Uncertainty Quantification Applied in Composite Material Modeling

Abstract

Material variability, or generally the noise that exists in nature, renders Uncertainty Quantification an important field in material modelling. Particularly inverse problems described by complex models arise difficulties in uncertainty quantification as model parameters are unknown or poorly constrained by the limited data available. When different materials merge, many of these problems arise in Composite Material Modeling. Even though there is a variety of uncertainty quantification methods, they are usually prohibitively computationally expensive, particularly when the models are highly dimensional or computationally expensive to solve. In the current work, for the first time in material science, we apply Hierarchical Bayesian Models (HBM), which consider all the different experiments separately and, through the information gained from them, builds a high-level parameter distribution quantifying the uncertainty between the samples. We extend the current work by formulating a Data-Driven model, and using the HBM framework, we simulate a composite laminate under consolidation. Considering the same problem from another perspective, we consider the data not as decrete points but as a part of a function. Thus every distinct data set can be considered as a function where Functional Principal Component analysis could be applied. We evaluate the distribution of coefficients for every data set and sampling from there; we can capture the uncertainty between the data sets using a real Data-Driven model. As Markov Chain Monte Carlo methods consist reliable methods for inverse problem solutions, we need a computationally cheap and efficient tool for thinning. Thus we introduce a novel derivative-free thinning method (DaFT) which renders the distribution representation much more computationally efficient. Given a fixed computational budget we can represent the desired distribution with the most representative samples allowing us to utilise a distribution with sufficient sampling.