Uncertainty Quantification in Modeling Metal Alloy Solidification

Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs—typically resulting from natural variability or measurement error—and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single “hyper-parameter” to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including “model failure”. This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty — to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.

During ground-based solidification, buoyancy flow can develop by the density difference in the hypoeutectic type of the alloys, such as Al-7 wt% Si alloy. Buoyancy flow can affect the thermal field, solute distribution in the melt, and the position and amount of the new grains. As solidification is a very complex process, it is not very easy to separate the different effects. Under microgravity conditions, natural convection does not exist or is strongly damped due to the absence of the buoyancy force. Therefore, experiments in microgravity conditions provide unique benchmark data for pure diffusive solidification conditions. Compared to the results of the ground-based and microgravity experiments, it is possible to get information on the effect of gravity (buoyancy force). In the framework of the CETSOL project, four microgravity solidification experiments were performed on grain refined (GF) and non-grain refined Al-7 wt% Si alloy onboard the International Space Station in the Materials Science Laboratory. These experiments aimed to study the effect of the solidification parameters (solid/liquid front velocity vSL, temperature gradient GSL) on the grain structure and dendritic microstructures. The microgravity environment eliminates the melt flow, which develops on Earth due to gravity. Four ground-based (GB) experiments were performed under Earth-like conditions with the same (similar) solidification parameters in a vertical Bridgman-type furnace having four heating zones. The detailed analysis of the grain structure, amount of eutectic, and secondary dendrite arm spacing (SDAS) for different process conditions is reported and compared with the results of the microgravity experiments. GB experiments showed that the microstructure was columnar in the samples that do not contain GF material or in case the solid/liquid (vSL front velocity was slow (0.02 mm/s)). In contrast, in the sample which contained GF material, progressive columnar/equiaxed transition (PCET) was observed at vSL = 0.077 mm/s and GSL = 3.9 K/mm. The secondary (SDAS) dendrite arm spacing follows the well-known power law, SDAS=K[t0]13, where K is a constant, and t0 is the local solidification time for both GB and µg experiments.

Uncertainty quantification and sensitivity analysis are essential for improving the modeling and estimation of greenhouse gas emissions in livestock farming to evaluate and reduce the impact of uncertainty in input parameters to model output. The present study is a comprehensive review of the sources of uncertainty and techniques used in uncertainty analysis, quantification, and sensitivity analysis. The search process involved rigorous selection criteria and articles retrieved from the Science Direct, Google Scholar, and Scopus databases and exported to RAYYAN for further screening. This review found that identifying the sources of uncertainty, implementing quantifying uncertainty, and analyzing sensitivity are of utmost importance in accurately estimating greenhouse gas emissions. This study proposes the development of an EcoPrecision framework for enhanced precision livestock farming, and estimation of emissions, to address the uncertainties in greenhouse gas emissions and climate change mitigation.

Uncertainty quantification in a resonant nonlinear MEMS structure

Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties.

Effect of cooling rate on microstructure and mechanical properties of gray cast iron

Predictions of secondary dendrite arm spacing (SDAS) for multicomponent aluminum alloys using a dendrite ripening model are compared with experimental observations. For six of the seven alloys studied, the predicted SDAS was within 20 pct of the measured SDAS. It was found that the final SDAS was dependent upon both the solidification time and the solute profile of the solidifying alloys. It is interesting that while the solidification times and the solute segregation during solidification varied significantly over the range of alloys, these two factors largely canceled each other out so that the predicted SDAS did not vary much between the alloys. The experimental and modeling results show that elements causing high constitutional undercooling near the beginning of solidification, e.g., Ti, which reduces the grain size substantially, have little effect on the SDAS. Instead, it was found that elements that strongly partitioned toward the end of solidification were more effective at restricting SDAS coarsening.

Development and uncertainty analysis of the dynamic simulation for HFETR with BMUS framework

Microstructure related analysis of tensile and fatigue properties for sand casting aluminum alloy cylinder head

In this work we propose an approach for accelerating Uncertainty Quantification (UQ) analysis in the context of Multifidelity applications. In the presence of complex multiphysics applications, which often require a prohibitive computational cost for each evaluation, mul- tifidelity UQ techniques try to accelerate the convergence of statistics by leveraging the in- formation collected from a larger number of a lower fidelity model realizations. However, at the-state-of-the-art, the performance of virtually all the multifidelity UQ techniques is related to the correlation between the high and low-fidelity models. In this work we proposed to design a multifidelity UQ framework based on the identification of independent important directions for each model. The main idea is that if the responses of each model can be represented in a common space, this latter can be shared to enhance the correlation when the samples are drawn with respect to it instead of the original variables. There are also two main additional advantages that follow from this approach. First, the models might be correlated even if their original parametrizations are chosen independently. Second, if the shared space between mod- els has a lower dimensionality than the original spaces, the UQ analysis might benefit from a dimension reduction standpoint. In this work we designed this general framework and we also tested it on several test problems ranging from analytical functions for verification purpose, up to more challenging application problems as an aero-thermo-structural analysis and a scramjet flow analysis.

<div class="section abstract"><div class="htmlview paragraph">Strength, creep, and fatigue of the chassis components are greatly influenced by the material used and its manufacturing process. Alloy wheel is one of the critical chassis components manufactured using the casting process. Secondary Dendrite Arm Spacing (SDAS) is one of the important microstructural parameters generated during the solidification stage of the casting process. SDAS has a significant role in altering the mechanical properties and the behavior of the component. Variation in solidification time and alloy composition will have a major impact in SDAS. The combined effect of SDAS with microstructural variations and the strength behavior has not been studied in earlier literature for an alloy wheel.</div><div class="htmlview paragraph">The scope of this study is to perform casting simulation for an alloy wheel, predict the SDAS and capture the variation of mechanical properties (yield strength, ultimate tensile strength & elongation). Further a few casting simulations were carried out by changing the solidification time and alloy composition to predict the variation of SDAS and its relationship with mechanical properties. The effect of SDAS on strength behavior of the wheel is studied by wheel simulation and correlated with test results.</div></div>

The correlation between thermal variables and secondary dendrite arm spacing during solidification of horizontal cylinders of Sn–Pb alloys

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

Sensitivity and Uncertainty

A methodology for uncertainty quantification and sensitivity analysis for responses subject to Monte Carlo uncertainty with application to fuel plate characteristics in the ATRC