Probabilistic safety analysis of structures under hybrid uncertainty

Abstract

SUMMARYThe probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives.

Hybrid reliability analysis for energy-absorbing composite structures based on evidence theory

“…That is to say, the results transformed by Bayes approach embody the maximum uncertainty, which means minimum subjective preference and maximum random. 23,36 Now, in order to prove this point, we make the following analysis.…”

“…The radius t is assumed as epistemic variable and is presented by ET. However, the data are often coming from multiple sources, and we can use evidence combination method as equations (23) to (25). The distributions can be represented by Table 2.…”

“…The basic probability mass associated with conflict K is calculated through equation (23). The BPA function m D ðAÞ is calculated through equation (24).…”

“…According the Dempster evidence combination method, the basic probability mass associated with conflict K and the BPA function m D ðAÞ are calculated through equations (23) and (24), respectively. Thereby, its BPA (c) the evidence combined is shown in Table 2 P f ½SEAðr, tÞ À SEA 0 0 ¼ 48:8568 þ 24:8199r À 15:9791t À 1:0271r 2 þ 1:3201tr À 1:4613t 2 À 60 ð29Þ P f ½P 0 À Pðr, tÞ 0 ¼ 10 À 2:5401r þ 3:6312t þ 0:2403r 2 À 0:2901tr À 0:0501t 2 À 8:7011…”

Reliability analysis of structures based on a probability‐uncertainty hybrid model

“…However, structural problems can be considered as “uncertain” in the absence of the knowledge about the theoretical model due to the parameter uncertainties, experts' judgments, and operational errors . Considering the existence of such uncertainties rather than eliminating them can lead to a more cost effective design . In engineering practice, in addition to randomness which can be obtained through statistical analysis, there are epistemic uncertainty caused by the loss of information, limited knowledge, and inevitable human errors, which are also called the aleatory and epistemic uncertainty.…”