Results for “Penalty method” — Page 13

NASA NTRS2023

Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

restricted Boltzmann machine↗

DOE OSTI2023

An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, here we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is $\mathscr{O}$(ϵ -3-δ ) , where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be $\mathscr{O}$(ϵ -1 ), we demonstrate that the result can be improved to $\mathscr{O}$(ϵ -2 ) , which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain $\mathscr{O}$(ϵ -1 log(1/ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

USAMP Low-Cost Mg Sheet Component Development and Demonstration Project

The overarching objective of this USAMP project was to develop and demonstrate door panels made from magnesium (Mg) sheet with a cost penalty over conventional steel stampings of no more than $\$5.50$/kg saved. The technical approach integrated experiments with advanced computational tools based on Integrated Computational Materials Engineering (ICME) methods to develop new alloy chemistries and their thermomechanical processing that promise improved formability and lower forming temperatures. A penultimate task before finally forming the stampings was to incorporate actual microstructure into models that would enable formability simulations. This approach would, for the first time, account for individual magnesium grains moving in an anisotropic fashion unlike that for aluminum or steel that have isotropic properties upon which the current simulation tools are based. In separate activities, new coatings and lubricants to facilitate forming and improved corrosion protection and joining strategies, were developed to ensure that the door could be produced with stated product requirements. A technical cost model, which included parts production, assembly, and paint for a door specifically designed for Mg sheet, showed the cost penalty to be between $\$4.26$ to $\$6.60$/kg saved, which enveloped the project’s cost targets. The cost of the coated Mg sheet was identified as the key driver for the cost penalty. The mass of the Mg-intensive door was 7.9 kg, which was 54% less than the baseline steel door.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Low-Cost Magnesium Alloy Sheet Component Development and Demonstration Project

The overarching objective of this USAMP project was to develop and demonstrate door panels made from magnesium (Mg) sheet with a cost penalty over conventional steel stampings of no more than $5.50/kg saved. The technical approach integrated experiments with advanced computational tools based on Integrated Computational Materials Engineering (ICME) methods to develop new alloy chemistries and their thermomechanical processing that promise improved formability and lower forming temperatures. A penultimate task before finally forming the stampings was to incorporate actual microstructure into models that would enable formability simulations. This approach would, for the first time, account for individual magnesium grains moving in an anisotropic fashion unlike that for aluminum or steel that have isotropic properties upon which the current simulation tools are based. In separate activities, new coatings and lubricants to facilitate forming and improved corrosion protection and joining strategies, were developed to ensure that the door could be produced with stated product requirements. A technical cost model, which included parts production, assembly, and paint for a door specifically designed for Mg sheet, showed the cost penalty to be between 4.26 USD to 6.60 USD/kg saved, which enveloped the project’s cost targets. The cost of the coated Mg sheet was identified as the key driver for the cost penalty. The mass of the Mg-intensive door was 7.9 kg, which was 54% less than the baseline steel door.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Convex Relaxation of Grid-Connected Energy Storage System Models With Complementarity Constraints in DC OPF

Including complementarity constraints in energy storage system (ESS) models in optimization problems ensure an optimal solution will not produce a physically unrealizable control strategy where there is simultaneous charging and discharging. However, the current approaches to impose complementarity constraints require the use of non-convex optimization methods. Here, we propose a convex relaxation for a common ESS model that has terms for both charging and discharging based on a penalty reformulation for use in a model predictive control (MPC) based optimal power flow (DC OPF) problem. In this approach, the complementarity constraints are omitted and a penalty term is added to the optimization objective function. For the DC OPF problem, we provide analysis for the conditions under which the convex relaxation of the complementarity constraint ensures that a solution with simultaneous ESS charging and discharging operation is suboptimal. Simulation results demonstrating ESS behavior with and without the penalty reformulation are provided for an MPC-based DC OPF problem on multiple IEEE test systems.

25 ENERGY STORAGE↗

NASA NTRS1973

Aircraft symmetric flight optimization

Review of the development of gradient techniques and their application to aircraft optimal performance computations in the vertical plane of flight. Results obtained using the method of gradients are presented for attitude- and throttle-control programs which extremize the fuel, range, and time performance indices subject to various trajectory and control constraints, including boundedness of engine throttle control. A penalty function treatment of state inequality constraints which generally appear in aircraft performance problems is outlined. Numerical results for maximum-range, minimum-fuel, and minimum-time climb paths for a hypothetical supersonic turbojet interceptor are presented and discussed. In addition, minimum-fuel climb paths subject to various levels of ground overpressure intensity constraint are indicated for a representative supersonic transport. A variant of the Gel'fand-Tsetlin 'method of ravines' is reviewed, and two possibilities for further development of continuous gradient processes are cited - namely, a projection version of conjugate gradients and a curvilinear search.

Falco, M.↗

DOE OSTI2020

Direct Nano‐Synthesis Methods Notably Benefit Mg‐Battery Cathode Performance

Abstract Rechargeable magnesium batteries are promising candidates for next‐generation electrochemical energy storage, but their development is severely hindered by sluggish solid‐state diffusion and significant desolvation penalties of the divalent cation. Studies suggest that nano‐sized electrode materials alleviate these issues by shortening diffusion lengths and increasing electrode/electrolyte interaction. Here, the effect of particle size and synthetic methodology on the electrochemical performance of four sulfide cathode materials in Mg batteries is investigated: layered TiS 2 , CuS, spinel Ti 2 S 4 , and CuCo 2 S 4 . In these sulfide hosts, the direct preparation of nano‐dimensional crystallites is critical to activate or improve electrochemistry. Even promising cathode materials can appear electrochemically inert when micron‐sized particles are investigated (e.g., CuCo 2 S 4 ), and mechanical milling leads to surface degradation of active material which severely limits performance. However, nano‐sized CuCo 2 S 4 prepared directly reaches a capacity nearly double that of ball‐milled material and delivers 350 mAh g −1 at 60 °C. This work provides synthetic considerations which may be crucial in the discovery and design of novel Mg cathode materials, so that promising candidates are not overlooked. By extension, in oxide materials where Mg 2+ diffusion is expected to be much more sluggish, this factor is anticipated to be even more important when screening for new hosts.

Blanc, Lauren E.↗

NASA NTRS1978

Extended duration Orbiter life support definition

Extending the baseline seven-day Orbiter mission to 30 days or longer and operating with a solar power module as the primary source for electrical power requires changes to the existing environmental control and life support (ECLS) system. The existing ECLS system imposes penalties on longer missions which limit the Orbiter capabilities and changes are required to enhance overall mission objectives. Some of these penalties are: large quantities of expendables, the need to dump or store large quantities of waste material, the need to schedule fuel cell operation, and a high landing weight penalty. This paper presents the study ground rules and examines the limitations of the present ECLS system against Extended Duration Orbiter mission requirements. Alternate methods of accomplishing ECLS functions for the Extended Duration Orbiter are discussed. The overall impact of integrating these options into the Orbiter are evaluated and significant Orbiter weight and volume savings with the recommended approaches are described.

Kleiner, G. N.↗

NASA NTRS1985

Expert systems and their use in augmenting design optimization

The challenging requirements that are evolving for future aircraft demand that each design be optimally integrated, for the penalties imposed by nonoptimal performance are significant. Classic numerical optimization algorithms have been and will continue to be important tools for aircraft designers. These methods are, however, limited to certain categories of aircraft design variables, leaving the remainder to be determined by the user. A method that makes use of knowledge-based expert systems offers the potential for aiding the conceptual design process in a way that is similar to that of numerical optimization, except that it would address discrete, discontinuous, abstract, or any other unoptimized aspect of vehicle design and integration. Other unique capabilities such as automatic discovery and learning in design may also be achievable in the near term. This paper discusses current practice in conceptual aircraft design and knowledge-based systems, and how knowledge-based systems can be used in conceptual design.

Kidwell, G. H.↗

NASA NTRSDate not supplied

Cruise Slotted Wing Design with Natural Laminar Flow for Transonic Commercial Transport Aircraft

The present computational study investigates the aerodynamic design and analysis of cruise slotted wings with natural laminar flow for transonic transport aircraft. The cruise slotted wing is a multielement wing concept that features an intermediate slot to achieve greater aft loading relative to supercritical wings for the potential benefit of reduced shock strength and pressure drag. Transonic near-cruise, off-design assessments have also shown improved drag rise characteristics due to the ability of the slot to mitigate boundary layer separation on the aft flap component. However, due to the decreased Reynolds number of the flap, the cruise slotted wing has historically incurred a skin-friction drag penalty relative to a conventional supercritical wing. To offset this penalty, a cruise slotted wing with the forward main element and aft flap element shaped to achieve natural laminar flow is desired. Toward this effort, a knowledge-based aerodynamic design method, CDISC, has been leveraged to design a partial-span cruise slotted wing with natural laminar flow for a Mach-0.8 variant of the Common Research Model. Drag comparisons will be provided at cruise and near-cruise, off-design conditions relative to both fully turbulent and natural laminar flow conventional wing designs. It is anticipated that pairing natural laminar flow technology with the cruise slotted wing architecture will allow for cruise drag performance similar to conventional laminar flow wings with improved drag rise characteristics and more limited laminar-flow sensitivity at off-design conditions. Preliminary results for a cruise slotted wing with laminar flow on the outboard wing section only have shown a 10-ct cruise drag reduction relative to a conventional supercritical wing, but a 8-ct penalty relative to the conventional NLF wing. The final paper will include results for a cruise slotted wing design with laminar flow on both the inboard and outboard wing sections.

CFD↗

NASA NTRSDate not supplied

Cruise Slotted Wing Design with Natural Laminar Flow for Transonic Commercial Transport Aircraft

The present computational study investigates the aerodynamic design and analysis of cruise slotted wings with natural laminar flow for transonic transport aircraft. The cruise slotted wing is a multielement wing concept that features an intermediate slot to achieve greater aft loading relative to supercritical wings for the potential benefit of reduced shock strength and pressure drag. Transonic near-cruise, off-design assessments have also shown improved drag rise characteristics due to the ability of the slot to mitigate boundary layer separation on the aft flap component. However, due to the decreased Reynolds number of the flap, the cruise slotted wing has historically incurred a skin-friction drag penalty relative to a conventional supercritical wing. To offset this penalty, a cruise slotted wing with the forward main element and aft flap element shaped to achieve natural laminar flow is desired. Toward this effort, a knowledge-based aerodynamic design method, CDISC, has been leveraged to design a partial-span cruise slotted wing with natural laminar flow for a Mach-0.8 variant of the Common Research Model. Drag comparisons will be provided at cruise and near-cruise, off-design conditions relative to both fully turbulent and natural laminar flow conventional wing designs. It is anticipated that pairing natural laminar flow technology with the cruise slotted wing architecture will allow for cruise drag performance similar to conventional laminar flow wings with improved drag rise characteristics and more limited laminar-flow sensitivity at off-design conditions. Preliminary results for a cruise slotted wing with laminar flow on the outboard wing section only have shown a 10-ct cruise drag reduction relative to a conventional supercritical wing, but a 8-ct penalty relative to the conventional NLF wing. The final paper will include results for a cruise slotted wing design with laminar flow on both the inboard and outboard wing sections.

Natural Laminar Flow↗

NASA NTRS2013

Mixed Integer Programming and Heuristic Scheduling for Space Communication

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Lee, Charles H.↗

NASA NTRSDate not supplied

Acoustic Liner Drag: Measurement Uncertainty Reduction and Application to Novel Perforate Geometries

In addition to developing acoustic liner concepts and characterizing their performance, the NASA Langley Liner Physics Team has investigated issues related to liner drag. A method to quantify relative drag of liner configurations was developed and employed to understand the effects of various liner features. It was observed that perforate shape could have a marked effect on the measured liner drag and led to the discovery of a low-drag geometry that cut the drag penalty between a perforate and a smooth wall by approximately 50%. Investigations of novel perforates to further reduce drag were stymied by measurement uncertainty that prevented further resolution of drag differences between configurations. The current study details efforts to understand the causes of this uncertainty and describe changes made to testing methods to reduce it. Previously evaluated perforates were retested with these improvements in the NASA Langley Grazing Flow Impedance Tube to determine their relative drag at a flow speed of Mach 0.5 without acoustic excitation. Their performance was compared to the previously identified low-drag geometry to see if further drag reductions could be realized.

drag↗

NASA NTRSDate not supplied

Acoustic Liner Drag: Measurement Uncertainty Reduction and Application to Novel Perforate Geometries

In addition to developing acoustic liner concepts and characterizing their performance, the NASA Langley Liner Physics Team has investigated issues related to liner drag. A method to quantify relative drag of liner configurations was developed and employed to understand the effects of various liner features. It was observed that perforate shape could have a marked effect on the measured liner drag and led to the discovery of a low-drag geometry that cut the drag penalty between a perforate and a smooth wall by approximately 50%. Investigations of novel perforates to further reduce drag were stymied by measurement uncertainty that prevented further resolution of drag differences between configurations. The current study details efforts to understand the causes of this uncertainty and describe changes made to testing methods to reduce it. Previously evaluated perforates were retested with these improvements in the NASA Langley Grazing Flow Impedance Tube to determine their relative drag at a flow speed of Mach 0.5 without acoustic excitation. Their performance was compared to the previously identified low-drag geometry to see if further drag reductions could be realized.

drag↗

NASA NTRS1980

Performability evaluation of the SIFT computer

The paper deals with the models, techniques, and evaluation methods that were successfully used to test the performance of the SIFT degradable computing system. The performance of the computer plus its air transport mission environment is modeled as a random variable, taking values in a set of 'accomplishment level'. The levels are defined in terms of four attributes of total system (computer plus environment) behavior, namely safety, no change in mission profile, no operational penalties, and no economic penalties. The base model of the total system is a stochastic process, whose states describe the internal structure of SIFT and the relevant conditions of its computational environment. Base model state trajectories are related to accomplishment levels via a special function, and solution methods are then used to determine the performability of the total system for various parameters of the computer and environment.

Meyer, J. F.↗

DOE OSTI2021

An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods

A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty function scheme equipped with a penalty-parameter updating rule. The feasible-start algorithm merely has to satisfy certain general requirements, and so is the updating rule. Under mild assumptions, the framework is proved to converge on CQPs with both inequality and equality constraints and, at a negligible additional cost per iteration, produces an infeasibility certificate, together with a feasible point for an (approximately) ℓ 1 -least relaxed feasible problem, when the given problem does not have a feasible solution. The framework is applied to a feasible-start constraint-reduced interior-point algorithm previously proved to be highly performant on problems with many more inequality constraints than variables (“imbalanced”). Numerical comparison with popular codes (OSQP, qpOASES, MOSEK) is reported on both randomly generated problems and support-vector machine classifier training problems. The results show that the former typically outperforms the latter on imbalanced problems. Finally, application of the proposed infeasible-start framework to other feasible-start algorithms is briefly considered, and is tested on a simplex iteration.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Sensor/Actuator Selection for the Constrained Variance Control Problem

The problem of designing a linear controller for systems subject to inequality variance constraints is considered. A quadratic penalty function approach is used to yield a linear controller. Both the weights in the quadratic penalty function and the locations of sensors and actuators are selected by successive approximations to obtain an optimal design which satisfies the input/output variance constraints. The method is applied to NASA's 64 meter Hoop-Column Space Antenna for satellite communications. In addition the solution for the control law, the main feature of these results is the systematic determination of actuator design requirements which allow the given input/output performance constraints to be satisfied.

Delorenzo, M. L.↗

NASA NTRS1986

Ada and cyclic runtime scheduling

An important issue that must be faced while introducing Ada into the real time world is efficient and prodictable runtime behavior. One of the most effective methods employed during the traditional design of a real time system is the cyclic executive. The role cyclic scheduling might play in an Ada application in terms of currently available implementations and in terms of implementations that might be developed especially to support real time system development is examined. The cyclic executive solves many of the problems faced by real time designers, resulting in a system for which it is relatively easy to achieve approporiate timing behavior. Unfortunately a cyclic executive carries with it a very high maintenance penalty over the lifetime of the software that is schedules. Additionally, these cyclic systems tend to be quite fragil when any aspect of the system changes. The findings are presented of an ongoing SofTech investigation into Ada methods for real time system development. The topics covered include a description of the costs involved in using cyclic schedulers, the sources of these costs, and measures for future systems to avoid these costs without giving up the runtime performance of a cyclic system.

Hood, Philip E.↗