Faculty Publications
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Item Universal Grey Number Systems for Uncertainty Quantification(Springer Science and Business Media Deutschland GmbH, 2023) Kumar, A.; Balu, A.S.In the recent past, modelling and analysis of structures with uncertain parameters have evoked significant interest.Physical imperfections, model flaws and system complexities can all be sources of uncertainty.In addition, the action loads (live, wind and earthquake) applied to a structure during its lifetime are not deterministic, hence for the proper performance assessment of the structural system, it is essential to properly account for these uncertainties.Uncertainties are usually described by probabilistic and non-probabilistic approaches.The growing interest in the non-probabilistic approach developed due to the incredibility of the probabilistic approach when data is insufficient.For estimating the ranges of the structural system’s response, the interval finite element approach looks to be acceptable, whose input parameters are defined in the ranges.However, the range of values predicted by the interval analysis suffers dependency problem.This can cause the computed findings to be overestimated.Although, the use of numerical truncation technique, parameterization of intervals and subinterval technique suggested by several researchers to avoid the dependency problem caused by general interval arithmetic.The physical rules (distributive law) are not violated by a universal grey numbers are a form of grey number and predict accurate results when compared with the interval approach.The universal grey number system is one such approach where computational efficiency and accuracy can be achieved when the input parameters are available in the ranges/interval. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.Item Analysis of structural systems with imprecise uncertainties using high dimensional model representation(World Scientific, 2021) Spoorthi, S.K.; Balu, A.S.Uncertainties present in any structural system inherently affect the performance and design of the system. The sources of uncertainties serve the basis for delineating the types as aleatory or epistemic. The probabilistic models can be considered as the most valuable strategies to deal with aleatory uncertainties, while convex models, possibility theory, evidence theory and Bayesian probability theory can be used to deal with epistemic uncertainty. However, when only scarce datasets are available and knowledge is incomplete, a more general framework, such as probability-box, is more appropriate to describe the uncertainty. Furthermore, analysis of complex and multi-dimensional structures is expensive and time consuming when numerical techniques are used. Therefore, simulation of such structures for many realisation of uncertain input becomes a challenging task in the uncertainty analysis. In this paper, complex structural systems with imprecise uncertain input are studied and evaluated efficiently by High Dimensional Model Representation based uncertainty analysis. © 2021 World Scientific Publishing Company.Item Epistemic uncertainty quantification in structural systems using improved universal grey theory(Elsevier Ltd, 2023) Kumar, A.; Balu, A.S.It is important to account for uncertainties in structures during the analysis and design. Based on the source and nature, the uncertainties can be classified as aleatory and epistemic. Aleatory uncertainties arise due to the intrinsic randomness nature of physical system, whereas epistemic uncertainties realize on account of insufficient knowledge. When the information about the system is grey (i.e., partially available as range or interval), methods such as combinatorial approach, interval methods (IM) and universal grey theory (UGT) are generally adopted. The combinatorial optimization becomes computationally expensive when the dimension of uncertain system is large. Interval analysis leads to overestimation due to violations of the physical law and dependency problem. The satisfaction of the physical law (distributive law) that arises out of defining the arithmetic relations, contributes to the UGT free from dependency problem, and makes the approach more efficient. The traditional UGT is ineffective in certain conditions, when either one or both the bounds are negative with the absolute value of the upper bound being smaller i.e.,x¯⩽x̲. Therefore, this paper proposes a necessary modification in arithmetic operations to overcome the incapability of traditional UGT. The efficiency of proposed method is demonstrated through three numerical examples. Comparisons have been made with the conventional techniques to substantiate the proposed methodology, and the results obtained show that the proposed method is computationally efficient in terms of efforts and accuracy. © 2023 Institution of Structural EngineersItem Belief reliability of structures with hybrid uncertainties(Springer Science and Business Media B.V., 2024) Metagudda, S.H.; Balu, A.S.Reliability of structures is evaluated by considering uncertainties present in the system, which can be characterized into aleatory and epistemic. Inherent randomness in the physical environment leads to aleatory, whereas insufficient knowledge about the system leads to epistemic uncertainty. For the reliability evaluation, ascertaining the sources of uncertainties poses a great challenge since both uncertainties coexist widely in structural systems. Aleatory uncertainties are quantified by probabilistic measures (such as first order reliability method, second order reliability method and Monte Carlo techniques), whereas epistemic uncertainties are quantified by various non-probabilistic approaches (such as interval analysis methods, evidence theory, possibility theory and fuzzy theory). However, major issues like interval extension problem and duality conditions that lead to overestimation hinder the versatility of application of such methods, thus uncertainty theory has been emerged to overcome these limitations. Given the existing uncertainties and limitations, a hybrid strategy has been constructed and referred to as “belief reliability”. A belief reliability metric is integration of three key factors: design margin, aleatory and epistemic uncertainty factor to evaluate the reliability of the structural system. In this paper, Monte Carlo simulation is adopted to account for aleatory uncertainty. On the other hand, epistemic uncertainty is quantified through adjustment factor approach using FMEA (failure mode effective analysis). Numerical examples are presented to substantiate the proposed methodology being applied to variety of problems both implicit and explicit nature in structural engineering. © Springer Nature B.V. 2024.