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At least 1,207 records · Page 67

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗

Structural/control system optimization with variable actuator masses

A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. Nonstructural lumped masses and control system design variables as well as structural sizing variables are all treated equally as independent design variables in the optimization process. Structural and control design variable linking schemes are used in order to avoid a prohibitively large increase in the total number of independent design variables. When actuator masses are treated as nonstructural lumped mass design variables, special consideration is given to the relation between the transient peak responses and the required actuator masses which is formulated as a behavior constraint form. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as design variable linkings, temporary constraint deletion and first order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples which involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, peak actuator forces, and relations between the peak responses and the actuator masses) are effectively solved by using the method presented.

Jin, Ik M.↗

SU-E-T-153: Burst-Mode Modulated Arc Therapy with Flattening-Filter-Free Beams Versus Flattening-Filtered Beams

Purpose: To compare the dosimetry and delivery of burst-mode modulated arc radiotherapy using flattening-filter-free (FFF) and flattening-filtered (FF) beams. Methods: Burst-mode modulated arc therapy (mARC, Siemens) plans were generated for six prostate cases with FFF and FF beam models, using the Elekta Monaco v. 5.00 planning system. One 360-degree arc was used for five cases, and for one case two 360-degree coplanar arcs were used. The maximum number of optimization points (OPs) per arc was set to 91, and OPs with less than 4 MU were disregarded. All plans were delivered on the Siemens Artiste linear accelerator with 6MV FF (300 MU/min) and comparable-energy FFF (2000 MU/min, labeled as 7UF) beams. Results: For all cases studied, the plans with FFF beams exhibited DVHs for the PTV, rectum, and bladder that were nearly identical to those for the plans with FF beams. The FFF plan yielded reduced dose to the right femoral head for 5 cases, and lower mean dose to the left femoral head for 4 cases. For all but the two-arc case, the FFF and FF plans resulted in an identical number of segments. The total number of MUs was slightly lower for the FF plans for five cases. The total delivery time per fraction was substantially lower for the FFF plans, ranging from 25 to 50 percent among all cases, as compared to the FF plans. Conclusion: For mARC plans, FFF and FF beams provided comparable PTV coverage and rectum and bladder sparing. For the femoral heads, the mean dose was slightly lower in most cases when using the FFF beam. Although the flat beam plans typically required slightly fewer MUs, FFF beams required substantially less time to deliver a plan of similar quality. This work was supported by Siemens Medical Solutions and the MCW Cancer Center Fotsch Foundation.

60 APPLIED LIFE SCIENCES↗

SU-E-T-368: Evaluating Dosimetric Outcome of Modulated Photon Radiotherapy (XMRT) Optimization for Head and Neck Patients

Purpose: The dosimetric outcome of optimized treatment plans obtained by modulating the photon beamlet energy and fluence on a small cohort of four Head and Neck (H and N) patients was investigated. This novel optimization technique is denoted XMRT for modulated photon radiotherapy. The dosimetric plans from XMRT for H and N treatment were compared to conventional, 6 MV intensity modulated radiotherapy (IMRT) optimization plans. Methods: An arrangement of two non-coplanar and five coplanar beams was used for all four H and N patients. Both XMRT and IMRT were subject to the same optimization algorithm, with XMRT optimization allowing both 6 and 18 MV beamlets while IMRT was restricted to 6 MV only. The optimization algorithm was based on a linear programming approach with partial-volume constraints implemented via the conditional value-at-risk method. H and N constraints were based off of those mentioned in the Radiation Therapy Oncology Group 1016 protocol. XMRT and IMRT solutions were assessed using metrics suggested by International Commission on Radiation Units and Measurements report 83. The Gurobi solver was used in conjunction with the CVX package to solve each optimization problem. Dose calculations and analysis were done in CERR using Monte Carlo dose calculation with VMC{sub ++}. Results: Both XMRT and IMRT solutions met all clinical criteria. Trade-offs were observed between improved dose uniformity to the primary target volume (PTV1) and increased dose to some of the surrounding healthy organs for XMRT compared to IMRT. On average, IMRT improved dose to the contralateral parotid gland and spinal cord while XMRT improved dose to the brainstem and mandible. Conclusion: Bi-energy XMRT optimization for H and N patients provides benefits in terms of improved dose uniformity to the primary target and reduced dose to some healthy structures, at the expense of increased dose to other healthy structures when compared with IMRT.

60 APPLIED LIFE SCIENCES↗

Efficient algorithm for locating and sizing series compensation devices in large power transmission grids: I. Model implementation

We explore optimization methods for planning the placement, sizing and operations of Flexible Alternating Current Transmission System (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to Series Compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l 1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of Linear Programs (LP) which are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop—a speed up that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically-sized networks that suffer congestion from a range of causes including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically-sized network.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Spot Size Optimization of the Scorpius Accelerator

The Scorpius Linear Induction Accelerator (LIA) is being developed by the Advanced Sources and Diagnostics (ASD) Project and will complement other U1a capabilities by providing a multi-pulse, DARHT-class, flash-radiography capability. Commissioning activities are expected to end in Spring of 2026. All of the diagnostics discussed in this chapter are relevant to LIAs that generate high-current relativistic electron beams, and some diagnostics will also be relevant to other accelerators. The Scorpius Accelerator will be the world’s most advance LIA. Although significant technological advancements have been incorporated throughout the machine, many performance aspects of Scorpius will be similar to those of FXR and DARHT Axis-I and -II. These LIAs offer the same challenges, whether it is suppressing beam instabilities, improving diagnostic accuracy, validating computer simulations and beam tunes, or reducing beam-target interaction effects. However, the ultimate figure of merit is consistent between these LIAs, which is spot size and dose.

43 PARTICLE ACCELERATORS↗

Validation of a computer code for analysis of subsonic aerodynamic performance of wings with flaps in combination with a canard or horizontal tail and an application to optimization

Extensive correlations of computer code results with experimental data are employed to illustrate the use of a linearized theory, attached flow method for the estimation and optimization of the longitudinal aerodynamic performance of wing-canard and wing-horizontal tail configurations which may employ simple hinged flap systems. Use of an attached flow method is based on the premise that high levels of aerodynamic efficiency require a flow that is as nearly attached as circumstances permit. The results indicate that linearized theory, attached flow, computer code methods (modified to include estimated attainable leading-edge thrust and an approximate representation of vortex forces) provide a rational basis for the estimation and optimization of aerodynamic performance at subsonic speeds below the drag rise Mach number. Generally, good prediction of aerodynamic performance, as measured by the suction parameter, can be expected for near optimum combinations of canard or horizontal tail incidence and leading- and trailing-edge flap deflections at a given lift coefficient (conditions which tend to produce a predominantly attached flow).

Carlson, Harry W.↗

An optimal control approach to the design of moving flight simulators

An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

Sivan, R.↗

Optimal Energy Dispatch of Distributed PVs for the Next Generation of Distribution Management Systems

Advanced Distribution Management Systems (ADMS) are being widely adopted by electric utilities for managing and optimizing the operations of their distribution systems. Distributed photovoltaic (DPV) systems with smart inverters can be controlled to adjust active power and reactive power outputs, and they are envisioned to become a part of (centrally or distributed) controllable assets managed by the ADMS for optimizing grid operations. This paper proposes an optimal energy dispatch strategy controlling DPV systems for regulating distribution voltages and achieving conservation voltage reduction. A convex optimization model is proposed with the use of linearized power flow, and the gradient projection algorithm is used to solve the optimal active power and reactive power outputs of smart inverters. The proposed optimal energy dispatch is implemented using an open-source ADMS platform, and simulation results have demonstrated the effectiveness of the proposed approach on improving distribution grid operations.

42 ENGINEERING↗

Optimal Control for Stochastic Delay Evolution Equations

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

97 MATHEMATICS AND COMPUTING↗

Study of free-piston Stirling engine driven linear alternators

The analysis, design and operation of single phase, single slot tubular permanent magnet linear alternator is presented. Included is the no-load and on-load magnetic field investigation, permanent magnet's leakage field analysis, parameter identification, design guidelines and an optimal design of a permanent magnet linear alternator. For analysis of the magnetic field, a simplified magnetic circuit is utilized. The analysis accounts for saturation, leakage and armature reaction.

Nasar, S. A.↗

On the design of optimal input signals in system identification

The problem of designing optimal inputs in the identification of linear systems with unknown random parameters is considered using a Bayesian approach. The information matrix, which is positive definite for the class of systems analyzed, gives a measure of performance for the system inputs. The computation of the optimal closed-loop input mappings is shown to be a nontrivial exercise in adaptive control. Deterministic optimal inputs are shown to be easily computable. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.

Lopez-Toledo, A. A.↗

A Framework for Scaling in Filtering and Linear Covariance Analysis

Scaling is used extensively for numerical optimization and trajectory optimization. Its use in the estimation community is almost nonexistent. This paper creates the framework for practical scaling in space navigation, in general, and linear covariance analysis, in particular.

D'souza, Christopher N.↗

Highly sensitive SPR PCF biosensors based on Ag/TiN and Ag/ZrN configurations

We numerically present and analyze a surface plasmon resonance (SPR) bimetallic photonic crystal fiber (PCF) biosensor using full vectorial finite element method. The bimetallic configuration is based on Silver and (TiN or ZrN) as alternative plasmonic materials. The reported design relies on PCF with an external channel to house the analyte. The inner surface of the channel is coated by a silver layer followed by TiN or ZrN to protect the silver layer from oxidation. The proposed biosensor can be implemented to detect the unknown analytes, organic chemicals, biological analytes, and biomolecules via the sensitive resonant peaks to the analyte refractive index variations for both polarized modes with high linearity. In this study, a comparison is made between the Ag/TiN configuration and the Ag/ZrN counterpart in terms of sensitivity, losses, and linearity. The geometrical parameters are optimized to achieve high refractive index sensitivities of 7000 nm/RIU for quasi-transverse electric (TE) mode and 6900 nm/RIU for quasi-transverse magnetic (TM) mode, respectively for the Ag/TiN configuration. However, the quasi TE and quasi TM modes achieve high sensitivity of 5300 and 5400 nm/RIU, respectively using the Ag/ZrN configuration. The standard PCF fabrication technologies can be used to fabricate the proposed SPR PCF biosensors.

36 MATERIALS SCIENCE↗

A meshing framework for digital twins for extrusion based additive manufacturing

Additive manufacturing (AM) allows for manufacturing of complex three-dimensional geometries not typically realizable with standard manufacturing practices. The internal microstructure of AM components has a significant impact on mechanical, vibrational, and shock properties and permits richer design space when this is controllable. Due to complex interactions of internal geometry of an extrusion-based AM component, it is common practice to assume homogeneous behavior or to perform characterization testing on specific toolpath configurations. To avoid testing or material waste, it is necessary to develop a consistently accurate numerical simulation framework with relevant boundary value problems that can handle the complicated geometry of internal material microstructure present in AM components. Herein, a framework is proposed to directly create computational meshes suitable for finite element analysis (FEA) of the fine-scale features generated from extrusion-based AM tool paths to maintain a strong process–structure–property-performance linkage. This mesh can be manually or automatically analyzed using standard FEA simulations such as quasi-static preloading or modal analysis. The framework allows an in-silico assessment of a target AM geometry where fine-scale features greatly impact quantities of design interest such as in soft elastomeric lattices where toolpath infill can greatly influence the self-contact of a structure in compression, which we use as a motivating exemplar. This approach greatly reduces both time and resource waste present in traditional build and test design cycles for non-intuitive design spaces, and acts as a tool for use in the production of a key component of a digital twin, a mesh suitable for finite element analysis. In conclusion, it also further allows for the exploration of toolpath infill to optimize component properties beyond simple linear properties such as density and stiffness.

Additive manufacturing↗

Nonequilibrium steady state transport of collective-qubit system in strong coupling regime

We investigate the steady state photon transport in a nonequilibrium collective-qubit model. By adopting the noninteracting blip approximation, which is applicable in the strong photon–qubit coupling regime, we describe the essential contribution of indirect qubit–qubit interaction to the population distribution, mediated by the photonic baths. The linear relations of both the optimal flux and noise power with the qubits system size are obtained. Moreover, the inversed power-law style for the finite-size scaling of the optimal photon–qubit coupling strength is exhibited, which is proposed to be universal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗