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At least 1,315 records · Page 73

Stochastic Waveform Estimation at the Fundamental Quantum Limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Axions↗

Comparison of open-source linear programming solvers.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.

Gearhart, Jared Lee↗

A two-phase investment model for optimal allocation of phasor measurement units considering transmission switching

Ensuring the reliability of an electrical power system requires a wide-area monitoring and full observability of the state variables. Phasor measurement units (PMUs) collect in real time synchronized phasors of voltages and currents which are used for the observability of the power grid. Due to the considerable cost of installing PMUs, it is not possible to equip all buses with PMUs. In this paper, we propose an integer linear programming model to determine the optimal PMU placement plan in two investment phases. In the first phase, PMUs are installed to achieve full observability of the power grid whereas additional PMUs are installed in the second phase to guarantee the N - 1 observability of the power grid. The proposed model also accounts for transmission switching and single contingencies such as failure of a PMU or a transmission line. Results are provided on several IEEE test systems which show that our proposed approach is a promising enhancement to the methods available for the optimal placement of PMUs.

Phasor measurement unit↗

4π Non-Coplanar Liver SBRT: A Novel Delivery Technique

Purpose: To improve the quality of liver stereotactic body radiation therapy (SBRT) treatments, a novel 4π framework was developed with accompanying algorithms to optimize non-coplanar beam orientations and fluences. The dose optimization is performed on a patient-specific deliverable beam geometry solution space, parameterized with patient and linear accelerator gantry orientations. Methods and Materials: Beams causing collision between the gantry and the couch or patient were eliminated by simulating all beam orientations using a precise computer assisted design model of the linear accelerator and a human subject. Integrated beam orientation and fluence map optimizations were performed on remaining beams using a greedy column generation method. Testing of the new method was performed on 10 liver SBRT cases previously treated with 50 to 60 Gy in 5 fractions using volumetric modulated arc therapy (VMAT). For each patient, both 14 and 22 non-coplanar fields were selected and optimized to meet the objective of ≥95% of the planning target volume (PTV) covered by 100% of the prescription dose. Doses to organs at risk, normal liver volumes receiving <15 Gy, integral dose, and 50% dose spillage volumes were compared against the delivered clinical VMAT plans. Results: Compared with the VMAT plans, the 4π plans yielded reduced 50% dose spillage volume and integral dose by 22% (range 10%-40%) and 19% (range 13%-26%), respectively. The mean normal liver volume receiving <15 Gy was increased by 51 cc (range 21-107 cc) with a 31% reduction of the mean normal liver dose. Mean doses to the left kidney and right kidney and maximum doses to the stomach and spinal cord were on average reduced by 70%, 51%, 67%, and 64% (P≤.05). Conclusions: This novel 4π non-coplanar radiation delivery technique significantly improved dose gradient, reduced high dose spillage, and improved organ at risk sparing compared with state of the art VMAT plans.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗

Optimizing design and dispatch of a renewable energy system with combined heat and power

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

24 POWER TRANSMISSION AND DISTRIBUTION↗

On helium 1083 nm line polarization during the impulsive phase of an X1 flare

We analyze spectropolarimetric data of the He i 1083 nm multiplet (1s2s{sup 3}S{sub 1}−1s2p{sup 3}P{sub 2,1,0}{sup o}) during the X1 flare SOL2014-03-29T17:48, obtained with the Facility Infrared Spectrometer (FIRS) at the Dunn Solar Telescope. While scanning active region NOAA 12017, the FIRS slit crossed a flare ribbon during the impulsive phase, when the helium line intensities turned into emission at ≲twice the continuum intensity. Their linear polarization profiles are of the same sign across the multiplet including 1082.9 nm, intensity-like, at ≲5% of the continuum intensity. Weaker Zeeman-induced linear polarization is also observed. Only the strongest linear polarization coincides with hard X-ray (HXR) emission at 30–70 keV observed by RHESSI. The polarization is generally more extended and lasts longer than the HXR emission. The upper J = 0 level of the 1082.9 nm component is unpolarizable; thus, lower-level polarization is the culprit. We make non-LTE radiative transfer calculations in thermal slabs optimized to fit only intensities. The linear polarizations are naturally reproduced, through a systematic change of sign with wavelength of the radiation anisotropy when slab optical depths of the 1082.9 component are ≲1. Neither are collisions with beams of particles needed, nor can they produce the same sign of polarization of the 1082.9 and 1083.0 nm components. The He i line polarization merely requires heating sufficient to produce slabs of the required thickness. Widely different polarizations of Hα, reported previously, are explained by different radiative anisotropies arising from slabs of different optical depths.

79 ASTRONOMY AND ASTROPHYSICS↗

Effects of walking velocity on vertical head and body movements during locomotion

Trunk and head movements were characterized over a wide range of walking speeds to determine the relationship between stride length, stepping frequency, vertical head translation, pitch rotation of the head, and pitch trunk rotation as a function of gait velocity. Subjects (26-44 years old) walked on a linear treadmill at velocities of 0.6-2.2 m/s. The head and trunk were modeled as rigid bodies, and rotation and translation were determined using a video-based motion analysis system. At walking speeds up to 1.2 m/s there was little head pitch movement in space, and the head pitch relative to the trunk was compensatory for trunk pitch. As walking velocity increased, trunk pitch remained approximately invariant, but a significant head translation developed. This head translation induced compensatory head pitch in space, which tended to point the head at a fixed point in front of the subject that remained approximately invariant with regard to walking speed. The predominant frequency of head translation and rotation was restricted to a narrow range from 1.4 Hz at 0.6 m/s to 2.5 Hz at 2.2 m/s. Within the range of 0.8-1.8 m/s, subjects tended to increase their stride length rather than step frequency to walk faster, maintaining the predominant frequency of head movement at close to 2.0 Hz. At walking speeds above 1.2 m/s, head pitch in space was highly coherent with, and compensatory for, vertical head translation. In the range 1.2-1.8 m/s, the power spectrum of vertical head translation was the most highly tuned, and the relationship between walking speed and head and trunk movements was the most linear. We define this as an optimal range of walking velocity with regard to head-trunk coordination. The coordination of head and trunk movement was less coherent at walking velocities below 1.2 m/s and above 1.8 m/s. These results suggest that two mechanisms are utilized to maintain a stable head fixation distance over the optimal range of walking velocities. The relative contribution of each mechanism to head orientation depends on the frequency of head movement and consequently on walking velocity. From consideration of the frequency characteristics of the compensatory head pitch, we infer that compensatory head pitch movements may be produced predominantly by the angular vestibulocollic reflex (aVCR) at low walking speeds and by the linear vestibulocollic reflex (1VCR) at the higher speeds.

NASA Discipline Neuroscience↗

Optimal aeroassisted coplanar orbital transfer using an energy model

The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

Halyo, Nesim↗

Multi-stage design of an optimal momentum management controller for the Space Station

This paper presents a multistage design scheme for determining an optimal control-moment-gyro momentum-management and attitude-control system for the Space Station Freedom. The Space Station equations of motion are linearized and block-decomposed into two block-decoupled subsystems using the matrix-sign algorithm. A sequential procedure is utilized for designing a linear-quadratic regulator for each subsystem, which optimally places the eigenvalues of the closed-loop subsystem in the region of an open sector, bounded by lines inclined at + or - pi/2k (for k = 2 or 3) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the s-plane. Simulation results are presented to compare the resultant designs.

Sunkel, J. W.↗

Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicit SSP Runge–Kutta methods with high linear order p lin ≤ 9 and nonlinear orders p = 2,3,4, that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order p lin ≤ 7 and nonlinear orders up to p = 4. Here, we also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.

97 MATHEMATICS AND COMPUTING↗

An efficient multilevel optimization method for engineering design

An efficient multilevel deisgn optimization technique is presented. The proposed method is based on the concept of providing linearized information between the system level and subsystem level optimization tasks. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to use. The disadvantage is that the coupling between subsystems is not dealt with in a precise mathematical manner.

Vanderplaats, G. N.↗

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

shape optimization↗