system health information from the perspective of economic and technical constraints. Optimization models confront different issues. For instance, many oil pipeline system performance models are inherently nonlinear, requiring nonlinear modelling. Optimization also confronts modeling uncertainties. Oil pipeline systems are among the most complicated and uncertain dynamic systems, as they include human elements, complex failure mechanisms, control systems, and most importantly component interactions. In this paper, an entropy-based Bayesian network optimization methodology for sensor selection and placement under uncertainty is developed. Entropy is a commonly used measure of information often been used to characterize uncertainty, particularly to quantify the effectiveness of measured signals of sensors in system health monitoring contexts. The entropy based Bayesian network optimization outlined herein also incorporates the effect that sensor reliability has on system information entropy content, which can also be related to the sensor cost. This approach is developed further by incorporating system information entropy and sensor costs in order to evaluate the performance of sensor combinations. The paper illustrates the approach using a simple oil pipeline network example. The so-called particle swarm optimization algorithm is used to solve the multi-objective optimization model, establishing the Pareto frontier. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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17 pages, 1444 KiB  
Article
Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications
by Isis Didier Lins, Márcio Das Chagas Moura, Enrique López Droguett and Thaís Lima Corrêa
Entropy 2018, 20(4), 223; https://0-doi-org.brum.beds.ac.uk/10.3390/e20040223 - 25 Mar 2018
Cited by 5 | Viewed by 4109
Abstract
The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull [...] Read more.
The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis’ non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters’ estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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26 pages, 1116 KiB  
Article
Notes on Computational Uncertainties in Probabilistic Risk/Safety Assessment
by Antoine Rauzy
Entropy 2018, 20(3), 162; https://0-doi-org.brum.beds.ac.uk/10.3390/e20030162 - 04 Mar 2018
Cited by 12 | Viewed by 3443
Abstract
In this article, we study computational uncertainties in probabilistic risk/safety assessment resulting from the computational complexity of calculations of risk indicators. We argue that the risk analyst faces the fundamental epistemic and aleatory uncertainties of risk assessment with a bounded calculation capacity, and [...] Read more.
In this article, we study computational uncertainties in probabilistic risk/safety assessment resulting from the computational complexity of calculations of risk indicators. We argue that the risk analyst faces the fundamental epistemic and aleatory uncertainties of risk assessment with a bounded calculation capacity, and that this bounded capacity over-determines both the design of models and the decisions that can be made from models. We sketch a taxonomy of modelling technologies and recall the main computational complexity results. Then, based on a review of state of the art assessment algorithms for fault trees and event trees, we make some methodological proposals aiming at drawing conceptual and practical consequences of bounded calculability. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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15 pages, 2060 KiB  
Article
Fully Adaptive Particle Filtering Algorithm for Damage Diagnosis and Prognosis
by Elaheh Rabiei, Enrique Lopez Droguett and Mohammad Modarres
Entropy 2018, 20(2), 100; https://0-doi-org.brum.beds.ac.uk/10.3390/e20020100 - 31 Jan 2018
Cited by 14 | Viewed by 4116
Abstract
A fully adaptive particle filtering algorithm is proposed in this paper which is capable of updating both state process models and measurement models separately and simultaneously. The approach is a significant step toward more realistic online monitoring or tracking damage. The majority of [...] Read more.
A fully adaptive particle filtering algorithm is proposed in this paper which is capable of updating both state process models and measurement models separately and simultaneously. The approach is a significant step toward more realistic online monitoring or tracking damage. The majority of the existing methods for Bayes filtering are based on predefined and fixed state process and measurement models. Simultaneous estimation of both state and model parameters has gained attention in recent literature. Some works have been done on updating the state process model. However, not many studies exist regarding an update of the measurement model. In most of the real-world applications, the correlation between measurements and the hidden state of damage is not defined in advance and, therefore, presuming an offline fixed measurement model is not promising. The proposed approach is based on optimizing relative entropy or Kullback–Leibler divergence through a particle filtering algorithm. The proposed algorithm is successfully applied to a case study of online fatigue damage estimation in composite materials. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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10936 KiB  
Article
Modal Strain Energy-Based Debonding Assessment of Sandwich Panels Using a Linear Approximation with Maximum Entropy
by Viviana Meruane, Matias Lasen, Enrique López Droguett and Alejandro Ortiz-Bernardin
Entropy 2017, 19(11), 619; https://0-doi-org.brum.beds.ac.uk/10.3390/e19110619 - 17 Nov 2017
Cited by 7 | Viewed by 3881
Abstract
Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins and core as a result of [...] Read more.
Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins and core as a result of manufacturing defects or impact loads, degrading their mechanical properties. To improve both the safety and functionality of these systems, structural damage assessment methodologies can be implemented. This article presents a damage assessment algorithm to localize and quantify debonds in sandwich panels. The proposed algorithm uses damage indices derived from the modal strain energy method and a linear approximation with a maximum entropy algorithm. Full-field vibration measurements of the panels were acquired using a high-speed 3D digital image correlation (DIC) system. Since the number of damage indices per panel is too large to be used directly in a regression algorithm, reprocessing of the data using principal component analysis (PCA) and kernel PCA has been performed. The results demonstrate that the proposed methodology accurately identifies debonding in composite panels. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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5869 KiB  
Article
Risk Assessment and Decision-Making under Uncertainty in Tunnel and Underground Engineering
by Yuanpu Xia, Ziming Xiong, Xin Dong and Hao Lu
Entropy 2017, 19(10), 549; https://0-doi-org.brum.beds.ac.uk/10.3390/e19100549 - 18 Oct 2017
Cited by 21 | Viewed by 7193
Abstract
The impact of uncertainty on risk assessment and decision-making is increasingly being prioritized, especially for large geotechnical projects such as tunnels, where uncertainty is often the main source of risk. Epistemic uncertainty, which can be reduced, is the focus of attention. In this [...] Read more.
The impact of uncertainty on risk assessment and decision-making is increasingly being prioritized, especially for large geotechnical projects such as tunnels, where uncertainty is often the main source of risk. Epistemic uncertainty, which can be reduced, is the focus of attention. In this study, the existing entropy-risk decision model is first discussed and analyzed, and its deficiencies are improved upon and overcome. Then, this study addresses the fact that existing studies only consider parameter uncertainty and ignore the influence of the model uncertainty. Here, focus is on the issue of model uncertainty and differences in risk consciousness with different decision-makers. The utility theory is introduced in the model. Finally, a risk decision model is proposed based on the sensitivity analysis and the tolerance cost, which can improve decision-making efficiency. This research can provide guidance or reference for the evaluation and decision-making of complex systems engineering problems, and indicate a direction for further research of risk assessment and decision-making issues. Full article
(This article belongs to the Special Issue Entropy for Characterization of Uncertainty in Risk and Reliability)
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