Thermal Management System Modeling by Sensitivity Analysis Guided Symbolic Regression
Paper submission for review for ASME IMECE 2025 conference.
Rahman, Farhan [Sandia National Laboratories (SNL-↗
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Model form and sensitivity analysis of CALPHAD-based nucleation models in b-stabilized Ti alloys
Accurate prediction of α-phase nucleation and growth in β-stabilized titanium alloys is crucial for designing heat treatments to optimize mechanical properties in additively manufactured lightweight components. Ideally, predictions of nucleation and growth would incorporate both top-down observations of past experimental heat treatments and bottom-up modeling of phase transformations; however, the appropriate method of combining these information sources is not self-evident. Combining top-down and bottom-up information requires a unified form of model that can connect between spatiotemporal scales, as well as sets of fitting parameters that can be identified by each data source. The selection of which parameters to fit to which data source can be made based on expert opinion, or by performing a sensitivity analysis. In solid-solid nucleation, direct observation of the nucleation and growth process is challenging. Most data on the heat treatment-controlled phase transformations are not in-situ. To predict the process and outcome of the nucleation, growth and coarsening of precipitates, theoretical models of the nucleation pathway are used to bridge the gap. Many sources of uncertainty affect the modeling of this nucleation process. It can be influenced by small variations in the thermomechanical processing history, chemical composition, and initial microstructure. If molecular dynamics (MD) simulations are used to determine thermodynamic quantities and inform CALPHAD modeling, additional uncertainty can be introduced and accounted for using Bayesian methods. Top-down uncertainties require additional steps to quantify. The influence of nucleation model form on the sensitivity of predictions to input parameters and physical conditions is the focus of this study. Classical nucleation theory (CNT) allows modeling to formulate the nucleation as homogeneous or, more commonly, heterogeneous. Non-classical nucleation models are also increasingly explored as a means of reconciling top-down and bottom-up data. In this study, the sensitivity of the intragranular nucleation of α in a β-annealed, slow-cooled aging (BASCA) heat treatment of β-stabilized Ti5553 alloy is explored using CNT and both heterogeneous and homogeneous assumptions. The Kampmann-Wagner Numerical model of precipitate nucleation and growth is employed. Using open-source tools (pyCalphad and thermodynamic modeling of TiMo as a surrogate system, a sensitivity analysis is performed to measure variations in key parameters, including chemical driving force, interfacial energy, and diffusivity, as they relate to predictions of precipitate number density. The inclusion of top-down and bottom-up data in selection of nucleation model form is discussed.
Rodriguez Negron, A. M.↗
A theoretical model for determining turbine flowmeter sensitivity
Analytical model of turbine-type flowmeter guides in the selection of valid extrapolation of available calibration data. An expression for flowmeter performance is developed to include the effects of fluid friction, bearing drag, and magnetic drag upon helical rotor design.
Smith, R. L.↗
Changes in Extratropical Storm Track Cloudiness 1983-2008: Observational Support for a Poleward Shift
Climate model simulations suggest that the extratropical storm tracks will shift poleward as a consequence of global warming. In this study the northern and southern hemisphere storm tracks over the Pacific and Atlantic ocean basins are studied using observational data, primarily from the International Satellite Cloud Climatology Project, ISCCP. Potential shifts in the storm tracks are examined using the observed cloud structures as proxies for cyclone activity. Different data analysis methods are employed, with the objective to address difficulties and uncertainties in using ISCCP data for regional trend analysis. In particular, three data filtering techniques are explored; excluding specific problematic regions from the analysis, regressing out a spurious viewing geometry effect, and excluding specific cloud types from the analysis. These adjustments all, to varying degree, moderate the cloud trends in the original data but leave the qualitative aspects of those trends largely unaffected. Therefore, our analysis suggests that ISCCP data can be used to interpret regional trends in cloudiness, provided that data and instrumental artefacts are recognized and accounted for. The variation in magnitude between trends emerging from application of different data correction methods, allows us to estimate possible ranges for the observational changes. It is found that the storm tracks, here represented by the extent of the midlatitude-centered band of maximum cloud cover over the studied ocean basins, experience a poleward shift as well as a narrowing over the 25 year period covered by ISCCP. The observed magnitudes of these effects are larger than in current generation climate models (CMIP3). The magnitude of the shift is particularly large in the northern hemisphere Atlantic. This is also the one of the four regions in which imperfect data primarily prevents us from drawing firm conclusions. The shifted path and reduced extent of the storm track cloudiness is accompanied by a regional reduction in total cloud cover. This decrease in cloudiness can primarily be ascribed to low level clouds, whereas the upper level cloud fraction actually increases, according to ISCCP. Independent satellite observations of radiative fluxes at the top of the atmosphere are consistent with the changes in total cloud cover. The shift in cloudiness is also supported by a shift in central position of the mid-troposphere meridional temperature gradient. We do not find support for aerosols playing a significant role in the satellite observed changes in cloudiness. The observed changes in storm track cloudiness can be related to local cloud-induced changes in radiative forcing, using ERBE and CERES radiative fluxes. The shortwave and the longwave components are found to act together, leading to a positive (warming) net radiative effect in response to the cloud changes in the storm track regions, indicative of positive cloud feedback. Among the CMIP3 models that simulate poleward shifts in all four storm track areas, all but one show decreasing cloud amount on a global mean scale in response to increased CO2 forcing, further consistent with positive cloud feedback. Models with low equilibrium climate sensitivity to a lesser extent than higher-sensitivity models simulate a poleward shift of the storm tracks.
Bender, Frida A-M.↗
Comparisons of Mixing Efficiency for the Strut Fuel Injector Obtained from Large-Eddy and Reynolds-Averaged Simulations, and Experiments
Mixing efficiency is obtained for a strut fuel injector at hypervelocity flow conditions by using large-eddy simulations (LES), Reynolds-averaged simulations (RAS), and experiments. The injector and flow conditions have been previously investigated by using RAS and experiments as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center (LaRC). Because the fidelity of LES is a strong function of the grid, the mixing efficiency is obtained on two grids, the coarser of which is a factor of two coarser in each of the three dimensions with respect to the fine grid. The RAS uses the two-equation linear eddy viscosity and diffusivity modeling of Menter. In RAS, the species diffusivity model exhibits a strong dependence on the turbulent Schmidt number, which is often adjusted until some metric of engineering interest, such as the mixing efficiency, matches the experimental data. In the absence of experimental data, scale-resolving simulations, such as LES, have been proposed as surrogates for experiments that could provide the data needed to “calibrate” the turbulent Schmidt number in the RAS models. This approach is followed because LES requires significantly more computational resources (CPU, data storage, and time) than RAS, making it prohibitive for use in many engineering applications and specifically for parameter exploration or optimization. Here we examine the mixing efficiency obtained from several RAS with different values of the turbulent Schmidt number, and compare the results with those obtained from the LES and experiments. In addition, the least squares fitting approach was used to demonstrate how to obtain an estimate for the turbulent Schmidt number from LES analytically. These estimates were then used together with prior knowledge about RAS model sensitivity to select a turbulence model that was expected to best match the LES data.
LES↗
Comparisons of Mixing Efficiency for the Strut Fuel Injector Obtained from Large-Eddy and Reynolds-Averaged Simulations, and Experiments
Mixing efficiency is obtained for a strut fuel injector at hypervelocity flow conditions by using large-eddy simulations (LES), Reynolds-averaged simulations (RAS), and experiments. The injector and flow conditions have been previously investigated by using RAS and experiments as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center (LaRC). Because the fidelity of LES is a strong function of the grid, the mixing efficiency is obtained on two grids, the coarser of which is a factor of two coarser in each of the three dimensions with respect to the fine grid. The RAS uses the two-equation linear eddy viscosity and diffusivity modeling of Menter. In RAS, the species diffusivity model exhibits a strong dependence on the turbulent Schmidt number, which is often adjusted until some metric of engineering interest, such as the mixing efficiency, matches the experimental data. In the absence of experimental data, scale-resolving simulations, such as LES, have been proposed as surrogates for experiments that could provide the data needed to “calibrate” the turbulent Schmidt number in the RAS models. This approach is followed because LES requires significantly more computational resources (CPU, data storage, and time) than RAS, making it prohibitive for use in many engineering applications and specifically for parameter exploration or optimization. Here we examine the mixing efficiency obtained from several RAS with different values of the turbulent Schmidt number, and compare the results with those obtained from the LES and experiments. In addition, the least squares fitting approach was used to demonstrate how to obtain an estimate for the turbulent Schmidt number from LES analytically. These estimates were then used together with prior knowledge about RAS model sensitivity to select a turbulence model that was expected to best match the LES data.
LES↗
Sensitivity of the boundary layer energy fluxes to forcing parameters in a simple climate model
Winter and summer surface temperatures and time-averaged boundary layer energy fluxes are calculated by utilizing the Saltzman-Ashe parameterization for boundary layer fluxes in a two-level static model. The results are found to agree with observed patterns. Within the framework of this simple model, sensitivity analyses of the time-averaged boundary layer energy fluxes are conducted. Based on these results some of the forcing parameters (such as the subsurface temperature, cloud cover, surface albedo, etc.) are arranged in a hierarchical order of importance. A generalized method of sensitivity analysis is also suggested.
Rao, M. S.↗
Informing Robust Functional Relationship Benchmarks: An Evaluation of the Temperature Sensitivity of Ecosystem Respiration Across the Arctic-Boreal Region
During land model development, simulated carbon dynamics are often benchmarked against observational data sets to evaluate model performance. Functional relationship benchmarks are the relationship between a driving variable (e.g., temperature) and a response variable (e.g., ecosystem respiration) and are a promising tool for assessing model performance by evaluating modeled sensitivities to changing environmental conditions. However, observed functional relationships can be influenced by choices made during data collection and throughout the benchmarking process, impacting the inferred skill of land models. To avoid misrepresenting a model's true performance, it is necessary to systematically evaluate best practices when constructing functional relationship benchmarks. We developed a set of guidelines for constructing functional relationship benchmarks, considering the choice of data set, number of daily observations, temporal extent, and temporal resolution across Alaska and Canada over a 20-year period from 2001 to 2020. The temperature sensitivity of ecosystem respiration from observations, evaluated through an apparent Q 10 , is highly variable both spatially and as a result of the data processing approach applied in the benchmark formation. When benchmarking 13 models from the Warming Permafrost Model Intercomparison Project (WrPMIP), the range in inferred model skill is substantially impacted by the choices applied in constructing functional relationship benchmarks. The inferred performance of a given model is most sensitive to the number of daily observations and temporal extent, followed by choice of benchmark data set and temporal averaging. Results from this analysis can guide the development of consistent and robust functional relationships for future model evaluation studies.
Poe, Jeralyn [Northern Arizona University, Flagsta↗
Provably conservative approximations to complex reliability models
Complex models can be the bases for derivation of provably conservative and optimistic reliability models that incorporate a reduced state space and fewer transitions; they accordingly possess solutions that are more cost-effective than those of the original complex models. Design space can thereby be extensively explored without incurring the expense of multiple complex model solutions. A conservative-optimistic pair of derived models produces a band that includes the solution to the complex model. Sensitivity analysis can be performed on this pair of models to determine those parameters of the original model that are most sensitive to change and therefore require further expense in obtaining tighter specifications.
Smotherman, M.↗
Using ARM Observations to Evaluate Process-Interactions in MCS Simulations Across Scales (Final Progress Report)
This project, funded by DOE Atmospheric System Research (DE-SC0020050), focused on improving the representation of mesoscale convective systems (MCSs) in numerical weather and climate models by leveraging high-resolution observations from the DOE Atmospheric Radiation Measurement (ARM) program. The research aimed to evaluate model sensitivities to grid spacing, microphysics, and planetary boundary layer (PBL) schemes, with a particular emphasis on improving convection parameterization for high-resolution modeling. Findings from this work highlight several key advancements. Model validation against ARM radar wind profiler data from the Southern Great Plains (SGP) and Manaus (MAO) sites revealed systematic biases in simulated convective mass flux profiles, leading to the development of an observationally constrained evaluation framework for diagnosing and improving model performance. Sensitivity analyses demonstrated that the representation of Amazonian MCSs was highly dependent on PBL scheme selection, while mid-latitude MCSs were more strongly influenced by microphysics parameterizations. A series of high-resolution WRF simulations, ranging from 4 km to 125 m grid spacing, provided insight into the behavior of convective drafts across scales. While updraft properties converged at sub-kilometer resolutions, biases in downdraft intensity persisted even at the finest resolution tested, emphasizing the need for further refinements in model physics. Additionally, comparisons of MCS vertical structures between mid-latitude and tropical environments revealed stronger updrafts and larger mass flux in mid-latitude MCSs, providing critical insights for improving climate model representations of storm-scale dynamics. The project’s findings have already contributed to advancing numerical modeling capabilities, particularly in WRF, MPAS, ICON, and DOE’s SCREAM model, by refining how convective processes are represented in high-resolution climate simulations. Results were disseminated through peer-reviewed publications, conference presentations, and ARM/ASR Research Highlights, engaging the broader scientific community. The project also provided valuable training opportunities for two postdoctoral researchers, who played central roles in model development, analysis, and dissemination of results. Their work contributed to several publications and conference presentations, helping prepare them for careers in atmospheric modeling. By improving the simulation of MCSs, this research directly supports the development of next-generation climate models capable of more accurately representing extreme precipitation and convective processes. The insights gained will inform future improvements in convective parameterization and guide the design of high-resolution weather and climate simulations, ultimately enhancing the reliability of climate projections and weather forecasts.
54 ENVIRONMENTAL SCIENCES↗
Earth System Model Parameter Adjustment Using a Green's Functions Approach
We demonstrate the practicality and effectiveness of using a Green's functions estimation approach for adjusting uncertain parameters in an Earth system model (ESM). This estimation approach has previously been applied to an intermediate-complexity climate model and to individual ESM components, e.g., ocean, sea ice, or carbon cycle components. Here, the Green's functions approach is applied to a state-of-the-art ESM that comprises a global atmosphere/land configuration of the Goddard Earth Observing System (GEOS) coupled to an ocean and sea ice configuration of the Massachusetts Institute of Technology general circulation model (MITgcm). Horizontal grid spacing is approximately 110 km for GEOS and 37–110 km for MITgcm. In addition to the reference GEOS-MITgcm simulation, we carried out a series of model sensitivity experiments, in which 20 uncertain parameters are perturbed. These “control” parameters can be used to adjust sea ice, microphysics, turbulence, radiation, and surface schemes in the coupled simulation. We defined eight observational targets: sea ice fraction, net surface shortwave radiation, downward longwave radiation, near-surface temperature, sea surface temperature, sea surface salinity, and ocean temperature and salinity at 300 m. We applied the Green's functions approach to optimize the values of the 20 control parameters so as to minimize a weighted least-squares distance between the model and the eight observational targets. The new experiment with the optimized parameters resulted in a total cost reduction of 9 % relative to a simulation that had already been adjusted using other methods. The optimized experiment attained a balanced cost reduction over most of the observational targets. We also report on results from a set of sensitivity experiments that are not used in the final optimized simulation but helped explore options and guided the optimization process. These experiments include an assessment of sensitivity to the number of control parameters and to the selection of observational targets and weights in the cost function. Based on these sensitivity experiments, we selected a specific definition for the cost function. The sensitivity experiments also revealed a decreasing overall cost as the number of control variables was increased. In summary, we recommend using the Green's functions estimation approach as an additional fine-tuning step in the model development process. The method is not a replacement for modelers' experience in choosing and adjusting sensitive model parameters. Instead, it is an additional practical and effective tool for carrying out final adjustments of uncertain ESM parameters.
Green's Function↗
Validation and moisture content sensitivity analysis of cross-laminated timber wall assemblies in EnergyPlus
Cross-laminated timber buildings are becoming more common in North America, with many numerical studies showing potential energy savings. However, no studies have validated any EnergyPlus heat transfer algorithms or quantified their accuracy in simulating CLT in building envelopes. This study empirically validates the heat flux predictions for each of EnergyPlus's heat transfer algorithms (Conduction Transfer Functions (CTF), Effective Moisture Penetration Depth (EMPD), Conduction Finite Difference (CondFD), and Heat and Moisture Transfer (HAMT)) for two different CLT ply thicknesses with both summer and winter boundary conditions measured in controlled lab experiments. It also evaluates the model sensitivity of heat flux and heating and cooling loads to moisture content. The 1D validation shows that the HAMT model is the most accurate among all algorithms. All EnergyPlus's heat flux predictions are accurate independent of CLT plate thickness for summer conditions. However, the three constant property algorithms (CTF, EMPD, and CondFD) underpredict heat flux throughout the whole day during winter conditions. The 1D sensitivity analysis indicates that elevated moisture content can increase peak heat fluxes through the material by up to 20 %. Finally, the whole building model sensitivity analysis shows increased heating load and slight cooling load variation due to increased moisture content when using constant property models. The analysis shows significantly lower peak thermal demand (7 % lower heating and 6 % lower cooling) and monthly thermal load (8 % less cooling and 6 % less heating) predictions when using HAMT vs a constant property model.
42 ENGINEERING↗
Land surface interaction
The topics covered include the following: land and climate modeling; sensitivity studies; the process of a land model; model-specific parameterizations; water stress; within-canopy resistances; partial vegetation; canopy temperature; and present experience with a land model coupled to a general circulation model.
Dickinson, Robert E.↗
Data-Driven Surrogate Modeling with Microstructure-Sensitivity of Viscoplastic Creep in Grade 91 Steel
Abstract To support the development of advanced steel alloys tailored to withstand extreme conditions, it is imperative to account for the mechanical performance of components, while considering the influence of local microstructure on the macroscopic response. To this end, this study focuses on the development of microstructure-sensitive constitutive models for the mechanical response of Grade 91 steel exposed to extreme thermo-mechanical environments. Polynomial chaos expansion (PCE) surrogates are used to emulate high-fidelity polycrystal simulations of the viscoplastic response of Grade 91 steel as a function of the microstructure fingerprint (e.g., dislocations and precipitates). To cover a wide temperature–stress domain, two separate PCE surrogates—one that captures softening and the other that captures hardening behavior—are combined using another (sparse) Gaussian process regression model. The resulting constitutive creep surrogate model is integrated within the MOOSE finite element framework to simulate the intricate effects of microstructure, in particular MX-phase precipitates, on a component with a graded microstructure. Surrogate sensitivity analysis is applied to quantify the relevant impact of spatially varying microstructure on the creep response in a test-case involving a Grade 91 alloy with a prototypical weld.
36 MATERIALS SCIENCE↗
Test and Analysis of Full-Scale 27.5-Foot-Diameter Stiffened Metallic Launch Vehicle Cylinders
The Shell Buckling Knockdown Factor Project (SBKF) was established with the goal of developing improved (i.e., less-conservative, more robust) shell buckling knockdown factors (KDFs) for modern launch-vehicle structures. To this end, SBKF has engaged in several activities to support the development, validation, and implementation of the new design factors, including subscale and full-scale structural testing. Tests on eight different subscale, 8-foot-diameter, integrally stiffened aluminum-lithium 2195 (Al-Li 2195) cylinders were conducted in order to obtain the majority of the required validation data. In addition, two full-scale, 27.5-foot-diameter, Al-Li 2195, integrally stiffened cylinders were tested to provide additional validation data and to determine structural scaling trends. Presented herein are the details of a recent analysis model development and test and analysis correlation effort on the full-scale test articles. The effects of selected modeling assumptions and approaches are discussed, and results from a modeling sensitivity study are presented. It was found that simplified finite element models, that assume nominal test article geometry and material properties, can predict the overall response characteristics well. However, several discrepancies in the test and analysis results were observed. A sensitivity study was performed to determine the effects of several modeling assumptions and address the observed discrepancies. The results from the study indicated that the evolution of local skin pocket buckling and the presence of residual stresses due to the manufacturing process can have a significant influence on the predicted buckling response of the cylinders considered.
Lovejoy, Andrew E.↗
Climate sensitivity with a seasonal cycle energy balance model
The sensitivity of climate which may have a local maximum as the ice cap passes through a midlatitude region where the atmosphere's transport efficiency varies strongly with latitude is examined. This behavior, found in a two level primitive equations climate model forced with annual mean insolation, was reproduced in an energy balance model (EBM) by making the diffusion coefficient a function of latitude. The two level seasonally varying EBM was applied and the global mean surface temperature vs. solar constant for this model are shown and two regions of enhanced sensitivity appear. The snowcover distributions around the year for three cases are shown.
Suarez, M. J.↗
Verification of Numerical Solutions for the Deployment of the Highly Nonlinear MARSIS Antenna Boom Lenticular Joints
The MARSIS antenna booms are constructed using lenticular hinges between straight boom segments in a novel design which allows the booms to be extremely lightweight while retaining a high stiffness and well defined structural properties once they are deployed. Lenticular hinges are elegant in form but are complicated to model as they deploy dynamically and require highly specialized nonlinear techniques founded on carefully measured mechanical properties. Results from component level testing were incorporated into a highly specialized ADAMS model which employed an automated damping algorithm to account for the discontinuous boom lengths formed during the deployment. Additional models with more limited capabilities were also developed in both DADS and ABAQUS to verify the ADAMS model computations and to help better define the numerical behavior of the models at the component and system levels. A careful comparison is made between the ADAMS and DADS models in a series of progressive steps in order to verify their numerical results. Different trade studies considered in the model development are outlined to demonstrate a suitable level of model fidelity. Some model sensitivities to various parameters are explored using subscale and full system models. Finally, some full system DADS models are exercised to illustrate the limitations of traditional modeling techniques for variable geometry systems which were overcome in the ADAMS model.
Mars↗
Challenges in Quantifying Pliocene Terrestrial Warming Revealed by Data-Model Discord
Comparing simulations of key warm periods in Earth history with contemporaneous geological proxy data is a useful approach for evaluating the ability of climate models to simulate warm, high-CO2 climates that are unprecedented in the more recent past. Here we use a global data set of confidence-assessed, proxy-based temperature estimates and biome reconstructions to assess the ability of eight models to simulate warm terrestrial climates of the Pliocene epoch. The Late Pliocene, 3.6-2.6 million years ago, is an accessible geological interval to understand climate processes of a warmer world4. We show that model-predicted surface air temperatures reveal a substantial cold bias in the Northern Hemisphere. Particularly strong data-model mismatches in mean annual temperatures (up to 18 C) exist in northern Russia. Our model sensitivity tests identify insufficient temporal constraints hampering the accurate configuration of model boundary conditions as an important factor impacting on data- model discrepancies. We conclude that to allow a more robust evaluation of the ability of present climate models to predict warm climates, future Pliocene data-model comparison studies should focus on orbitally defined time slices.
Salzmann, Ulrich↗