A new possibilistic reliability index definition

In this work, a new and efficient definition for a reliability index is explored for real structural engineering problems. The main innovative aspect is that it is based on a possibilistic criteria instead of a probabilistic one. Its definition deals with engineering cases where uncertain parameters of basic structural reliability problems can be operatively treated as fuzzy variables. A fuzzy-based version of classic Cornell proposed reliability index is discussed. Consequently, differences and advantages with respect to other non-probabilistic reliability measures reported in literature are critically analyzed with reference to well-specified criterions. Finally, two numerical examples are illustrated. The first, in the framework of the materials strength problem, is a simple comparison between these fuzzy reliability indicators, and is developed to clarify the applicability of our proposal. Subsequently, another more realistic numerical example is proposed; it is developed to appreciate its effectiveness in reliability assessment of complex structural systems.

[1]  James J. Buckley,et al.  Fuzzy Probabilities : New Approach and Applications , 2005 .

[2]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[3]  Giuseppe Quaranta,et al.  Fuzzy Time-Dependent Reliability Analysis of RC Beams Subject to Pitting Corrosion , 2008 .

[4]  C A Cornell,et al.  A PROBABILITY BASED STRUCTURAL CODE , 1969 .

[5]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[6]  Wolfgang Graf,et al.  Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness , 2006 .

[7]  Achintya Haldar,et al.  A random-fuzzy analysis of existing structures , 1992 .

[8]  G. Klir.  Uncertainty and Information: Foundations of Generalized Information Theory , 2005 .

[9]  Marco Savoia,et al.  Structural reliability analysis through fuzzy number approach, with application to stability , 2002 .

[10]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[11]  R. Langley.  UNIFIED APPROACH TO PROBABILISTIC AND POSSIBILISTIC ANALYSIS OF UNCERTAIN SYSTEMS , 2000 .

[12]  Giuseppe Quaranta,et al.  Fuzzy-based robust structural optimization , 2008 .

[13]  Subrata Chakraborty,et al.  Probabilistic safety analysis of structures under hybrid uncertainty , 2007 .

[14]  Isaac E. Elishakoff,et al.  Fuzzy sets based interpretation of the safety factor , 2006, Fuzzy Sets Syst..

[15]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[16]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[17]  Bilal M. Ayyub,et al.  Uncertainty Modeling and Analysis in Civil Engineering , 1997 .

[18]  Isaac Elishakoff,et al.  Four Alternative Definitions of the Fuzzy Safety Factor , 2006 .

[19]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[20]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..