Computational fluid dynamics (CFD)-based wear predictions are computationally expensive to evaluate, even with a high-performance computing infrastructure. Thus, it is difficult to provide accurate local wear predictions in a timely manner. Data-driven approaches provide a more computationally efficient way to approximate the CFD wear predictions without running the actual CFD wear models. In this paper, a machine learning (ML) approach, termed WearGP, is presented to approximate the 3D local wear predictions, using numerical wear predictions from steady-state CFD simulations as training and testing datasets. The proposed framework is built on Gaussian process (GP) and utilized to predict wear in a much shorter time. The WearGP framework can be segmented into three stages. At the first stage, the training dataset is built by using a number of CFD simulations in the order of O(102). At the second stage, the data cleansing and data mining processes are performed, where the nodal wear solutions are extracted from the solution database to build a training dataset. At the third stage, the wear predictions are made, using trained GP models. Two CFD case studies including 3D slurry pump impeller and casing are used to demonstrate the WearGP framework, in which 144 training and 40 testing data points are used to train and test the proposed method, respectively. The numerical accuracy, computational efficiency and effectiveness between the WearGP framework and CFD wear model for both slurry pump impellers and casings are compared. It is shown that the WearGP framework can achieve highly accurate results that are comparable with the CFD results, with a relatively small size training dataset, with a computational time reduction on the order of 105 to 106.
This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the interface defining the discontinuity. Instead, we utilize an epistemic description of the uncertainty in the location of a discontinuity to produce robust bounds on sample-based estimates of probabilistic quantities of interest. We demonstrate that two common machine learning strategies for classification, one based on nearest neighbors (Voronoi cells) and one based on support vector machines, provide reasonable descriptions of the region where the discontinuity may reside. In higher dimensional spaces, we demonstrate that support vector machines are more accurate for discontinuities defined by smooth interfaces. We also show how gradient information, often available via adjoint-based approaches, can be used to define indicators to effectively detect a discontinuity and to decompose the samples into clusters using an unsupervised learning technique. Numerical results demonstrate the epistemic bounds on probabilistic quantities of interest for simplistic models and for a compressible fluid model with a shock-induced discontinuity.
Bayesian optimization is an effective surrogate-based optimization method that has been widely used for simulation-based applications. However, the traditional Bayesian optimization (BO) method is only applicable to single-fidelity applications, whereas multiple levels of fidelity exist in reality. In this work, we propose a bi-fidelity known/unknown constrained Bayesian optimization method for design applications. The proposed framework, called sBF-BO-2CoGP, is built on a two-level CoKriging method to predict the objective function. An external binary classifier, which is also another CoKriging model, is used to distinguish between feasible and infeasible regions. The sBF-BO-2CoGP method is demonstrated using a numerical example and a flip-chip application for design optimization to minimize the warpage deformation under thermal loading conditions.
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.