Model Calibration of the Liquid Mercury Spallation Target using\n Evolutionary Neural Networks and Sparse Polynomial Expansions

Abstract

The mercury constitutive model predicting the strain and stress in the target\nvessel plays a central role in improving the lifetime prediction and future\ntarget designs of the mercury targets at the Spallation Neutron Source (SNS).\nWe leverage the experiment strain data collected over multiple years to improve\nthe mercury constitutive model through a combination of large-scale simulations\nof the target behavior and the use of machine learning tools for parameter\nestimation. We present two interdisciplinary approaches for surrogate-based\nmodel calibration of expensive simulations using evolutionary neural networks\nand sparse polynomial expansions. The experiments and results of the two\nmethods show a very good agreement for the solid mechanics simulation of the\nmercury spallation target. The proposed methods are used to calibrate the\ntensile cutoff threshold, mercury density, and mercury speed of sound during\nintense proton pulse experiments. Using strain experimental data from the\nmercury target sensors, the newly calibrated simulations achieve 7\\% average\nimprovement on the signal prediction accuracy and 8\\% reduction in mean\nabsolute error compared to previously reported reference parameters, with some\nsensors experiencing up to 30\\% improvement. The proposed calibrated\nsimulations can significantly aid in fatigue analysis to estimate the mercury\ntarget lifetime and integrity, which reduces abrupt target failure and saves a\ntremendous amount of costs. However, an important conclusion from this work\npoints out to a deficiency in the current constitutive model based on the\nequation of state in capturing the full physics of the spallation reaction.\nGiven that some of the calibrated parameters that show a good agreement with\nthe experimental data can be nonphysical mercury properties, we need a more\nadvanced two-phase flow model to capture bubble dynamics and mercury\ncavitation.\n