Aviation Risk Analysis: U-bowtie Model Based on Chance Theory

Abstract

Risk analysis is a crucial component in any aviation application. The conventional risk analysis schemes for systems encompassing large amounts of data are based on the probability theory. However, in some practical systems, the components of complex systems may have few or even zero samples, in which case the risk cannot be evaluated simply via statistics. This paper proposes a novel aviation risk analysis scheme based on the chance theory, which is a generation of both probability theory and uncertainty theory. In this paper, a U-bowtie model is first established according to the graphic structure and step-wise analysis process. A risk belief metric is utilized, and the risk variable is modified by a logic algorithm based on the operational law of chance theory. Then, several risk belief formulas are built for different respective system configurations; the risk of output events in the U-bowtie model can be calculated via the corresponding formulas. Additionally, the most contributed basic event and the most effective measurement can be obtained through sensitivity analysis. The effectiveness of the proposed scheme is validated by a case study. The results presented here may represent an innovative approach to managing risk in larger classes of complex systems.INDEX TERMS Aviation risk, chance theory, U-bowtie analysis, sensitivity analysis.

Research on Comparision between Deterministic Method and Uncertain Method for Solving Uncertain Multiobjective Programming

“…According to the numerical characteristics of uncertain vectors, it is easy to see that the E-UMP problem (21) and EV-UMP problem (24) are deterministic multiobjective programming models derived from the initial UMP problem (20). To illustrate the relationship between the efficient solutions of these two deterministic models and the efficient solutions of the initial UMP problem (20), some definitions are defined, as follows.…”

“…By assigning corresponding weights to the objective functions in the E-UMP problem (21) or EV-UMP problem (24), the following deterministic single-objective programming (DSP) models…”

“…In practical decision-making problems, it is assumed that the objective functions in E-UMP problem (21) or EV-UMP problem (24) have ideal values; then, the best decisionmaking scheme is to make all the objective functions meet the corresponding ideal values. However, since the objective functions in the E-UMP problem (21) or EV-UMP problem (24) are usually conflicting and contradictory, a best decision-making scheme often does not exist. Hence, the next best thing is to find the sub-optimal decision-making scheme that makes the objective functions match their ideal objective values as closely as possible.…”

“…Definition 10. (Weak E-Efficiency) We say that the feasible solution x * ∈ S is an expected-value weak efficient solution to the UMP problem (20) if it is a Pareto weak efficient solution to the E-UMP problem (21), that is, there is no x ∈ S, such that…”

“…In order to solve this type of indeterminacy, called uncertainty, with an expert degree of belief, this paper introduces the uncertainty theory founded by professor Liu in 2007 [12] and refined in 2010 based on normality, duality, subadditivity, and product axioms [13]. To date, a high number of studies have proved that uncertainty theory is a branch of mathematics used to model human uncertainty and has been widely used, not only in theoretical fields such as Liu [14], Wang et al [15], Liu and Yao [16], Wen et al [17], etc., but also in application fields such as Zheng et al [18], Zheng et al [19], Zhang et al [20], and Wang et al [21], etc. However, except for the concepts of efficient solution and the expected-value model based on uncertain variables mentioned in the literatures [14,22], the research on uncertain multi-objective programming (UMP) based on uncertain theory is not in-depth enough.…”