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DOE OSTI2026

Designing a Robust MEA-Based Post-Combustion Carbon Capture Process with Capture Rate Guarantees

This work presents an application of the nonlinear two-stage robust optimization solver PyROS to the model-based design and operation of a monoethanolamine scrubbing process for CO2 capture under epistemic uncertainty. Through this application, risk-averse process designs are successfully obtained for CO2 capture targets ranging from 90% to over 99%. In particular, the risk-averse solutions for CO2 capture targets of up to 98% are shown to be only marginally more expensive than their nominally optimal counterparts. Thus, the results demonstrate the utility of recently developed nonlinear robust optimization approaches for the solution of large-scale chemical process models under uncertainty.

20 FOSSIL-FUELED POWER PLANTS↗

NASA NTRS2014

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

HUB LOADS↗

DOE OSTI2024

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

NASA NTRS1988

Integrated nonlinear structural analysis and design

An integrated approach to the design optimization of structures which require nonlinear analysis is proposed. The optimization process begins with a linearized structural response and the amount of nonlinearity is increased as the optimum design becomes closer. The proposed approach has the potential of reducing substantially the computational cost of the optimization. Two truss examples are used for demonstration.

Haftka, Raphael T.↗

NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗

NASA NTRS1977

Power converter design optimization

Utilizing the demonstrated capability of nonlinear programming algorithms, a practical design optimization approach for power converters is established to conceive a design to meet all power-circuit performance requirements and concurrently optimize a defined quantity such as weight or losses. In addition, to facilitate a cost-effective design, the computer-aided approach provides a means to readily assess (1) the weight-efficiency tradeoff, (2) impacts of converter requirements and component characteristics on a given design, and (3) optimum power system configurations.

Yu, Y.↗

NASA NTRS1995

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Feng, Dan↗

NASA NTRS1978

Estimation and filter stability of stochastic delay systems

Linear and nonlinear filtering for stochastic delay systems are studied. A representation theorem for conditional moment functionals is obtained, which, in turn, is used to derive stochastic differential equations describing the optimal linear or nonlinear filter. A complete characterization of the optimal filter is given for linear systems with Gaussian noise. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.

Kwong, R. H.↗

NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗

NASA NTRS1974

A method for determining optimum phasing of a multiphase propulsion system for a single-stage vehicle with linearized inert weight

A general analytical treatment is presented of a single-stage vehicle with multiple propulsion phases. A closed-form solution for the cost and for the performance and a derivation of the optimal phasing of the propulsion are included. Linearized variations in the inert weight elements are included, and the function to be minimized can be selected. The derivation of optimal phasing results in a set of nonlinear algebraic equations for optimal fuel volumes, for which a solution method is outlined. Three specific example cases are analyzed: minimum gross lift-off weight, minimum inert weight, and a minimized general function for a two-phase vehicle. The results for the two-phase vehicle are applied to the dual-fuel rocket. Comparisons with single-fuel vehicles indicate that dual-fuel vehicles can have lower inert weight either by development of a dual-fuel engine or by parallel burning of separate engines from lift-off.

Martin, J. A.↗

NASA NTRS1991

Neighboring optimal guidance for aeroassisted noncoplanar orbital transfer

The fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in preference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions. The results are presented to a typical aeroassisted noncoplanar orbital transfer problem.

Naidu, D. S.↗

NASA NTRS1982

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Hargrove, A.↗

NASA NTRS2021

Convex Optimization Guidance for Precision Landing on Titan

Precision landing is an anticipated technology for future interplanetary missions. Autonomous spacecraft Entry, Descent and Landing (EDL) on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. In this paper, a successive convexification guidance algorithm is utilized to simulate autonomous precision landing sequences on Saturn’s moon Titan. Due to its unique geophysical features, studying the science of matter within Titan’s atmosphere and beneath its surface is one of NASA’s most important planetary science objectives. As part of the Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, low mass compared to the prospective payload and capabilities of precise autonomous delivery. This paper focuses on path optimization and guidance law development for high-fidelity dynamics parafoil tuning in the dense and adverse wind atmosphere of Titan, defined as a nonlinear and nonconvex optimal control problem. The powerful successive convexification method is used to solve the problem accordingly. The algorithm is designed such that the converged solution adheres to the nonlinear dynamics and kinematics in accordance with the original formulation, while respecting the state and control constraints. The six-degree-of-freedom (6DoF) simulations results show that this robust method is suitable for autonomous interplanetary applications.

Mooij, Edwin↗

NASA NTRS1993

Optimization of microscopic and macroscopic second order optical nonlinearities

Nonlinear optical materials (NLO) can be used to extend the useful frequency range of lasers. Frequency generation is important for laser-based remote sensing and optical data storage. Another NLO effect, the electro-optic effect, can be used to modulate the amplitude, phase, or polarization state of an optical beam. Applications of this effect in telecommunications and in integrated optics include the impression of information on an optical carrier signal or routing of optical signals between fiber optic channels. In order to utilize these effects most effectively, it is necessary to synthesize materials which respond to applied fields very efficiently. In this talk, it will be shown how the development of a fundamental understanding of the science of nonlinear optics can lead to a rational approach to organic molecules and materials with optimized properties. In some cases, figures of merit for newly developed materials are more than an order of magnitude higher than those of currently employed materials. Some of these materials are being examined for phased-array radar and other electro-optic switching applications.

Marder, Seth R.↗

NASA NTRS1991

Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

Two matched filter theory based schemes are described and illustrated for obtaining maximized and time correlated gust loads for a nonlinear aircraft. The first scheme is computationally fast because it uses a simple 1-D search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multi-dimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

Scott, Robert C.↗

NASA NTRS1976

Computational alternatives to obtain time optimal jet engine control

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

Basso, R. J.↗

NASA NTRS1996

Parallelization of a Parabolized Navier-Stokes Solver with a Design Optimizer

The design of future supersonic aircraft, such as the High Speed Civil Transport (HSCT), will rely heavily on computational methods for aircraft design and the prediction of the complex aerodynamics encountered in flight. Parabolized Navier-Stokes (PNS) equation flow solvers are recognized as efficient and accurate computational tools for the solution of supersonic and hypersonic flow-fields, while design optimizers have the potential to be valuable tools within the overall design process. Presently, however, the execution of the flow solver in conjunction with a design optimizer presents a computationally intensive and formidable problem. To meet the challenges and increasing demand for multidisciplinary numerical tools which are faster, more robust and provide greater functionality, alternative strategies are explored to increase computational throughput by coupling a design optimizer and flow solver in a parallel processing environment. To address this problem the parallel processing of a PNS flow solver with a nonlinear constraint design optimizer is investigated as an alternative computational method.

Pallis, J. M.↗

DOE OSTI2025

Massive νs through the CNN lens: interpreting the field-level neutrino mass information in weak lensing

Modern cosmological surveys probe the Universe deep into the nonlinear regime, where massive neutrinos suppress cosmic structure. Traditional cosmological analyses, which use the 2-point correlation function to extract information, are no longer optimal in the nonlinear regime, and there is thus much interest in extracting beyond-2-point information to improve constraints on neutrino mass. Quantifying and interpreting the beyond-2-point information is thus a pressing task. We study the field-level information in weak lensing convergence maps using convolution neural networks. We find that the network performance increases as higher source redshifts and smaller scales are considered — investigating up to a source redshift of 2.5 and ℓ max ≃ 10 4 — verifying that massive neutrinos leave a distinct effect on weak lensing. However, the performance of the network significantly drops after scaling out the 2-point information from the maps, implying that most of the field-level information can be found in the 2-point correlation function alone. We quantify these findings in terms of the likelihood ratio and also use Integrated Gradient saliency maps to interpret which parts of the map the network is learning the most from. We find that, in the absence of noise, the network extracts a similar amount of information from the most overdense and underdense regions. However, upon adding noise, the information in underdense regions is distorted as noise disproportionately washes out void-like structures.

Golshan, Malika [University of California, Berkele↗