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At least 883 records · Page 49

Sensitivity Analysis of Wing Aeroelastic Responses

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency, and torsional frequency is calculated analytically. A strip theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model and solved as an eigenvalue problem to determine the critical speed of the wing. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.

Issac, Jason Cherian↗

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗

Constant-Momentum Acceleration Time-of-Flight Mass Spectrometry with Energy Focusing

Fundamental aspects of constant--momentum acceleration time-­of-­flight mass spectrometry (CMA-TOFMS) are explored as a means to improve mass resolution. By accelerating all ions to the same momentum, rather than to the same energy, the effects of the initial ion spatial and energy distributions upon the total ion flight time are decoupled. This decoupling permits the initial spatial distribution of ions in the acceleration region to be optimized independently and energy focus, including ion turn-around-time error, to be accomplished with a linear-field reflectron. Constant-momentum acceleration also linearly disperses ions across time according to mass-to-change (m/z) ratio, instead of the quadratic relationship between flight time and m/z found in conventional TOFMS. Here, CMA-TOFMS is shown to achieve simultaneous spatial and energy focusing over a selected portion of the mass spectrum. An orthogonal-acceleration time-of-flight outfitted with a reduced-pressure dc glow discharge (GD) ionization source is used to demonstrate CMA-TOFMS with atomic ions. The influence of experimental parameters such as the amplitude and width of the time-dependent CMA pulse on mass resolution is investigated, and a useful CMA-TOFMS focusing window of 2 to 18 Da is found for GD-CMA-TOFMS.

Dennis, Elise A.↗

Efficient on-chip terahertz generation and detection with GaN photoconductive emitters

Photoconductive emitters for terahertz generation hold promise for highly efficient down-conversion of optical photons because it is not constrained by the Manley-Rowe relation. Existing terahertz photoconductive devices, however, faces limits in efficiency due to the semiconductor properties of commonly used GaAs materials. Here, we demonstrate that large bandgap semiconductor GaN, characterized by its high breakdown electric field, facilitates the highly efficient generation of terahertz waves in a coplanar stripline waveguide. Towards this goal, we investigated the excitonic contribution to the electro-optic response of GaN under static electric field both through experiments and first-principles calculations, revealing a robust excitonic Stark shift. Using this electro-optic effect, we developed a novel ultraviolet pump-probe spectroscopy for in-situ characterization of the terahertz electric field strength generated by the GaN photoconductive emitter. Our findings show that terahertz power scales quadratically with optical excitation power and applied electric field over a broad parameter range. We achieved an optical-to-terahertz conversion efficiency approaching 100% within the 0.03–1 THz bandwidth at the highest bias field (116 kV/cm) in our experiment. Further optimization of GaN-based terahertz generation devices could achieve even greater optical-to-terahertz conversion efficiencies.

Uzundal, Can B↗

Optimal filters for the moving lens effect

We assess the prospects for detecting the moving lens effect using cosmological surveys. The bulk motion of cosmological structure induces a small-scale dipolar temperature anisotropy of the cosmic microwave radiation, centered around halos and oriented along the transverse velocity field. We introduce a set of optimal filters for this signal and forecast that a high significance detection can be made with upcoming experiments. We discuss the prospects for reconstructing the bulk transverse velocity field on large scales using matched filters, finding good agreement with previous work using quadratic estimators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Research on output feedback control of systems with ill-conditioned dynamics

The accuracy of a two time scale approach to the output feedback regulator design problem is examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. A sequential numerical algorithm is defined which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. A procedure for optimally zeroing selected gain elements in an output feedback gain matrix is developed and demonstrated. A summary of conference and journal publications from this research is also provided.

Calise, A. J.↗

Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.

Baart, M. L.↗

H2, fixed architecture, control design for large scale systems

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu↗

A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling

Design and operation decisions of manufacturing plants can often be expressed within a hierarchical structure, where optimal decisions at lower operating level provide constraints for the decision raking at a higher decision level. In this work, we are addressing the case of a hierarchical design and scheduling optimization problem. The integration of design and scheduling decisions can play a big role in designing economically profitable plants and improving their operational performance. This problem can be expressed as a bi-level problem, where design related decisions occur at the upper level and operational scheduling decisions at the lower level. Since discrete decisions are involved in both optimization levels, the resulting formulation typically corresponds to bi-level mixed-integer programming problems (B-MIP). The solution of B-MIP problems is very challenging, and typically requires the use of global optimization techniques, with many algorithms not able to guarantee feasibility. To overcome the challenges in solving this class of problems we propose the use of a multi-parametric based algorithm for the solution of bi-level mixed-integer linear and quadratic programming problems, capable of providing the exact and global solution. The main idea of this approach is to treat the lower scheduling problem as a multi-parametric programming problem in which the design decisions are considered as parameters. Here, the resulting parametric solutions can then be substituted into the upper level design problem, which can be solved as a set of single-level deterministic programming problems. Through the developed formulation and algorithm we are able to supply the decision makers with the exact solution of the integrated design and scheduling problem.

42 ENGINEERING↗

Inference of gravitational lensing and patchy reionization with future CMB data

We develop an optimal Bayesian solution for jointly inferring secondary signals in the Cosmic Microwave Background (CMB) originating from gravitational lensing and from patchy screening during the epoch of reionization. This method is able to extract full information content from the data, improving upon previously considered quadratic estimators for lensing and screening. Here, we forecast constraints using the Marginal Unbiased Score Expansion (MUSE) method, and show that they are largely dominated by CMB polarization, and depend on the exact details of reionization. For models consistent with current data which produce the largest screening signals, a detection (3 σ) of the cross-correlation between lensing and screening is possible with SPT-3G, and a detection of the auto-correlation is possible with CMB-S4. Models with the lowest screening signals evade the sensitivity of SPT-3G, but are still possible to detect with CMB-S4 via their lensing cross-correlation.

79 ASTRONOMY AND ASTROPHYSICS↗

ParChain: a framework for parallel hierarchical agglomerative clustering using nearest-neighbor chain

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative clustering (HAC) algorithms, and using the framework we obtain novel parallel algorithms for the complete linkage, average linkage, and Ward's linkage criteria. Compared to most previous parallel HAC algorithms, which require quadratic memory, our new algorithms require only linear memory, and are scalable to large data sets. ParChain is based on our parallelization of the nearest-neighbor chain algorithm, and enables multiple clusters to be merged on every round. We introduce two key optimizations that are critical for efficiency: a range query optimization that reduces the number of distance computations required when finding nearest neighbors of clusters, and a caching optimization that stores a subset of previously computed distances, which are likely to be reused. Experimentally, we show that our highly-optimized implementations using 48 cores with two-way hyper-threading achieve 5.8--110.1x speedup over state-of-the-art parallel HAC algorithms and achieve 13.75--54.23x self-relative speedup. Compared to state-of-the-art algorithms, our algorithms require up to 237.3x less space. Our algorithms are able to scale to data set sizes with tens of millions of points, which existing algorithms are not able to handle.

Computer Science↗

SU-E-T-502: Initial Results of a Comparison of Treatment Plans Produced From Automated Prioritized Planning Method and a Commercial Treatment Planning System

Purpose We developed an automated treatment planning system based on a hierarchical goal programming approach. To demonstrate the feasibility of our method, we report the comparison of prostate treatment plans produced from the automated treatment planning system with those produced by a commercial treatment planning system. Methods In our approach, we prioritized the goals of the optimization, and solved one goal at a time. The purpose of prioritization is to ensure that higher priority dose-volume planning goals are not sacrificed to improve lower priority goals. The algorithm has four steps. The first step optimizes dose to the target structures, while sparing key sensitive organs from radiation. In the second step, the algorithm finds the best beamlet weight to reduce toxicity risks to normal tissue while holding the objective function achieved in the first step as a constraint, with a small amount of allowed slip. Likewise, the third and fourth steps introduce lower priority normal tissue goals and beam smoothing. We compared with prostate treatment plans from Memorial Sloan Kettering Cancer Center developed using Eclipse, with a prescription dose of 72 Gy. A combination of liear, quadratic, and gEUD objective functions were used with a modified open source solver code (IPOPT). Results Initial plan results on 3 different cases show that the automated planning system is capable of competing or improving on expert-driven eclipse plans. Compared to the Eclipse planning system, the automated system produced up to 26% less mean dose to rectum and 24% less mean dose to bladder while having the same D95 (after matching) to the target. Conclusion We have demonstrated that Pareto optimal treatment plans can be generated automatically without a trial-and-error process. The solver finds an optimal plan for the given patient, as opposed to database-driven approaches that set parameters based on geometry and population modeling.

60 APPLIED LIFE SCIENCES↗

SU-C-202-04: Adapting Biologically Optimized Dose Escalation Based On Mid-Treatment PET/CT for Non-Small-Cell Lung Cancer

Purpose: To develop a biological modeling strategy which incorporates the response observed on the mid-treatment PET/CT into a dose escalation design for adaptive radiotherapy of non-small-cell lung cancer. Method: FDG-PET/CT was acquired midway through standard fractionated treatment and registered to pre-treatment planning PET/CT to evaluate radiation response of lung cancer. Each mid-treatment PET voxel was assigned the median SUV inside a concentric 1cm-diameter sphere to account for registration and imaging uncertainties. For each voxel, the planned radiation dose, pre- and mid-treatment SUVs were used to parameterize the linear-quadratic model, which was then utilized to predict the SUV distribution after the full prescribed dose. Voxels with predicted post-treatment SUV≥2 were identified as the resistant target (response arm). An adaptive simultaneous integrated boost was designed to escalate dose to the resistant target as high as possible, while keeping prescription dose to the original target and lung toxicity intact. In contrast, an adaptive target volume was delineated based only on the intensity of mid-treatment PET/CT (intensity arm), and a similar adaptive boost plan was optimized. The dose escalation capability of the two approaches was compared. Result: Images of three patients were used in this planning study. For one patient, SUV prediction indicated complete response and no necessary dose escalation. For the other two, resistant targets defined in the response arm were multifocal, and on average accounted for 25% of the pre-treatment target, compared to 67% in the intensity arm. The smaller response arm targets led to a 6Gy higher mean target dose in the adaptive escalation design. Conclusion: This pilot study suggests that adaptive dose escalation to a biologically resistant target predicted from a pre- and mid-treatment PET/CT may be more effective than escalation based on the mid-treatment PET/CT alone. More plans and ultimately clinical protocols are needed to validate this approach. MSKCC has a research agreement with Varian Medical System.

60 APPLIED LIFE SCIENCES↗

Optimization of the structural and control system for LSS with reduced-order model

The objective is the simultaneous design of the structural and control system for space structures. The minimum weight of the structure is the objective function, and the constraints are placed on the closed loop distribution of the frequencies and the damping parameters. The controls approach used is linear quadratic regulator with constant feedback. A reduced-order control system is used. The effect of uncontrolled modes is taken into consideration by the model error sensitivity suppression (MESS) technique which modified the weighting parameters for the control forces. For illustration, an ACOSS-FOUR structure is designed for a different number of controlled modes with specified values for the closed loop damping parameters and frequencies. The dynamic response of the optimum designs for an initial disturbance is compared.

Khot, N. S.↗

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

97 MATHEMATICS AND COMPUTING↗

Design Optimization for a Maglev System Employing Flux Eliminating Coils

Flux eliminating coils have received no little attention over the past thirty years as an alternative for realizing lift in a MAGLEV system. When the magnets on board the vehicle are displaced from the equilibrium or null flux point of these coils, they induce current in those coils which act to restore the coil to its null flux or centerline position. The question being addressed in this paper is that of how to choose the best coil for a given system. What appears at first glance to be an innocent question is in fact one that is actually quite involved, encompassing both the global economics and physics of the system. The real key in analyzing that question is to derive an optimization index or functional which represents the cost of the system subject to constraints, the primary constraint being that the vehicle lift itself at a certain threshold speed. Outlined in this paper is one scenario for realizing a total system design which uses sequential quadratic programming techniques.

Davey, Kent R.↗

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗

SU-G-TeP3-13: The Role of Nanoscale Energy Deposition in the Development of Gold Nanoparticle-Enhanced Radiotherapy

Purpose: Gold nanoparticles (GNPs) can enhance radiotherapy effects. The high photoelectric cross section of gold relative to tissue, particularly at lower energies, leads to localized dose enhancement. However in a clinical context, photon energies must also be sufficient to reach a target volume at a given depth. These properties must be balanced to optimize such a therapy. Given that nanoscale energy deposition patterns around GNPs play a role in determining biological outcomes, in this work we seek to establish their role in this optimization process. Methods: The PENELOPE Monte Carlo code was used to generate spherical dose deposition kernels in 1000 nm diameter spheres around 50 nm diameter GNPs in response to monoenergetic photons incident on the GNP. Induced “lesions” were estimated by either a local effect model (LEM) or a mean dose model (MDM). The ratio of these estimates was examined for a range of photon energies (10 keV to 2 MeV), for three sets of linear-quadratic parameters. Results: The models produce distinct differences in expected lesion values, the lower the alpha-beta ratio, the greater the difference. The ratio of expected lesion values remained constant within 5% for energies of 40 keV and above across all parameter sets and rose to a difference of 35% for lower energies only for the lowest alpha-beta ratio. Conclusion: Consistent with other work, these calculations suggest nanoscale energy deposition patterns matter in predicting biological response to GNP-enhanced radiotherapy. However the ratio of expected lesions between the different models is largely independent of energy, indicating that GNP-enhanced radiotherapy scenarios can be optimized in photon energy without consideration of the nanoscale patterns. Special attention may be warranted for energies of 20 keV or below and low alpha-beta ratios.

60 APPLIED LIFE SCIENCES↗