Details
| Original language | English |
|---|---|
| Pages (from-to) | 4-29 |
| Number of pages | 26 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 37 |
| Issue number | 1-2 |
| Early online date | 16 Mar 2013 |
| Publication status | Published - May 2013 |
| Externally published | Yes |
Abstract
Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue.
Keywords
- Evidence theory, Fuzzy probabilities, Imprecise probabilities, Probability bounds analysis, Uncertainty modeling
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 37, No. 1-2, 05.2013, p. 4-29.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Imprecise probabilities in engineering analyses
AU - Beer, Michael
AU - Ferson, Scott
AU - Kreinovich, Vladik
N1 - Funding Information: This paper was written with partial support from the National Institutes of Health (SBIR project RC3LM010794), although the opinions herein should not be ascribed to it.
PY - 2013/5
Y1 - 2013/5
N2 - Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue.
AB - Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical differences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved. This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another. This paper was especially prepared for this special issue and reflects, in various ways, the thinking and presentation preferences of the authors, who are also the guest editors for this special issue.
KW - Evidence theory
KW - Fuzzy probabilities
KW - Imprecise probabilities
KW - Probability bounds analysis
KW - Uncertainty modeling
UR - http://www.scopus.com/inward/record.url?scp=84876905886&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2013.01.024
DO - 10.1016/j.ymssp.2013.01.024
M3 - Article
AN - SCOPUS:84876905886
VL - 37
SP - 4
EP - 29
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
IS - 1-2
ER -