SEARCH · Engineering Papers

Results for “uncertainty Quantification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Bayesian Symbolic Regression: Addressing Challenges in Estimating Fractional Bayes Factors and Application to Fatigue Crack Growth Modeling

This research pioneers advancements in computational mechanics by integrating Bayesian-based uncertainty quantification into symbolic regression, specifically focusing on the critical task of accurately estimating the fractional Bayes factor for selecting arbitrary equations. In our exploration, we rigorously study two prominent methods—sequential Monte Carlo and the Laplace approximation—employed for computing the fractional Bayes factor. Our findings underscore the limitations of the Laplace approximation, revealing its diminished accuracy in nonlinear and multimodal scenarios. Specifically, the Laplace approximation is shown to underpredict fractional Bayes factor on a wide set of equations associated with a symbolic regression benchmark. This comparative analysis sheds light on the nuanced performance of these techniques, guiding researchers toward more informed choices in uncertainty quantification within symbolic regression. Furthermore, we showcase the practical utility of these enhanced symbolic regression tools through their application to a real-world problem in fatigue crack growth modeling, emphasizing their efficacy in capturing the complexities of mechanical systems.

Geoffrey Bomarito↗

NASA NTRSDate not supplied

The Effect of Fiber-Angle Fidelity on the Linear Response of Tow-steered Composite Plates

Composite laminate tailoring is traditionally performed by uniformly changing the in-plane ply orientation to obtain the desired mechanical performance. The emergence of tow-steered plies, where the fibers follow a prescribed curvilinear path, have increased the tailorability of composite laminates. However, characterizing the behavior of tow-steered laminates using finite element analysis is challenging because additional, and often numerous, orientation definitions may be required. The additional orientation definitions detrimentally increase the computational cost and hinder the use of advanced analysis techniques, such as Monte Carlo or uncertainty quantification, in the design process. To reduce computational cost without adversely affecting mechanics-based performance, the results of a parametric study that was used to investigate the effects of fiber-angle fidelity, element size, and tow-steered radius-of-curvature on various loading scenarios for tow-steered composite plates are presented. The three loading scenarios that were analyzed using finite element analysis included an axial tension load, an applied constant through-thickness-direction pressure load, and an axial compression load. Results for mechanics-based metrics of interest are presented and discussed for each loading scenario. Little sensitivity (less than one percent difference) to the effect of fiber-angle fidelity is observed in the mechanics-based metrics until the coarse-end of the considered range. Sensitivity to element size generally dominates the observed results for the mechanics-based metrics. Notable reductions in the preprocessing time are observed for increasingly coarse element size and fiber-rounding parameters. The preprocessing times decreased up to three orders of magnitude from a few thousand seconds to a few seconds without loss of accuracy in the mechanics-based metrics. Such increased computational performance is of particular interest to the structural design and analysis communities that may be conducting large counts of finite-element analyses, such as in other parametric studies, Monte-Carlo analyses, uncertainty quantification, or tow-steered optimization.

tow-steered composites↗

NASA NTRS1993

Quantification of uncertainties in composites

An integrated methodology is developed for computationally simulating the probabilistic composite material properties at all composite scales. The simulation requires minimum input consisting of the description of uncertainties at the lowest scale (fiber and matrix constituents) of the composite and in the fabrication process variables. The methodology allows the determination of the sensitivity of the composite material behavior to all the relevant primitive variables. This information is crucial for reducing the undesirable scatter in composite behavior at its macro scale by reducing the uncertainties in the most influential primitive variables at the micro scale. The methodology is computationally efficient. The computational time required by the methodology described herein is an order of magnitude less than that for Monte Carlo Simulation. The methodology has been implemented into the computer code PICAN (Probabilistic Integrated Composite ANalyzer). The accuracy and efficiency of the methodology/code are demonstrated by simulating the uncertainties in the heat-transfer, thermal, and mechanical properties of a typical laminate and comparing the results with the Monte Carlo simulation method and experimental data. The important observation is that the computational simulation for probabilistic composite mechanics has sufficient flexibility to capture the observed scatter in composite properties.

Liaw, D. G.↗

NASA NTRS1993

Quantification of uncertainties in the performance of smart composite structures

A composite wing with spars, bulkheads, and built-in control devices is evaluated using a method for the probabilistic assessment of smart composite structures. Structural responses (such as change in angle of attack, vertical displacements, and stresses in regular plies with traditional materials and in control plies with mixed traditional and actuation materials) are probabilistically assessed to quantify their respective scatter. Probabilistic sensitivity factors are computed to identify those parameters that have a significant influence on a specific structural response. Results show that the uncertainties in the responses of smart composite structures can be quantified. Responses such as structural deformation, ply stresses, frequencies, and buckling loads in the presence of defects can be reliably controlled to satisfy specified design requirements.

Shiao, Michael C.↗

NASA NTRS2012

Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.

Baurle, Robert A.↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

NASA NTRSDate not supplied

Uncertainty Reduction With Multi-Model Monte Carlo for Crystal Plasticity Simulations of Additively Manufactured Metals

In this work, multi-model Monte Carlo estimators are developed to reduce uncertainty in quantities of interest (QoIs) extracted from crystal plasticity simulations of additively manufactured (AM) metals. A significant concern in AM parts is uncertainty in mechanical properties caused in part by complex microstructures that arise from the AM process. Quantifying uncertainty in microstructure-sensitive behavior using experiments alone is costly, especially when mechanical allowables must be established. Quantitative relationships among microstructure, micromechanical metrics like slip accumulation, crack initiation, and failure are also difficult to capture with limited experiments. Crystal plasticity material models instead enable computational prediction of micromechanical stress and strain fields given a discretized microstructure. However, high-fidelity finely discretized crystal plasticity simulations are computationally expensive, while lower-fidelity models are less accurate and generally biased, making uncertainty quantification and reduction computationally difficult as well. Multi-model Monte Carlo methods leverage correlations between high- and low-fidelity models to produce unbiased estimators for QoIs with reduced uncertainty relative to standard Monte Carlo. Crystal plasticity QoIs considered in this work include yield strength and the mean and extreme values of micromechanical fields that are relevant to crack initiation. Multi-model Monte Carlo estimators are developed for each individual QoI and several groups of QoIs. The results of this work establish relationships among model correlations, sample allocation, and uncertainty reduction for different combinations of QoIs and demonstrate a trend of less uncertainty reduction as QoIs become more sensitive to local microstructure. Limitations from using pilot samples to estimate model covariances and train low-fidelity models are also addressed. The uncertainty reduction achieved by multi-model Monte Carlo is an important step toward using computational mechanics models to predict microstructure-sensitive crack initiation and failure in AM parts.

uncertainty quantification↗

NASA NTRSDate not supplied

Integrated Process-Structure-Property Simulations for Additive Manufacturing Using the Open-Source Materialite Package

The microstructure and properties of additively manufactured (AM) metals are strongly dependent on process conditions. Therefore, process-structure-property (PSP) simulations are a useful tool for exploring process parameter space, studying process variations, and quantifying uncertainty in material properties. However, integrating process-structure and structure-property simulations often involves connecting multiple software packages. Each package may use unique data structures and require substantial domain knowledge. This presentation demonstrates PSP simulation capabilities of Materialite, an open-source package developed at NASA Langley Research Center. Materialite simplifies model linkages by using a common data structure and model interface, enabling straightforward simulation across a PSP model chain. Physics-based models, including kinetic Monte Carlo and crystal plasticity, are implemented within the package. The model interface is also intended to simplify implementation of new models and enable integration with external simulation tools. Example use cases include uncertainty quantification with PSP models and GPU-accelerated powder bed fusion AM process models.

additive manufacturing↗

NASA NTRS2018

Dynamics and Control of Quadcopter in Uncertain Environment

We consider problem of dynamics, control, and uncertainty quantification for quadcopter. We use the 6DOF model of quadcopter dynamics, linear quadratic regulator and linear quadratic Gaussian control of quadcopter in the presence of dynamical disturbances, measurement noise, hidden dynamical variables, dashing GPS signal, and wind gusts to predict quadcopter trajectory. We identify key sources of uncertainties and report on progress in development of a system that estimates the probability of safety-critical events using a set of algorithms based on the trajectory predictions.

uncertainty quantification↗

NASA NTRSDate not supplied

Differential Equation Approximation Using Gradient-Boosted Quantile Regression

The operation of cyber-physical-human (CPH) systems is subject to various epistemic and aleatory uncertainties. Overall trustworthiness of CPH systems relies on the trustworthiness of its components and their interactions. It is important that computational models comprising the cyber component of CPH provide predictions accompanied by a measure of confidence in model outcomes. Uncertainty quantification (UQ) and propagation are especially important in safety critical CPH systems. Gradient-boosted trees is a modeling approach capable both of learning the dynamics of a system and performing UQ. In this paper, we devise a method for using gradient boosting to learn the dynamics of a second order differential equation and estimate uncertainty at the same time. We do this by creating a custom loss function that trains the model to approximate the second derivative of a noisy time series, and to penalize based on a parameter that corresponds to the desired quantile. The resulting gradient boosting model can simulate stochastic trajectories of the system given a single starting point, that is, it can estimate both the expected trajectory and its uncertainty. We show that the uncertainty estimation is well calibrated and that the model can learn the dynamics even in the presence of noise. We demonstrate the approach on a simple cartpole system.

Autonomous systems↗

NASA NTRSDate not supplied

CFD Validation Study of a Hypersonic Cone-Slice-Flap Variable Geometry Configuration

Model validation is the process of determining the degree of accuracy between physical reality and the model. The result of model validation can either be used to improve the model through calibration or quantify the model-form uncertainty. This work focuses on providing the model-form uncertainty through an area metric for a hypersonic cone-slice-flap variable geometry configuration given uncertainty in both the simulation and experimental data. The research here compares two different turbulence models for the simulations. For a variable geometry, performing uncertainty quantification to capture the model-form uncertainty on every configuration is computationally challenging. This work lays out a procedure that can give an accurate representation of the model-form uncertainty using a small number of high-fidelity runs and many low-fidelity runs on multiple configurations. Running this comparison provides a quantifiable measurement for the accuracy of each turbulence model for this type of design. The high-fidelity CFD solver used was VULCAN-CFD and the low-fidelity results came from Cart3D. The experimental data came from the 20-Inch Mach 6 Tunnel located at NASA Langley Research Center. The present work showed that the using both the Spalart and Allamaras and Menter Shear-Stress Transport turbulence models overpredicted the drag and lift coefficient, while underpredicting the pitching moment coefficient. The model-form uncertainty estimate resulted in up to a 13.6% change in the total uncertainty for the drag coefficient, up to a 57.4% change in total uncertainty for the lift coefficient, and up to a 100% change in total uncertainty for the pitching moment coefficient.

Laura M. White↗

NASA NTRSDate not supplied

CFD Validation Study of a Hypersonic Cone-Slice-Flap Variable Geometry Configuration

Model validation is the process of determining the degree of accuracy between physical reality and the model. The result of model validation can either be used to improve the model through calibration or quantify the model-form uncertainty. This work focuses on providing the model-form uncertainty through an area metric for a hypersonic cone-slice-flap variable geometry configuration given uncertainty in both the simulation and experimental data. For a variable geometry, performing uncertainty quantification to capture the model-form uncertainty on every configuration is computationally challenging. This work lays out a procedure that can give an accurate representation of the model-form uncertainty using a small number of high-fidelity runs and many low-fidelity runs on multiple configurations. Running this comparison provides a quantifiable measurement for the accuracy of each turbulence model for this type of design. The high-fidelity CFD solver used was VULCAN-CFD and the low-fidelity results came from Cart3D. The experimental data came from the 20-Inch Mach 6 Tunnel located at NASA Langley Research Center. The present work showed that the turbulence simulation overpredicted the drag and lift coefficient, while underpredicting the pitching moment coefficient. The model-form uncertainty estimate resulted up to a 13.6% change in the total uncertainty for the drag coefficient, up to a 57.4% change in total uncertainty for the lift coefficient, and up to a 100% change in total uncertainty for the pitching moment coefficient.

Laura White↗

NASA NTRS2022

Monte-Carlo Analysis of Minimum Thermocouple Depths using Icarus

Icarus is a three-dimensional, unstructured, finite-volume material response solver developed at NASA Ames Research Center and has been verified against other NASA material response tools like FIAT, which have a long history of successfully designing thermal protection system (TPS). Icarus solves a set of conservation equations for mass and energy and uses Darcy’s Law in place of momentum conservation. An ecosystem of material response tools has been built around a general-purposed Icarus library that in addition to the typical material response analysis also supports TPS sizing (1-D and multi-dimensional), uncertainty quantification, and has been successfully integrated into a multi-physics architecture built around US3D. In this paper, a brief overview of Icarus and its capabilities will be presented using an illustrative Monte Carlo analysis of the one-dimensional, in-depth material response of a representative Dragonfly trajectory.

Material Response↗

NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry, Descent, and Landing Database

This work focuses on evaluating machine learning methods and their applicability to the generation of an aerodynamic database, particularly for trajectory analysis of a capsule during entry, descent, and landing with a focus on uncertainty quantification. The source data to be used is the wind tunnel and computational data for the Integrated Design Assessment Team (IDAT) configuration of the Orion project, which has been publicly released. The methods used to generate the proposed databases are designed to naturally include a prediction interval, which will be evaluated both for their mean response as well as how well the prediction interval performs. These machine learning methods are compared to a traditionally generated database used by the Orion team as a baseline. It is found that while these machine learning methods perform well, the Orion database tends to still outperform them showing that engineering experience is still needed to make the best database possible. However, these methods still provide comparable results with significantly less effort.

Orion↗

NASA NTRSDate not supplied

Comparisons of Performance Metrics and Machine Learning Methods on an Entry Descent and Landing Database

Orion↗

NASA NTRS2017

Multifidelity, Multidisciplinary Design Under Uncertainty with Non-Intrusive Polynomial Chaos

The primary objective of this work is to develop an approach for multifidelity uncertainty quantification and to lay the framework for future design under uncertainty efforts. In this study, multifidelity is used to describe both the fidelity of the modeling of the physical systems, as well as the difference in the uncertainty in each of the models. For computational efficiency, a multifidelity surrogate modeling approach based on non-intrusive polynomial chaos using the point-collocation technique is developed for the treatment of both multifidelity modeling and multifidelity uncertainty modeling. Two stochastic model problems are used to demonstrate the developed methodologies: a transonic airfoil model and multidisciplinary aircraft analysis model. The results of both showed the multifidelity modeling approach was able to predict the output uncertainty predicted by the high-fidelity model as a significant reduction in computational cost.

West, Thomas K., IV↗

NASA NTRSDate not supplied

A Preliminary Assessment of Step Effects on the BOLT Geometry in Mach 6 Flow

An infrared thermography measurement technique has been installed in the Langley Aerothermodynamic Laboratory. The system is calibrated for use with commercially available thermoplastics and ceramic materials, and to the surface temperature ranges when exposed to the facility hypersonic flow. Herein an uncertainty quantification is performed, revealing 5% surface temperature and 20% heat transfer uncertainty bands to two-sigma confidence. As a first application of the test measurement technique, an investigation was conducted to explore the correlation between the height of forward facing (FF) and rearward facing (RF) two-dimensional steps, free stream Reynolds number, and the onset of boundary layer transition from laminar to turbulent in Mach 6 flow on a 50% scale Boundary Layer Transition (BOLT) flight test vehicle geometry. Computational predictions were generated to identify potential x/L locations of transition onset for various flow conditions with a smooth outer mold line geometry and are compared to experimental results. The BOLT Step Test was conducted in the NASA Langley Aerothermodynamic Laboratory 20-inch Mach 6 wind tunnel at Reynolds numbers between 1.4 and 11.3 million conditions for various step heights. Data were collected using a developmental infrared thermography test technique and reduced to heat transfer for comparison with CFD solutions. This is a preliminary assessment of the developmental infrared thermography test technique used to acquire and reduce the experimental data. insight into the ongoing comparative analysis of the effects of FF and RF steps on boundary layer transition for the BOLT geometry in Mach 6 flow.

BOLT↗

NASA NTRSDate not supplied

A Preliminary Assessment of Step Effects on the BOLT Geometry in Mach 6 Flow

BOLT↗