Microgravity vibration isolation: Optimal preview and feedback control

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Knospe, C. R.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.

1992-01-01

In order to achieve adequate low-frequency vibration isolation for certain space experiments an active control is needed, due to inherent passive-isolator limitations. Proposed here are five possible state-space models for a one-dimensional vibration isolation system with a quadratic performance index. The five models are subsets of a general set of nonhomogeneous state space equations which includes disturbance terms. An optimal control is determined, using a differential equations approach, for this class of problems. This control is expressed in terms of constant, Linear Quadratic Regulator (LQR) feedback gains and constant feedforward (preview) gains. The gains can be easily determined numerically. They result in a robust controller and offers substantial improvements over a control that uses standard LQR feedback alone.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

NASA Astrophysics Data System (ADS)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

An optimal consumption and investment problem with quadratic utility and negative wealth constraints.

PubMed

Roh, Kum-Hwan; Kim, Ji Yeoun; Shin, Yong Hyun

2017-01-01

In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

NASA Astrophysics Data System (ADS)

Kendrick, Rachel

Intensity-modulated radiation therapy is used to better conform the radiation dose to the target, which includes avoiding healthy tissue. Planning programs employ optimization methods to search for the best fluence of each photon beam, and therefore to create the best treatment plan. The Computational Environment for Radiotherapy Research (CERR), a program written in MATLAB, was used to examine some commonly-used algorithms for one 5-beam plan. Algorithms include the genetic algorithm, quadratic programming, pattern search, constrained nonlinear optimization, simulated annealing, the optimization method used in Varian EclipseTM, and some hybrids of these. Quadratic programing, simulated annealing, and a quadratic/simulated annealing hybrid were also separately compared using different prescription doses. The results of each dose-volume histogram as well as the visual dose color wash were used to compare the plans. CERR's built-in quadratic programming provided the best overall plan, but avoidance of the organ-at-risk was rivaled by other programs. Hybrids of quadratic programming with some of these algorithms seems to suggest the possibility of better planning programs, as shown by the improved quadratic/simulated annealing plan when compared to the simulated annealing algorithm alone. Further experimentation will be done to improve cost functions and computational time.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Automation of reverse engineering process in aircraft modeling and related optimization problems

NASA Technical Reports Server (NTRS)

Li, W.; Swetits, J.

1994-01-01

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamzam, Ahmed, S.; Zhaoy, Changhong; Dall'Anesey, Emiliano

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated usingmore » two unbalanced multiphase distribution feeders with both wye and delta connections.« less

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Electrochemical oxidation of ampicillin antibiotic at boron-doped diamond electrodes and process optimization using response surface methodology.

PubMed

Körbahti, Bahadır K; Taşyürek, Selin

2015-03-01

Electrochemical oxidation and process optimization of ampicillin antibiotic at boron-doped diamond electrodes (BDD) were investigated in a batch electrochemical reactor. The influence of operating parameters, such as ampicillin concentration, electrolyte concentration, current density, and reaction temperature, on ampicillin removal, COD removal, and energy consumption was analyzed in order to optimize the electrochemical oxidation process under specified cost-driven constraints using response surface methodology. Quadratic models for the responses satisfied the assumptions of the analysis of variance well according to normal probability, studentized residuals, and outlier t residual plots. Residual plots followed a normal distribution, and outlier t values indicated that the approximations of the fitted models to the quadratic response surfaces were very good. Optimum operating conditions were determined at 618 mg/L ampicillin concentration, 3.6 g/L electrolyte concentration, 13.4 mA/cm(2) current density, and 36 °C reaction temperature. Under response surface optimized conditions, ampicillin removal, COD removal, and energy consumption were obtained as 97.1 %, 92.5 %, and 71.7 kWh/kg CODr, respectively.

A reduced successive quadratic programming strategy for errors-in-variables estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

Optimization of Culture Conditions for Enhanced Growth, Lipid and Docosahexaenoic Acid (DHA) Production of Aurantiochytrium SW1 by Response Surface Methodology.

PubMed

Nazir, Yusuf; Shuib, Shuwahida; Kalil, Mohd Sahaid; Song, Yuanda; Hamid, Aidil Abdul

2018-06-11

In this study, optimization of growth, lipid and DHA production of Aurantiochytrium SW1 was carried out using response surface methodology (RSM) in optimizing initial fructose concentration, agitation speed and monosodium glutamate (MSG) concentration. Central composite design was applied as the experimental design and analysis of variance (ANOVA) was used to analyze the data. ANOVA analysis revealed that the process which adequately represented by quadratic model was significant (p < 0.0001) for all the response. All the three factors were significant (p < 0.005) in influencing the biomass and lipid data while only two factors (agitation speed and MSG) gave significant effect on DHA production (p < 0.005). The estimated optimal conditions for enhanced growth, lipid and DHA production were 70 g/L fructose, 250 rpm agitation speed and 10 g/L MSG. Consequently, the quadratic model was validated by applying the estimated optimum conditions, which confirmed the model validity where 19.0 g/L biomass, 9.13 g/L lipid and 4.75 g/L of DHA were produced. The growth, lipid and DHA were 28, 36 and 35% respectively higher than that produced in the original medium prior to optimization.

Influence of cellulose derivative and ethylene glycol on optimization of lornoxicam transdermal formulation.

PubMed

Shahzad, Yasser; Khan, Qalandar; Hussain, Talib; Shah, Syed Nisar Hussain

2013-10-01

Lornoxicam containing topically applied lotions were formulated and optimized with the aim to deliver it transdermally. The formulated lotions were evaluated for pH, viscosity and in vitro permeation studies through silicone membrane using Franz diffusion cells. Data were fitted to linear, quadratic and cubic models and best fit model was selected to investigate the influence of variables, namely hydroxypropyl methylcellulose (HPMC) and ethylene glycol (EG) on permeation of lornoxicam from topically applied lotion formulations. The best fit quadratic model revealed that low level of HPMC and intermediate level of EG in the formulation was optimum for enhancing the drug flux across silicone membrane. FT-IR analysis confirmed absence of drug-polymer interactions. Selected optimized lotion formulation was then subjected to accelerated stability testing, sensatory perception testing and in vitro permeation across rabbit skin. The drug flux from the optimized lotion across rabbit skin was significantly better that that from the control formulation. Furthermore, sensatory perception test rated a higher acceptability while lotion was stable over stability testing period. Therefore, use of Box-Wilson statistical design successfully elaborated the influence of formulation variables on permeation of lornoxicam form topical formulations, thus, helped in optimization of the lotion formulation. Copyright © 2013 Elsevier B.V. All rights reserved.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

NASA Astrophysics Data System (ADS)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Advanced Energy Storage Management in Distribution Network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Guodong; Ceylan, Oguzhan; Xiao, Bailu

2016-01-01

With increasing penetration of distributed generation (DG) in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. In this paper, an iterative mixed integer quadratic constrained quadratic programming model to optimize the operation of a three phase unbalanced distribution system with high penetration of Photovoltaic (PV) panels, DG and energy storage (ES) is developed. The proposed model minimizes not only the operating cost, including fuel cost and purchasing cost, but also voltage deviations and power loss. The optimization model is based on the linearized sensitivity coefficients between state variables (e.g., node voltages) andmore » control variables (e.g., real and reactive power injections of DG and ES). To avoid slow convergence when close to the optimum, a golden search method is introduced to control the step size and accelerate the convergence. The proposed algorithm is demonstrated on modified IEEE 13 nodes test feeders with multiple PV panels, DG and ES. Numerical simulation results validate the proposed algorithm. Various scenarios of system configuration are studied and some critical findings are concluded.« less

Analysis of explicit model predictive control for path-following control

PubMed Central

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

Analysis of explicit model predictive control for path-following control.

PubMed

Lee, Junho; Chang, Hyuk-Jun

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

Quantum optimization for training support vector machines.

PubMed

Anguita, Davide; Ridella, Sandro; Rivieccio, Fabio; Zunino, Rodolfo

2003-01-01

Refined concepts, such as Rademacher estimates of model complexity and nonlinear criteria for weighting empirical classification errors, represent recent and promising approaches to characterize the generalization ability of Support Vector Machines (SVMs). The advantages of those techniques lie in both improving the SVM representation ability and yielding tighter generalization bounds. On the other hand, they often make Quadratic-Programming algorithms no longer applicable, and SVM training cannot benefit from efficient, specialized optimization techniques. The paper considers the application of Quantum Computing to solve the problem of effective SVM training, especially in the case of digital implementations. The presented research compares the behavioral aspects of conventional and enhanced SVMs; experiments in both a synthetic and real-world problems support the theoretical analysis. At the same time, the related differences between Quadratic-Programming and Quantum-based optimization techniques are considered.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

Neural Meta-Memes Framework for Combinatorial Optimization

NASA Astrophysics Data System (ADS)

Song, Li Qin; Lim, Meng Hiot; Ong, Yew Soon

In this paper, we present a Neural Meta-Memes Framework (NMMF) for combinatorial optimization. NMMF is a framework which models basic optimization algorithms as memes and manages them dynamically when solving combinatorial problems. NMMF encompasses neural networks which serve as the overall planner/coordinator to balance the workload between memes. We show the efficacy of the proposed NMMF through empirical study on a class of combinatorial problem, the quadratic assignment problem (QAP).

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

PubMed

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example for an extreme concave case. Quadratic programming is an alternative approach for inverse planning which generates clinically satisfying plans in comparison to the clinical system and constitutes an efficient optimization process characterized by uniqueness and reproducibility of the solution.

Linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1988-01-01

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

A tight upper bound for quadratic knapsack problems in grid-based wind farm layout optimization

NASA Astrophysics Data System (ADS)

Quan, Ning; Kim, Harrison M.

2018-03-01

The 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Linear quadratic regulators with eigenvalue placement in a horizontal strip

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1987-01-01

A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.

Optimization of Fish Protection System to Increase Technosphere Safety

NASA Astrophysics Data System (ADS)

Khetsuriani, E. D.; Fesenko, L. N.; Larin, D. S.

2017-11-01

The article is concerned with field study data. Drawing upon prior information and considering structural features of fish protection devices, we decided to conduct experimental research while changing three parameters: process pressure PCT, stream velocity Vp and washer nozzle inclination angle αc. The variability intervals of examined factors are shown in the Table 1. The conicity angle was assumed as a constant one. The box design B3 was chosen as a baseline being close to D-optimal designs in its statistical characteristics. The number of device rotations and its fish fry protection efficiency were accepted as the output functions of optimization. The numerical values of regression coefficients of quadratic equations describing the behavior of optimization functions Y1 and Y2 and their formulaic errors were calculated upon the test results in accordance with the planning matrix. The adequacy or inadequacy of the obtained quadratic regression model is judged via checking the condition whether Fexp ≤ Ftheor.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

A trust region approach with multivariate Padé model for optimal circuit design

NASA Astrophysics Data System (ADS)

Abdel-Malek, Hany L.; Ebid, Shaimaa E. K.; Mohamed, Ahmed S. A.

2017-11-01

Since the optimization process requires a significant number of consecutive function evaluations, it is recommended to replace the function by an easily evaluated approximation model during the optimization process. The model suggested in this article is based on a multivariate Padé approximation. This model is constructed using data points of ?, where ? is the number of parameters. The model is updated over a sequence of trust regions. This model avoids the slow convergence of linear models of ? and has features of quadratic models that need interpolation data points of ?. The proposed approach is tested by applying it to several benchmark problems. Yield optimization using such a direct method is applied to some practical circuit examples. Minimax solution leads to a suitable initial point to carry out the yield optimization process. The yield is optimized by the proposed derivative-free method for active and passive filter examples.

Multi-parameter optimization of piezoelectric actuators for multi-mode active vibration control of cylindrical shells

NASA Astrophysics Data System (ADS)

Hu, K. M.; Li, Hua

2018-07-01

A novel technique for the multi-parameter optimization of distributed piezoelectric actuators is presented in this paper. The proposed method is designed to improve the performance of multi-mode vibration control in cylindrical shells. The optimization parameters of actuator patch configuration include position, size, and tilt angle. The modal control force of tilted orthotropic piezoelectric actuators is derived and the multi-parameter cylindrical shell optimization model is established. The linear quadratic energy index is employed as the optimization criterion. A geometric constraint is proposed to prevent overlap between tilted actuators, which is plugged into a genetic algorithm to search the optimal configuration parameters. A simply-supported closed cylindrical shell with two actuators serves as a case study. The vibration control efficiencies of various parameter sets are evaluated via frequency response and transient response simulations. The results show that the linear quadratic energy indexes of position and size optimization decreased by 14.0% compared to position optimization; those of position and tilt angle optimization decreased by 16.8%; and those of position, size, and tilt angle optimization decreased by 25.9%. It indicates that, adding configuration optimization parameters is an efficient approach to improving the vibration control performance of piezoelectric actuators on shells.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1980-01-01

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached to skin

NASA Astrophysics Data System (ADS)

Otiefy, R. A. H.; Negm, H. M.

2010-12-01

The main objective of this research is to study the capability of piezoelectric (PZT) self-sensing actuators to suppress the transonic wing box flutter, which is a flow-structure interaction phenomenon. The unsteady general frequency modified transonic small disturbance (TSD) equation is used to model the transonic flow about the wing. The wing box structure and piezoelectric actuators are modeled using the equivalent plate method, which is based on the first order shear deformation plate theory (FSDPT). The piezoelectric actuators are bonded to the skin. The optimal electromechanical coupling conditions between the piezoelectric actuators and the wing are collected from previous work. Three main different control strategies, a linear quadratic Gaussian (LQG) which combines the linear quadratic regulator (LQR) with the Kalman filter estimator (KFE), an optimal static output feedback (SOF), and a classic feedback controller (CFC), are studied and compared. The optimum actuator and sensor locations are determined using the norm of feedback control gains (NFCG) and norm of Kalman filter estimator gains (NKFEG) respectively. A genetic algorithm (GA) optimization technique is used to calculate the controller and estimator parameters to achieve a target response.

Estimation of positive semidefinite correlation matrices by using convex quadratic semidefinite programming.

PubMed

Fushiki, Tadayoshi

2009-07-01

The correlation matrix is a fundamental statistic that is used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used in the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume the approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.

The optimal location of piezoelectric actuators and sensors for vibration control of plates

NASA Astrophysics Data System (ADS)

Kumar, K. Ramesh; Narayanan, S.

2007-12-01

This paper considers the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQR performance is taken as objective for finding the optimal location of sensor-actuator pairs. The problem is formulated using the finite element method (FEM) as multi-input-multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero-one optimization problem. A genetic algorithm (GA) is used to solve the zero-one optimization problem. Different classical control strategies like direct proportional feedback, constant-gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness.

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

PubMed

Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming

2016-10-17

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

Modeling and optimization by particle swarm embedded neural network for adsorption of zinc (II) by palm kernel shell based activated carbon from aqueous environment.

PubMed

Karri, Rama Rao; Sahu, J N

2018-01-15

Zn (II) is one the common pollutant among heavy metals found in industrial effluents. Removal of pollutant from industrial effluents can be accomplished by various techniques, out of which adsorption was found to be an efficient method. Applications of adsorption limits itself due to high cost of adsorbent. In this regard, a low cost adsorbent produced from palm oil kernel shell based agricultural waste is examined for its efficiency to remove Zn (II) from waste water and aqueous solution. The influence of independent process variables like initial concentration, pH, residence time, activated carbon (AC) dosage and process temperature on the removal of Zn (II) by palm kernel shell based AC from batch adsorption process are studied systematically. Based on the design of experimental matrix, 50 experimental runs are performed with each process variable in the experimental range. The optimal values of process variables to achieve maximum removal efficiency is studied using response surface methodology (RSM) and artificial neural network (ANN) approaches. A quadratic model, which consists of first order and second order degree regressive model is developed using the analysis of variance and RSM - CCD framework. The particle swarm optimization which is a meta-heuristic optimization is embedded on the ANN architecture to optimize the search space of neural network. The optimized trained neural network well depicts the testing data and validation data with R 2 equal to 0.9106 and 0.9279 respectively. The outcomes indicates that the superiority of ANN-PSO based model predictions over the quadratic model predictions provided by RSM. Copyright © 2017 Elsevier Ltd. All rights reserved.

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

In Proc. Conf. on Decision and Control, pages 881-886, Bahamas, 2004. [7] G. Chesi, A. Garulli, A. Tesi , and A. Vicino. LMI-based computation of...Minneapolis, MN, 2006, pp. 117-122. [10] G. Chesi, A. Garulli, A. Tesi . and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions...Convex Optimization. Cambridge Univ. Press. Chesi, G., A. Garulli, A. Tesi and A. Vicino (2005). LMI-based computation of optimal quadratic Lyapunov

Experimental design and response surface modelling for optimization of vat dye from water by nano zero valent iron (NZVI).

PubMed

Arabi, Simin; Sohrabi, Mahmoud Reza

2013-01-01

In this study, NZVI particles was prepared and studied for the removal of vat green 1 dye from aqueous solution. A four-factor central composite design (CCD) combined with response surface modeling (RSM) to evaluate the combined effects of variables as well as optimization was employed for maximizing the dye removal by prepared NZVI based on 30 different experimental data obtained in a batch study. Four independent variables, viz. NZVI dose (0.1-0.9 g/L), pH (1.5-9.5), contact time (20-100 s), and initial dye concentration (10-50 mg/L) were transform to coded values and quadratic model was built to predict the responses. The significant of independent variables and their interactions were tested by the analysis of variance (ANOVA). Adequacy of the model was tested by the correlation between experimental and predicted values of the response and enumeration of prediction errors. The ANOVA results indicated that the proposed model can be used to navigate the design space. Optimization of the variables for maximum adsorption of dye by NZVI particles was performed using quadratic model. The predicted maximum adsorption efficiency (96.97%) under the optimum conditions of the process variables (NZVI dose 0.5 g/L, pH 4, contact time 60 s, and initial dye concentration 30 mg/L) was very close to the experimental value (96.16%) determined in batch experiment. In the optimization, R2 and R2adj correlation coefficients for the model were evaluated as 0.95 and 0.90, respectively.

Portfolio optimization using fuzzy linear programming

NASA Astrophysics Data System (ADS)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

Wind turbine power tracking using an improved multimodel quadratic approach.

PubMed

Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

2010-07-01

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Optimization by nonhierarchical asynchronous decomposition

NASA Technical Reports Server (NTRS)

Shankar, Jayashree; Ribbens, Calvin J.; Haftka, Raphael T.; Watson, Layne T.

1992-01-01

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness.

Enhancement of docosahexaenoic acid production by Schizochytrium SW1 using response surface methodology

NASA Astrophysics Data System (ADS)

Nazir, Mohd Yusuf Mohd; Al-Shorgani, Najeeb Kaid Nasser; Kalil, Mohd Sahaid; Hamid, Aidil Abdul

2015-09-01

In this study, three factors (fructose concentration, agitation speed and monosodium glutamate (MSG) concentration) were optimized to enhance DHA production by Schizochytrium SW1 using response surface methodology (RSM). Central composite design was applied as the experimental design and analysis of variance (ANOVA) was used to analyze the data. The experiments were conducted using 500 mL flask with 100 mL working volume at 30°C for 96 hours. ANOVA analysis revealed that the process was adequately represented significantly by the quadratic model (p<0.0001) and two of the factors namely agitation speed and MSG concentration significantly affect DHA production (p<0.005). Level of influence for each variable and quadratic polynomial equation were obtained for DHA production by multiple regression analyses. The estimated optimum conditions for maximizing DHA production by SW1 were 70 g/L fructose, 250 rpm agitation speed and 12 g/L MSG. Consequently, the quadratic model was validated by applying of the estimated optimum conditions, which confirmed the model validity and 52.86% of DHA was produced.

Dynamics and Control of Tethered Antennas/Reflectors in Orbit

DTIC Science & Technology

1992-02-01

reflector system. The optimal linear quadratic Gaussian (LQG) digital con- trol of the orbiting tethered antenna/reflector system is analyzed. The...flexibility of both the antenna and the tether are included in this high order system model. With eight point actuators optimally positioned together with...able to maintain satisfactory pointing accuracy for low and moderate altitude orbits under the influence of solar pressure. For the higher altitudes a

An optimal control approach to the design of moving flight simulators

NASA Technical Reports Server (NTRS)

Sivan, R.; Ish-Shalom, J.; Huang, J.-K.

1982-01-01

An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Sunarsih; Kartono

2018-01-01

In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

The dynamic model of enterprise revenue management

NASA Astrophysics Data System (ADS)

Mitsel, A. A.; Kataev, M. Yu; Kozlov, S. V.; Korepanov, K. V.

2017-01-01

The article presents the dynamic model of enterprise revenue management. This model is based on the quadratic criterion and linear control law. The model is founded on multiple regression that links revenues with the financial performance of the enterprise. As a result, optimal management is obtained so as to provide the given enterprise revenue, namely, the values of financial indicators that ensure the planned profit of the organization are acquired.

Permutation flow-shop scheduling problem to optimize a quadratic objective function

NASA Astrophysics Data System (ADS)

Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

2017-09-01

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

Optimal Fermentation Conditions of Hyaluronidase Inhibition Activity on Asparagus cochinchinensis Merrill by Weissella cibaria.

PubMed

Kim, Minji; Kim, Won-Baek; Koo, Kyoung Yoon; Kim, Bo Ram; Kim, Doohyun; Lee, Seoyoun; Son, Hong Joo; Hwang, Dae Youn; Kim, Dong Seob; Lee, Chung Yeoul; Lee, Heeseob

2017-04-28

This study was conducted to evaluate the hyaluronidase (HAase) inhibition activity of Asparagus cochinchinesis (AC) extracts following fermentation by Weissella cibaria through response surface methodology. To optimize the HAase inhibition activity, a central composite design was introduced based on four variables: the concentration of AC extract ( X 1 : 1-5%), amount of starter culture ( X 2 : 1-5%), pH ( X 3 : 4-8), and fermentation time ( X 4 : 0-10 days). The experimental data were fitted to quadratic regression equations, the accuracy of the equations was analyzed by ANOVA, and the regression coefficients for the surface quadratic model of HAase inhibition activity in the fermented AC extract were estimated by the F test and the corresponding p values. The HAase inhibition activity indicated that fermentation time was most significant among the parameters within the conditions tested. To validate the model, two different conditions among those generated by the Design Expert program were selected. Under both conditions, predicted and experimental data agreed well. Moreover, the content of protodioscin (a well-known compound related to anti-inflammation activity) was elevated after fermentation of the AC extract at the optimized fermentation condition.

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

He, Changhong; Coleman, Thomas F.; Li, Yuying

2008-12-01

In [T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton-Jacobian-Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration.

Optimization on Paddy Crops in Central Java (with Solver, SVD on Least Square and ACO (Ant Colony Algorithm))

NASA Astrophysics Data System (ADS)

Parhusip, H. A.; Trihandaru, S.; Susanto, B.; Prasetyo, S. Y. J.; Agus, Y. H.; Simanjuntak, B. H.

2017-03-01

Several algorithms and objective functions on paddy crops have been studied to get optimal paddy crops in Central Java based on the data given from Surakarta and Boyolali. The algorithms are linear solver, least square and Ant Colony Algorithms (ACO) to develop optimization procedures on paddy crops modelled with Modified GSTAR (Generalized Space-Time Autoregressive) and nonlinear models where the nonlinear models are quadratic and power functions. The studied data contain paddy crops from Surakarta and Boyolali determining the best period of planting in the year 1992-2012 for Surakarta where 3 periods for planting are known and the optimal amount of paddy crops in Boyolali in the year 2008-2013. Having these analyses may guide the local agriculture government to give a decision on rice sustainability in its region. The best period for planting in Surakarta is observed, i.e. the best period is in September-December based on the data 1992-2012 by considering the planting area, the cropping area, and the paddy crops are the most important factors to be taken into account. As a result, we can refer the paddy crops in this best period (about 60.4 thousand tons per year) as the optimal results in 1992-2012 where the used objective function is quadratic. According to the research, the optimal paddy crops in Boyolali about 280 thousand tons per year where the studied factors are the amount of rainfalls, the harvested area and the paddy crops in 2008-2013. In this case, linear and power functions are studied to be the objective functions. Compared to all studied algorithms, the linear solver is still recommended to be an optimization tool for a local agriculture government to predict paddy crops in future.

Half-quadratic variational regularization methods for speckle-suppression and edge-enhancement in SAR complex image

NASA Astrophysics Data System (ADS)

Zhao, Xia; Wang, Guang-xin

2008-12-01

Synthetic aperture radar (SAR) is an active remote sensing sensor. It is a coherent imaging system, the speckle is its inherent default, which affects badly the interpretation and recognition of the SAR targets. Conventional methods of removing the speckle is studied usually in real SAR image, which reduce the edges of the images at the same time as depressing the speckle. Morever, Conventional methods lost the information about images phase. Removing the speckle and enhancing the target and edge simultaneously are still a puzzle. To suppress the spckle and enhance the targets and the edges simultaneously, a half-quadratic variational regularization method in complex SAR image is presented, which is based on the prior knowledge of the targets and the edge. Due to the non-quadratic and non- convex quality and the complexity of the cost function, a half-quadratic variational regularization variation is used to construct a new cost function,which is solved by alternate optimization. In the proposed scheme, the construction of the model, the solution of the model and the selection of the model peremeters are studied carefully. In the end, we validate the method using the real SAR data.Theoretic analysis and the experimental results illustrate the the feasibility of the proposed method. Further more, the proposed method can preserve the information about images phase.

On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation

NASA Astrophysics Data System (ADS)

Liu, Jiakun; Trudinger, Neil S.; Wang, Xu-Jia

2015-03-01

In this paper we study local properties of cost and potential functions in optimal transportation. We prove that in a proper normalization process, the cost function is uniformly smooth and converges locally smoothly to a quadratic cost x · y, while the potential function converges to a quadratic function. As applications we obtain the interior W 2, p estimates and sharp C 1, α estimates for the potentials, which satisfy a Monge-Ampère type equation. The W 2, p estimate was previously proved by Caffarelli for the quadratic transport cost and the associated standard Monge-Ampère equation.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Further efforts in optimizing nonlinear optical molecules

NASA Astrophysics Data System (ADS)

Dirk, Carl W.; Caballero, Noel; Tan, Alarice; Kuzyk, Mark G.; Cheng, Lap-Tak A.; Katz, Howard E.; Shilling, Marcia; King, Lori A.

1993-02-01

We summarize some of our past work in the field on optimizing molecules for second order and third order nonlinear optical applications. We also present some previously unpublished results suggesting a particular optimization of the popular cyano- and nitrovinyl acceptor groups. In addition we provide some new quadratic electro-optic results which serve to further verify our choice of a restricted three-level model suitable for optimizing third order nonlinearities in molecules. Finally we present a new squarylium dye with a large third order optical nonlinearity (-9.5 X 10-34 cm7/esu2; EFISH (gamma) at 1906 nm).

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

NASA Astrophysics Data System (ADS)

Landsman, Zinoviy

2008-10-01

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.

PubMed

Li, Yanyan; Raghavarao, Damaraju; Chervoneva, Inna

2017-01-01

The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé's linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations.

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

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

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

An EOQ model of time quadratic and inventory dependent demand for deteriorated items with partially backlogged shortages under trade credit

NASA Astrophysics Data System (ADS)

Singh, Pushpinder; Mishra, Nitin Kumar; Singh, Vikramjeet; Saxena, Seema

2017-07-01

In this paper a single buyer, single supplier inventory model with time quadratic and stock dependent demand for a finite planning horizon has been studied. Single deteriorating item which suffers shortage, with partial backlogging and some lost sales is considered. Model is divided into two scenarios, one with non permissible delay in payment and other with permissible delay in payment. Latter is called, centralized system, where supplier offers trade credit to retailer. In the centralized system cost saving is shared amongst the two. The objective is to study the difference in minimum costs borne by retailer and supplier, under two scenarios including the above mentioned parameters. To obtain optimal solution of the problem the model is solved analytically. Numerical example and a comparative study are then discussed supported by sensitivity analysis of each parameter.

Modified optimal control pilot model for computer-aided design and analysis

NASA Technical Reports Server (NTRS)

Davidson, John B.; Schmidt, David K.

1992-01-01

This paper presents the theoretical development of a modified optimal control pilot model based upon the optimal control model (OCM) of the human operator developed by Kleinman, Baron, and Levison. This model is input compatible with the OCM and retains other key aspects of the OCM, such as a linear quadratic solution for the pilot gains with inclusion of control rate in the cost function, a Kalman estimator, and the ability to account for attention allocation and perception threshold effects. An algorithm designed for each implementation in current dynamic systems analysis and design software is presented. Example results based upon the analysis of a tracking task using three basic dynamic systems are compared with measured results and with similar analyses performed with the OCM and two previously proposed simplified optimal pilot models. The pilot frequency responses and error statistics obtained with this modified optimal control model are shown to compare more favorably to the measured experimental results than the other previously proposed simplified models evaluated.

Model-based sensor-less wavefront aberration correction in optical coherence tomography.

PubMed

Verstraete, Hans R G W; Wahls, Sander; Kalkman, Jeroen; Verhaegen, Michel

2015-12-15

Several sensor-less wavefront aberration correction methods that correct nonlinear wavefront aberrations by maximizing the optical coherence tomography (OCT) signal are tested on an OCT setup. A conventional coordinate search method is compared to two model-based optimization methods. The first model-based method takes advantage of the well-known optimization algorithm (NEWUOA) and utilizes a quadratic model. The second model-based method (DONE) is new and utilizes a random multidimensional Fourier-basis expansion. The model-based algorithms achieve lower wavefront errors with up to ten times fewer measurements. Furthermore, the newly proposed DONE method outperforms the NEWUOA method significantly. The DONE algorithm is tested on OCT images and shows a significantly improved image quality.

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, X; Belcher, AH; Wiersma, R

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimizationmore » and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n–1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n–1/2-rate. PMID:23087487

Modeling and optimization aspects of radiation induced grafting of 4-vinylpyridene onto partially fluorinated films

NASA Astrophysics Data System (ADS)

Nasef, Mohamed Mahmoud; Ahmad Ali, Amgad; Saidi, Hamdani; Ahmad, Arshad

2014-01-01

Modeling and optimization aspects of radiation induced grafting (RIG) of 4-vinylpyridine (4-VP) onto partially fluorinated polymers such as poly(ethylene-co-tetrafluoroethene) (ETFE) and poly(vinylidene fluoride) (PVDF) films were comparatively investigated using response surface method (RSM). The effects of independent parameters: absorbed dose, monomer concentration, grafting time and reaction temperature on the response, grafting yield (GY) were correlated through two quadratic models. The results of this work confirm that RSM is a reliable tool not only for optimization of the reaction parameters and prediction of GY in RIG processes, but also for the reduction of the number of the experiments, monomer consumption and absorbed dose leading to an improvement of the overall reaction cost.

Production and optimization of polyhydroxyalkanoates from non-edible Calophyllum inophyllum oil using Cupriavidus necator.

PubMed

Arumugam, A; Senthamizhan, S G; Ponnusami, V; Sudalai, S

2018-06-01

Polyhydroxyalkanoates (PHA) are biodegradable polymers found in the cellular masses of a wide range of bacterial species and the demand for PHA is steadily growing. In this work we have produced PHA from a low-cost substrate, Calophyllum inophyllum oil, using Cupriavidus necator. Effects of various process parameters such as Oil concentration, Nitrogen source and inoculum size on the production of PHA were studied using Response Surface Methodology. A quadratic equation was used in the model to fit the experimental data. It was found that the model could satisfactorily predict the PHA yield (R 2 =99.17%). Linear, quadratic and interaction terms used in the model were found to be statistically significant. Maximum PHA yield of 10.6gL -1 was obtained under the optimized conditions of oil concentration - 17.5%, inoculum concentration - 50mL/L and nitrogen content - 1.125gL -1 , respectively. The product obtained was characterized using FTIR and NMR to confirm that it was PHA. The results demonstrate that C. inophyllum oil, a non-edible oil, can be potentially used as a low-cost substrate for the production of PHA. Copyright © 2018 Elsevier B.V. All rights reserved.

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

1989-01-01

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Optimal control of the gear shifting process for shift smoothness in dual-clutch transmissions

NASA Astrophysics Data System (ADS)

Li, Guoqiang; Görges, Daniel

2018-03-01

The control of the transmission system in vehicles is significant for the driving comfort. In order to design a controller for smooth shifting and comfortable driving, a dynamic model of a dual-clutch transmission is presented in this paper. A finite-time linear quadratic regulator is proposed for the optimal control of the two friction clutches in the torque phase for the upshift process. An integral linear quadratic regulator is introduced to regulate the relative speed difference between the engine and the slipping clutch under the optimization of the input torque during the inertia phase. The control objective focuses on smoothing the upshift process so as to improve the driving comfort. Considering the available sensors in vehicles for feedback control, an observer design is presented to track the immeasurable variables. Simulation results show that the jerk can be reduced both in the torque phase and inertia phase, indicating good shift performance. Furthermore, compared with conventional controllers for the upshift process, the proposed control method can reduce shift jerk and improve shift quality.

Design and implementation of fuzzy-PD controller based on relation models: A cross-entropy optimization approach

NASA Astrophysics Data System (ADS)

Anisimov, D. N.; Dang, Thai Son; Banerjee, Santo; Mai, The Anh

2017-07-01

In this paper, an intelligent system use fuzzy-PD controller based on relation models is developed for a two-wheeled self-balancing robot. Scaling factors of the fuzzy-PD controller are optimized by a Cross-Entropy optimization method. A linear Quadratic Regulator is designed to bring a comparison with the fuzzy-PD controller by control quality parameters. The controllers are ported and run on STM32F4 Discovery Kit based on the real-time operating system. The experimental results indicate that the proposed fuzzy-PD controller runs exactly on embedded system and has desired performance in term of fast response, good balance and stabilize.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, W; Randeniya, K; Grosshans, D

2016-06-15

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 functionmore » 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.« less

A new numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

PubMed

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

2016-01-01

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.

Quadratic correlation filters for optical correlators

NASA Astrophysics Data System (ADS)

Mahalanobis, Abhijit; Muise, Robert R.; Vijaya Kumar, Bhagavatula V. K.

2003-08-01

Linear correlation filters have been implemented in optical correlators and successfully used for a variety of applications. The output of an optical correlator is usually sensed using a square law device (such as a CCD array) which forces the output to be the squared magnitude of the desired correlation. It is however not a traditional practice to factor the effect of the square-law detector in the design of the linear correlation filters. In fact, the input-output relationship of an optical correlator is more accurately modeled as a quadratic operation than a linear operation. Quadratic correlation filters (QCFs) operate directly on the image data without the need for feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required to detect peaks in the outputs of multiple linear filters, but choosing a winner among them is an error prone task. In contrast, all channels in a QCF work together to optimize the same performance metric and produce a combined output that leads to considerable simplification of the post-processing. In this paper, we propose a novel approach to the design of quadratic correlation based on the Fukunaga Koontz transform. Although quadratic filters are known to be optimum when the data is Gaussian, it is expected that they will perform as well as or better than linear filters in general. Preliminary performance results are provided that show that quadratic correlation filters perform better than their linear counterparts.

Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ardema, Mark

2006-01-01

This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

Optimization for minimum sensitivity to uncertain parameters

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.; Sobieszczanski-Sobieski, Jaroslaw

1994-01-01

A procedure to design a structure for minimum sensitivity to uncertainties in problem parameters is described. The approach is to minimize directly the sensitivity derivatives of the optimum design with respect to fixed design parameters using a nested optimization procedure. The procedure is demonstrated for the design of a bimetallic beam for minimum weight with insensitivity to uncertainties in structural properties. The beam is modeled with finite elements based on two dimensional beam analysis. A sequential quadratic programming procedure used as the optimizer supplies the Lagrange multipliers that are used to calculate the optimum sensitivity derivatives. The method was perceived to be successful from comparisons of the optimization results with parametric studies.

Optimization of natural lipstick formulation based on pitaya (Hylocereus polyrhizus) seed oil using D-optimal mixture experimental design.

PubMed

Kamairudin, Norsuhaili; Gani, Siti Salwa Abd; Masoumi, Hamid Reza Fard; Hashim, Puziah

2014-10-16

The D-optimal mixture experimental design was employed to optimize the melting point of natural lipstick based on pitaya (Hylocereus polyrhizus) seed oil. The influence of the main lipstick components-pitaya seed oil (10%-25% w/w), virgin coconut oil (25%-45% w/w), beeswax (5%-25% w/w), candelilla wax (1%-5% w/w) and carnauba wax (1%-5% w/w)-were investigated with respect to the melting point properties of the lipstick formulation. The D-optimal mixture experimental design was applied to optimize the properties of lipstick by focusing on the melting point with respect to the above influencing components. The D-optimal mixture design analysis showed that the variation in the response (melting point) could be depicted as a quadratic function of the main components of the lipstick. The best combination of each significant factor determined by the D-optimal mixture design was established to be pitaya seed oil (25% w/w), virgin coconut oil (37% w/w), beeswax (17% w/w), candelilla wax (2% w/w) and carnauba wax (2% w/w). With respect to these factors, the 46.0 °C melting point property was observed experimentally, similar to the theoretical prediction of 46.5 °C. Carnauba wax is the most influential factor on this response (melting point) with its function being with respect to heat endurance. The quadratic polynomial model sufficiently fit the experimental data.

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

Digital robust active control law synthesis for large order flexible structure using parameter optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.

1988-01-01

A generic procedure for the parameter optimization of a digital control law for a large-order flexible flight vehicle or large space structure modeled as a sampled data system is presented. A linear quadratic Guassian type cost function was minimized, while satisfying a set of constraints on the steady-state rms values of selected design responses, using a constrained optimization technique to meet multiple design requirements. Analytical expressions for the gradients of the cost function and the design constraints on mean square responses with respect to the control law design variables are presented.

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

NASA Astrophysics Data System (ADS)

Gaddy, Melissa R.; Yıldız, Sercan; Unkelbach, Jan; Papp, Dávid

2018-01-01

Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

A multilevel control system for the large space telescope. [numerical analysis/optimal control

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Sundareshan, S. K.; Vukcevic, M. B.

1975-01-01

A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques.

Ant Colony Optimization for Markowitz Mean-Variance Portfolio Model

NASA Astrophysics Data System (ADS)

Deng, Guang-Feng; Lin, Woo-Tsong

This work presents Ant Colony Optimization (ACO), which was initially developed to be a meta-heuristic for combinatorial optimization, for solving the cardinality constraints Markowitz mean-variance portfolio model (nonlinear mixed quadratic programming problem). To our knowledge, an efficient algorithmic solution for this problem has not been proposed until now. Using heuristic algorithms in this case is imperative. Numerical solutions are obtained for five analyses of weekly price data for the following indices for the period March, 1992 to September, 1997: Hang Seng 31 in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei 225 in Japan. The test results indicate that the ACO is much more robust and effective than Particle swarm optimization (PSO), especially for low-risk investment portfolios.

Optimal coordination and control of posture and movements.

PubMed

Johansson, Rolf; Fransson, Per-Anders; Magnusson, Måns

2009-01-01

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

NASA Astrophysics Data System (ADS)

Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

2017-09-01

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

Manpower Targets and Educational Investments

ERIC Educational Resources Information Center

Ritzen, Jo M.

1976-01-01

Discusses the use of quadratic programming to calculate the optimal distribution of educational investments required to closely approach manpower targets when financial resources are insufficient to meet manpower targets completely. Demonstrates use of the quadratic programming approach by applying it to the training of supervisory technicians in…

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

PubMed Central

Wang, Di; Kleinberg, Robert D.

2009-01-01

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

Application of Modified Particle Swarm Optimization Method for Parameter Extraction of 2-D TEC Mapping

NASA Astrophysics Data System (ADS)

Toker, C.; Gokdag, Y. E.; Arikan, F.; Arikan, O.

2012-04-01

Ionosphere is a very important part of Space Weather. Modeling and monitoring of ionospheric variability is a major part of satellite communication, navigation and positioning systems. Total Electron Content (TEC), which is defined as the line integral of the electron density along a ray path, is one of the parameters to investigate the ionospheric variability. Dual-frequency GPS receivers, with their world wide availability and efficiency in TEC estimation, have become a major source of global and regional TEC modeling. When Global Ionospheric Maps (GIM) of International GPS Service (IGS) centers (http://iono.jpl.nasa.gov/gim.html) are investigated, it can be observed that regional ionosphere along the midlatitude regions can be modeled as a constant, linear or a quadratic surface. Globally, especially around the magnetic equator, the TEC surfaces resemble twisted and dispersed single centered or double centered Gaussian functions. Particle Swarm Optimization (PSO) proved itself as a fast converging and an effective optimization tool in various diverse fields. Yet, in order to apply this optimization technique into TEC modeling, the method has to be modified for higher efficiency and accuracy in extraction of geophysical parameters such as model parameters of TEC surfaces. In this study, a modified PSO (mPSO) method is applied to regional and global synthetic TEC surfaces. The synthetic surfaces that represent the trend and small scale variability of various ionospheric states are necessary to compare the performance of mPSO over number of iterations, accuracy in parameter estimation and overall surface reconstruction. The Cramer-Rao bounds for each surface type and model are also investigated and performance of mPSO are tested with respect to these bounds. For global models, the sample points that are used in optimization are obtained using IGS receiver network. For regional TEC models, regional networks such as Turkish National Permanent GPS Network (TNPGN-Active) receiver sites are used. The regional TEC models are grouped into constant (one parameter), linear (two parameters), and quadratic (six parameters) surfaces which are functions of latitude and longitude. Global models require seven parameters for single centered Gaussian and 13 parameters for double centered Gaussian function. The error criterion is the normalized percentage error for both the surface and the parameters. It is observed that mPSO is very successful in parameter extraction of various regional and global models. The normalized reconstruction error varies from 10-4 for constant surfaces to 10-3 for quadratic surfaces in regional models, sampled with regional networks. Even for the cases of a severe geomagnetic storm that affects measurements globally, with IGS network, the reconstruction error is on the order of 10-1 even though individual parameters have higher normalized errors. The modified PSO technique proved itself to be a useful tool for parameter extraction of more complicated TEC models. This study is supported by TUBITAK EEEAG under Grant No: 109E055.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Prediction and optimization of the laccase-mediated synthesis of the antimicrobial compound iodine (I2).

PubMed

Schubert, M; Fey, A; Ihssen, J; Civardi, C; Schwarze, F W M R; Mourad, S

2015-01-10

An artificial neural network (ANN) and genetic algorithm (GA) were applied to improve the laccase-mediated oxidation of iodide (I(-)) to elemental iodine (I2). Biosynthesis of iodine (I2) was studied with a 5-level-4-factor central composite design (CCD). The generated ANN network was mathematically evaluated by several statistical indices and revealed better results than a classical quadratic response surface (RS) model. Determination of the relative significance of model input parameters, ranking the process parameters in order of importance (pH>laccase>mediator>iodide), was performed by sensitivity analysis. ANN-GA methodology was used to optimize the input space of the neural network model to find optimal settings for the laccase-mediated synthesis of iodine. ANN-GA optimized parameters resulted in a 9.9% increase in the conversion rate. Copyright © 2014 Elsevier B.V. All rights reserved.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

NASA Technical Reports Server (NTRS)

Richter, hanz; Singaraju, Anil; Litt, Jonathan S.

2008-01-01

Model predictive control is a strategy well-suited to handle the highly complex, nonlinear, uncertain, and constrained dynamics involved in aircraft engine control problems. However, it has thus far been infeasible to implement model predictive control in engine control applications, because of the combination of model complexity and the time allotted for the control update calculation. In this paper, a multiplexed implementation is proposed that dramatically reduces the computational burden of the quadratic programming optimization that must be solved online as part of the model-predictive-control algorithm. Actuator updates are calculated sequentially and cyclically in a multiplexed implementation, as opposed to the simultaneous optimization taking place in conventional model predictive control. Theoretical aspects are discussed based on a nominal model, and actual computational savings are demonstrated using a realistic commercial engine model.

Simultaneous structural and control optimization via linear quadratic regulator eigenstructure assignment

NASA Technical Reports Server (NTRS)

Becus, G. A.; Lui, C. Y.; Venkayya, V. B.; Tischler, V. A.

1987-01-01

A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Algorithm For Optimal Control Of Large Structures

NASA Technical Reports Server (NTRS)

Salama, Moktar A.; Garba, John A..; Utku, Senol

1989-01-01

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

On the asymptotic optimality and improved strategies of SPTB heuristic for open-shop scheduling problem

NASA Astrophysics Data System (ADS)

Bai, Danyu; Zhang, Zhihai

2014-08-01

This article investigates the open-shop scheduling problem with the optimal criterion of minimising the sum of quadratic completion times. For this NP-hard problem, the asymptotic optimality of the shortest processing time block (SPTB) heuristic is proven in the sense of limit. Moreover, three different improvements, namely, the job-insert scheme, tabu search and genetic algorithm, are introduced to enhance the quality of the original solution generated by the SPTB heuristic. At the end of the article, a series of numerical experiments demonstrate the convergence of the heuristic, the performance of the improvements and the effectiveness of the quadratic objective.

Numerical Solution of the Electron Heat Transport Equation and Physics-Constrained Modeling of the Thermal Conductivity via Sequential Quadratic Programming Optimization in Nuclear Fusion Plasmas

NASA Astrophysics Data System (ADS)

Paloma, Cynthia S.

The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the proposed modeling method.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

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.

On Optimizing H. 264/AVC Rate Control by Improving R-D Model and Incorporating HVS Characteristics

NASA Astrophysics Data System (ADS)

Zhu, Zhongjie; Wang, Yuer; Bai, Yongqiang; Jiang, Gangyi

2010-12-01

The state-of-the-art JVT-G012 rate control algorithm of H.264 is improved from two aspects. First, the quadratic rate-distortion (R-D) model is modified based on both empirical observations and theoretical analysis. Second, based on the existing physiological and psychological research findings of human vision, the rate control algorithm is optimized by incorporating the main characteristics of the human visual system (HVS) such as contrast sensitivity, multichannel theory, and masking effect. Experiments are conducted, and experimental results show that the improved algorithm can simultaneously enhance the overall subjective visual quality and improve the rate control precision effectively.

Optimization of Progressive Freeze Concentration on Apple Juice via Response Surface Methodology

NASA Astrophysics Data System (ADS)

Samsuri, S.; Amran, N. A.; Jusoh, M.

2018-05-01

In this work, a progressive freeze concentration (PFC) system was developed to concentrate apple juice and was optimized by response surface methodology (RSM). The effects of various operating conditions such as coolant temperature, circulation flowrate, circulation time and shaking speed to effective partition constant (K) were investigated. Five different level of central composite design (CCD) was employed to search for optimal concentration of concentrated apple juice. A full quadratic model for K was established by using method of least squares. A coefficient of determination (R2) of this model was found to be 0.7792. The optimum conditions were found to be coolant temperature = -10.59 °C, circulation flowrate = 3030.23 mL/min, circulation time = 67.35 minutes and shaking speed = 30.96 ohm. A validation experiment was performed to evaluate the accuracy of the optimization procedure and the best K value of 0.17 was achieved under the optimized conditions.

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2012-01-01

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery - part II: an illustrative example.

PubMed

Cevenini, Gabriele; Barbini, Emanuela; Scolletta, Sabino; Biagioli, Bonizella; Giomarelli, Pierpaolo; Barbini, Paolo

2007-11-22

Popular predictive models for estimating morbidity probability after heart surgery are compared critically in a unitary framework. The study is divided into two parts. In the first part modelling techniques and intrinsic strengths and weaknesses of different approaches were discussed from a theoretical point of view. In this second part the performances of the same models are evaluated in an illustrative example. Eight models were developed: Bayes linear and quadratic models, k-nearest neighbour model, logistic regression model, Higgins and direct scoring systems and two feed-forward artificial neural networks with one and two layers. Cardiovascular, respiratory, neurological, renal, infectious and hemorrhagic complications were defined as morbidity. Training and testing sets each of 545 cases were used. The optimal set of predictors was chosen among a collection of 78 preoperative, intraoperative and postoperative variables by a stepwise procedure. Discrimination and calibration were evaluated by the area under the receiver operating characteristic curve and Hosmer-Lemeshow goodness-of-fit test, respectively. Scoring systems and the logistic regression model required the largest set of predictors, while Bayesian and k-nearest neighbour models were much more parsimonious. In testing data, all models showed acceptable discrimination capacities, however the Bayes quadratic model, using only three predictors, provided the best performance. All models showed satisfactory generalization ability: again the Bayes quadratic model exhibited the best generalization, while artificial neural networks and scoring systems gave the worst results. Finally, poor calibration was obtained when using scoring systems, k-nearest neighbour model and artificial neural networks, while Bayes (after recalibration) and logistic regression models gave adequate results. Although all the predictive models showed acceptable discrimination performance in the example considered, the Bayes and logistic regression models seemed better than the others, because they also had good generalization and calibration. The Bayes quadratic model seemed to be a convincing alternative to the much more usual Bayes linear and logistic regression models. It showed its capacity to identify a minimum core of predictors generally recognized as essential to pragmatically evaluate the risk of developing morbidity after heart surgery.

Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization.

PubMed

Li, Zhijun; Xia, Yuanqing; Su, Chun-Yi; Deng, Jun; Fu, Jun; He, Wei

2015-08-01

In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Extensions of D-optimal Minimal Designs for Symmetric Mixture Models

PubMed Central

Raghavarao, Damaraju; Chervoneva, Inna

2017-01-01

The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé's linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. In This Paper, Extensions Of The D-Optimal Minimal Designs Are Developed For A General Mixture Model To Allow Additional Interior Points In The Design Space To Enable Prediction Of The Entire Response Surface Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations. PMID:29081574

Synthesis of robust nonlinear autopilots using differential game theory

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1991-01-01

A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

Factorization and reduction methods for optimal control of distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Powers, R. K.

1985-01-01

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Nonlinear time-series-based adaptive control applications

NASA Technical Reports Server (NTRS)

Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.

1991-01-01

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Implications of the degree of controllability of controlled plants in the sense of LQR optimal control

NASA Astrophysics Data System (ADS)

Xia, Yaping; Yin, Minghui; Zou, Yun

2018-01-01

In this paper, the relationship between the degree of controllability (DOC) of controlled plants and the corresponding quadratic optimal performance index in LQR control is investigated for the electro-hydraulic synchronising servo control systems and wind turbine systems, respectively. It is shown that for these two types of systems, the higher the DOC of a controlled plant is, the better the quadratic optimal performance index is. It implies that in some LQR controller designs, the measure of the DOC of a controlled plant can be used as an index for the optimisation of adjustable plant parameters, by which the plant can be controlled more effectively.

DE and NLP Based QPLS Algorithm

NASA Astrophysics Data System (ADS)

Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo

As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.

Direct Optimal Control of Duffing Dynamics

NASA Technical Reports Server (NTRS)

Oz, Hayrani; Ramsey, John K.

2002-01-01

The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

NASA Astrophysics Data System (ADS)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

Substructural controller synthesis

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1989-01-01

A decentralized design procedure which combines substructural synthesis, model reduction, decentralized controller design, subcontroller synthesis, and controller reduction is proposed for the control design of flexible structures. The structure to be controlled is decomposed into several substructures, which are modeled by component mode synthesis methods. For each substructure, a subcontroller is designed by using the linear quadratic optimal control theory. Then, a controller synthesis scheme called Substructural Controller Synthesis (SCS) is used to assemble the subcontrollers into a system controller, which is to be used to control the whole structure.

Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests

PubMed Central

Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit

2014-01-01

In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the Pearson-normal kernel, and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online. PMID:24764609

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

NASA Astrophysics Data System (ADS)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

NASA Astrophysics Data System (ADS)

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Optimization of thermo-alkaline disintegration of sewage sludge for enhanced biogas yield.

PubMed

Shehu, Muhammad Sani; Abdul Manan, Zainuddin; Alwi, Sharifah Rafidah Wan

2012-06-01

Optimization of thermo-alkaline disintegration of sewage sludge for enhanced biogas yield was carried out using response surface methodology (RSM) and Box-Behnken design of experiment. The individual linear and quadratic effects as well as the interactive effects of temperature, NaOH concentration and time on the degree of disintegration were investigated. The optimum degree of disintegration achieved was 61.45% at 88.50 °C, 2.29 M NaOH (24.23%w/w total solids) and 21 min retention time. Linear and quadratic effects of temperature are most significant in affecting the degree of disintegration. The coefficient of determination (R(2)) of 99.5% confirms that the model used in predicting the degree of disintegration process has a very good fitness with the experimental variables. The disintegrated sludge increased the biogas yield by 36%v/v compared to non-disintegrated sludge. The RSM with Box-Behnken design is an effective tool in predicting the optimum degree of disintegration of sewage sludge for increased biogas yield. Copyright © 2012 Elsevier Ltd. All rights reserved.

A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems

NASA Astrophysics Data System (ADS)

Ebrahimzadeh, Faezeh; Tsai, Jason Sheng-Hong; Chung, Min-Ching; Liao, Ying Ting; Guo, Shu-Mei; Shieh, Leang-San; Wang, Li

2017-01-01

Contrastive to Part 1, Part 2 presents a generalised optimal linear quadratic digital tracker (LQDT) with universal applications for the discrete-time (DT) systems. This includes (1) a generalised optimal LQDT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQDT design for non-square non-minimum phase DT systems to achieve a minimum-phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square DT systems; and (4) a one-learning-epoch input-constrained iterative learning LQDT design for the repetitive DT systems.

A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

PubMed Central

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem.

PubMed

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.

Vibration suppression of a piezo-equipped cylindrical shell in a broad-band frequency domain

NASA Astrophysics Data System (ADS)

Loghmani, Ali; Danesh, Mohammad; Kwak, Moon K.; Keshmiri, Mehdi

2017-12-01

This paper focuses on the dynamic modeling of a cylindrical shell equipped with piezoceramic sensors and actuators, as well as the design of a broad band multi-input and multi-output linear quadratic Gaussian controller for the suppression of vibrations. The optimal locations of actuators are derived by Genetic Algorithm (GA) to effectively control the specific structural modes of the cylinder. The dynamic model is derived based on the Sanders shell theory and the energy approach for both the cylinder and the piezoelectric transducers, all of which reflect the piezoelectric effect. The natural vibration characteristics of the cylindrical shell are investigated both theoretically and experimentally. The theoretical predictions are in good agreement with the experimental results. Then, the broad band multi-input and multi-output linear quadratic Gaussian controller was designed and applied to the test article. An active vibration control experiment is carried out on the cylindrical shell and the digital control system is used to implement the proposed control algorithm. The experimental results show that vibrations of the cylindrical shell can be suppressed by the piezoceramic sensors and actuators along with the proposed controller. The optimal location of the actuators makes the proposed control system more efficient than other configurations.

A review of distributed parameter groundwater management modeling methods

USGS Publications Warehouse

Gorelick, Steven M.

1983-01-01

Models which solve the governing groundwater flow or solute transport equations in conjunction with optimization techniques, such as linear and quadratic programing, are powerful aquifer management tools. Groundwater management models fall in two general categories: hydraulics or policy evaluation and water allocation. Groundwater hydraulic management models enable the determination of optimal locations and pumping rates of numerous wells under a variety of restrictions placed upon local drawdown, hydraulic gradients, and water production targets. Groundwater policy evaluation and allocation models can be used to study the influence upon regional groundwater use of institutional policies such as taxes and quotas. Furthermore, fairly complex groundwater-surface water allocation problems can be handled using system decomposition and multilevel optimization. Experience from the few real world applications of groundwater optimization-management techniques is summarized. Classified separately are methods for groundwater quality management aimed at optimal waste disposal in the subsurface. This classification is composed of steady state and transient management models that determine disposal patterns in such a way that water quality is protected at supply locations. Classes of research missing from the literature are groundwater quality management models involving nonlinear constraints, models which join groundwater hydraulic and quality simulations with political-economic management considerations, and management models that include parameter uncertainty.

A Review of Distributed Parameter Groundwater Management Modeling Methods

NASA Astrophysics Data System (ADS)

Gorelick, Steven M.

1983-04-01

Models which solve the governing groundwater flow or solute transport equations in conjunction with optimization techniques, such as linear and quadratic programing, are powerful aquifer management tools. Groundwater management models fall in two general categories: hydraulics or policy evaluation and water allocation. Groundwater hydraulic management models enable the determination of optimal locations and pumping rates of numerous wells under a variety of restrictions placed upon local drawdown, hydraulic gradients, and water production targets. Groundwater policy evaluation and allocation models can be used to study the influence upon regional groundwater use of institutional policies such as taxes and quotas. Furthermore, fairly complex groundwater-surface water allocation problems can be handled using system decomposition and multilevel optimization. Experience from the few real world applications of groundwater optimization-management techniques is summarized. Classified separately are methods for groundwater quality management aimed at optimal waste disposal in the subsurface. This classification is composed of steady state and transient management models that determine disposal patterns in such a way that water quality is protected at supply locations. Classes of research missing from the literature are groundwater quality management models involving nonlinear constraints, models which join groundwater hydraulic and quality simulations with political-economic management considerations, and management models that include parameter uncertainty.

Subsurface water parameters: optimization approach to their determination from remotely sensed water color data.

PubMed

Jain, S C; Miller, J R

1976-04-01

A method, using an optimization scheme, has been developed for the interpretation of spectral albedo (or spectral reflectance) curves obtained from remotely sensed water color data. This method used a two-flow model of the radiation flow and solves for the albedo. Optimization fitting of predicted to observed reflectance data is performed by a quadratic interpolation method for the variables chlorophyll concentration and scattering coefficient. The technique is applied to airborne water color data obtained from Kawartha Lakes, Sargasso Sea, and Nova Scotia coast. The modeled spectral albedo curves are compared to those obtained experimentally, and the computed optimum water parameters are compared to ground truth values. It is shown that the backscattered spectral signal contains information that can be interpreted to give quantitative estimates of the chlorophyll concentration and turbidity in the waters studied.

Box-Behnken design for investigation of microwave-assisted extraction of patchouli oil

NASA Astrophysics Data System (ADS)

Kusuma, Heri Septya; Mahfud, Mahfud

2015-12-01

Microwave-assisted extraction (MAE) technique was employed to extract the essential oil from patchouli (Pogostemon cablin). The optimal conditions for microwave-assisted extraction of patchouli oil were determined by response surface methodology. A Box-Behnken design (BBD) was applied to evaluate the effects of three independent variables (microwave power (A: 400-800 W), plant material to solvent ratio (B: 0.10-0.20 g mL-1) and extraction time (C: 20-60 min)) on the extraction yield of patchouli oil. The correlation analysis of the mathematical-regression model indicated that quadratic polynomial model could be employed to optimize the microwave extraction of patchouli oil. The optimal extraction conditions of patchouli oil was microwave power 634.024 W, plant material to solvent ratio 0.147648 g ml-1 and extraction time 51.6174 min. The maximum patchouli oil yield was 2.80516% under these optimal conditions. Under the extraction condition, the experimental values agreed with the predicted results by analysis of variance. It indicated high fitness of the model used and the success of response surface methodology for optimizing and reflect the expected extraction condition.

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov’s fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization. PMID:28461707

Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

NASA Astrophysics Data System (ADS)

Sobolic, Frantisek M.

Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

Single step optimization of manipulator maneuvers with variable structure control

NASA Technical Reports Server (NTRS)

Chen, N.; Dwyer, T. A. W., III

1987-01-01

One step ahead optimization has been recently proposed for spacecraft attitude maneuvers as well as for robot manipulator maneuvers. Such a technique yields a discrete time control algorithm implementable as a sequence of state-dependent, quadratic programming problems for acceleration optimization. Its sensitivity to model accuracy, for the required inversion of the system dynamics, is shown in this paper to be alleviated by a fast variable structure control correction, acting between the sampling intervals of the slow one step ahead discrete time acceleration command generation algorithm. The slow and fast looping concept chosen follows that recently proposed for optimal aiming strategies with variable structure control. Accelerations required by the VSC correction are reserved during the slow one step ahead command generation so that the ability to overshoot the sliding surface is guaranteed.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Optimal execution in high-frequency trading with Bayesian learning

NASA Astrophysics Data System (ADS)

Du, Bian; Zhu, Hongliang; Zhao, Jingdong

2016-11-01

We consider optimal trading strategies in which traders submit bid and ask quotes to maximize the expected quadratic utility of total terminal wealth in a limit order book. The trader's bid and ask quotes will be changed by the Poisson arrival of market orders. Meanwhile, the trader may update his estimate of other traders' target sizes and directions by Bayesian learning. The solution of optimal execution in the limit order book is a two-step procedure. First, we model an inactive trading with no limit order in the market. The dealer simply holds dollars and shares of stocks until terminal time. Second, he calibrates his bid and ask quotes to the limit order book. The optimal solutions are given by dynamic programming and in fact they are globally optimal. We also give numerical simulation to the value function and optimal quotes at the last part of the article.

Decomposition method for zonal resource allocation problems in telecommunication networks

NASA Astrophysics Data System (ADS)

Konnov, I. V.; Kashuba, A. Yu

2016-11-01

We consider problems of optimal resource allocation in telecommunication networks. We first give an optimization formulation for the case where the network manager aims to distribute some homogeneous resource (bandwidth) among users of one region with quadratic charge and fee functions and present simple and efficient solution methods. Next, we consider a more general problem for a provider of a wireless communication network divided into zones (clusters) with common capacity constraints. We obtain a convex quadratic optimization problem involving capacity and balance constraints. By using the dual Lagrangian method with respect to the capacity constraint, we suggest to reduce the initial problem to a single-dimensional optimization problem, but calculation of the cost function value leads to independent solution of zonal problems, which coincide with the above single region problem. Some results of computational experiments confirm the applicability of the new methods.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

Extended Decentralized Linear-Quadratic-Gaussian Control

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2000-01-01

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

A stochastic model for optimizing composite predictors based on gene expression profiles.

PubMed

Ramanathan, Murali

2003-07-01

This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras

NASA Technical Reports Server (NTRS)

Byrnes, C. I.

1980-01-01

It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov-Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard

2008-02-01

In a linear Gauss-Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov-Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.

Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing

NASA Technical Reports Server (NTRS)

Adams, W. M., Jr.; Tiffany, S. H.

1983-01-01

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Linking normative models of natural tasks to descriptive models of neural response.

PubMed

Jaini, Priyank; Burge, Johannes

2017-10-01

Understanding how nervous systems exploit task-relevant properties of sensory stimuli to perform natural tasks is fundamental to the study of perceptual systems. However, there are few formal methods for determining which stimulus properties are most useful for a given natural task. As a consequence, it is difficult to develop principled models for how to compute task-relevant latent variables from natural signals, and it is difficult to evaluate descriptive models fit to neural response. Accuracy maximization analysis (AMA) is a recently developed Bayesian method for finding the optimal task-specific filters (receptive fields). Here, we introduce AMA-Gauss, a new faster form of AMA that incorporates the assumption that the class-conditional filter responses are Gaussian distributed. Then, we use AMA-Gauss to show that its assumptions are justified for two fundamental visual tasks: retinal speed estimation and binocular disparity estimation. Next, we show that AMA-Gauss has striking formal similarities to popular quadratic models of neural response: the energy model and the generalized quadratic model (GQM). Together, these developments deepen our understanding of why the energy model of neural response have proven useful, improve our ability to evaluate results from subunit model fits to neural data, and should help accelerate psychophysics and neuroscience research with natural stimuli.

Retrieve polarization aberration from image degradation: a new measurement method in DUV lithography

NASA Astrophysics Data System (ADS)

Xiang, Zhongbo; Li, Yanqiu

2017-10-01

Detailed knowledge of polarization aberration (PA) of projection lens in higher-NA DUV lithographic imaging is necessary due to its impact to imaging degradations, and precise measurement of PA is conductive to computational lithography techniques such as RET and OPC. Current in situ measurement method of PA thorough the detection of degradations of aerial images need to do linear approximation and apply the assumption of 3-beam/2-beam interference condition. The former approximation neglects the coupling effect of the PA coefficients, which would significantly influence the accuracy of PA retrieving. The latter assumption restricts the feasible pitch of test masks in higher-NA system, conflicts with the Kirhhoff diffraction model of test mask used in retrieving model, and introduces 3D mask effect as a source of retrieving error. In this paper, a new in situ measurement method of PA is proposed. It establishes the analytical quadratic relation between the PA coefficients and the degradations of aerial images of one-dimensional dense lines in coherent illumination through vector aerial imaging, which does not rely on the assumption of 3-beam/2- beam interference and linear approximation. In this case, the retrieval of PA from image degradation can be convert from the nonlinear system of m-quadratic equations to a multi-objective quadratic optimization problem, and finally be solved by nonlinear least square method. Some preliminary simulation results are given to demonstrate the correctness and accuracy of the new PA retrieving model.

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

PubMed

Liang, X B; Wang, J

2000-01-01

This paper presents a continuous-time recurrent neural-network model for nonlinear optimization with any continuously differentiable objective function and bound constraints. Quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network. The proposed recurrent neural network has the following characteristics. 1) It is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network. If the objective function to be minimized is convex, then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network. 2) The recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region. 3) The recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region. 4) For minimizing any strictly convex quadratic objective function subject to bound constraints, the recurrent neural network is globally exponentially stable for almost any positive network parameters. Simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints.

QSPIN: A High Level Java API for Quantum Computing Experimentation

NASA Technical Reports Server (NTRS)

Barth, Tim

2017-01-01

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

Genetics-based control of a mimo boiler-turbine plant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimeo, R.M.; Lee, K.Y.

1994-12-31

A genetic algorithm is used to develop an optimal controller for a non-linear, multi-input/multi-output boiler-turbine plant. The algorithm is used to train a control system for the plant over a wide operating range in an effort to obtain better performance. The results of the genetic algorithm`s controller designed from the linearized plant model at a nominal operating point. Because the genetic algorithm is well-suited to solving traditionally difficult optimization problems it is found that the algorithm is capable of developing the controller based on input/output information only. This controller achieves a performance comparable to the standard linear quadratic regulator.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coffrin, Carleton James; Hijazi, Hassan L; Van Hentenryck, Pascal R

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% ofmore » the open cases considered, leaving only 8 for future investigation.« less

Issues in the digital implementation of control compensators. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moroney, P.

1979-01-01

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Random vibrations of quadratic damping systems. [optimum damping analysis for automobile suspension system

NASA Technical Reports Server (NTRS)

Sireteanu, T.

1974-01-01

An oscillating system with quadratic damping subjected to white noise excitation is replaced by a nonlinear, statistically equivalent system for which the associated Fokker-Planck equation can be exactly solved. The mean square responses are calculated and the optimum damping coefficient is determined with respect to the minimum mean square acceleration criteria. An application of these results to the optimization of automobile suspension damping is given.

Optimization of cold-adapted lysozyme production from the psychrophilic yeast Debaryomyces hansenii using statistical experimental methods.

PubMed

Wang, Quanfu; Hou, Yanhua; Yan, Peisheng

2012-06-01

Statistical experimental designs were employed to optimize culture conditions for cold-adapted lysozyme production of a psychrophilic yeast Debaryomyces hansenii. In the first step of optimization using Plackett-Burman design (PBD), peptone, glucose, temperature, and NaCl were identified as significant variables that affected lysozyme production, the formula was further optimized using a four factor central composite design (CCD) to understand their interaction and to determine their optimal levels. A quadratic model was developed and validated. Compared to the initial level (18.8 U/mL), the maximum lysozyme production (65.8 U/mL) observed was approximately increased by 3.5-fold under the optimized conditions. Cold-adapted lysozymes production was first optimized using statistical experimental methods. A 3.5-fold enhancement of microbial lysozyme was gained after optimization. Such an improved production will facilitate the application of microbial lysozyme. Thus, D. hansenii lysozyme may be a good and new resource for the industrial production of cold-adapted lysozymes. © 2012 Institute of Food Technologists®

Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach

NASA Astrophysics Data System (ADS)

Pinto, Rafael S.; Saa, Alberto

2015-12-01

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function ωTL ω , where ω stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix. Many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition. A computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.

Optimization of a bundle divertor for FED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hively, L.M.; Rothe, K.E.; Minkoff, M.

1982-01-01

Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations.

Order-Constrained Solutions in K-Means Clustering: Even Better than Being Globally Optimal

ERIC Educational Resources Information Center

Steinley, Douglas; Hubert, Lawrence

2008-01-01

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that…

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Scalability of surrogate-assisted multi-objective optimization of antenna structures exploiting variable-fidelity electromagnetic simulation models

NASA Astrophysics Data System (ADS)

Koziel, Slawomir; Bekasiewicz, Adrian

2016-10-01

Multi-objective optimization of antenna structures is a challenging task owing to the high computational cost of evaluating the design objectives as well as the large number of adjustable parameters. Design speed-up can be achieved by means of surrogate-based optimization techniques. In particular, a combination of variable-fidelity electromagnetic (EM) simulations, design space reduction techniques, response surface approximation models and design refinement methods permits identification of the Pareto-optimal set of designs within a reasonable timeframe. Here, a study concerning the scalability of surrogate-assisted multi-objective antenna design is carried out based on a set of benchmark problems, with the dimensionality of the design space ranging from six to 24 and a CPU cost of the EM antenna model from 10 to 20 min per simulation. Numerical results indicate that the computational overhead of the design process increases more or less quadratically with the number of adjustable geometric parameters of the antenna structure at hand, which is a promising result from the point of view of handling even more complex problems.

Optimization of Photooxidative Removal of Phenazopyridine from Water

NASA Astrophysics Data System (ADS)

Saeid, Soudabeh; Behnajady, Mohammad A.; Tolvanen, Pasi; Salmi, Tapio

2018-05-01

The photooxidative removal of analgesic pharmaceutical compound phenazopyridine (PhP) from aqueous solutions by UV/H2O2 system with a re-circulated photoreactor was investigated. Response surface methodology (RSM) was employed to optimize the effect of operational parameters on the photooxidative removal efficiency. The investigated variables were: the initial PhP and H2O2 concentrations, irradiation time, volume of solution and pH. The analysis of variance (ANOVA) of quadratic model demonstrated that the described model was highly significant. The predicted values of the photooxidative removal efficiency were found to be in a fair agreement with experimental values ( R 2 = 0.9832, adjusted R 2 = 0.9716). The model predicted that the optimal reaction conditions for a maximum removal of PhP (>98%) were: initial PhP concentration less than 23 mg L-1, initial concentration of H2O2 higher than 470 mg L-1, solution volume less than 500 mL, pH close to 2 and irradiation time longer than 6 min.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Application of statistical experimental methodology to optimize bioremediation of n-alkanes in aquatic environment.

PubMed

Zahed, Mohammad Ali; Aziz, Hamidi Abdul; Mohajeri, Leila; Mohajeri, Soraya; Kutty, Shamsul Rahman Mohamed; Isa, Mohamed Hasnain

2010-12-15

Response surface methodology (RSM) was employed to optimize nitrogen and phosphorus concentrations for removal of n-alkanes from crude oil contaminated seawater samples in batch reactors. Erlenmeyer flasks were used as bioreactors; each containing 250 mL dispersed crude oil contaminated seawater, indigenous acclimatized microorganism and different amounts of nitrogen and phosphorus based on central composite design (CCD). Samples were extracted and analyzed according to US-EPA protocols using a gas chromatograph. During 28 days of bioremediation, a maximum of 95% total aliphatic hydrocarbons removal was observed. The obtained Model F-value of 267.73 and probability F<0.0001 implied the model was significant. Numerical condition optimization via a quadratic model, predicted 98% n-alkanes removal for a 20-day laboratory bioremediation trial using nitrogen and phosphorus concentrations of 13.62 and 1.39 mg/L, respectively. In actual experiments, 95% removal was observed under these conditions. Copyright © 2010 Elsevier B.V. All rights reserved.

Optimization of Manganese Reduction in Biotreated POME onto 3A Molecular Sieve and Clinoptilolite Zeolites.

PubMed

Jami, Mohammed S; Rosli, Nurul-Shafiqah; Amosa, Mutiu K

2016-06-01

Availability of quality-certified water is pertinent to the production of food and pharmaceutical products. Adverse effects of manganese content of water on the corrosion of vessels and reactors necessitate that process water is scrutinized for allowable concentration levels before being applied in the production processes. In this research, optimization of the adsorption process conditions germane to the removal of manganese from biotreated palm oil mill effluent (BPOME) using zeolite 3A subsequent to a comparative adsorption with clinoptilolite was studied. A face-centered central composite design (FCCCD) of the response surface methodology (RSM) was adopted for the study. Analysis of variance (ANOVA) for response surface quadratic model revealed that the model was significant with dosage and agitation speed connoting the main significant process factors for the optimization. R(2) of 0.9478 yielded by the model was in agreement with predicted R(2). Langmuir and pseudo-second-order suggest the adsorption mechanism involved monolayer adsorption and cation exchanging.

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts. [(computerized simulation)

NASA Technical Reports Server (NTRS)

Seldner, K.

1976-01-01

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

Modeling of Mean-VaR portfolio optimization by risk tolerance when the utility function is quadratic

NASA Astrophysics Data System (ADS)

Sukono, Sidi, Pramono; Bon, Abdul Talib bin; Supian, Sudradjat

2017-03-01

The problems of investing in financial assets are to choose a combination of weighting a portfolio can be maximized return expectations and minimizing the risk. This paper discusses the modeling of Mean-VaR portfolio optimization by risk tolerance, when square-shaped utility functions. It is assumed that the asset return has a certain distribution, and the risk of the portfolio is measured using the Value-at-Risk (VaR). So, the process of optimization of the portfolio is done based on the model of Mean-VaR portfolio optimization model for the Mean-VaR done using matrix algebra approach, and the Lagrange multiplier method, as well as Khun-Tucker. The results of the modeling portfolio optimization is in the form of a weighting vector equations depends on the vector mean return vector assets, identities, and matrix covariance between return of assets, as well as a factor in risk tolerance. As an illustration of numeric, analyzed five shares traded on the stock market in Indonesia. Based on analysis of five stocks return data gained the vector of weight composition and graphics of efficient surface of portfolio. Vector composition weighting weights and efficient surface charts can be used as a guide for investors in decisions to invest.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Study of motion of optimal bodies in the soil of grid method

NASA Astrophysics Data System (ADS)

Kotov, V. L.; Linnik, E. Yu

2016-11-01

The paper presents a method of calculating the optimum forms in axisymmetric numerical method based on the Godunov and models elastoplastic soil vedium Grigoryan. Solved two problems in a certain definition of generetrix rotation of the body of a given length and radius of the base, having a minimum impedance and maximum penetration depth. Numerical calculations are carried out by a modified method of local variations, which allows to significantly reduce the number of operations at different representations of generetrix. Significantly simplify the process of searching for optimal body allows the use of a quadratic model of local interaction for preliminary assessments. It is noted the qualitative similarity of the process of convergence of numerical calculations for solving the optimization problem based on local interaction model and within the of continuum mechanics. A comparison of the optimal bodies with absolutely optimal bodies possessing the minimum resistance of penetration below which is impossible to achieve under given constraints on the geometry. It is shown that the conical striker with a variable vertex angle, which equal to the angle of the solution is absolutely optimal body of minimum resistance of penetration for each value of the velocity of implementation will have a final depth of penetration is only 12% more than the traditional body absolutely optimal maximum depth penetration.

Ethanol mediated As(III) adsorption onto Zn-loaded pinecone biochar: Experimental investigation, modeling, and optimization using hybrid artificial neural network-genetic algorithm approach.

PubMed

Zafar, Mohd; Van Vinh, N; Behera, Shishir Kumar; Park, Hung-Suck

2017-04-01

Organic matters (OMs) and their oxidization products often influence the fate and transport of heavy metals in the subsurface aqueous systems through interaction with the mineral surfaces. This study investigates the ethanol (EtOH)-mediated As(III) adsorption onto Zn-loaded pinecone (PC) biochar through batch experiments conducted under Box-Behnken design. The effect of EtOH on As(III) adsorption mechanism was quantitatively elucidated by fitting the experimental data using artificial neural network and quadratic modeling approaches. The quadratic model could describe the limiting nature of EtOH and pH on As(III) adsorption, whereas neural network revealed the stronger influence of EtOH (64.5%) followed by pH (20.75%) and As(III) concentration (14.75%) on the adsorption phenomena. Besides, the interaction among process variables indicated that EtOH enhances As(III) adsorption over a pH range of 2 to 7, possibly due to facilitation of ligand-metal(Zn) binding complexation mechanism. Eventually, hybrid response surface model-genetic algorithm (RSM-GA) approach predicted a better optimal solution than RSM, i.e., the adsorptive removal of As(III) (10.47μg/g) is facilitated at 30.22mg C/L of EtOH with initial As(III) concentration of 196.77μg/L at pH5.8. The implication of this investigation might help in understanding the application of biochar for removal of various As(III) species in the presence of OM. Copyright © 2016. Published by Elsevier B.V.

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

NASA Astrophysics Data System (ADS)

Yang, Peng; Peng, Yongfei; Ye, Bin; Miao, Lixin

2017-09-01

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics' performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.

Approximate optimal tracking control for near-surface AUVs with wave disturbances

NASA Astrophysics Data System (ADS)

Yang, Qing; Su, Hao; Tang, Gongyou

2016-10-01

This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Combined control-structure optimization

NASA Technical Reports Server (NTRS)

Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.

1989-01-01

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

[Optimization of ultrasonic-assisted extraction of total flavonoids from leaves of the Artocarpus heterophyllus by response surface methodology].

PubMed

Wang, Hong-wu; Liu, Yan-qing; Wang, Yuan-hong

2011-07-01

To investigate the ultrasonic-assisted extract on of total flavonoids from leaves of the Artocarpus heterophyllus. Investigated the effects of ethanol concentration, extraction time, and liquid-solid ratio on flavonoids yield. A 17-run response surface design involving three factors at three levels was generated by the Design-Expert software and experimental data obtained were subjected to quadratic regression analysis to create a mathematical model describing flavonoids extraction. The optimum ultrasonic assisted extraction conditions were: ethanol volume fraction 69.4% and liquid-solid ratio of 22.6:1 for 32 min. Under these optimized conditions, the yield of flavonoids was 7.55 mg/g. The Box-Behnken design and response surface analysis can well optimize the ultrasonic-assisted extraction of total flavonoids from Artocarpus heterophyllus.

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

Optimal helicopter trajectory planning for terrain following flight

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

Helicopters operating in high threat areas have to fly close to the earth surface to minimize the risk of being detected by the adversaries. Techniques are presented for low altitude helicopter trajectory planning. These methods are based on optimal control theory and appear to be implementable onboard in realtime. Second order necessary conditions are obtained to provide a criterion for finding the optimal trajectory when more than one extremal passes through a given point. A second trajectory planning method incorporating a quadratic performance index is also discussed. Trajectory planning problem is formulated as a differential game. The objective is to synthesize optimal trajectories in the presence of an actively maneuvering adversary. Numerical methods for obtaining solutions to these problems are outlined. As an alternative to numerical method, feedback linearizing transformations are combined with the linear quadratic game results to synthesize explicit nonlinear feedback strategies for helicopter pursuit-evasion. Some of the trajectories generated from this research are evaluated on a six-degree-of-freedom helicopter simulation incorporating an advanced autopilot. The optimal trajectory planning methods presented are also useful for autonomous land vehicle guidance.

Reliable numerical computation in an optimal output-feedback design

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, Richard D.; Grodsinsky, Carlos M.; Allaire, Paul E.; Lewis, David W.; Knospe, Carl R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platform. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) exp 4. Low frequency accelerations are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.; Knospe, C. R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Advanced rotorcraft control using parameter optimization

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

Optimization of CMCase production from sorghum straw by Aspergillus terreus SUK-1 under solid substrate fermentation using response surface methodology

NASA Astrophysics Data System (ADS)

Tibin, El Mubarak Musa; Al-Shorgani, Najeeb Kaid Naseer; Abuelhassan, Nawal Noureldaim; Hamid, Aidil Abdul; Kalil, Mohd Sahaid; Yusoff, Wan Mohtar Wan

2013-11-01

The cellulase production using sorghum straw as substrate by fungal culture of Aspergillus terreus SUK-1 was investigated in solid substrate fermentation (SSF). The optimum CMCase was achieved by testing most effective fermentation parameters which were: incubation temperature, pH and moisture content using Response Surface Methodology (RSM) based on Central Composite Design (CCD). The carboxymethyl cellulase activity (CMCase) was measured as the defining factor. The results were analysed by analysis of variance (ANOVA) and the regression quadratic model was obtained. The model was found to be significant (p<0.05) and the effect of temperature (25-40°C) and pH (4-7) was found to be not significant on CMCase activity whereas the moisture content was significant in the SSF conditions employed. The high yield of predicted CMCase activity (0.2 U/ml) was obtained under the optimized conditions (temperature 40 □C, pH 5.4 and moisture content of 80%). The model was validated by applying the optimized conditions and it was found that the model was valid.

Radiotherapy Dose Fractionation under Parameter Uncertainty

NASA Astrophysics Data System (ADS)

Davison, Matt; Kim, Daero; Keller, Harald

2011-11-01

In radiotherapy, radiation is directed to damage a tumor while avoiding surrounding healthy tissue. Tradeoffs ensue because dose cannot be exactly shaped to the tumor. It is particularly important to ensure that sensitive biological structures near the tumor are not damaged more than a certain amount. Biological tissue is known to have a nonlinear response to incident radiation. The linear quadratic dose response model, which requires the specification of two clinically and experimentally observed response coefficients, is commonly used to model this effect. This model yields an optimization problem giving two different types of optimal dose sequences (fractionation schedules). Which fractionation schedule is preferred depends on the response coefficients. These coefficients are uncertainly known and may differ from patient to patient. Because of this not only the expected outcomes but also the uncertainty around these outcomes are important, and it might not be prudent to select the strategy with the best expected outcome.

First-Principles-Driven Model-Based Optimal Control of the Current Profile in NSTX-U

NASA Astrophysics Data System (ADS)

Ilhan, Zeki; Barton, Justin; Wehner, William; Schuster, Eugenio; Gates, David; Gerhardt, Stefan; Kolemen, Egemen; Menard, Jonathan

2014-10-01

Regulation in time of the toroidal current profile is one of the main challenges toward the realization of the next-step operational goals for NSTX-U. A nonlinear, control-oriented, physics-based model describing the temporal evolution of the current profile is obtained by combining the magnetic diffusion equation with empirical correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives. In this work, the proposed model is embedded into the control design process to synthesize a time-variant, linear-quadratic-integral, optimal controller capable of regulating the safety factor profile around a desired target profile while rejecting disturbances. Neutral beam injectors and the total plasma current are used as actuators to shape the current profile. The effectiveness of the proposed controller in regulating the safety factor profile in NSTX-U is demonstrated via closed-loop predictive simulations carried out in PTRANSP. Supported by PPPL.

LQG control of a deformable mirror adaptive optics system with time-delayed measurements

NASA Astrophysics Data System (ADS)

Anderson, David J.

1991-12-01

This thesis proposes a linear quadratic Gaussian (LQG) control law for a ground-based deformable mirror adaptive optics system. The incoming image wavefront is distorted, primarily in phase, due to the turbulent effects of the earth's atmosphere. The adaptive optics system attempts to compensate for the distortion with a deformable mirror. A Hartman wavefront sensor measures the degree of distortion in the image wavefront. The measurements are input to a Kalman filter which estimates the system states. The state estimates are processed by a linear quadratic regulator which generates the appropriate control voltages to apply to the deformable mirror actuators. The dynamics model for the atmospheric phase distortion consists of 14 Zernike coefficient states; each modeled as a first-order linear time-invariant shaping filter driven by zero-mean white Gaussian noise. The dynamics of the deformable mirror are also model as 14 Zernike coefficients with first-order deterministic dynamics. A significant reduction in total wavefront phase distortion is achieved in the presence of time-delayed measurements. Wavefront sensor sampling rate is the major factor limiting system performance. The Multimode Simulation for Optimal Filter Evaluation (MSOFE) software is the performance evaluation tool of choice for this research.

Optimizing chemical conditioning for odour removal of undigested sewage sludge in drying processes.

PubMed

Vega, Esther; Monclús, Hèctor; Gonzalez-Olmos, Rafael; Martin, Maria J

2015-03-01

Emission of odours during the thermal drying in sludge handling processes is one of the main sources of odour problems in wastewater treatment plants. The objective of this work was to assess the use of the response surface methodology as a technique to optimize the chemical conditioning process of undigested sewage sludges, in order to improve the dewaterability, and to reduce the odour emissions during the thermal drying of the sludge. Synergistic effects between inorganic conditioners (iron chloride and calcium oxide) were observed in terms of sulphur emissions and odour reduction. The developed quadratic models indicated that optimizing the conditioners dosage is possible to increase a 70% the dewaterability, reducing a 50% and 54% the emission of odour and volatile sulphur compounds respectively. The optimization of the conditioning process was validated experimentally. Copyright © 2014 Elsevier Ltd. All rights reserved.

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

2014-05-01

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

Application of quadratic optimization to supersonic inlet control

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Zeller, J. R.

1971-01-01

The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Yunbin, E-mail: zhaoyy@maths.bham.ac.u

2010-12-15

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the conditionmore » number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.« less

Process optimization for osmo-dehydrated carambola (Averrhoa carambola L) slices and its storage studies.

PubMed

Roopa, N; Chauhan, O P; Raju, P S; Das Gupta, D K; Singh, R K R; Bawa, A S

2014-10-01

An osmotic-dehydration process protocol for Carambola (Averrhoacarambola L.,), an exotic star shaped tropical fruit, was developed. The process was optimized using Response Surface Methodology (RSM) following Central Composite Rotatable Design (CCRD). The experimental variables selected for the optimization were soak solution concentration (°Brix), soaking temperature (°C) and soaking time (min) with 6 experiments at central point. The effect of process variables was studied on solid gain and water loss during osmotic dehydration process. The data obtained were analyzed employing multiple regression technique to generate suitable mathematical models. Quadratic models were found to fit well (R(2), 95.58 - 98.64 %) in describing the effect of variables on the responses studied. The optimized levels of the process variables were achieved at 70°Brix, 48 °C and 144 min for soak solution concentration, soaking temperature and soaking time, respectively. The predicted and experimental results at optimized levels of variables showed high correlation. The osmo-dehydrated product prepared at optimized conditions showed a shelf-life of 10, 8 and 6 months at 5 °C, ambient (30 ± 2 °C) and 37 °C, respectively.

Rotor design optimization using a free wake analysis

NASA Technical Reports Server (NTRS)

Quackenbush, Todd R.; Boschitsch, Alexander H.; Wachspress, Daniel A.; Chua, Kiat

1993-01-01

The aim of this effort was to develop a comprehensive performance optimization capability for tiltrotor and helicopter blades. The analysis incorporates the validated EHPIC (Evaluation of Hover Performance using Influence Coefficients) model of helicopter rotor aerodynamics within a general linear/quadratic programming algorithm that allows optimization using a variety of objective functions involving the performance. The resulting computer code, EHPIC/HERO (HElicopter Rotor Optimization), improves upon several features of the previous EHPIC performance model and allows optimization utilizing a wide spectrum of design variables, including twist, chord, anhedral, and sweep. The new analysis supports optimization of a variety of objective functions, including weighted measures of rotor thrust, power, and propulsive efficiency. The fundamental strength of the approach is that an efficient search for improved versions of the baseline design can be carried out while retaining the demonstrated accuracy inherent in the EHPIC free wake/vortex lattice performance analysis. Sample problems are described that demonstrate the success of this approach for several representative rotor configurations in hover and axial flight. Features that were introduced to convert earlier demonstration versions of this analysis into a generally applicable tool for researchers and designers is also discussed.

Optimising reversed-phase liquid chromatographic separation of an acidic mixture on a monolithic stationary phase with the aid of response surface methodology and experimental design.

PubMed

Wang, Y; Harrison, M; Clark, B J

2006-02-10

An optimization strategy for the separation of an acidic mixture by employing a monolithic stationary phase is presented, with the aid of experimental design and response surface methodology (RSM). An orthogonal array design (OAD) OA(16) (2(15)) was used to choose the significant parameters for the optimization. The significant factors were optimized by using a central composite design (CCD) and the quadratic models between the dependent and the independent parameters were built. The mathematical models were tested on a number of simulated data set and had a coefficient of R(2) > 0.97 (n = 16). On applying the optimization strategy, the factor effects were visualized as three-dimensional (3D) response surfaces and contour plots. The optimal condition was achieved in less than 40 min by using the monolithic packing with the mobile phase of methanol/20 mM phosphate buffer pH 2.7 (25.5/74.5, v/v). The method showed good agreement between the experimental data and predictive value throughout the studied parameter space and were suitable for optimization studies on the monolithic stationary phase for acidic compounds.

Optimal estimation of large structure model errors. [in Space Shuttle controller design

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1979-01-01

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Planning Under Uncertainty: Methods and Applications

DTIC Science & Technology

2010-06-09

begun research into fundamental algorithms for optimization and re?optimization of continuous optimization problems (such as linear and quadratic... algorithm yields a 14.3% improvement over the original design while saving 68.2 % of the simulation evaluations compared to standard sample-path...They provide tools for building and justifying computational algorithms for such problems. Year. 2010 Month: 03 Final Research under this grant

Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously

NASA Astrophysics Data System (ADS)

Long, Kai; Wang, Xuan; Gu, Xianguang

2017-09-01

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

Neural Network and Response Surface Methodology for Rocket Engine Component Optimization

NASA Technical Reports Server (NTRS)

Vaidyanathan, Rajkumar; Papita, Nilay; Shyy, Wei; Tucker, P. Kevin; Griffin, Lisa W.; Haftka, Raphael; Fitz-Coy, Norman; McConnaughey, Helen (Technical Monitor)

2000-01-01

The goal of this work is to compare the performance of response surface methodology (RSM) and two types of neural networks (NN) to aid preliminary design of two rocket engine components. A data set of 45 training points and 20 test points obtained from a semi-empirical model based on three design variables is used for a shear coaxial injector element. Data for supersonic turbine design is based on six design variables, 76 training, data and 18 test data obtained from simplified aerodynamic analysis. Several RS and NN are first constructed using the training data. The test data are then employed to select the best RS or NN. Quadratic and cubic response surfaces. radial basis neural network (RBNN) and back-propagation neural network (BPNN) are compared. Two-layered RBNN are generated using two different training algorithms, namely solverbe and solverb. A two layered BPNN is generated with Tan-Sigmoid transfer function. Various issues related to the training of the neural networks are addressed including number of neurons, error goals, spread constants and the accuracy of different models in representing the design space. A search for the optimum design is carried out using a standard gradient-based optimization algorithm over the response surfaces represented by the polynomials and trained neural networks. Usually a cubic polynominal performs better than the quadratic polynomial but exceptions have been noticed. Among the NN choices, the RBNN designed using solverb yields more consistent performance for both engine components considered. The training of RBNN is easier as it requires linear regression. This coupled with the consistency in performance promise the possibility of it being used as an optimization strategy for engineering design problems.

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

An integrated Taguchi and response surface methodological approach for the optimization of an HPLC method to determine glimepiride in a supersaturatable self-nanoemulsifying formulation.

PubMed

Dash, Rajendra Narayan; Mohammed, Habibuddin; Humaira, Touseef

2016-01-01

We studied the application of Taguchi orthogonal array (TOA) design during the development of an isocratic stability indicating HPLC method for glimepiride as per TOA design; twenty-seven experiments were conducted by varying six chromatographic factors. Percentage of organic phase was the most significant (p < 0.001) on retention time, while buffer pH had the most significant (p < 0.001) effect on tailing factor and theoretical plates. TOA design has shortcoming, which identifies the only linear effect, while ignoring the quadratic and interaction effects. Hence, a response surface model for each response was created including the linear, quadratic and interaction terms. The developed models for each response found to be well predictive bearing an acceptable adjusted correlation coefficient (0.9152 for retention time, 0.8985 for tailing factor and 0.8679 for theoretical plates). The models were found to be significant (p < 0.001) having a high F value for each response (15.76 for retention time, 13.12 for tailing factor and 9.99 for theoretical plates). The optimal chromatographic condition uses acetonitrile - potassium dihydrogen phosphate (pH 4.0; 30 mM) (50:50, v/v) as the mobile phase. The temperature, flow rate and injection volume were selected as 35 ± 2 °C, 1.0 mL min(-1) and 20 μL respectively. The method was validated as per ICH guidelines and was found to be specific for analyzing glimepiride from a novel supersaturatable self-nanoemulsifying formulation.

Estimation of the standardized ileal digestible valine to lysine ratio required for 25- to 120-kilogram pigs fed low crude protein diets supplemented with crystalline amino acids.

PubMed

Liu, X T; Ma, W F; Zeng, X F; Xie, C Y; Thacker, P A; Htoo, J K; Qiao, S Y

2015-10-01

Four 28-d experiments were conducted to determine the standardized ileal digestible (SID) valine (Val) to lysine (Lys) ratio required for 26- to 46- (Exp. 1), 49- to 70- (Exp. 2), 71- to 92- (Exp. 3), and 94- to 119-kg (Exp. 4) pigs fed low CP diets supplemented with crystalline AA. The first 3 experiments utilized 150 pigs (Duroc × Landrace × Large White), while Exp. 4 utilized 90 finishing pigs. Pigs in all 4 experiments were randomly allocated to 1 of 5 diets with 6 pens per treatment (3 pens of barrows and 3 pens of gilts) and 5 pigs per pen for the first 3 experiments and 3 pigs per pen for Exp. 4. Diets for all experiments were formulated to contain SID Val to Lys ratios of 0.55, 0.60, 0.65, 0.70, or 0.75. In Exp. 1 (26 to 46 kg), ADG increased (linear, = 0.039; quadratic, = 0.042) with an increasing dietary Val:Lys ratio. The SID Val:Lys ratio to maximize ADG was 0.62 using a linear broken-line model and 0.71 using a quadratic model. In Exp. 2 (49 to 70 kg), ADG increased (linear, = 0.021; quadratic, = 0.042) as the SID Val:Lys ratio increased. G:F improved (linear, = 0.039) and serum urea nitrogen (SUN) decreased (linear, = 0.021; quadratic, = 0.024) with an increased SID Val:Lys ratio. The SID Val:Lys ratios to maximize ADG as well as to minimize SUN levels were 0.67 and 0.65, respectively, using a linear broken-line model and 0.72 and 0.71, respectively, using a quadratic model. In Exp. 3 (71 to 92 kg), ADG increased (linear, = 0.007; quadratic, = 0.022) and SUN decreased (linear, = 0.011; quadratic, = 0.034) as the dietary SID Val:Lys ratio increased. The SID Val:Lys ratios to maximize ADG as well as to minimize SUN levels were 0.67 and 0.67, respectively, using a linear broken-line model and 0.72 and 0.74, respectively, using a quadratic model. In Exp. 4 (94 to 119 kg), ADG increased (linear, = 0.041) and G:F was improved (linear, = 0.004; quadratic, = 0.005) as the dietary SID Val:Lys ratio increased. The SID Val:Lys ratio to maximize G:F was 0.68 using a linear broken-line model and 0.72 using a quadratic model. Carcass traits and muscle quality were not influenced by SID Val:Lys ratio. In conclusion, the dietary SID Val:Lys ratios required for 26- to 46-, 49- to 70-, 71- to 92-, and 94- to 119-kg pigs were estimated to be 0.62, 0.66, 0.67, and 0.68, respectively, using a linear broken-line model and 0.71, 0.72, 0.73, and 0.72, respectively, using a quadratic model.

A toolbox model of evolution of metabolic pathways on networks of arbitrary topology.

PubMed

Pang, Tin Yau; Maslov, Sergei

2011-05-01

In prokaryotic genomes the number of transcriptional regulators is known to be proportional to the square of the total number of protein-coding genes. A toolbox model of evolution was recently proposed to explain this empirical scaling for metabolic enzymes and their regulators. According to its rules, the metabolic network of an organism evolves by horizontal transfer of pathways from other species. These pathways are part of a larger "universal" network formed by the union of all species-specific networks. It remained to be understood, however, how the topological properties of this universal network influence the scaling law of functional content of genomes in the toolbox model. Here we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We prove that critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for quadratic scaling. We further generalize the rules of the model to incorporate reactions with multiple substrates/products as well as branched and cyclic metabolic pathways. To achieve its metabolic tasks, the new model employs evolutionary optimized pathways with minimal number of reactions. Numerical simulations of this realistic model on the universal network of all reactions in the KEGG database produced approximately quadratic scaling between the number of regulated pathways and the size of the metabolic network. To quantify the geometrical structure of individual pathways, we investigated the relationship between their number of reactions, byproducts, intermediate, and feedback metabolites. Our results validate and explain the ubiquitous appearance of the quadratic scaling for a broad spectrum of topologies of underlying universal metabolic networks. They also demonstrate why, in spite of "small-world" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.

Dynamical properties of a prey-predator-scavenger model with quadratic harvesting

NASA Astrophysics Data System (ADS)

Gupta, R. P.; Chandra, Peeyush

2017-08-01

In this paper, we propose and analyze an extended model for the prey-predator-scavenger in presence of harvesting to study the effects of harvesting of predator as well as scavenger. The positivity, boundedness and persistence conditions are derived for the proposed model. The model undergoes a Hopf-bifurcation around the co-existing equilibrium point. It is also observed that the model is capable of exhibiting period doubling route to chaos. It is pointed out that a suitable amount of harvesting of predator can control the chaotic dynamics and make the system stable. An extensive numerical simulation is performed to validate the analytic findings. The associated control problem for the proposed model has been analyzed for optimal harvesting.

Active distribution network planning considering linearized system loss

NASA Astrophysics Data System (ADS)

Li, Xiao; Wang, Mingqiang; Xu, Hao

2018-02-01

In this paper, various distribution network planning techniques with DGs are reviewed, and a new distribution network planning method is proposed. It assumes that the location of DGs and the topology of the network are fixed. The proposed model optimizes the capacities of DG and the optimal distribution line capacity simultaneously by a cost/benefit analysis and the benefit is quantified by the reduction of the expected interruption cost. Besides, the network loss is explicitly analyzed in the paper. For simplicity, the network loss is appropriately simplified as a quadratic function of difference of voltage phase angle. Then it is further piecewise linearized. In this paper, a piecewise linearization technique with different segment lengths is proposed. To validate its effectiveness and superiority, the proposed distribution network planning model with elaborate linearization technique is tested on the IEEE 33-bus distribution network system.

Optimization Models for Scheduling of Jobs

PubMed Central

Indika, S. H. Sathish; Shier, Douglas R.

2006-01-01

This work is motivated by a particular scheduling problem that is faced by logistics centers that perform aircraft maintenance and modification. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). Specifically, a number of jobs have already been scheduled for processing at the facility; the starting times, durations, and work station assignments for these jobs are assumed to be known. We are interested in how best to schedule a number of new jobs that the facility will be processing in the near future. We first develop a mixed integer quadratic programming model (MIQP) for this problem. Since the exact solution of this MIQP formulation is time consuming, we develop a heuristic procedure, based on existing bin packing techniques. This heuristic is further enhanced by application of certain local optimality conditions. PMID:27274921

Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch.

PubMed

Bache, Morten; Nielsen, Hanne; Laegsgaard, Jesper; Bang, Ole

2006-06-01

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

DOE PAGES

Li, Mingjie; Zhou, Ping; Wang, Hong; ...

2017-09-19

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refiningmore » system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.« less

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Mingjie; Zhou, Ping; Wang, Hong

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refiningmore » system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.« less

A new approach to synthesis of benzyl cinnamate: Optimization by response surface methodology.

PubMed

Zhang, Dong-Hao; Zhang, Jiang-Yan; Che, Wen-Cai; Wang, Yun

2016-09-01

In this work, the new approach to synthesis of benzyl cinnamate by enzymatic esterification of cinnamic acid with benzyl alcohol is optimized by response surface methodology. The effects of various reaction conditions, including temperature, enzyme loading, substrate molar ratio of benzyl alcohol to cinnamic acid, and reaction time, are investigated. A 5-level-4-factor central composite design is employed to search for the optimal yield of benzyl cinnamate. A quadratic polynomial regression model is used to analyze the experimental data at a 95% confidence level (P<0.05). The coefficient of determination of this model is found to be 0.9851. Three sets of optimum reaction conditions are established, and the verified experimental trials are performed for validating the optimum points. Under the optimum conditions (40°C, 31mg/mL enzyme loading, 2.6:1 molar ratio, 27h), the yield reaches 97.7%, which provides an efficient processes for industrial production of benzyl cinnamate. Copyright © 2016 Elsevier Ltd. All rights reserved.

Topology optimization of embedded piezoelectric actuators considering control spillover effects

NASA Astrophysics Data System (ADS)

Gonçalves, Juliano F.; De Leon, Daniel M.; Perondi, Eduardo A.

2017-02-01

This article addresses the problem of active structural vibration control by means of embedded piezoelectric actuators. The topology optimization method using the solid isotropic material with penalization (SIMP) approach is employed in this work to find the optimum design of actuators taken into account the control spillover effects. A coupled finite element model of the structure is derived assuming a two-phase material and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The undesirable effects of the feedback control on the residual modes are limited by including a spillover constraint term containing the residual controllability Gramian eigenvalues. The optimization of the shape and placement of the conventionally embedded piezoelectric actuators are performed using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the additional constraint.

Optimization of Hyaluronidase Inhibition Activity from Prunus davidiana (Carriere) Franch Fruit Extract Fermented by its Isolated Bacillus subtilis Strain SPF4211.

PubMed

Kim, Won-Baek; Park, So Hae; Koo, Kyoung Yoon; Kim, Bo Ram; Kim, Minji; Lee, Heeseob

2016-09-28

Strain SPF4211, having hyaluronidase (HAase) inhibition activity, was isolated from P. davidiana (Carriere) Franch fruit (PrDF) sugar extract. The phenotypic and biochemical properties based on 16S rDNA sequencing and an API 50 CHB kit suggested that the organism was B. subtilis. To optimize the HAase inhibition activity of PrDF extract by fermentation of strain SPF4211, a central composite design (CCD) was introduced based on three variables: concentration of PrDF extract (X₁: 1-5%), amount of starter culture (X₂: 1-5%), and fermentation time (X₃: 0-7 days). The experimental data were fitted with quadratic regression equations, and the accuracy of the equations was analyzed by ANOVA. The statistical model predicted the highest HAase inhibition activity of 37.936% under the optimal conditions of X₁ = 1%, X₂ = 2.53%, and X₃ = 7 days. The optimized conditions were validated by observation of an actual HAase inhibition activity of 38.367% from extract of PrDF fermented by SPF4211. These results agree well with the predicted model value.

Statistical Optimization of Reactive Plasma Cladding to Synthesize a WC-Reinforced Fe-Based Alloy Coating

NASA Astrophysics Data System (ADS)

Wang, Miqi; Zhou, Zehua; Wu, Lintao; Ding, Ying; Xu, Feilong; Wang, Zehua

2018-04-01

A new compound Fe-W-C powder for reactive plasma cladding was fabricated by precursor carbonization process using sucrose as a precursor. The application of quadratic general rotary unitized design was highlighted to develop a mathematical model to predict and accomplish the desired surface hardness of plasma-cladded coating. The microstructure and microhardness of the coating with optimal parameters were also investigated. According to the developed empirical model, the optimal process parameters were determined as follows: 1.4 for C/W atomic ratio, 20 wt.% for W content, 130 A for scanning current and 100 mm/min (1.67 mm/s) for scanning rate. The confidence level of the model was 99% according to the results of the F-test and lack-of-fit test. Microstructural study showed that the dendritic structure was comprised of a mechanical mixture of α-Fe and carbides, while the interdendritic structure was a eutectic of α-Fe and carbides in the composite coating with optimal parameters. WC phase generation can be confirmed from the XRD pattern. Due to good preparation parameters, the average microhardness of cladded coating can reach 1120 HV0.1, which was four times the substrate microhardness.

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics.

PubMed

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-08-01

RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of [Formula: see text]. Subsequently, numerous faster 'Sankoff-style' approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity ([Formula: see text] quartic time). Breaking this barrier, we introduce the novel Sankoff-style algorithm 'sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)', which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff's original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. © The Author 2015. Published by Oxford University Press.

Central composite rotatable design for investigation of microwave-assisted extraction of ginger (Zingiber officinale)

NASA Astrophysics Data System (ADS)

Fadzilah, R. Hanum; Sobhana, B. Arianto; Mahfud, M.

2015-12-01

Microwave-assisted extraction technique was employed to extract essential oil from ginger. The optimal condition for microwave assisted extraction of ginger were determined by resposnse surface methodology. A central composite rotatable design was applied to evaluate the effects of three independent variables. The variables is were microwave power 400 - 800W as X1, feed solvent ratio of 0.33 -0.467 as X2 and feed size 1 cm, 0.25 cm and less than 0.2 cm as X3. The correlation analysis of mathematical modelling indicated that quadratic polynomial could be employed to optimize microwave assisted extraction of ginger. The optimal conditions to obtain highest yield of essential oil were : microwave power 597,163 W : feed solvent ratio and size of feed less than 0.2 cm.

Demonstration and Validation of the Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long-Term Monitoring (LTM) of Groundwater at Military and Government Sites

DTIC Science & Technology

2010-08-01

Long - Term Monitoring (LTM) of Groundwater at Military and...Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long - Term Monitoring (LTM) of Groundwater at Military and Government Sites 5a. CONTRACT NUMBER...Council LTM long - term monitoring LTMO long - term monitoring optimization LWQR locally weighted quadratic regression LZ Lower Zone MCL

Quadratic Programming for Allocating Control Effort

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2005-01-01

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; den Hertog, Dick; Siem, Alex Y. D.; Kaanders, Johannes H. A. M.; Huizenga, Henk

2008-11-01

Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.

Ant colony optimization for solving university facility layout problem

NASA Astrophysics Data System (ADS)

Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

2013-04-01

Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

NASA Astrophysics Data System (ADS)

Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

2016-03-01

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

Central composite rotatable design for investigation of microwave-assisted extraction of okra pod hydrocolloid.

PubMed

Samavati, Vahid

2013-10-01

Microwave-assisted extraction (MAE) technique was employed to extract the hydrocolloid from okra pods (OPH). The optimal conditions for microwave-assisted extraction of OPH were determined by response surface methodology. A central composite rotatable design (CCRD) was applied to evaluate the effects of three independent variables (microwave power (X1: 100-500 W), extraction time (X2: 30-90 min), and extraction temperature (X3: 40-90 °C)) on the extraction yield of OPH. The correlation analysis of the mathematical-regression model indicated that quadratic polynomial model could be employed to optimize the microwave extraction of OPH. The optimal conditions to obtain the highest recovery of OPH (14.911±0.27%) were as follows: microwave power, 395.56 W; extraction time, 67.11 min and extraction temperature, 73.33 °C. Under these optimal conditions, the experimental values agreed with the predicted ones by analysis of variance. It indicated high fitness of the model used and the success of response surface methodology for optimizing OPH extraction. After method development, the DPPH radical scavenging activity of the OPH was evaluated. MAE showed obvious advantages in terms of high extraction efficiency and radical scavenging activity of extract within the shorter extraction time. Copyright © 2013 Elsevier B.V. All rights reserved.

Swimming of a sphere in a viscous incompressible fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.; Jones, R. B.

2017-08-01

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1994-01-01

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1994-01-01

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Self-Efficacy and Interest: Experimental Studies of Optimal Incompetence.

ERIC Educational Resources Information Center

Silvia, Paul J.

2003-01-01

To test the optimal incompetence hypothesis (high self-efficacy lowers task interest), 30 subjects rated interest, perceived difficulty, and confidence of success in different tasks. In study 2, 33 subjects completed a dart-game task in easy, moderate, and difficult conditions. In both, interest was a quadratic function of self-efficacy,…

The trust-region self-consistent field method in Kohn-Sham density-functional theory.

PubMed

Thøgersen, Lea; Olsen, Jeppe; Köhn, Andreas; Jørgensen, Poul; Sałek, Paweł; Helgaker, Trygve

2005-08-15

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints.

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

On-Board Real-Time Optimization Control for Turbo-Fan Engine Life Extending

NASA Astrophysics Data System (ADS)

Zheng, Qiangang; Zhang, Haibo; Miao, Lizhen; Sun, Fengyong

2017-11-01

A real-time optimization control method is proposed to extend turbo-fan engine service life. This real-time optimization control is based on an on-board engine mode, which is devised by a MRR-LSSVR (multi-input multi-output recursive reduced least squares support vector regression method). To solve the optimization problem, a FSQP (feasible sequential quadratic programming) algorithm is utilized. The thermal mechanical fatigue is taken into account during the optimization process. Furthermore, to describe the engine life decaying, a thermal mechanical fatigue model of engine acceleration process is established. The optimization objective function not only contains the sub-item which can get fast response of the engine, but also concludes the sub-item of the total mechanical strain range which has positive relationship to engine fatigue life. Finally, the simulations of the conventional optimization control which just consider engine acceleration performance or the proposed optimization method have been conducted. The simulations demonstrate that the time of the two control methods from idle to 99.5 % of the maximum power are equal. However, the engine life using the proposed optimization method could be surprisingly increased by 36.17 % compared with that using conventional optimization control.

Statistical optimization of process parameters for the simultaneous adsorption of Cr(VI) and phenol onto Fe-treated tea waste biomass

NASA Astrophysics Data System (ADS)

Gupta, Ankur; Balomajumder, Chandrajit

2017-12-01

In this study, simultaneous removal of Cr(VI) and phenol from binary solution was carried out using Fe-treated tea waste biomass. The effect of process parameters such as adsorbent dose, pH, initial concentration of Cr(VI) (mg/L), and initial concentration of phenol (mg/L) was optimized. The analysis of variance of the quadratic model demonstrates that the experimental results are in good agreement with the predicted values. Based on experimental design at an initial concentration of 55 mg/L of Cr(VI), 27.50 mg/L of phenol, pH 2.0, 15 g/L adsorbent dose, 99.99% removal of Cr(VI), and phenol was achieved.

Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities

DOE PAGES

Coffrin, Carleton James; Hijazi, Hassan L; Van Hentenryck, Pascal R

2016-12-01

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% ofmore » the open cases considered, leaving only 8 for future investigation.« less

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

[Optimization of application parameters of soil seed bank in vegetation recovery via response surface methodology].

PubMed

He, Meng-Xuan; Li, Hong-Yuan; Mo, Xun-Qiang; Meng, Wei-Qing; Yang, Jia-Nan

2014-08-01

The thickness of surface soil, the covering thickness and the number of adding arbor seeds are all important factors to be considered in the application of soil seed bank (SSB) for vegetation recovery. To determine the optimal conditions, the Box-Behnken central composite design with three parameters and three levels was conducted and Design-Expert was used for response surface optimization. Finally, the optimal model and optimal level of each parameter were selected. The quadratic model was more suitable for response surface optimization (P < 0.0001), indicating the model had good statistical significance which could express ideal relations between all the independent variable and dependent variable. For the optimum condition, the thickness of surface soil was 4.3 cm, the covering thickness was 2 cm, and the number of adding arbor seeds was 224 ind x m(-2), under which the number of germinated seedlings could be reached up to 6222 plants x m(-2). During the process of seed germination, significant interactions between the thickness of surface soil and the covering thickness, as well as the thickness of surface soil and the number of adding arbor seeds were found, but the relationship between the covering thickness and the number of adding arbor seeds was relatively unremarkable. Among all the parameters, the thickness of surface soil was the most important one, which had the steepest curve and the largest standardized coefficient.

Optimal Link Removal for Epidemic Mitigation: A Two-Way Partitioning Approach

PubMed Central

Enns, Eva A.; Mounzer, Jeffrey J.; Brandeau, Margaret L.

2011-01-01

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erdős-Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-perform so ther intuitive link removal algorithms, such as removing links in order of edge centrality. PMID:22115862

Gaussian Mean Field Lattice Gas

NASA Astrophysics Data System (ADS)

Scoppola, Benedetto; Troiani, Alessio

2018-03-01

We study rigorously a lattice gas version of the Sherrington-Kirckpatrick spin glass model. In discrete optimization literature this problem is known as unconstrained binary quadratic programming and it belongs to the class NP-hard. We prove that the fluctuations of the ground state energy tend to vanish in the thermodynamic limit, and we give a lower bound of such ground state energy. Then we present a heuristic algorithm, based on a probabilistic cellular automaton, which seems to be able to find configurations with energy very close to the minimum, even for quite large instances.

Adiabatic Quantum Computation with Neutral Cesium

NASA Astrophysics Data System (ADS)

Hankin, Aaron; Parazzoli, L.; Chou, Chin-Wen; Jau, Yuan-Yu; Burns, George; Young, Amber; Kemme, Shanalyn; Ferdinand, Andrew; Biedermann, Grant; Landahl, Andrew; Ivan H. Deutsch Collaboration; Mark Saffman Collaboration

2013-05-01

We are implementing a new platform for adiabatic quantum computation (AQC) based on trapped neutral atoms whose coupling is mediated by the dipole-dipole interactions of Rydberg states. Ground state cesium atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. University of New Mexico: Ivan H. Deutsch, Tyler Keating, Krittika Goyal.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Polynomials to model the growth of young bulls in performance tests.

PubMed

Scalez, D C B; Fragomeni, B O; Passafaro, T L; Pereira, I G; Toral, F L B

2014-03-01

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

Optimization of process variables for decolorization of Disperse Yellow 211 by Bacillus subtilis using Box-Behnken design.

PubMed

Sharma, Praveen; Singh, Lakhvinder; Dilbaghi, Neeraj

2009-05-30

Decolorization of textile azo dye Disperse Yellow 211 (DY 211) was carried out from simulated aqueous solution by bacterial strain Bacillus subtilis. Response surface methodology (RSM), involving Box-Behnken design matrix in three most important operating variables; temperature, pH and initial dye concentration was successfully employed for the study and optimization of decolorization process. The total 17 experiments were conducted in the study towards the construction of a quadratic model. According to analysis of variance (ANOVA) results, the proposed model can be used to navigate the design space. Under optimized conditions the bacterial strain was able to decolorize DY 211 up to 80%. Model indicated that initial dye concentration of 100 mgl(-1), pH 7 and a temperature of 32.5 degrees C were found optimum for maximum % decolorization. Very high regression coefficient between the variables and the response (R(2)=0.9930) indicated excellent evaluation of experimental data by polynomial regression model. The combination of the three variables predicted through RSM was confirmed through confirmatory experiments, hence the bacterial strain holds a great potential for the treatment of colored textile effluents.

Normalized distance aggregation of discriminative features for person reidentification

NASA Astrophysics Data System (ADS)

Hou, Li; Han, Kang; Wan, Wanggen; Hwang, Jenq-Neng; Yao, Haiyan

2018-03-01

We propose an effective person reidentification method based on normalized distance aggregation of discriminative features. Our framework is built on the integration of three high-performance discriminative feature extraction models, including local maximal occurrence (LOMO), feature fusion net (FFN), and a concatenation of LOMO and FFN called LOMO-FFN, through two fast and discriminant metric learning models, i.e., cross-view quadratic discriminant analysis (XQDA) and large-scale similarity learning (LSSL). More specifically, we first represent all the cross-view person images using LOMO, FFN, and LOMO-FFN, respectively, and then apply each extracted feature representation to train XQDA and LSSL, respectively, to obtain the optimized individual cross-view distance metric. Finally, the cross-view person matching is computed as the sum of the optimized individual cross-view distance metric through the min-max normalization. Experimental results have shown the effectiveness of the proposed algorithm on three challenging datasets (VIPeR, PRID450s, and CUHK01).

Effect of brewing conditions on antioxidant properties of rosehip tea beverage: study by response surface methodology.

PubMed

İlyasoğlu, Huri; Arpa, Tuba Eda

2017-10-01

The aim of this study was to investigate the effects of brewing conditions (infusion time and temperature) on the antioxidant properties of rosehip tea beverage. The ascorbic acid content, total phenolic content (TPC), and ferric reducing antioxidant power (FRAP) of rosehip tea beverage were analysed. A two-factor and three-level central composite design was applied to evaluate the effects of the variables on the responses. The best quadratic models were obtained for all responses. The generated models were validated under the optimal conditions. At the optimal conditions, the rosehip tea beverage had 3.15 mg 100 mL -1 of ascorbic acid, 61.44 mg 100 mL -1 of TPC, and 2591 µmol of FRAP. The best brewing conditions for the rosehip tea beverage were found to be an infusion time of 6-8 min at temperatures of 84-86 °C.

Simulation of superconducting tapes and coils with convex quadratic programming method

NASA Astrophysics Data System (ADS)

Zhang, Yan; Song, Yuntao; Wang, Lei; Liu, Xufeng

2015-08-01

Second-generation (2G) high-temperature superconducting coated conductors are playing an increasingly important role in power applications due to their large current density under high magnetic fields. In this paper, we conclude and explore the ability and possible potential of J formulation from the mathematical modeling point of view. An equivalent matrix form of J formulation has been presented and a relation between electromagnetic quantities and Karush-Kuhn-Tucker (KKT) conditions in optimization theory has been discovered. The use of the latest formulae to calculate inductance in a coil system and the primal-dual interior-point method algorithm is a trial to make the process of modeling stylized and build a bridge to commercial optimization solvers. Two different dependences of the critical current density on the magnetic field have been used in order to make a comparison with those published papers.

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

Modeling parameters that characterize pacing of elite female 800-m freestyle swimmers.

PubMed

Lipińska, Patrycja; Allen, Sian V; Hopkins, Will G

2016-01-01

Pacing offers a potential avenue for enhancement of endurance performance. We report here a novel method for characterizing pacing in 800-m freestyle swimming. Websites provided 50-m lap and race times for 192 swims of 20 elite female swimmers between 2000 and 2013. Pacing for each swim was characterized with five parameters derived from a linear model: linear and quadratic coefficients for effect of lap number, reductions from predicted time for first and last laps, and lap-time variability (standard error of the estimate). Race-to-race consistency of the parameters was expressed as intraclass correlation coefficients (ICCs). The average swim was a shallow negative quadratic with slowest time in the eleventh lap. First and last laps were faster by 6.4% and 3.6%, and lap-time variability was ±0.64%. Consistency between swimmers ranged from low-moderate for the linear and quadratic parameters (ICC = 0.29 and 0.36) to high for the last-lap parameter (ICC = 0.62), while consistency for race time was very high (ICC = 0.80). Only ~15% of swimmers had enough swims (~15 or more) to provide reasonable evidence of optimum parameter values in plots of race time vs. each parameter. The modest consistency of most of the pacing parameters and lack of relationships between parameters and performance suggest that swimmers usually compensated for changes in one parameter with changes in another. In conclusion, pacing in 800-m elite female swimmers can be characterized with five parameters, but identifying an optimal pacing profile is generally impractical.

Optimization of Adhesive Pastes for Dental Caries Prevention.

PubMed

Sodata, Patteera; Juntavee, Apa; Juntavee, Niwut; Peerapattana, Jomjai

2017-11-01

Dental caries prevention products available on the market contain only remineralizing agents or antibacterial agents. This study aimed to develop adhesive pastes containing calcium phosphate and α-mangostin for dental caries prevention using the optimization technique. Calcium phosphate was used as a remineralizing agent, and extracted α-mangostin was used as an antibacterial agent. The effect of the independent variables, which were fumed silica, Eudragit ® EPO, polyethylene glycol, and ethyl alcohol, on the responses was investigated. The drying time, erosion rate, calcium release rate, and α-mangostin release rate were established as the measured responses. An equation and a model of the relationship were constructed. An optimal formulation was obtained, and its effect on dental caries prevention was investigated using the pH-cycling model. The quadratic equation revealed that the drying time, calcium release rate, and α-mangostin release rate tended to decrease when increasing the fumed silica and decreasing other factors. The erosion rate tended to increase when decreasing Eudragit ® EPO and increasing other factors. The observed responses of the optimal adhesive pastes were not significantly different from the predicted responses. This result demonstrated that optimization is an efficient technique in the formulation development of the adhesive pastes. In addition, the optimal adhesive pastes could enhance acid resistance activity to the tooth enamel.

Optimal cure cycle design of a resin-fiber composite laminate

NASA Technical Reports Server (NTRS)

Hou, Jean W.; Sheen, Jeenson

1987-01-01

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

CSOLNP: Numerical Optimization Engine for Solving Non-linearly Constrained Problems.

PubMed

Zahery, Mahsa; Maes, Hermine H; Neale, Michael C

2017-08-01

We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package version, 1) alongside some improvements. CSOLNP solves non-linearly constrained optimization problems using a Sequential Quadratic Programming (SQP) algorithm. CSOLNP, NPSOL (a very popular implementation of SQP method in FORTRAN (Gill et al., 1986, User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming (No. SOL-86-2). Stanford, CA: Stanford University Systems Optimization Laboratory), and SLSQP (another SQP implementation available as part of the NLOPT collection (Johnson, 2014, The NLopt nonlinear-optimization package. Retrieved from http://ab-initio.mit.edu/nlopt)) are three optimizers available in OpenMx package. These optimizers are compared in terms of runtimes, final objective values, and memory consumption. A Monte Carlo analysis of the performance of the optimizers was performed on ordinal and continuous models with five variables and one or two factors. While the relative difference between the objective values is less than 0.5%, CSOLNP is in general faster than NPSOL and SLSQP for ordinal analysis. As for continuous data, none of the optimizers performs consistently faster than the others. In terms of memory usage, we used Valgrind's heap profiler tool, called Massif, on one-factor threshold models. CSOLNP and NPSOL consume the same amount of memory, while SLSQP uses 71 MB more memory than the other two optimizers.

Effect of simultaneous variation in temperature and ammonia concentration on percent fertilization and hatching in Crassostrea ariakensis.

PubMed

Hui, Wang; Jiahui, Liu; Hongshuai, Yang; Jin, Liu; Zhigang, Liu

2014-04-01

The combined effects of temperature and ammonia concentration on the percent fertilization and percent hatching in Crassostrea ariakensis were examined under laboratory conditions using the central composite design and response surface methodology. The results indicated: (1) The linear effects of temperature and ammonia concentration on the percent fertilization were significant (P<0.05), and the quadratic effects were highly significant (P<0.01). The interactive effect between temperature and ammonia concentration on the percent fertilization was not significant (P>0.05). (2) The linear effect of temperature on the percent hatching was highly significant (P<0.01), and that of ammonia concentration was nonsignificant (P>0.05). The quadratic effects of temperature and ammonia concentration on the percent hatching were highly significant (P<0.01). The interaction on the percent hatching was not significant (P>0.05). Temperature was more important than ammonia in influencing the fertilization and hatching in C. ariakensis. (3) The model equations of the percent fertilization and hatching towards temperature and ammonia concentration were established, with the coefficients of determination R(2)=99.4% and 99.76%, respectively. Through the lack-of-fit test, these models were of great adequacy. The predictive coefficients of determination for the two model equations were as high as 94.6% and 98.03%, respectively, showing that they could be used for practical projection. (4) Via the statistical simultaneous optimization technique, the optimal factor level combination, i.e., 25°C/0.038mgmL(-1), was derived, at which the greatest percent fertilization 95.25% and hatching 83.26% was achieved, with the desirability being 97.81%. Our results may provide advantageous guidelines for the successful reproduction of C. ariakensis. Copyright © 2014 Elsevier Ltd. All rights reserved.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

PubMed

Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

2017-03-01

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Optimal conditions for bioremediation of oily seawater.

PubMed

Zahed, Mohammad Ali; Aziz, Hamidi Abdul; Isa, Mohamed Hasnain; Mohajeri, Leila; Mohajeri, Soraya

2010-12-01

To determine the influence of nutrients on the rate of biodegradation, a five-level, three-factor central composite design (CCD) was employed for bioremediation of seawater artificially contaminated with crude oil. Removal of total petroleum hydrocarbons (TPH) was the dependent variable. Samples were extracted and analyzed according to US-EPA protocols. A significant (R(2)=0.9645, P<0.0001) quadratic polynomial mathematical model was generated. Removal from samples not subjected to optimization and removal by natural attenuation were 53.3% and 22.6%, respectively. Numerical optimization was carried out based on desirability functions for maximum TPH removal. For an initial crude oil concentration of 1g/L supplemented with 190.21 mg/L nitrogen and 12.71 mg/L phosphorus, the Design-Expert software predicted 60.9% hydrocarbon removal; 58.6% removal was observed in a 28-day experiment. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Optimized Assistive Human-Robot Interaction Using Reinforcement Learning.

PubMed

Modares, Hamidreza; Ranatunga, Isura; Lewis, Frank L; Popa, Dan O

2016-03-01

An intelligent human-robot interaction (HRI) system with adjustable robot behavior is presented. The proposed HRI system assists the human operator to perform a given task with minimum workload demands and optimizes the overall human-robot system performance. Motivated by human factor studies, the presented control structure consists of two control loops. First, a robot-specific neuro-adaptive controller is designed in the inner loop to make the unknown nonlinear robot behave like a prescribed robot impedance model as perceived by a human operator. In contrast to existing neural network and adaptive impedance-based control methods, no information of the task performance or the prescribed robot impedance model parameters is required in the inner loop. Then, a task-specific outer-loop controller is designed to find the optimal parameters of the prescribed robot impedance model to adjust the robot's dynamics to the operator skills and minimize the tracking error. The outer loop includes the human operator, the robot, and the task performance details. The problem of finding the optimal parameters of the prescribed robot impedance model is transformed into a linear quadratic regulator (LQR) problem which minimizes the human effort and optimizes the closed-loop behavior of the HRI system for a given task. To obviate the requirement of the knowledge of the human model, integral reinforcement learning is used to solve the given LQR problem. Simulation results on an x - y table and a robot arm, and experimental implementation results on a PR2 robot confirm the suitability of the proposed method.

Optimal control theory (OWEM) applied to a helicopter in the hover and approach phase

NASA Technical Reports Server (NTRS)

Born, G. J.; Kai, T.

1975-01-01

A major difficulty in the practical application of linear-quadratic regulator theory is how to choose the weighting matrices in quadratic cost functions. The control system design with optimal weighting matrices was applied to a helicopter in the hover and approach phase. The weighting matrices were calculated to extremize the closed loop total system damping subject to constraints on the determinants. The extremization is really a minimization of the effects of disturbances, and interpreted as a compromise between the generalized system accuracy and the generalized system response speed. The trade-off between the accuracy and the response speed is adjusted by a single parameter, the ratio of determinants. By this approach an objective measure can be obtained for the design of a control system. The measure is to be determined by the system requirements.

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Methotrexate loading in chitosan nanoparticles at a novel pH: Response surface modeling, optimization and characterization.

PubMed

Hashad, Rania A; Ishak, Rania A H; Geneidi, Ahmed S; Mansour, Samar

2016-10-01

The aim of this study was to assess the feasibility of employing a novel but critical formulation pH (6.2) to encapsulate an anionic model drug (methotrexate, MTX) into chitosan(Cs)-tripolyphosphate nanoparticles(NPs). A response surface methodology using a three-level full factorial design was applied studying the effects of two independent variables namely; Cs concentration and MTX concentration. The responses investigated were the entrapment efficiency (EE%), mean hydrodynamic particle size (PS), polydispersity index (PDI) and zeta potential (ZP). In order to simultaneously optimize the series of models obtained, the desirability function approach was applied with a goal to produce high percent of MTX encapsulated into highly charged Cs-TPP NPs of homogenous optimum PS. MTX-loaded CsNPs were successfully prepared at the novel pH applied. The suggested significant models were found quadratic for EE, PS and ZP responses, while 2-factor interaction model for PDI. The optimization overlay graph showed that the maximum global desirability, D=0.856, was reached when the conditions were set at high Cs and MTX concentration. Thus, the use of such optimized conditions, at this novel pH, achieved a maximum drug EE% (73.38%) into NPs characterized by optimum PS (232.6nm), small PDI value (0.195) and highly surface charged (+18.4mV). Copyright © 2016 Elsevier B.V. All rights reserved.

Influence of yield surface curvature on the macroscopic yielding and ductile failure of isotropic porous plastic materials

NASA Astrophysics Data System (ADS)

Dæhli, Lars Edvard Bryhni; Morin, David; Børvik, Tore; Hopperstad, Odd Sture

2017-10-01

Numerical unit cell models of an approximative representative volume element for a porous ductile solid are utilized to investigate differences in the mechanical response between a quadratic and a non-quadratic matrix yield surface. A Hershey equivalent stress measure with two distinct values of the yield surface exponent is employed as the matrix description. Results from the unit cell calculations are further used to calibrate a heuristic extension of the Gurson model which incorporates effects of the third deviatoric stress invariant. An assessment of the porous plasticity model reveals its ability to describe the unit cell response to some extent, however underestimating the effect of the Lode parameter for the lower triaxiality ratios imposed in this study when compared to unit cell simulations. Ductile failure predictions by means of finite element simulations using a unit cell model that resembles an imperfection band are then conducted to examine how the non-quadratic matrix yield surface influences the failure strain as compared to the quadratic matrix yield surface. Further, strain localization predictions based on bifurcation analyses and imperfection band analyses are undertaken using the calibrated porous plasticity model. These simulations are then compared to the unit cell calculations in order to elucidate the differences between the various modelling strategies. The current study reveals that strain localization analyses using an imperfection band model and a spatially discretized unit cell are in reasonable agreement, while the bifurcation analyses predict higher strain levels at localization. Imperfection band analyses are finally used to calculate failure loci for the quadratic and the non-quadratic matrix yield surface under a wide range of loading conditions. The underlying matrix yield surface is demonstrated to have a pronounced influence on the onset of strain localization.

Rapid Adsorption of Heavy Metals by Fe3O4/Talc Nanocomposite and Optimization Study Using Response Surface Methodology

PubMed Central

Kalantari, Katayoon; Ahmad, Mansor B.; Masoumi, Hamid Reza Fard; Shameli, Kamyar; Basri, Mahiran; Khandanlou, Roshanak

2014-01-01

Fe3O4/talc nanocomposite was used for removal of Cu(II), Ni(II), and Pb(II) ions from aqueous solutions. Experiments were designed by response surface methodology (RSM) and a quadratic model was used to predict the variables. The adsorption parameters such as adsorbent dosage, removal time, and initial ion concentration were used as the independent variables and their effects on heavy metal ion removal were investigated. Analysis of variance was incorporated to judge the adequacy of the models. Optimal conditions with initial heavy metal ion concentration of 100, 92 and 270 mg/L, 120 s of removal time and 0.12 g of adsorbent amount resulted in 72.15%, 50.23%, and 91.35% removal efficiency for Cu(II), Ni(II), and Pb(II), respectively. The predictions of the model were in good agreement with experimental results and the Fe3O4/talc nanocomposite was successfully used to remove heavy metals from aqueous solutions. PMID:25050784

Rapid adsorption of heavy metals by Fe3O4/talc nanocomposite and optimization study using response surface methodology.

PubMed

Kalantari, Katayoon; Ahmad, Mansor B; Masoumi, Hamid Reza Fard; Shameli, Kamyar; Basri, Mahiran; Khandanlou, Roshanak

2014-07-21

Fe3O4/talc nanocomposite was used for removal of Cu(II), Ni(II), and Pb(II) ions from aqueous solutions. Experiments were designed by response surface methodology (RSM) and a quadratic model was used to predict the variables. The adsorption parameters such as adsorbent dosage, removal time, and initial ion concentration were used as the independent variables and their effects on heavy metal ion removal were investigated. Analysis of variance was incorporated to judge the adequacy of the models. Optimal conditions with initial heavy metal ion concentration of 100, 92 and 270 mg/L, 120 s of removal time and 0.12 g of adsorbent amount resulted in 72.15%, 50.23%, and 91.35% removal efficiency for Cu(II), Ni(II), and Pb(II), respectively. The predictions of the model were in good agreement with experimental results and the Fe3O4/talc nanocomposite was successfully used to remove heavy metals from aqueous solutions.

Optimal radiotherapy dose schedules under parametric uncertainty

NASA Astrophysics Data System (ADS)

Badri, Hamidreza; Watanabe, Yoichi; Leder, Kevin

2016-01-01

We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variability in normal and tumor tissue radiosensitivity or sparing factor of the organs-at-risk (OAR) are not accounted for during radiation scheduling, the performance of the therapy may be strongly degraded or the OAR may receive a substantially larger dose than the allowable threshold. This paper proposes a stochastic radiation scheduling concept to incorporate inter-patient variability into the scheduling optimization problem. Our method is based on a probabilistic approach, where the model parameters are given by a set of random variables. Our probabilistic formulation ensures that our constraints are satisfied with a given probability, and that our objective function achieves a desired level with a stated probability. We used a variable transformation to reduce the resulting optimization problem to two dimensions. We showed that the optimal solution lies on the boundary of the feasible region and we implemented a branch and bound algorithm to find the global optimal solution. We demonstrated how the configuration of optimal schedules in the presence of uncertainty compares to optimal schedules in the absence of uncertainty (conventional schedule). We observed that in order to protect against the possibility of the model parameters falling into a region where the conventional schedule is no longer feasible, it is required to avoid extremal solutions, i.e. a single large dose or very large total dose delivered over a long period. Finally, we performed numerical experiments in the setting of head and neck tumors including several normal tissues to reveal the effect of parameter uncertainty on optimal schedules and to evaluate the sensitivity of the solutions to the choice of key model parameters.

Efficient Online Optimized Quantum Control for Adiabatic Quantum Computation

NASA Astrophysics Data System (ADS)

Quiroz, Gregory

Adiabatic quantum computation (AQC) relies on controlled adiabatic evolution to implement a quantum algorithm. While control evolution can take many forms, properly designed time-optimal control has been shown to be particularly advantageous for AQC. Grover's search algorithm is one such example where analytically-derived time-optimal control leads to improved scaling of the minimum energy gap between the ground state and first excited state and thus, the well-known quadratic quantum speedup. Analytical extensions beyond Grover's search algorithm present a daunting task that requires potentially intractable calculations of energy gaps and a significant degree of model certainty. Here, an in situ quantum control protocol is developed for AQC. The approach is shown to yield controls that approach the analytically-derived time-optimal controls for Grover's search algorithm. In addition, the protocol's convergence rate as a function of iteration number is shown to be essentially independent of system size. Thus, the approach is potentially scalable to many-qubit systems.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

NASA Astrophysics Data System (ADS)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

Rate-Based Model Predictive Control of Turbofan Engine Clearance

NASA Technical Reports Server (NTRS)

DeCastro, Jonathan A.

2006-01-01

An innovative model predictive control strategy is developed for control of nonlinear aircraft propulsion systems and sub-systems. At the heart of the controller is a rate-based linear parameter-varying model that propagates the state derivatives across the prediction horizon, extending prediction fidelity to transient regimes where conventional models begin to lose validity. The new control law is applied to a demanding active clearance control application, where the objectives are to tightly regulate blade tip clearances and also anticipate and avoid detrimental blade-shroud rub occurrences by optimally maintaining a predefined minimum clearance. Simulation results verify that the rate-based controller is capable of satisfying the objectives during realistic flight scenarios where both a conventional Jacobian-based model predictive control law and an unconstrained linear-quadratic optimal controller are incapable of doing so. The controller is evaluated using a variety of different actuators, illustrating the efficacy and versatility of the control approach. It is concluded that the new strategy has promise for this and other nonlinear aerospace applications that place high importance on the attainment of control objectives during transient regimes.

Locally optimal control under unknown dynamics with learnt cost function: application to industrial robot positioning

NASA Astrophysics Data System (ADS)

Guérin, Joris; Gibaru, Olivier; Thiery, Stéphane; Nyiri, Eric

2017-01-01

Recent methods of Reinforcement Learning have enabled to solve difficult, high dimensional, robotic tasks under unknown dynamics using iterative Linear Quadratic Gaussian control theory. These algorithms are based on building a local time-varying linear model of the dynamics from data gathered through interaction with the environment. In such tasks, the cost function is often expressed directly in terms of the state and control variables so that it can be locally quadratized to run the algorithm. If the cost is expressed in terms of other variables, a model is required to compute the cost function from the variables manipulated. We propose a method to learn the cost function directly from the data, in the same way as for the dynamics. This way, the cost function can be defined in terms of any measurable quantity and thus can be chosen more appropriately for the task to be carried out. With our method, any sensor information can be used to design the cost function. We demonstrate the efficiency of this method through simulating, with the V-REP software, the learning of a Cartesian positioning task on several industrial robots with different characteristics. The robots are controlled in joint space and no model is provided a priori. Our results are compared with another model free technique, consisting in writing the cost function as a state variable.

Alternatives for Jet Engine Control

NASA Technical Reports Server (NTRS)

Leake, R. J.; Sain, M. K.

1976-01-01

Approaches are developed as alternatives to current design methods which rely heavily on linear quadratic and Riccati equation methods. The main alternatives are discussed in two broad categories, local multivariable frequency domain methods and global nonlinear optimal methods.

Control of Vibratory Energy Harvesters in the Presence of Nonlinearities and Power-Flow Constraints

NASA Astrophysics Data System (ADS)

Cassidy, Ian L.

Over the past decade, a significant amount of research activity has been devoted to developing electromechanical systems that can convert ambient mechanical vibrations into usable electric power. Such systems, referred to as vibratory energy harvesters, have a number of useful of applications, ranging in scale from self-powered wireless sensors for structural health monitoring in bridges and buildings to energy harvesting from ocean waves. One of the most challenging aspects of this technology concerns the efficient extraction and transmission of power from transducer to storage. Maximizing the rate of power extraction from vibratory energy harvesters is further complicated by the stochastic nature of the disturbance. The primary purpose of this dissertation is to develop feedback control algorithms which optimize the average power generated from stochastically-excited vibratory energy harvesters. This dissertation will illustrate the performance of various controllers using two vibratory energy harvesting systems: an electromagnetic transducer embedded within a flexible structure, and a piezoelectric bimorph cantilever beam. Compared with piezoelectric systems, large-scale electromagnetic systems have received much less attention in the literature despite their ability to generate power at the watt--kilowatt scale. Motivated by this observation, the first part of this dissertation focuses on developing an experimentally validated predictive model of an actively controlled electromagnetic transducer. Following this experimental analysis, linear-quadratic-Gaussian control theory is used to compute unconstrained state feedback controllers for two ideal vibratory energy harvesting systems. This theory is then augmented to account for competing objectives, nonlinearities in the harvester dynamics, and non-quadratic transmission loss models in the electronics. In many vibratory energy harvesting applications, employing a bi-directional power electronic drive to actively control the harvester is infeasible due to the high levels of parasitic power required to operate the drive. For the case where a single-directional drive is used, a constraint on the directionality of power-flow is imposed on the system, which necessitates the use of nonlinear feedback. As such, a sub-optimal controller for power-flow-constrained vibratory energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance controller. Finally, the last section of this dissertation explores a numerical approach to compute optimal discretized control manifolds for systems with power-flow constraints. Unlike the sub-optimal nonlinear controller, the numerical controller satisfies the necessary conditions for optimality by solving the stochastic Hamilton-Jacobi equation.

Correction of aeroheating-induced intensity nonuniformity in infrared images

NASA Astrophysics Data System (ADS)

Liu, Li; Yan, Luxin; Zhao, Hui; Dai, Xiaobing; Zhang, Tianxu

2016-05-01

Aeroheating-induced intensity nonuniformity effects severely influence the effective performance of an infrared (IR) imaging system in high-speed flight. In this paper, we propose a new approach to the correction of intensity nonuniformity in IR images. The basic assumption is that the low-frequency intensity bias is additive and smoothly varying so that it can be modeled as a bivariate polynomial and estimated by using an isotropic total variation (TV) model. A half quadratic penalty method is applied to the isotropic form of TV discretization. And an alternating minimization algorithm is adopted for solving the optimization model. The experimental results of simulated and real aerothermal images show that the proposed correction method can effectively improve IR image quality.

Discrete-time pilot model. [human dynamics and digital simulation

NASA Technical Reports Server (NTRS)

Cavalli, D.

1978-01-01

Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.

Grid Block Design Based on Monte Carlo Simulated Dosimetry, the Linear Quadratic and Hug–Kellerer Radiobiological Models

PubMed Central

Gholami, Somayeh; Nedaie, Hassan Ali; Longo, Francesco; Ay, Mohammad Reza; Dini, Sharifeh A.; Meigooni, Ali S.

2017-01-01

Purpose: The clinical efficacy of Grid therapy has been examined by several investigators. In this project, the hole diameter and hole spacing in Grid blocks were examined to determine the optimum parameters that give a therapeutic advantage. Methods: The evaluations were performed using Monte Carlo (MC) simulation and commonly used radiobiological models. The Geant4 MC code was used to simulate the dose distributions for 25 different Grid blocks with different hole diameters and center-to-center spacing. The therapeutic parameters of these blocks, namely, the therapeutic ratio (TR) and geometrical sparing factor (GSF) were calculated using two different radiobiological models, including the linear quadratic and Hug–Kellerer models. In addition, the ratio of the open to blocked area (ROTBA) is also used as a geometrical parameter for each block design. Comparisons of the TR, GSF, and ROTBA for all of the blocks were used to derive the parameters for an optimum Grid block with the maximum TR, minimum GSF, and optimal ROTBA. A sample of the optimum Grid block was fabricated at our institution. Dosimetric characteristics of this Grid block were measured using an ionization chamber in water phantom, Gafchromic film, and thermoluminescent dosimeters in Solid Water™ phantom materials. Results: The results of these investigations indicated that Grid blocks with hole diameters between 1.00 and 1.25 cm and spacing of 1.7 or 1.8 cm have optimal therapeutic parameters (TR > 1.3 and GSF~0.90). The measured dosimetric characteristics of the optimum Grid blocks including dose profiles, percentage depth dose, dose output factor (cGy/MU), and valley-to-peak ratio were in good agreement (±5%) with the simulated data. Conclusion: In summary, using MC-based dosimetry, two radiobiological models, and previously published clinical data, we have introduced a method to design a Grid block with optimum therapeutic response. The simulated data were reproduced by experimental data. PMID:29296035

Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave-convex FP problem--in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper.

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

PubMed

Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

2005-01-01

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

On Vieta's Formulas and the Determination of a Set of Positive Integers by Their Sum and Product

ERIC Educational Resources Information Center

Valahas, Theodoros; Boukas, Andreas

2011-01-01

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

Optimizing pulsed Nd:YAG laser beam welding process parameters to attain maximum ultimate tensile strength for thin AISI316L sheet using response surface methodology and simulated annealing algorithm

NASA Astrophysics Data System (ADS)

Torabi, Amir; Kolahan, Farhad

2018-07-01

Pulsed laser welding is a powerful technique especially suitable for joining thin sheet metals. In this study, based on experimental data, pulsed laser welding of thin AISI316L austenitic stainless steel sheet has been modeled and optimized. The experimental data required for modeling are gathered as per Central Composite Design matrix in Response Surface Methodology (RSM) with full replication of 31 runs. Ultimate Tensile Strength (UTS) is considered as the main quality measure in laser welding. Furthermore, the important process parameters including peak power, pulse duration, pulse frequency and welding speed are selected as input process parameters. The relation between input parameters and the output response is established via full quadratic response surface regression with confidence level of 95%. The adequacy of the regression model was verified using Analysis of Variance technique results. The main effects of each factor and the interactions effects with other factors were analyzed graphically in contour and surface plot. Next, to maximum joint UTS, the best combinations of parameters levels were specified using RSM. Moreover, the mathematical model is implanted into a Simulated Annealing (SA) optimization algorithm to determine the optimal values of process parameters. The results obtained by both SA and RSM optimization techniques are in good agreement. The optimal parameters settings for peak power of 1800 W, pulse duration of 4.5 ms, frequency of 4.2 Hz and welding speed of 0.5 mm/s would result in a welded joint with 96% of the base metal UTS. Computational results clearly demonstrate that the proposed modeling and optimization procedures perform quite well for pulsed laser welding process.

Identification of terrain cover using the optimum polarimetric classifier

NASA Technical Reports Server (NTRS)

Kong, J. A.; Swartz, A. A.; Yueh, H. A.; Novak, L. M.; Shin, R. T.

1988-01-01

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Dictionary Indexing of Electron Channeling Patterns.

PubMed

Singh, Saransh; De Graef, Marc

2017-02-01

The dictionary-based approach to the indexing of diffraction patterns is applied to electron channeling patterns (ECPs). The main ingredients of the dictionary method are introduced, including the generalized forward projector (GFP), the relevant detector model, and a scheme to uniformly sample orientation space using the "cubochoric" representation. The GFP is used to compute an ECP "master" pattern. Derivative free optimization algorithms, including the Nelder-Mead simplex and the bound optimization by quadratic approximation are used to determine the correct detector parameters and to refine the orientation obtained from the dictionary approach. The indexing method is applied to poly-silicon and shows excellent agreement with the calibrated values. Finally, it is shown that the method results in a mean disorientation error of 1.0° with 0.5° SD for a range of detector parameters.

Information distribution in distributed microprocessor based flight control systems

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1977-01-01

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

Optimization of Fermentation Medium for Extracellular Lipase Production from Aspergillus niger Using Response Surface Methodology

PubMed Central

Jia, Jia; Yang, Xiaofeng; Wu, Zhiliang; Zhang, Qian; Lin, Zhi; Guo, Hongtao; Lin, Carol Sze Ki; Wang, Jianying; Wang, Yunshan

2015-01-01

Lipase produced by Aspergillus niger is widely used in various industries. In this study, extracellular lipase production from an industrial producing strain of A. niger was improved by medium optimization. The secondary carbon source, nitrogen source, and lipid were found to be the three most influential factors for lipase production by single-factor experiments. According to the statistical approach, the optimum values of three most influential parameters were determined: 10.5 g/L corn starch, 35.4 g/L soybean meal, and 10.9 g/L soybean oil. Using this optimum medium, the best lipase activity was obtained at 2,171 U/mL, which was 16.4% higher than using the initial medium. All these results confirmed the validity of the model. Furthermore, results of the Box-Behnken Design and quadratic models analysis indicated that the carbon to nitrogen (C/N) ratio significantly influenced the enzyme production, which also suggested that more attention should be paid to the C/N ratio for the optimization of enzyme production. PMID:26366414

Ant system: optimization by a colony of cooperating agents.

PubMed

Dorigo, M; Maniezzo, V; Colorni, A

1996-01-01

An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call ant system (AS). We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical traveling salesman problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the ant system (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics-global data structure revision, distributed communication and probabilistic transitions of the AS.

The significance of fructose and MSG in affecting lipid and docosahexaenoic acid (DHA) production of Aurantiochytrium sp. SW1

NASA Astrophysics Data System (ADS)

Rahman, Shariffah Nurhidayah Syed Abdul; Kalil, Mohd Sahaid; Hamid, Aidil Abdul

2018-04-01

Optimization of fermentation medium for the production of docosahexaenoic acid (DHA) by Aurantiochytrium sp. SW1 was carried out. In this study, levels of fructose, monosodium glutamate (MSG) and sea salt were optimized for enhanced lipid and DHA production using response surface methodology (RSM). The design contains a total of 20 runs with 6 central points replication. Cultivation was carried out in 500 mL flasks containing 100 mL nitrogen limited medium at 30°C for 96h. Sequential model sum of squares (SS) revealed that the system was adequately represented by a quadratic model (p<0.0001). ANOVA results showed that fructose and MSG as a single factor has significant positive effect on the DHA content of SW1. The estimated optimal levels of the factors were 100 g/L fructose, 8 g/L MSG and 47% sea salt. Subsequent cultivation employing the suggested values confirmed that the predicted response values were experimentally achievable and reproducible, where 8.82 g/L DHA (51.34% g/g lipid) was achieved.

Reconstruction of Sensory Stimuli Encoded with Integrate-and-Fire Neurons with Random Thresholds

PubMed Central

Lazar, Aurel A.; Pnevmatikakis, Eftychios A.

2013-01-01

We present a general approach to the reconstruction of sensory stimuli encoded with leaky integrate-and-fire neurons with random thresholds. The stimuli are modeled as elements of a Reproducing Kernel Hilbert Space. The reconstruction is based on finding a stimulus that minimizes a regularized quadratic optimality criterion. We discuss in detail the reconstruction of sensory stimuli modeled as absolutely continuous functions as well as stimuli with absolutely continuous first-order derivatives. Reconstruction results are presented for stimuli encoded with single as well as a population of neurons. Examples are given that demonstrate the performance of the reconstruction algorithms as a function of threshold variability. PMID:24077610

Quadratic Optimization in the Problems of Active Control of Sound

NASA Technical Reports Server (NTRS)

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Constraint Optimization Problem For The Cutting Of A Cobalt Chrome Refractory Material

NASA Astrophysics Data System (ADS)

Lebaal, Nadhir; Schlegel, Daniel; Folea, Milena

2011-05-01

This paper shows a complete approach to solve a given problem, from the experimentation to the optimization of different cutting parameters. In response to an industrial problem of slotting FSX 414, a Cobalt-based refractory material, we have implemented a design of experiment to determine the most influent parameters on the tool life, the surface roughness and the cutting forces. After theses trials, an optimization approach has been implemented to find the lowest manufacturing cost while respecting the roughness constraints and cutting force limitation constraints. The optimization approach is based on the Response Surface Method (RSM) using the Sequential Quadratic programming algorithm (SQP) for a constrained problem. To avoid a local optimum and to obtain an accurate solution at low cost, an efficient strategy, which allows improving the RSM accuracy in the vicinity of the global optimum, is presented. With these models and these trials, we could apply and compare our optimization methods in order to get the lowest cost for the best quality, i.e. a satisfying surface roughness and limited cutting forces.

Aggregation of LoD 1 building models as an optimization problem

NASA Astrophysics Data System (ADS)

Guercke, R.; Götzelmann, T.; Brenner, C.; Sester, M.

3D city models offered by digital map providers typically consist of several thousands or even millions of individual buildings. Those buildings are usually generated in an automated fashion from high resolution cadastral and remote sensing data and can be very detailed. However, not in every application such a high degree of detail is desirable. One way to remove complexity is to aggregate individual buildings, simplify the ground plan and assign an appropriate average building height. This task is computationally complex because it includes the combinatorial optimization problem of determining which subset of the original set of buildings should best be aggregated to meet the demands of an application. In this article, we introduce approaches to express different aspects of the aggregation of LoD 1 building models in the form of Mixed Integer Programming (MIP) problems. The advantage of this approach is that for linear (and some quadratic) MIP problems, sophisticated software exists to find exact solutions (global optima) with reasonable effort. We also propose two different heuristic approaches based on the region growing strategy and evaluate their potential for optimization by comparing their performance to a MIP-based approach.

Multicomponent Therapeutics of Berberine Alkaloids

PubMed Central

Luo, Jiaoyang; Yan, Dan; Yang, Meihua; Dong, Xiaoping; Xiao, Xiaohe

2013-01-01

Although berberine alkaloids (BAs) are reported to be with broad-spectrum antibacterial and antiviral activities, the interactions among BAs have not been elucidated. In the present study, methicillin-resistant Staphylococcus aureus (MRSA) was chosen as a model organism, and modified broth microdilution was applied for the determination of the fluorescence absorption values to calculate the anti-MRSA activity of BAs. We have initiated four steps to seek the optimal combination of BAs that are (1) determining the anti-MRSA activity of single BA, (2) investigating the two-component combination to clarify the interactions among BAs by checkerboard assay, (3) investigating the multicomponent combination to determine the optimal ratio by quadratic rotation-orthogonal combination design, and (4) in vivo and in vitro validation of the optimal combination. The results showed that the interactions among BAs are related to their concentrations. The synergetic combinations included “berberine and epiberberine,” “jatrorrhizine and palmatine” and “jatrorrhizine and coptisine”; the antagonistic combinations included “coptisine and epiberberine”. The optimal combination was berberine : coptisine : jatrorrhizine : palmatine : epiberberine = 0.702 : 0.863 : 1 : 0.491 : 0.526, and the potency of the optimal combination on cyclophosphamide-immunocompromised mouse model was better than the natural combinations of herbs containing BAs. PMID:23634170

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

NASA Astrophysics Data System (ADS)

Hardiyanti, Y.; Haekal, M.; Waris, A.; Haryanto, F.

2016-08-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin.

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

NASA Technical Reports Server (NTRS)

Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen

2014-01-01

The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.

Sequential Quadratic Programming Algorithms for Optimization

DTIC Science & Technology

1989-08-01

quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

EUD-based biological optimization for carbon ion therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brüningk, Sarah C., E-mail: sarah.brueningk@icr.ac.uk; Kamp, Florian; Wilkens, Jan J.

2015-11-15

Purpose: Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalentmore » uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. Methods: In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Results: Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose–volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. Conclusions: EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.« less

Determination of full piezoelectric complex parameters using gradient-based optimization algorithm

NASA Astrophysics Data System (ADS)

Kiyono, C. Y.; Pérez, N.; Silva, E. C. N.

2016-02-01

At present, numerical techniques allow the precise simulation of mechanical structures, but the results are limited by the knowledge of the material properties. In the case of piezoelectric ceramics, the full model determination in the linear range involves five elastic, three piezoelectric, and two dielectric complex parameters. A successful solution to obtaining piezoceramic properties consists of comparing the experimental measurement of the impedance curve and the results of a numerical model by using the finite element method (FEM). In the present work, a new systematic optimization method is proposed to adjust the full piezoelectric complex parameters in the FEM model. Once implemented, the method only requires the experimental data (impedance modulus and phase data acquired by an impedometer), material density, geometry, and initial values for the properties. This method combines a FEM routine implemented using an 8-noded axisymmetric element with a gradient-based optimization routine based on the method of moving asymptotes (MMA). The main objective of the optimization procedure is minimizing the quadratic difference between the experimental and numerical electrical conductance and resistance curves (to consider resonance and antiresonance frequencies). To assure the convergence of the optimization procedure, this work proposes restarting the optimization loop whenever the procedure ends in an undesired or an unfeasible solution. Two experimental examples using PZ27 and APC850 samples are presented to test the precision of the method and to check the dependency of the frequency range used, respectively.

Jerk Minimization Method for Vibration Control in Buildings

NASA Technical Reports Server (NTRS)

Abatan, Ayo O.; Yao, Leummim

1997-01-01

In many vibration minimization control problems for high rise buildings subject to strong earthquake loads, the emphasis has been on a combination of minimizing the displacement, the velocity and the acceleration of the motion of the building. In most cases, the accelerations that are involved are not necessarily large but the change in them (jerk) are abrupt. These changes in magnitude or direction are responsible for most building damage and also create discomfort like motion sickness for inhabitants of these structures because of the element of surprise. We propose a method of minimizing also the jerk which is the sudden change in acceleration or the derivative of the acceleration using classical linear quadratic optimal controls. This was done through the introduction of a quadratic performance index involving the cost due to the jerk; a special change of variable; and using the jerk as a control variable. The values of the optimal control are obtained using the Riccati equation.

Analytical and simulator study of advanced transport

NASA Technical Reports Server (NTRS)

Levison, W. H.; Rickard, W. W.

1982-01-01

An analytic methodology, based on the optimal-control pilot model, was demonstrated for assessing longitidunal-axis handling qualities of transport aircraft in final approach. Calibration of the methodology is largely in terms of closed-loop performance requirements, rather than specific vehicle response characteristics, and is based on a combination of published criteria, pilot preferences, physical limitations, and engineering judgment. Six longitudinal-axis approach configurations were studied covering a range of handling qualities problems, including the presence of flexible aircraft modes. The analytical procedure was used to obtain predictions of Cooper-Harper ratings, a solar quadratic performance index, and rms excursions of important system variables.

GPU-based optimal control for RWM feedback in tokamaks

DOE PAGES

Clement, Mitchell; Hanson, Jeremy; Bialek, Jim; ...

2017-08-23

The design and implementation of a Graphics Processing Unit (GPU) based Resistive Wall Mode (RWM) controller to perform feedback control on the RWM using Linear Quadratic Gaussian (LQG) control is reported herein. Also, the control algorithm is based on a simplified DIII-D VALEN model. By using NVIDIA’s GPUDirect RDMA framework, the digitizer and output module are able to write and read directly to and from GPU memory, eliminating memory transfers between host and GPU. In conclusion, the system and algorithm was able to reduce plasma response excited by externally applied fields by 32% during development experiments.

GPU-based optimal control for RWM feedback in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clement, Mitchell; Hanson, Jeremy; Bialek, Jim

The design and implementation of a Graphics Processing Unit (GPU) based Resistive Wall Mode (RWM) controller to perform feedback control on the RWM using Linear Quadratic Gaussian (LQG) control is reported herein. Also, the control algorithm is based on a simplified DIII-D VALEN model. By using NVIDIA’s GPUDirect RDMA framework, the digitizer and output module are able to write and read directly to and from GPU memory, eliminating memory transfers between host and GPU. In conclusion, the system and algorithm was able to reduce plasma response excited by externally applied fields by 32% during development experiments.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1985-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Model test on the relationship feed energy and protein ratio to the production and quality of milk protein

NASA Astrophysics Data System (ADS)

Hartanto, R.; Jantra, M. A. C.; Santosa, S. A. B.; Purnomoadi, A.

2018-01-01

The purpose of this research was to find an appropriate relationship model between the feed energy and protein ratio with the amount of production and quality of milk proteins. This research was conducted at Getasan Sub-district, Semarang Regency, Central Java Province, Indonesia using 40 samples (Holstein Friesian cattle, lactation period II-III and lactation month 3-4). Data were analyzed using linear and quadratic regressions, to predict the production and quality of milk protein from feed energy and protein ratio that describe the diet. The significance of model was tested using analysis of variance. Coefficient of determination (R2), residual variance (RV) and root mean square prediction error (RMSPE) were reported for the developed equations as an indicator of the goodness of model fit. The results showed no relationship in milk protein (kg), milk casein (%), milk casein (kg) and milk urea N (mg/dl) as function of CP/TDN. The significant relationship was observed in milk production (L or kg) and milk protein (%) as function of CP/TDN, both in linear and quadratic models. In addition, a quadratic change in milk production (L) (P = 0.003), milk production (kg) (P = 0.003) and milk protein concentration (%) (P = 0.026) were observed with increase of CP/TDN. It can be concluded that quadratic equation was the good fitting model for this research, because quadratic equation has larger R2, smaller RV and smaller RMSPE than those of linear equation.

Optimization of β-cyclodextrin-based flavonol extraction from apple pomace using response surface methodology.

PubMed

Parmar, Indu; Sharma, Sowmya; Rupasinghe, H P Vasantha

2015-04-01

The present study investigated five cyclodextrins (CDs) for the extraction of flavonols from apple pomace powder and optimized β-CD based extraction of total flavonols using response surface methodology. A 2(3) central composite design with β-CD concentration (0-5 g 100 mL(-1)), extraction temperature (20-72 °C), extraction time (6-48 h) and second-order quadratic model for the total flavonol yield (mg 100 g(-1) DM) was selected to generate the response surface curves. The optimal conditions obtained were: β-CD concentration, 2.8 g 100 mL(-1); extraction temperature, 45 °C and extraction time, 25.6 h that predicted the extraction of 166.6 mg total flavonols 100 g(-1) DM. The predicted amount was comparable to the experimental amount of 151.5 mg total flavonols 100 g(-1) DM obtained from optimal β-CD based parameters, thereby giving a low absolute error and adequacy of fitted model. In addition, the results from optimized extraction conditions showed values similar to those obtained through previously established solvent based sonication assisted flavonol extraction procedure. To the best of our knowledge, this is the first study to optimize aqueous β-CD based flavonol extraction which presents an environmentally safe method for value-addition to under-utilized bio resources.

Extrinsic and intrinsic index finger muscle attachments in an OpenSim upper-extremity model.

PubMed

Lee, Jong Hwa; Asakawa, Deanna S; Dennerlein, Jack T; Jindrich, Devin L

2015-04-01

Musculoskeletal models allow estimation of muscle function during complex tasks. We used objective methods to determine possible attachment locations for index finger muscles in an OpenSim upper-extremity model. Data-driven optimization algorithms, Simulated Annealing and Hook-Jeeves, estimated tendon locations crossing the metacarpophalangeal (MCP), proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints by minimizing the difference between model-estimated and experimentally-measured moment arms. Sensitivity analysis revealed that multiple sets of muscle attachments with similar optimized moment arms are possible, requiring additional assumptions or data to select a single set of values. The most smooth muscle paths were assumed to be biologically reasonable. Estimated tendon attachments resulted in variance accounted for (VAF) between calculated moment arms and measured values of 78% for flex/extension and 81% for ab/adduction at the MCP joint. VAF averaged 67% at the PIP joint and 54% at the DIP joint. VAF values at PIP and DIP joints partially reflected the constant moment arms reported for muscles about these joints. However, all moment arm values found through optimization were non-linear and non-constant. Relationships between moment arms and joint angles were best described with quadratic equations for tendons at the PIP and DIP joints.

Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

2011-12-01

This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Entanglement in a model for Hawking radiation: An application of quadratic algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bambah, Bindu A., E-mail: bbsp@uohyd.ernet.in; Mukku, C., E-mail: mukku@iiit.ac.in; Shreecharan, T., E-mail: shreecharan@gmail.com

2013-03-15

Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, wemore » study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.« less

[Joint effects of water temperature and salinity on the expression of gill Hsp70 gene in Pinctada martensii (Dunker)].

PubMed

Wang, Ya-Nan; Wang, Hui; Zhu, Xiao-Wen; Luo, Ming-Ming; Liu, Zhi-Gang; Du, Xiao-Dong

2012-12-01

By using central composite experimental design and response surface method, the joint effects of water temperature (16-40 degrees C) and salinity (10-50) on the expression of gill Hsp70 gene in Pinctada martensii (Dunker) were studied under laboratory conditions. The results showed that the linear and quadratic effects of temperature on the expression of gill Hsp70 gene were significant, the linear effect of salinity was not significant, while the quadratic effect of salinity was significant. The interactive effect of temperature and salinity was not significant, and the effect of temperature was greater than that of salinity. The model equation of the gill Hsp70 gene expression was established, with the R2, Adj. R2, and Pred. R2 as high as 98.7%, 97.4%, and 89.2%, respectively, suggesting that the overarching predictive capability of the model was very satisfactory, and could be practicably applied for prediction. Through the optimization of the model, the expression of the gill Hsp70 gene reached its minimum (0.5276) when the temperature was 26.78 degrees C and the salinity was 29.33, with the desirability value being 98%. These experimental results could offer theoretical reference for the high expression of gill Hsp70 gene in P. martensii, the maintenance of cell internal environment stability, and the enhancement of P. martensii stress resistance.

Multi-objective design optimization and control of magnetorheological fluid brakes for automotive applications

NASA Astrophysics Data System (ADS)

Shamieh, Hadi; Sedaghati, Ramin

2017-12-01

The magnetorheological brake (MRB) is an electromechanical device that generates a retarding torque through employing magnetorheological (MR) fluids. The objective of this paper is to design, optimize and control an MRB for automotive applications considering. The dynamic range of a disk-type MRB expressing the ratio of generated toque at on and off states has been formulated as a function of the rotational speed, geometrical and material properties, and applied electrical current. Analytical magnetic circuit analysis has been conducted to derive the relation between magnetic field intensity and the applied electrical current as a function of the MRB geometrical and material properties. A multidisciplinary design optimization problem has then been formulated to identify the optimal brake geometrical parameters to maximize the dynamic range and minimize the response time and weight of the MRB under weight, size and magnetic flux density constraints. The optimization problem has been solved using combined genetic and sequential quadratic programming algorithms. Finally, the performance of the optimally designed MRB has been investigated in a quarter vehicle model. A PID controller has been designed to regulate the applied current required by the MRB in order to improve vehicle’s slipping on different road conditions.

Slushy weightings for the optimal pilot model. [considering visual tracking task

NASA Technical Reports Server (NTRS)

Dillow, J. D.; Picha, D. G.; Anderson, R. O.

1975-01-01

A pilot model is described which accounts for the effect of motion cues in a well defined visual tracking task. The effect of visual and motion cues are accounted for in the model in two ways. First, the observation matrix in the pilot model is structured to account for the visual and motion inputs presented to the pilot. Secondly, the weightings in the quadratic cost function associated with the pilot model are modified to account for the pilot's perception of the variables he considers important in the task. Analytic results obtained using the pilot model are compared to experimental results and in general good agreement is demonstrated. The analytic model yields small improvements in tracking performance with the addition of motion cues for easily controlled task dynamics and large improvements in tracking performance with the addition of motion cues for difficult task dynamics.

Ghost-free, finite, fourth-order D = 3 gravity.

PubMed

Deser, S

2009-09-04

Canonical analysis of a recently proposed linear + quadratic curvature gravity model in D = 3 establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing D > 3 quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode's second-derivative nature forfeits finiteness.

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

2012-01-01

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

Dynamics and Control of a Quadrotor with Active Geometric Morphing

NASA Astrophysics Data System (ADS)

Wallace, Dustin A.

Quadrotors are manufactured in a wide variety of shapes, sizes, and performance levels to fulfill a multitude of roles. Robodub Inc. has patented a morphing quadrotor which will allow active reconfiguration between various shapes for performance optimization across a wider spectrum of roles. The dynamics of the system are studied and modeled using Newtonian Mechanics. Controls are developed and simulated using both Linear Quadratic and Numerical Nonlinear Optimal control for a symmetric simplificiation of the system dynamics. Various unique vehicle capabilities are investigated, including novel single-throttle flight control using symmetric geometric morphing, as well as recovery from motor loss by reconfiguring into a trirotor configuration. The system dynamics were found to be complex and highly nonlinear. All attempted control strategies resulted in controllability, suggesting further research into each may lead to multiple viable control strategies for a physical prototype.

Optimization of Bread Enriched with Garcinia mangostana Pericarp Powder

NASA Astrophysics Data System (ADS)

Ibrahim, U. K.; Salleh, R. Mohd; Maqsood-ul-Hague, S. N. S.; Hashib, S. Abd; Karim, S. F. Abd

2018-05-01

The aim of present work is to optimize the formulation of bread enhanced with Garcinia mangostana pericarp powder with the combination of baking process conditions. The independent variables used were baking time (15 - 30 minutes), baking temperature (180 - 220°C) and pericarp powder concentration (0.5 - 2.0%). The physical and chemical properties of bread sample such as antioxidant activity, phenolic content, moisture analysis and colour parameters were studied. Bread dough without fortification of pericarp powder was used as control. Data obtained were analyzed by multiple regressions and the significant model such as linear and quadratic with variables interactions were used. As a conclusion, the optimum baking conditions were found at 213°C baking temperature with 23 minutes baking time and addition of 0.87% for Garcinia mangostana pericarp powder to the bread formulation.

Method for optimizing channelized quadratic observers for binary classification of large-dimensional image datasets

PubMed Central

Kupinski, M. K.; Clarkson, E.

2015-01-01

We present a new method for computing optimized channels for channelized quadratic observers (CQO) that is feasible for high-dimensional image data. The method for calculating channels is applicable in general and optimal for Gaussian distributed image data. Gradient-based algorithms for determining the channels are presented for five different information-based figures of merit (FOMs). Analytic solutions for the optimum channels for each of the five FOMs are derived for the case of equal mean data for both classes. The optimum channels for three of the FOMs under the equal mean condition are shown to be the same. This result is critical since some of the FOMs are much easier to compute. Implementing the CQO requires a set of channels and the first- and second-order statistics of channelized image data from both classes. The dimensionality reduction from M measurements to L channels is a critical advantage of CQO since estimating image statistics from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. In a simulation study we compare the performance of ideal and Hotelling observers to CQO. The optimal CQO channels are calculated using both eigenanalysis and a new gradient-based algorithm for maximizing Jeffrey's divergence (J). Optimal channel selection without eigenanalysis makes the J-CQO on large-dimensional image data feasible. PMID:26366764

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics

PubMed Central

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-01-01

Motivation: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of O(n6). Subsequently, numerous faster ‘Sankoff-style’ approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity (≥ quartic time). Results: Breaking this barrier, we introduce the novel Sankoff-style algorithm ‘sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)’, which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff’s original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25838465

Determination of Strength Exercise Intensities Based on the Load-Power-Velocity Relationship

PubMed Central

Jandačka, Daniel; Beremlijski, Petr

2011-01-01

The velocity of movement and applied load affect the production of mechanical power output and subsequently the extent of the adaptation stimulus in strength exercises. We do not know of any known function describing the relationship of power and velocity and load in the bench press exercise. The objective of the study is to find a function modeling of the relationship of relative velocity, relative load and mechanical power output for the bench press exercise and to determine the intensity zones of the exercise for specifically focused strength training of soccer players. Fifteen highly trained soccer players at the start of a competition period were studied. The subjects of study performed bench presses with the load of 0, 10, 30, 50, 70 and 90% of the predetermined one repetition maximum with maximum possible speed of movement. The mean measured power and velocity for each load (kg) were used to develop a multiple linear regression function which describes the quadratic relationship between the ratio of power (W) to maximum power (W) and the ratios of the load (kg) to one repetition maximum (kg) and the velocity (m•s−1) to maximal velocity (m•s−1). The quadratic function of two variables that modeled the searched relationship explained 74% of measured values in the acceleration phase and 75% of measured values from the entire extent of the positive power movement in the lift. The optimal load for reaching maximum power output suitable for the dynamics effort strength training was 40% of one repetition maximum, while the optimal mean velocity would be 75% of maximal velocity. Moreover, four zones: maximum power, maximum velocity, velocity-power and strength-power were determined on the basis of the regression function. PMID:23486484

Determination of strength exercise intensities based on the load-power-velocity relationship.

PubMed

Jandačka, Daniel; Beremlijski, Petr

2011-06-01

The velocity of movement and applied load affect the production of mechanical power output and subsequently the extent of the adaptation stimulus in strength exercises. We do not know of any known function describing the relationship of power and velocity and load in the bench press exercise. The objective of the study is to find a function modeling of the relationship of relative velocity, relative load and mechanical power output for the bench press exercise and to determine the intensity zones of the exercise for specifically focused strength training of soccer players. Fifteen highly trained soccer players at the start of a competition period were studied. The subjects of study performed bench presses with the load of 0, 10, 30, 50, 70 and 90% of the predetermined one repetition maximum with maximum possible speed of movement. The mean measured power and velocity for each load (kg) were used to develop a multiple linear regression function which describes the quadratic relationship between the ratio of power (W) to maximum power (W) and the ratios of the load (kg) to one repetition maximum (kg) and the velocity (m•s(-1)) to maximal velocity (m•s(-1)). The quadratic function of two variables that modeled the searched relationship explained 74% of measured values in the acceleration phase and 75% of measured values from the entire extent of the positive power movement in the lift. The optimal load for reaching maximum power output suitable for the dynamics effort strength training was 40% of one repetition maximum, while the optimal mean velocity would be 75% of maximal velocity. Moreover, four zones: maximum power, maximum velocity, velocity-power and strength-power were determined on the basis of the regression function.

Tipping points? Curvilinear associations between activity level and mental development in toddlers.

PubMed

Flom, Megan; Cohen, Madeleine; Saudino, Kimberly J

2017-05-01

The Theory of Optimal Stimulation (Zentall & Zentall, Psychological Bulletin, 94, 1983, 446) posits that the relation between activity level (AL) and cognitive performance follows an inverted U shape where midrange AL predicts better cognitive performance than AL at the extremes. We explored this by fitting linear and quadratic models predicting mental development from AL assessed via multiple methods (parent ratings, observations, and actigraphs) and across multiple situations (laboratory play, laboratory test, home) in over 600 twins (2- and 3-year olds). Only observed AL in the laboratory was curvilinearly related to mental development scores. Results replicated across situations, age, and twin samples, providing strong support for the optimal stimulation model for this measure of AL in early childhood. Different measures of AL provide different information. Observations of AL which include both qualitative and quantitative aspects of AL within structured situations are able to capture beneficial aspects of normative AL as well as detriments of both low and high AL. © 2016 Association for Child and Adolescent Mental Health.

Optimal Solar PV Arrays Integration for Distributed Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Omitaomu, Olufemi A; Li, Xueping

2012-01-01

Solar photovoltaic (PV) systems hold great potential for distributed energy generation by installing PV panels on rooftops of residential and commercial buildings. Yet challenges arise along with the variability and non-dispatchability of the PV systems that affect the stability of the grid and the economics of the PV system. This paper investigates the integration of PV arrays for distributed generation applications by identifying a combination of buildings that will maximize solar energy output and minimize system variability. Particularly, we propose mean-variance optimization models to choose suitable rooftops for PV integration based on Markowitz mean-variance portfolio selection model. We further introducemore » quantity and cardinality constraints to result in a mixed integer quadratic programming problem. Case studies based on real data are presented. An efficient frontier is obtained for sample data that allows decision makers to choose a desired solar energy generation level with a comfortable variability tolerance level. Sensitivity analysis is conducted to show the tradeoffs between solar PV energy generation potential and variability.« less

Response Surface Methodology for the Optimization of Preparation of Biocomposites Based on Poly(lactic acid) and Durian Peel Cellulose

PubMed Central

Penjumras, Patpen; Abdul Rahman, Russly; Talib, Rosnita A.; Abdan, Khalina

2015-01-01

Response surface methodology was used to optimize preparation of biocomposites based on poly(lactic acid) and durian peel cellulose. The effects of cellulose loading, mixing temperature, and mixing time on tensile strength and impact strength were investigated. A central composite design was employed to determine the optimum preparation condition of the biocomposites to obtain the highest tensile strength and impact strength. A second-order polynomial model was developed for predicting the tensile strength and impact strength based on the composite design. It was found that composites were best fit by a quadratic regression model with high coefficient of determination (R 2) value. The selected optimum condition was 35 wt.% cellulose loading at 165°C and 15 min of mixing, leading to a desirability of 94.6%. Under the optimum condition, the tensile strength and impact strength of the biocomposites were 46.207 MPa and 2.931 kJ/m2, respectively. PMID:26167523

Integrating uniform design and response surface methodology to optimize thiacloprid suspension

PubMed Central

Li, Bei-xing; Wang, Wei-chang; Zhang, Xian-peng; Zhang, Da-xia; Mu, Wei; Liu, Feng

2017-01-01

A model 25% suspension concentrate (SC) of thiacloprid was adopted to evaluate an integrative approach of uniform design and response surface methodology. Tersperse2700, PE1601, xanthan gum and veegum were the four experimental factors, and the aqueous separation ratio and viscosity were the two dependent variables. Linear and quadratic polynomial models of stepwise regression and partial least squares were adopted to test the fit of the experimental data. Verification tests revealed satisfactory agreement between the experimental and predicted data. The measured values for the aqueous separation ratio and viscosity were 3.45% and 278.8 mPa·s, respectively, and the relative errors of the predicted values were 9.57% and 2.65%, respectively (prepared under the proposed conditions). Comprehensive benefits could also be obtained by appropriately adjusting the amount of certain adjuvants based on practical requirements. Integrating uniform design and response surface methodology is an effective strategy for optimizing SC formulas. PMID:28383036

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Bio-inspired computational heuristics to study Lane-Emden systems arising in astrophysics model.

PubMed

Ahmad, Iftikhar; Raja, Muhammad Asif Zahoor; Bilal, Muhammad; Ashraf, Farooq

2016-01-01

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.

Optimization of cascade blade mistuning. I - Equations of motion and basic inherent properties

NASA Technical Reports Server (NTRS)

Nissim, E.

1985-01-01

Attention is given to the derivation of the equations of motion of mistuned compressor blades, interpolating aerodynamic coefficients by means of quadratic expressions in the reduced frequency. If the coefficients of the quadratic expressions are permitted to assume complex values, excellent accuracy is obtained and Pade rational expressions are obviated. On the basis of the resulting equations, it is shown analytically that the sum of all the real parts of the eigenvalues is independent of the mistuning introduced into the system. Blade mistuning is further treated through the aerodynamic energy approach, and the limiting vibration modes associated with alternative mistunings are identified.

Use of nonlinear programming to optimize performance response to energy density in broiler feed formulation.

PubMed

Guevara, V R

2004-02-01

A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.

Optimization of diesel oil biodegradation in seawater using statistical experimental methodology.

PubMed

Xia, Wenxiang; Li, Jincheng; Xia, Yan; Song, Zhiwen; Zhou, Jihong

2012-01-01

Petroleum hydrocarbons released into the environment can be harmful to higher organisms, but they can be utilized by microorganisms as the sole source of energy for metabolism. To investigate the optimal conditions of diesel oil biodegradation, the Plackett-Burman (PB) design was used for the optimization in the first step, and N source (NaNO₃), P source (KH₂PO₄) and pH were found to be significant factors affecting oil degradation. Then the response surface methodology (RSM) using a central composite design (CCD) was adopted for the augmentation of diesel oil biodegradation and a fitted quadratic model was obtained. The model F-value of 27.25 and the low probability value (<0.0001) indicate that the model is significant and that the concentration of NaNO₃N, KH₂PO₄ and pH had significant effects on oil removal during the study. Three-dimensional response surface plots were constructed by plotting the response (oil degradation efficiency) on the z-axis against any two independent variables, and the optimal biodegradation conditions of diesel oil (original total petroleum hydrocarbons 125 mg/L) were determined as follows: NaNO₃ 0.143 g, KH₂PO₄ 0.022 g and pH 7.4. These results fit quite well with the C, N and P ratio in biological cells. Results from the present study might provide a new method to estimate the optimal nitrogen and phosphorus concentration in advance for oil biodegradation according to the composition of petroleum.

Modeling and verification of process parameters for the production of tannase by Aspergillus oryzae under submerged fermentation using agro-wastes.

PubMed

Varadharajan, Venkatramanan; Vadivel, Sudhan Shanmuga; Ramaswamy, Arulvel; Sundharamurthy, Venkatesaprabhu; Chandrasekar, Priyadharshini

2017-01-01

Tannase production by Aspergillus oryzae using various agro-wastes as substrates by submerged fermentation was studied in this research. The microbe was isolated from degrading corn kernel obtained from the corn fields at Tiruchengode, India. The microbial identification was done using 18S rRNA gene analysis. The agro-wastes chosen for the study were pomegranate rind, Cassia auriculata flower, black gram husk, and tea dust. The process parameters chosen for optimization study were substrate concentration, pH, temperature, and incubation period. During one variable at a time optimization, the pomegranate rind extract produced maximum tannase activity of 138.12 IU/mL and it was chosen as the best substrate for further experiments. The quadratic model was found to be the effective model for prediction of tannase production by A. oryzae. The optimized conditions predicted by response surface methodology (RSM) with genetic algorithm (GA) were 1.996% substrate concentration, pH of 4.89, temperature of 34.91 °C, and an incubation time of 70.65 H with maximum tannase activity of 138.363 IU/mL. The confirmatory experiment under optimized conditions showed tannase activity of 139.22 IU/mL. Hence, RSM-GA pair was successfully used in this study to optimize the process parameters required for the production of tannase using pomegranate rind. © 2015 International Union of Biochemistry and Molecular Biology, Inc.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

Output Feedback Adaptive Control of Non-Minimum Phase Systems Using Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Hashemi, Kelley E.; Yucelen, Tansel; Arabi, Ehsan

2018-01-01

This paper describes output feedback adaptive control approaches for non-minimum phase SISO systems with relative degree 1 and non-strictly positive real (SPR) MIMO systems with uniform relative degree 1 using the optimal control modification method. It is well-known that the standard model-reference adaptive control (MRAC) cannot be used to control non-SPR plants to track an ideal SPR reference model. Due to the ideal property of asymptotic tracking, MRAC attempts an unstable pole-zero cancellation which results in unbounded signals for non-minimum phase SISO systems. The optimal control modification can be used to prevent the unstable pole-zero cancellation which results in a stable adaptation of non-minimum phase SISO systems. However, the tracking performance using this approach could suffer if the unstable zero is located far away from the imaginary axis. The tracking performance can be recovered by using an observer-based output feedback adaptive control approach which uses a Luenberger observer design to estimate the state information of the plant. Instead of explicitly specifying an ideal SPR reference model, the reference model is established from the linear quadratic optimal control to account for the non-minimum phase behavior of the plant. With this non-minimum phase reference model, the observer-based output feedback adaptive control can maintain stability as well as tracking performance. However, in the presence of the mismatch between the SPR reference model and the non-minimum phase plant, the standard MRAC results in unbounded signals, whereas a stable adaptation can be achieved with the optimal control modification. An application of output feedback adaptive control for a flexible wing aircraft illustrates the approaches.

Importance of the cutoff value in the quadratic adaptive integrate-and-fire model.

PubMed

Touboul, Jonathan

2009-08-01

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value V(c) or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing V(c) can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.

Incorporating deliverable monitor unit constraints into spot intensity optimization in intensity modulated proton therapy treatment planning

PubMed Central

Cao, Wenhua; Lim, Gino; Li, Xiaoqiang; Li, Yupeng; Zhu, X. Ronald; Zhang, Xiaodong

2014-01-01

The purpose of this study is to investigate the feasibility and impact of incorporating deliverable monitor unit (MU) constraints into spot intensity optimization in intensity modulated proton therapy (IMPT) treatment planning. The current treatment planning system (TPS) for IMPT disregards deliverable MU constraints in the spot intensity optimization (SIO) routine. It performs a post-processing procedure on an optimized plan to enforce deliverable MU values that are required by the spot scanning proton delivery system. This procedure can create a significant dose distribution deviation between the optimized and post-processed deliverable plans, especially when small spot spacings are used. In this study, we introduce a two-stage linear programming (LP) approach to optimize spot intensities and constrain deliverable MU values simultaneously, i.e., a deliverable spot intensity optimization (DSIO) model. Thus, the post-processing procedure is eliminated and the associated optimized plan deterioration can be avoided. Four prostate cancer cases at our institution were selected for study and two parallel opposed beam angles were planned for all cases. A quadratic programming (QP) based model without MU constraints, i.e., a conventional spot intensity optimization (CSIO) model, was also implemented to emulate the commercial TPS. Plans optimized by both the DSIO and CSIO models were evaluated for five different settings of spot spacing from 3 mm to 7 mm. For all spot spacings, the DSIO-optimized plans yielded better uniformity for the target dose coverage and critical structure sparing than did the CSIO-optimized plans. With reduced spot spacings, more significant improvements in target dose uniformity and critical structure sparing were observed in the DSIO- than in the CSIO-optimized plans. Additionally, better sparing of the rectum and bladder was achieved when reduced spacings were used for the DSIO-optimized plans. The proposed DSIO approach ensures the deliverability of optimized IMPT plans that take into account MU constraints. This eliminates the post-processing procedure required by the TPS as well as the resultant deteriorating effect on ultimate dose distributions. This approach therefore allows IMPT plans to adopt all possible spot spacings optimally. Moreover, dosimetric benefits can be achieved using smaller spot spacings. PMID:23835656

Design of a compensation for an ARMA model of a discrete time system. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mainemer, C. I.

1978-01-01

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

NASA Astrophysics Data System (ADS)

Sutrisno, Widowati, Tjahjana, R. Heru

2017-12-01

The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

Adiabatic Quantum Computing via the Rydberg Blockade

NASA Astrophysics Data System (ADS)

Keating, Tyler; Goyal, Krittika; Deutsch, Ivan

2012-06-01

We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. We model a realistic architecture, including the effects of magnetic level structure, with qubits encoded into the clock states of ^133Cs, effective B-fields implemented through microwaves and light shifts, and atom-atom coupling achieved by excitation to a high-lying Rydberg level. Including the fundamental effects of photon scattering we find a high fidelity for the two-qubit implementation.

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

NASA Technical Reports Server (NTRS)

Panossian, H.

2008-01-01

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Experimental design and optimization of leaching process for recovery of valuable chemical elements (U, La, V, Mo, Yb and Th) from low-grade uranium ore.

PubMed

Zakrzewska-Koltuniewicz, Grażyna; Herdzik-Koniecko, Irena; Cojocaru, Corneliu; Chajduk, Ewelina

2014-06-30

The paper deals with experimental design and optimization of leaching process of uranium and associated metals from low-grade, Polish ores. The chemical elements of interest for extraction from the ore were U, La, V, Mo, Yb and Th. Sulphuric acid has been used as leaching reagent. Based on the design of experiments the second-order regression models have been constructed to approximate the leaching efficiency of elements. The graphical illustrations using 3-D surface plots have been employed in order to identify the main, quadratic and interaction effects of the factors. The multi-objective optimization method based on desirability approach has been applied in this study. The optimum condition have been determined as P=5 bar, T=120 °C and t=90 min. Under these optimal conditions, the overall extraction performance is 81.43% (for U), 64.24% (for La), 98.38% (for V), 43.69% (for Yb) and 76.89% (for Mo) and 97.00% (for Th). Copyright © 2014 Elsevier B.V. All rights reserved.

A neural network based implementation of an MPC algorithm applied in the control systems of electromechanical plants

NASA Astrophysics Data System (ADS)

Marusak, Piotr M.; Kuntanapreeda, Suwat

2018-01-01

The paper considers application of a neural network based implementation of a model predictive control (MPC) control algorithm to electromechanical plants. Properties of such control plants implicate that a relatively short sampling time should be used. However, in such a case, finding the control value numerically may be too time-consuming. Therefore, the current paper tests the solution based on transforming the MPC optimization problem into a set of differential equations whose solution is the same as that of the original optimization problem. This set of differential equations can be interpreted as a dynamic neural network. In such an approach, the constraints can be introduced into the optimization problem with relative ease. Moreover, the solution of the optimization problem can be obtained faster than when the standard numerical quadratic programming routine is used. However, a very careful tuning of the algorithm is needed to achieve this. A DC motor and an electrohydraulic actuator are taken as illustrative examples. The feasibility and effectiveness of the proposed approach are demonstrated through numerical simulations.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Digital robust control law synthesis using constrained optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivekananda

1989-01-01

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks.

PubMed

Li, Zhijun; Ge, Shuzhi Sam; Liu, Sibang

2014-08-01

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First,more » the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Wang, Chenyu; Li, Mingjie

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

DOE PAGES

Zhou, Ping; Wang, Chenyu; Li, Mingjie; ...

2018-01-31

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, themore » modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.« less

Consideration of computer limitations in implementing on-line controls. M.S. Thesis

NASA Technical Reports Server (NTRS)

Roberts, G. K.

1976-01-01

A formal statement of the optimal control problem which includes the interval of dicretization as an optimization parameter, and extend this to include selection of a control algorithm as part of the optimization procedure, is formulated. The performance of the scalar linear system depends on the discretization interval. Discrete-time versions of the output feedback regulator and an optimal compensator, and the use of these results in presenting an example of a system for which fast partial-state-feedback control better minimizes a quadratic cost than either a full-state feedback control or a compensator, are developed.

Spatial analysis of the distribution of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) and losses in maize crop productivity using geostatistics.

PubMed

Farias, Paulo R S; Barbosa, José C; Busoli, Antonio C; Overal, William L; Miranda, Vicente S; Ribeiro, Susane M

2008-01-01

The fall armyworm, Spodoptera frugiperda (J.E. Smith), is one of the chief pests of maize in the Americas. The study of its spatial distribution is fundamental for designing correct control strategies, improving sampling methods, determining actual and potential crop losses, and adopting precise agricultural techniques. In São Paulo state, Brazil, a maize field was sampled at weekly intervals, from germination through harvest, for caterpillar densities, using quadrates. In each of 200 quadrates, 10 plants were sampled per week. Harvest weights were obtained in the field for each quadrate, and ear diameters and lengths were also sampled (15 ears per quadrate) and used to estimate potential productivity of the quadrate. Geostatistical analyses of caterpillar densities showed greatest ranges for small caterpillars when semivariograms were adjusted for a spherical model that showed greatest fit. As the caterpillars developed in the field, their spatial distribution became increasingly random, as shown by a model adjusted to a straight line, indicating a lack of spatial dependence among samples. Harvest weight and ear length followed the spherical model, indicating the existence of spatial variability of the production parameters in the maize field. Geostatistics shows promise for the application of precise methods in the integrated control of pests.

Statistical optimization of medium components and growth conditions by response surface methodology to enhance phenol degradation by Pseudomonas putida.

PubMed

Annadurai, Gurusamy; Ling, Lai Yi; Lee, Jiunn-Fwu

2008-02-28

In this work, a four-level Box-Behnken factorial design was employed combining with response surface methodology (RSM) to optimize the medium composition for the degradation of phenol by pseudomonas putida (ATCC 31800). A mathematical model was then developed to show the effect of each medium composition and their interactions on the biodegradation of phenol. Response surface method was using four levels like glucose, yeast extract, ammonium sulfate and sodium chloride, which also enabled the identification of significant effects of interactions for the batch studies. The biodegradation of phenol on Pseudomonas putida (ATCC 31800) was determined to be pH-dependent and the maximum degradation capacity of microorganism at 30 degrees C when the phenol concentration was 0.2 g/L and the pH of the solution was 7.0. Second order polynomial regression model was used for analysis of the experiment. Cubic and quadratic terms were incorporated into the regression model through variable selection procedures. The experimental values are in good agreement with predicted values and the correlation coefficient was found to be 0.9980.

Optimization of CO2 laser cutting parameters on Austenitic type Stainless steel sheet

NASA Astrophysics Data System (ADS)

Parthiban, A.; Sathish, S.; Chandrasekaran, M.; Ravikumar, R.

2017-03-01

Thin AISI 316L stainless steel sheet widely used in sheet metal processing industries for specific applications. CO2 laser cutting is one of the most popular sheet metal cutting processes for cutting of sheets in different profile. In present work various cutting parameters such as laser power (2000 watts-4000 watts), cutting speed (3500mm/min - 5500 mm/min) and assist gas pressure (0.7 Mpa-0.9Mpa) for cutting of AISI 316L 2mm thickness stainless sheet. This experimentation was conducted based on Box-Behenken design. The aim of this work is to develop a mathematical model kerf width for straight and curved profile through response surface methodology. The developed mathematical models for straight and curved profile have been compared. The Quadratic models have the best agreement with experimental data, and also the shape of the profile a substantial role in achieving to minimize the kerf width. Finally the numerical optimization technique has been used to find out best optimum laser cutting parameter for both straight and curved profile cut.

Limb darkening and exoplanets - II. Choosing the best law for optimal retrieval of transit parameters

NASA Astrophysics Data System (ADS)

Espinoza, Néstor; Jordán, Andrés

2016-04-01

Very precise measurements of exoplanet transit light curves both from ground- and space-based observatories make it now possible to fit the limb-darkening coefficients in the transit-fitting procedure rather than fix them to theoretical values. This strategy has been shown to give better results, as fixing the coefficients to theoretical values can give rise to important systematic errors which directly impact the physical properties of the system derived from such light curves such as the planetary radius. However, studies of the effect of limb-darkening assumptions on the retrieved parameters have mostly focused on the widely used quadratic limb-darkening law, leaving out other proposed laws that are either simpler or better descriptions of model intensity profiles. In this work, we show that laws such as the logarithmic, square-root and three-parameter law do a better job that the quadratic and linear laws when deriving parameters from transit light curves, both in terms of bias and precision, for a wide range of situations. We therefore recommend to study which law to use on a case-by-case basis. We provide code to guide the decision of when to use each of these laws and select the optimal one in a mean-square error sense, which we note has a dependence on both stellar and transit parameters. Finally, we demonstrate that the so-called exponential law is non-physical as it typically produces negative intensities close to the limb and should therefore not be used.

Extremal entanglement witnesses

NASA Astrophysics Data System (ADS)

Hansen, Leif Ove; Hauge, Andreas; Myrheim, Jan; Sollid, Per Øyvind

2015-02-01

We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus TrΩρ≥0 when Ω is a witness and ρ is a pure product state, ρ=ψψ† with ψ=ϕ⊗χ. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value f(ϕ,χ)=TrΩρ as a function of vectors ϕ and χ is a positive semidefinite biquadratic form. Every zero of f(ϕ,χ) imposes strong real-linear constraints on f and Ω. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of f(ϕ,χ) is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Adiabatic quantum computation with neutral atoms via the Rydberg blockade

NASA Astrophysics Data System (ADS)

Goyal, Krittika; Deutsch, Ivan

2011-05-01

We study a trapped-neutral-atom implementation of the adiabatic model of quantum computation whereby the Hamiltonian of a set of interacting qubits is changed adiabatically so that its ground state evolves to the desired output of the algorithm. We employ the ``Rydberg blockade interaction,'' which previously has been used to implement two-qubit entangling gates in the quantum circuit model. Here it is employed via off-resonant virtual dressing of the excited levels, so that atoms always remain in the ground state. The resulting dressed-Rydberg interaction is insensitive to the distance between the atoms within a certain blockade radius, making this process robust to temperature and vibrational fluctuations. Single qubit interactions are implemented with global microwaves and atoms are locally addressed with light shifts. With these ingredients, we study a protocol to implement the two-qubit Quadratic Unconstrained Binary Optimization (QUBO) problem. We model atom trapping, addressing, coherent evolution, and decoherence. We also explore collective control of the many-atom system and generalize the QUBO problem to multiple qubits. We study a trapped-neutral-atom implementation of the adiabatic model of quantum computation whereby the Hamiltonian of a set of interacting qubits is changed adiabatically so that its ground state evolves to the desired output of the algorithm. We employ the ``Rydberg blockade interaction,'' which previously has been used to implement two-qubit entangling gates in the quantum circuit model. Here it is employed via off-resonant virtual dressing of the excited levels, so that atoms always remain in the ground state. The resulting dressed-Rydberg interaction is insensitive to the distance between the atoms within a certain blockade radius, making this process robust to temperature and vibrational fluctuations. Single qubit interactions are implemented with global microwaves and atoms are locally addressed with light shifts. With these ingredients, we study a protocol to implement the two-qubit Quadratic Unconstrained Binary Optimization (QUBO) problem. We model atom trapping, addressing, coherent evolution, and decoherence. We also explore collective control of the many-atom system and generalize the QUBO problem to multiple qubits. We acknowledge funding from the AQUARIUS project, Sandia National Laboratories

Multivariate optimization of a synergistic blend of oleoresin sage (Salvia officinalis L.) and ascorbyl palmitate to stabilize sunflower oil.

PubMed

Upadhyay, Rohit; Mishra, Hari Niwas

2016-04-01

The simultaneous optimization of a synergistic blend of oleoresin sage (SAG) and ascorbyl palmitate (AP) in sunflower oil (SO) was performed using central composite and rotatable design coupled with principal component analysis (PCA) and response surface methodology (RSM). The physicochemical parameters viz., peroxide value, anisidine value, free fatty acids, induction period, total polar matter, antioxidant capacity and conjugated diene value were considered as response variables. PCA reduced the original set of correlated responses to few uncorrelated principal components (PC). The PC1 (eigen value, 5.78; data variance explained, 82.53 %) was selected for optimization using RSM. The quadratic model adequately described the data (R (2) = 0. 91, p < 0.05) and lack of fit was insignificant (p > 0.05). The contour plot of PC 1 score indicated the optimal synergistic combination of 1289.19 and 218.06 ppm for SAG and AP, respectively. This combination of SAG and AP resulted in shelf life of 320 days at 25 °C estimated using linear shelf life prediction model. In conclusion, the versatility of PCA-RSM approach has resulted in an easy interpretation in multiple response optimizations. This approach can be considered as a useful guide to develop new oil blends stabilized with food additives from natural sources.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Thermal response test data of five quadratic cross section precast pile heat exchangers.

PubMed

Alberdi-Pagola, Maria

2018-06-01

This data article comprises records from five Thermal Response Tests (TRT) of quadratic cross section pile heat exchangers. Pile heat exchangers, typically referred to as energy piles, consist of traditional foundation piles with embedded heat exchanger pipes. The data presented in this article are related to the research article entitled "Comparing heat flow models for interpretation of precast quadratic pile heat exchanger thermal response tests" (Alberdi-Pagola et al., 2018) [1]. The TRT data consists of measured inlet and outlet temperatures, fluid flow and injected heat rate recorded every 10 min. The field dataset is made available to enable model verification studies.

Project WISH: The Emerald City

NASA Technical Reports Server (NTRS)

Oz, Hayrani; Dunne, Jim; Butchar, Stan; George, Tommy; Hellstrom, Rob; Kringen, Tricia; Owens, George; Perrea, Mike; Semeraro, Paul; Thorndike, Phil

1992-01-01

Phase 3 of Project WISH saw the evolution of the Emerald City (E-City) from a collection of specialized independent analyses and ideas to a working structural design integrated with major support systems and analyses. Emphasis was placed on comparing and contrasting the closed and open cycle gas core nuclear rocket engines to further determine the optimum propulsive system for the E-City. Power and thermal control requirements were then defined and the question of how to meet these requirements was addressed. Software was developed to automate the mission/system/configuration analysis so changes dictated by various subsystem constraints could be managed efficiently and analyzed interactively. In addition, the liquid hydrogen propellant tank was statically designed for minimum mass and shape optimization using a finite element modeling package called SDRC I-DEAS. Spoke and shaft cross-sectional areas were optimized on ASTROS (Automated Structural Optimization System) for mass minimization. A structural dynamic analysis of the optimal structure also conducted using ASTROS enabled a study of the modes, frequencies, displacements, and accelerations of the E-City. Finally, the attitude control system design began with an initial mass moment of inertia analysis and was then designed and optimized using linear quadratic regulator control theory.

Removal of Zinc from Aqueous Solution by Optimized Oil Palm Empty Fruit Bunches Biochar as Low Cost Adsorbent

PubMed Central

Salleh, M. A. Mohd; Asady, Bahareh

2017-01-01

This study aims to produce optimized biochar from oil palm empty fruit bunches (OPEFB), as a green, low cost adsorbent for uptake of zinc from aqueous solution. The impact of pyrolysis conditions, namely, highest treatment temperature (HTT), heating rate (HR), and residence time (RT) on biochar yield and adsorption capacity towards zinc, was investigated. Mathematical modeling and optimization of independent variables were performed employing response surface methodology (RSM). HTT was found to be the most influential variable, followed by residence time and heating rate. Based on the central composite design (CCD), two quadratic models were developed to correlate three independent variables to responses. The optimum production condition for OPEFB biochar was found as follows: HTT of 615°C, HR of 8°C/min, and RT of 128 minutes. The optimum biochar showed 15.18 mg/g adsorption capacity for zinc and 25.49% of yield which was in agreement with the predicted values, satisfactory. Results of the characterization of optimum product illustrated well-developed BET surface area and porous structure in optimum product which favored its sorptive ability. PMID:28420949

SU-E-T-573: The Robustness of a Combined Margin Recipe for Uncertainties During Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stroom, J; Vieira, S; Greco, C

2014-06-01

Purpose: To investigate the variability of a safety margin recipe that combines CTV and PTV margins quadratically, with several tumor, treatment, and user related factors. Methods: Margin recipes were calculated by monte-carlo simulations in 5 steps. 1. A spherical tumor with or without isotropic microscopic was irradiated with a 5 field dose plan2. PTV: Geometric uncertainties were introduced using systematic (Sgeo) and random (sgeo) standard deviations. CTV: Microscopic disease distribution was modelled by semi-gaussian (Smicro) with varying number of islets (Ni)3. For a specific uncertainty set (Sgeo, sgeo, Smicro(Ni)), margins were varied until pre-defined decrease in TCP or dose coveragemore » was fulfilled. 4. First, margin recipes were calculated for each of the three uncertainties separately. CTV and PTV recipes were then combined quadratically to yield a final recipe M(Sgeo, sgeo, Smicro(Ni)).5. The final M was verified by simultaneous simulations of the uncertainties.Now, M has been calculated for various changing parameters like margin criteria, penumbra steepness, islet radio-sensitivity, dose conformity, and number of fractions. We subsequently investigated A: whether the combined recipe still holds in all these situations, and B: what the margin variation was in all these cases. Results: We found that the accuracy of the combined margin recipes remains on average within 1mm for all situations, confirming the correctness of the quadratic addition. Depending on the specific parameter, margin factors could change such that margins change over 50%. Especially margin recipes based on TCP-criteria are more sensitive to more parameters than those based on purely geometric Dmin-criteria. Interestingly, measures taken to minimize treatment field sizes (by e.g. optimizing dose conformity) are counteracted by the requirement of larger margins to get the same tumor coverage. Conclusion: Margin recipes combining geometric and microscopic uncertainties quadratically are accurate under varying circumstances. However margins can change up to 50% for different situations.« less

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

NASA Astrophysics Data System (ADS)

Tyson, Jon

2009-03-01

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Ježek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

NASA Technical Reports Server (NTRS)

Kottapalli, Sesi; Leyland, Jane

2014-01-01

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

End-point controller design for an experimental two-link flexible manipulator using convex optimization

NASA Technical Reports Server (NTRS)

Oakley, Celia M.; Barratt, Craig H.

1990-01-01

Recent results in linear controller design are used to design an end-point controller for an experimental two-link flexible manipulator. A nominal 14-state linear-quadratic-Gaussian (LQG) controller was augmented with a 528-tap finite-impulse-response (FIR) filter designed using convex optimization techniques. The resulting 278-state controller produced improved end-point trajectory tracking and disturbance rejection in simulation and experimentally in real time.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Support Vector Machine algorithm for regression and classification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Chenggang; Zavaljevski, Nela

2001-08-01

The software is an implementation of the Support Vector Machine (SVM) algorithm that was invented and developed by Vladimir Vapnik and his co-workers at AT&T Bell Laboratories. The specific implementation reported here is an Active Set method for solving a quadratic optimization problem that forms the major part of any SVM program. The implementation is tuned to specific constraints generated in the SVM learning. Thus, it is more efficient than general-purpose quadratic optimization programs. A decomposition method has been implemented in the software that enables processing large data sets. The size of the learning data is virtually unlimited by themore » capacity of the computer physical memory. The software is flexible and extensible. Two upper bounds are implemented to regulate the SVM learning for classification, which allow users to adjust the false positive and false negative rates. The software can be used either as a standalone, general-purpose SVM regression or classification program, or be embedded into a larger software system.« less

Extremal Optimization for Quadratic Unconstrained Binary Problems

NASA Astrophysics Data System (ADS)

Boettcher, S.

We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Development of Quadratic Programming Algorithm Based on Interior Point Method with Estimation Mechanism of Active Constraints

NASA Astrophysics Data System (ADS)

Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka

Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.

An optimal state estimation model of sensory integration in human postural balance

NASA Astrophysics Data System (ADS)

Kuo, Arthur D.

2005-09-01

We propose a model for human postural balance, combining state feedback control with optimal state estimation. State estimation uses an internal model of body and sensor dynamics to process sensor information and determine body orientation. Three sensory modalities are modeled: joint proprioception, vestibular organs in the inner ear, and vision. These are mated with a two degree-of-freedom model of body dynamics in the sagittal plane. Linear quadratic optimal control is used to design state feedback and estimation gains. Nine free parameters define the control objective and the signal-to-noise ratios of the sensors. The model predicts statistical properties of human sway in terms of covariance of ankle and hip motion. These predictions are compared with normal human responses to alterations in sensory conditions. With a single parameter set, the model successfully reproduces the general nature of postural motion as a function of sensory environment. Parameter variations reveal that the model is highly robust under normal sensory conditions, but not when two or more sensors are inaccurate. This behavior is similar to that of normal human subjects. We propose that age-related sensory changes may be modeled with decreased signal-to-noise ratios, and compare the model's behavior with degraded sensors against experimental measurements from older adults. We also examine removal of the model's vestibular sense, which leads to instability similar to that observed in bilateral vestibular loss subjects. The model may be useful for predicting which sensors are most critical for balance, and how much they can deteriorate before posture becomes unstable.

Finite Element Simulation of Articular Contact Mechanics with Quadratic Tetrahedral Elements

PubMed Central

Maas, Steve A.; Ellis, Benjamin J.; Rawlins, David S.; Weiss, Jeffrey A.

2016-01-01

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037

Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

2011-01-01

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

A New Navigation Satellite Clock Bias Prediction Method Based on Modified Clock-bias Quadratic Polynomial Model

NASA Astrophysics Data System (ADS)

Wang, Y. P.; Lu, Z. P.; Sun, D. S.; Wang, N.

2016-01-01

In order to better express the characteristics of satellite clock bias (SCB) and improve SCB prediction precision, this paper proposed a new SCB prediction model which can take physical characteristics of space-borne atomic clock, the cyclic variation, and random part of SCB into consideration. First, the new model employs a quadratic polynomial model with periodic items to fit and extract the trend term and cyclic term of SCB; then based on the characteristics of fitting residuals, a time series ARIMA ~(Auto-Regressive Integrated Moving Average) model is used to model the residuals; eventually, the results from the two models are combined to obtain final SCB prediction values. At last, this paper uses precise SCB data from IGS (International GNSS Service) to conduct prediction tests, and the results show that the proposed model is effective and has better prediction performance compared with the quadratic polynomial model, grey model, and ARIMA model. In addition, the new method can also overcome the insufficiency of the ARIMA model in model recognition and order determination.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Optimal vibration control of a rotating plate with self-sensing active constrained layer damping

NASA Astrophysics Data System (ADS)

Xie, Zhengchao; Wong, Pak Kin; Lo, Kin Heng

2012-04-01

This paper proposes a finite element model for optimally controlled constrained layer damped (CLD) rotating plate with self-sensing technique and frequency-dependent material property in both the time and frequency domain. Constrained layer damping with viscoelastic material can effectively reduce the vibration in rotating structures. However, most existing research models use complex modulus approach to model viscoelastic material, and an additional iterative approach which is only available in frequency domain has to be used to include the material's frequency dependency. It is meaningful to model the viscoelastic damping layer in rotating part by using the anelastic displacement fields (ADF) in order to include the frequency dependency in both the time and frequency domain. Also, unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate in which the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator under an linear quadratic regulation (LQR) controller. After being compared with verified data, this newly proposed finite element model is validated and could be used for future research.

Experimental Validation of an Integrated Controls-Structures Design Methodology

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Gupta, Sandeep; Elliot, Kenny B.; Walz, Joseph E.

1996-01-01

The first experimental validation of an integrated controls-structures design methodology for a class of large order, flexible space structures is described. Integrated redesign of the controls-structures-interaction evolutionary model, a laboratory testbed at NASA Langley, was described earlier. The redesigned structure was fabricated, assembled in the laboratory, and experimentally tested against the original structure. Experimental results indicate that the structure redesigned using the integrated design methodology requires significantly less average control power than the nominal structure with control-optimized designs, while maintaining the required line-of-sight pointing performance. Thus, the superiority of the integrated design methodology over the conventional design approach is experimentally demonstrated. Furthermore, amenability of the integrated design structure to other control strategies is evaluated, both analytically and experimentally. Using Linear-Quadratic-Guassian optimal dissipative controllers, it is observed that the redesigned structure leads to significantly improved performance with alternate controllers as well.

Product demand forecasts using wavelet kernel support vector machine and particle swarm optimization in manufacture system

NASA Astrophysics Data System (ADS)

Wu, Qi

2010-03-01

Demand forecasts play a crucial role in supply chain management. The future demand for a certain product is the basis for the respective replenishment systems. Aiming at demand series with small samples, seasonal character, nonlinearity, randomicity and fuzziness, the existing support vector kernel does not approach the random curve of the sales time series in the space (quadratic continuous integral space). In this paper, we present a hybrid intelligent system combining the wavelet kernel support vector machine and particle swarm optimization for demand forecasting. The results of application in car sale series forecasting show that the forecasting approach based on the hybrid PSOWv-SVM model is effective and feasible, the comparison between the method proposed in this paper and other ones is also given, which proves that this method is, for the discussed example, better than hybrid PSOv-SVM and other traditional methods.

Enzymatic catalysis treatment method of meat industry wastewater using lacasse.

PubMed

Thirugnanasambandham, K; Sivakumar, V

2015-01-01

The process of meat industry produces in a large amount of wastewater that contains high levels of colour and chemical oxygen demand (COD). So they must be pretreated before their discharge into the ecological system. In this paper, enzymatic catalysis (EC) was adopted to treat the meat wastewater. Box-Behnken design (BBD), an experimental design for response surface methodology (RSM), was used to create a set of 29 experimental runs needed for optimizing of the operating conditions. Quadratic regression models with estimated coefficients were developed to describe the colour and COD removals. The experimental results show that EC could effectively reduce colour (95 %) and COD (86 %) at the optimum conditions of enzyme dose of 110 U/L, incubation time of 100 min, pH of 7 and temperature of 40 °C. RSM could be effectively adopted to optimize the operating multifactors in complex EC process.

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is notmore » assumed that the iterates lie on a compact set.« less

Optimization of structures to satisfy a flutter velocity constraint by use of quadratic equation fitting. M.S. Thesis

NASA Technical Reports Server (NTRS)

Motiwalla, S. K.

1973-01-01

Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

Partial discharge localization in power transformers based on the sequential quadratic programming-genetic algorithm adopting acoustic emission techniques

NASA Astrophysics Data System (ADS)

Liu, Hua-Long; Liu, Hua-Dong

2014-10-01

Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And localization results based on the SQP-GA are compared with some algorithms such as the GA, some other intelligent and non-intelligent algorithms. The results of calculating examples both stimulated and spot experiments demonstrate that the localization method based on the SQP-GA can effectively prevent the results from getting trapped into the local optimum values, and the localization method is of great feasibility and very suitable for the field applications, and the precision of localization is enhanced, and the effectiveness of localization is ideal and satisfactory.

Understanding the optics to aid microscopy image segmentation.

PubMed

Yin, Zhaozheng; Li, Kang; Kanade, Takeo; Chen, Mei

2010-01-01

Image segmentation is essential for many automated microscopy image analysis systems. Rather than treating microscopy images as general natural images and rushing into the image processing warehouse for solutions, we propose to study a microscope's optical properties to model its image formation process first using phase contrast microscopy as an exemplar. It turns out that the phase contrast imaging system can be relatively well explained by a linear imaging model. Using this model, we formulate a quadratic optimization function with sparseness and smoothness regularizations to restore the "authentic" phase contrast images that directly correspond to specimen's optical path length without phase contrast artifacts such as halo and shade-off. With artifacts removed, high quality segmentation can be achieved by simply thresholding the restored images. The imaging model and restoration method are quantitatively evaluated on two sequences with thousands of cells captured over several days.

Time domain simulation of novel photovoltaic materials

NASA Astrophysics Data System (ADS)

Chung, Haejun

Thin-film silicon-based solar cells have operated far from the Shockley- Queisser limit in all experiments to date. Novel light-trapping structures, however, may help address this limitation. Finite-difference time domain simulation methods offer the potential to accurately determine the light-trapping potential of arbitrary dielectric structures, but suffer from materials modeling problems. In this thesis, existing dispersion models for novel photovoltaic materials will be reviewed, and a novel dispersion model, known as the quadratic complex rational function (QCRF), will be proposed. It has the advantage of accurately fitting experimental semiconductor dielectric values over a wide bandwidth in a numerically stable fashion. Applying the proposed dispersion model, a statistically correlated surface texturing method will be suggested, and light absorption rates of it will be explained. In future work, these designs will be combined with other structures and optimized to help guide future experiments.

Mixture-mixture design for the fingerprint optimization of chromatographic mobile phases and extraction solutions for Camellia sinensis.

PubMed

Borges, Cleber N; Bruns, Roy E; Almeida, Aline A; Scarminio, Ieda S

2007-07-09

A composite simplex centroid-simplex centroid mixture design is proposed for simultaneously optimizing two mixture systems. The complementary model is formed by multiplying special cubic models for the two systems. The design was applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Camellia sinensis Chinese tea plant. The extraction mixtures investigated contained varying proportions of ethyl acetate, ethanol and dichloromethane while the mobile phase was made up of varying proportions of methanol, acetonitrile and a methanol-acetonitrile-water (MAW) 15%:15%:70% mixture. The experiments were block randomized corresponding to a split-plot error structure to minimize laboratory work and reduce environmental impact. Coefficients of an initial saturated model were obtained using Scheffe-type equations. A cumulative probability graph was used to determine an approximate reduced model. The split-plot error structure was then introduced into the reduced model by applying generalized least square equations with variance components calculated using the restricted maximum likelihood approach. A model was developed to calculate the number of peaks observed with the chromatographic detector at 210 nm. A 20-term model contained essentially all the statistical information of the initial model and had a root mean square calibration error of 1.38. The model was used to predict the number of peaks eluted in chromatograms obtained from extraction solutions that correspond to axial points of the simplex centroid design. The significant model coefficients are interpreted in terms of interacting linear, quadratic and cubic effects of the mobile phase and extraction solution components.

A meta-model analysis of a finite element simulation for defining poroelastic properties of intervertebral discs.

PubMed

Nikkhoo, Mohammad; Hsu, Yu-Chun; Haghpanahi, Mohammad; Parnianpour, Mohamad; Wang, Jaw-Lin

2013-06-01

Finite element analysis is an effective tool to evaluate the material properties of living tissue. For an interactive optimization procedure, the finite element analysis usually needs many simulations to reach a reasonable solution. The meta-model analysis of finite element simulation can be used to reduce the computation of a structure with complex geometry or a material with composite constitutive equations. The intervertebral disc is a complex, heterogeneous, and hydrated porous structure. A poroelastic finite element model can be used to observe the fluid transferring, pressure deviation, and other properties within the disc. Defining reasonable poroelastic material properties of the anulus fibrosus and nucleus pulposus is critical for the quality of the simulation. We developed a material property updating protocol, which is basically a fitting algorithm consisted of finite element simulations and a quadratic response surface regression. This protocol was used to find the material properties, such as the hydraulic permeability, elastic modulus, and Poisson's ratio, of intact and degenerated porcine discs. The results showed that the in vitro disc experimental deformations were well fitted with limited finite element simulations and a quadratic response surface regression. The comparison of material properties of intact and degenerated discs showed that the hydraulic permeability significantly decreased but Poisson's ratio significantly increased for the degenerated discs. This study shows that the developed protocol is efficient and effective in defining material properties of a complex structure such as the intervertebral disc.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

PubMed

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Did recent world record marathon runners employ optimal pacing strategies?

PubMed

Angus, Simon D

2014-01-01

We apply statistical analysis of high frequency (1 km) split data for the most recent two world-record marathon runs: Run 1 (2:03:59, 28 September 2008) and Run 2 (2:03:38, 25 September 2011). Based on studies in the endurance cycling literature, we develop two principles to approximate 'optimal' pacing in the field marathon. By utilising GPS and weather data, we test, and then de-trend, for each athlete's field response to gradient and headwind on course, recovering standardised proxies for power-based pacing traces. The resultant traces were analysed to ascertain if either runner followed optimal pacing principles; and characterise any deviations from optimality. Whereas gradient was insignificant, headwind was a significant factor in running speed variability for both runners, with Runner 2 targeting the (optimal) parallel variation principle, whilst Runner 1 did not. After adjusting for these responses, neither runner followed the (optimal) 'even' power pacing principle, with Runner 2's macro-pacing strategy fitting a sinusoidal oscillator with exponentially expanding envelope whilst Runner 1 followed a U-shaped, quadratic form. The study suggests that: (a) better pacing strategy could provide elite marathon runners with an economical pathway to significant performance improvements at world-record level; and (b) the data and analysis herein is consistent with a complex-adaptive model of power regulation.

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1999-01-01

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Convergence analysis of evolutionary algorithms that are based on the paradigm of information geometry.

PubMed

Beyer, Hans-Georg

2014-01-01

The convergence behaviors of so-called natural evolution strategies (NES) and of the information-geometric optimization (IGO) approach are considered. After a review of the NES/IGO ideas, which are based on information geometry, the implications of this philosophy w.r.t. optimization dynamics are investigated considering the optimization performance on the class of positive quadratic objective functions (the ellipsoid model). Exact differential equations describing the approach to the optimizer are derived and solved. It is rigorously shown that the original NES philosophy optimizing the expected value of the objective functions leads to very slow (i.e., sublinear) convergence toward the optimizer. This is the real reason why state of the art implementations of IGO algorithms optimize the expected value of transformed objective functions, for example, by utility functions based on ranking. It is shown that these utility functions are localized fitness functions that change during the IGO flow. The governing differential equations describing this flow are derived. In the case of convergence, the solutions to these equations exhibit an exponentially fast approach to the optimizer (i.e., linear convergence order). Furthermore, it is proven that the IGO philosophy leads to an adaptation of the covariance matrix that equals in the asymptotic limit-up to a scalar factor-the inverse of the Hessian of the objective function considered.

An Optimization Method for the Reduction of Propeller Unsteady Forces.

DTIC Science & Technology

1988-02-01

unsteady forces and the determination of skew distribulee has been developed. The current method provides an efficient propeller design tool capable...62633N HM35 SF33321 DN305 123 11. TITLE (ft .WC*i=iW) An Optimization Method for the Reduction of Propeller Unsteady Forces 12. PERSONAL AUTHOR(S) T.S...of determining a variety of cubic or quadratic skew distributioms, subject to constraints, which minimize the unsteady forces produced by the various

Application of IFT and SPSA to servo system control.

PubMed

Rădac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan

2011-12-01

This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.

Optimization of the structural and control system for LSS with reduced-order model

NASA Technical Reports Server (NTRS)

Khot, N. S.

1989-01-01

The objective is the simultaneous design of the structural and control system for space structures. The minimum weight of the structure is the objective function, and the constraints are placed on the closed loop distribution of the frequencies and the damping parameters. The controls approach used is linear quadratic regulator with constant feedback. A reduced-order control system is used. The effect of uncontrolled modes is taken into consideration by the model error sensitivity suppression (MESS) technique which modified the weighting parameters for the control forces. For illustration, an ACOSS-FOUR structure is designed for a different number of controlled modes with specified values for the closed loop damping parameters and frequencies. The dynamic response of the optimum designs for an initial disturbance is compared.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

A quadratic regression modelling on paddy production in the area of Perlis

NASA Astrophysics Data System (ADS)

Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2017-08-01

Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piepel, Gregory F.; Pasquini, Benedetta; Cooley, Scott K.

In recent years, multivariate optimization has played an increasing role in analytical method development. ICH guidelines recommend using statistical design of experiments to identify the design space, in which multivariate combinations of composition variables and process variables have been demonstrated to provide quality results. Considering a microemulsion electrokinetic chromatography method (MEEKC), the performance of the electrophoretic run depends on the proportions of mixture components (MCs) of the microemulsion and on the values of process variables (PVs). In the present work, for the first time in the literature, a mixture-process variable (MPV) approach was applied to optimize a MEEKC method formore » the analysis of coenzyme Q10 (Q10), ascorbic acid (AA), and folic acid (FA) contained in nutraceuticals. The MCs (buffer, surfactant-cosurfactant, oil) and the PVs (voltage, buffer concentration, buffer pH) were simultaneously changed according to a MPV experimental design. A 62-run MPV design was generated using the I-optimality criterion, assuming a 46-term MPV model allowing for special-cubic blending of the MCs, quadratic effects of the PVs, and some MC-PV interactions. The obtained data were used to develop MPV models that express the performance of an electrophoretic run (measured as peak efficiencies of Q10, AA, and FA) in terms of the MCs and PVs. Contour and perturbation plots were drawn for each of the responses. Finally, the MPV models and criteria for the peak efficiencies were used to develop the design space and an optimal subregion (i.e., the settings of the mixture MCs and PVs that satisfy the respective criteria), as well as a unique optimal combination of MCs and PVs.« less

Optimization of flask culture medium and conditions for hyaluronic acid production by a Streptococcus equisimilis mutant nc2168.

PubMed

Chen, Yong-Hao; Li, Jun; Liu, Li; Liu, Hong-Zhi; Wang, Qiang

2012-10-01

A mutant designated NC2168, which was selected from wild-type Streptococcus equisimilis CVCC55116 by ultraviolet ray combined with(60)Co-γ ray treatment and does not produce streptolysin, was employed to produce hyaluronic acid (HA). In order to increase the output of HA in a flask, the culture medium and conditions for NC2168 were optimized in this study. The influence of culture medium ingredients including carbon sources, nitrogen sources and metal ions on HA production was evaluated using factional factorial design. The mathematical model, which represented the effect of each medium component and their interaction on the yield of HA, was established by the quadratic rotary combination design and response surface method. The model estimated that, a maximal yield of HA could be obtained when the concentrations of yeast extract, peptone, glucose, and MgSO4 were set at 3 g/100 mL, 2 g/100 mL, 0.5 g/100 mL and 0.15 g/100 mL, respectively. Compared with the values obtained by other runs in the experimental design, the optimized medium resulted in a remarkable increase in the output of HA and the maximum of the predicted HA production was 174.76 mg/L. The model developed was accurate and reliable for predicting the production of HA by NC2168.Cultivation conditions were optimized by an orthogonal experimental design and the optimal conditions were as follows: temperature 33°C, pH 7.8, agitation speed 200 rpm, medium volume 20 mL.

Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

PubMed

Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

2016-03-21

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Some Results on Proper Eigenvalues and Eigenvectors with Applications to Scaling.

ERIC Educational Resources Information Center

McDonald, Roderick P.; And Others

1979-01-01

Problems in avoiding the singularity problem in analyzing matrices for optimal scaling are addressed. Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. (Author/JKS)

A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

DTIC Science & Technology

2015-04-29

can be converted to a quadratic unconstrained binary optimization ( QUBO ) problem that uses 0/1-valued variables, and so they are often used...Frontiers in Physics, 2:5 (12 Feb 2014). [7] “Programming with QUBOs ,” (instructional document) D-Wave: The Quantum Computing Company, 2013. [8

A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem

DTIC Science & Technology

1990-09-01

Electr6nica e Inform’itica Industrial E.T.S. Ingenieros Industriales Universidad Polit6cnica, Madrid Technical Report SOL 90-12 September 1990 -Y...MURRAY* AND FRANCISCO J. PRIETOt *Systems Optimization Laboratory Department of Operations Research Stanford University tDept. de Automitica, Ingenieria

Assessing Spurious Interaction Effects in Structural Equation Modeling

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Li, Ming

2015-01-01

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could…

Optimal solution and optimality condition of the Hunter-Saxton equation

NASA Astrophysics Data System (ADS)

Shen, Chunyu

2018-02-01

This paper is devoted to the optimal distributed control problem governed by the Hunter-Saxton equation with constraints on the control. We first investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary conditions. In contrast with our previous research, the proof of solution mapping is local Lipschitz continuous, which is one big improvement. Second, based on the well-posedness result, we find a unique optimal control and optimal solution for the controlled system with the quadratic cost functional. Moreover, we establish the sufficient and necessary optimality condition of an optimal control by means of the optimal control theory, not limited to the necessary condition, which is another major novelty of this paper. We also discuss the optimality conditions corresponding to two physical meaningful distributed observation cases.

Optimization of urban water supply portfolios combining infrastructure capacity expansion and water use decisions

NASA Astrophysics Data System (ADS)

Medellin-Azuara, J.; Fraga, C. C. S.; Marques, G.; Mendes, C. A.

2015-12-01

The expansion and operation of urban water supply systems under rapidly growing demands, hydrologic uncertainty, and scarce water supplies requires a strategic combination of various supply sources for added reliability, reduced costs and improved operational flexibility. The design and operation of such portfolio of water supply sources merits decisions of what and when to expand, and how much to use of each available sources accounting for interest rates, economies of scale and hydrologic variability. The present research provides a framework and an integrated methodology that optimizes the expansion of various water supply alternatives using dynamic programming and combining both short term and long term optimization of water use and simulation of water allocation. A case study in Bahia Do Rio Dos Sinos in Southern Brazil is presented. The framework couples an optimization model with quadratic programming model in GAMS with WEAP, a rain runoff simulation models that hosts the water supply infrastructure features and hydrologic conditions. Results allow (a) identification of trade offs between cost and reliability of different expansion paths and water use decisions and (b) evaluation of potential gains by reducing water system losses as a portfolio component. The latter is critical in several developing countries where water supply system losses are high and often neglected in favor of more system expansion. Results also highlight the potential of various water supply alternatives including, conservation, groundwater, and infrastructural enhancements over time. The framework proves its usefulness for planning its transferability to similarly urbanized systems.

Optimal design of microtube recuperators for an indirect supercritical carbon dioxide recompression closed Brayton cycle

DOE PAGES

Jiang, Yuan; Liese, Eric; Zitney, Stephen E.; ...

2018-02-25

This paper presents a baseline design and optimization approach developed in Aspen Custom Modeler (ACM) for microtube shell-and-tube exchangers (MSTEs) used for high- and low-temperature recuperation in a 10 MWe indirect supercritical carbon dioxide (sCO 2) recompression closed Brayton cycle (RCBC). The MSTE-type recuperators are designed using one-dimensional models with thermal-hydraulic correlations appropriate for sCO 2 and properties models that capture considerable nonlinear changes in CO 2 properties near the critical and pseudo-critical points. Using the successive quadratic programming (SQP) algorithm in ACM, optimal recuperator designs are obtained for either custom or industry-standard microtubes considering constraints based on current advancedmore » manufacturing techniques. The three decision variables are the number of tubes, tube pitch-to-diameter ratio, and tube diameter. Five different objective functions based on different key design measures are considered: minimization of total heat transfer area, heat exchanger volume, metal weight, thermal residence time, and maximization of compactness. Sensitivities studies indicate the constraint on the maximum number of tubes per shell does affect the number of parallel heat exchanger trains but not the tube selection, total number of tubes, tube length and other key design measures in the final optimal design when considering industry-standard tubes. In this study, the optimally designed high- and low-temperature recuperators have 47,000 3/32 inch tubes and 63,000 1/16 inch tubes, respectively. In addition, sensitivities to the design temperature approach and maximum allowable pressure drop are studied, since these specifications significantly impact the optimal design of the recuperators as well as the thermal efficiency and the economic performance of the entire sCO 2 Brayton cycle.« less

Optimal design of microtube recuperators for an indirect supercritical carbon dioxide recompression closed Brayton cycle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Yuan; Liese, Eric; Zitney, Stephen E.

This paper presents a baseline design and optimization approach developed in Aspen Custom Modeler (ACM) for microtube shell-and-tube exchangers (MSTEs) used for high- and low-temperature recuperation in a 10 MWe indirect supercritical carbon dioxide (sCO 2) recompression closed Brayton cycle (RCBC). The MSTE-type recuperators are designed using one-dimensional models with thermal-hydraulic correlations appropriate for sCO 2 and properties models that capture considerable nonlinear changes in CO 2 properties near the critical and pseudo-critical points. Using the successive quadratic programming (SQP) algorithm in ACM, optimal recuperator designs are obtained for either custom or industry-standard microtubes considering constraints based on current advancedmore » manufacturing techniques. The three decision variables are the number of tubes, tube pitch-to-diameter ratio, and tube diameter. Five different objective functions based on different key design measures are considered: minimization of total heat transfer area, heat exchanger volume, metal weight, thermal residence time, and maximization of compactness. Sensitivities studies indicate the constraint on the maximum number of tubes per shell does affect the number of parallel heat exchanger trains but not the tube selection, total number of tubes, tube length and other key design measures in the final optimal design when considering industry-standard tubes. In this study, the optimally designed high- and low-temperature recuperators have 47,000 3/32 inch tubes and 63,000 1/16 inch tubes, respectively. In addition, sensitivities to the design temperature approach and maximum allowable pressure drop are studied, since these specifications significantly impact the optimal design of the recuperators as well as the thermal efficiency and the economic performance of the entire sCO 2 Brayton cycle.« less

Treatment of an actual slaughterhouse wastewater by integration of biological and advanced oxidation processes: Modeling, optimization, and cost-effectiveness analysis.

PubMed

Bustillo-Lecompte, Ciro Fernando; Mehrvar, Mehrab

2016-11-01

Biological and advanced oxidation processes are combined to treat an actual slaughterhouse wastewater (SWW) by a sequence of an anaerobic baffled reactor, an aerobic activated sludge reactor, and a UV/H2O2 photoreactor with recycle in continuous mode at laboratory scale. In the first part of this study, quadratic modeling along with response surface methodology are used for the statistical analysis and optimization of the combined process. The effects of the influent total organic carbon (TOC) concentration, the flow rate, the pH, the inlet H2O2 concentration, and their interaction on the overall treatment efficiency, CH4 yield, and H2O2 residual in the effluent of the photoreactor are investigated. The models are validated at different operating conditions using experimental data. Maximum TOC and total nitrogen (TN) removals of 91.29 and 86.05%, respectively, maximum CH4 yield of 55.72%, and minimum H2O2 residual of 1.45% in the photoreactor effluent were found at optimal operating conditions. In the second part of this study, continuous distribution kinetics is applied to establish a mathematical model for the degradation of SWW as a function of time. The agreement between model predictions and experimental values indicates that the proposed model could describe the performance of the combined anaerobic-aerobic-UV/H2O2 processes for the treatment of SWW. In the final part of the study, the optimized combined anaerobic-aerobic-UV/H2O2 processes with recycle were evaluated using a cost-effectiveness analysis to minimize the retention time, the electrical energy consumption, and the overall incurred treatment costs required for the efficient treatment of slaughterhouse wastewater effluents. Copyright © 2016 Elsevier Ltd. All rights reserved.

An optimization model for the US Air-Traffic System

NASA Technical Reports Server (NTRS)

Mulvey, J. M.

1986-01-01

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Using the Firefly optimization method to weight an ensemble of rainfall forecasts from the Brazilian developments on the Regional Atmospheric Modeling System (BRAMS)

NASA Astrophysics Data System (ADS)

dos Santos, A. F.; Freitas, S. R.; de Mattos, J. G. Z.; de Campos Velho, H. F.; Gan, M. A.; da Luz, E. F. P.; Grell, G. A.

2013-09-01

In this paper we consider an optimization problem applying the metaheuristic Firefly algorithm (FY) to weight an ensemble of rainfall forecasts from daily precipitation simulations with the Brazilian developments on the Regional Atmospheric Modeling System (BRAMS) over South America during January 2006. The method is addressed as a parameter estimation problem to weight the ensemble of precipitation forecasts carried out using different options of the convective parameterization scheme. Ensemble simulations were performed using different choices of closures, representing different formulations of dynamic control (the modulation of convection by the environment) in a deep convection scheme. The optimization problem is solved as an inverse problem of parameter estimation. The application and validation of the methodology is carried out using daily precipitation fields, defined over South America and obtained by merging remote sensing estimations with rain gauge observations. The quadratic difference between the model and observed data was used as the objective function to determine the best combination of the ensemble members to reproduce the observations. To reduce the model rainfall biases, the set of weights determined by the algorithm is used to weight members of an ensemble of model simulations in order to compute a new precipitation field that represents the observed precipitation as closely as possible. The validation of the methodology is carried out using classical statistical scores. The algorithm has produced the best combination of the weights, resulting in a new precipitation field closest to the observations.

Optimal feed-forward compensation for PWM dc/dc converters with 'linear' and 'quadratic' conversion ratio

NASA Astrophysics Data System (ADS)

Calderone, Luigi; Pinola, Licia; Varoli, Vincenzo

1992-04-01

The paper describes an analytical procedure to optimize the feed-forward compensation for any PWM dc/dc converters. The aims of achieving zero dc audiosusceptibility was found to be possible for the buck, buck-boost, Cuk, and SEPIC cells; for the boost converter, however, only nonoptimal compensation is feasible. Rules for the design of PWM controllers and procedures for the evaluation of the hardware-introduced errors are discussed. A PWM controller implementing the optimal feed-forward compensation for buck-boost, Cuk, and SEPIC cells is described and fully experimentally characterized.

Nonlinear model for an optical read-only-memory disk readout channel based on an edge-spread function.

PubMed

Kobayashi, Seiji

2002-05-10

A point-spread function (PSF) is commonly used as a model of an optical disk readout channel. However, the model given by the PSF does not contain the quadratic distortion generated by the photo-detection process. We introduce a model for calculating an approximation of the quadratic component of a signal. We show that this model can be further simplified when a read-only-memory (ROM) disk is assumed. We introduce an edge-spread function by which a simple nonlinear model of an optical ROM disk readout channel is created.

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

NASA Technical Reports Server (NTRS)

Parrish, Nathan L.; Scheeres, Daniel J.

2017-01-01

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

SU-E-T-503: IMRT Optimization Using Monte Carlo Dose Engine: The Effect of Statistical Uncertainty.

PubMed

Tian, Z; Jia, X; Graves, Y; Uribe-Sanchez, A; Jiang, S

2012-06-01

With the development of ultra-fast GPU-based Monte Carlo (MC) dose engine, it becomes clinically realistic to compute the dose-deposition coefficients (DDC) for IMRT optimization using MC simulation. However, it is still time-consuming if we want to compute DDC with small statistical uncertainty. This work studies the effects of the statistical error in DDC matrix on IMRT optimization. The MC-computed DDC matrices are simulated here by adding statistical uncertainties at a desired level to the ones generated with a finite-size pencil beam algorithm. A statistical uncertainty model for MC dose calculation is employed. We adopt a penalty-based quadratic optimization model and gradient descent method to optimize fluence map and then recalculate the corresponding actual dose distribution using the noise-free DDC matrix. The impacts of DDC noise are assessed in terms of the deviation of the resulted dose distributions. We have also used a stochastic perturbation theory to theoretically estimate the statistical errors of dose distributions on a simplified optimization model. A head-and-neck case is used to investigate the perturbation to IMRT plan due to MC's statistical uncertainty. The relative errors of the final dose distributions of the optimized IMRT are found to be much smaller than those in the DDC matrix, which is consistent with our theoretical estimation. When history number is decreased from 108 to 106, the dose-volume-histograms are still very similar to the error-free DVHs while the error in DDC is about 3.8%. The results illustrate that the statistical errors in the DDC matrix have a relatively small effect on IMRT optimization in dose domain. This indicates we can use relatively small number of histories to obtain the DDC matrix with MC simulation within a reasonable amount of time, without considerably compromising the accuracy of the optimized treatment plan. This work is supported by Varian Medical Systems through a Master Research Agreement. © 2012 American Association of Physicists in Medicine.

Parameter optimization of an inerter-based isolator for passive vibration control of Michelangelo's Rondanini Pietà

NASA Astrophysics Data System (ADS)

Siami, A.; Karimi, H. R.; Cigada, A.; Zappa, E.; Sabbioni, E.

2018-01-01

Preserving cultural heritage against earthquake and ambient vibrations can be an attractive topic in the field of vibration control. This paper proposes a passive vibration isolator methodology based on inerters for improving the performance of the isolation system of the famous statue of Michelangelo Buonarroti Pietà Rondanini. More specifically, a five-degree-of-freedom (5DOF) model of the statue and the anti-seismic and anti-vibration base is presented and experimentally validated. The parameters of this model are tuned according to the experimental tests performed on the assembly of the isolator and the structure. Then, the developed model is used to investigate the impact of actuation devices such as tuned mass-damper (TMD) and tuned mass-damper-inerter (TMDI) in vibration reduction of the structure. The effect of implementation of TMDI on the 5DOF model is shown based on physical limitations of the system parameters. Simulation results are provided to illustrate effectiveness of the passive element of TMDI in reduction of the vibration transmitted to the statue in vertical direction. Moreover, the optimal design parameters of the passive system such as frequency and damping coefficient will be calculated using two different performance indexes. The obtained optimal parameters have been evaluated by using two different optimization algorithms: the sequential quadratic programming method and the Firefly algorithm. The results prove significant reduction in the transmitted vibration to the structure in the presence of the proposed tuned TMDI, without imposing a large amount of mass or modification to the structure of the isolator.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

USGS Publications Warehouse

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Ming; Feng, Wei; Marnay, Chris

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 retailmore » 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.« less

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

DOE PAGES

Jin, Ming; Feng, Wei; Marnay, Chris; ...

2018-06-07

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 retailmore » 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.« less

Formulation and Statistical Optimization of Culture Medium for Improved Production of Antimicrobial Compound by Streptomyces sp. JAJ06

PubMed Central

Arul Jose, Polpass; Sivakala, Kunjukrishnan Kamalakshi; Jebakumar, Solomon Robinson David

2013-01-01

Streptomyces sp. JAJ06 is a seawater-dependent antibiotic producer, previously isolated and characterised from an Indian coastal solar saltern. This paper reports replacement of seawater with a defined salt formulation in production medium and subsequent statistical media optimization to ensure consistent as well as improved antibiotic production by Streptomyces sp. JAJ06. This strain was observed to be proficient to produce antibiotic compound with incorporation of chemically defined sodium-chloride-based salt formulation instead of seawater into the production medium. Plackett-Burman design experiment was applied, and three media constituents, starch, KBr, and CaCO3, were recognised to have significant effect on the antibiotic production of Streptomyces JAJ06 at their individual levels. Subsequently, Response surface methodology with Box-Behnken design was employed to optimize these influencing medium constituents for the improved antibiotic production of Streptomyces sp. JAJ06. A total of 17 experiments were conducted towards the construction of a quadratic model and a second-order polynomial equation. Optimum levels of medium constituents were obtained by analysis of the model and numerical optimization method. When the strain JAJ06 was cultivated in the optimized medium, the antibiotic activity was increased to 173.3 U/mL, 26.8% increase as compared to the original (136.7 U/mL). This study found a useful way to cultivate Streptomyces sp. JAJ06 for enhanced production of antibiotic compound. PMID:24454383

The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot

NASA Astrophysics Data System (ADS)

Hwang, Donghyeok; Tahk, Min-Jea

2018-04-01

The performance characteristics of the autopilot must have a fast response to intercept a maneuvering target and reasonable robustness for system stability under the effect of un-modeled dynamics and noise. By the conventional approach, the three-loop autopilot design is handled by time constant, damping factor and open-loop crossover frequency to achieve the desired performance requirements. Note that the general optimal theory can be also used to obtain the same gain as obtained from the conventional approach. The key idea of using optimal control technique for feedback gain design revolves around appropriate selection and interpretation of the performance index for which the control is optimal. This paper derives an explicit expression, which relates the weight parameters appearing in the quadratic performance index to the design parameters such as open-loop crossover frequency, phase margin, damping factor, or time constant, etc. Since all set of selection of design parameters do not guarantee existence of optimal control law, explicit inequalities, which are named the optimality criteria for the three-loop autopilot (OC3L), are derived to find out all set of design parameters for which the control law is optimal. Finally, based on OC3L, an efficient gain selection procedure is developed, where time constant is set to design objective and open-loop crossover frequency and phase margin as design constraints. The effectiveness of the proposed technique is illustrated through numerical simulations.

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

2017-01-01

In this paper we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three-band model, while leaving the flat band dispersionless. We find a small gap is also opened at the quadratic band touching point by two-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this three-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

Photocatalytic water splitting over titania supported copper and nickel oxide in photoelectrochemical cell; optimization of photoconversion efficiency

NASA Astrophysics Data System (ADS)

Muti Mohamed, Norani; Bashiri, Robabeh; Kait, Chong Fai; Sufian, Suriati

2018-04-01

we investigated the influence of fluctuating the preparation variables of TiO2 on the efficiency of photocatalytic water splitting in photoelectrochemical (PEC) cell. Hydrothermal associated sol-gel technique was applied to synthesis modified TiO2 with nickel and copper oxide. The variation of water (mL), acid (mL) and total metal loading (%) were mathematically modelled using central composite design (CCD) from the response surface method (RSM) to explore the single and combined effects of parameters on the system performance. The experimental data were fitted using quadratic polynomial regression model from analysis of variance (ANOVA). The coefficient of determination value of 98% confirms the linear relationship between the experimental and predicted values. The amount of water had maximum effect on the photoconversion efficiency due to a direct effect on the crystalline and the number of defects on the surface of photocatalyst. The optimal parameter ratios with maximum photoconversion efficiency were 16 mL, 3 mL and 5 % for water, acid and total metal loading, respectively.

Optimization of reaction parameters of radiation induced grafting of 1-vinylimidazole onto poly(ethylene-co-tetraflouroethene) using response surface method

NASA Astrophysics Data System (ADS)

Nasef, Mohamed Mahmoud; Aly, Amgad Ahmed; Saidi, Hamdani; Ahmad, Arshad

2011-11-01

Radiation induced grafting of 1-vinylimidazole (1-VIm) onto poly(ethylene-co-tetraflouroethene) (ETFE) was investigated. The grafting parameters such as absorbed dose, monomer concentration, grafting time and temperature were optimized using response surface method (RSM). The Box-Behnken module available in the design expert software was used to investigate the effect of reaction conditions (independent parameters) varied in four levels on the degree of grafting ( G%) (response parameter). The model yielded a polynomial equation that relates the linear, quadratic and interaction effects of the independent parameters to the response parameter. The analysis of variance (ANOVA) was used to evaluate the results of the model and detect the significant values for the independent parameters. The optimum parameters to achieve a maximum G% were found to be monomer concentration of 55 vol%, absorbed dose of 100 kGy, time in the range of 14-20 h and a temperature of 61 °C. Fourier transform infrared (FTIR), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) were used to investigate the properties of the obtained films and provide evidence for grafting.

Application of Response Surface Methodology on Leaching of Iron from Partially Laterised Khondalite Rocks: A Bauxite Mining Waste

NASA Astrophysics Data System (ADS)

Swain, Ranjita; Bhima Rao, R.

2018-04-01

In the present investigation, response surface methodology (RSM) is used for a quadratic model that continuously controls the process parameters. This model is used to optimize the removal of iron oxide from Partially Laterised Khondalite (PLK) rocks which is influenced by several independent variables namely acid concentration, time and temperature. Second order response functions are produced for leaching of iron oxide from PLK rocks-a bauxite mining waste. In RSM, Box-Behnken design is used for the process optimization to achieve maximum removal of iron oxide. The influence of the process variables of leaching of iron oxide is presented in the form of 3-D response graphs. The results of this investigation reveals that 3 M hydrochloric acid concentration, 240 min time and 373 K temperature are found to be the best conditions for removal of 99% Fe2O3. The product obtain at this condition contain 80% brightness which is suitable for ceramic and filler industry applications. The novelity of the work is that the waste can be a value added product after suitable physical beneficiation and chemical treatment.

Sustained release biodegradable solid lipid microparticles: Formulation, evaluation and statistical optimization by response surface methodology.

PubMed

Hanif, Muhammad; Khan, Hafeez Ullah; Afzal, Samina; Mahmood, Asif; Maheen, Safirah; Afzal, Khurram; Iqbal, Nabila; Andleeb, Mehwish; Abbas, Nazar

2017-12-20

For preparing nebivolol loaded solid lipid microparticles (SLMs) by the solvent evaporation microencapsulation process from carnauba wax and glyceryl monostearate, central composite design was used to study the impact of independent variables on yield (Y1), entrapment efficiency (Y2) and drug release (Y3). SLMs having a 10-40 μm size range, with good rheological behavior and spherical smooth surfaces, were produced. Fourier transform infrared spectroscopy, differential scanning calorimetry and X-ray diffractometry pointed to compatibility between formulation components and the zeta-potential study confirmed better stability due to the presence of negative charge (-20 to -40 mV). The obtained outcomes for Y1 (29-86 %), Y2 (45-83 %) and Y3 (49-86 %) were analyzed by polynomial equations and the suggested quadratic model were validated. Nebivolol release from SLMs at pH 1.2 and 6.8 was significantly (p < 0.05) affected by lipid concentration. The release mechanism followed Higuchi and zero order models, while n > 0.85 value (Korsmeyer- Peppas) suggested slow erosion along with diffusion. The optimized SLMs have the potential to improve nebivolol oral bioavailability.

Evaluation of on-line pulse control for vibration suppression in flexible spacecraft

NASA Technical Reports Server (NTRS)

Masri, Sami F.

1987-01-01

A numerical simulation was performed, by means of a large-scale finite element code capable of handling large deformations and/or nonlinear behavior, to investigate the suitability of the nonlinear pulse-control algorithm to suppress the vibrations induced in the Spacecraft Control Laboratory Experiment (SCOLE) components under realistic maneuvers. Among the topics investigated were the effects of various control parameters on the efficiency and robustness of the vibration control algorithm. Advanced nonlinear control techniques were applied to an idealized model of some of the SCOLE components to develop an efficient algorithm to determine the optimal locations of point actuators, considering the hardware on the SCOLE project as distributed in nature. The control was obtained from a quadratic optimization criterion, given in terms of the state variables of the distributed system. An experimental investigation was performed on a model flexible structure resembling the essential features of the SCOLE components, and electrodynamic and electrohydraulic actuators were used to investigate the applicability of the control algorithm with such devices in addition to mass-ejection pulse generators using compressed air.

Optimization of formulation of soy-cakes baked in infrared-microwave combination oven by response surface methodology.

PubMed

Şakıyan, Özge

2015-05-01

The aim of present work is to optimize the formulation of a functional cake (soy-cake) to be baked in infrared-microwave combination oven. For this optimization process response surface methodology was utilized. It was also aimed to optimize the processing conditions of the combination baking. The independent variables were the baking time (8, 9, 10 min), the soy flour concentration (30, 40, 50 %) and the DATEM (diacetyltartaric acid esters of monoglycerides) concentration (0.4, 0.6 and 0.8 %). The quality parameters that were examined in the study were specific volume, weight loss, total color change and firmness of the cake samples. The results were analyzed by multiple regression; and the significant linear, quadratic, and interaction terms were used in the second order mathematical model. The optimum baking time, soy-flour concentration and DATEM concentration were found as 9.5 min, 30 and 0.72 %, respectively. The corresponding responses of the optimum points were almost comparable with those of conventionally baked soy-cakes. So it may be declared that it is possible to produce high quality soy cakes in a very short time by using infrared-microwave combination oven.

Project Wish: The Emerald City, phase 3

NASA Technical Reports Server (NTRS)

1992-01-01

Phase 3 of Project Wish saw the evolution of the Emerald City (E-City) from a collection of specialized independent analyses and ideas to a working structural design integrated with major support systems and analyses. Emphasis was placed on comparing and contrasting the closed and open cycle gas core nuclear rocket engines to further determine the optimum propulsive system for the C-City. Power and thermal control requirements were then defined and the question of how to meet these requirements was addressed. Software was developed to automate the mission/system/configuration analysis so changes dictated by various subsystems constraints could be managed efficiently and analyzed interactively. In addition, the liquid hydrogen propellant tank was statically designed for minimum mass and shape optimization using a finite element modeling package called SDRC I-DEAS while spoke and shaft cross-sectional areas were optimized on ASTROS (Automated Structural Optimization System). A structural dynamic analysis also conducted using ASTROS enabled a study of the displacements, accelerations, modes and frequencies of the C-City. Finally, the attitude control system design began with an initial mass moment of inertia analysis and was then designed and optimized using linear quadratic regulator control theory.

Error analysis of finite element method for Poisson–Nernst–Planck equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

The Development and Application of Random Matrix Theory in Adaptive Signal Processing in the Sample Deficient Regime

DTIC Science & Technology

2014-09-01

optimal diagonal loading which minimizes the MSE. The be- havior of optimal diagonal loading when the arrival process is composed of plane waves embedded...observation vectors. The examples of the ensemble correlation matrix corresponding to the input process consisting of a single or multiple plane waves...Y ∗ij is a complex-conjugate of Yij. This result is used in order to evaluate the expectations of different quadratic forms. The Poincare -Nash

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

NASA Technical Reports Server (NTRS)

Younis, Bassam A.; Gatski, Thomas B.; Speziale, Charles G.

1994-01-01

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

PubMed

McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

2013-12-13

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

PubMed

D'Amico, María Belén; Calandrini, Guillermo L

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

NASA Astrophysics Data System (ADS)

D'Amico, María Belén; Calandrini, Guillermo L.

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

Bottom friction optimization for a better barotropic tide modelling

NASA Astrophysics Data System (ADS)

Boutet, Martial; Lathuilière, Cyril; Son Hoang, Hong; Baraille, Rémy

2015-04-01

At a regional scale, barotropic tides are the dominant source of variability of currents and water heights. A precise representation of these processes is essential because of their great impacts on human activities (submersion risks, marine renewable energies, ...). Identified sources of error for tide modelling at a regional scale are the followings: bathymetry, boundary forcing and dissipation due to bottom friction. Nevertheless, bathymetric databases are nowadays known with a good accuracy, especially over shelves, and global tide models performances are better than ever. The most promising improvement is thus the bottom friction representation. The method used to estimate bottom friction is the simultaneous perturbation stochastic approximation (SPSA) which consists in the approximation of the gradient based on a fixed number of cost function measurements, regardless of the dimension of the vector to be estimated. Indeed, each cost function measurement is obtained by randomly perturbing every component of the parameter vector. An important feature of SPSA is its relative ease of implementation. In particular, the method does not require the development of tangent linear and adjoint version of the circulation model. Experiments are carried out to estimate bottom friction with the HYbrid Coordinate Ocean Model (HYCOM) in barotropic mode (one isopycnal layer). The study area is the Northeastern Atlantic margin which is characterized by strong currents and an intense dissipation. Bottom friction is parameterized with a quadratic term and friction coefficient is computed with the water height and the bottom roughness. The latter parameter is the one to be estimated. Assimilated data are the available tide gauge observations. First, the bottom roughness is estimated taking into account bottom sediment natures and bathymetric ranges. Then, it is estimated with geographical degrees of freedom. Finally, the impact of the estimation of a mixed quadratic/linear friction is evaluated.

Particle drag history in a subcritical post-shock flow - data analysis method and uncertainty

NASA Astrophysics Data System (ADS)

Ding, Liuyang; Bordoloi, Ankur; Adrian, Ronald; Prestridge, Kathy; Arizona State University Team; Los Alamos National Laboratory Team

2017-11-01

A novel data analysis method for measuring particle drag in an 8-pulse particle tracking velocimetry-accelerometry (PTVA) experiment is described. We represented the particle drag history, CD(t) , using polynomials up to the third order. An analytical model for continuous particle position history was derived by integrating an equation relating CD(t) with particle velocity and acceleration. The coefficients of CD(t) were then calculated by fitting the position history model to eight measured particle locations in the sense of least squares. A preliminary test with experimental data showed that the new method yielded physically more reasonable particle velocity and acceleration history compared to conventionally adopted polynomial fitting. To fully assess and optimize the performance of the new method, we performed a PTVA simulation by assuming a ground truth of particle motion based on an ensemble of experimental data. The results indicated a significant reduction in the RMS error of CD. We also found that for particle locating noise between 0.1 and 3 pixels, a range encountered in our experiment, the lowest RMS error was achieved by using the quadratic CD(t) model. Furthermore, we will also discuss the optimization of the pulse timing configuration.

Batch versus column modes for the adsorption of radioactive metal onto rice husk waste: conditions optimization through response surface methodology.

PubMed

Kausar, Abida; Bhatti, Haq Nawaz; Iqbal, Munawar; Ashraf, Aisha

2017-09-01

Batch and column adsorption modes were compared for the adsorption of U(VI) ions using rice husk waste biomass (RHWB). Response surface methodology was employed for the optimization of process variables, i.e., (pH (A), adsorbent dose (B), initial ion concentration (C)) in batch mode. The B, C and C 2 affected the U(VI) adsorption significantly in batch mode. The developed quadratic model was found to be validated on the basis of regression coefficient as well as analysis of variance. The predicted and actual values were found to be correlated well, with negligible residual value, and B, C and C 2 were significant terms. The column study was performed considering bed height, flow rate and initial metal ion concentration, and adsorption efficiency was evaluated through breakthrough curves and bed depth service time and Thomas models. Adsorption was found to be dependent on bed height and initial U(VI) ion concentration, and flow rate decreased the adsorption capacity. Thomas models fitted well to the U(VI) adsorption onto RHWB. Results revealed that RHWB has potential to remove U(VI) ions and batch adsorption was found to be efficient versus column mode.

Supercritical Carbon Dioxide Extraction of Flavonoids from Pomelo (Citrus grandis (L.) Osbeck) Peel and Their Antioxidant Activity

PubMed Central

He, Jin-Zhe; Shao, Ping; Liu, Jian-Hua; Ru, Qiao-Mei

2012-01-01

Supercritical carbon dioxide (SC-CO2) extraction of flavonoids from pomelo (Citrus grandis (L.) Osbeck) peel and their antioxidant activity were investigated. Box-Behnken design combined with response surface methodology was employed to maximize the extraction yield of flavonoids. Correlation analysis of the mathematical-regression model indicated that a quadratic polynomial model could be used to optimize the SC-CO2 extraction of flavonoids. The optimal conditions for obtaining the highest extraction yield of flavonoids from pomelo peel were a temperature of 80 °C, a pressure of 39 MPa and a static extraction time of 49 min in the presence of 85% ethanol as modifier. Under these conditions, the experimental yield was 2.37%, which matched positively with the value predicted by the model. Furthermore, flavonoids obtained by SC-CO2 extraction showed a higher scavenging activity on hydroxyl, 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS) radicals than those obtained by conventional solvent extraction (CSE). Therefore, SC-CO2 extraction can be considered as a suitable technique for the obtainment of flavonoids from pomelo peel. PMID:23202938

Model Predictive Control considering Reachable Range of Wheels for Leg / Wheel Mobile Robots

NASA Astrophysics Data System (ADS)

Suzuki, Naito; Nonaka, Kenichiro; Sekiguchi, Kazuma

2016-09-01

Obstacle avoidance is one of the important tasks for mobile robots. In this paper, we study obstacle avoidance control for mobile robots equipped with four legs comprised of three DoF SCARA leg/wheel mechanism, which enables the robot to change its shape adapting to environments. Our previous method achieves obstacle avoidance by model predictive control (MPC) considering obstacle size and lateral wheel positions. However, this method does not ensure existence of joint angles which achieves reference wheel positions calculated by MPC. In this study, we propose a model predictive control considering reachable mobile ranges of wheels positions by combining multiple linear constraints, where each reachable mobile range is approximated as a convex trapezoid. Thus, we achieve to formulate a MPC as a quadratic problem with linear constraints for nonlinear problem of longitudinal and lateral wheel position control. By optimization of MPC, the reference wheel positions are calculated, while each joint angle is determined by inverse kinematics. Considering reachable mobile ranges explicitly, the optimal joint angles are calculated, which enables wheels to reach the reference wheel positions. We verify its advantages by comparing the proposed method with the previous method through numerical simulations.

Sono-assisted adsorption of a textile dye on milk vetch-derived charcoal supported by silica nanopowder.

PubMed

Jorfi, Sahand; Darvishi Cheshmeh Soltani, Reza; Ahmadi, Mehdi; Khataee, Alireza; Safari, Mahdi

2017-02-01

This study was performed to assess the efficiency of silica nanopowder (SNP)/milk vetch-derived charcoal (MVDC) nanocomposite coupled with the ultrasonic irradiation named sono-adsorption process for treating water-contained Basic Red 46 (BR46) dye. Field emission scanning electron microscopy (FE-SEM), X-ray diffraction (XRD), Brunauer-Emmett-Teller (BET) and Fourier transform infrared spectroscopy (FT-IR) were performed for the characterization of as-prepared adsorbent. The sono-assisted adsorption process was optimized using response surface optimization on the basis of central composite design by the application of quadratic model. Accordingly, the color removal can be retained more than 93% by an initial BR46 concentration of 8 mg/L, sonication time of 31 min, adsorbent dosage of 1.2 g/L and initial pH of 9. The pseudo-second order kinetic model described the sono-assisted adsorption of BR46 reasonably well (R 2  > 0.99). The intra-particular diffusion kinetic model pointed out that the sono-assisted adsorption of BR46 onto SNP/MVDC nanocomposite was diffusion controlled as well as that ultrasonication enhanced the diffusion rate. Copyright © 2016 Elsevier Ltd. All rights reserved.

Application of response surface methodology (RSM) for optimizing coagulation process of paper recycling wastewater using Ocimum basilicum.

PubMed

Mosaddeghi, Mohammad Reza; Pajoum Shariati, Farshid; Vaziri Yazdi, Seyed Ali; Nabi Bidhendi, Gholamreza

2018-06-21

The wastewater produced in a pulp and paper industry is one of the most polluted industrial wastewaters, and therefore its treatment requires complex processes. One of the simple and feasible processes in pulp and paper wastewater treatment is coagulation and flocculation. Overusing a chemical coagulant can produce a large volume of sludge and increase costs and health concerns. Therefore, the use of natural and plant-based coagulants has been recently attracted the attention of researchers. One of the advantages of using Ocimum basilicum as a coagulant is a reduction in the amount of chemical coagulant required. In this study, the effect of basil mucilage has been investigated as a plant-based coagulant together with alum for treatment of paper recycling wastewater. Response surface methodology (RSM) was used to optimize the process of chemical coagulation based on a central composite rotatable design (CCRD). Quadratic models for colour reduction and TSS removal with coefficients of determination of R 2 >96 were obtained using the analysis of variance. Under optimal conditions, removal efficiencies of colour and total suspended solids (TSS) were 85% and 82%, respectively.

Pressurized liquid extraction of anthocyanins and biflavonoids from Schinus terebinthifolius Raddi: A multivariate optimization.

PubMed

Feuereisen, Michelle M; Gamero Barraza, Mariana; Zimmermann, Benno F; Schieber, Andreas; Schulze-Kaysers, Nadine

2017-01-01

Response surface methodology was employed to investigate the effects of pressurized liquid extraction (PLE) parameters on the recovery of phenolic compounds (anthocyanins, biflavonoids) from Brazilian pepper (Schinus terebinthifolius Raddi) fruits. The effects of temperature, static time, and ethanol as well as acid concentration on the polyphenol yield were described well by quadratic models (p<0.0001). A significant influence of the ethanol concentration (p<0.0001) and several interactions (p<0.05) were identified. Identification of the biflavonoid I3',II8-binaringenin in drupes of S. terebinthifolius was achieved by UHPLC-MS(2). Interestingly, at high extraction temperatures (>75°C), an artifact occurred and was tentatively identified as a diastereomer of I3',II8-binaringenin. Multivariate optimization led to high yields of phenolic compounds from the exocarp/drupes at 100/75°C, 10/10min, 54.5/54.2% ethanol, and 5/0.03% acetic acid. This study demonstrates that PLE is well suited for the extraction of phenolic compounds from S. terebinthifolius and can efficiently be optimized by response surface methodology. Copyright © 2016 Elsevier Ltd. All rights reserved.

A quantum annealing approach for fault detection and diagnosis of graph-based systems

NASA Astrophysics Data System (ADS)

Perdomo-Ortiz, A.; Fluegemann, J.; Narasimhan, S.; Biswas, R.; Smelyanskiy, V. N.

2015-02-01

Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping of this combinatorial problem to quadratic unconstrained binary optimization (QUBO), and the experimental results of instances embedded onto a quantum annealing device with 509 quantum bits. Besides being the first time a quantum approach has been proposed for problems in the advanced diagnostics community, to the best of our knowledge this work is also the first research utilizing the route Problem → QUBO → Direct embedding into quantum hardware, where we are able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization. We discuss some of the programmability challenges in the current generation of the quantum device as well as a few possible ways to extend this work to more complex arbitrary network graphs.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Modeling the improvement of ultrafiltration membrane mass transfer when using biofiltration pretreatment in surface water applications.

PubMed

Netcher, Andrea C; Duranceau, Steven J

2016-03-01

In surface water treatment, ultrafiltration (UF) membranes are widely used because of their ability to supply safe drinking water. Although UF membranes produce high-quality water, their efficiency is limited by fouling. Improving UF filtrate productivity is economically desirable and has been attempted by incorporating sustainable biofiltration processes as pretreatment to UF with varying success. The availability of models that can be applied to describe the effectiveness of biofiltration on membrane mass transfer are lacking. In this work, UF water productivity was empirically modeled as a function of biofilter feed water quality using either a quadratic or Gaussian relationship. UF membrane mass transfer variability was found to be governed by the dimensionless mass ratio between the alkalinity (ALK) and dissolved organic carbon (DOC). UF membrane productivity was optimized when the biofilter feed water ALK to DOC ratio fell between 10 and 14. Copyright © 2015 Elsevier Ltd. All rights reserved.

Optimal Design of Experiments by Combining Coarse and Fine Measurements

NASA Astrophysics Data System (ADS)

Lee, Alpha A.; Brenner, Michael P.; Colwell, Lucy J.

2017-11-01

In many contexts, it is extremely costly to perform enough high-quality experimental measurements to accurately parametrize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high-resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

Cooking quality and starch digestibility of gluten free pasta using new bean flour.

PubMed

Giuberti, Gianluca; Gallo, Antonio; Cerioli, Carla; Fortunati, Paola; Masoero, Francesco

2015-05-15

The use of rice/leguminous blend may be nutritionally convenient in gluten free product manufacturing. Gluten free spaghetti was prepared with rice flour and different concentrations of bean flour (included at levels of 0%, 20% and 40%, w/w) derived from a new developed white-seeded low phytic acid and lectin free (ws+lpa+lf) bean cultivar. Protein, ash and dietary fibre contents increased linearly (P<0.05) while total starch decreased quadratically (P<0.05) with the inclusion of ws+lpa+lf bean flour. The colour of spaghetti was influenced (P<0.05) by ws+lpa+lf bean inclusion. With respect to 0% spaghetti, the inclusion of ws+lpa+lf bean increased linearly (P<0.05) the optimal cooking time and the water absorption capacity, without affecting cooking loss and texture properties. The ws+lpa+lf bean inclusion increases quadratically (P<0.05) the resistant starch content, while decreasing quadratically (P<0.05) the in vitro glycemic index. The partial replacement of rice flour with bean flour can favourably be used in gluten free spaghetti formulation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Design of Linear-Quadratic-Regulator for a CSTR process

NASA Astrophysics Data System (ADS)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

Fast Algorithms for Designing Unimodular Waveform(s) With Good Correlation Properties

NASA Astrophysics Data System (ADS)

Li, Yongzhe; Vorobyov, Sergiy A.

2018-03-01

In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding optimization problems can quickly grow to large scale with increasing the code length and number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are non-convex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as non-convex quartic optimization problems in frequency domain, and then simplify them into quadratic problems by utilizing the majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or non-convex optimization problems. While designing our fast algorithms, we find out and use inherent algebraic structures in the objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form which allows to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

Homotopy method for optimization of variable-specific-impulse low-thrust trajectories

NASA Astrophysics Data System (ADS)

Chi, Zhemin; Yang, Hongwei; Chen, Shiyu; Li, Junfeng

2017-11-01

The homotopy method has been used as a useful tool in solving fuel-optimal trajectories with constant-specific-impulse low thrust. However, the specific impulse is often variable for many practical solar electric power-limited thrusters. This paper investigates the application of the homotopy method for optimization of variable-specific-impulse low-thrust trajectories. Difficulties arise when the two commonly-used homotopy functions are employed for trajectory optimization. The optimal power throttle level and the optimal specific impulse are coupled with the commonly-used quadratic and logarithmic homotopy functions. To overcome these difficulties, a modified logarithmic homotopy function is proposed to serve as a gateway for trajectory optimization, leading to decoupled expressions of both the optimal power throttle level and the optimal specific impulse. The homotopy method based on this homotopy function is proposed. Numerical simulations validate the feasibility and high efficiency of the proposed method.

Optimization of Cubic Polynomial Functions without Calculus

ERIC Educational Resources Information Center

Taylor, Ronald D., Jr.; Hansen, Ryan

2008-01-01

In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…

Acceleration-Augmented LQG Control of an Active Magnetic Bearing

NASA Technical Reports Server (NTRS)

Feeley, Joseph J.

1993-01-01

A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal control formulation provides a convenient method of trading-off fast transient response and force attenuation as control objectives.