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Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Hsia, Wei Shen↗

A Boltzmann machine for the organization of intelligent machines

A three-tier structure consisting of organization, coordination, and execution levels forms the architecture of an intelligent machine using the principle of increasing precision with decreasing intelligence from a hierarchically intelligent control. This system has been formulated as a probabilistic model, where uncertainty and imprecision can be expressed in terms of entropies. The optimal strategy for decision planning and task execution can be found by minimizing the total entropy in the system. The focus is on the design of the organization level as a Boltzmann machine. Since this level is responsible for planning the actions of the machine, the Boltzmann machine is reformulated to use entropy as the cost function to be minimized. Simulated annealing, expanding subinterval random search, and the genetic algorithm are presented as search techniques to efficiently find the desired action sequence and illustrated with numerical examples.

Moed, Michael C.↗

Linear tracking systems with applications to aircraft control system design

A class of optimal linear time invariant tracking systems, both in continuous time and discrete time, of which the number of inputs (which are restricted to be step functions) is equal to the number of system outputs, is studied. Along with derivation of equations and design procedures, two discretization schemes are presented, constraining either the control or its time derivative, to be a constant over each sampling period. Descriptions are given for the linearized model of the F-8C aircraft longitudinal dynamics, and the C* handling qualities criterion, which then serve as an illustration of the applications of these linear tracking designs. A suboptimal reduced state design is also presented. Numerical results are given for both the continuous time and discrete time designs.

Lee, W. H.↗

Nonlinear singularly perturbed optimal control problems with singular arcs

A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.

Ardema, M. D.↗

A First and Second Order Moment Approach to Probabilistic Control Synthesis

This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗

Optimization of Lyot Coronagrah focal plane masks for improved low-order wavefront sensing

The WFIRST Coronagraph uses a Low-Order Wavefront Sensing and Control (LOWFS/C) subsystem to stabilize the stellar wavefront. This is true for the Hybrid Lyot Coronagraph (HLC), the Shaped Pupil Coronagraph (SPC) spectrograph, and the SPC wide field of view modes. For the SPC spectrograph, we have found via modeling and simulations that a focal plane mask (FPM) with an elliptical phase dimple can reduce the LOWFS errors significantly compared to the conventional, circular phase dimple. For HLC designs, we concurrently optimized the FPM parameters and deformable mirror shapes using our open-source software toolbox, the Fast Linearized Coronagraph Optimizer (FALCO). This process resulted in new FPMs with non-uniform central-area phase modulation. We have found in numerical simulations that such FPMs still provide sufficient LOWFS performance. In this paper, we will present the LOWFS performance for several new HLC and SPC FPM designs.

Riggs, A.J. Eldorado↗

Supersonic wing and wing-body shape optimization using an adjoint formulation

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used to~eviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

Reuther, James↗

Precision Reconstruction of Rational Conformal Field Theory from Exact Fixed-Point Tensor Network

The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real-space renormalization group (RG) scheme. Numerically approximate fixed-point (FP) tensors are widely used to extract the conformal data of the underlying conformal field theory (CFT) describing critical phenomena. In this paper, we present an explicit analytical construction of the FP tensor for 2D rational CFT. We define it as a correlation function between the “boundary-changing operators” (BCO) on triangles. Our construction fully captures all the real-space RG conditions. We also provide concrete examples, such as Ising, Yang-Lee, and tricritical Ising models, to compute the scaling dimensions explicitly based on the corresponding FP tensor. The BCO descendants turn out to be an optimal basis such that truncation in bond dimensions naturally produces comparable accuracies with the leading existing FP algorithms. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door toward understanding CFT in higher dimensions. Published by the American Physical Society 2025

Cheng, Gong (ORCID:0009000891587404)↗

Multiscale Dynamics of Reactive Fronts in the Subsurface

Understanding and predicting flow and reactive transport in rocks (i.e. geologic porous media) is critical to many technologies at the heart of the energy transition, including CO 2 sequestration and H2 storage. However, accurate modeling and prediction of these systems is very complex because physico-chemical processes that occur at very small spatial scales, i.e. in the pores of the rocks, can dramatically control the system performance at the field scale (km). For example, precipitation reactions at the pore-scale can lead to large permeability changes at the field scale and dramatically alter the migration of stored gases. Properly accounting for multi-scale coupling effects is critical to achieve predictivity and confidence in model outputs, which then can guide design and optimization at the system-scale. This can be achieved through the development of rigorous mathematical models that can appropriately account for fine-scale effects at the large scale. The final report of the Early Career award DE-SC0019075 “Multiscale dynamics of reactive fronts in the subsurface” summarizes the mathematical, numerical and experimental advancements to study and predict reactive transport in geologic porous media across scales.

58 GEOSCIENCES↗

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

The optimization of trajectories for coplanar, aeroassisted orbital transfer (AOT) from a high earth orbit (HEO) to a low earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous earth orbit (GEO). During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called a grazing trajectory. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the contrifugal force due to the earth's curvature, the weight, and the Coriolis force due to the earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. The real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Miele, A.↗

Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, P. V.↗

An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes constrained optimization techniques to exploit the flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters while maintaining performance requirements; it thus provides a systematic approach for choosing values for eigensystem design variables. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Numerical results indicate that the methods provide feedback control laws that make the stability of the nominal closed loop systems less sensitive to changes in dynamic pressure, while maintaining acceptable control power and robustness constraints.

Fennell, Robert E.↗

Trajectory optimization for the National aerospace plane

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Lu, Ping↗

Evolutionary optimization of a Genetically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: Genetic Algorithms and Differential Evolution to successfully optimize a benchmark structural optimization problem. An non-traditional solution to the benchmark problem is presented in this paper, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, Patrick V.↗

Evaluating the Effectiveness of an Ultrasonic Acoustic Deterrent in Reducing Bat Fatalities at Wind Energy Facilities

This project was designed to use thermal video cameras and fatality monitoring to evaluate the effectiveness of an ultrasonic acoustic deterrent (UAD) on bat activity and mortality, respectively. Our goals were to redesign the UAD device and installation infrastructure, determine the placement on wind turbines to optimize safety, compatibility and functionality, and to compare the mortality among the following conditions: Control (deterrents off and turbines feathered up to the manufacturer’s cut-in speed of 3.5 m/s), Deterrent (deterrents on and turbines feathered up to the manufacturer’s cut-in speed of 3.5 m/s), Curtailment (deterrents off and turbines feathered up to 5/ m/s), and combination (deterrents on and turbines feathered up to 5 m/s). The project was divided into a Feasibility Study and Comparative Study. The objectives for the Feasibility Study were to develop an installation strategy, redesign a previous iteration of a UAD to improve performance and weatherization, and test the effectiveness of the deterrents on bat activity. The Feasibility Study was intended to work out potential issues using a relatively small number of devices prior to manufacturing and installing numerous devices for a larger-scale comparative study. The division of the project into these separate studies was based on previous experience and the challenges of assessing the capabilities of an untested UAD. During the initial development and manufacturing of the UAD, NRG Systems decided to use a piezoelectric transducer rather than an electrostatic transducer, which was used by a previous device (i.e. Deaton UAD). NRG Systems conducted lab testing (i.e., IP67 or Ingress Protection) to ensure no water or dust ingress. In addition, shock/drop trials and variations in temperature exposure were conducted as part of the reliability testing. NRG Systems also developed a communications system to allow for continuous performance monitoring of the UADs. For the Feasibility Study, we installed 6 UADs on each of 2 Gamesa G90 2-MW wind turbines (Turbine 14 and 8) at the South Chestnut Wind Energy Facility, Pennsylvania and monitored activity under control and treatment (i.e. Deterrent) conditions using thermal video monitoring. There are two major sources of variation in bat activity (beyond the anticipated treatment effect): 1) environment around the turbines might inherently favor more activity at one than the other; 2) weather conditions on any given night or within season difference (e.g., migration later during the study period) might favor more activity on some nights than on other nights. Because we could only monitor two turbines on any night, we sought to control the potential influences of these two sources by alternating the turbine on which deterrents were activated each night. If there were no loss of data due to technical failures, this design would result in an equal number of deterrent and control nights at each turbine through the monitoring period, balancing the effects of both sources of variation. We compared the time bats spent and the number of events that occurred in overlapping cameras FOV as an indicator of risk, since 80% of the overlapping FOV of the cameras was in the RSA. Equipment failures, majority due to lightning, resulted in only 17 nights with useable data, with unbalanced treatment assignment within turbines and uneven distribution of treatment assignment throughout the observational period. This resulted in a confounding of treatment assignment and seasonal change. Deterrent treatment was measured at Turbine 14 on only 2 of the first 8 usable nights (spanning the period from 8/18-9/17), whereas 6 times on Turbine 8. From 9/18-927, deterrent was on at Turbine 14 on 6 of the remaining 10 nights, and 4 on Turbine 8. We recorded a total of 1,057 bats and observed a reduction in number of events and duration of events at the UAD-activated turbine when it was Turbine 14. When Turbine 8 had the UAD activated, we observed no difference in number or duration of events. Variation between turbines is not unusual and can cause issues when study designs have no true replication, i.e., multiple turbines per treatment. Within-turbine differences suggested a trend for reduced activity when UADs were activated, particularly for Turbine 14. These results may be caused by the overall higher bat activity at Turbine 8 and confounding of treatment assignment and seasonal trends. We mapped 58 bat events in 3-dimensional space (3D), 30 and 28 events during control and treatment conditions, respectively. We observed bats crossing the rotor plane under both control and treatment conditions and observed a total of 40 confirmed or near-collisions (i.e., target close to blade but no visual confirmation of a strike) out of a total of 1,491 medium and high confidence bat observations (880 control, 611 at treatment). Twice as many collisions/possible collisions were observed during control conditions. Given the challenges with the equipment and potential confounding of the data (i.e., different activity levels at the two wind turbines), we were unable to determine whether this initial turbine placement and orientation was optimal. Given no new information on how best to install the devices, we elected to use the same placement and orientation for the comparative study. For the Comparative Study, the objectives were to investigate the relative mortality rates among 4 treatments. We searched the area within 90 m of each turbine daily to recover the highest number of fresh fatalities possible. We were unable to detect a clear reduction in mortality from deterrents alone for any individual species. Surprisingly, mortality rate of the eastern red bat (Lasiurus borealis) was estimated to be 1.3–4.2 times as much when turbines were operating normally and UADs were on than when UADs were off. Reduction in mortality of all bat species combined due to curtailment of turbines was estimated to be between 0%–38%. This effect was nullified when, in addition to curtailment, UADs were on, with 95% confidence interval ranging from a 45% reduction to a 36% increase in mortality. This was likely due to the large proportion of eastern red bats in the total carcass population. Mortality of all low-frequency echolocating bats combined (i.e. hoary bat [L. cinereus], big brown bat [Eptesicus fuscus], silver-haired bat [Lasionycteris noctivagans]) relative to control was lower when curtailed (95% CI: 0%–74%), but the addition of UADs had no detectable effect (95%CI: 13%–79%). The combined treatment reduced mortality in silver-haired bats relative to control by 11%–99%, compared to curtailment (81% reduction–67% increase) or deterrent (82% reduction–67% increase) alone. Because silver-haired bats comprised a large proportion of low-frequency calling bats found during this study, a similar effect was seen for that group. The higher mortality observed for eastern red bats at UAD compared to control could have been caused by several factors, such as the effective range of the UAD, particularly at higher frequencies, behavior, positioning of the devices on the nacelle, or a combination of these. We used 3D thermal videography to compare control and UAD bat behavior from two turbines using a total of 203 3D bat-tracks across 34 nights. We recorded a similar number of bat-tracks between treatment groups, with 51% and 49% for control and UAD, respectively. Due to potential differences in bat behavior around spinning vs stationary turbine blades, we examined UAD effectiveness separately for non-operating turbines (feathered below cut-in speed of 3.5 m/s) and operating (normal operation above wind speed of 3.5 m/s). We found a higher proportion of bat-tracks at operating turbines (82%) compared to non-operating turbines (18%), although this does not account for overall time turbines were operating versus not. At non-operating turbines the UAD appears to be effective at reducing the amount of time, flight length, and number of passes through the rotor plane, compared to control. In addition, we found bats approached turbines similarly between control and treatment turbines, with 61% of control and 63% of UAD bat-tracks originating leeward of the hub. In contrast, at operating turbines, we saw little change in bat behavior in response to UADs. For example, we found an increase in the average duration of bat-tracks between non-operating and operating turbines for UAD but at control turbines we found average duration decreased once turbines became operational. Both control and UAD had a high proportion of bat-tracks that crossed the rotor plane (i.e., collision risk) originate from the windward side when turbines were operational 65% to 92%, respectively. Given that the UAD devices closest to the blades were orientated parallel to the blades, its possible bats were not exposed to the signal until they were close to the turbine blades, as suggested by the slightly higher mean duration within 5 meters of the blades for UAD turbines. Future research should consider concentrating UAD intensity on the areas of risk (i.e. blades) with enough buffer to allow bats to react to the sound before entering the rotor-swept area (RSA). In addition, investigating the potential of installing UAD units windward of the turbine blades (e.g. a hub-mounted UAD), particularly since even under control conditions, a relatively high proportion (65%) of crosses through the blade plane originated windward. 3D thermal videography provided valuable information on future testing strategies (e.g. device placement, UAD orientation) to improve UAD effectiveness when bats are at risk (i.e., operating wind turbines). Across the entire project we experienced issues with the operation and communication with the UADs. Most of the issues occurred during the Feasibility Study and were resolved prior to the Comparability Study. Additional challenges surfaced during the Comparability Study but were remedied immediately and are thought to have little impact on the results. We had logistical constraints at the project that limited our ability use traditional methods in our camera calibration. Several calibrations showed inaccurate scales, which may have been related to inadequate spatial coverage of “points” in the camera calibration volume. Because we were using actual video recordings of bats at a wind turbine, the behavior of bats could have concentrated “points” in specific areas of the turbine (i.e. leeward of nacelle), and limited “points” in other areas, resulting in camera calibration issues. We have plans to address these inconsistencies and improving the software and related methodologies by early 2020.

17 WIND ENERGY↗

Drift-kinetic effects of tungsten on plasma response to RMP in ITER

Here, effects of high- Z ( Z is the particle charge number) tungsten impurity ions on the plasma response to the resonant magnetic perturbation (RMP) field are numerically investigated for the ITER 15 MA baseline scenario, where the tungsten contribution to the plasma response is computed with a drift-kinetic model while the bulk thermal particle contributions follow the fluid approximation. The study yields three highlights: (i) the drift-kinetic contribution of the tungsten impurity exerts minor influence on the plasma response compared to that computed by the pure fluid model without tungsten; (ii) a new figure of merit, based on the resonant spectrum perturbation at the plasma boundary surface, results in different optimal coil phasing compared to that previously obtained by maximizing the edge-peeling plasma response; (iii) the optimal $n = 3$ RMP (for edge localized mode (ELM) control, $n$ is the toroidal mode number) is found to induce a large tungsten particle influx near the plasma edge associated with the neoclassical toroidal viscosity. The study thus provides useful data on the compatibility of the full tungsten wall with RMP ELM control in ITER.

ITER↗

Universal time scalings of sensitivity in Markovian quantum metrology

Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear, and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗