Epistemic uncertainty quantification in structural systems using improved universal grey theory

Abstract

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, wheneither 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.