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Time-dependent reliability of aging bridges exposed to imprecise deterioration information
Published in Hiroshi Yokota, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations, 2021
The result of bridge reliability assessment may be dramatically sensitive to the selection of the probability distributions of the random inputs (Ellingwood 2001). In the presence of imprecise deterioration information, the incompletely-informed random variable can be quantified by a family of candidate probability distributions rather than a single known distribution function. This is the basic concept of imprecise probability (Walley 2000). Correspondingly, the bridge reliability incorporating incompletely-informed random variables (e.g., resistance deterioration) can no longer be uniquely determined. A practical way to represent an imprecise probability is to use a probability bounding approach by considering the lower and upper bounds of the imprecise probability functions. Under this context, approaches of interval estimate of reliability have been used to deal with reliability problems with imprecise probabilistic information (Tang and Ang 2007), including the probability-box method (Ferson et al. 2003), random set and Dempster-Shafer evidence theory (Baudrit et al. 2008, Limbourg and De Rocquigny 2010, Alvarez et al. 2018), fuzzy random variables (Möller and Beer 2004), and others. These methods are closely related to each other, and may often be used as equivalent for the purpose of reliability assessment (Ferson et al. 2003, Zhang 2012). However, the bounds of bridge reliability estimated using a probability bounding approach may be overly conservative in some cases, due to the fact that it only considers the bounds of the distribution function, thus some useful information inside the bounds may be lost. This fact calls for an improved approach for reliability bound estimate of aging bridges which can take full use of the imprecise information of the variable(s).
Basic principles of ERM
Published in Terje Aven, Shital Thekdi, Enterprise Risk Management, 2019
The distinction between GK and SK to assess risk leads to a new type of approach. We find, however, similar ideas in the Bayesian method, where a prior distribution and the underlying probability model are established on the basis of generic knowledge and combined with observations and measurements representing SK, to produce an integrated distribution reflecting the total knowledge. The Bayesian method has a strong theoretical foundation and can be useful in many cases to systematically update knowledge. The approach presented above differs, however, from the Bayesian approach in many ways. First, it is a qualitative approach, not a quantitative approach as the Bayesian one. The strengths of quantitative analysis are well known, as are the weaknesses of qualitative studies. Probabilistic quantification and the use of Bayes’ formula make it possible to systematically combine knowledge about unknown quantities and observations (measurements). Using qualitative approaches, the stringency of the probability theory is lost, and it is not possible to ensure the same level of coherency in judgements. However, quantification also has strong limitations. To use a probability to represent uncertainty means that important aspects of risk are not reflected, aspects that are important to properly evaluate the significance of the risk and make the right decisions. The argumentation for this assertion is well known (see, for example, Flage et al. 2014; Aven 2014) but, to quickly recap, a probability representing or expressing uncertainty is conditional on some knowledge, and this knowledge could be more or less strong and even erroneous. For the proper use of the risk assessment, it is not enough to only report the probability numbers, as these reflect “conditional risk”. The assessment may, for example, be based on a belief that the system studied has some specified properties, but in real life it could, in fact, have others, and this can lead to negative surprises (see examples in Aven 2017b). The use of imprecise probability or interval probabilities (Flage et al. 2014, Section 2.2.2) makes the transformation from knowledge to the probabilities more objective but does not eliminate the issue of the underlying knowledge being weak or wrong. Such intervals will also reduce the information value of the assessments, as the intervals seek to avoid incorporating analysts’ judgements.
Time-dependent mechanism reliability analysis with imprecise probability distributions based on envelope function
Published in Mechanics Based Design of Structures and Machines, 2023
Zheng Zhang, Changcong Zhou, Qi Chang, Haihe Li, Zhufeng Yue
The interval model has been widely used in the traditional time-independent reliability analysis. Ben-Haim (1995) proposed a nonprobabilistic reliability method based on the convex set model. Based on the nonprobabilistic reliability index, Li et al. (2013) developed the GRS method and proposed two GRS indices. Wang, Lu, and Cheng (2013) discussed the GRS indices for the imprecise probability distributions. However, the application of interval model in the study of time-dependent reliability is relatively rare. Zhu, Xuan, and Hai (2016) introduced a novel method to solve the tolerance reliability analysis problems of mechanism. Wang et al. (2018) developed the reliability analysis method of the motion mechanism under three types of hybrid uncertainties based on the first-passage method. Therefore, there is few work that has ever been presented to investigate the time-dependent mechanism reliability and sensitivity analysis simultaneously with imprecise probability distribution. To address this issue, two procedures based on numerical simulation method and the envelope function method are proposed and discussed in this work.
Risk-averse two-stage distributionally robust optimisation for logistics planning in disaster relief management
Published in International Journal of Production Research, 2023
Duo Wang, Kai Yang, Lixing Yang
First, uncertainties abound in a realistic disaster relief logistics planning problem. This results in various risks that should not be disregarded; otherwise, an inefficient relief distribution will be yielded. Moreover, because the exact probability distribution information of the uncertain variables cannot be obtained in advance, decision-makers can only use partial information regarding the probability distribution. Hence, we developed a risk-averse DRO model to provide decision support. The computational results indicate that overlooking the differences in the distribution information will result in both high decision-making risks and additional costs. It is note worthy that the proposed WMCVaR-based DRO model can avoid the risk caused by imprecise probability distribution information. Therefore, decision-makers can obtain reasonable logistics planning in disaster relief and hedge against uncertainties resulting from imprecise probability distribution information by employing the proposed DRO method.
Unifying neighbourhood and distortion models: part II – new models and synthesis
Published in International Journal of General Systems, 2020
Ignacio Montes, Enrique Miranda, Sébastien Destercke
In our companion paper, we analysed some properties of the credal set and its associated lower prevision/probability for three of the usual distortion models within the imprecise probability theory: the pari mutuel (PMM), linear vacuous (LV) and constant odds ratio (COR) models. In this second part of our study, we will investigate the features of the polytopes induced by classic distances such as the total variation, the Kolmogorov and the distances. To avoid having too many technicalities and unnecessary details in an already long study, we will assume that for all , and also that δ will be chosen small enough such that the lower probability induced by in Equation (2) satisfies (or, equivalently, that is included in ). Some details about the general case are given in Appendix 2.