Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Quadratic 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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

MAXIMUM LIKELIHOOD ANALYSIS OF SYSTEMATIC ERRORS IN INTERFEROMETRIC OBSERVATIONS OF THE COSMIC MICROWAVE BACKGROUND

We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that does not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r = 0.01 at 28 < l < 384, Gaussian-distributed pointing errors must be controlled to 0. Degree-Sign 7 root mean square for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28 < l < 88 would be changed at {approx}10% level. With the same instrumental configuration, we find that the pointing errors would slightly bias the 2{sigma} upper limit of the tensor-to-scalar ratio r by {approx}10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Embedded Sensors and Controls to Improve Component Performance and Reliability - System Dynamics Modeling and Control System Design

This report documents the current status of the modeling, control design, and embedded control research for the magnetic bearing canned rotor pump being used as a demonstration platform for deeply integrating instrumentation and controls (I&C) into nuclear power plant components. This pump is a highly inter-connected thermo/electro/mechanical system that requires an active control system to operate. Magnetic bearings are inherently unstable system and without active, moment by moment control, the rotor would contact fixed surfaces in the pump causing physical damage. This report details the modeling of the pump rotordynamics, fluid forces, electromagnetic properties of the protective cans, active magnetic bearings, power electronics, and interactions between different dynamical models. The system stability of the unforced and controlled rotor are investigated analytically. Additionally, controllers are designed using proportional derivative (PD) control, proportional integral derivative (PID) control, voltage control, and linear quadratic regulator (LQR) control. Finally, a design optimization problem that joins the electrical, mechanical, magnetic, and control system design into one problem to balance the opposing needs of various design criteria using the embedded system approach is presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A robust approach to Gaussian process implementation

Abstract. Gaussian process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset has a large number of observations. To address this challenge, we introduce a scalable GP algorithm, termed MuyGPs, which incorporates nearest-neighbor and leave-one-out cross-validation during training. This approach enables the evaluation of large spatial datasets with state-of-the-art accuracy and speed in certain spatial problems. Despite these advantages, conventional quadratic loss functions used in the MuyGPs optimization, such as root mean squared error (RMSE), are highly influenced by outliers. We explore the behavior of MuyGPs in cases involving outlying observations and, subsequently, develop a robust approach to handle and mitigate their impact. Specifically, we introduce a novel leave-one-out loss function based on the pseudo-Huber function (LOOPH) that effectively accounts for outliers in large spatial datasets within the MuyGPs framework. Our simulation study shows that the LOOPH loss method maintains accuracy despite outlying observations, establishing MuyGPs as a powerful tool for mitigating unusual observation impacts in the large data regime. In the analysis of US ozone data, MuyGPs provides accurate predictions and uncertainty quantification, demonstrating its utility in managing data anomalies. Through these efforts, we advance the understanding of GP regression in spatial contexts.

Mukangango, Juliette↗
NASA NTRS1989

An algorithm for the solution of dynamic linear programs

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

Psiaki, Mark L.↗
NASA NTRS1993

Adjoint methods for aerodynamic wing design

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

Grossman, Bernard↗
NASA NTRS2025

Robust Trajectory Optimization for NRHO Rendezvous Using SPICE Kernel Relative Motion

In this paper, robust optimization is performed on trajectory correction maneuvers during the lunar lander return phase of an Artemis mission, treating the trajectory from one hour after low lunar orbit departure to arrival in the vicinity of the lunar Gateway as a relative motion problem. To enable rapid stochastic optimization techniques requiring many candidate trajectories, SPICE kernel relative motion as implemented by the Quadratic Interpolated State Transition (QIST) system is used as the underlying dynamics propagation. The optimization is performed with a genetic optimizer using linear covariance (LinCov) software in a simplified operational context, taking into account the availability of navigation sensors with varying measurement models, ranges, and accuracies. No numerical integration is used, since the relative motion around Gateway is fully characterized with the a priori computation of the QIST coefficients. Maneuver placements are computed to optimize the minimum 3σ delta-v of the trajectory, the position dispersion at a target point, and a convex combination of these two metrics. An order of magnitude runtime improvement is provided over legacy methods with less than 10% error introduced. All QIST results are shown to be in-family with legacy methods. The tradespace for optimal delta-v design is found to range from 77.0 to 93.9 m/s, while the range of optimal dispersion is between 1.4 and 11.7 km.

Relative Motion↗
DOE OSTI2016

SU-G-TeP3-01: A New Approach for Calculating Variable Relative Biological Effectiveness in IMPT Optimization

Purpose: To investigate the impact of a new approach for calculating relative biological effectiveness (RBE) in intensity-modulated proton therapy (IMPT) optimization on RBE-weighted dose distributions. This approach includes the nonlinear RBE for the high linear energy transfer (LET) region, which was revealed by recent experiments at our institution. In addition, this approach utilizes RBE data as a function of LET without using dose-averaged LET in calculating RBE values. Methods: We used a two-piece function for calculating RBE from LET. Within the Bragg peak, RBE is linearly correlated to LET. Beyond the Bragg peak, we use a nonlinear (quadratic) RBE function of LET based on our experimental. The IMPT optimization was devised to incorporate variable RBE by maximizing biological effect (based on the Linear Quadratic model) in tumor and minimizing biological effect in normal tissues. Three glioblastoma patients were retrospectively selected from our institution in this study. For each patient, three optimized IMPT plans were created based on three RBE resolutions, i.e., fixed RBE of 1.1 (RBE-1.1), variable RBE based on linear RBE and LET relationship (RBE-L), and variable RBE based on linear and quadratic relationship (RBE-LQ). The RBE weighted dose distributions of each optimized plan were evaluated in terms of different RBE values, i.e., RBE-1.1, RBE-L and RBE-LQ. Results: The RBE weighted doses recalculated from RBE-1.1 based optimized plans demonstrated an increasing pattern from using RBE-1.1, RBE-L to RBE-LQ consistently for all three patients. The variable RBE (RBE-L and RBE-LQ) weighted dose distributions recalculated from RBE-L and RBE-LQ based optimization were more homogenous within the targets and better spared in the critical structures than the ones recalculated from RBE-1.1 based optimization. Conclusion: We implemented a new approach for RBE calculation and optimization and demonstrated potential benefits of improving tumor coverage and normal sparing in IMPT planning.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1991

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Chang, Bor-Chin↗
NASA NTRS1993

On convexity of H-infinity Riccati solutions and its applications

The celebrated two-Riccati-equation solution to a standard H-infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H-infinity controllers if the optimal H-infinity norm or gamma, an upper bound of a suboptimal H-infinity norm, is given. In this note, some properties of these H-infinity Riccati solutions are revealed. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H-infinity norm.

Li, X. P.↗
DOE OSTI2018

Design of a Robust Digital Control System for the Rectification Column Used in the Production of Divinyl

A complex optimization criterion that takes into account the integral quadratic error and the stability margin of a robust digital control system for the rectification column used for the butylene-divinyl fraction is proposed. The influence of the weight coefficient, taking into account the ratio of the performance and stability indicators, on the dynamic characteristics of the system is investigated. High system performance and system stability indices over a sufficiently broad range of variation of the parameters of the rectification column are achieved through the use of the proposed optimization criterion and a stability estimation algorithm in the synthesis of a robust digital control system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2000

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Joshi, Suresh M.↗
DOE OSTI2016

Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r {sub s} ( z {sub d} ). Among the considered models the best value of χ{sup 2} is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Multiplier-continuation algorthms for constrained optimization

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming.

Lundberg, Bruce N.↗
DOE OSTI2018

Microgrid to enable optimal distributed energy retail and end-user demand response

In the face of unprecedented challenges in environmental sustainability and grid resilience, there is an increasingly held consensus regarding the adoption of distributed and renewable energy resources such as microgrids (MGs), and the utilization of flexible electric loads by demand response (DR) to potentially drive a necessary paradigm shift in energy production and consumption patterns. However, the potential value of distributed generation and demand flexibility has not yet been fully realized in the operation of MGs. This study investigates the pricing and operation strategy with DR for a MG retailer in an integrated energy system (IES). Based on co-optimizing retail rates and MG dispatch formulated as a mixed integer quadratic programming (MIQP) problem, our model devises a dynamic pricing scheme that reflects the cost of generation and promotes DR, in tandem with an optimal dispatch plan that exploits spark spread and facilitates the integration of renewables, resulting in improved retailer profits and system stability. Main issues like integrated energy coupling and customer bill reduction are addressed during pricing to ensure rates competitiveness and customer protection. By evaluating on real datasets, the system is demonstrated to optimally coordinate storage, renewables, and combined heat and power (CHP), reduce carbon dioxide emission while maintaining profits, and effectively alleviate the PV curtailment problem. Finally, the model can be used by retailers and MG operators to optimize their operations, as well as regulators to design new utility rates in support of the ongoing transformation of energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Evaluating the effects of real power losses in optimal power flow based storage integration

This study proposes a DC optimal power flow (DCOPF) with losses formulation (the `-DCOPF+S problem) and uses it to investigate the role of real power losses in OPF based grid-scale storage integration. We derive the `- DCOPF+S problem by augmenting a standard DCOPF with storage (DCOPF+S) problem to include quadratic real power loss approximations. This procedure leads to a multi-period nonconvex quadratically constrained quadratic program, which we prove can be solved to optimality using either a semidefinite or second order cone relaxation. Our approach has some important benefits over existing models. It is more computationally tractable than ACOPF with storage (ACOPF+S) formulations and the provably exact convex relaxations guarantee that an optimal solution can be attained for a feasible problem. Adding loss approximations to a DCOPF+S model leads to a more accurate representation of locational marginal prices, which have been shown to be critical to determining optimal storage dispatch and siting in prior ACOPF+S based studies. Case studies demonstrate the improved accuracy of the `-DCOPF+S model over a DCOPF+S model and the computational advantages over an ACOPF+S formulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2014

Finite Energy and Bounded Attacks on Control System Sensor Signals

Control system networks are increasingly being connected to enterprise level networks. These connections leave critical industrial controls systems vulnerable to cyber-attacks. Most of the effort in protecting these cyber-physical systems (CPS) has been in securing the networks using information security techniques and protection and reliability concerns at the control system level against random hardware and software failures. However, besides these failures the inability of information security techniques to protect against all intrusions means that the control system must be resilient to various signal attacks for which new analysis and detection methods need to be developed. In this paper, sensor signal attacks are analyzed for observer-based controlled systems. The threat surface for sensor signal attacks is subdivided into denial of service, finite energy, and bounded attacks. In particular, the error signals between states of attack free systems and systems subject to these attacks are quantified. Optimal sensor and actuator signal attacks for the finite and infinite horizon linear quadratic (LQ) control in terms of maximizing the corresponding cost functions are computed. The closed-loop system under optimal signal attacks are provided. Illustrative numerical examples are provided together with an application to a power network with distributed LQ controllers.

Cyber-physical↗