arXiv subjects

Ashley Scillitoe

Publications and source records attributed to Ashley Scillitoe.

6 recordsLinked to original sources

arXiv2022

Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of computational engineering applications. In this paper, we describe a Bayesian formulation of polynomial approximations capable of incorporating uncertainties in input data. Through different priors in a hierarchical structure, this permits us to incorporate expert knowledge on the inference task via different approaches. These include beliefs of sparsity in the model; approximate knowledge of the polynomial coefficients (e.g. through low-fidelity estimates) or output mean, and correlated models that share similar functional and/or physical behaviours. We show that through a Bayesian framework, such prior knowledge can be leveraged to produce orthogonal polynomial approximations with enhanced predictive accuracy.

cs.CE↗

arXiv2021

Blade Envelopes Part I: Concept and Methodology

Blades manufactured through flank and point milling will likely exhibit geometric variability. Gauging the aerodynamic repercussions of such variability, prior to manufacturing a component, is challenging enough, let alone trying to predict what the amplified impact of any in-service degradation will be. While rules of thumb that govern the tolerance band can be devised based on expected boundary layer characteristics at known regions and levels of degradation, it remains a challenge to translate these insights into quantitative bounds for manufacturing. In this work, we tackle this challenge by leveraging ideas from dimension reduction to construct low-dimensional representations of aerodynamic performance metrics. These low-dimensional models can identify a subspace which contains designs that are invariant in performance -- the inactive subspace. By sampling within this subspace, we design techniques for drafting manufacturing tolerances and for quantifying whether a scanned component should be used or scrapped. We introduce the blade envelope as a computational manufacturing guide for a blade that is also amenable to qualitative visualizations. In this paper, the first of two parts, we discuss its underlying concept and detail its computational methodology, assuming one is interested only in the single objective of ensuring that the loss of all manufactured blades remains constant. To demonstrate the utility of our ideas we devise a series of computational experiments with the Von Karman Institute's LS89 turbine blade.

cs.CE↗

arXiv2021

Blade Envelopes Part II: Multiple Objectives and Inverse Design

Blade envelopes offer a set of data-driven tolerance guidelines for manufactured components based on aerodynamic analysis. In Part I of this two-part paper, a workflow for the formulation of blade envelopes is described and demonstrated. In Part II, this workflow is extended to accommodate multiple objectives. This allows engineers to prescribe manufacturing guidelines that take into account multiple performance criteria. The quality of a manufactured blade can be correlated with features derived from the distribution of primal flow quantities over the surface. We show that these distributions can be accounted for in the blade envelope using vector-valued models derived from discrete surface flow measurements. Our methods result in a set of variables that allows flexible and independent control over multiple flow characteristics and performance metrics, similar in spirit to inverse design methods. The augmentations to the blade envelope workflow presented in this paper are demonstrated on the LS89 turbine blade, focusing on the control of loss, mass flow and the isentropic Mach number distribution. Finally, we demonstrate how blade envelopes can be used to visualize invariant designs by producing a 3D render of the envelope using 3D modelling software.

cs.CE↗

arXiv2021

Polynomial Ridge Flowfield Estimation

Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations. This paper introduces the idea of using spatially correlated polynomial ridge functions for rapid flowfield estimation. Dimension reducing ridge functions are obtained for numerous points within training flowfields. The functions can then be used to predict flow variables for new, previously unseen, flowfields. Their dimension reducing nature alleviates the problems associated with visualising high dimensional datasets, enabling improved understanding of design spaces and potentially providing valuable physical insights. The proposed framework is computationally efficient; consisting of either readily parallelisable tasks, or linear algebra operations. To further reduce the computational cost, ridge functions need only be computed at only a small number of subsampled locations. The flow physics encoded within covariance matrices obtained from the training flowfields can then be used to predict flow quantities, conditional upon those predicted by the ridge functions at the sampled points. To demonstrate the efficacy of the framework, the incompressible flow around an ensemble of aerofoils is used as a test case. On unseen aerofoils the ridge functions' predictive accuracy is found to be reasonably competitive with a state-of-the-art convolutional neural network (CNN). The local ridge functions can also be reused to obtain surrogate models for integral quantities such a loss coefficient, which is advantageous in situations where long-term storage of the CFD data is problematic. Finally, use of the ridge framework with varying boundary conditions is demonstrated on a three dimensional transonic wing flow.

physics.flu-dyn↗

arXiv2021

Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests

Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of this uncertainty is essential since the predictive capability of a data-driven model diminishes when predicting physics not seen during training. In this work, we explore the suitability of Mondrian forests (MF's) for data-driven turbulence modelling. MF's are claimed to possess many of the advantages of the commonly used random forest (RF) machine learning algorithm, whilst offering principled uncertainty estimates. An example test case is constructed, with a turbulence anisotropy constant derived from high fidelity turbulence resolving simulations. Shapley values, borrowed from game theory, are used to interpret the MF predictions. Predictive uncertainty is found to be large in regions where the training data is not representative. Additionally, the MF predictive uncertainty is found to exhibit stronger correlation with predictive errors compared to an a priori statistical distance measure, which indicates it is a better measure of prediction confidence. The MF predictive uncertainty is also found to be better calibrated and less computationally costly than the uncertainty estimated from applying jackknifing to random forest predictions. Finally, Mondrian forests are used to predict the Reynolds discrepancies in a convergent-divergent channel, which are subsequently propagated through a modified CFD solver. The resulting flowfield predictions are in close agreement with the high fidelity data. A procedure for sampling the Mondrian forests' uncertainties is introduced. Propagating these samples enables quantification of the uncertainty in output quantities of interest.

physics.flu-dyn↗

arXiv2018

Effect of Mesh Quality on Flux Reconstruction in Multi-Dimensions

Theoretical methods are developed to understand the effect of non-uniform grids on Flux Reconstruction (FR) in multi-dimensions. The analysis reveals that the same effect of expanding and contracting grids is seen in two dimensions as in one dimension. Namely, that expansions cause instability and contractions cause excess dissipation. Subsequent numerical experiments on the Taylor-Green Vortex with jittered elements show the effect of localised regions of expansion and contraction, with an initial increase in the kinetic energy observed on non-uniform meshes. Some comparison is made between second-order FR and second-order finite volume (FV). FR is found to be more resilient to mesh deformation, however, FV is found to be more resolved when operated at second order on the same mesh. In both cases, it is recommended that a kinetic energy preserving/conservation formulation should be used as this can greatly increase resilience to mesh deformation.

math.NA↗