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NASA NTRS2005

Multivariate Parameter Sets for Optimal Synthesis of Compliant Mechanisms

This paper will propose the use of control maps along with discretized elements or meshes in the design parameter set for optimizing compliant mechanisms. The use of control maps will be demonstrated to encode the motion of groups of nodes or control points within a compliant mechanism design with simple mapping rules. The technique will serve as an alternative to increased mesh size or node wandering techniques that have been proposed to increase the number of alternative design shapes that may be considered. As an alternative approach, the proposed control map parameterization has the significant benefit that it minimizes the number of design parameters necessary (parameters increase linearly with the mesh size) in describing a given design making it computationally efficient. A limited number of tiles can produce a map that has a significant effect on the final shape. If the tiles are chosen appropriately, the problems such as material overlap and non-convex mesh elements are avoided automatically. This paper will describe the implementation of these control maps and provide several examples showing their implementation in the compliant mechanism topology synthesis process.

Shibakov, Alex↗
DOE OSTI2017

Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT* when using the proposed Grandparent-Connection (GP) or Focused-Refinement (FR) algorithms. Next, the Goal Tree algorithm for replanning with unexpected static obstacles is detailed and proven to be asymptotically optimal. A multi-agent collision avoidance problem in obstacle environments is approached via the RRT*, leading to the novel Sampling-Based Collision Avoidance (SBCA) algorithm. The SBCA algorithm is proven to guarantee collision free trajectories for all of the agents, even when subject to uncertainties in the knowledge of the other agents’ positions and velocities. Given that a solution exists, we prove that livelocks and deadlock will lead to the cost to the goal being decreased. We introduce a new deconfliction maneuver that decreases the cost-to-come at each step. This new maneuver removes the possibility of livelocks and allows a result to be formed that proves convergence to the goal configurations. Finally, we present a limited range Graph-based Spatial Load Balancing (GSLB) algorithm which fairly divides a non-convex space among multiple agents that are subject to differential constraints and have a limited travel distance. The GSLB is proven to converge to a solution when maximizing the area covered by the agents. The analysis for each of the above mentioned algorithms is confirmed in simulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Physiological asymmetry in etiolated pea epicotyls: relation to patterns of auxin distribution and phototropic behavior

Etiolated pea seedlings require transformation of Pr phytochrome to Pfr before they display optimal phototropic response to unilateral blue light. This study investigates the possible role of auxin transport in explaining these phenomena. Labeled [2-14C]IAA applied to the intact terminal buds of dark-grown and red light-treated pea seedlings was measured 210 min later on the shaded and illuminated sides of the epicotyl as a function of direction and duration of irradiation with blue light. Totally darkened epicotyls show an asymmetry in distribution of radioactivity in the upper growth zone of the epicotyl, in favor of the side under the concave part of the apical hook. Red light, which greatly potentiates curvature toward subsequent unilateral blue light, lowers this asymmetry. Blue light directed to the epicotyl of red-pretreated plants in a plane parallel to the hook and from the side bearing the convex portion of the hook induces positive phototropic curvature as well as a surplus of radioactivity on the illuminated side of the upper epicotyl and on the shaded side of the lower growth zone of the epicotyl. Light directed to the side bearing the concave part of the hook also causes an accumulation of counts in the upper part of the lighted side but produces neither curvature of the epicotyl nor accumulation of counts in the lower shaded side. Because of this built-in physiological asymmetry in the growth zone just below the apical hook, it is difficult to explain the effects of red and blue light on curvature in terms of patterns of auxin distribution alone.

NASA Program Space Biology↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
DOE OSTI2022

Distributionally Robust Decision Making Leveraging Conditional Distributions

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

Chen, Yuxiao↗
DOE OSTI2018

Fundamental Solutions for Two-Point Boundary Value Problems in Orbital Mechanics

We consider a two-point boundary value problem (TPBVP) in orbital mechanics involving a small body (e.g., a spacecraft or asteroid) and N larger bodies. The least action principle TPBVP formulation is converted into an initial value problem via the addition of an appropriate terminal cost to the action functional. The latter formulation is used to obtain a fundamental solution, which may be used to solve the TPBVP for a variety of boundary conditions within a certain class. In particular, the method of convex duality allows one to interpret the least action principle as a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. In the case where the time duration is less than a specific bound, there exists a unique critical point for the resulting differential game, which yields the fundamental solution given in terms of the solutions of associated Riccati equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A centralized-based method to determine the local voltage control strategies of distributed generator operation in active distribution networks

The increasing penetration of distributed generators (DGs) exacerbates the risk of voltage violations in active distribution networks (ADNs). The var capacity provided by DG inverters is a potential solution for voltage regulation. The conventional centralized control strategies limited by computation and communication burdens are difficult to meet the requirement of rapid voltage control. However, the local control strategies based on real-time measurements have a fast response to the frequent fluctuations of DG outputs. The performance of these local controllers depends on the tuning of the control parameters. This paper proposes a centralized-based method to determine the local voltage control strategies for DGs. A centralized parameter tuning model of control curves is built, in which and curves of DG inverters are mathematically formulated based on piecewise linearization. The original mixed-integer nonlinear programming (MINLP) model is converted into an effectively solved mixed-integer second-order cone programming (MISOCP) model using convex relaxation. The potential benefits of DG inverters are explored to regulate both reactive and curtailed active power, based on local voltage measurements. Case studies on a modified PG&E 69-node distribution system are carried out to verify the effectiveness of the proposed method. Results show that power losses of ADNs are significantly reduced and voltage profiles are also improved.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

Polynuclear Aromatic Hydrocarbons with Curved Surfaces: Buckyballs

The discovery of a new allotropic form of elemental carbon – the fullerenes – and subsequently other novel forms of elemental carbon with pyramidalized surfaces, most notably single-walled and multi-walled carbon nanotubes, introduced a novel structural motif to the polycyclic aromatic hydrocarbons (PAHs) with nonplanar surfaces. Our research program supported by BES DOE grant DE-FG02-04ER15514 has dealt with the synthesis, structural studies, and chemistry of the novel curved-surface PAHs with carbon frameworks structurally related to fullerenes. They are referred to as “buckybowls”. We prepared several new buckybowls and, even more importantly, developed the efficient, gram-scale synthetic methodologies for the preparation of small buckybowls, most notably corannulene (C20H10) and its derivatives. In addition, the employment of the corannulene-based synthons previously developed in our laboratory led to a number of highly nonplanar molecular architectures with two or more corannulene subunits with a potential for the applications as novel materials in separation sciences, nanoelectronics, photovoltaics and catalysis. In collaboration with Professor Angelici (Iowa State) we prepared and characterized several transition metal complexes of corannulene, providing the first structural characterization of η6 metal complexes of buckybowls by a single crystal X-ray diffraction. In addition to the definitive structural characterization of the complexes we demonstrated that the (η6-C6Me6)Ru2+ unit in some relatively stable complexes activate the corannulene ligand to react with proper nucleophiles suggesting that such complexex may be used in catalysis. (Section C). We have explored the efficiency of the dispersion-based interactions of curved-surface conjugated carbon networks by high-level computational models. We showed that the curvature of such networks does not reduce the van der Waals attractions as compared to the planar systems of similar size. We than concentrated on the design, synthesis and testing of the previously unknown molecular receptors with corannulene pincers which are capable of forming the strong ball-and-socket inclusion complexes with fullerenes in solution and in the solid state. Buckycatcher I (a molecular receptor with two corannulene pincers preorganized on a tetrabensocyclooctatetraene tether) inclusion complexes with fullerenes provided the first experimental evidence for the importance of concave-convex π – π interactions in the supramolecular chemistry of fullerene carbon cages with buckybowls. C60@Buckycatcher I has become the prototypical supramolecular system formed by the relatively weak (on the atom-to-atom bases) and has been extensively used by the computational community to test the quality of the theoretical models. In addition, Buckycatcher I shows an exceptional ability to adopt other guest molecules and several its inclusion complexes and/or solvates have been structurally characterized. These unusual structures show the potential of the buckycatchers to be tested as novel organic materials. “Intelligent design” of molecular receptors with corannulene receptors using computational approach allowing for a priori prediction of their binding potentials led to the preparation of other buckycatchers. Both bi- and tridentate corannulene pincers were tested and two of the bidentate receptors (Buckycatchers II and III) exhibited the outstanding affinity toward fullerenes, significantly exciding Buckycatcher I performance. Careful tailoring of the tethers resulted in the optimization of binding energies of the receptors with guest carbon cages and in the reduction of the entropy/solvation penalties. Practical preparation of dicorannulenopentacene opens a new avenue for the synthesis of a pool of bis-corannulene receptors possessing polar groups on their dibenzobarrelene tether. The polar “anchors” can be used to attach these efficient fullerene receptors to solid supports in order to modify their surfaces with the potential applications in separation sciences, catalysis and photovoltaic materials. additionally, the presence of such groups will improve the solubility of the receptors in polar solvents, expanding the scope of their supramolecular chemistry in solutions. Rigorous studies of thermodynamics of host-guest association of molecular clips and tweezers in organic solvents with C60/C70 inclusion complexes with Buckycatcher I as a model system have provided a full set of thermodynamical data including ΔG, ΔH, and –TΔS, for the formation of the inclusion complexes over a range of temperatures and in several solvents. Both 1H NMR and Isothermal Calorimetry (ITC) titrations provide virtually identical association constants, confirming the reliability of the results. WE have shown that thermodynamics of the host-guest complex formation is more complicated than anticipated and proposed by the existing computational models. These data are of premium importance for the testing of the computational solvation models and for a deeper understanding of the supramolecular interactions in organic solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗
DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗
DOE OSTI2017

High-Throughput Combinatorial Development of High-Entropy Alloys For Light-Weight Structural Applications

The primary limitation of today’s lightweight structural alloys is that specific yield strengths (SYS) higher than 200MPa x cc/g (typical value for titanium alloys) are extremely difficult to achieve. This holds true especially at a cost lower than 5dollars/kg (typical value for magnesium alloys). Recently, high-entropy alloys (HEA) have shown promising SYS, yet the large composition space of HEA makes screening compositions complex and time-consuming. Over the course of this 2-year project we started from 150 billion compositions and reduced the number of potential low-density (<5g/cc), low-cost (<5dollars/kg) high-entropy alloy (LDHEA) candidates that are single-phase, disordered, solid-solution (SPSS) to a few thousand compositions. This was accomplished by means of machine learning to guide design for SPSS LDHEA based on a combination of recursive partitioning, an extensive, experimental HEA database compiled from 24 literature sources, and 91 calculated parameters serving as phenomenological selection rules. Machine learning shows an accuracy of 82% in identifying which compositions of a separate, smaller, experimental HEA database are SPSS HEA. Calculation of Phase Diagrams (CALPHAD) shows an accuracy of 71-77% for the alloys supported by the CALPHAD database, where 30% of the compiled HEA database is not supported by CALPHAD. In addition to machine learning, and CALPHAD, a third tool was developed to aid design of SPSS LDHEA. Phase diagrams were calculated by constructing the Gibbs-free energy convex hull based on easily accessible enthalpy and entropy terms. Surprisingly, accuracy was 78%. Pursuing these LDHEA candidates by high-throughput experimental methods resulted in SPSS LDHEA composed of transition metals (e.g. Cr, Mn, Fe, Ni, Cu) alloyed with Al, yet the high concentration of Al, necessary to bring the mass density below 5.0g/cc, makes these materials hard and brittle, body-centered-cubic (BCC) alloys. A related, yet multi-phase BCC alloy, based on Al-Cr-Fe-Ni, shows compressive strain >10% and specific compressive yield strength of 229 MPa x cc/g, yet does not show ductility in tensile tests due to cleavage. When replacing Cr in Al-Cr-Fe-based 4- and 5-element LDHEA with Mn, hardness drops 2x. Combined with compression test results, including those on the ternaries Al-Cr-Fe and Al-Mn-Fe suggest that Al-Mn-Fe-based LDHEA are still worth pursuing. These initial results only represent one compressive stress-strain curve per composition without any property optimization. As such, reproducibility needs to be followed by optimization to show their full potential. When including Li, Mg, and Zn, single-phase Li-Mg-Al-Ti-Zn LDHEA has been found with a specific ultimate compressive strength of 289MPa x cc/g. Al-Ti-Mn-Zn showed a specific ultimate compressive strength of 73MPa x cc/g. These initial results after hot isostatic pressing (HIP) of the ball-milled powders represent the lower end of what is possible, since no secondary processing (e.g. extrusion) has been performed to optimize strength and ductility. Compositions for multi-phase (e.g. dual-phase) LDHEA were identified largely by automated searches through CALPHAD databases, while screening for large face-centered-cubic (FCC) volume fractions, followed by experimental verification. This resulted in several new alloys. Li-Mg-Al-Mn-Fe and Mg-Mn-Fe-Co ball-milled powders upon HIP show specific ultimate compressive strengths of 198MPa x cc/g and 45MPa x cc/g, respectively. Several malleable quarternary Al-Zn-based alloys have been found upon arc/induction melting, yet with limited specific compressive yield strength (<75 MPa x cc/g). These initial results are all without any optimization for strength and/or ductility. High-throughput experimentation allowed us to triple the existing experimental HEA database as published in the past 10 years in less than 2 years which happened at a rate 10x higher than previous methods. Furthermore, we showed that high-throughput thin-film combinatorial methods can be used to get insight in isothermal phase diagram slices. Although it is straightforward to map hardness as a function of composition for sputtered, thin-film, compositional gradients by nano-indentation and compare the results to micro-indentation on bulk samples, the simultaneous impact of composition, roughness, film density, and microstructure on hardness requires monitoring all these properties as a function of location on the compositional gradient, including dissecting the impact of these 4 factors on the hardness map. These additional efforts impact throughput significantly. This work shows that a lot of progress has been made over the years in predicting phase formation that aids the discovery of new alloys, yet that a lot of work needs to be done to predict phases more accurately for LDHEA, whether done by CALPHAD or by other means. More importantly, more work needs to be done to predict mechanical properties of novel alloys, like yield strength, and ductility. Furthermore, this work shows that there is a need for the generation of an empirical alloy database covering strategic points in a multi-dimensional composition space to allow for faster and more accurate predictive interpolations to identify the oasis in the dessert more quickly. Finally, this work suggests that it is worth pursuing a ductile alloy with a SYS > 300 MPa x cc/g in a mass density range of 6-7 g/cc, since the chances for a single-phase or majority-phase FCC increase significantly. Today’s lightweight steels are in this density range.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Volumetric Assessment of UPRITE Exercises From Marker-Based Motion Capture

BACKGROUND Lack of volumetric data on full-body movement of exercises presents a challenge to ensuring the fit of crew member’s full range of motion on the International Space Station (ISS). The Upright Proprioception Retention via In-flight Training and Evaluation (UPRITE) is a sensorimotor countermeasure device designed for maintaining crew members’ proprioception in a microgravity environment. A footplate—attached to a static base—rotates in two degrees of freedom (pitch and roll) up to a 20 deg angle. An initial volumetric assessment assuming an upright standing posture produced a cone-like shape with a narrow bottom and wide top. Such general volumetric assessments risk creating an overly conservative volume estimate, taking up more space than is necessary on the already limited interior space of the ISS, and neglecting necessary volume due to oversimplifying assumptions. Rather, higher-fidelity volumetric assessments offer more comprehensive insights in an environment where every area counts. The main objective of this work is to provide the spatial parameters of exercises on the UPRITE such that it is placed on the ISS according to its volumetric demands or that usage is adjusted to fit the available space. METHODS In 2023, a data collection was performed originally to inform loads and dynamics of system use and was recently leveraged for volumetric assessment. Three human subjects representing different body types (~63-76 inches in stature) performed a variety of board manipulations using UPRITE with body weight offload. The test collected the 3D positional data of a modified full-body Plug-in Gait marker set [1] via a 16-camera OptiTrack MoCap system. After processing – filling marker gaps and trimming data – in OptiTrack Motive, the recorded marker location data, which included device markers, was exported to a readable trajectory file. To accurately represent the full volume defining landmarks, additional markers were digitally added to an unscaled Modified Full Body Model [2]. The model was then scaled according to its subject parameters upon which an inverse kinematics analysis was performed. A custom plugin yielded model marker location data files. Volumetric analyses were performed on the recorded trajectory and model trajectory files using a custom Python-built tool that extracted the marker location data and plotted it in a 3D space. Concerned with only the maximum volume of the motion, a 3D convex hull analysis was applied to the plot, extracting the vertices or external points of the eventual 3D CAD output, dubbed aptly as a “volume shell”. This overall approach was based on guidance in a NASA-STD-3001 Technical Brief [3]. RESULTS AND DISCUSSION Batch volumetric assessment on the exercises for each subject was performed, producing high-fidelity volume shells in minimal time. Preliminary results highlighted the value in higher-fidelity volumes based on collected data when possible. For example, revolving a single posture in the cone assessment would not have sufficiently captured a single leg stance; rather, it would need to involve swinging the leg both forward and back. Additional observations and the maximal dimensions of the volumes, including those based on scaled data for ISS anthropometric requirements, will be presented at the Human Research Program Investigator’s Workshop. CONCLUSIONS While this work’s primary objective was for the UPRITE-to-ISS integration, the tool built to conduct this analysis has wide applications for future exercise systems as an informational tool for optimal device placement. The tool and its findings also have implications for exercise device design and spacecraft interior considerations on Gateway, the Lunar Pressurized Rover, and beyond. REFERENCES [1] Bell, C. A., et al. (2023) Recent Improvements and Verification of a Full Body Model in OpenSim. NASA Human Research Program Investigator’s Workshop. https://ntrs.nasa.gov/citations/20230001080 [2] Lostroscio, K., et al (2023) The Digital Astronaut Simulation. AHFE International Conference on Human Factors in Design, Engineering, and Computing for All. [3] Exercise Overview. (2023) NASA-STD-3001 Technical Brief. https://www.nasa.gov/wp-content/uploads/2023/12/ochmo-tb-031-exercise-overview.pdf?emrc=9d454c?emrc=9d454c

L D Quinto↗
DOE OSTI2020

Proppant embedment in coal and shale: Impacts of stress hardening and sorption

During methane production in CBM reservoirs, the influence of proppant embedment and permeability damage cannot be neglected – especially where the wall-rock is soft. Effective stresses are elevated during methane recovery, increasing both normal loading stress and confinement and simultaneously overprinting sorption-induced volumetric strains. Experiments and analytic modeling are conducted to define key mechanisms controlling these competitive effects. We independently measure overall sample compaction (external LVDT) and local strain (strain gauge) in the matrix to deconvolve proppant embedment in a propped fracture for different conditions of confining stress. The results show symptomatic behaviors of elastic (shale) and elastoplastic (coal) responses of embedment. Different from shale, the evolution of embedment is convex upwards with increased stress where indented depth increases more rapidly as loading stress increases under constant confinement. In addition, a stress-hardening effect is found to play a pivotal role in determining the characteristics of indentation, which are examined in terms of evolution profiles, deformation regimes, embedment slopes, curvatures, yield points and irreversible indentations. Based on the experimental observations a semianalytical model predicts indentation and the evolution of propped permeability under recreated in-situ stress conditions. A simplified case study is conducted to further illustrate the evolution of aperture and permeability of a propped fracture in CBM reservoirs. The modeling results suggest that proppant embedment is significantly overestimated if the variable stress-hardening (VSH) effect is neglected, especially when effective stress is large. Moreover, a decrease in indentation depth possibly occurs during late stage methane production, resulting in a reversal/recovery in fracture closure. This is because desorption-induced shrinkage becomes the predominant effect, causing an increase in aperture and a reduction in the indented volume of proppant. The resulting recovery in permeability implies that the propped coal fracture has the potential to optimally facilitate methane production as a pathway, even at high closure stresses generated by methane drainage.

01 COAL, LIGNITE, AND PEAT↗
NASA NTRS2016

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.

Scruggs, T.↗
NASA NTRS1993

Techniques for estimating Space Station aerodynamic characteristics

A method was devised and calculations were performed to determine the effects of reflected molecules on the aerodynamic force and moment coefficients for a body in free molecule flow. A procedure was developed for determining the velocity and temperature distributions of molecules reflected from a surface of arbitrary momentum and energy accommodation. A system of equations, based on momentum and energy balances for the surface, incident, and reflected molecules, was solved by a numerical optimization technique. The minimization of a 'cost' function, developed from the set of equations, resulted in the determination of the defining properties of the flow reflected from the arbitrary surface. The properties used to define both the incident and reflected flows were: average temperature of the molecules in the flow, angle of the flow with respect to a vector normal to the surface, and the molecular speed ratio. The properties of the reflected flow were used to calculate the contribution of multiply reflected molecules to the force and moments on a test body in the flow. The test configuration consisted of two flat plates joined along one edge at a right angle to each other. When force and moment coefficients of this 90 deg concave wedge were compared to results that did not include multiple reflections, it was found that multiple reflections could nearly double lift and drag coefficients, with nearly a 50 percent increase in pitching moment for cases with specular or nearly specular accommodation. The cases of diffuse or nearly diffuse accommodation often had minor reductions in axial and normal forces when multiple reflections were included. There were several cases of intermediate accommodation where the addition of multiple reflection effects more than tripled the lift coefficient over the convex technique.

Thomas, Richard E.↗