Search NASA⌕ Search

SEARCH · Search NASA

Results for “Optimality conditions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24

On optimal soft-decision demodulation

Wozencraft and Kennedy have suggested that the appropriate demodulator criterion of goodness is the cut-off rate of the discrete memoryless channel created by the modulation system; the criterion of goodness adopted in this note is the symmetric cut-off rate which differs from the former criterion only in that the signals are assumed equally likely. Massey's necessary condition for optimal demodulation of binary signals is generalized to M-ary signals. It is shown that the optimal demodulator decision regions in likelihood space are bounded by hyperplanes. An iterative method is formulated for finding these optimal decision regions from an initial good quess. For additive white Gaussian noise, the corresponding optimal decision regions in signal space are bounded by hypersurfaces with hyperplane asymptotes; these asymptotes themselves bound the decision regions of a demodulator which, in several examples, is shown to be virtually optimal. In many cases, the necessary condition for demodulator optimality is also sufficient, but a counter example to its general sufficiency is given.

Lee, L. N.↗

Necessary and sufficient conditions under which an H2 optimal control problem has a unique solution

A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.

Chen, Ben M.↗

Application of Contraction Mappings to the Control of Nonlinear Systems

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Killingsworth, W. R., Jr.↗

A homotopy algorithm for digital optimal projection control GASD-HADOC

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

Collins, Emmanuel G., Jr.↗

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimization of key energy and performance metrics for drug product manufacturing

During the development of pharmaceutical manufacturing processes, detailed systems-based analysis and optimization are required to control and regulate critical quality attributes within specific ranges, to maintain product performance. As discussions on carbon footprint, sustainability, and energy efficiency are gaining prominence, the development and utilization of these concepts in pharmaceutical manufacturing are seldom reported, which limits the potential of pharmaceutical industry in maximizing key energy and performance metrics. Based on an integrated modeling and techno-economic analysis framework previously developed by the authors, this study presents the development of a combined sensitivity analysis and optimization approach to minimize energy consumption while maintaining product quality and meeting operational constraints in a pharmaceutical process. The optimal input process conditions identified were validated against experiments and good agreement resulted between simulated and experimental data. Here, the results also allowed for a comparison of the capital and operational costs for batch and continuous manufacturing schemes under nominal and optimized conditions. Using the nominal batch operations as a basis, the optimized batch operation results in a 71.7% reduction of energy consumption, whereas the optimized continuous case results in an energy saving of 83.3%.

59 BASIC BIOLOGICAL SCIENCES↗

Numerical framework for integrated additive manufacturing-compression molding (AM-CM) of thermoplastic composites

Additive manufacturing-compression molding (AM-CM) has emerged as a transformative technology in advanced composite manufacturing. Additive manufacturing (AM) offers high design flexibility and the ability to produce complex geometries with precisely aligned fibers in the preferred orientation. Compression molding (CM) enhances composite materials by providing excellent dimensional stability, reduced porosity, high production rates, and a smooth surface finish. Despite these advantages, extensive integrated analysis is required to optimize processing conditions for improved fiber orientation distribution (FOD) and porosity control. Here, this study develops a comprehensive numerical model to simulate the AM-CM manufacturing process. The model isolates the effects of both the AM and CM phases while also capturing their integration. Additionally, it accounts for heat transfer, temperature-dependent viscosity, and fiber orientation in the extruded fiber-filled polymer, accurately representing material behavior during processing. This approach enables the analysis of interactions between deposited beads of complex strand shapes and their interface regions after full compression. Moreover, the model predicts key parameters such as polymer flowability, fiber orientation, and temperature evolution in AM-CM parts. By optimizing processing conditions, it facilitates a controlled and predictable microstructure.

36 MATERIALS SCIENCE↗

A Reactive-Ion Etch for Patterning Piezoelectric Thin Film

Reactive-ion etching (RIE) under conditions described below has been found to be a suitable means for patterning piezoelectric thin films made from such materials as PbZr(1-x)Ti(x)O3 or Ba(x)Sr(1.x)TiO3. In the original application for which this particular RIE process was developed, PbZr(1-x)Ti(x)O3 films 0.5 microns thick are to be sandwiched between Pt electrode layers 0.1 microns thick and Ir electrode layers 0.1 microns thick to form piezoelectric capacitor structures. Such structures are typical of piezoelectric actuators in advanced microelectromechanical systems now under development or planned to be developed in the near future. RIE of PbZr(1-x)Ti(x)O3 is usually considered to involve two major subprocesses: an ion-assisted- etching reaction, and a sputtering subprocess that removes reactive byproducts. RIE is favored over other etching techniques because it offers a potential for a high degree of anisotropy, high-resolution pattern definition, and good process control. However, conventional RIE is not ideal for patterning PbZr(1-x)Ti(x)O3 films at a thickness as great as that in the original intended application. In order to realize the potential benefits mentioned above, it is necessary to optimize process conditions . in particular, the composition of the etching gas and the values of such other process parameters as radio-frequency power, gas pressure, gas-flow rate, and duration of the process. Guidelines for determining optimum conditions can be obtained from experimental determination of etch rates as functions of these parameters. Etch-gas mixtures of BCl3 and Cl2, some also including Ar, have been found to offer a high degree of selectivity as needed for patterning of PbZr(1-x)Ti(x)O3 films on top of Ir electrode layers in thin-film capacitor structures. The selectivity is characterized by a ratio of approx.10:1 (rate of etching PbZr(1-x)Ti(x)O3 divided by rate of etching Ir and IrO(x)). At the time of reporting the information for this article, several experiments on RIE in BCl3 and Cl2 (and sometimes Ar) had demonstrated the 10:1 selectivity ratio, and further experiments to enhance understanding and obtain further guidance for optimizing process conditions were planned.

Yang, Eui-Hyeok↗

Growth of a mat-forming photograph in the presence of UV radiation

Knowledge of the survival and growth of microorganisms in the presence of ultraviolet radiation is important for understanding the potential for life to exist in environments exposed to high fluxes of UV radiation. The growth of a mat-forming phototrophic prokaryote, Chloroflexus aurantiacus, was examined in the presence of continuous high UV irradiation under otherwise optimal growth conditions. Evidence was sought for an intrinsic ability to grow in the presence of UV radiation in a carefully chosen organism known to be unusually resistant to UV radiation, of ancient lineage among the phototrophs, to resemble ancient microfossils from the Precambrian, and to be a mat-former. It was assumed that even a high intrinsic UV resistance would be inadequate for survival and growth in the presence of very high UV fluxes, and iron (Fe3+) was selected as a common, abundant UV-absorbing substance that might protest microorganisms growing in or under iron-bearing sediments. The effectiveness of Fe(3+) was tested as a UV protective agent at low concentrations in thin layers. It was concluded that intrinsic UV resistance in some organisms may account for growth, not just survival, of these organisms when exposed to high UV fluxes under otherwise optimal growth conditions in an anoxic environment. It was also concluded that Fe(3+) bearing sediments of 1 mm or less in thickness may provide an adequate shield against high UV fluxes permitting the growth of microorganisms just below their surface. As long as growth conditions were met, then the evolution and development of microorganisms would not be hampered by high UV fluxes impinging upon the surface of iron-bearing sediments.

Pierson, Beverly K.↗

Determination of optimal control using imbedding of the terminal conditions

The utility of a method to solve optimal control problems is discussed with emphasis placed on the solutions of singular optimal control problems. The method involves imbedding the optimization problem of interest in a family of optimization problems which are parameterized by their terminal conditions. The solution to the optimization problem is obtained by collapsing the terminal conditions of the family of problems onto those of the original problem, while appropriately modifying the control function to account for the changing terminal conditions. The utility of this method is illustrated by obtaining the solution to an aerial attack problem where the attacking vehicle must maneuver subject to control limitations so as to place the enemy in a certain relative position for launching a missile in the shortest possible time.

Montgomery, R. C.↗

Deep Learning-Based Adaptive Remedial Action Scheme with Security Margin for Renewable-Dominated Power Grids

The Remedial Action Scheme (RAS) is designed to take corrective actions after detecting predetermined conditions to maintain system transient stability in large interconnected power grids. However, since RAS is usually designed based on a few selected typical operating conditions, it is not optimal in operating conditions that are not considered in the offline design, especially under frequently and dramatically varying operating conditions due to the increasing integration of intermittent renewables. The deep learning-based RAS is proposed to enhance the adaptivity of RAS to varying operating conditions. During the training, a customized loss function is developed to penalize the negative loss and suggest corrective actions with a security margin to avoid triggering under-frequency and over-frequency relays. Simulation results of the reduced United States Western Interconnection system model demonstrate that the proposed deep learning–based RAS can provide optimal corrective actions for unseen operating conditions while maintaining a sufficient security margin.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

42 ENGINEERING↗

Equivalent Area Targets for Inverse Design Optimization With Changing Low-Boom Cruise Conditions

This paper provides theoretical and numerical justifications for inverse design optimization of reversed equivalent area (A e,r ) of low-boom supersonic aircraft when the cruise condition changes during the optimization iterations. A modified linear theory for steady flow around a supersonic projectile is used to establish the accuracy of A e,r -based body-of-revolution approximation of a low-boom supersonic aircraft for undertrack sonic boom analysis using computational fluid dynamics off-body pressure. As a result, designing a low-boom shape of the off-body pressure at three body lengths below the aircraft is equivalent to designing a low-boom A e,r shape. A Bezier curve with eight control points is used to define an A e,r target for inverse design optimization of A e,r of a supersonic aircraft. To make an A e,r target matchable by a low-boom supersonic aircraft, the A e,r target must have the minimal perceived level of decibels (PLdB) for sonic boom and satisfy two constraints defined by the cruise condition, effective length, and two nondimensional parameters. Numerical results are used to verify that, for different cruise conditions, all optimized A e,r targets with PLdB below 70 can be approximately generated by scaling one of them if the targets have the same nondimensional parameters and approximately the same effective length.

multidisciplinary optimization↗

Optimizing Transmission of Acoustic Signals to Monitor Internal Conditions of Canisters for Dry Storage of Commercial Spent Nuclear Fuel

Safe storage of spent nuclear fuel (SNF) is critical to the nuclear fuel cycle and the future of nuclear energy. In the United States, SNF is stored primarily via two methods regulated by the U.S. Nuclear Regulatory Commission: wet storage in SNF pools and dry storage in dry cask storage systems (DCSSs). After about five years of cooling in spent fuel pools, the fuel assemblies are transferred into DCSSs, and the systems are filled with helium and sealed by welding. Deterioration of conditions inside of a DCSS is reflected in changes in the internal gas properties; this motivates the development of acoustic techniques to monitor internal gas properties, over extended storage periods, using sensors mounted on the exterior of the storage packages. However, a major challenge in collecting acoustic signals is the impedance mismatch between the steel canister shell and the gas. Only a small fraction of the ultrasonic signal can be transmitted through the gas medium. This paper documents experimental studies conducted on a full-scale canister mock-up to capture the gas-borne signals. Damping materials were pasted on the outside, and blocking and unblocking tests were conducted to identify the gas-borne signal. The results show that the excitation frequency plays an important role in maximizing the gas-borne signals. The gas-borne signal was successfully detected at around the theoretical time-of-flight. A high signal-to-noise ratio was achieved in the measurements. Next, the acoustic impedance matching layers were introduced, and the gas signal was drastically improved compared with that using no AIM layers.

Spent nuclear fuel (SNF), Canisters, Internal cond↗

Practical benzylation of N,N -substituted ethanolamines related to chemical warfare agents for analysis and detection by Electron Ionization Gas Chromatography-Mass Spectrometry

The benzylation of three, low-molecular weight N,N-disubstituted ethanolamines related to chemical warfare agents (CWAs) to furnish derivatives with improved Gas Chromatography-Mass Spectrometry (GC-MS) profiles is described. Due to their low molecular weight and polar nature, N,N-disubstituted ethanolamines are notoriously difficult to detect by routine GC-MS analyses during Organisation for the Prohibition of Chemical Weapons (OPCW) proficiency tests (PTs), particularly in scenarios when they are present at low levels (~1-10 ppm) amidst more abundant interferences. Our studies revealed that the optimal derivatization conditions involved the treatment of the ethanolamine with benzyl bromide in the presence of an inorganic base (e.g., Na 2 CO 3 ) in dichloromethane at 55 °C for 2 hours. This optimized set of conditions were then successfully applied to the derivatization of N,N-dimethylethanolamine, N,N-diethylethanolamine and N,N-diisopropylethanolamine present separately at 1 and 10 μg/mL concentrations in a glycerol-rich matrix sample featured in the 48 th OPCW PT. The benzylated derivatives of the three ethanolamines possessed retention times long enough to clear the massive glycerol-containing matrix interferences. In conclusion, the protocol herein is introduced as an alternative method for derivatization of these CWA and pharmaceutically important species and should find broad applicability in laboratories where their routine forensic analysis is carried out.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance of sweeping gas membrane distillation for treating produced water: Modeling and experiments

Membrane distillation (MD) has shown promise for desalination of produced water (PW), but there are very few studies reported on the performance of MD with real PW and the characteristics of the fouling and scaling in MD. Among different MD configurations, sweeping gas MD (SGMD) is the least studied configuration. Here we report the application of SGMD for treating high-salinity PW (123 g L -1 ). The SGMD operating conditions were first carefully optimized through pure water MD experiments by varying operating conditions. The flux evaluation was accompanied by a detailed Aspen Custom Modeler simulation based on the electrolyte-NRTL thermodynamic model to better understand the heat and mass transfer in the feed and permeate channel. Supported by experiments, modeling results confirmed the partial condensation of the vapor in the permeate channel. Furthermore, it was concluded that the saturation of the sweeping gas is controlling the overall mass transfer through the membrane. Selected membranes and optimized conditions were then used to conduct short-term and long-term performance tests with PW. In long-term MD test, the concentration of the PW increased by a factor of two (50% water recovery), while the membrane exhibited small flux decline. Elemental analysis showed that strontium and sodium were the major scalant compounds.

42 ENGINEERING↗

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗