Evidence-Based Fuzzy Approach for the Safety Analysis of Uncertain Systems

Rao, Singiresu S.; Annamdas, Kiran K.

doi:10.2514/1.35715

Cited by 15 publications

(7 citation statements)

References 3 publications

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“…Earlier fuzzy approach has been applied to safety analysis [22], random system properties [23] and optimal design [24]. In contrast, PCE approach [25] for material uncertainty effect on vibration control of smart composite plate and High Dimensional Model Representation (HDMR) approach are proposed [26] for the propagation of fuzzy uncertain variables through…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Bottom up surrogate based approach for stochastic frequency response analysis of laminated composite plates

Dey

Mukhopadhyay

Spickenheuer

et al. 2016

Composite Structures

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  Fuzzy uncertainty propagation in free vibration of composite plate is analyzed.  Gram-Schmidt polynomial chaos expansion is employed as surrogate.  Design points are selected using D-optimal design algorithm.  Fuzzy mode shapes and frequency response functions are presented.

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Section: Accepted Manuscriptmentioning

confidence: 99%

Bottom up surrogate based approach for stochastic frequency response analysis of laminated composite plates

Dey

Mukhopadhyay

Spickenheuer

et al. 2016

Composite Structures

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“…Both the model inputs and the observed experimental evidence are where the uncertainties come from. Previous studies about the treatment of epistemic uncertainty utilize methods such as evidence theory [14,15], fuzzy sets [16], entropy model [17,18], and convex models of uncertainty [19], intended basically for uncertainty quantification, and it is not clear how to implement model validation under epistemic uncertainty. The model validation method in this paper deals with the situation where the epistemic uncertainty arises from the sparse and imprecise data concerning the model inputs, and the input quantities as well as the observed experimental evidence are in the form of both point form and interval form, with the method of Dempster-Shafer (D-S) evidence theory.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Evidential Model Validation under Epistemic Uncertainty

Deng

2018

Mathematical Problems in Engineering

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This paper proposes evidence theory based methods to both quantify the epistemic uncertainty and validate computational model. Three types of epistemic uncertainty concerning input model data, that is, sparse points, intervals, and probability distributions with uncertain parameters, are considered. Through the proposed methods, the given data will be described as corresponding probability distributions for uncertainty propagation in the computational model, thus, for the model validation. The proposed evidential model validation method is inspired by the idea of Bayesian hypothesis testing and Bayes factor, which compares the model predictions with the observed experimental data so as to assess the predictive capability of the model and help the decision making of model acceptance. Developed by the idea of Bayes factor, the frame of discernment of Dempster-Shafer evidence theory is constituted and the basic probability assignment (BPA) is determined. Because the proposed validation method is evidence based, the robustness of the result can be guaranteed, and the most evidence-supported hypothesis about the model testing will be favored by the BPA. The validity of proposed methods is illustrated through a numerical example.

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“…In the possibilistic interpretation of uncertainty [(Denga et al (2012), Möller and Beer, (2004)], the fuzzy variables can be thought as generalized interval variables, allowing one to use the techniques intended for the interval analysis such as classical interval arithmetic [Moore (1966)], affine analysis [Degrauwe et al (2010)] or vertex theorems [Qiu et al (2005)]. Fuzzy based uncertainty quantification is found to be adopted in various engineering analyses [Babuška and Silva (2014), Rao and Annamdas (2008), Díaz-Madroñero et al (2004), Chandrashekhar and Ganguli (2009), Chowdhury and Adhikari (2012), Altmann et al (2012)].…”

Section: Introductionmentioning

confidence: 99%

Spatially varying fuzzy multi-scale uncertainty propagation in unidirectional fibre reinforced composites

Naskar

Mukhopadhyay

Sriramula

2019

Composite Structures

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This article presents a non-probabilistic fuzzy based multi-scale uncertainty propagation framework for studying the dynamic and stability characteristics of composite laminates with spatially varying system properties. Most of the studies concerning the uncertainty quantification of composites rely on probabilistic analyses, where the prerequisite is to have the statistical distribution of stochastic input parameters. In many engineering problems, these statistical distributions remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based approach could be appropriate to characterize the effect of uncertainty. A novel concept of fuzzy representative volume element (FRVE) is developed here for accounting the spatially varying non-probabilistic source-uncertainties at the input level. Such approach of uncertainty modelling is physically more relevant than the prevalent way of modelling non-probabilistic uncertainty without considering the ply-level spatial variability. An efficient radial basis function based stochastic algorithm coupled with the fuzzy finite element model of composites is developed for the multi-scale uncertainty propagation involving multi-synchronous triggering parameters. The concept of a fuzzy factor of safety (FFoS) is discussed in this paper for evaluation of safety factor in the non-probabilistic regime. The results reveal that the present physically relevant approach of modelling fuzzy uncertainty considering plylevel spatial variability obtains significantly lower fuzzy bounds of the global responses compared to the conventional approach of non-probabilistic modelling neglecting the spatially varying attributes.

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Evidence-Based Fuzzy Approach for the Safety Analysis of Uncertain Systems

Cited by 15 publications

References 3 publications

Bottom up surrogate based approach for stochastic frequency response analysis of laminated composite plates

Bottom up surrogate based approach for stochastic frequency response analysis of laminated composite plates

Evidential Model Validation under Epistemic Uncertainty

Spatially varying fuzzy multi-scale uncertainty propagation in unidirectional fibre reinforced composites

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