An Improved Sampling Technique For Accelerated Numerical Simulations with Hybrid Uncertainties

F. Pourkamali-Anaraki, M.A. Hariri-Ardebili, S. Sattar University of Massachusetts Lowell, United States

Keywords: material uncertainty, finite element analysis, machine learning, computational cost

Summary:

In many engineering problems, there are two classes of uncertainty that contribute to risk-based decision making: aleatory (i.e., natural randomness) and epistemic (i.e., scientific uncertainty). For example, we often encounter significant epistemic uncertainty regarding material properties. As a result, we should create a vast database of probabilistic models to understand the implications of these uncertainties better. A common approach centers on validated numerical simulations such as finite element (FE) analysis. In this case, the physical domain of the problem at hand is discretized into a large number of “finite elements,” and we use an iterative scheme for the incremental analysis of the system. Depending on the nature of the problem (e.g., number of elements, number of load increments, convergence behavior, etc.), the run time may take from few minutes to a couple of days (or even weeks). Therefore, reducing the computational cost in a principled way is a significant contribution across many engineering domains. In this work, we propose a new strategy for selecting a small fraction of influential simulations that allow us to accurately predict a quantity of interest (QoI) for the entire set of simulations. The proposed method employs K-medoids clustering, an unsupervised machine learning (ML) technique, to identify groups of similar features in the input parameter space. Then, we use the corresponding QoIs in a mathematical optimization problem to estimate the target values of remaining simulations (known as matrix completion). Hence, this approach holds great potential to reduce the required number of FE simulations, which will lead to significant computational savings in many engineering problems.