Browsing by Author "Balu, A S."

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Structural Reliability Analysis with Imprecise Uncertainties
(National Institute of Technology Karnataka, Surathkal, 2021) K, Spoorthi S.; Balu, A S.
Analysis and design involves consideration of many factors which are inherently uncertain. Reliability analysis requires information about the uncertainties in the system, and structural reliability is the probability of a structure performing its purpose adequately for the period of time intended under the operating conditions encountered. Many approaches developed for dealing with the uncertainties demand a mathematical representation of uncertainties on the basis of available information. Probability theory is the most customary technique to describe the uncertainties as random variables characterised by the probability density functions (PDF). However, if the data is inaccurate, ambiguous and incomplete, it is inept to form the PDF, and hence the conventional probabilistic approach becomes inadequate. Therefore, the imprecise parameters should be treated appropriately for improving the reliability of the system. If the information about the uncertainty is insufficient and non-stochastic in nature, the approaches based on interval analysis or fuzzy set theory can be adopted in uncertainty quantification. Hybrid approaches are also available to handle the situations where both the nature of uncertainties namely aleatory and epistemic are uniquely present in the system. In reality, when the aleatory uncertainty is characterised with imprecise parameters, none of the above approaches yields a reliable and optimum design. In such situations, the concepts of probability-box (p-box) can be adopted for characterising the uncertainties. Uncertainty analysis of multi-dimensional and highly nonlinear structures using simulation-based methods is cumbersome, and the hybridity demands the exploration of entire domain of bounds on imprecision. Response surface methods facilitate surrogate models to reduce the effort involved during the simulation. High dimensional model representation (HDMR) is a computationally efficient technique developed for the parameter interaction in physical problems. Therefore, in the present work, HDMR based uncertainty analysis is developed for estimating the structural reliability in the presence of various imprecise uncertainties. The methodology involves characterising the imprecise uncertainties as p-box variables, developing limit state functions using HDMR techniques, and estimating the reliability by interval Monte-Carlo simulations. Furthermore, as the prediction of structural behaviour might diverge due to the presence of various uncertainties, an attempt has been made by studying the systems with hybrid uncertainties from four different sources. The results of the numerical examples are compared with the traditional approaches to demonstrate the efficiency of the methodology.
Time-Dependent Failure Possibility Analysis of Reinforced Concrete Structures
(National Institute of Technology Karnataka, Surathkal, 2021) Woju, Utino Worabo.; Balu, A S.
Structural performance depends on the design, construction, environment, utilization, and reliability aspects. From these, other factors can be controlled by adopting proper design and construction techniques, but the environmental factors are difficult to control. Hence, the environmental factors in the analysis and design are mostly not considered sufficient in practice; however, they have significant effects on the performance of the structures in the design life. It is in this light that this study aimed at performing the time-dependent safety and serviceability performance analysis of reinforced concrete structures majorly considering environmental factors such as creep, shrinkage, and corrosion that possess uncertainty. To achieve the desired objective, a simply supported reinforced concrete beam was designed and detailed to Eurocode (EC2). Different design parameters such as corrosion parameters, creep and shrinkage, the time-dependent properties of the material have been identified and modeled through a thorough literature review. The empirical equations provided in design codes were modified to consider the time-variant parameters in time-dependent performance analysis. In the presence of uncertainty of parameters, it is impossible to obtain the absolute reliability of the structure. The sources of uncertainties in reinforced concrete are the randomness of variables, mathematical models, physical models, environmental factors, and gross error. Uncertainties broadly classified as aleatory and epistemic uncertainties. This research mainly addressed the epistemic uncertainty of reinforced concrete structure to handle the imprecise data using fuzzy concepts. The fuzziness of variables identified and their membership functions were generated by MATLAB R2018a using the heuristic method. In addition to the identification of fuzziness of variables, the study further extended to design optimization and performance level evaluation of reinforced concrete structure using fuzzy relation and fuzzy composition to explore the application of fuzzy concepts. In the design of reinforced concrete structure using fuzzy relation and composition methods, the design is taken as optimum when the performance degree of membership tends to unity. Failure possibility is a measure of safety when a structure encounters with fuzzy uncertainties. If uncertainties are time-dependent, the possibility of performance under zero results in time-dependent failure possibility, and it becomes more pronounced during improper consideration of environmental factors. Therefore, in this study, time-dependent parameters are taken into account for exploring the effects of environmental factors in reinforced concrete structures. Possible failure modes were identified and estimated using modified time-variant empirical equations to consider the propagation of input variables that are characterized by membership functions to output responses. Then, the time-dependent failure possibility is evaluated by the numerical optimization procedure. Real-time data has been collected from the city of Addis Ababa, Ethiopia for the case study to substantiate the methodology presented in this study. From the detailed modeling and analysis, considering the moderate corrosion rate with corresponding ambient temperature and relative humidity of the considered site, the structure safely performs for less than half of its design life.
Uncertainty Quantification in Structural Systems Using Universal Grey Theory
(National Institute of Technology Karnataka, Surathkal, 2024) Kumar, Akshay; Balu, A S.
In recent years, increasing attention has been directed toward addressing uncertainties in engineering systems, which may arise from both aleatory and epistemic sources. Aleatory uncertainty originates from the inherent randomness of physical systems, whereas epistemic uncertainty stems from incomplete or limited knowledge. The present study focuses exclusively on the quantification of epistemic uncertainty in engineering systems. When system information is imprecise or partially available in the form of intervals or ranges, methods such as the combinatorial approach, interval methods (IM), and Universal Grey Theory (UGT) are commonly employed. However, as system dimensionality increases, significant challenges arise. Combinatorial optimization becomes computationally expensive for large-scale systems, while interval methods often lead to overestimation due to dependency issues and violations of physical laws. To overcome these limitations, UGT offers a promising alternative by satisfying distributive laws, thereby effectively addressing dependency problems and improving computational efficiency. Nevertheless, traditional UGT faces limitations in situations where one or both interval bounds are negative and the upper bound has a smaller absolute value. To address this issue, the present study proposes a necessary modification to the arithmetic operations within the UGT framework. Another critical aspect of efficiently quantifying epistemic uncertainty in large-scale systems is computational cost. Finite element–based uncertainty analysis is often computationally demanding for high-dimensional systems. Although metamodeling techniques such as the Response Surface Method (RSM) and Kriging can approximate original models, their computational expense increases significantly with system dimensionality. High Dimensional Model Representation (HDMR), a variant of RSM, emerges as a computationally efficient alternative for handling large-scale systems. To effectively quantify epistemic uncertainty in high-dimensional systems, this study proposes an integrated HDMR–UGT–based formulation. In this approach, HDMR is employed to construct response surfaces using finite element simulations, while UGT is utilized for explicit uncertainty propagation and prediction of response bounds. The proposed methodology is validated through numerical examples, demonstrating high accuracy and significant computational efficiency in exclusively quantifying epistemic uncertainty. Comparative studies with conventional techniques further confirm the effectiveness of the proposed HDMR–UGT formulation in reducing computational effort while maintaining high accuracy in the analysis of engineering systems subjected to epistemic uncertainty.