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    Multicut-high dimensional model representation for reliability bounds estimation
    (Springer International Publishing, 2015) Balu, A.S.; Rao, B.N.
    The structural reliability analysis in presence of mixed uncertain variables demands more computation as the entire configuration of fuzzy variables needs to be explored. The existence of multiple design points plays an important role in the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this chapter, a method for estimating the reliability bounds of structural systems involving multiple design points in presence of mixed uncertain variables is presented. The proposed method involves weight function to identify multiple design points, multicut-high dimensional model representation for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables and fast Fourier transform for solving the convolution integral. © Springer International Publishing Switzerland 2015
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    Confidence bounds on failure probability using MHDMR
    (Springer India, 2015) Balu, A.S.; Rao, B.N.
    The structural reliability analysis in presence of mixed uncertain variables demands more computation as the entire configuration of fuzzy variables needs to be explored. Moreover the existence of multiple design points plays an important role in the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this paper a novel uncertain analysis method for estimating the failure probability bounds of structural systems involving multiple design points in presence of mixed uncertain variables is presented. The proposed method involves weight function to identify multiple design points, multicut-high dimensional model representation technique 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 the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability analysis involving any number of fuzzy and random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through two examples. © Springer India 2015.
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    Fuzzy structural analysis using surrogate models
    (IGI Global, 2016) Balu, A.S.; Rao, B.N.
    The exponential growth of computational power during the last few decades has enabled the finite element analysis of many real-life engineering systems which are too complex to be analytically solved in a closed form. In the traditional deterministic finite element analysis, system parameters such as mass, geometry and material properties are assumed to be known precisely and defined exactly. However, in practice most of the data used in the solution process of many practical engineering systems are either collected from experiments or acquired as empirical data from the past, which are usually ill defined, imprecise and uncertain in nature. This work presents a practical approach based on High Dimensional Model Representation (HDMR) for analyzing the response of structures with fuzzy parameters. The proposed methodology involves integrated finite element modelling, HDMR based surrogate model, and explicit fuzzy analysis procedures. © 2017 by IGI Global. All rights reserved.
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    Stability Analysis of Structural Systems with Epistemic Uncertainties
    (Springer, 2024) Kumar, A.; Balu, A.S.
    Safety of structures is ensured by considering the sufficient strength of the structural element and geometric stability of the structure. In structural engineering, the failure of a structural system is characterized by material failure and geometric instability. Material failure occurs when the stresses induced in the structural element reach its yield strength, whereas the instability of the structure is due to the structural geometry and size only, which is known as buckling. It is of utmost significance to perform the stability analysis for the safety of structure. In most of the stability analyses, the structural property and load parameters are considered as certain, which is not the case in practical situations as the load applied to structure is never certain. In the present study, the stability analysis of structure is performed considering the uncertainty in the input parameters. Universal grey number theory and interval analysis are used to perform the stability analysis of the structural system and the results are compared with the combinatorial method (which is estimated to predict the accurate ranges). Results obtained from interval analysis were found to be overestimated because of the violation of the physical law and dependency problem in its arithmetic process whereas the Universal grey number theory showed confirming results with the combinatorial method, as universal grey theory obeys the physical law and does not suffer the dependency problem. In the present study, it is found that the universal grey number theory is computationally efficient when compared with the interval and combinatorial methods. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
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    HDMR-Based Model Update in Structural Damage Identification
    (World Scientific Publishing Co. Pte Ltd wspc@wspc.com.sg, 2019) Naveen, B.O.; Balu, A.S.
    This paper presents a practical approach of model updating based on high-dimensional model representation (HDMR). The proposed methodology involves integrated finite element modeling, obtaining explicit relationships between the structural responses and parameters using HDMR and minimization of objective function developed using structural responses obtained from HDMR approximation functions using genetic algorithm. First, the efficiency of the proposed method is demonstrated by considering a simply supported beam example. Later model updating of an existing bridge is considered to check the adequacy of the proposed method. © 2019 World Scientific Publishing Company.
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    Inverse response surface method for structural reliability analysis
    (Springer Science and Business Media Deutschland GmbH, 2020) Nagesh, M.; Balu, A.S.
    Reliability-based design of complex structural systems is a computationally tedious task. In order to reduce the computational effort, approximation methods, such as classical response surface method, Kriging model and artificial neural network, can be adopted. Response surface model is a conventional method, where the limit state function is approximated using a suitable surrogate model. For the construction of response surface, variables of stochastic model should be known well in advance. However, the design parameters are unknown during initial stages of reliability-based design optimization (RBDO). For such structural design cases using RBDO, an adaptive inverse response surface procedure is proposed in this paper. The procedure is developed by coupling the adaptive response surface method with suitable experimental design (Halton low-discrepancy sequence sampling) for estimating reliability indicators and artificial neural network-based inverse reliability method for design optimization. The validity and accuracy of the proposed method are tested on example with explicit nonlinear limit state function. © Springer Nature Singapore Pte Ltd 2020.
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    Failure Mode Recognition of Columns Using Artificial Neural Network
    (IOP Publishing Ltd custserv@iop.org, 2020) Edward, C.; Balu, A.S.
    Columns are one of the most vital segments in bridgessince its post-seismic behaviour is of much importance. The retrofitting methods and rehabilitation strategies of bridges mainly rely on the identification of the failure mode of columns. It has been witnessed in various studies on columns that the mode of failure highly depends on section and material properties and there is no specific boundary between the modes, which makes their identification more sophisticated. This paper uses an artificial neural network to predict the modes of failure by analysing the effects of such soft computing methods. In this study, machine- learning models were generated from the experimental data of 253 columns of rectangular cross-section and its accuracy of failure mode prediction was evaluated by considering failure modes mainly flexure, flexure-shear, and shear. The optimal input parameters have also been evaluated for the machine-learning algorithm that enhances the efficiency of failure mode prediction. © Published under licence by IOP Publishing Ltd.
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    Optimisation of Trapezoidal Corrugated Plate Girder
    (IOP Publishing Ltd custserv@iop.org, 2020) Dhakate, S.; Balu, A.S.
    Trapezoidal Corrugated web girders is a newly developed structural design. The major advantage of such design of web is that the corrugated webs enhance the stability of beam against buckling, which results in a very economical design by the reduction in the use of web stiffeners. The flanges are made up of flat plates and welded to the trapezoidal web sheet with the modern manufacturing process and modern advance welding technology. The flanges are mainly used to provide flexural strength to the beam and web are used to increase the shear capacity of the beam. Main reason for the failure of the web is the steel yielding or web buckling. Other possible failure reasons are lateral torsional buckling of the girder and local flange buckling, separately or in combination. This paper presents a new technological solution of such a system, composed by web made of trapezoidal shape. The buckling strength of the girder is studied under different geometrical modifications performing a nonlinear finite element analysis in ANSYS. © Published under licence by IOP Publishing Ltd.
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    ANN Based Design Parameter Estimation for Structural Systems
    (IOP Publishing Ltd custserv@iop.org, 2020) Nagesh, M.; Balu, A.S.
    Estimation of the probability of failure of multi-dimensional structural systems is expensive from the computation perspective. To decrease the burden of computation, one can use simple approximation methods like Surrogate models, Kriging model, Support vector machine, Artificial neural network, and more based on the suitability for the problems. In Surrogate or Response surface modeling, the limit state function of any system is suitably approximated by making use of known mathematical models like polynomials, exponentials, etc. During the construction of surrogates, variables in the model should be well known prior to the approximation. In practical consideration, the design parameters are the unknowns that need to be evaluated before reliability-based design. Inverse Response surface procedure is proposed in the paper to address the above-mentioned issue. The procedure developed is the combination of adaptive Response surface method with appropriate experimental design i.e. Halton low discrepancy sequence sampling technique for evaluating the probability of failure or reliability index and an Artificial neural network is utilised as an inverse reliability procedure for design optimisation. The method gives an accurate result and the efficiency is increased for the same number of iterations in comparison to the work of David Lehky and Martina Somodikova [1] with Latin hypercube sampling as experimental design. © Published under licence by IOP Publishing Ltd.
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    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.