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At least 1,009 records · Page 56

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The dynamics and control of large flexible space structures - 12, supplement 11

The rapid 2-D slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls is considered. Pontryagin's Maximum Principle is applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two point boundary value problem is then solved by using the quasilinearization technique, and the near minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The tradeoff between the minimum time and the minimum flexible amplitude requirements is discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing. The SCOLE station-keeping closed loop dynamics are re-examined by employing a slightly different method for developing the equations of motion in which higher order terms in the expressions for the mast modal shape functions are now included. A preliminary study on the effect of actuator mass on the closed loop dynamics of large space systems is conducted. A numerical example based on a coupled two-mass two-spring system illustrates the effect of changes caused in the mass and stiffness matrices on the closed loop system eigenvalues. In certain cases the need for redesigning control laws previously synthesized, but not accounting for actuator masses, is indicated.

Bainum, Peter M.↗

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Murphy, Patrick Charles↗

Development of a Multiobjective Optimization Procedure for Sonic Boom Minimization

A design optimization procedure for improved sonic boom and aerodynamic performance of high speed aircraft is presented. The multiobjective optimization procedure simultaneously minimizes the sonic boom at a given distance from the aircraft and the drag-to-lift ratio (C(sub D)/C(sub L)) Of the aircraft. Upper and lower bounds are also imposed on the lift coefficient. The Kreisselmeier - Steinhauser function is used for the multiobjective optimization formulation. A discrete semi-analytical aerodynamic sensitivity analysis procedure coupled with an analytical grid sensitivity analysis technique is used for evaluating design sensitivities. The use of the semi-analytical sensitivity analysis techniques results in significant computational savings. The flow equations are solved using a three-dimensional parabolized Navier-Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. A nonlinear programming technique and an approximate analysis procedure are used for the optimization. The optimization procedure developed is applied to the design of two high speed configurations, namely, a doubly swept wing-body configuration and a delta wing-body configuration. For the two sweep case only, minimization of the first peak in the pressure signature is performed first by optimizing only the nose radius and length of the aircraft. Minimization of the second peak in the pressure signature is performed next by optimizing only the wing geometric parameters. Significant improvements are obtained in the sonic boom characteristics and the aerodynamic performance of the wing-body configurations.

Narayan, J. R.↗

Optimization to Generate Equations of State for Hydrogen Production

On a high level, the larger project in question, HydroGEN, aims to develop software used for finding equations of state (EOS) to optimize catalyst configuration for H 2 production through water splitting. In particular, this summer project focused on solving the nonlinear equations used in fitting the equations. This problem involved using Python to solve a linear system with nonlinear constraints. In order for this to be achieved, Pyomo was used to build a model and the solver Ipopt, interior point optimizer, was used. Pyomo is a Python-based language developed at Sandia; it is an optimization modeling language. Rather than solving the entire problem at once, a toy problem was created, simplifying the problem down to the most important focus. This problem had a known solution, comparable to the calculated solution to assess accuracy and as progress was made towards finding solutions, complexity was gradually added to the problem. After building and solving the toy problem, it was found that it gave reasonably accurate solutions, better compared to the two existing solvers previously used with this project in terms of functionality. The solver is now ready for implementation into the project’s main software.

08 HYDROGEN↗

Rapid in-plane maneuvering of the flexible orbiting SCOLE

The rapid two-dimensional slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls has been considered. Pontryagin's Maximum Principle has been applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two-point boundary-value problem is then solved by using the quasilinearization technique, and the near-minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The trade-off between the minimum time and the minimum flexible amplitude requirements has been discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing.

Bainum, Peter M.↗

Interpretable inverse-designed cavity for on-chip nonlinear photon pair generation

Inverse design is a powerful tool in wave physics for compact, high-performance devices. To date, applications in photonics have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the “black box” nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at a rate of 1.1 MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

42 ENGINEERING↗

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimum Design of High-Speed Prop-Rotors

An integrated multidisciplinary optimization procedure is developed for application to rotary wing aircraft design. The necessary disciplines such as dynamics, aerodynamics, aeroelasticity, and structures are coupled within a closed-loop optimization process. The procedure developed is applied to address two different problems. The first problem considers the optimization of a helicopter rotor blade and the second problem addresses the optimum design of a high-speed tilting proprotor. In the helicopter blade problem, the objective is to reduce the critical vibratory shear forces and moments at the blade root, without degrading rotor aerodynamic performance and aeroelastic stability. In the case of the high-speed proprotor, the goal is to maximize the propulsive efficiency in high-speed cruise without deteriorating the aeroelastic stability in cruise and the aerodynamic performance in hover. The problems studied involve multiple design objectives; therefore, the optimization problems are formulated using multiobjective design procedures. A comprehensive helicopter analysis code is used for the rotary wing aerodynamic, dynamic and aeroelastic stability analyses and an algorithm developed specifically for these purposes is used for the structural analysis. A nonlinear programming technique coupled with an approximate analysis procedure is used to perform the optimization. The optimum blade designs obtained in each case are compared to corresponding reference designs.

Chattopadhyay, Aditi↗

Designing a drone delivery network with automated battery swapping machines

Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.

25 ENERGY STORAGE↗

Optimal low-thrust, three-burn orbit transfers with large plane changes

Optimal low-thrust, three-burn solutions have been obtained for orbit transfers between a 28.5-degree inclined low earth orbit and a series of 63.4-degree inclined circular orbits as well as a series of 63.4-degree inclined elliptical orbits with twelve hour periods. Solutions have also been obtained for orbit transfers between 97-degree inclined orbits and a 57-degree inclined low earth orbit. Thrust to weight ratios as low as 0.02 were considered. A hybrid nonlinear programming method was used to obtain the solutions. Analysis of the optimal steering during various burns reveals a natural division of the steering strategies into two categories based on whether a burn results in a change predominantly in semi-major axis or orbit plane. The similarity of these optimal steering strategies to previously obtained simple near-optimal steering strategies is discussed.

Zondervan, K. P.↗

Supporting cost-effective watershed management strategies for Chesapeake Bay using a modeling and optimization framework

Extensive efforts to adaptively manage nutrient pollution rely on Chesapeake Bay Program’s (Phase 6) Watershed Model, called Chesapeake Assessment Scenario Tool (CAST), which helps decision-makers plan and track implementation of Best Management Practices (BMPs). We describe mathematical characteristics of CAST and develop a constrained nonlinear BMP-subset model, software, and visualization framework. This represents the first publicly available optimization framework for exploring least-cost strategies of pollutant load control for the United States’ largest estuary. The optimization identifies implementation options for a BMP subset modeled with load reduction effectiveness factors, and the web interface facilitates interactive exploration of >30,000 solutions organized by objective, nutrient control level, and for ~200 counties. We assess framework performance and demonstrate modeled cost improvements when comparing optimization-suggested proposals with proposals inspired by jurisdiction plans. Stakeholder feedback highlights the framework’s current utility for investigating cost-effective tradeoffs and its usefulness as a foundation for future analysis of restoration strategies.

54 ENVIRONMENTAL SCIENCES↗

High-Power Fiber Lasers Using Photonic Band Gap Materials

High-power fiber lasers (HPFLs) would be made from photonic band gap (PBG) materials, according to the proposal. Such lasers would be scalable in the sense that a large number of fiber lasers could be arranged in an array or bundle and then operated in phase-locked condition to generate a superposition and highly directed high-power laser beam. It has been estimated that an average power level as high as 1,000 W per fiber could be achieved in such an array. Examples of potential applications for the proposed single-fiber lasers include welding and laser surgery. Additionally, the bundled fibers have applications in beaming power through free space for autonomous vehicles, laser weapons, free-space communications, and inducing photochemical reactions in large-scale industrial processes. The proposal has been inspired in part by recent improvements in the capabilities of single-mode fiber amplifiers and lasers to produce continuous high-power radiation. In particular, it has been found that the average output power of a single strand of a fiber laser can be increased by suitably changing the doping profile of active ions in its gain medium to optimize the spatial overlap of the electromagnetic field with the distribution of active ions. Such optimization minimizes pump power losses and increases the gain in the fiber laser system. The proposal would expand the basic concept of this type of optimization to incorporate exploitation of the properties (including, in some cases, nonlinearities) of PBG materials to obtain power levels and efficiencies higher than are now possible. Another element of the proposal is to enable pumping by concentrated sunlight. Somewhat more specifically, the proposal calls for exploitation of the properties of PBG materials to overcome a number of stubborn adverse phenomena that have impeded prior efforts to perfect HPFLs. The most relevant of those phenomena is amplified spontaneous emission (ASE), which causes saturation of gain and power at undesirably low levels, and scattering of light from dopants. In designing a given fiber laser for reduced ASE, care must be taken to maintain a correct fiber structure for eventual scaling to an array of many such lasers such that the interactions among all the members of the array would cause them to operate in phase lock. Hence, the problems associated with improving a single-fiber laser are not entirely separate from the bundling problem, and some designs for individual fiber lasers may be better than others if the fibers are to be incorporated into bundles. Extensive calculations, expected to take about a year, must be performed in order to determine design parameters before construction of prototype individual and fiber lasers can begin. The design effort can be expected to include calculations to optimize overlaps between the electromagnetic modes and the gain media and calculations of responses of PBG materials to electromagnetic fields. Design alternatives and physical responses that may be considered include simple PBG fibers with no intensity-dependent responses, PBG fibers with intensity- dependent band-gap shifting (see figure), and broad-band pumping made possible by use of candidate broad-band pumping media in place of the air or vacuum gaps used in prior PBG fibers.

DiDomenico, Leo↗

Low thrust space vehicle trajectory optimization using regularized variables

Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.

Schwenzfeger, K. J.↗

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Fleming, P.↗

A direct method for synthesizing low-order optimal feedback control laws with application to flutter suppression

A direct method of synthesizing a low-order optimal feedback control law for a high order system is presented. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean square steady state responses and control inputs. The controller is shown to be equivalent to a partial state estimator. The method is applied to the problem of active flutter suppression. Numerical results are presented for a 20th order system representing an aeroelastic wind-tunnel wing model. Low-order controllers (fourth and sixth order) are compared with a full order (20th order) optimal controller and found to provide near optimal performance with adequate stability margins.

Mukhopadhyay, V.↗

Optimizing spectral phase transfer in four-wave mixing with gas-filled capillaries

Four-wave mixing (FWM) in gas-filled hollow-core capillaries, a nonlinear optical process that mixes signal and pump photon frequencies to generate idler frequency photons, offers a method for precise spectral phase transfer from signal to idler at ultrashort timescales and extreme powers. However, this regime is challenged by competing linear and nonlinear dynamics, leading to significant trade-offs between spectral phase transfer and conversion efficiency. Our computational investigation focuses on the upconversion of femtosecond pulses from the infrared (IR) to the ultraviolet (UV), a range notoriously difficult to manipulate. We explore an intermediate energy regime that strikes an optimal balance between FWM-mediated phase-transfer fidelity and nonlinear conversion efficiency. By adjusting the energy ratios and spectral phase profiles of the input signal, we achieve conversion efficiencies of approximately 5-15% while maintaining an effective quasi-linear spectral phase transfer. These findings will contribute to establishing first-principles and scaling laws essential for applications such as high-precision imaging, spectroscopy, quantum transduction, and distributed entangled interconnects, facilitating advanced control of ultrafast photonic and electronic wavepackets in quantum materials with unprecedented spatial and temporal precision.

Zhang, Hao↗

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗