Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

A stochastic constrained optimization technique and its application to detector array processing.

A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.

Winkler, L. P.↗
DOE OSTI2023

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗
DOE OSTI2026

Closed-Loop Wind Turbine Controllers for Active Wake Mixing Strategies

Wind turbine active wake mixing (AWM) is an exciting new field of research where dynamic actuation, usually on the blade pitch angles, is used to increase wind farm-wide power production. From a controls perspective, the current state-of-the-art AWM strategies are very simple: a dynamic, usually periodic, reference signal is prescribed to actuators in an open-loop (OL) fashion. The actuation is then presumed to have a certain desired effect on the system, i.e., the wind turbine and the flow it affects. However, this system is highly nonlinear and experiences disturbances in the form of wind variations that are not known a priori. As a result, the OL approach might not yield optimal results. In this article, a novel approach is presented, which closes the loop on AWM controllers. A feedback loop is implemented, which uses measurements of the individual blade bending moments that are widely available on modern wind turbines to determine the individual blade pitch angles. A proof of concept of this implementation is presented in this article, and a thorough comparison with the OL method is executed using high-fidelity flow simulations. These simulations show that the novel closed-loop controller does not substantially increase wake mixing but achieves similar performance as the OL controller while reducing fatigue loads on the controlled turbine.

17 WIND ENERGY↗
DOE OSTI2025

Multi-Agent Hierarchical Deep Reinforcement Learning for HVAC Control With Flexible DERs

As electricity consumption in commercial and residential buildings continues to rise, reducing energy costs presents an increasing challenge. Heating, ventilating, and air-conditioning (HVAC) systems, which typically account for 40%-50% of a building's energy use, are prime targets for energy savings. Intelligent control of HVAC temperature through the exploitation of HVAC load flexibility brings significant potential to reduce energy consumption and electricity expenses. The nonlinear models of HVAC systems challenge traditional control methods, while the uncertainty introduced by HVAC load flexibility complicates distributed energy resource (DER) management using conventional optimal dispatch techniques. In response to these challenges, we propose a hierarchical multi-agent deep reinforcement learning (DRL) approach. The lower-level agents focus on balancing comfort and energy conservation, while the upper-level DRL agents optimize the use of DERs to reduce peak demand based on the control outcomes of the HVAC by the lower-level agents. Here, in the upper-level agents, we incorporate a multi-agent structure based on ensemble learning, which acts based on historical and current data without relying on precise load forecasting to address the delayed rewarding issue in DRL. This allows for the effective reduction of energy costs. The proposed method is tested using a real-world microgrid comprising 413 buildings in Southern California, and the results demonstrate that our approach can significantly reduce overall electricity bills while ensuring the comfort of consumers and residents.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Optimization and stabilization of Fermilab Booster using hybrid Bayesian/RL framework

PIPII project will raise Fermilab Booster intensity and ramp rate. Beam losses will limit average power and are hard to simulate. Presently, Booster uses operator-guided empirical tuning. This task is challenging due to high dimensionality, multiple objectives, critical safety constraints, and drifts. We developed a synergistic suite of Bayesian optimization (BO) and reinforcement learning (RL) tools to optimize and stabilize beam losses. First, active learning was used to build a rough model. Data was collected parasitically using two novel safety constraint types – nonlinear input space restrictions (based on optics model), and uncertainty constraints (to stop bad steps/beam aborts). We then applied online multi-objective BO with scalarized objectives and fitting to improve/rebalance losses, increasing safety margins by 25%. Using BO model as a safety veto, we tried several on/off-policy RL agents for long term stabilization; SAC had best performance. We found that adding contextual (state) information further improved performance, eventually integrating key knobs like linac phase and temperature into the parameter space. Long term testing is ongoing to enable operational use.

Kuklev, Nikita [Fermilab]↗
NASA NTRS1981

On-line optimization of aircraft altitude and flight path angle dynamics

The optimization of aircraft altitude and flight path angle dynamics is addressed in a form suitable for on-line computation and control. The approach here is a direct extension of the work reported by Calise (1979), where singular perturbation methods were used to optimize position, energy and heading dynamics; it thus represents an optimal control solution that models all of the primary trajectory related dynamics. It is pointed out that the resulting algorithm can be regarded as a nonlinear feedback control law. The minimum time intercept of a fixed terminal point is used in setting the framework in which the analytical results are developed. The main theoretical result is that the dynamics, while not completely separable, can be approximated by singular perturbation methods when the control model includes relative position dynamics.

Calise, A. J.↗
NASA NTRS1991

Range optimization for a supersonic aircraft

Range optimal trajectories for an aircraft flying in the vertical plane are obtained from Pontryagin's Minimum Principle. Control variables are load factor n which appears nonlinearly in the equations of motion and throttle setting eta, which appears only linearly. Both controls are subject to fixed bounds, namely eta between values of 0 and 1 and absolute value of n not greater than n(max). Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. For fixed flight time, fixed initial coordinates, and partially fixed final coordinates, the effect of the load factor limit absolute value of n not greater than n(max) is studied. Upon varying n(max), six different switching structures are obtained. All trajectories involve singular control along arcs with active dynamic pressure limit.

Seywald, Hans↗
NASA NTRS2012

Real-Time Frequency Response Estimation Using Joined-Wing SensorCraft Aeroelastic Wind-Tunnel Data

A new method is presented for estimating frequency responses and their uncertainties from wind-tunnel data in real time. The method uses orthogonal phase-optimized multi- sine excitation inputs and a recursive Fourier transform with a least-squares estimator. The method was first demonstrated with an F-16 nonlinear flight simulation and results showed that accurate short period frequency responses were obtained within 10 seconds. The method was then applied to wind-tunnel data from a previous aeroelastic test of the Joined- Wing SensorCraft. Frequency responses describing bending strains from simultaneous control surface excitations were estimated in a time-efficient manner.

Grauer, Jared A↗
NASA NTRSDate not supplied

Feasibility Study of a Multi-Tilt-Rotor Aircraft as the Artemis Lunar Training Vehicle

The Lunar Landing Research Vehicles (LLRVs) and the Lunar Landing Training Vehicles (LLTVs) provided astronauts of the Apollo program with essential experience and confidence required to complete the missions, and contributed to six successful manned landings on the moon. The primary challenge in terrestrial training was being able to replicate the ratio of tilt angle to linear acceleration that a pilot would experience in lunar gravity. Presently, as the Artemis program seeks to return humans to the Moon by 2025, engineers are evaluating suitable platforms to serve as an In-Flight Trainer (IFT) or Artemis Lunar Training Vehicle (ALTV) for astronauts training in the task of manual landing. The program is investigating the viability of current technology in the field of electric vertical takeoff and landing (eVTOL) vehicles and is evaluating using a multi-tilt-rotor aircraft platform as a candidate for a preliminary ALTV. The tilt-rotor capability enables the vehicle attitude to be decoupled from its flight path, which is a crucial requirement in realistically simulating lunar gravity on Earth. Other key considerations include compensating for a lack of aerodynamic forces while flying through the atmosphere of Earth, as well as the ability to simulate the dynamics of multiple different lander designs for the Human Landing System (HLS) program. This paper details the feasibility study and presents a preliminary flight control architecture for an IFT based on a notional multi-tilt-rotor platform. The model-following control law, based on nonlinear dynamic inversion (NDI), removes the need for gain scheduling. The inner-loop dynamic control allocation strategy consists of a static portion that is optimized offline for trim while compensating for the difference in gravity and a dynamic portion that is computed in real time. The reference model consists of the full closed-loop dynamics of a generic HLS design. The modularity of the flight control architecture enables evaluation of multiple HLS concepts with minimal modifications to the control law. Simulation results of the multi-tilt-rotor configuration following the final portion of the Apollo 11 descent trajectory are shown.

Jing Pei↗
NASA NTRS1973

Maximum likelihood identification and optimal input design for identifying aircraft stability and control derivatives

A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.

Stepner, D. E.↗
NASA NTRS2003

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.↗
NASA NTRS1996

Optical amplifiers for coherent lidar

We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.

Fork, Richard↗
DOE OSTI2022

Development of a Control Co-Design Modeling Tool for Marine Hydrokinetic Turbines: Preprint

This report describes the ongoing and planned development of the software package CT-Opt (Current/Tidal Optimization), a control co-design modeling tool for marine hydrokinetic turbines. The commercialization of these turbines has faced significant challenges due to the complex, multidisciplinary nature of their design and the extreme environmental conditions of their operation. This project aims to create a modeling tool that will enable the efficient design of robust, cost-competitive hydrokinetic turbine systems. Rather than using traditional optimization methods, CT-Opt combines multiple models across a range of fidelities to enable coupled optimization of the system design and system controller via a control co-design approach. With this method, the parameters that affect system performance are considered more comprehensively at every stage of the design process. The lowest-fidelity, frequency-domain model called by CT-Opt is RAFT (Response Amplitudes of Floating Turbines), which was originally developed by the National Renewable Energy Laboratory (NREL) to model response amplitudes of floating offshore wind turbines. The highest-fidelity, time-domain model is OpenFAST, which was developed by NREL for land-based and offshore wind turbines. As part of the CT-Opt project, new functionalities will be added to RAFT and OpenFAST to enable the accurate simulation of fixed and floating marine hydrokinetic turbines. In addition to expanding the capabilities of RAFT and OpenFAST, new midfidelity models will be developed. These models will be based on RAFT and OpenFAST and will consist of linearized, state-space models derived from the fully coupled, nonlinear OpenFAST equations and derivative function surrogate models that approximate the nonlinear system behavior. Each model will be coupled with controllers to allow control co-design methods to be applied both within models and across fidelity levels, enabling efficient system optimization.

control co-design↗
DOE OSTI2023

Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security

Cyber-Physical Systems (CPSs) like the power grid are critically important but also increasingly vulnerable; ensuring reliable system operation in the face of disruptions is becoming more and more challenging. Multi-Level Optimization (MLO) is a powerful way to model adversarial interactions, which naturally makes it applicable to studying CPS security. However, MLO typically does not address underlying system dynamics, and incorporating nonlinear dynamics is generally infeasible. In this paper, we show how to combine MLO with the Koopman Operator (KO) to remedy this. The KO maps nonlinear dynamics to a lifted space in which those dynamics are linear, thus making it ideal for use with MLO. Moreover, the structure of the KO also provides convenient ways to incorporate domain knowledge into the data-driven process of learning the KO representation of a given system. Here we then demonstrate the use of MLO-KO on a small example problem taken from the power grid domain, discuss the scalability and computational cost of MLO-KO, and identify future research directions for this work.

42 ENGINEERING↗
DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Tradeoffs in single stage drift step recovery diode generator design

A high-voltage generator of nanosecond pulses utilizing a drift step recovery diode (DSRD) as an opening switch in the compression section is designed to operate at peak voltages of 4 kV and repetition rates of 2 MHz in burst mode at reduced voltages. The generator is used to perform empirical studies on the output metrics of a DSRD generator with a focus on matching the circuit of the reverse current loop parameters and DSRD to the load. The dynamic impedance introduced by nonlinear elements in the DSRD was investigated with respect to the driving circuit by varying the number of DSRDs connected in series. Experimental results indicate that optimization of the driving circuit for the DSRD is key to minimizing losses and achieving optimal pulse compression. Furthermore, the results also indicate trends in DSRD performance as larger storage inductances and longer pumping times are used, limiting the pulse compression capabilities of a single stage DSRD generator.

Electrical properties and parameters↗