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

Abstract

The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.

Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

“…Nonetheless, some other design variables may lack sufficient data, which can be estimated by domain experts and regarded as uncertain variables. The structure cannot be simply considered to be a random or uncertain structure model under mixed aleatory and epistemic uncertainties [37]. This section put forward an advanced structural reliability assessment method for this issue depending on chance measure and belief reliability theory.…”

“…Over the last decades, numerous reliability assessment methods based on probability theory have been developed, including first-order reliability method (FORM) [23], second-order fourth moment [29] Monte Carlo simulation (MCS) [24], FORM-sampling simulation method [22], envelope function method [28], response surface method (RSM) [6], and Bayesian networks method [26]. Although these probabilistic methods typically make sense in uncertainty quantification and propagation when the structure is mainly affected by aleatory uncertainty, they do not work well in the scenarios involving great epistemic uncertainty [37]. For example, the distribution of input factors may not be precisely obtained due to insufficient sample data.…”

“…In recent years, chance theory has been successfully used in various fields such as project scheduling [11], uncertain random risk analysis [8], uncertain random programming [25], and systems reliability analysis [31,38]. Especially, a hybrid model of structural reliability analysis based on chance theory was proposed by Zhang [37] in 2019, and a new reliability index was proposed. However, this method has the following disadvantages.…”

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

“…Due to the abovementioned definitions of the soft failure and the hard failure, system failure is the competing result between them. According to the studies about the uncertainty theory–based belief reliability metrics, 22,23,43 at a given time t , the reliability function of the soft failure based on the chance measure can be expressed as …”

Reliability Analysis for Electronic Devices Using Generalized Exponential Distribution

“…Abbasi et al [7] presented the modeling and verification process for the reliability analysis of electrical system components. Zhang et al [8] discussed the hybrid reliability analysis problems when the aleatory and epistemic uncertainties coexist in a structure. Hu and Peng [9] introduced a dynamic model with random and dependent transition probabilities for non-repairable discrete-time multi-state systems.…”