Bayesian optimization for materials design

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality

Multi-fidelity Metamodels Nourished by Reduced Order Models

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Characterization of geometric uncertainty in gas turbine engine components using CMM data

Measurements of component geometry are routinely made for inspection during manufacturing. Typically this results in ‘clouds’ of points or pixels depending upon the measuring system. Examples include points form laserbased or touch-probe co-ordinate measuring machines (CMMs). The point density may vary as will the cost and time taken to make measurements. There can also be gaps and occlusions in data, and sometimes it is only practical to collect sparse sets or points in a single dimension.This data often provides an untapped source of quantitative uncertainty information pertaining to manufacturing methods. It is proposed that state-of-the-art uncertainty propagation and robust design optimization approaches, often demonstrated using assumed normal input distributions in existing parameters, can be improved by incorporating these data. Inclusion of this information requires, however, that the point cloud be converted to an appropriate parametric form.Although the design intent of a component may be described using simple geometric primitives joined with tangency or at vertices, manufactured geometry may not exhibit the same simple form, and line and surface segment end locations are notoriously difficult to locate where there is tangency or shallow angles. In this paper we present an approach to first characterise point cloud measurements as curves or surfaces using Kriging, allowing for gaps in data by extension to universal Kriging. We then propose a novel method for the reduction of variables to parameterize curves and surfaces again using Kriging models in order to facilitate practical analysis of performance uncertainty. The techniques are demonstrated by application to a gas turbine engine blade to disc joint where the contact surface shape is measured and the notch stresses are critical to component performance

Consultant and Specialist Services

Modal analysis classicaly used signals that respect the Shannon/Nyquist theory. Compressive sampling (or Compressed Sampling, CS) is a recent development in digital signal processing that offers the potential of high resolution capture of physical signals from relatively few measurements, typically well below the number expected from the requirements of the Shannon/Nyquist sampling theorem. This technique combines two key ideas: sparse representation through an informed choice of linear basis for the class of signals under study; and incoherent (eg. pseudorandom) measurements of the signal to extract the maximum amount of information from the signal using a minimum amount of measurements. We propose one classical demonstration of CS in modal identification of a multi-harmonic impulse response function. Then one original application in modeshape reconstruction of a plate under vibration. Comparing classical L2 inversion and L1 optimization to recover sparse spatial data randomly localized sensors on the plate demonstrates the superiority of L1 reconstruction (RMSE)