Bayesian Selection of Optimal Physics-Based Model and Modeling Error for Nonlinear Dynamical Systems.
Abstract not provided.
Bisaillon, Philippe↗
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Approximating a linear multiplicative objective in watershed management optimization
Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.
54 ENVIRONMENTAL SCIENCES↗
DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.
The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.
99 GENERAL AND MISCELLANEOUS↗
A Polyhedral Outer-approximation, Dynamic-discretization optimization solver, 1.x
In this software, we implement an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) to global optimality. The algorithm combines ideas that exploit the structure of convex relaxations to MINLPs and bound tightening procedures
Bent, Rusell↗
Optimal fabrication processes for unidirectional metal-matrix composites: A computational simulation
A method is proposed for optimizing the fabrication process of unidirectional metal matrix composites. The temperature and pressure histories are optimized such that the residual microstresses of the composite at the end of the fabrication process are minimized and the material integrity throughout the process is ensured. The response of the composite during the fabrication is simulated based on a nonlinear micromechanics theory. The optimal fabrication problem is formulated and solved with non-linear programming. Application cases regarding the optimization of the fabrication cool-down phases of unidirectional ultra-high modulus graphite/copper and silicon carbide/titanium composites are presented.
Saravanos, D. A.↗
Coherent control of plasma dynamics by feedback-optimized wavefront manipulation
Plasmas generated by an intense laser pulse can support coherent structures such as large amplitude wakefield that can affect the outcome of an experiment. We investigate the coherent control of plasma dynamics by feedback-optimized wavefront manipulation using a deformable mirror. The experimental outcome is directly used as feedback in an evolutionary algorithm for optimization of the phase front of the driving laser pulse. In this paper, we applied this method to two different experiments: (i) acceleration of electrons in laser driven plasma waves and (ii) self-compression of optical pulses induced by ionization nonlinearity. The manipulation of the laser wavefront leads to orders of magnitude improvement to electron beam properties such as the peak charge, beam divergence, and transverse emittance. The demonstration of coherent control for plasmas opens new possibilities for future laser-based accelerators and their applications.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A new approach to optimization for aerodynamic applications
A new approach to solving optimization problems that involve nonlinear partial differential equations is presented. The approach eliminates the need for an inner-outer iterative procedure, solving the partial differential equation only once, thereby reducing the cost of computation to an extent which would allow its use as a practical tool in optimization problems. The approach is tested on a single design parameter problem through the use of a specially developed scheme. The results indicate comparable convergence properties for the present iterative process and the standard iterative scheme. The presented ideas are also applicable to multidesign parameter problems.
Rizk, M. H.↗
Evaluation of the capacity of communication lines with nonlinear finite memory
We propose a method for calculating the capacity of a finite-memory channel up to the square of the nonlinear memory parameter. A comparison with a regular Gaussian model is performed, in which the Kerr nonlinearity is considered as an additional Gaussian noise. The estimate by the regular Gaussian model is shown to yield a greater capacity as compared with the estimate obtained by the nonlinear memory model. The optimal signal powers, providing the maximum mutual information, are found to be equal. (paper)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Investigations into the feasibility of optical-CT 3D dosimetry with minimal use of refractively matched fluids
Purpose: In optical-CT, the use of a refractively matched polyurethane solid-tank in place of a fluid bath has the potential to greatly increase practical convenience, reduce cost, and possibly improve the efficacy of flood corrections. This work investigates the feasibility of solid-tank optical-CT imaging for 3D dosimetry through computer simulation. Methods: A MATLAB ray-tracing simulation platform, ScanSim, was used to model a parallel-source telecentric optical-CT imaging system through a polyurethane solid-tank containing a central cylindrical hollow into which PRESAGE radiochromic dosimeters can be placed. A small amount of fluid fills the 1–5 mm gap between the dosimeter and the walls of the tank. The use of the solid-tank reduces the required amount of fluid by approximately 97%. To characterize the efficacy of solid-tank, optical-CT scanning simulations investigated sensitivity to refractive index (RI) mismatches between dosimeter, solid-tank, and fluid, for a variety of dosimeter (RI = 1.5–1.47) and fluid (RI = 1.55–1.0) combinations. Efficacy was evaluated through the usable radius (r{sub u}) metric, defined as the fraction of the radius of the dosimeter where measured dose is predicted to be within 2% of the ground truth entered into the simulation. Additional simulations examined the effect of increasing gap size (1–5 mm) between the dosimeter and solid-tank well. The effects of changing the lens tolerance (0.5°–5.0°) were also investigated. Results: As the RI mismatch between the dosimeter and solid-tank increased from 0 to 0.02, the usable radius decreased from 97.6% to 50.2%. The optimal fluid RI decreased nonlinearly from 1.5 to 1.34 as the mismatch increased and was up to 9% lower than the tank. Media mismatches between the dosimeter and solid-tank also exacerbate the effects of changing the gap size, with no easily quantifiable relationship with usable radius. Generally, the optimal fluid RI value increases as gap size increases and is closely matched to the dosimeter at large gap sizes (>3 mm). Increasing the telecentric lens tolerance increases the usable radius for all refractive media combinations and improves the maximum usable radius of mismatched media to that of perfectly matched media for tolerances >5.0°. The maximum usable radius can be improved up to a factor of 2 when lens tolerances are small (<1.0°). Conclusions: Dry solid-tank optical-CT imaging in a telecentric system is feasible if the dosimeter RI is a close match with the solid-tank (<0.01 difference), providing accurate dose measurements within ±2% of true dose to over 80% of the dosimeter volume. In order to achieve accurate measurements over 96% of the dosimeter volume (representing out to 2 mm from the dosimeter edge), the dosimeter-tank RI mismatch must be less than 0.005. Optimal results occur when the RI of the dosimeter and tank is the same, in which case the fluid will have the same RI. If mismatches between the tank and dosimeter RI occur, the RI of the matching fluid needs to be fine tuned to achieve the highest usable radius.
61 RADIATION PROTECTION AND DOSIMETRY↗
Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study
We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Preliminary Design of Low-Thrust Interplanetary Missions
For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.
Sims, Jon A.↗
Structural efficiency studies of corrugated compression panels with curved caps and beaded webs
Curved cross-sectional elements are employed in structural concepts for minimum-mass compression panels. Corrugated panel concepts with curved caps and beaded webs are optimized by using a nonlinear mathematical programming procedure and a rigorous buckling analysis. These panel geometries are shown to have superior structural efficiencies compared with known concepts published in the literature. Fabrication of these efficient corrugation concepts became possible by advances made in the art of superplastically forming of metals. Results of the mass optimization studies of the concepts are presented as structural efficiency charts for axial compression.
Davis, R. C.↗
Finite element engine blade structural optimization
The Structural Tailoring of Engine Blades (STAEBL) computer program was developed to perform engine fan blade numerical optimizations. These blade optimizations seek a minimum weight or cost design that satisfies realistic blade design constraints, by tuning one to twenty design variables. The STAEBL system has been generalized to include both fan and compressor blade numerical optimizations. The system analyses have been significantly improved through the inclusion of an efficient plate finite element analysis for blade stress and frequency determinations. Additionally, a finite element based approximate severe foreign object damage (FOD) analysis has been included. The new FOD analysis gives very accurate estimates of the full nonlinear bird ingestion solution. Optimizations of fan and compressor blades have been performed using the system, showing significant cost and weight reductions, while comparing very favorably with refined design validation procedures.
Brown, K. W.↗
The poststall nonlinear dynamics and control of an F-18: A preliminary investigation
The successful high angle of attack (HAOA) operation of fighter aircraft will necessarily require the introduction of a new onboard control methodology that address the nonlinearity of the system when flown at the stall/poststall limits of the craft's flight envelope. As a precursor to this task, a researcher endeavored to familarize himself with the dynamics of one specific aircraft, the F-18, when it is flown at HAOA. This was accomplished by conducting a number of real time flight sorties using the NASA-Langley Research Center's F-18 simulator, which was operated with a pilot in the loop. In addition to developing a first hand familarity with the aircraft's dynamic characteristic at HAOA, work was also performed to identify the input/output operational footprint of the F-18's control surfaces. This investigator proposes to employ the nonlinear models of the plant identified this summer in a subsequent research effort that will make it possible to fly the F-18 effectively at poststall angles of attack. The controller design used there will rely on a new technique proposed by this investigator that provides for the automatic generation of online optimal control solutions for nonlinear dynamic systems.
Patten, William N.↗
Analysis and comparison of several numerical optimization methods.
Numerical method solution of nonlinear two- point boundary value problem associated with optimum transfer of spacecraft
STEEPEST DESCENT METHOD↗
Optimizing microfluidic flow cell geometry for in situ resonant soft X-ray characterization of molecular nanostructures
Liquid-phase resonant soft X-ray scattering (LP-RSoXS) is an emerging label-free technique to probe chemically resolved nanostructures of molecular or hybrid materials in liquid environments. Still, quantitative analysis is hindered by the pressure-induced deformation of thin silicon nitride (SiN) membranes used as windows in microfluidic flow cells, which attenuates the signal in nonlinear ways, making experimental optimization difficult. Here, in this work, we directly characterize this deformation under experimental conditions for a variety of cell configurations. We use this to develop a predictive model that combines transmission effects of SiN bowing, incident X-ray beam profiles, and material-dependent resonant scattering cross sections to simulate the effective scattering intensity at the detector across the carbon K-edge. Maps of the total signal across the flow cell window reveal that increasing the window width and polymer concentration shifts the anisotropic intensity distributions from the center toward the edges of the window. It was determined that an optimal SiN thickness of 50 nm, with a window aperture of 104 μm, maximizes the total signal for typical solute concentrations and energies across the carbon K-edge. Our results overturn the assumption that corner regions dominate the scattering signal, offering explicit design guidelines for maximizing LP-RSoXS signals and significantly advancing the quantitative application of this technique to the characterization of molecular and hybrid nanostructured materials in liquids.
Grabner, Devin [Washington State Univ., Pullman, W↗
An engineering optimization method with application to STOL-aircraft approach and landing trajectories
An optimization method has been developed that computes the optimal open loop inputs for a dynamical system by observing only its output. The method reduces to static optimization by expressing the inputs as series of functions with parameters to be optimized. Since the method is not concerned with the details of the dynamical system to be optimized, it works for both linear and nonlinear systems. The method and the application to optimizing longitudinal landing paths for a STOL aircraft with an augmented wing are discussed. Noise, fuel, time, and path deviation minimizations are considered with and without angle of attack, acceleration excursion, flight path, endpoint, and other constraints.
Jacob, H. G.↗
A numerical-perturbation method for the nonlinear analysis of structural vibrations
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Nayfeh, A. H.↗