Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear constraints”

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 91 records · Page 5

Constrained optimization for image restoration using nonlinear programming

The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.

Yeh, C.-L.↗

Optimum constrained image restoration filters

The research described centered on development of an optimum image restoration filter (IRF) minimizing the radius of gyration of the corrected or composite system point-spread function (P-SF) subject to contraints, and reducing 2-dimensional spatial smearing or blurring of an image. The constraints are imposed on the radius of gyration of the IRF P-SF, the total restored image noise power, and the shape of the composite system frequency spectrum. The image degradation corresponds to mapping many points from the original image into a single resolution element. The P-SF is obtained as solution to a set of simultaneous differential equations obeying nonlinear integral constraints. Truncation errors due to edge effects are controlled by constraining the radius of gyration of the IRF P-SF. An iterative technique suppresses sidelobes of the composite system P-SF.

Riemer, T. E.↗

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program.

Khot, N. S.↗

Riemannian Optimization Applied to AC Optimal Power Flow

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. This is done by using the Julia programming language and the Julia packages PowerModels.jl and Manopt.jl.

AC optimal power flow↗

Vibro-impact analysis and characterization of pipeline conveying fluids with multi-segmented motion-limiting constraints

Previous studies of the cantilevered pipeline conveying fluid system have included motion-limiting constraints in the form of trilinear springs. While this is desirable in experimental scenarios, it may not be representative of real-world applications. Therefore, here, this study focuses on multi-segmented motion-limiting constraints. As this type of motion-limiting constraint has not been investigated with a cantilevered pipeline system, a wide variety of outer and inner constraint stiffness and constraint gap sizes are investigated in this study to gain a comprehensive understanding of how the multi-segmented constraints affect the dynamics of the cantilevered pipeline. In this effort, bifurcation diagrams, phase portraits, Poincare maps, time histories, and power spectra are used to investigate the dynamics of the system, and the fluid flow speeds where dynamic characteristics are considered. In general, it is found that critical flow speeds like when the pipe sticks in the constraints are reduced as the constraint stiffnesses are increased. Additionally, the sticking flow speed occurred at lower flow speeds as the gap sizes of the inner and outer constraints decrease, and a larger constraint offset results in a smaller inner gap size leading to critical behaviors occurring at earlier flow speeds.

97 MATHEMATICS AND COMPUTING↗

Hybrid model predictive control techniques for safety factor profile and stored energy regulation while incorporating NBI constraints

Abstract A novel hybrid Model Predictive Control (MPC) algorithm has been designed for simultaneous safety factor ( q ) profile and stored energy ( w ) control while incorporating the pulse-width-modulation constraints associated with the neutral beam injection (NBI) system. Regulation of the q -profile has been extensively shown to be a key factor for improved confinement as well as non-inductive sustainment of the plasma current. Simultaneous control of w is necessary to prevent the triggering of pressure-driven magnetohydrodynamic instabilities as the controller shapes the q profile. Conventional MPC schemes proposed for q -profile control have considered the NBI powers as continuous-time signals, ignoring the discrete-time nature of these actuators and leading in some cases to performance loss. The hybrid MPC scheme in this work has the capability of incorporating the discrete-time actuator dynamics as additional constraints. In nonlinear simulations, the proposed hybrid MPC scheme demonstrates improved q -profile+ w control performance for NSTX-U operating scenarios.

Physics↗

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗

Numerical Codes for the DESC-LSST Analysis Pipeline: Core Cosmology Library Standard Modules and Beyond wCDM Modules (Final Technical Report)

The overall objective of the project is to investigate and develop specific software modules and analysis components for the software pipeline of LSST Dark Energy Science Collaboration (DESC). Following the key projects of DESC Science Roadmap (SRM), we will write and test computer codes for the Core Cosmology Library (CCL) in order to complete its modules, functionalities, and interface to work with the analysis pipelines from the five science probes of DESC (parts of SRM deliverables CX4.2TJP, CX6.2CS). We will also code modules for CCL to test models beyond w-Cold-Dark-Matter (wCDM) and modification to gravity (MG). Interfaces for MG models will also be developed for the TJPCOSMO software which is the main pipeline of the Theory and Joint Probe (TJP) working group (deliverable TJP2.3). In order to use the full power of LSST data to constrain MG models, we will also work on constraints from nonlinear regime by running and analyzing MG N-Body simulations using a Parameterized-Post-Friedmann framework into the Gadget-2 simulation package (deliverable TJP2.2). Preliminary results for the simulations were obtained in the past. In collaboration with other DESC groups, we plan to make these simulations feedable to cosmic emulators that are practical for likelihood analyzes (deliverable TJP2.2, parts of CX6.2CS). We will also modify and integrate our current codes for consistency tests between data sets and probes into the pipeline (parts of deliverables CX8.2TJP, TJP2.3). We understand that other groups will contribute to some of these objectives but our team will focus and collaborate with others on the particular part of testing MG and models beyond wCDM and refine the DESC pipeline for this purpose. PI has been coordinating his work with the TJP and CS working groups and the DESC management team. PI is a full member of DESC since June 2013. He and his students have been contributing to LSST-DESC activities and work including TJP telecons, collaboration meetings, hack-weeks, and workshops. PI chaired or co-chaired sessions at collaboration meetings and hack-weeks about testing gravity and models beyond wCDM using LSST. He is coordinating the TJP2 projects for testing models beyond wCDM including the writing of DESC-research-note, development of code for pipeline, and N-Body simulations for MG and beyond wCDM models testable with LSST analyses. As stressed in the DESC white paper, SRM, and P5 report, one of the important questions in understanding cosmic acceleration and dark energy is to be able to distinguish whether the acceleration is due to a dark energy component in the universe or a modification to gravity. Answering these questions will have a significant impact on the question of cosmic acceleration and dark energy. The methods that we will use include analytical work, numerical code, and N-Body simulations. A first approach that that we will use consists of using growth rate parameters that enter the perturbed dynamics equations. These parameters take distinctive values for distinct gravity theories and have potential to distinguish between Dark Energy and Modified Gravity. The second method is to look for inconsistencies in Dark Energy parameter spaces using specific combinations of cosmological data sets. Our investigation addresses the Dark Energy problem that is relevant to the mission of the HEP program to understand how our universe works at its most fundamental level. It will allow us to make progress on the HEP mission to explore the nature of Dark Energy and the basic nature of space and time using future surveys such as LSST. The investigation supports the DOE HEP program Cosmic Frontier as it will contribute to the study and understanding of dark energy and fundamental properties of the universe. The investigation contributes directly to LSST-DESC key projects and their deliverables as described in the Science Road-map document to build analysis pipeline and to test dark energy and beyond wCDM models using LSST.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Optimization of system reliability by the sequential unconstrained minimization technique

The reliability of a complex system was optimized by a new approach for implementing the sequential unconstrained minimization technique (SUMT) with the aid of Hooke and Jeeves pattern search and heuristic programming. Two optimization problems were considered. In the first, the system reliability was maximized subject to a nonlinear weight constraint. In the second, the weight of the system was minimized without violating the requirements of the minimal system reliability and the minimum reliability for each component. The sensitivities of the system reliability and that of the system weight to the reliability of each component were determined under optimal conditions.

Hwang, C. L.↗

Optimization of multi-constrained structures based on optimality criteria

A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Rizzi, P.↗

Surface tension-driven convections

The study of time-dependent flows generated by surface-tension gradients in thin liquid layers is reported. Numerical techniques for dealing with the complete float-zone process were investigated. In particular, finite element methods with fast iterative procedures, using multipoint constraints and nonlinear optimization were examined.

Ostrach, S.↗

Programming the gradient projection algorithm

The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.

Hargrove, A.↗

An efficient multilevel optimization method for engineering design

An efficient multilevel deisgn optimization technique is presented. The proposed method is based on the concept of providing linearized information between the system level and subsystem level optimization tasks. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to use. The disadvantage is that the coupling between subsystems is not dealt with in a precise mathematical manner.

Vanderplaats, G. N.↗

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Roithmayr, Carlos M.↗

Adaptive nonlinear optimization of the signal-to-noise ratio of an array subject to a constraint.

Investigation of a stochastic projected gradient algorithm which can be used to find a constrained optimum point for a concave or convex objective function subject to nonlinear constraints. When the constraint consists of only one linear equation, convergence to the constrained optimum value is proven, and bounds are obtained for the rate of convergence of the algorithm to the constrained optimum value. This algorithm is then applied to the nonlinear problem of automatically making an array of detectors form a beam in a desired direction in space when unknown interfering noise is present so as to maximize the signal-to-noise ratio subject to a constraint on the supergain ratio.

Winkler, L. P.↗

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

97 MATHEMATICS AND COMPUTING↗

Structural/control system optimization with variable actuator masses

A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. Nonstructural lumped masses and control system design variables as well as structural sizing variables are all treated equally as independent design variables in the optimization process. Structural and control design variable linking schemes are used in order to avoid a prohibitively large increase in the total number of independent design variables. When actuator masses are treated as nonstructural lumped mass design variables, special consideration is given to the relation between the transient peak responses and the required actuator masses which is formulated as a behavior constraint form. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as design variable linkings, temporary constraint deletion and first order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples which involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, peak actuator forces, and relations between the peak responses and the actuator masses) are effectively solved by using the method presented.

Jin, Ik M.↗

Lyapunov-based nonlinear control of nonautonomous systems with individual input constraints

A control algorithm that can locally stabilize a specific class of multi-input multi-output nonautonomous nonlinear dynamical systems while satisfying individual input constraints is developed. The proposed Lyapunov-based state-feedback control law inherently accounts for the actuator amplitude saturation limits without the need for computationally expensive real-time optimization techniques. In addition to the control law, a formal definition for the local “controllable region” within which the controller can asymptotically drive the system states to the origin and satisfy the input saturation limits is also presented. The nonautonomous nature of the system dynamics implies that the “controllable region” continuously evolves with time. Therefore, a sufficient condition to maintain the system states within the “controllable region” is proposed in this work to make practical implementation feasible. The effectiveness of the controller is tested for a specific control problem arising in tokamaks, which are toroidal devices that use strong magnetic fields to confine a plasma (hot ionized gas). Here, the primary emphasis of tokamak research is to regulate the plasma properties around predetermined values to achieve stable plasma confinement. Nonlinear simulations show that the proposed controller can achieve the desired plasma control objectives in a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗