An optimization-inspired solver for inequality constrained nonlinear solid mechanics.
Abstract not provided.
Tupek, Michael↗
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Results for “Nonlinear optimization”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Incorporating Empirical Nonlinear Efficiency into Control Co-Optimization of a Real World Heaving Point Absorber using WecOptTool
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Gaebele, Daniel↗
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 CO<sub>2</sub> capture under epistemic uncertainty. Through this application, risk-averse process designs are successfully obtained for CO<sub>2</sub> capture targets ranging from 90% to over 99%. In particular, the risk-averse solutions for CO<sub>2</sub> 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↗
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↗
Polarisation analysis of optimal conditions for stationary second-harmonic generation in a solid-state laser
The Jones matrix method is used to study the optimal conditions for steady-state generation through intracavity frequency conversion in a solid-state laser under type-II phase matching based on a weakly anisotropic model of an active medium (amplitude and phase anisotropy) and a nonlinear element. The optimal rotation angles of the nonlinear element are found. (nonlinear optical phenomena)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Frequency Recovery in Power Grids Using High-Performance Computing
Maintaining electric power system stability is paramount, especially in extreme contingencies involving unexpected outages of multiple generators or transmission lines that are typical during severe weather events. Such outages often lead to large supply-demand mismatches followed by subsequent system frequency deviations from their nominal value. The extent of frequency deviations is an important metric of system resilience, and its timely mitigation is a central goal of power system operation and control. This paper develops a novel nonlinear model predictive control (NMPC) method to minimize frequency deviations when the grid is affected by an unforeseen loss of multiple components. Our method is based on a novel multi-period alternating current optimal power flow (ACOPF) formulation that accurately models both nonlinear electric power flow physics and the primary and secondary frequency response of generator control mechanisms. We develop a distributed parallel Julia package for solving the large-scale nonlinear optimization problems that result from our NMPC method and thereby address realistic test instances on existing high-performance computing architectures. Our method demonstrates superior performance in terms of frequency recovery over existing industry practices, where generator levels are set based on the solution of single-period classical ACOPF models.
nonlinear model predictive control↗
Optimal Control of Evolution Mixed Variational Inclusions
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Low-Frequency Oscillations in Optical Measurements of Metal-Nanoparticle Vibrations
Time-resolved optical measurements of vibrating metal nanoparticles have been used extensively to probe the ultrafast mechanical properties of the nanoparticles and of the surrounding liquid, but nearly all investigations so far have been limited to the linear regime. Herein, we report the observation of a low-frequency oscillating signal in transient-absorption measurements of nanoparticles with octahedral gold cores and cubic silver shells; the signal appears at the difference of two mechanical vibrational frequencies in the particles, suggesting a nonlinear mixing process. We tentatively attribute this proposed mixing to a nonlinear coupling between a vibrational mode of the nanoparticle and its optical-frequency plasmon resonance. The optimization of this nonlinear transduction may enable high-efficiency opto-mechanical frequency mixing in the GHz-THz frequency regime.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
mystic - a brief introduction
The mystic framework enables the solving of difficult optimization problems through three major innovations: (1) plug-and-play component-based optimization algorithms, (2) the ability to dynamically construct and apply generalzed trnasforms, K , where x' = K(x) , and (3) workflows providing asynchronous execution and statefulness. These features, in conjunction with supporting packages pathos , pyina , and klepto , can provide massively-parallel scalable workflows for quickly solving optimization problems in complex nonlinear spaces. mystic can be used to simplify non-convex optimization problems by transforming away nonlinearities through user-built kernel transforms. This tutorial demonstrates using mystic for machine learning with automated dimensional-reduction, using embarrasingly parallel solver ensembles to find an accurate interpolated surrogate for a nonlinear surface, and the determination of worst-case bounds on expectation value of an objective function under uncertainty.
97 MATHEMATICS AND COMPUTING↗
An Optimal System of One-dimensional Symmetry Lie Algebras of Coupled Nonlinear Schroedinger Equations
This paper is devoted to finding an optimal system of one-dimensional subalgebras of an eight-dimensional Lie algebra of point symmetry transformations, admitted by a system of two coupled nonlinear Schroedinger equations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
MULTI-OBJECTIVE ONLINE OPTIMIZATION OF BEAM LIFETIME AT APS
In this paper, online optimization of beam lifetime at the APS (Advanced Photon Source) storage ring is presented. A general genetic algorithm (GA) is developed and employed for some online optimizations in the APS storage ring. Sextupole magnets in 40 sectors of the APS storage ring are employed as variables for the online nonlinear beam dynamics optimization. The algorithm employs several optimization objectives and is designed to run with topup mode or beam current decay mode. Up to 50\% improvement of beam lifetime is demonstrated, without affecting the transverse beam sizes and other relevant parameters. In some cases, the top-up injection efficiency is also improved.
APS↗
Numerical study of a confocal ultrasonic setup for creation of cavitation
Acoustic cavitation is used for various therapeutic applications such as local enhancement of drug delivery, histotripsy or hyperthermia. One of the utmost important parameter for cavitation creation is the rarefaction pressure. The typical magnitude of the rarefaction pressure required to initiate cavitation from gas dissolved in tissue is beyond the range of the megapascal. Because nonlinear effects need to be taken into account, a numerical simulator based on the Westervelt equation was used to study the pressure waveform and the acoustic field generated by a setup for creation of cavitation consisting of two high intensity focused ultrasound transducers mounted confocally. At constant acoustic power, simulations with only one and both transducers from the confocal setup showed that the distortion of the pressure waveform due to the combined effects of nonlinearity and diffraction is less pronounced when both confocal transducers are used. Consequently, the confocal setup generates a greater peak negative pressure at focus which is more favorable for cavitation initiation. Comparison between the confocal setup and a single transducer with the same total emitting surface puts in evidence the role of the spatial separation of the two beams. Furthermore, it has been previously shown that the location of the peak negative pressure created by a single transducer shifts from focus towards the transducers in the presence of nonlinear effects. The simulator was used to study a configuration where the acoustical axes of transducers intersect on the peak negative pressure instead of the geometrical focus. For a representative confocal setup, namely moderate nonlinear effects, a 2% increase of the peak negative pressure and 8% decrease of the peak positive pressure resulted from this configuration. These differences tend to increase by increasing nonlinear effects. Although the optimal position of the transducers varies with the nonlinear regimen, the intersection point remains the location of the peak negative pressure in any case. Thus, unlike the location of the peak negative pressure for a single transducer can shift by a few millimeters, the focal point of a confocal device is independent of the power. This point is particularly important for therapeutic applications, frequently requiring high spatial accuracy. An experiment conducted shows that cavitation creation can be achieved easier with confocal ultrasound.
42 ENGINEERING↗
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↗
Efficient derivative computation for unsteady fatigue-constrained nonlinear aero-structural wind turbine blade optimization
Gradient-based optimization offers significant efficiency advantages for wind turbine blade design, but its application has often been limited by the cost and accuracy of finite-difference derivative calculations, especially when fatigue constraints are considered. In this work, we systematically compare and evaluate four differentiation techniques, namely algorithmic differentiation, implicit differentiation, sparsity exploitation, and parallelization, to determine their effectiveness in computing accurate gradients through time-domain aero-structural simulations. By integrating these techniques with unsteady nonlinear aerodynamic and structural models, we develop software designed for accurate gradient computation. We show that combining these techniques addresses memory and runtime challenges associated with long simulations required by design load cases. Specifically, the most effective combination reduces derivative computation wall time by over an order of magnitude compared to finite differencing while maintaining superior accuracy. We demonstrate this approach in a proof-of-concept aero-structural optimization of a wind turbine blade that improves the cost of energy by 12.78 %. This comparative study establishes a viable approach for fatigue-aware blade design that balances computational efficiency with modeling accuracy.
17 WIND ENERGY↗
Topography-based Flood Planning and Optimization Capability Development Report
Globally, water-related disasters are among the most frequent and costly natural hazards. Flooding inflicts catastrophic damage on critical infrastructure and population, resulting in substantial economic and social costs. NISAC is developing LeveeSim, a suite of nonlinear and network optimization models, to predict optimal barrier placement to protect critical regions and infrastructure during flood events. LeveeSim currently includes a high-performance flood model to simulate overland flow, as well as a network optimization model to predict optimal barrier placement during a flood event. The LeveeSim suite models the effects of flooding in predefined regions. By manipulating a domain’s underlying topography, developers altered flood propagation to reduce detrimental effects in areas of interest. This numerical altering of a domain’s topography is analogous to building levees, placing sandbags, etc. To induce optimal changes in topography, NISAC used a novel application of an optimization algorithm to minimize flooding effects in regions of interest. To develop LeveeSim, NISAC constructed and coupled hydrodynamic and optimization algorithms. NISAC first implemented its existing flood modeling software to use massively parallel graphics processing units (GPUs), which allowed for the simulation of larger domains and longer timescales. NISAC then implemented a network optimization model to predict optimal barrier placement based on output from flood simulations. As proof of concept, NISAC developed five simple test scenarios, and optimized topographic solutions were compared with intuitive solutions. Finally, as an early validation example, barrier placement was optimized to protect an arbitrary region in a simulation of the historic Taum Sauk dam breach.
42 ENGINEERING↗
Customizable wave tailoring nonlinear materials enabled by bilevel inverse design
Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.
Science & Technology - Other Topics↗
Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations
Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumor tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear controller for nonlinear wave energy converters
The present invention is directed to a nonlinear controller for nonlinear wave energy converters (WECs). As an example of the invention, a nonlinear dynamic model is developed for a geometrically right-circular cylinder WEC design for the heave-only motion, or a single degree-of-freedom (DOF). The linear stiffness term is replaced by a nonlinear cubic hardening spring term to demonstrate the performance of a nonlinear WEC as compared to an optimized linear WEC. By exploiting the nonlinear physics in the nonlinear controller, equivalent power and energy capture, as well as simplified operational performance is observed for the nonlinear cubic hardening spring controller when compared to an optimized linear controller.
Wilson, David G.↗