Faculty Publications

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Author: search.filters.author.Balu, A.S.Subject: search.filters.subject.Uncertainty analysis

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Now showing 1 - 6 of 6
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    Efficient assessment of structural reliability in presence of random and fuzzy uncertainties
    (American Society of Mechanical Engineers (ASME), 2014) Balu, A.S.; Rao, B.N.
    This paper presents an efficient uncertainty analysis for estimating the possibility distribution of structural reliability in presence of mixed uncertain variables. The proposed method involves high dimensional model representation for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In this methodology, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods, thus the computational efficiency is accomplished. The proposed method is applicable for structural reliability estimation involving any number of fuzzy and random variables with any kind of distribution. Copyright © 2014 by ASME.
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    Failure Probability of Structural Systems in the Presence of Imprecise Uncertainties
    (Springer, 2019) Spoorthi, S.K.; Balu, A.S.
    Structural reliability evaluation is considered to be the solution for modern complex engineering systems possessing uncertain parameters. Reliability estimation involves probabilistic theory when the uncertainties are defined as random variables, whereas with limited resources, it is strenuous to estimate precise parameters in the structural model. Therefore, for such cases, imprecise parameters should be treated appropriately in the design and analysis stage for the improvement of serviceability of the system. On the other side, analyses involving multi-dimensional, computationally expensive, and highly nonlinear structures are formidable in simulation-based methods in the presence of uncertainties. An efficient uncertainty analysis procedure is presented in this paper for analysing the systems with imprecise uncertainties defined as probability-box variables. The estimated bounds of failure probability for the numerical examples from structural mechanics are compared with the traditional approaches to demonstrate the efficiency of the methodology. © 2019, The Institution of Engineers (India).
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    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.
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    Time-dependent failure possibility of structures involving epistemic uncertainty
    (Elsevier Ltd, 2022) Worabo Woju, U.; Balu, A.S.
    Time-dependent failure possibility (TDFP) is the possibility of performance less than zero under fuzzy uncertainty in the given time interval. Failure possibility of structures gets accelerated by improper consideration of input variables, mathematical and structural models, and environmental factors. To explore the environmental factors in structures, the time-variant creep and shrinkage model for concrete structures, and deterioration of steel cross-section and other material properties due to corrosion, and increment of action on the structure with time are considered. A real-time data has been collected from the city of Addis Ababa, Ethiopia for the case study to substantiate the methodology presented in this paper. In this paper, identification the possible failure modes, estimation of the time-dependent performance of failure modes, generating membership function (MF) of fuzzy input and output variables, and finally, the TDFP evaluated from MF of output quantities. Because of its simplicity and frequent application, triangular MF is used to characterize epistemic uncertainty of parameters. However, the failure possibility analysis is a complex problem for practicing engineering that needs a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate TDFP of structures involving epistemic uncertainty. The effectives of SLOM has been checked by adaptive SORM Breitung's algorithm. To enhance the validation of the proposed approach, several examples are thoroughly carried out that indicate the SLOM is bit conservative compared with SORM Breitung's algorithm in such a way that their maximum recorded percentage difference is 9.464%. © 2022 Elsevier Ltd
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    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 Engineers
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    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.