Multi-objective Optimization of Problems with Epistemic Uncertainty

Limbourg, Philipp

doi:10.1007/978-3-540-31880-4_29

Cited by 60 publications

(52 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a more general tool for uncertainty analysis, evidence theory has also been applied to many areas, including artificial intelligence (particularly in the development of expert systems) (Bae et al, 2004b;Nikolaidis and Haftka, 2001), object detection and approximate reasoning (Lowrance et al, 1986;Perrin et al, 2004;Xu and Smets, 1996;Borotschnig et al, 1999), design optimization (Mourelatos and Zhou, 2005), multidisciplinary design optimization (Agarwal et al, 2004), uncertainty quantification (Bae et al, 2004a;, risk and reliability evaluation (Yang et al, 2011b), remote sensing classification (Lee et al, 1987), pattern recognition and image analysis, decision making (Buckley, 1988;Limbourg, 2005), data fusion (Delmotte and Borne, 1998;Hall and Llinas, 1997;Sun et al, 2008;Yang et al, 2011a) and fault diagnosis (Fan and Zuo, 2006a;Wu et al, 1990). The popularity of evidence theory has risen, however, because evidence theory requires epistemological assumptions that are at odds with those underlying classical and Bayesian probability theories (Fioretti, 2004).…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

“…One is theoretic development related to the fundamentals of reliability theory, e.g. imprecise reliability (Walley, 1991;Utkin and Coolen, 2007;Kozine and Filimonov, 2000) and fuzzy reliability (Cai et al, 1991a;1991b;1993;Huang et al, 2004;; the other is computational (or algorithmic) development in analysis and the design method, e.g., data fusion technology applied to reliability assessment (Hall and Llinas, 1997;Zhang et al, 2010a;Sun et al, 2008;Yang, 2011a; and optimum design methods (Youn and Choi, 2004b;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005a;Limbourg, 2005;Mourelatos and Zhou, 2005;Huang et al, 2006a;2012a). These are illustrated in the sections that follow.…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

“…• Lack of information in input data, small sample size, insufficient information or scarce data (Chen et al, 1999;Mourelatos and Zhou, 2004;Nikolaidis and Haftka, 2001;Huang et al, 2004; • Imprecise data or lack of knowledge Youn and Choi, 2004a;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005b;2006d;Limbourg, 2005;Mourelatos and Zhou, 2005) • Large-scale, complex or costly systems (Zhuang et al, 2000) …”

Section: Ajeasmentioning

confidence: 99%

See 2 more Smart Citations

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

show abstract

Section: General Topics Of Applicationsmentioning

confidence: 99%

Section: General Topics Of Applicationsmentioning

confidence: 99%

Section: Ajeasmentioning

confidence: 99%

See 1 more Smart Citation

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

show abstract

“…In practice, this multi-objective optimization problem has to be faced in a situation in which some constraints and/or the objective functions are affected by uncertainty. To effectively tackle this problem, a number of approaches have been already propounded in the literature considering different framework for uncertainty representation: probability distributions in [12], [17], [24], fuzzy sets in [29] and [42], and plausibility and belief functions in [30]. This problem is not considered in this work.…”

Section: Introductionmentioning

confidence: 99%

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

Baraldi

Compare

Zio

2013

Information Sciences

View full text Add to dashboard Cite

To cite this version:Piero Baraldi, Michele Compare, Enrico Zio. Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer Theory of Evidence. Information Sciences, Elsevier, 2013, 245, pp.112 -131 Abstract: The aim of this work is to assess the performance of a maintenance policy when a stochastic model of the life of the component of interest is known, but relies on parameters that are imprecisely known, and only through information elicited from experts. The case in which the information used to feed the model comes from a single expert has been investigated by the authors in a previous work. This paper deals with the different situation in which a number of experts are involved in the elicitation of the uncertain parameters; in particular, each expert provides an interval he/she believes containing the unknown value of the parameter which he/she is knowledgeable about. The different type of available information calls for the development of a different method to represent and propagate the associated uncertainty. Resorting to Probability theory to address this issue is questionable. Then, a technique based on the Dempster-Shafer Theory of Evidence (DSTE) is embraced in this work, which allows facing a practical case study concerning the check valve of a turbo-pump lubricating system in a Nuclear Power Plant. The output of such method consists of couples of Lower and Upper cumulative distributions describing the uncertainty in the maintenance performance indicators of interest (i.e., unavailability and costs), which accounts for both the aleatory and epistemic contributions.

show abstract

“…There is a plethora of work on optimization under uncertainty, see e.g., [3] and [4]. Pareto analysis and uncertainty is explored in [5], [6] and [7] which all consider intervals on objectives for Pareto dominance. In [5] and [6] probability distributions are used to distinguish designs which have overlapping valuations.…”

Section: Introductionmentioning

confidence: 99%

Pareto Analysis with Uncertainty

Hendriks

Geilen²,

Basten³

2011

2011 IFIP 9th International Conference on Embedded and Ubiquitous Computing

View full text Add to dashboard Cite

Abstract-Pareto analysis is a broadly applicable method to model and analyze tradeoffs in multi-objective optimization problems. The set of Pareto optimal solutions is guaranteed to contain the best solution for any arbitrary cost function or selection procedure. This work introduces a method to explicitly take uncertainty into account during Pareto analysis. A solution is not modeled by a single point in the solution space, but rather by a set of such points. This is useful in settings with much uncertainty, such as during model-based design space exploration for embedded systems. A bounding-box abstraction is introduced as a finite representation of Pareto optimal solutions under uncertainty. It is shown that the set of Pareto optimal solutions in the proposed approach still captures exactly the potentially best solutions for any cost function as well as any way of reducing the amount of uncertainty. During model-based design space exploration, for instance, design and implementation choices that are made during the development process reduce the amount of uncertainty. Steps in such a refinement trajectory can render previously Pareto optimal solutions suboptimal. The presented results provide a way to ensure that early selections in the refinement process remain valid.

show abstract

Multi-objective Optimization of Problems with Epistemic Uncertainty

Cited by 60 publications

References 26 publications

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

Pareto Analysis with Uncertainty

Contact Info

Product

Resources

About