Bernardini, A: Bounding Uncertainty in Civil Engineering
(Sprache: Englisch)
Taking an engineering approach rather than a mathematical one, this book presents the basic ideas and methods of Random Sets in Civil Engineering with the aid of simple worked-out examples and suggested problems. It offers a gentle introduction to the subject.
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Taking an engineering approach rather than a mathematical one, this book presents the basic ideas and methods of Random Sets in Civil Engineering with the aid of simple worked-out examples and suggested problems. It offers a gentle introduction to the subject.
Klappentext zu „Bernardini, A: Bounding Uncertainty in Civil Engineering “
Taking an engineering, rather than a mathematical, approach, Bounding uncertainty in Civil Engineering - Theoretical Background deals with the mathematical theories that use convex sets of probability distributions to describe the input data and/or the final response of systems. The particular point of view of the authors is centered on the applications to civil engineering problems, and the theory of random sets has been adopted as a basic and relatively simple model. However, the authors have tried to elucidate its connections to the more general theory of imprecise probabilities, Choquet capacities, fuzzy sets, p-boxes, convex sets of parametric probability distributions, and approximate reasoning both in one dimension and in several dimensions with associated joint spaces. If choosing the theory of random sets may lead to some loss of generality, it has, on the other hand, allowed for a self-contained selection of the topics and a more unified presentation of the theoreticalcontents and algorithms. With over 80 examples worked out step by step, the book should assist newcomers to the subject (who may otherwise find it difficult to navigate a vast and dispersed literature) in applying the techniques described to their own specific problems.
In engineering contexts, random sets are useful when there is scarce or imprecise information as well as when a model for the engineering system is imprecise (e.g., discretization errors, different competing models, upper and lower bounds in limit analysis). Random sets generalize the concept of random variables from point measures to set measures; equivalently, they embody a convex set of probability measures.
Taking an engineering approach rather than a mathematical one, Random Sets in Civil Engineering is a gentle introduction to the subject that does not require advanced mathematical knowledge. Basic ideas and methods are presented and demonstrated with the aid of simple worked-out examples and suggested problems. Connections are clarified to the more general theory of imprecise probabilities and to other non classical models of uncertainty and approximate reasoning in decision making (e.g., fuzzy sets and evidence theory).
The book serves as a reference for practicing engineers involved in planning, design, construction and management of civil infrastructures, as well as a graduate-level textbook. Readers interested in uncertainty modelling will find general solutions and algorithms, which may also be applied to problems in other fields beyond engineering.
In the second volume of the book (to be planned in the future), the application of the new methods is demonstrated for selected examples with real case-histories from civil engineering: reliability analysis of structures, soil and rock slopes, rock mass characterization, optimization of tunnel reinforcement and lining, evaluation of seismic vulnerability of buildings and damage scenarios in urban areas.
Taking an engineering approach rather than a mathematical one, Random Sets in Civil Engineering is a gentle introduction to the subject that does not require advanced mathematical knowledge. Basic ideas and methods are presented and demonstrated with the aid of simple worked-out examples and suggested problems. Connections are clarified to the more general theory of imprecise probabilities and to other non classical models of uncertainty and approximate reasoning in decision making (e.g., fuzzy sets and evidence theory).
The book serves as a reference for practicing engineers involved in planning, design, construction and management of civil infrastructures, as well as a graduate-level textbook. Readers interested in uncertainty modelling will find general solutions and algorithms, which may also be applied to problems in other fields beyond engineering.
In the second volume of the book (to be planned in the future), the application of the new methods is demonstrated for selected examples with real case-histories from civil engineering: reliability analysis of structures, soil and rock slopes, rock mass characterization, optimization of tunnel reinforcement and lining, evaluation of seismic vulnerability of buildings and damage scenarios in urban areas.
Inhaltsverzeichnis zu „Bernardini, A: Bounding Uncertainty in Civil Engineering “
Motivation.- Review of Theory of Probability and Notation.- Random Sets and Imprecise Probabilities.- Random Relations.- Inclusion and Mapping of Random Sets/Relations.- Approximate Reasoning.
Bibliographische Angaben
- Autoren: Alberto Bernardini , Fulvio Tonon
- 2010, 322 Seiten, Masse: 16,4 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3642111890
- ISBN-13: 9783642111891
- Erscheinungsdatum: 11.03.2010
Sprache:
Englisch
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