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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, Perry A.↗
DOE OSTI2021

Post-compression of long-wave infrared 2 picosecond sub-terawatt pulses in bulk materials

We have experimentally demonstrated the post-compression of a long-wave infrared (9.2 μm) 150 GW peak power pulse from 2 ps to less than 500 fs using a sequence of two bulk materials with negative group velocity dispersion (GVD). The compression resulted in up to 1.6-fold increase of the peak power and up to 2.8-fold increase of the intensity in the center of a quasi-Gaussian beam. The partial decoupling of the self-phase modulation and chirp compensation stages by using two materials with significantly different ratios of nonlinear refractive index to GVD provides accurate optimization of the compression mechanism and promises a viable path to scaling peak powers to supra-terawatt levels. During the preparatory study, we measured, for the first time to our knowledge, the nonlinear refractive indices of NaCl, KCl, and BaF 2 for picosecond pulses in the long-wave infrared region.

43 PARTICLE ACCELERATORS↗
NASA NTRS1999

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics (CFD). The focus here is on those methods particularly well-suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid CFD algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid CFDs in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, James C., III↗
NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗
NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗
DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
NASA NTRS1992

Generating Far-Infrared Radiation By Two-Wave Mixing

Far-infrared radiation 1 to 6 GHz generated by two-wave mixing in asymmetrically grown GaAs/AlxGa1-xAs multiple-quantum-well devices. Two near-infrared semiconductor diode lasers phase-locked. Outputs amplified, then combined in semiconductor nonlinear multiple-quantum-well planar waveguide. Necessary to optimize design of device with respect to three factors: high degree of confinement of electromagnetic field in nonlinear medium to maximize power density, phase matching to extend length of zone of interaction between laser beams in non-linear medium, and nonlinear susceptibility. Devices used as tunable local oscillators in heterodyne-detection radiometers.

Borenstain, Shmuel↗
NASA NTRS1992

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗
NASA NTRS1990

Time-optical spinup maneuvers of flexible spacecraft

Attitude controllers for spacecraft have been based on the assumption that the bodies being controlled are rigid. Future spacecraft, however, may be quite flexible. Many applications require spinning up/down these vehicles. In this work the minimum time control of these maneuvers is considered. The time-optimal control is shown to possess an important symmetry property. Taking advantage of this property, the necessary and sufficient conditions for optimality are transformed into a system of nonlinear algebraic equations in the control switching times during one half of the maneuver, the maneuver time, and the costates at the mid-maneuver time. These equations can be solved using a homotopy approach. Control spillover measures are introduced and upper bounds on these measures are obtained. For a special case these upper bounds can be expressed in closed form for an infinite dimensional evaluation model. Rotational stiffening effects are ignored in the optimal control analysis. Based on a heuristic argument a simple condition is given which justifies the omission of these nonlinear effects. This condition is validated by numerical simulation.

Singh, G.↗
NASA NTRS1983

Optimal large-angle maneuvers with vibration suppression

Some methods and applications which determine optimal maneuver controls are overviewed. The main aspects of optimal control theory are summarized and the essential ideas involved in a class of methods ('continuation' or 'homotopy' methods) which are useful in solving the resulting two-point boundary value problems are discussed. Several low dimensioned, nonlinear maneuvers of multiple rigid-body configurations using optimal momentum transfer are discussed. Several linear and nonlinear flexible-body maneuvers are then presented and include distributed controls, vibration suppression/arrest, and computational issues. Finally, the key problem areas in which future research appears most urgent are identified.

Turner, J. D.↗
NASA NTRS1999

Optimized System Identification

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Juang, Jer-Nan↗
NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗
DOE OSTI2025

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Biomass char gasification kinetic rates compared to data, including ash effects

This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.

09 BIOMASS FUELS↗
DOE OSTI2025

Online regularization of Poincaré map of storage rings with Shannon entropy

A measurable chaos indicator is used as the online optimization objective in tuning a complicated nonlinear system—the National Synchrotron Light Source-II storage ring. Through analyzing the Shannon entropy in measured Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantified and then used for an online regularization of these maps. The method itself is general and applicable to other tunable nonlinear systems as well. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗