Structural uncertainty quantification with partial information

Quantifying the impact of uncertainty in material properties and ground motion records on the structural response is essential in implementing the performance-based earthquake engineering framework. Within the finite element approach with implicit limit states, a large number of nonlinear transient simulations are typically required to quantify the impact of potential epistemic and aleatory random variables (RVs). This paper's contribution is twofold: First, we discuss how to develop a series of matrices that combine various realizations of hybrid epistemic-aleatory RVs. For this purpose, we modify the classical Cloud analysis (CLA) method (with only aleatory variability) to Extended CLA(which incorporates the epistemic uncertainties) and Scaled CLA(which uses higher scale factor) methods. Second, multiple matrix completion methods are proposed and applied to the generated dataset. The matrix completion is a means to estimate the simulation results for the entire set of input parameters by analyzing only a small subset of data. Our proposed algorithm includes both sampling techniques (for choosing a subset of representative simulations using unsupervised machine learning) and further refinement using regression analysis techniques, such as neural networks. The proposed algorithm is applied to a complex tower, and the structural responses (i.e., displacements and base shear) are estimated. Results show that the proposed algorithm can effectively estimate the response from a full set of nonlinear simulations. Further recommendations on choosing the optimal percentage of initial simulations are provided to develop fragility functions.

Automated summary

Quantifying the impact of uncertainty in material properties and ground motion records on structural response is crucial in performance-based earthquake engineering. This paper proposes an algorithm that combines different realizations of hybrid epistemic-aleatory RVs, utilizes matrix completion methods, and applies sampling techniques and regression analysis for estimating structural responses. The algorithm is successfully applied to a complex tower, showing its effectiveness in estimating responses and providing recommendations for choosing the optimal percentage of initial simulations.