Adaptive sampling for accelerating neutron diffraction-based strain mapping ^*

Abstract

Neutron diffraction is a useful technique for mapping residual strains in dense metal objects. The technique works by placing an object in the path of a neutron beam, measuring the diffracted signals and inferring the local lattice strain values from the measurement. In order to map the strains across the entire object, the object is stepped one position at a time in the path of the neutron beam, typically in raster order, and at each position a strain value is estimated. Typical dwell times at neutron diffraction instruments result in an overall measurement that can take several hours to map an object that is several tens of centimeters in each dimension at a resolution of a few millimeters, during which the end users do not have an estimate of the global strain features and are at risk of incomplete information in case of instruments outages. In this paper, we propose an object adaptive sampling strategy to measure the significant points first. We start with a small initial uniform set of measurement points across the object to be mapped, compute the strain in those positions and use a machine learning technique to predict the next position to measure in the object. Specifically,we use a Bayesian optimization based on a Gaussian process regression method to infer the underlying strain field from a sparse set of measurements and predict the next most informative positions to measure based on estimates of the mean and variance in the strain fields estimated from the previously measured points. We demonstrate our real-time measure-infer-predict workflow on additively manufactured steel parts- demonstrating that we can get an accurate strain estimate even with 30-40% of the typical number of measurements - leading the path to faster strain mapping with useful real-time feedback. We emphasize that the proposed method is general and can be used for fast mapping of other material properties such as phase fractions from time-consuming point-wise neutron measurements.

Validating the Use of Gaussian Process Regression for Adaptive Mapping of Residual Stress Fields

“…This result also highlights the advantage of the GP-based approach, where a researcher could connect the GP as part of a library for dynamically driving experiments. Venkatakrishnan et al [8] demonstrated the use of GP to dynamically sample a strain field using the GPR to identify the next measurement location. A higher-level implementation of this approach could add additional control to dynamically adjust the measurement gauge Effects of the strain gradients on how the GP and Bayesian optimization select points are highlighted in Figure 6, where the selection operation identifies a higher density near the strain gradients in LTT while a more uniform grid evolves for MS.…”

“…This work uses the GPR approach presented in [ 8 ] to reconstruct the strain fields from a subset of experimental data points. GP has become a popular machine-learning technique that can infer values of unknown points on a grid from a partial set of measurements [ 13 ].…”

“…Recently, the authors proposed using Bayesian optimization and Gaussian process regression (GPR) as a novel approach for reducing the number of independent data measurements needed to reconstruct 2D strain fields [ 8 ]. The core idea behind the system was a measure–infer–predict loop to sequentially make measurements such that important regions (defined in some manner) are sampled first, thereby leading to a better overall view of the strains in the sample, compared to a sequential point-wise raster scanning approach.…”