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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Fuzzy Logic Controller↗
DOE OSTI2022

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2023

Towards Soil Moisture Profile Estimation in the Root Zone Using L- and P-Band Radiometer Observations: A Coherent Modelling Approach

Precision irrigation management and crop water stress assessment rely on accurate estimation of root zone soil moisture. However, only the top 5cm soil moisture can be estimated using the two current passive microwave satellite missions, Soil Moisture and Ocean Salinity (SMOS) and Soil Moisture Active Passive (SMAP), which operate at L-band (wavelength of ~21cm). Since the contributing depth of the soil to brightness temperature increases with observation wavelength, it is expected that a P-band (wavelength of ~40cm) radiometer could potentially provide soil moisture information from deeper layers of the soil profile. Moreover, by combining both L- and P- bands, it is hypothesized that the soil moisture profile can be estimated even beyond their individual observation depths. The aim of this study was to demonstrate the potential of combined L-band and P-band radiometer observations to estimate the soil moisture profile under flat bare soil using a stratified coherent forward model. Brightness temperature observations at L-band and P-band from a tower based experimental site across a dry (April 2019) and a wet (March 2020) period, covering different soil moisture profile shapes, were used in this study. Results from an initial synthetic study showed that the performance of a combined L-band and P-band approach was better than the performance of using either band individually, with an average depth over which reliable soil moisture profile information could be estimated (i.e. with a target root mean square error (RMSE) of less than 0.04 m3/m3) being 20cm for linear and 15cm for second-order polynomial functions. Other functions were also tested but found to have a poorer performance. Applying the method to the tower-based brightness temperature achieved an average estimation depth of 28cm (20cm) and 5cm (5cm) during the dry and wet periods respectively when using a second-order polynomial (linear) function. These findings highlight the opportunity of a satellite mission with L-band and P-band observations to accurately estimate the soil moisture profile to as deep as 30cm globally.

Foad Brakhasi↗
DOE OSTI2023

Interface flux recovery framework for constructing partitioned heterogeneous time-integration methods

A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. Here, in this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time-integrators from the explicit Runge-Kutta and Adams-Moulton families.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗
DOE OSTI2023

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval 0,2, multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite K* polynomial moment, with K* depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.

Physics↗
DOE OSTI2020

Improving galaxy clustering measurements with deep learning: analysis of the DECaLS DR7 data

ABSTRACT Robust measurements of cosmological parameters from galaxy surveys rely on our understanding of systematic effects that impact the observed galaxy density field. In this paper, we present, validate, and implement the idea of adopting the systematics mitigation method of artificial neural networks for modelling the relationship between the target galaxy density field and various observational realities including but not limited to Galactic extinction, seeing, and stellar density. Our method by construction allows a wide class of models and alleviates overtraining by performing k-fold cross-validation and dimensionality reduction via backward feature elimination. By permuting the choice of the training, validation, and test sets, we construct a selection mask for the entire footprint. We apply our method on the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Emission Line Galaxies (ELGs) selection from the Dark Energy Camera Legacy Survey (DECaLS) Data Release 7 and show that the spurious large-scale contamination due to imaging systematics can be significantly reduced by up-weighting the observed galaxy density using the selection mask from the neural network and that our method is more effective than the conventional linear and quadratic polynomial functions. We perform extensive analyses on simulated mock data sets with and without systematic effects. Our analyses indicate that our methodology is more robust to overfitting compared to the conventional methods. This method can be utilized in the catalogue generation of future spectroscopic galaxy surveys such as eBOSS and Dark Energy Spectroscopic Instrument (DESI) to better mitigate observational systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2002

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Wang, Z. J.↗
DOE OSTI2026

Statistical Correlation of Heliostat Pointing Deviation With Wind

This work was carried out as part of the Heliostat Consortium (HelioCon) Field Deployment subtask with the aim to develop a reduced order model framework for correlating wind speed and pointing deviation of a heliostat facet. There are only sparse field measurements of heliostat pointing deviations and accompanying wind conditions published in the literature. Heliostat test standards, such as IEC 62862-4-3, propose a suite of tests including laser pointing repeatability at wind speeds below 4 m/s, and provide technical requirements for heliostat slope and tracking deviations in coarse average wind speed bins of 4 m/s, 6 m/s, and 8 m/s. In addressing the gap of the variation of heliostat pointing deviation with wind speed, field measurements of laser pointing on a grid target and wind conditions were analyzed in this study at the Third-Party Metrology Platform at the National Laboratory of the Rockies (NLR) Flatirons Campus. Horizontal pointing deviations were found to follow a logarithmic relationship with peak wind speed, whereas vertical pointing deviations follow an exponential relationship with peak wind speed. Both horizontal and vertical pointing deviations also follow a second order polynomial relationship, as expected from the proportionality of elastic loads and deformations with the square of wind speed. The results indicate that heliostat facet pointing deviations in the vertical direction increase at a faster rate than in the horizontal direction with increasing wind speed over the tested range, however these are dependent on the heliostat structural design. Next steps are recommended for additional field measurements to confirm a linear relationship of pointing deviation with applied moment on a heliostat facet, and to distinguish between gravity-induced and wind-induced pointing deviations at different elevation angles. The derived correlations in the preliminary analysis in this report serve as a case study for heliostat developers and plant operators to estimate the wind-induced pointing deviations and their variation with peak gust wind speed. Next steps in future work would recommend higher resolution and longer duration datasets for different elevation angles and wind directions to reduce uncertainties and variance of collected laser beam spot data and their correlations with bin-averaged wind speed.

17 WIND ENERGY↗
DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Dorobantu, Andrei↗
DOE OSTI2022

Efficient method for estimating the time evolution of the proto-neutron star mass and radius from a supernova neutrino signal

In this paper, we present a novel method to estimate the time evolution of the proto-neutron star (PNS) structure from the neutrino signal in a core-collapse supernova (CCSN). Employing recent results from multidimensional CCSN simulations, we delve into a relation between the total emitted neutrino energy (TONE) and PNS mass/radius, and we find that they are strongly correlated with each other. We fit the relation by simple polynomial functions connecting the TONE to the mass and radius of the PNS as a function of time. By combining another fitting function representing the correlation between the TONE and the cumulative number of events at each neutrino observatory, the PNS mass and radius can be retrieved from purely observed neutrino data. We demonstrate retrievals of PNS mass and radius from mock data of the neutrino signal, and we assess the capability of our proposed method. While underlining the limitations of the method, we also discuss the importance of the joint analysis with the gravitational wave signal. This would reduce uncertainties of parameter estimations in our method, and may narrow down the possible neutrino oscillation model. The proposed method is a very easy and inexpensive computation, which will be useful in real data analysis of the CCSN neutrino signal.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Correlation and prediction of dynamic human isolated joint strength from lean body mass

A relationship between a person's lean body mass and the amount of maximum torque that can be produced with each isolated joint of the upper extremity was investigated. The maximum dynamic isolated joint torque (upper extremity) on 14 subjects was collected using a dynamometer multi-joint testing unit. These data were reduced to a table of coefficients of second degree polynomials, computed using a least squares regression method. All the coefficients were then organized into look-up tables, a compact and convenient storage/retrieval mechanism for the data set. Data from each joint, direction and velocity, were normalized with respect to that joint's average and merged into files (one for each curve for a particular joint). Regression was performed on each one of these files to derive a table of normalized population curve coefficients for each joint axis, direction, and velocity. In addition, a regression table which included all upper extremity joints was built which related average torque to lean body mass for an individual. These two tables are the basis of the regression model which allows the prediction of dynamic isolated joint torques from an individual's lean body mass.

Pandya, Abhilash K.↗
NASA NTRS2002

Software for Estimating Costs of Testing Rocket Engines

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Hines, Merion M.↗
NASA NTRS2004

Software for Estimating Costs of Testing Rocket Engines

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Hines, Merlon M.↗
NASA NTRS2003

Software for Estimating Costs of Testing Rocket Engines

A high-level parametric mathematical model for estimating the costs of testing rocket engines and components at Stennis Space Center has been implemented as a Microsoft Excel program that generates multiple spreadsheets. The model and the program are both denoted, simply, the Cost Estimating Model (CEM). The inputs to the CEM are the parameters that describe particular tests, including test types (component or engine test), numbers and duration of tests, thrust levels, and other parameters. The CEM estimates anticipated total project costs for a specific test. Estimates are broken down into testing categories based on a work-breakdown structure and a cost-element structure. A notable historical assumption incorporated into the CEM is that total labor times depend mainly on thrust levels. As a result of a recent modification of the CEM to increase the accuracy of predicted labor times, the dependence of labor time on thrust level is now embodied in third- and fourth-order polynomials.

Hines, Merlon M.↗
DOE OSTI2020

Data-Driven Many-Body Models for Molecular Fluids: CO 2 /H 2 O Mixtures as a Case Study

In this study, we extend the scope of the many-body TTM-nrg and MB-nrg potential energy functions (PEFs), originally introduced for halide ion–water and alkali-metal ion–water interactions, to the modeling of carbon dioxide (CO2) and water (H2O) mixtures as prototypical examples of molecular fluids. Both TTM-nrg and MB-nrg PEFs are derived entirely from electronic structure data obtained at the coupled cluster level of theory and are, by construction, compatible with MB-pol, a many-body PEF that has been shown to accurately reproduce the properties of water. Although both TTM-nrg and MB-nrg PEFs adopt the same functional forms for describing permanent electrostatics, polarization, and dispersion, they differ in the representation of short-range contributions, with the TTM-nrg PEFs relying on conventional Born–Mayer expressions and the MB-nrg PEFs employing multidimensional permutationally invariant polynomials. By providing a physically correct description of many-body effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO 2 –CO 2 and CO 2 –H 2 O dimers and the energetics of small clusters, as well as to correctly reproduce various properties in both gas and liquid phases. Furthermore, building upon previous studies of aqueous systems, our analysis provides further evidence for the accuracy and efficiency of the MB-nrg framework in representing molecular interactions in fluid mixtures at different temperature and pressure conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2000

Global Design Optimization for Fluid Machinery Applications

Recent experiences in utilizing the global optimization methodology, based on polynomial and neural network techniques for fluid machinery design are summarized. Global optimization methods can utilize the information collected from various sources and by different tools. These methods offer multi-criterion optimization, handle the existence of multiple design points and trade-offs via insight into the entire design space can easily perform tasks in parallel, and are often effective in filtering the noise intrinsic to numerical and experimental data. Another advantage is that these methods do not need to calculate the sensitivity of each design variable locally. However, a successful application of the global optimization method needs to address issues related to data requirements with an increase in the number of design variables and methods for predicting the model performance. Examples of applications selected from rocket propulsion components including a supersonic turbine and an injector element and a turbulent flow diffuser are used to illustrate the usefulness of the global optimization method.

Shyy, Wei↗