Pranay Seshadri

Pranay Seshadri, Akil Narayan, Sankaran Mahadevan

This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an existing tensor grid using QR column pivoting. For polynomial interpolation using hyperbolic or total order sets, we then solve the following square least squares problem. For polynomial approximation, we use a column pruning heuristic that removes columns based on the highest total orders and then solves the tall least squares problem. While we provide bounds on the condition number of such tall submatrices, it is difficult to ascertain how column pruning effects solution accuracy as this is problem specific. We conclude with numerical experiments on an analytical function and a model piston problem that show the efficacy of our approach compared with randomized subsampling. We also show an example where this method fails.

Pranay Seshadri, Gianluca Iaccarino, Tiziano Ghisu

Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by reviewing classical methods for finding suitable quadrature points for polynomial approximation in both the univariate and multivariate setting. Then, we categorize recent advances into those that propose a new sampling approach and those centered on an optimization strategy. The sampling approaches yield a favorable discretization of the domain, while the optimization methods pick a subset of the discretized samples that minimize certain objectives. While not all strategies follow this two-stage approach, most do. Sampling techniques covered include subsampling quadratures, Christoffel, induced and Monte Carlo methods. Optimization methods discussed range from linear programming ideas and Newton's method to greedy procedures from numerical linear algebra. Our exposition is aided by examples that implement some of the aforementioned strategies.

Bryn Noel Ubald, Pranay Seshadri, Andrew Duncan

This study proposes a radically alternate approach for extracting quantitative information from schlieren images. The method uses a scaled, derivative enhanced Gaussian process model to obtain true density estimates from two corresponding schlieren images with the knife-edge at horizontal and vertical orientations. We illustrate our approach on schlieren images taken from a wind tunnel sting model, a supersonic aircraft in flight, and a high-order numerical shock tube simulation.

Sławomir Konrad Tadeja, Krzysztof Kutt, Yupu Lu et al.

In this paper, we present a Virtual Reality (VR) based environment where the engineer interacts with incoming data from a fleet of aeroengines. This data takes the form of 3D computer-aided design (CAD) engine models coupled with characteristic plots for the subsystems of each engine. Both the plots and models can be interacted with and manipulated using speech or gestural input. The characteristic data is ported to a knowledge-based system underpinned by a knowledge-graph storing complex domain knowledge. This permits the system to respond to queries about the current state and health of each aeroengine asset. Responses to these questions require some degree of analysis, which is handled by a semantic knowledge representation layer managing information on aeroengine subsystems. This paper represents a significant step forward for aeroengine analysis in a bespoke VR environment and brings us a step closer to a Jarvis-like system for aeroengine analytics.

Chun Yui Wong, Pranay Seshadri, Geoffrey T. Parks

To maximise fuel economy, bladed components in aero-engines operate close to material limits. The severe operating environment leads to in-service damage on compressor and turbine blades, having a profound and immediate impact on the performance of the engine. Current methods of blade visual inspection are mainly based on borescope imaging. During these inspections, the sentencing of components under inspection requires significant manual effort, with a lack of systematic approaches to avoid human biases. To perform fast and accurate sentencing, we propose an automatic workflow based on deep learning for detecting damage present on rotor blades using borescope videos. Building upon state-of-the-art methods from computer vision, we show that damage statistics can be presented for each blade in a blade row separately, and demonstrate the workflow on two borescope videos.

Slawomir Konrad Tadeja, Pranay Seshadri, Per Ola Kristensson

One of today's most propitious immersive technologies is virtual reality (VR). This term is colloquially associated with headsets that transport users to a bespoke, built-for-purpose immersive 3D virtual environment. It has given rise to the field of immersive analytics---a new field of research that aims to use immersive technologies for enhancing and empowering data analytics. However, in developing such a new set of tools, one has to ask whether the move from standard hardware setup to a fully immersive 3D environment is justified---both in terms of efficiency and development costs. To this end, in this paper, we present the AeroVR--an immersive aerospace design environment with the objective of aiding the component aerodynamic design process by interactively visualizing performance and geometry. We decompose the design of such an environment into function structures, identify the primary and secondary tasks, present an implementation of the system, and verify the interface in terms of usability and expressiveness. We deploy AeroVR on a prototypical design study of a compressor blade for an engine.

Pranay Seshadri, Shaowu Yuchi, Shahrokh Shahpar et al.

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades---under the same parametrization---largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection---a non-linear least squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

Pranay Seshadri

In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy (Fernandes et al. 1998) with a conjugate gradient solver. Numerical results contrast this approach---in terms of running times and accuracy---against the direct approach.