Statistical Machine Learning and Sampling for Composite Fabrication and Performance

摘要

We apply manifold learning and sampling to the tasks of fabrication,manufacturing, and testing of composites. We specifically address the challengeassociated with statistical inference on these tasks from a small size sample.Limitations on the sample size could emanate from constraints on computationalresources as well as constraints on physical experiments. In either case, the analystis typically presented with a short table that contains observations of environmentalconditions and quantities of interest (QoI). In the case of numerical simulations, theQoIs can be at the discretion of the analyst while in a laboratory setting these aretypically limited by access to sensing devices. We augment the statisticalknowledge captured by the available dataset with knowledge of physics constraints(eg conservation laws) in order to enhance the predictive value of the dataset.Imposing these constraints typically requires additional experiments (either physicalor numerical). We proceed differently as we discover, within the dataset, anintrinsic structure that is consistent with the manner in which the available data isinterrelated. To that end, we rely on diffusion maps, a recent data-analyticsprocedure. This allows us to rapidly characterize feasible domains for complexphenomena involving multiscale and Multiphysics interactions. We augment thediffusion map procedure with a stochastic sampler guaranteed to sample on themanifold, thus allowing us to impute a very large sample that is consistent with thestatistics of the original dataset and its learned intrinsic features.We demonstrate the application of this procedure to a decoupled representation ofcomposite behavior which consists of the fabrication and manufacturing stage, andthe loading stage, including multiscale structural performance.