Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

NASA Astrophysics Data System (ADS)

Prasanth, Rajanampalli Seshasai Srinivasa; Hans Raj, Kandikonda

2017-04-01

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

NASA Technical Reports Server (NTRS)

Hargrove, A.

1982-01-01

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming.

PubMed

Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan

2011-12-01

In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.

Reduction of the Nonlinear Phase Shift Induced by Stimulated Brillouin Scattering for Bi-Directional Pumping Configuration System Using Particle Swarm Optimization Algorithm

NASA Astrophysics Data System (ADS)

Al-Asadi, H. A.

2013-02-01

We present a theoretical analysis of an additional nonlinear phase shift of backward Stokes wave based on stimulated Brillouin scattering in the system with a bi-directional pumping scheme. We optimize three parameters of the system: the numerical aperture, the optical loss and the pumping wavelength to minimize an additional nonlinear phase shift of backward Stokes waves due to stimulated Brillouin scattering. The optimization is performed with various Brillouin pump powers and the optical reflectivity values are based on the modern, global evolutionary computation algorithm, particle swarm optimization. It is shown that the additional nonlinear phase shift of backward Stokes wave varies with different optical fiber lengths, and can be minimized to less than 0.07 rad according to the particle swarm optimization algorithm for 5 km. The bi-directional pumping configuration system is shown to be efficient when it is possible to transmit the power output to advanced when frequency detuning is negative and delayed when it is positive, with the optimum values of the three parameters to achieve the reduction of an additional nonlinear phase shift.

Modern meta-heuristics based on nonlinear physics processes: A review of models and design procedures

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.

2016-10-01

Meta-heuristic algorithms are problem-solving methods which try to find good-enough solutions to very hard optimization problems, at a reasonable computation time, where classical approaches fail, or cannot even been applied. Many existing meta-heuristics approaches are nature-inspired techniques, which work by simulating or modeling different natural processes in a computer. Historically, many of the most successful meta-heuristic approaches have had a biological inspiration, such as evolutionary computation or swarm intelligence paradigms, but in the last few years new approaches based on nonlinear physics processes modeling have been proposed and applied with success. Non-linear physics processes, modeled as optimization algorithms, are able to produce completely new search procedures, with extremely effective exploration capabilities in many cases, which are able to outperform existing optimization approaches. In this paper we review the most important optimization algorithms based on nonlinear physics, how they have been constructed from specific modeling of a real phenomena, and also their novelty in terms of comparison with alternative existing algorithms for optimization. We first review important concepts on optimization problems, search spaces and problems' difficulty. Then, the usefulness of heuristics and meta-heuristics approaches to face hard optimization problems is introduced, and some of the main existing classical versions of these algorithms are reviewed. The mathematical framework of different nonlinear physics processes is then introduced as a preparatory step to review in detail the most important meta-heuristics based on them. A discussion on the novelty of these approaches, their main computational implementation and design issues, and the evaluation of a novel meta-heuristic based on Strange Attractors mutation will be carried out to complete the review of these techniques. We also describe some of the most important application areas, in broad sense, of meta-heuristics, and describe free-accessible software frameworks which can be used to make easier the implementation of these algorithms.

Pulmonary Nodule Recognition Based on Multiple Kernel Learning Support Vector Machine-PSO

PubMed Central

Zhu, Zhichuan; Zhao, Qingdong; Liu, Liwei; Zhang, Lijuan

2018-01-01

Pulmonary nodule recognition is the core module of lung CAD. The Support Vector Machine (SVM) algorithm has been widely used in pulmonary nodule recognition, and the algorithm of Multiple Kernel Learning Support Vector Machine (MKL-SVM) has achieved good results therein. Based on grid search, however, the MKL-SVM algorithm needs long optimization time in course of parameter optimization; also its identification accuracy depends on the fineness of grid. In the paper, swarm intelligence is introduced and the Particle Swarm Optimization (PSO) is combined with MKL-SVM algorithm to be MKL-SVM-PSO algorithm so as to realize global optimization of parameters rapidly. In order to obtain the global optimal solution, different inertia weights such as constant inertia weight, linear inertia weight, and nonlinear inertia weight are applied to pulmonary nodules recognition. The experimental results show that the model training time of the proposed MKL-SVM-PSO algorithm is only 1/7 of the training time of the MKL-SVM grid search algorithm, achieving better recognition effect. Moreover, Euclidean norm of normalized error vector is proposed to measure the proximity between the average fitness curve and the optimal fitness curve after convergence. Through statistical analysis of the average of 20 times operation results with different inertial weights, it can be seen that the dynamic inertial weight is superior to the constant inertia weight in the MKL-SVM-PSO algorithm. In the dynamic inertial weight algorithm, the parameter optimization time of nonlinear inertia weight is shorter; the average fitness value after convergence is much closer to the optimal fitness value, which is better than the linear inertial weight. Besides, a better nonlinear inertial weight is verified. PMID:29853983

Pulmonary Nodule Recognition Based on Multiple Kernel Learning Support Vector Machine-PSO.

PubMed

Li, Yang; Zhu, Zhichuan; Hou, Alin; Zhao, Qingdong; Liu, Liwei; Zhang, Lijuan

2018-01-01

Pulmonary nodule recognition is the core module of lung CAD. The Support Vector Machine (SVM) algorithm has been widely used in pulmonary nodule recognition, and the algorithm of Multiple Kernel Learning Support Vector Machine (MKL-SVM) has achieved good results therein. Based on grid search, however, the MKL-SVM algorithm needs long optimization time in course of parameter optimization; also its identification accuracy depends on the fineness of grid. In the paper, swarm intelligence is introduced and the Particle Swarm Optimization (PSO) is combined with MKL-SVM algorithm to be MKL-SVM-PSO algorithm so as to realize global optimization of parameters rapidly. In order to obtain the global optimal solution, different inertia weights such as constant inertia weight, linear inertia weight, and nonlinear inertia weight are applied to pulmonary nodules recognition. The experimental results show that the model training time of the proposed MKL-SVM-PSO algorithm is only 1/7 of the training time of the MKL-SVM grid search algorithm, achieving better recognition effect. Moreover, Euclidean norm of normalized error vector is proposed to measure the proximity between the average fitness curve and the optimal fitness curve after convergence. Through statistical analysis of the average of 20 times operation results with different inertial weights, it can be seen that the dynamic inertial weight is superior to the constant inertia weight in the MKL-SVM-PSO algorithm. In the dynamic inertial weight algorithm, the parameter optimization time of nonlinear inertia weight is shorter; the average fitness value after convergence is much closer to the optimal fitness value, which is better than the linear inertial weight. Besides, a better nonlinear inertial weight is verified.

Cognitive Nonlinear Radar

DTIC Science & Technology

2013-01-01

intelligently selecting waveform parameters using adaptive algorithms. The adaptive algorithms optimize the waveform parameters based on (1) the EM...the environment. 15. SUBJECT TERMS cognitive radar, adaptive sensing, spectrum sensing, multi-objective optimization, genetic algorithms, machine...detection and classification block diagram. .........................................................6 Figure 5. Genetic algorithm block diagram

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A novel track-before-detect algorithm based on optimal nonlinear filtering for detecting and tracking infrared dim target

NASA Astrophysics Data System (ADS)

Tian, Yuexin; Gao, Kun; Liu, Ying; Han, Lu

2015-08-01

Aiming at the nonlinear and non-Gaussian features of the real infrared scenes, an optimal nonlinear filtering based algorithm for the infrared dim target tracking-before-detecting application is proposed. It uses the nonlinear theory to construct the state and observation models and uses the spectral separation scheme based Wiener chaos expansion method to resolve the stochastic differential equation of the constructed models. In order to improve computation efficiency, the most time-consuming operations independent of observation data are processed on the fore observation stage. The other observation data related rapid computations are implemented subsequently. Simulation results show that the algorithm possesses excellent detection performance and is more suitable for real-time processing.

Incorporation of Fixed Installation Costs into Optimization of Groundwater Remediation with a New Efficient Surrogate Nonlinear Mixed Integer Optimization Algorithm

NASA Astrophysics Data System (ADS)

Shoemaker, Christine; Wan, Ying

2016-04-01

Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).

Variational Trajectory Optimization Tool Set: Technical description and user's manual

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Queen, Eric M.; Cavanaugh, Michael D.; Wetzel, Todd A.; Moerder, Daniel D.

1993-01-01

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

An NN-Based SRD Decomposition Algorithm and Its Application in Nonlinear Compensation

PubMed Central

Yan, Honghang; Deng, Fang; Sun, Jian; Chen, Jie

2014-01-01

In this study, a neural network-based square root of descending (SRD) order decomposition algorithm for compensating for nonlinear data generated by sensors is presented. The study aims at exploring the optimized decomposition of data 1.00,0.00,0.00 and minimizing the computational complexity and memory space of the training process. A linear decomposition algorithm, which automatically finds the optimal decomposition of N subparts and reduces the training time to 1N and memory cost to 1N, has been implemented on nonlinear data obtained from an encoder. Particular focus is given to the theoretical access of estimating the numbers of hidden nodes and the precision of varying the decomposition method. Numerical experiments are designed to evaluate the effect of this algorithm. Moreover, a designed device for angular sensor calibration is presented. We conduct an experiment that samples the data of an encoder and compensates for the nonlinearity of the encoder to testify this novel algorithm. PMID:25232912

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

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

Sun, Y.; Borland, Michael

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

Application of GA, PSO, and ACO algorithms to path planning of autonomous underwater vehicles

NASA Astrophysics Data System (ADS)

Aghababa, Mohammad Pourmahmood; Amrollahi, Mohammad Hossein; Borjkhani, Mehdi

2012-09-01

In this paper, an underwater vehicle was modeled with six dimensional nonlinear equations of motion, controlled by DC motors in all degrees of freedom. Near-optimal trajectories in an energetic environment for underwater vehicles were computed using a numerical solution of a nonlinear optimal control problem (NOCP). An energy performance index as a cost function, which should be minimized, was defined. The resulting problem was a two-point boundary value problem (TPBVP). A genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO) algorithms were applied to solve the resulting TPBVP. Applying an Euler-Lagrange equation to the NOCP, a conjugate gradient penalty method was also adopted to solve the TPBVP. The problem of energetic environments, involving some energy sources, was discussed. Some near-optimal paths were found using a GA, PSO, and ACO algorithms. Finally, the problem of collision avoidance in an energetic environment was also taken into account.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

NASA Technical Reports Server (NTRS)

Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.

1992-01-01

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Optimization of autoregressive, exogenous inputs-based typhoon inundation forecasting models using a multi-objective genetic algorithm

NASA Astrophysics Data System (ADS)

Ouyang, Huei-Tau

2017-07-01

Three types of model for forecasting inundation levels during typhoons were optimized: the linear autoregressive model with exogenous inputs (LARX), the nonlinear autoregressive model with exogenous inputs with wavelet function (NLARX-W) and the nonlinear autoregressive model with exogenous inputs with sigmoid function (NLARX-S). The forecast performance was evaluated by three indices: coefficient of efficiency, error in peak water level and relative time shift. Historical typhoon data were used to establish water-level forecasting models that satisfy all three objectives. A multi-objective genetic algorithm was employed to search for the Pareto-optimal model set that satisfies all three objectives and select the ideal models for the three indices. Findings showed that the optimized nonlinear models (NLARX-W and NLARX-S) outperformed the linear model (LARX). Among the nonlinear models, the optimized NLARX-W model achieved a more balanced performance on the three indices than the NLARX-S models and is recommended for inundation forecasting during typhoons.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

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

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

DOE PAGES

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard; ...

2017-06-06

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

Design optimization of single mixed refrigerant LNG process using a hybrid modified coordinate descent algorithm

NASA Astrophysics Data System (ADS)

Qyyum, Muhammad Abdul; Long, Nguyen Van Duc; Minh, Le Quang; Lee, Moonyong

2018-01-01

Design optimization of the single mixed refrigerant (SMR) natural gas liquefaction (LNG) process involves highly non-linear interactions between decision variables, constraints, and the objective function. These non-linear interactions lead to an irreversibility, which deteriorates the energy efficiency of the LNG process. In this study, a simple and highly efficient hybrid modified coordinate descent (HMCD) algorithm was proposed to cope with the optimization of the natural gas liquefaction process. The single mixed refrigerant process was modeled in Aspen Hysys® and then connected to a Microsoft Visual Studio environment. The proposed optimization algorithm provided an improved result compared to the other existing methodologies to find the optimal condition of the complex mixed refrigerant natural gas liquefaction process. By applying the proposed optimization algorithm, the SMR process can be designed with the 0.2555 kW specific compression power which is equivalent to 44.3% energy saving as compared to the base case. Furthermore, in terms of coefficient of performance (COP), it can be enhanced up to 34.7% as compared to the base case. The proposed optimization algorithm provides a deep understanding of the optimization of the liquefaction process in both technical and numerical perspectives. In addition, the HMCD algorithm can be employed to any mixed refrigerant based liquefaction process in the natural gas industry.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Proceedings of the Conference on Moments and Signal

NASA Astrophysics Data System (ADS)

Purdue, P.; Solomon, H.

1992-09-01

The focus of this paper is (1) to describe systematic methodologies for selecting nonlinear transformations for blind equalization algorithms (and thus new types of cumulants), and (2) to give an overview of the existing blind equalization algorithms and point out their strengths as well as weaknesses. It is shown that all blind equalization algorithms belong in one of the following three categories, depending where the nonlinear transformation is being applied on the data: (1) the Bussgang algorithms, where the nonlinearity is in the output of the adaptive equalization filter; (2) the polyspectra (or Higher-Order Spectra) algorithms, where the nonlinearity is in the input of the adaptive equalization filter; and (3) the algorithms where the nonlinearity is inside the adaptive filter, i.e., the nonlinear filter or neural network. We describe methodologies for selecting nonlinear transformations based on various optimality criteria such as MSE or MAP. We illustrate that such existing algorithms as Sato, Benveniste-Goursat, Godard or CMA, Stop-and-Go, and Donoho are indeed special cases of the Bussgang family of techniques when the nonlinearity is memoryless. We present results that demonstrate the polyspectra-based algorithms exhibit faster convergence rate than Bussgang algorithms. However, this improved performance is at the expense of more computations per iteration. We also show that blind equalizers based on nonlinear filters or neural networks are more suited for channels that have nonlinear distortions.

Trajectory optimization of spacecraft high-thrust orbit transfer using a modified evolutionary algorithm

NASA Astrophysics Data System (ADS)

Shirazi, Abolfazl

2016-10-01

This article introduces a new method to optimize finite-burn orbital manoeuvres based on a modified evolutionary algorithm. Optimization is carried out based on conversion of the orbital manoeuvre into a parameter optimization problem by assigning inverse tangential functions to the changes in direction angles of the thrust vector. The problem is analysed using boundary delimitation in a common optimization algorithm. A method is introduced to achieve acceptable values for optimization variables using nonlinear simulation, which results in an enlarged convergence domain. The presented algorithm benefits from high optimality and fast convergence time. A numerical example of a three-dimensional optimal orbital transfer is presented and the accuracy of the proposed algorithm is shown.

Image reconstruction and scan configurations enabled by optimization-based algorithms in multispectral CT

NASA Astrophysics Data System (ADS)

Chen, Buxin; Zhang, Zheng; Sidky, Emil Y.; Xia, Dan; Pan, Xiaochuan

2017-11-01

Optimization-based algorithms for image reconstruction in multispectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In this work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for the standard scan configuration, the emphasis is on investigating the algorithm’s potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which has potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or x-ray illumination coverage in MCT.

Variable-Metric Algorithm For Constrained Optimization

NASA Technical Reports Server (NTRS)

Frick, James D.

1989-01-01

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

A Polyhedral Outer-approximation, Dynamic-discretization optimization solver, 1.x

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

Bent, Rusell; Nagarajan, Harsha; Sundar, Kaarthik

2017-09-25

In this software, we implement an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) to global optimality. The algorithm combines ideas that exploit the structure of convex relaxations to MINLPs and bound tightening procedures

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Interactive optimization approach for optimal impulsive rendezvous using primer vector and evolutionary algorithms

NASA Astrophysics Data System (ADS)

Luo, Ya-Zhong; Zhang, Jin; Li, Hai-yang; Tang, Guo-Jin

2010-08-01

In this paper, a new optimization approach combining primer vector theory and evolutionary algorithms for fuel-optimal non-linear impulsive rendezvous is proposed. The optimization approach is designed to seek the optimal number of impulses as well as the optimal impulse vectors. In this optimization approach, adding a midcourse impulse is determined by an interactive method, i.e. observing the primer-magnitude time history. An improved version of simulated annealing is employed to optimize the rendezvous trajectory with the fixed-number of impulses. This interactive approach is evaluated by three test cases: coplanar circle-to-circle rendezvous, same-circle rendezvous and non-coplanar rendezvous. The results show that the interactive approach is effective and efficient in fuel-optimal non-linear rendezvous design. It can guarantee solutions, which satisfy the Lawden's necessary optimality conditions.

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

NASA Technical Reports Server (NTRS)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.; Kelly, Lon C.

2005-01-01

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Motion Cueing Algorithm Development: Piloted Performance Testing of the Cueing Algorithms

NASA Technical Reports Server (NTRS)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.; Kelly, Lon C.

2005-01-01

The relative effectiveness in simulating aircraft maneuvers with both current and newly developed motion cueing algorithms was assessed with an eleven-subject piloted performance evaluation conducted on the NASA Langley Visual Motion Simulator (VMS). In addition to the current NASA adaptive algorithm, two new cueing algorithms were evaluated: the optimal algorithm and the nonlinear algorithm. The test maneuvers included a straight-in approach with a rotating wind vector, an offset approach with severe turbulence and an on/off lateral gust that occurs as the aircraft approaches the runway threshold, and a takeoff both with and without engine failure after liftoff. The maneuvers were executed with each cueing algorithm with added visual display delay conditions ranging from zero to 200 msec. Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. Piloted performance parameters for the approach maneuvers, the vertical velocity upon touchdown and the runway touchdown position, were also analyzed but did not show any noticeable difference among the cueing algorithms. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input analysis shows pilot-induced oscillations on a straight-in approach were less prevalent compared to the optimal algorithm. The augmented turbulence cues increased workload on an offset approach that the pilots deemed more realistic compared to the NASA adaptive algorithm. The takeoff with engine failure showed the least roll activity for the nonlinear algorithm, with the least rudder pedal activity for the optimal algorithm.

Application of multi-objective nonlinear optimization technique for coordinated ramp-metering

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

Haj Salem, Habib; Farhi, Nadir; Lebacque, Jean Patrick, E-mail: abib.haj-salem@ifsttar.fr, E-mail: nadir.frahi@ifsttar.fr, E-mail: jean-patrick.lebacque@ifsttar.fr

2015-03-10

This paper aims at developing a multi-objective nonlinear optimization algorithm applied to coordinated motorway ramp metering. The multi-objective function includes two components: traffic and safety. Off-line simulation studies were performed on A4 France Motorway including 4 on-ramps.

Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks.

PubMed

Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang

2017-11-01

The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.

Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm

NASA Astrophysics Data System (ADS)

Kania, Adhe; Sidarto, Kuntjoro Adji

2016-02-01

Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.

Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.

2001-01-01

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

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

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

PubMed Central

Ramani, Sathish; Liu, Zhihao; Rosen, Jeffrey; Nielsen, Jon-Fredrik; Fessler, Jeffrey A.

2012-01-01

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Stein's Unbiased Risk Estimate— SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance σ2), and GCV (that does not need σ2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type ℓ1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly sub-optimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms. PMID:22531764

Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics.

PubMed

Zhao, Meng; Ding, Baocang

2015-03-01

This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

An efficient algorithm for function optimization: modified stem cells algorithm

NASA Astrophysics Data System (ADS)

Taherdangkoo, Mohammad; Paziresh, Mahsa; Yazdi, Mehran; Bagheri, Mohammad Hadi

2013-03-01

In this paper, we propose an optimization algorithm based on the intelligent behavior of stem cell swarms in reproduction and self-organization. Optimization algorithms, such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO) algorithm, Ant Colony Optimization (ACO) algorithm and Artificial Bee Colony (ABC) algorithm, can give solutions to linear and non-linear problems near to the optimum for many applications; however, in some case, they can suffer from becoming trapped in local optima. The Stem Cells Algorithm (SCA) is an optimization algorithm inspired by the natural behavior of stem cells in evolving themselves into new and improved cells. The SCA avoids the local optima problem successfully. In this paper, we have made small changes in the implementation of this algorithm to obtain improved performance over previous versions. Using a series of benchmark functions, we assess the performance of the proposed algorithm and compare it with that of the other aforementioned optimization algorithms. The obtained results prove the superiority of the Modified Stem Cells Algorithm (MSCA).

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

Graf, Peter; Dykes, Katherine; Scott, George

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

PubMed

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Multiobjective genetic algorithm conjunctive use optimization for production, cost, and energy with dynamic return flow

NASA Astrophysics Data System (ADS)

Peralta, Richard C.; Forghani, Ali; Fayad, Hala

2014-04-01

Many real water resources optimization problems involve conflicting objectives for which the main goal is to find a set of optimal solutions on, or near to the Pareto front. E-constraint and weighting multiobjective optimization techniques have shortcomings, especially as the number of objectives increases. Multiobjective Genetic Algorithms (MGA) have been previously proposed to overcome these difficulties. Here, an MGA derives a set of optimal solutions for multiobjective multiuser conjunctive use of reservoir, stream, and (un)confined groundwater resources. The proposed methodology is applied to a hydraulically and economically nonlinear system in which all significant flows, including stream-aquifer-reservoir-diversion-return flow interactions, are simulated and optimized simultaneously for multiple periods. Neural networks represent constrained state variables. The addressed objectives that can be optimized simultaneously in the coupled simulation-optimization model are: (1) maximizing water provided from sources, (2) maximizing hydropower production, and (3) minimizing operation costs of transporting water from sources to destinations. Results show the efficiency of multiobjective genetic algorithms for generating Pareto optimal sets for complex nonlinear multiobjective optimization problems.

Wind Farm Turbine Type and Placement Optimization

NASA Astrophysics Data System (ADS)

Graf, Peter; Dykes, Katherine; Scott, George; Fields, Jason; Lunacek, Monte; Quick, Julian; Rethore, Pierre-Elouan

2016-09-01

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. This document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Wind farm turbine type and placement optimization

DOE PAGES

Graf, Peter; Dykes, Katherine; Scott, George; ...

2016-10-03

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

A Robustly Stabilizing Model Predictive Control Algorithm

NASA Technical Reports Server (NTRS)

Ackmece, A. Behcet; Carson, John M., III

2007-01-01

A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation.

Lyapunov optimal feedback control of a nonlinear inverted pendulum

NASA Technical Reports Server (NTRS)

Grantham, W. J.; Anderson, M. J.

1989-01-01

Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

A novel algorithm using an orthotropic material model for topology optimization

NASA Astrophysics Data System (ADS)

Tong, Liyong; Luo, Quantian

2017-09-01

This article presents a novel algorithm for topology optimization using an orthotropic material model. Based on the virtual work principle, mathematical formulations for effective orthotropic material properties of an element containing two materials are derived. An algorithm is developed for structural topology optimization using four orthotropic material properties, instead of one density or area ratio, in each element as design variables. As an illustrative example, minimum compliance problems for linear and nonlinear structures are solved using the present algorithm in conjunction with the moving iso-surface threshold method. The present numerical results reveal that: (1) chequerboards and single-node connections are not present even without filtering; (2) final topologies do not contain large grey areas even using a unity penalty factor; and (3) the well-known numerical issues caused by low-density material when considering geometric nonlinearity are resolved by eliminating low-density elements in finite element analyses.

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.

An efficient identification approach for stable and unstable nonlinear systems using Colliding Bodies Optimization algorithm.

PubMed

Pal, Partha S; Kar, R; Mandal, D; Ghoshal, S P

2015-11-01

This paper presents an efficient approach to identify different stable and practically useful Hammerstein models as well as unstable nonlinear process along with its stable closed loop counterpart with the help of an evolutionary algorithm as Colliding Bodies Optimization (CBO) optimization algorithm. The performance measures of the CBO based optimization approach such as precision, accuracy are justified with the minimum output mean square value (MSE) which signifies that the amount of bias and variance in the output domain are also the least. It is also observed that the optimization of output MSE in the presence of outliers has resulted in a very close estimation of the output parameters consistently, which also justifies the effective general applicability of the CBO algorithm towards the system identification problem and also establishes the practical usefulness of the applied approach. Optimum values of the MSEs, computational times and statistical information of the MSEs are all found to be the superior as compared with those of the other existing similar types of stochastic algorithms based approaches reported in different recent literature, which establish the robustness and efficiency of the applied CBO based identification scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Multiobjective optimization of temporal processes.

PubMed

Song, Zhe; Kusiak, Andrew

2010-06-01

This paper presents a dynamic predictive-optimization framework of a nonlinear temporal process. Data-mining (DM) and evolutionary strategy algorithms are integrated in the framework for solving the optimization model. DM algorithms learn dynamic equations from the process data. An evolutionary strategy algorithm is then applied to solve the optimization problem guided by the knowledge extracted by the DM algorithm. The concept presented in this paper is illustrated with the data from a power plant, where the goal is to maximize the boiler efficiency and minimize the limestone consumption. This multiobjective optimization problem can be either transformed into a single-objective optimization problem through preference aggregation approaches or into a Pareto-optimal optimization problem. The computational results have shown the effectiveness of the proposed optimization framework.

Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Hanquan

2016-03-01

In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

NASA Astrophysics Data System (ADS)

Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun

2017-02-01

In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.

Joint optimization of maintenance, buffers and machines in manufacturing lines

NASA Astrophysics Data System (ADS)

Nahas, Nabil; Nourelfath, Mustapha

2018-01-01

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning

2018-06-01

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

Applications of New Surrogate Global Optimization Algorithms including Efficient Synchronous and Asynchronous Parallelism for Calibration of Expensive Nonlinear Geophysical Simulation Models.

NASA Astrophysics Data System (ADS)

Shoemaker, C. A.; Pang, M.; Akhtar, T.; Bindel, D.

2016-12-01

New parallel surrogate global optimization algorithms are developed and applied to objective functions that are expensive simulations (possibly with multiple local minima). The algorithms can be applied to most geophysical simulations, including those with nonlinear partial differential equations. The optimization does not require simulations be parallelized. Asynchronous (and synchronous) parallel execution is available in the optimization toolbox "pySOT". The parallel algorithms are modified from serial to eliminate fine grained parallelism. The optimization is computed with open source software pySOT, a Surrogate Global Optimization Toolbox that allows user to pick the type of surrogate (or ensembles), the search procedure on surrogate, and the type of parallelism (synchronous or asynchronous). pySOT also allows the user to develop new algorithms by modifying parts of the code. In the applications here, the objective function takes up to 30 minutes for one simulation, and serial optimization can take over 200 hours. Results from Yellowstone (NSF) and NCSS (Singapore) supercomputers are given for groundwater contaminant hydrology simulations with applications to model parameter estimation and decontamination management. All results are compared with alternatives. The first results are for optimization of pumping at many wells to reduce cost for decontamination of groundwater at a superfund site. The optimization runs with up to 128 processors. Superlinear speed up is obtained for up to 16 processors, and efficiency with 64 processors is over 80%. Each evaluation of the objective function requires the solution of nonlinear partial differential equations to describe the impact of spatially distributed pumping and model parameters on model predictions for the spatial and temporal distribution of groundwater contaminants. The second application uses an asynchronous parallel global optimization for groundwater quality model calibration. The time for a single objective function evaluation varies unpredictably, so efficiency is improved with asynchronous parallel calculations to improve load balancing. The third application (done at NCSS) incorporates new global surrogate multi-objective parallel search algorithms into pySOT and applies it to a large watershed calibration problem.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Probability distribution functions for unit hydrographs with optimization using genetic algorithm

NASA Astrophysics Data System (ADS)

Ghorbani, Mohammad Ali; Singh, Vijay P.; Sivakumar, Bellie; H. Kashani, Mahsa; Atre, Atul Arvind; Asadi, Hakimeh

2017-05-01

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters.

PubMed

Wynant, Willy; Abrahamowicz, Michal

2016-11-01

Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

Ascent guidance algorithm using lidar wind measurements

NASA Technical Reports Server (NTRS)

Cramer, Evin J.; Bradt, Jerre E.; Hardtla, John W.

1990-01-01

The formulation of a general nonlinear programming guidance algorithm that incorporates wind measurements in the computation of ascent guidance steering commands is discussed. A nonlinear programming (NLP) algorithm that is designed to solve a very general problem has the potential to address the diversity demanded by future launch systems. Using B-splines for the command functional form allows the NLP algorithm to adjust the shape of the command profile to achieve optimal performance. The algorithm flexibility is demonstrated by simulation of ascent with dynamic loading constraints through a set of random wind profiles with and without wind sensing capability.

A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1991-01-01

The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.

Visualizing and improving the robustness of phase retrieval algorithms

DOE PAGES

Tripathi, Ashish; Leyffer, Sven; Munson, Todd; ...

2015-06-01

Coherent x-ray diffractive imaging is a novel imaging technique that utilizes phase retrieval and nonlinear optimization methods to image matter at nanometer scales. We explore how the convergence properties of a popular phase retrieval algorithm, Fienup's HIO, behave by introducing a reduced dimensionality problem allowing us to visualize and quantify convergence to local minima and the globally optimal solution. We then introduce generalizations of HIO that improve upon the original algorithm's ability to converge to the globally optimal solution.

Visualizing and improving the robustness of phase retrieval algorithms

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

Tripathi, Ashish; Leyffer, Sven; Munson, Todd

Coherent x-ray diffractive imaging is a novel imaging technique that utilizes phase retrieval and nonlinear optimization methods to image matter at nanometer scales. We explore how the convergence properties of a popular phase retrieval algorithm, Fienup's HIO, behave by introducing a reduced dimensionality problem allowing us to visualize and quantify convergence to local minima and the globally optimal solution. We then introduce generalizations of HIO that improve upon the original algorithm's ability to converge to the globally optimal solution.

Cyclical parthenogenesis algorithm for layout optimization of truss structures with frequency constraints

NASA Astrophysics Data System (ADS)

Kaveh, A.; Zolghadr, A.

2017-08-01

Structural optimization with frequency constraints is seen as a challenging problem because it is associated with highly nonlinear, discontinuous and non-convex search spaces consisting of several local optima. Therefore, competent optimization algorithms are essential for addressing these problems. In this article, a newly developed metaheuristic method called the cyclical parthenogenesis algorithm (CPA) is used for layout optimization of truss structures subjected to frequency constraints. CPA is a nature-inspired, population-based metaheuristic algorithm, which imitates the reproductive and social behaviour of some animal species such as aphids, which alternate between sexual and asexual reproduction. The efficiency of the CPA is validated using four numerical examples.

Magnetic localization and orientation of the capsule endoscope based on a random complex algorithm.

PubMed

He, Xiaoqi; Zheng, Zizhao; Hu, Chao

2015-01-01

The development of the capsule endoscope has made possible the examination of the whole gastrointestinal tract without much pain. However, there are still some important problems to be solved, among which, one important problem is the localization of the capsule. Currently, magnetic positioning technology is a suitable method for capsule localization, and this depends on a reliable system and algorithm. In this paper, based on the magnetic dipole model as well as magnetic sensor array, we propose nonlinear optimization algorithms using a random complex algorithm, applied to the optimization calculation for the nonlinear function of the dipole, to determine the three-dimensional position parameters and two-dimensional direction parameters. The stability and the antinoise ability of the algorithm is compared with the Levenberg-Marquart algorithm. The simulation and experiment results show that in terms of the error level of the initial guess of magnet location, the random complex algorithm is more accurate, more stable, and has a higher "denoise" capacity, with a larger range for initial guess values.

Modular and configurable optimal sequence alignment software: Cola.

PubMed

Zamani, Neda; Sundström, Görel; Höppner, Marc P; Grabherr, Manfred G

2014-01-01

The fundamental challenge in optimally aligning homologous sequences is to define a scoring scheme that best reflects the underlying biological processes. Maximising the overall number of matches in the alignment does not always reflect the patterns by which nucleotides mutate. Efficiently implemented algorithms that can be parameterised to accommodate more complex non-linear scoring schemes are thus desirable. We present Cola, alignment software that implements different optimal alignment algorithms, also allowing for scoring contiguous matches of nucleotides in a nonlinear manner. The latter places more emphasis on short, highly conserved motifs, and less on the surrounding nucleotides, which can be more diverged. To illustrate the differences, we report results from aligning 14,100 sequences from 3' untranslated regions of human genes to 25 of their mammalian counterparts, where we found that a nonlinear scoring scheme is more consistent than a linear scheme in detecting short, conserved motifs. Cola is freely available under LPGL from https://github.com/nedaz/cola.

Integrated optimization of nonlinear R/C frames with reliability constraints

NASA Technical Reports Server (NTRS)

Soeiro, Alfredo; Hoit, Marc

1989-01-01

A structural optimization algorithm was researched including global displacements as decision variables. The algorithm was applied to planar reinforced concrete frames with nonlinear material behavior submitted to static loading. The flexural performance of the elements was evaluated as a function of the actual stress-strain diagrams of the materials. Formation of rotational hinges with strain hardening were allowed and the equilibrium constraints were updated accordingly. The adequacy of the frames was guaranteed by imposing as constraints required reliability indices for the members, maximum global displacements for the structure and a maximum system probability of failure.

Improved mine blast algorithm for optimal cost design of water distribution systems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Guen Yoo, Do; Kim, Joong Hoon

2015-12-01

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms.

Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

PubMed

Arrieta-Camacho, Juan José; Biegler, Lorenz T

2005-12-01

Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics.

PubMed

Fu, Yue; Chai, Tianyou

2016-12-01

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

Algorithmic Perspectives on Problem Formulations in MDO

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia M.; Lewis, Robert Michael

2000-01-01

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

Metaheuristic Optimization and its Applications in Earth Sciences

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

A common but challenging task in modelling geophysical and geological processes is to handle massive data and to minimize certain objectives. This can essentially be considered as an optimization problem, and thus many new efficient metaheuristic optimization algorithms can be used. In this paper, we will introduce some modern metaheuristic optimization algorithms such as genetic algorithms, harmony search, firefly algorithm, particle swarm optimization and simulated annealing. We will also discuss how these algorithms can be applied to various applications in earth sciences, including nonlinear least-squares, support vector machine, Kriging, inverse finite element analysis, and data-mining. We will present a few examples to show how different problems can be reformulated as optimization. Finally, we will make some recommendations for choosing various algorithms to suit various problems. References 1) D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Trans. Evolutionary Computation, Vol. 1, 67-82 (1997). 2) X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, (2008). 3) X. S. Yang, Mathematical Modelling for Earth Sciences, Dunedin Academic Press, (2008).

Nonlinear optimization with linear constraints using a projection method

NASA Technical Reports Server (NTRS)

Fox, T.

1982-01-01

Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Behcet A.; Carson, John M., III

2005-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

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.

Observability-Based Guidance and Sensor Placement

NASA Astrophysics Data System (ADS)

Hinson, Brian T.

Control system performance is highly dependent on the quality of sensor information available. In a growing number of applications, however, the control task must be accomplished with limited sensing capabilities. This thesis addresses these types of problems from a control-theoretic point-of-view, leveraging system nonlinearities to improve sensing performance. Using measures of observability as an information quality metric, guidance trajectories and sensor distributions are designed to improve the quality of sensor information. An observability-based sensor placement algorithm is developed to compute optimal sensor configurations for a general nonlinear system. The algorithm utilizes a simulation of the nonlinear system as the source of input data, and convex optimization provides a scalable solution method. The sensor placement algorithm is applied to a study of gyroscopic sensing in insect wings. The sensor placement algorithm reveals information-rich areas on flexible insect wings, and a comparison to biological data suggests that insect wings are capable of acting as gyroscopic sensors. An observability-based guidance framework is developed for robotic navigation with limited inertial sensing. Guidance trajectories and algorithms are developed for range-only and bearing-only navigation that improve navigation accuracy. Simulations and experiments with an underwater vehicle demonstrate that the observability measure allows tuning of the navigation uncertainty.

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

PubMed

Zhang, Junfeng; Chen, Wei; Gao, Mingyi; Shen, Gangxiang

2017-10-30

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

NASA Astrophysics Data System (ADS)

Chen, Wei

2015-07-01

In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

NASA Astrophysics Data System (ADS)

Li, Shuang; Zhu, Yongsheng; Wang, Yukai

2014-02-01

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.

Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

NASA Astrophysics Data System (ADS)

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

2018-07-01

This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

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.

Performance of Grey Wolf Optimizer on large scale problems

NASA Astrophysics Data System (ADS)

Gupta, Shubham; Deep, Kusum

2017-01-01

For solving nonlinear continuous problems of optimization numerous nature inspired optimization techniques are being proposed in literature which can be implemented to solve real life problems wherein the conventional techniques cannot be applied. Grey Wolf Optimizer is one of such technique which is gaining popularity since the last two years. The objective of this paper is to investigate the performance of Grey Wolf Optimization Algorithm on large scale optimization problems. The Algorithm is implemented on 5 common scalable problems appearing in literature namely Sphere, Rosenbrock, Rastrigin, Ackley and Griewank Functions. The dimensions of these problems are varied from 50 to 1000. The results indicate that Grey Wolf Optimizer is a powerful nature inspired Optimization Algorithm for large scale problems, except Rosenbrock which is a unimodal function.

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

Hierarchical optimal control of large-scale nonlinear chemical processes.

PubMed

Ramezani, Mohammad Hossein; Sadati, Nasser

2009-01-01

In this paper, a new approach is presented for optimal control of large-scale chemical processes. In this approach, the chemical process is decomposed into smaller sub-systems at the first level, and a coordinator at the second level, for which a two-level hierarchical control strategy is designed. For this purpose, each sub-system in the first level can be solved separately, by using any conventional optimization algorithm. In the second level, the solutions obtained from the first level are coordinated using a new gradient-type strategy, which is updated by the error of the coordination vector. The proposed algorithm is used to solve the optimal control problem of a complex nonlinear chemical stirred tank reactor (CSTR), where its solution is also compared with the ones obtained using the centralized approach. The simulation results show the efficiency and the capability of the proposed hierarchical approach, in finding the optimal solution, over the centralized method.

All-Optical Implementation of the Ant Colony Optimization Algorithm

PubMed Central

Hu, Wenchao; Wu, Kan; Shum, Perry Ping; Zheludev, Nikolay I.; Soci, Cesare

2016-01-01

We report all-optical implementation of the optimization algorithm for the famous “ant colony” problem. Ant colonies progressively optimize pathway to food discovered by one of the ants through identifying the discovered route with volatile chemicals (pheromones) secreted on the way back from the food deposit. Mathematically this is an important example of graph optimization problem with dynamically changing parameters. Using an optical network with nonlinear waveguides to represent the graph and a feedback loop, we experimentally show that photons traveling through the network behave like ants that dynamically modify the environment to find the shortest pathway to any chosen point in the graph. This proof-of-principle demonstration illustrates how transient nonlinearity in the optical system can be exploited to tackle complex optimization problems directly, on the hardware level, which may be used for self-routing of optical signals in transparent communication networks and energy flow in photonic systems. PMID:27222098

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

PubMed

Sun, Kangkang; Sui, Shuai; Tong, Shaocheng

2018-04-01

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Real-time trajectory optimization on parallel processors

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1993-01-01

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

NASA Astrophysics Data System (ADS)

Wang, Liwei; Liu, Xinggao; Zhang, Zeyin

2017-02-01

An efficient primal-dual interior-point algorithm using a new non-monotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented.

Chaotic Teaching-Learning-Based Optimization with Lévy Flight for Global Numerical Optimization.

PubMed

He, Xiangzhu; Huang, Jida; Rao, Yunqing; Gao, Liang

2016-01-01

Recently, teaching-learning-based optimization (TLBO), as one of the emerging nature-inspired heuristic algorithms, has attracted increasing attention. In order to enhance its convergence rate and prevent it from getting stuck in local optima, a novel metaheuristic has been developed in this paper, where particular characteristics of the chaos mechanism and Lévy flight are introduced to the basic framework of TLBO. The new algorithm is tested on several large-scale nonlinear benchmark functions with different characteristics and compared with other methods. Experimental results show that the proposed algorithm outperforms other algorithms and achieves a satisfactory improvement over TLBO.

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.

Improved Speech Coding Based on Open-Loop Parameter Estimation

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Chen, Ya-Chin; Longman, Richard W.

2000-01-01

A nonlinear optimization algorithm for linear predictive speech coding was developed early that not only optimizes the linear model coefficients for the open loop predictor, but does the optimization including the effects of quantization of the transmitted residual. It also simultaneously optimizes the quantization levels used for each speech segment. In this paper, we present an improved method for initialization of this nonlinear algorithm, and demonstrate substantial improvements in performance. In addition, the new procedure produces monotonically improving speech quality with increasing numbers of bits used in the transmitted error residual. Examples of speech encoding and decoding are given for 8 speech segments and signal to noise levels as high as 47 dB are produced. As in typical linear predictive coding, the optimization is done on the open loop speech analysis model. Here we demonstrate that minimizing the error of the closed loop speech reconstruction, instead of the simpler open loop optimization, is likely to produce negligible improvement in speech quality. The examples suggest that the algorithm here is close to giving the best performance obtainable from a linear model, for the chosen order with the chosen number of bits for the codebook.

Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao

In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

1992-01-01

The papers presented at the symposium cover aerodynamics, design applications, propulsion systems, high-speed flight, structures, controls, sensitivity analysis, optimization algorithms, and space structures applications. Other topics include helicopter rotor design, artificial intelligence/neural nets, and computational aspects of optimization. Papers are included on flutter calculations for a system with interacting nonlinearities, optimization in solid rocket booster application, improving the efficiency of aerodynamic shape optimization procedures, nonlinear control theory, and probabilistic structural analysis of space truss structures for nonuniform thermal environmental effects.

Online optimization of storage ring nonlinear beam dynamics

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

Huang, Xiaobiao; Safranek, James

2015-08-01

We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short period of time. Experimental setup and results are presented.

Inversion of 2-D DC resistivity data using rapid optimization and minimal complexity neural network

NASA Astrophysics Data System (ADS)

Singh, U. K.; Tiwari, R. K.; Singh, S. B.

2010-02-01

The backpropagation (BP) artificial neural network (ANN) technique of optimization based on steepest descent algorithm is known to be inept for its poor performance and does not ensure global convergence. Nonlinear and complex DC resistivity data require efficient ANN model and more intensive optimization procedures for better results and interpretations. Improvements in the computational ANN modeling process are described with the goals of enhancing the optimization process and reducing ANN model complexity. Well-established optimization methods, such as Radial basis algorithm (RBA) and Levenberg-Marquardt algorithms (LMA) have frequently been used to deal with complexity and nonlinearity in such complex geophysical records. We examined here the efficiency of trained LMA and RB networks by using 2-D synthetic resistivity data and then finally applied to the actual field vertical electrical resistivity sounding (VES) data collected from the Puga Valley, Jammu and Kashmir, India. The resulting ANN reconstruction resistivity results are compared with the result of existing inversion approaches, which are in good agreement. The depths and resistivity structures obtained by the ANN methods also correlate well with the known drilling results and geologic boundaries. The application of the above ANN algorithms proves to be robust and could be used for fast estimation of resistive structures for other complex earth model also.

Wiener Chaos and Nonlinear Filtering

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

Lototsky, S.V.

2006-11-15

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. Themore » paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.« less

NARMAX model identification of a palm oil biodiesel engine using multi-objective optimization differential evolution

NASA Astrophysics Data System (ADS)

Mansor, Zakwan; Zakaria, Mohd Zakimi; Nor, Azuwir Mohd; Saad, Mohd Sazli; Ahmad, Robiah; Jamaluddin, Hishamuddin

2017-09-01

This paper presents the black-box modelling of palm oil biodiesel engine (POB) using multi-objective optimization differential evolution (MOODE) algorithm. Two objective functions are considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. The mathematical model used in this study to represent the POB system is nonlinear auto-regressive moving average with exogenous input (NARMAX) model. Finally, model validity tests are applied in order to validate the possible models that was obtained from MOODE algorithm and lead to select an optimal model.

Rayleigh wave nonlinear inversion based on the Firefly algorithm

NASA Astrophysics Data System (ADS)

Zhou, Teng-Fei; Peng, Geng-Xin; Hu, Tian-Yue; Duan, Wen-Sheng; Yao, Feng-Chang; Liu, Yi-Mou

2014-06-01

Rayleigh waves have high amplitude, low frequency, and low velocity, which are treated as strong noise to be attenuated in reflected seismic surveys. This study addresses how to identify useful shear wave velocity profile and stratigraphic information from Rayleigh waves. We choose the Firefly algorithm for inversion of surface waves. The Firefly algorithm, a new type of particle swarm optimization, has the advantages of being robust, highly effective, and allows global searching. This algorithm is feasible and has advantages for use in Rayleigh wave inversion with both synthetic models and field data. The results show that the Firefly algorithm, which is a robust and practical method, can achieve nonlinear inversion of surface waves with high resolution.

Flight control optimization from design to assessment application on the Cessna Citation X business aircraft =

NASA Astrophysics Data System (ADS)

Boughari, Yamina

New methodologies have been developed to optimize the integration, testing and certification of flight control systems, an expensive process in the aerospace industry. This thesis investigates the stability of the Cessna Citation X aircraft without control, and then optimizes two different flight controllers from design to validation. The aircraft's model was obtained from the data provided by the Research Aircraft Flight Simulator (RAFS) of the Cessna Citation business aircraft. To increase the stability and control of aircraft systems, optimizations of two different flight control designs were performed: 1) the Linear Quadratic Regulation and the Proportional Integral controllers were optimized using the Differential Evolution algorithm and the level 1 handling qualities as the objective function. The results were validated for the linear and nonlinear aircraft models, and some of the clearance criteria were investigated; and 2) the Hinfinity control method was applied on the stability and control augmentation systems. To minimize the time required for flight control design and its validation, an optimization of the controllers design was performed using the Differential Evolution (DE), and the Genetic algorithms (GA). The DE algorithm proved to be more efficient than the GA. New tools for visualization of the linear validation process were also developed to reduce the time required for the flight controller assessment. Matlab software was used to validate the different optimization algorithms' results. Research platforms of the aircraft's linear and nonlinear models were developed, and compared with the results of flight tests performed on the Research Aircraft Flight Simulator. Some of the clearance criteria of the optimized H-infinity flight controller were evaluated, including its linear stability, eigenvalues, and handling qualities criteria. Nonlinear simulations of the maneuvers criteria were also investigated during this research to assess the Cessna Citation X's flight controller clearance, and therefore, for its anticipated certification.

A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

PubMed

Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

2007-01-01

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

A Swarm Optimization Genetic Algorithm Based on Quantum-Behaved Particle Swarm Optimization.

PubMed

Sun, Tao; Xu, Ming-Hai

2017-01-01

Quantum-behaved particle swarm optimization (QPSO) algorithm is a variant of the traditional particle swarm optimization (PSO). The QPSO that was originally developed for continuous search spaces outperforms the traditional PSO in search ability. This paper analyzes the main factors that impact the search ability of QPSO and converts the particle movement formula to the mutation condition by introducing the rejection region, thus proposing a new binary algorithm, named swarm optimization genetic algorithm (SOGA), because it is more like genetic algorithm (GA) than PSO in form. SOGA has crossover and mutation operator as GA but does not need to set the crossover and mutation probability, so it has fewer parameters to control. The proposed algorithm was tested with several nonlinear high-dimension functions in the binary search space, and the results were compared with those from BPSO, BQPSO, and GA. The experimental results show that SOGA is distinctly superior to the other three algorithms in terms of solution accuracy and convergence.

An improved grey wolf optimizer algorithm for the inversion of geoelectrical data

NASA Astrophysics Data System (ADS)

Li, Si-Yu; Wang, Shu-Ming; Wang, Peng-Fei; Su, Xiao-Lu; Zhang, Xin-Song; Dong, Zhi-Hui

2018-05-01

The grey wolf optimizer (GWO) is a novel bionics algorithm inspired by the social rank and prey-seeking behaviors of grey wolves. The GWO algorithm is easy to implement because of its basic concept, simple formula, and small number of parameters. This paper develops a GWO algorithm with a nonlinear convergence factor and an adaptive location updating strategy and applies this improved grey wolf optimizer (improved grey wolf optimizer, IGWO) algorithm to geophysical inversion problems using magnetotelluric (MT), DC resistivity and induced polarization (IP) methods. Numerical tests in MATLAB 2010b for the forward modeling data and the observed data show that the IGWO algorithm can find the global minimum and rarely sinks to the local minima. For further study, inverted results using the IGWO are contrasted with particle swarm optimization (PSO) and the simulated annealing (SA) algorithm. The outcomes of the comparison reveal that the IGWO and PSO similarly perform better in counterpoising exploration and exploitation with a given number of iterations than the SA.

Fast Optimization for Aircraft Descent and Approach Trajectory

NASA Technical Reports Server (NTRS)

Luchinsky, Dmitry G.; Schuet, Stefan; Brenton, J.; Timucin, Dogan; Smith, David; Kaneshige, John

2017-01-01

We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

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.

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.

Genetic algorithms for multicriteria shape optimization of induction furnace

NASA Astrophysics Data System (ADS)

Kůs, Pavel; Mach, František; Karban, Pavel; Doležel, Ivo

2012-09-01

In this contribution we deal with a multi-criteria shape optimization of an induction furnace. We want to find shape parameters of the furnace in such a way, that two different criteria are optimized. Since they cannot be optimized simultaneously, instead of one optimum we find set of partially optimal designs, so called Pareto front. We compare two different approaches to the optimization, one using nonlinear conjugate gradient method and second using variation of genetic algorithm. As can be seen from the numerical results, genetic algorithm seems to be the right choice for this problem. Solution of direct problem (coupled problem consisting of magnetic and heat field) is done using our own code Agros2D. It uses finite elements of higher order leading to fast and accurate solution of relatively complicated coupled problem. It also provides advanced scripting support, allowing us to prepare parametric model of the furnace and simply incorporate various types of optimization algorithms.

A Novel Hybrid Firefly Algorithm for Global Optimization.

PubMed

Zhang, Lina; Liu, Liqiang; Yang, Xin-She; Dai, Yuntao

Global optimization is challenging to solve due to its nonlinearity and multimodality. Traditional algorithms such as the gradient-based methods often struggle to deal with such problems and one of the current trends is to use metaheuristic algorithms. In this paper, a novel hybrid population-based global optimization algorithm, called hybrid firefly algorithm (HFA), is proposed by combining the advantages of both the firefly algorithm (FA) and differential evolution (DE). FA and DE are executed in parallel to promote information sharing among the population and thus enhance searching efficiency. In order to evaluate the performance and efficiency of the proposed algorithm, a diverse set of selected benchmark functions are employed and these functions fall into two groups: unimodal and multimodal. The experimental results show better performance of the proposed algorithm compared to the original version of the firefly algorithm (FA), differential evolution (DE) and particle swarm optimization (PSO) in the sense of avoiding local minima and increasing the convergence rate.

A Novel Hybrid Firefly Algorithm for Global Optimization

PubMed Central

Zhang, Lina; Liu, Liqiang; Yang, Xin-She; Dai, Yuntao

2016-01-01

Global optimization is challenging to solve due to its nonlinearity and multimodality. Traditional algorithms such as the gradient-based methods often struggle to deal with such problems and one of the current trends is to use metaheuristic algorithms. In this paper, a novel hybrid population-based global optimization algorithm, called hybrid firefly algorithm (HFA), is proposed by combining the advantages of both the firefly algorithm (FA) and differential evolution (DE). FA and DE are executed in parallel to promote information sharing among the population and thus enhance searching efficiency. In order to evaluate the performance and efficiency of the proposed algorithm, a diverse set of selected benchmark functions are employed and these functions fall into two groups: unimodal and multimodal. The experimental results show better performance of the proposed algorithm compared to the original version of the firefly algorithm (FA), differential evolution (DE) and particle swarm optimization (PSO) in the sense of avoiding local minima and increasing the convergence rate. PMID:27685869

A general optimality criteria algorithm for a class of engineering optimization problems

NASA Astrophysics Data System (ADS)

Belegundu, Ashok D.

2015-05-01

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N. V.

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test. PMID:23469172

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.

Embedded algorithms within an FPGA-based system to process nonlinear time series data

NASA Astrophysics Data System (ADS)

Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.

2008-03-01

This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better computational and power efficiency.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

NASA Astrophysics Data System (ADS)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Hybrid Optimization Parallel Search PACKage

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

2009-11-10

HOPSPACK is open source software for solving optimization problems without derivatives. Application problems may have a fully nonlinear objective function, bound constraints, and linear and nonlinear constraints. Problem variables may be continuous, integer-valued, or a mixture of both. The software provides a framework that supports any derivative-free type of solver algorithm. Through the framework, solvers request parallel function evaluation, which may use MPI (multiple machines) or multithreading (multiple processors/cores on one machine). The framework provides a Cache and Pending Cache of saved evaluations that reduces execution time and facilitates restarts. Solvers can dynamically create other algorithms to solve subproblems, amore » useful technique for handling multiple start points and integer-valued variables. HOPSPACK ships with the Generating Set Search (GSS) algorithm, developed at Sandia as part of the APPSPACK open source software project.« less

Optimization of cutting parameters for machining time in turning process

NASA Astrophysics Data System (ADS)

Mavliutov, A. R.; Zlotnikov, E. G.

2018-03-01

This paper describes the most effective methods for nonlinear constraint optimization of cutting parameters in the turning process. Among them are Linearization Programming Method with Dual-Simplex algorithm, Interior Point method, and Augmented Lagrangian Genetic Algorithm (ALGA). Every each of them is tested on an actual example – the minimization of production rate in turning process. The computation was conducted in the MATLAB environment. The comparative results obtained from the application of these methods show: The optimal value of the linearized objective and the original function are the same. ALGA gives sufficiently accurate values, however, when the algorithm uses the Hybrid function with Interior Point algorithm, the resulted values have the maximal accuracy.

Large-Scale Multiantenna Multisine Wireless Power Transfer

NASA Astrophysics Data System (ADS)

Huang, Yang; Clerckx, Bruno

2017-11-01

Wireless Power Transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, Radio Frequency identification (RFID) networks, etc. Although there has been some progress towards multi-antenna multi-sine WPT design, the large-scale design of WPT, reminiscent of massive MIMO in communications, remains an open challenge. In this paper, we derive efficient multiuser algorithms based on a generalizable optimization framework, in order to design transmit sinewaves that maximize the weighted-sum/minimum rectenna output DC voltage. The study highlights the significant effect of the nonlinearity introduced by the rectification process on the design of waveforms in multiuser systems. Interestingly, in the single-user case, the optimal spatial domain beamforming, obtained prior to the frequency domain power allocation optimization, turns out to be Maximum Ratio Transmission (MRT). In contrast, in the general weighted sum criterion maximization problem, the spatial domain beamforming optimization and the frequency domain power allocation optimization are coupled. Assuming channel hardening, low-complexity algorithms are proposed based on asymptotic analysis, to maximize the two criteria. The structure of the asymptotically optimal spatial domain precoder can be found prior to the optimization. The performance of the proposed algorithms is evaluated. Numerical results confirm the inefficiency of the linear model-based design for the single and multi-user scenarios. It is also shown that as nonlinear model-based designs, the proposed algorithms can benefit from an increasing number of sinewaves.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Research on numerical method for multiple pollution source discharge and optimal reduction program

NASA Astrophysics Data System (ADS)

Li, Mingchang; Dai, Mingxin; Zhou, Bin; Zou, Bin

2018-03-01

In this paper, the optimal method for reduction program is proposed by the nonlinear optimal algorithms named that genetic algorithm. The four main rivers in Jiangsu province, China are selected for reducing the environmental pollution in nearshore district. Dissolved inorganic nitrogen (DIN) is studied as the only pollutant. The environmental status and standard in the nearshore district is used to reduce the discharge of multiple river pollutant. The research results of reduction program are the basis of marine environmental management.

Direct position determination for digital modulation signals based on improved particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Yu, Wan-Ting; Yu, Hong-yi; Du, Jian-Ping; Wang, Ding

2018-04-01

The Direct Position Determination (DPD) algorithm has been demonstrated to achieve a better accuracy with known signal waveforms. However, the signal waveform is difficult to be completely known in the actual positioning process. To solve the problem, we proposed a DPD method for digital modulation signals based on improved particle swarm optimization algorithm. First, a DPD model is established for known modulation signals and a cost function is obtained on symbol estimation. Second, as the optimization of the cost function is a nonlinear integer optimization problem, an improved Particle Swarm Optimization (PSO) algorithm is considered for the optimal symbol search. Simulations are carried out to show the higher position accuracy of the proposed DPD method and the convergence of the fitness function under different inertia weight and population size. On the one hand, the proposed algorithm can take full advantage of the signal feature to improve the positioning accuracy. On the other hand, the improved PSO algorithm can improve the efficiency of symbol search by nearly one hundred times to achieve a global optimal solution.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

PubMed

Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

2018-01-01

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

2017-10-01

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Optimizing Support Vector Machine Parameters with Genetic Algorithm for Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Manurung, Jonson; Mawengkang, Herman; Zamzami, Elviawaty

2017-12-01

Support vector machine (SVM) is a popular classification method known to have strong generalization capabilities. SVM can solve the problem of classification and linear regression or nonlinear kernel which can be a learning algorithm for the ability of classification and regression. However, SVM also has a weakness that is difficult to determine the optimal parameter value. SVM calculates the best linear separator on the input feature space according to the training data. To classify data which are non-linearly separable, SVM uses kernel tricks to transform the data into a linearly separable data on a higher dimension feature space. The kernel trick using various kinds of kernel functions, such as : linear kernel, polynomial, radial base function (RBF) and sigmoid. Each function has parameters which affect the accuracy of SVM classification. To solve the problem genetic algorithms are proposed to be applied as the optimal parameter value search algorithm thus increasing the best classification accuracy on SVM. Data taken from UCI repository of machine learning database: Australian Credit Approval. The results show that the combination of SVM and genetic algorithms is effective in improving classification accuracy. Genetic algorithms has been shown to be effective in systematically finding optimal kernel parameters for SVM, instead of randomly selected kernel parameters. The best accuracy for data has been upgraded from kernel Linear: 85.12%, polynomial: 81.76%, RBF: 77.22% Sigmoid: 78.70%. However, for bigger data sizes, this method is not practical because it takes a lot of time.

An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China.

PubMed

Zhang, Liping; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2014-06-01

In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO-NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt-Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt-Winters exponential smoothing method. Copyright © 2014. Published by Elsevier Ltd.

Direct adaptive performance optimization of subsonic transports: A periodic perturbation technique

NASA Technical Reports Server (NTRS)

Espana, Martin D.; Gilyard, Glenn

1995-01-01

Aircraft performance can be optimized at the flight condition by using available redundancy among actuators. Effective use of this potential allows improved performance beyond limits imposed by design compromises. Optimization based on nominal models does not result in the best performance of the actual aircraft at the actual flight condition. An adaptive algorithm for optimizing performance parameters, such as speed or fuel flow, in flight based exclusively on flight data is proposed. The algorithm is inherently insensitive to model inaccuracies and measurement noise and biases and can optimize several decision variables at the same time. An adaptive constraint controller integrated into the algorithm regulates the optimization constraints, such as altitude or speed, without requiring and prior knowledge of the autopilot design. The algorithm has a modular structure which allows easy incorporation (or removal) of optimization constraints or decision variables to the optimization problem. An important part of the contribution is the development of analytical tools enabling convergence analysis of the algorithm and the establishment of simple design rules. The fuel-flow minimization and velocity maximization modes of the algorithm are demonstrated on the NASA Dryden B-720 nonlinear flight simulator for the single- and multi-effector optimization cases.

Solving the infeasible trust-region problem using approximations.

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

Renaud, John E.; Perez, Victor M.; Eldred, Michael Scott

2004-07-01

The use of optimization in engineering design has fueled the development of algorithms for specific engineering needs. When the simulations are expensive to evaluate or the outputs present some noise, the direct use of nonlinear optimizers is not advisable, since the optimization process will be expensive and may result in premature convergence. The use of approximations for both cases is an alternative investigated by many researchers including the authors. When approximations are present, a model management is required for proper convergence of the algorithm. In nonlinear programming, the use of trust-regions for globalization of a local algorithm has been provenmore » effective. The same approach has been used to manage the local move limits in sequential approximate optimization frameworks as in Alexandrov et al., Giunta and Eldred, Perez et al. , Rodriguez et al., etc. The experience in the mathematical community has shown that more effective algorithms can be obtained by the specific inclusion of the constraints (SQP type of algorithms) rather than by using a penalty function as in the augmented Lagrangian formulation. The presence of explicit constraints in the local problem bounded by the trust region, however, may have no feasible solution. In order to remedy this problem the mathematical community has developed different versions of a composite steps approach. This approach consists of a normal step to reduce the amount of constraint violation and a tangential step to minimize the objective function maintaining the level of constraint violation attained at the normal step. Two of the authors have developed a different approach for a sequential approximate optimization framework using homotopy ideas to relax the constraints. This algorithm called interior-point trust-region sequential approximate optimization (IPTRSAO) presents some similarities to the two normal-tangential steps algorithms. In this paper, a description of the similarities is presented and an expansion of the two steps algorithm is presented for the case of approximations.« less

Enhanced Particle Swarm Optimization Algorithm: Efficient Training of ReaxFF Reactive Force Fields.

PubMed

Furman, David; Carmeli, Benny; Zeiri, Yehuda; Kosloff, Ronnie

2018-06-12

Particle swarm optimization (PSO) is a powerful metaheuristic population-based global optimization algorithm. However, when it is applied to nonseparable objective functions, its performance on multimodal landscapes is significantly degraded. Here we show that a significant improvement in the search quality and efficiency on multimodal functions can be achieved by enhancing the basic rotation-invariant PSO algorithm with isotropic Gaussian mutation operators. The new algorithm demonstrates superior performance across several nonlinear, multimodal benchmark functions compared with the rotation-invariant PSO algorithm and the well-established simulated annealing and sequential one-parameter parabolic interpolation methods. A search for the optimal set of parameters for the dispersion interaction model in the ReaxFF- lg reactive force field was carried out with respect to accurate DFT-TS calculations. The resulting optimized force field accurately describes the equations of state of several high-energy molecular crystals where such interactions are of crucial importance. The improved algorithm also presents better performance compared to a genetic algorithm optimization method in the optimization of the parameters of a ReaxFF- lg correction model. The computational framework is implemented in a stand-alone C++ code that allows the straightforward development of ReaxFF reactive force fields.

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.

An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

NASA Astrophysics Data System (ADS)

Milic, Vladimir; Kasac, Josip; Novakovic, Branko

2015-10-01

This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

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.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Using genetic algorithms to determine near-optimal pricing, investment and operating strategies in the electric power industry

NASA Astrophysics Data System (ADS)

Wu, Dongjun

Network industries have technologies characterized by a spatial hierarchy, the "network," with capital-intensive interconnections and time-dependent, capacity-limited flows of products and services through the network to customers. This dissertation studies service pricing, investment and business operating strategies for the electric power network. First-best solutions for a variety of pricing and investment problems have been studied. The evaluation of genetic algorithms (GA, which are methods based on the idea of natural evolution) as a primary means of solving complicated network problems, both w.r.t. pricing: as well as w.r.t. investment and other operating decisions, has been conducted. New constraint-handling techniques in GAs have been studied and tested. The actual application of such constraint-handling techniques in solving practical non-linear optimization problems has been tested on several complex network design problems with encouraging initial results. Genetic algorithms provide solutions that are feasible and close to optimal when the optimal solution is know; in some instances, the near-optimal solutions for small problems by the proposed GA approach can only be tested by pushing the limits of currently available non-linear optimization software. The performance is far better than several commercially available GA programs, which are generally inadequate in solving any of the problems studied in this dissertation, primarily because of their poor handling of constraints. Genetic algorithms, if carefully designed, seem very promising in solving difficult problems which are intractable by traditional analytic methods.

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

A Structure-Adaptive Hybrid RBF-BP Classifier with an Optimized Learning Strategy

PubMed Central

Wen, Hui; Xie, Weixin; Pei, Jihong

2016-01-01

This paper presents a structure-adaptive hybrid RBF-BP (SAHRBF-BP) classifier with an optimized learning strategy. SAHRBF-BP is composed of a structure-adaptive RBF network and a BP network of cascade, where the number of RBF hidden nodes is adjusted adaptively according to the distribution of sample space, the adaptive RBF network is used for nonlinear kernel mapping and the BP network is used for nonlinear classification. The optimized learning strategy is as follows: firstly, a potential function is introduced into training sample space to adaptively determine the number of initial RBF hidden nodes and node parameters, and a form of heterogeneous samples repulsive force is designed to further optimize each generated RBF hidden node parameters, the optimized structure-adaptive RBF network is used for adaptively nonlinear mapping the sample space; then, according to the number of adaptively generated RBF hidden nodes, the number of subsequent BP input nodes can be determined, and the overall SAHRBF-BP classifier is built up; finally, different training sample sets are used to train the BP network parameters in SAHRBF-BP. Compared with other algorithms applied to different data sets, experiments show the superiority of SAHRBF-BP. Especially on most low dimensional and large number of data sets, the classification performance of SAHRBF-BP outperforms other training SLFNs algorithms. PMID:27792737

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

AUC-Maximizing Ensembles through Metalearning.

PubMed

LeDell, Erin; van der Laan, Mark J; Petersen, Maya

2016-05-01

Area Under the ROC Curve (AUC) is often used to measure the performance of an estimator in binary classification problems. An AUC-maximizing classifier can have significant advantages in cases where ranking correctness is valued or if the outcome is rare. In a Super Learner ensemble, maximization of the AUC can be achieved by the use of an AUC-maximining metalearning algorithm. We discuss an implementation of an AUC-maximization technique that is formulated as a nonlinear optimization problem. We also evaluate the effectiveness of a large number of different nonlinear optimization algorithms to maximize the cross-validated AUC of the ensemble fit. The results provide evidence that AUC-maximizing metalearners can, and often do, out-perform non-AUC-maximizing metalearning methods, with respect to ensemble AUC. The results also demonstrate that as the level of imbalance in the training data increases, the Super Learner ensemble outperforms the top base algorithm by a larger degree.

AUC-Maximizing Ensembles through Metalearning

PubMed Central

LeDell, Erin; van der Laan, Mark J.; Peterson, Maya

2016-01-01

Area Under the ROC Curve (AUC) is often used to measure the performance of an estimator in binary classification problems. An AUC-maximizing classifier can have significant advantages in cases where ranking correctness is valued or if the outcome is rare. In a Super Learner ensemble, maximization of the AUC can be achieved by the use of an AUC-maximining metalearning algorithm. We discuss an implementation of an AUC-maximization technique that is formulated as a nonlinear optimization problem. We also evaluate the effectiveness of a large number of different nonlinear optimization algorithms to maximize the cross-validated AUC of the ensemble fit. The results provide evidence that AUC-maximizing metalearners can, and often do, out-perform non-AUC-maximizing metalearning methods, with respect to ensemble AUC. The results also demonstrate that as the level of imbalance in the training data increases, the Super Learner ensemble outperforms the top base algorithm by a larger degree. PMID:27227721

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Using Approximations to Accelerate Engineering Design Optimization

NASA Technical Reports Server (NTRS)

Torczon, Virginia; Trosset, Michael W.

1998-01-01

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

A superlinear interior points algorithm for engineering design optimization

NASA Technical Reports Server (NTRS)

Herskovits, J.; Asquier, J.

1990-01-01

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

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.

Novel procedure for characterizing nonlinear systems with memory: 2017 update

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

NASA Astrophysics Data System (ADS)

Mansfield, Christopher M.; Shoemaker, Christine A.

1999-05-01

This paper extends earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequately approximated by the simpler confined-aquifer analysis.

Investigation on application of genetic algorithms to optimal reactive power dispatch of power systems

NASA Astrophysics Data System (ADS)

Wu, Q. H.; Ma, J. T.

1993-09-01

A primary investigation into application of genetic algorithms in optimal reactive power dispatch and voltage control is presented. The application was achieved, based on (the United Kingdom) National Grid 48 bus network model, using a novel genetic search approach. Simulation results, compared with that obtained using nonlinear programming methods, are included to show the potential of applications of the genetic search methodology in power system economical and secure operations.

Algorithms for the optimization of RBE-weighted dose in particle therapy.

PubMed

Horcicka, M; Meyer, C; Buschbacher, A; Durante, M; Krämer, M

2013-01-21

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

Algorithms for the optimization of RBE-weighted dose in particle therapy

NASA Astrophysics Data System (ADS)

Horcicka, M.; Meyer, C.; Buschbacher, A.; Durante, M.; Krämer, M.

2013-01-01

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

Global optimization algorithm for heat exchanger networks

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

Quesada, I.; Grossmann, I.E.

This paper deals with the global optimization of heat exchanger networks with fixed topology. It is shown that if linear area cost functions are assumed, as well as arithmetic mean driving force temperature differences in networks with isothermal mixing, the corresponding nonlinear programming (NLP) optimization problem involves linear constraints and a sum of linear fractional functions in the objective which are nonconvex. A rigorous algorithm is proposed that is based on a convex NLP underestimator that involves linear and nonlinear estimators for fractional and bilinear terms which provide a tight lower bound to the global optimum. This NLP problem ismore » used within a spatial branch and bound method for which branching rules are given. Basic properties of the proposed method are presented, and its application is illustrated with several example problems. The results show that the proposed method only requires few nodes in the branch and bound search.« less

Symmetric log-domain diffeomorphic Registration: a demons-based approach.

PubMed

Vercauteren, Tom; Pennec, Xavier; Perchant, Aymeric; Ayache, Nicholas

2008-01-01

Modern morphometric studies use non-linear image registration to compare anatomies and perform group analysis. Recently, log-Euclidean approaches have contributed to promote the use of such computational anatomy tools by permitting simple computations of statistics on a rather large class of invertible spatial transformations. In this work, we propose a non-linear registration algorithm perfectly fit for log-Euclidean statistics on diffeomorphisms. Our algorithm works completely in the log-domain, i.e. it uses a stationary velocity field. This implies that we guarantee the invertibility of the deformation and have access to the true inverse transformation. This also means that our output can be directly used for log-Euclidean statistics without relying on the heavy computation of the log of the spatial transformation. As it is often desirable, our algorithm is symmetric with respect to the order of the input images. Furthermore, we use an alternate optimization approach related to Thirion's demons algorithm to provide a fast non-linear registration algorithm. First results show that our algorithm outperforms both the demons algorithm and the recently proposed diffeomorphic demons algorithm in terms of accuracy of the transformation while remaining computationally efficient.

Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery.

PubMed

Altmann, Yoann; Halimi, Abderrahim; Dobigeon, Nicolas; Tourneret, Jean-Yves

2012-06-01

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

Chaos control in solar fed DC-DC boost converter by optimal parameters using nelder-mead algorithm powered enhanced BFOA

NASA Astrophysics Data System (ADS)

Sudhakar, N.; Rajasekar, N.; Akhil, Saya; Jyotheeswara Reddy, K.

2017-11-01

The boost converter is the most desirable DC-DC power converter for renewable energy applications for its favorable continuous input current characteristics. In other hand, these DC-DC converters known as practical nonlinear systems are prone to several types of nonlinear phenomena including bifurcation, quasiperiodicity, intermittency and chaos. These undesirable effects has to be controlled for maintaining normal periodic operation of the converter and to ensure the stability. This paper presents an effective solution to control the chaos in solar fed DC-DC boost converter since the converter experiences wide range of input power variation which leads to chaotic phenomena. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Nelder-Mead Enhanced Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The results are compared with the traditional methods. The obtained results of the proposed system ensures the operation of the converter within the controllable region.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization.

PubMed

Yang, C; Jiang, W; Chen, D-H; Adiga, U; Ng, E G; Chiu, W

2009-03-01

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

MONSS: A multi-objective nonlinear simplex search approach

NASA Astrophysics Data System (ADS)

Zapotecas-Martínez, Saúl; Coello Coello, Carlos A.

2016-01-01

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.

A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control.

PubMed

Han, Min; Fan, Jianchao; Wang, Jun

2011-09-01

A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays.

Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

NASA Astrophysics Data System (ADS)

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data.

PubMed

Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun

2008-05-15

Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software

LMI-Based Generation of Feedback Laws for a Robust Model Predictive Control Algorithm

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Carson, John M., III

2007-01-01

This technical note provides a mathematical proof of Corollary 1 from the paper 'A Nonlinear Model Predictive Control Algorithm with Proven Robustness and Resolvability' that appeared in the 2006 Proceedings of the American Control Conference. The proof was omitted for brevity in the publication. The paper was based on algorithms developed for the FY2005 R&TD (Research and Technology Development) project for Small-body Guidance, Navigation, and Control [2].The framework established by the Corollary is for a robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems that guarantees the resolvability of the associated nite-horizon optimal control problem in a receding-horizon implementation. Additional details of the framework are available in the publication.

Deterministic Design Optimization of Structures in OpenMDAO Framework

NASA Technical Reports Server (NTRS)

Coroneos, Rula M.; Pai, Shantaram S.

2012-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

NASA Astrophysics Data System (ADS)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one step to any point in the near-optimal region, and each iterate generates a new, feasible alternative. We use the method to generate alternatives that span the near-optimal regions of simple and more complicated water management problems and may be preferred to optimal solutions. We also discuss extensions to handle non-linear equity constraints.

Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1990-01-01

Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.

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.

Application of genetic algorithms in nonlinear heat conduction problems.

PubMed

Kadri, Muhammad Bilal; Khan, Waqar A

2014-01-01

Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry.

Study on Temperature and Synthetic Compensation of Piezo-Resistive Differential Pressure Sensors by Coupled Simulated Annealing and Simplex Optimized Kernel Extreme Learning Machine

PubMed Central

Li, Ji; Hu, Guoqing; Zhou, Yonghong; Zou, Chong; Peng, Wei; Alam SM, Jahangir

2017-01-01

As a high performance-cost ratio solution for differential pressure measurement, piezo-resistive differential pressure sensors are widely used in engineering processes. However, their performance is severely affected by the environmental temperature and the static pressure applied to them. In order to modify the non-linear measuring characteristics of the piezo-resistive differential pressure sensor, compensation actions should synthetically consider these two aspects. Advantages such as nonlinear approximation capability, highly desirable generalization ability and computational efficiency make the kernel extreme learning machine (KELM) a practical approach for this critical task. Since the KELM model is intrinsically sensitive to the regularization parameter and the kernel parameter, a searching scheme combining the coupled simulated annealing (CSA) algorithm and the Nelder-Mead simplex algorithm is adopted to find an optimal KLEM parameter set. A calibration experiment at different working pressure levels was conducted within the temperature range to assess the proposed method. In comparison with other compensation models such as the back-propagation neural network (BP), radius basis neural network (RBF), particle swarm optimization optimized support vector machine (PSO-SVM), particle swarm optimization optimized least squares support vector machine (PSO-LSSVM) and extreme learning machine (ELM), the compensation results show that the presented compensation algorithm exhibits a more satisfactory performance with respect to temperature compensation and synthetic compensation problems. PMID:28422080

Study on Temperature and Synthetic Compensation of Piezo-Resistive Differential Pressure Sensors by Coupled Simulated Annealing and Simplex Optimized Kernel Extreme Learning Machine.

PubMed

Li, Ji; Hu, Guoqing; Zhou, Yonghong; Zou, Chong; Peng, Wei; Alam Sm, Jahangir

2017-04-19

As a high performance-cost ratio solution for differential pressure measurement, piezo-resistive differential pressure sensors are widely used in engineering processes. However, their performance is severely affected by the environmental temperature and the static pressure applied to them. In order to modify the non-linear measuring characteristics of the piezo-resistive differential pressure sensor, compensation actions should synthetically consider these two aspects. Advantages such as nonlinear approximation capability, highly desirable generalization ability and computational efficiency make the kernel extreme learning machine (KELM) a practical approach for this critical task. Since the KELM model is intrinsically sensitive to the regularization parameter and the kernel parameter, a searching scheme combining the coupled simulated annealing (CSA) algorithm and the Nelder-Mead simplex algorithm is adopted to find an optimal KLEM parameter set. A calibration experiment at different working pressure levels was conducted within the temperature range to assess the proposed method. In comparison with other compensation models such as the back-propagation neural network (BP), radius basis neural network (RBF), particle swarm optimization optimized support vector machine (PSO-SVM), particle swarm optimization optimized least squares support vector machine (PSO-LSSVM) and extreme learning machine (ELM), the compensation results show that the presented compensation algorithm exhibits a more satisfactory performance with respect to temperature compensation and synthetic compensation problems.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints.

PubMed

Fan, Bo; Yang, Qinmin; Tang, Xiaoyu; Sun, Youxian

2018-06-01

In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.

Optimal Golomb Ruler Sequences Generation for Optical WDM Systems: A Novel Parallel Hybrid Multi-objective Bat Algorithm

NASA Astrophysics Data System (ADS)

Bansal, Shonak; Singh, Arun Kumar; Gupta, Neena

2017-02-01

In real-life, multi-objective engineering design problems are very tough and time consuming optimization problems due to their high degree of nonlinearities, complexities and inhomogeneity. Nature-inspired based multi-objective optimization algorithms are now becoming popular for solving multi-objective engineering design problems. This paper proposes original multi-objective Bat algorithm (MOBA) and its extended form, namely, novel parallel hybrid multi-objective Bat algorithm (PHMOBA) to generate shortest length Golomb ruler called optimal Golomb ruler (OGR) sequences at a reasonable computation time. The OGRs found their application in optical wavelength division multiplexing (WDM) systems as channel-allocation algorithm to reduce the four-wave mixing (FWM) crosstalk. The performances of both the proposed algorithms to generate OGRs as optical WDM channel-allocation is compared with other existing classical computing and nature-inspired algorithms, including extended quadratic congruence (EQC), search algorithm (SA), genetic algorithms (GAs), biogeography based optimization (BBO) and big bang-big crunch (BB-BC) optimization algorithms. Simulations conclude that the proposed parallel hybrid multi-objective Bat algorithm works efficiently as compared to original multi-objective Bat algorithm and other existing algorithms to generate OGRs for optical WDM systems. The algorithm PHMOBA to generate OGRs, has higher convergence and success rate than original MOBA. The efficiency improvement of proposed PHMOBA to generate OGRs up to 20-marks, in terms of ruler length and total optical channel bandwidth (TBW) is 100 %, whereas for original MOBA is 85 %. Finally the implications for further research are also discussed.

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, O. O.; Nguyen, D. T.; Baddourah, M. A.; Qin, J.

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

NASA Astrophysics Data System (ADS)

Lv, Yongfeng; Na, Jing; Yang, Qinmin; Wu, Xing; Guo, Yu

2016-01-01

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

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.

A real-time guidance algorithm for aerospace plane optimal ascent to low earth orbit

NASA Technical Reports Server (NTRS)

Calise, A. J.; Flandro, G. A.; Corban, J. E.

1989-01-01

Problems of onboard trajectory optimization and synthesis of suitable guidance laws for ascent to low Earth orbit of an air-breathing, single-stage-to-orbit vehicle are addressed. A multimode propulsion system is assumed which incorporates turbojet, ramjet, Scramjet, and rocket engines. An algorithm for generating fuel-optimal climb profiles is presented. This algorithm results from the application of the minimum principle to a low-order dynamic model that includes angle-of-attack effects and the normal component of thrust. Maximum dynamic pressure and maximum aerodynamic heating rate constraints are considered. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. A nonlinear transformation technique is employed to derived a feedback controller for tracking the computed trajectory. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.

Two neural network algorithms for designing optimal terminal controllers with open final time

NASA Technical Reports Server (NTRS)

Plumer, Edward S.

1992-01-01

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

A nonlinear bi-level programming approach for product portfolio management.

PubMed

Ma, Shuang

2016-01-01

Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

The application of immune genetic algorithm in main steam temperature of PID control of BP network

NASA Astrophysics Data System (ADS)

Li, Han; Zhen-yu, Zhang

In order to overcome the uncertainties, large delay, large inertia and nonlinear property of the main steam temperature controlled object in the power plant, a neural network intelligent PID control system based on immune genetic algorithm and BP neural network is designed. Using the immune genetic algorithm global search optimization ability and good convergence, optimize the weights of the neural network, meanwhile adjusting PID parameters using BP network. The simulation result shows that the system is superior to conventional PID control system in the control of quality and robustness.

Sizing of complex structure by the integration of several different optimal design algorithms

NASA Technical Reports Server (NTRS)

Sobieszczanski, J.

1974-01-01

Practical design of large-scale structures can be accomplished with the aid of the digital computer by bringing together in one computer program algorithms of nonlinear mathematical programing and optimality criteria with weight-strength and other so-called engineering methods. Applications of this approach to aviation structures are discussed with a detailed description of how the total problem of structural sizing can be broken down into subproblems for best utilization of each algorithm and for efficient organization of the program into iterative loops. Typical results are examined for a number of examples.

Genetic Algorithm Tuned Fuzzy Logic for Gliding Return Trajectories

NASA Technical Reports Server (NTRS)

Burchett, Bradley T.

2003-01-01

The problem of designing and flying a trajectory for successful recovery of a reusable launch vehicle is tackled using fuzzy logic control with genetic algorithm optimization. The plant is approximated by a simplified three degree of freedom non-linear model. A baseline trajectory design and guidance algorithm consisting of several Mamdani type fuzzy controllers is tuned using a simple genetic algorithm. Preliminary results show that the performance of the overall system is shown to improve with genetic algorithm tuning.

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.

Improving stability and strength characteristics of framed structures with nonlinear behavior

NASA Technical Reports Server (NTRS)

Pezeshk, Shahram

1990-01-01

In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt with the optimization of truss and plane frame structures.

Genetic algorithm optimized rainfall-runoff fuzzy inference system for row crop watersheds with claypan soils

USDA-ARS?s Scientific Manuscript database

The fuzzy logic algorithm has the ability to describe knowledge in a descriptive human-like manner in the form of simple rules using linguistic variables, and provides a new way of modeling uncertain or naturally fuzzy hydrological processes like non-linear rainfall-runoff relationships. Fuzzy infe...

MULTI-OBJECTIVE ONLINE OPTIMIZATION OF BEAM LIFETIME AT APS

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

Sun, Yipeng

In this paper, online optimization of beam lifetime at the APS (Advanced Photon Source) storage ring is presented. A general genetic algorithm (GA) is developed and employed for some online optimizations in the APS storage ring. Sextupole magnets in 40 sectors of the APS storage ring are employed as variables for the online nonlinear beam dynamics optimization. The algorithm employs several optimization objectives and is designed to run with topup mode or beam current decay mode. Up to 50\\% improvement of beam lifetime is demonstrated, without affecting the transverse beam sizes and other relevant parameters. In some cases, the top-upmore » injection efficiency is also improved.« less

Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

NASA Astrophysics Data System (ADS)

Sun, Cheng-Yu; Wang, Yan-Yan; Wu, Dun-Shi; Qin, Xiao-Jun

2017-12-01

At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

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.

Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

NASA Astrophysics Data System (ADS)

Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

2013-09-01

In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Performance evaluation of firefly algorithm with variation in sorting for non-linear benchmark problems

NASA Astrophysics Data System (ADS)

Umbarkar, A. J.; Balande, U. T.; Seth, P. D.

2017-06-01

The field of nature inspired computing and optimization techniques have evolved to solve difficult optimization problems in diverse fields of engineering, science and technology. The firefly attraction process is mimicked in the algorithm for solving optimization problems. In Firefly Algorithm (FA) sorting of fireflies is done by using sorting algorithm. The original FA is proposed with bubble sort for ranking the fireflies. In this paper, the quick sort replaces bubble sort to decrease the time complexity of FA. The dataset used is unconstrained benchmark functions from CEC 2005 [22]. The comparison of FA using bubble sort and FA using quick sort is performed with respect to best, worst, mean, standard deviation, number of comparisons and execution time. The experimental result shows that FA using quick sort requires less number of comparisons but requires more execution time. The increased number of fireflies helps to converge into optimal solution whereas by varying dimension for algorithm performed better at a lower dimension than higher dimension.

A multiobjective optimization model and an orthogonal design-based hybrid heuristic algorithm for regional urban mining management problems.

PubMed

Wu, Hao; Wan, Zhong

2018-02-01

In this paper, a multiobjective mixed-integer piecewise nonlinear programming model (MOMIPNLP) is built to formulate the management problem of urban mining system, where the decision variables are associated with buy-back pricing, choices of sites, transportation planning, and adjustment of production capacity. Different from the existing approaches, the social negative effect, generated from structural optimization of the recycling system, is minimized in our model, as well as the total recycling profit and utility from environmental improvement are jointly maximized. For solving the problem, the MOMIPNLP model is first transformed into an ordinary mixed-integer nonlinear programming model by variable substitution such that the piecewise feature of the model is removed. Then, based on technique of orthogonal design, a hybrid heuristic algorithm is developed to find an approximate Pareto-optimal solution, where genetic algorithm is used to optimize the structure of search neighborhood, and both local branching algorithm and relaxation-induced neighborhood search algorithm are employed to cut the searching branches and reduce the number of variables in each branch. Numerical experiments indicate that this algorithm spends less CPU (central processing unit) time in solving large-scale regional urban mining management problems, especially in comparison with the similar ones available in literature. By case study and sensitivity analysis, a number of practical managerial implications are revealed from the model. Since the metal stocks in society are reliable overground mineral sources, urban mining has been paid great attention as emerging strategic resources in an era of resource shortage. By mathematical modeling and development of efficient algorithms, this paper provides decision makers with useful suggestions on the optimal design of recycling system in urban mining. For example, this paper can answer how to encourage enterprises to join the recycling activities by government's support and subsidies, whether the existing recycling system can meet the developmental requirements or not, and what is a reasonable adjustment of production capacity.

Calculation of a double reactive azeotrope using stochastic optimization approaches

NASA Astrophysics Data System (ADS)

Mendes Platt, Gustavo; Pinheiro Domingos, Roberto; Oliveira de Andrade, Matheus

2013-02-01

An homogeneous reactive azeotrope is a thermodynamic coexistence condition of two phases under chemical and phase equilibrium, where compositions of both phases (in the Ung-Doherty sense) are equal. This kind of nonlinear phenomenon arises from real world situations and has applications in chemical and petrochemical industries. The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. The robust calculation of reactive azeotropes can be conducted by several approaches, such as interval-Newton/generalized bisection algorithms and hybrid stochastic-deterministic frameworks. In this paper, we investigate the numerical aspects of the calculation of reactive azeotropes using two metaheuristics: the Luus-Jaakola adaptive random search and the Firefly algorithm. Moreover, we present results for a system (with industrial interest) with more than one azeotrope, the system isobutene/methanol/methyl-tert-butyl-ether (MTBE). We present convergence patterns for both algorithms, illustrating - in a bidimensional subdomain - the identification of reactive azeotropes. A strategy for calculation of multiple roots in nonlinear systems is also applied. The results indicate that both algorithms are suitable and robust when applied to reactive azeotrope calculations for this "challenging" nonlinear system.

Enhanced nonlinearity interval mapping scheme for high-performance simulation-optimization of watershed-scale BMP placement

NASA Astrophysics Data System (ADS)

Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn

2015-03-01

Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

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.

Hysteresis modeling and identification of a dielectric electro-active polymer actuator using an APSO-based nonlinear Preisach NARX fuzzy model

NASA Astrophysics Data System (ADS)

Truong, Bui Ngoc Minh; Nam, Doan Ngoc Chi; Ahn, Kyoung Kwan

2013-09-01

Dielectric electro-active polymer (DEAP) materials are attractive since they are low cost, lightweight and have a large deformation capability. They have no operating noise, very low electric power consumption and higher performance and efficiency than competing technologies. However, DEAP materials generally have strong hysteresis as well as uncertain and nonlinear characteristics. These disadvantages can limit the efficiency in the use of DEAP materials. To address these limitations, this research will present the combination of the Preisach model and the dynamic nonlinear autoregressive exogenous (NARX) fuzzy model-based adaptive particle swarm optimization (APSO) identification algorithm for modeling and identification of the nonlinear behavior of one typical type of DEAP actuator. Firstly, open loop input signals are applied to obtain nonlinear features and to investigate the responses of the DEAP actuator system. Then, a Preisach model can be combined with a dynamic NARX fuzzy structure to estimate the tip displacement of a DEAP actuator. To optimize all unknown parameters of the designed combination, an identification scheme based on a least squares method and an APSO algorithm is carried out. Finally, experimental validation research is carefully completed, and the effectiveness of the proposed model is evaluated by employing various input signals.

Robotic fish tracking method based on suboptimal interval Kalman filter

NASA Astrophysics Data System (ADS)

Tong, Xiaohong; Tang, Chao

2017-11-01

Autonomous Underwater Vehicle (AUV) research focused on tracking and positioning, precise guidance and return to dock and other fields. The robotic fish of AUV has become a hot application in intelligent education, civil and military etc. In nonlinear tracking analysis of robotic fish, which was found that the interval Kalman filter algorithm contains all possible filter results, but the range is wide, relatively conservative, and the interval data vector is uncertain before implementation. This paper proposes a ptimization algorithm of suboptimal interval Kalman filter. Suboptimal interval Kalman filter scheme used the interval inverse matrix with its worst inverse instead, is more approximate nonlinear state equation and measurement equation than the standard interval Kalman filter, increases the accuracy of the nominal dynamic system model, improves the speed and precision of tracking system. Monte-Carlo simulation results show that the optimal trajectory of sub optimal interval Kalman filter algorithm is better than that of the interval Kalman filter method and the standard method of the filter.

Multi-Objective Control Optimization for Greenhouse Environment Using Evolutionary Algorithms

PubMed Central

Hu, Haigen; Xu, Lihong; Wei, Ruihua; Zhu, Bingkun

2011-01-01

This paper investigates the issue of tuning the Proportional Integral and Derivative (PID) controller parameters for a greenhouse climate control system using an Evolutionary Algorithm (EA) based on multiple performance measures such as good static-dynamic performance specifications and the smooth process of control. A model of nonlinear thermodynamic laws between numerous system variables affecting the greenhouse climate is formulated. The proposed tuning scheme is tested for greenhouse climate control by minimizing the integrated time square error (ITSE) and the control increment or rate in a simulation experiment. The results show that by tuning the gain parameters the controllers can achieve good control performance through step responses such as small overshoot, fast settling time, and less rise time and steady state error. Besides, it can be applied to tuning the system with different properties, such as strong interactions among variables, nonlinearities and conflicting performance criteria. The results implicate that it is a quite effective and promising tuning method using multi-objective optimization algorithms in the complex greenhouse production. PMID:22163927

Structural optimization of framed structures using generalized optimality criteria

NASA Technical Reports Server (NTRS)

Kolonay, R. M.; Venkayya, Vipperla B.; Tischler, V. A.; Canfield, R. A.

1989-01-01

The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.

DTIC Science & Technology

1980-01-01

de Silva [141, and Weisman and Wood [76). A particular direct search algorithm, the simplex method, has been cited for having the potential for...spaced discrete points on a line which makes the direction suitable for an efficient integer search technique based on Fibonacci numbers. Two...defined by a subset of variables. The complex algorithm is particularly well suited for this subspace search for two reasons. First, the complex method

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.; Nguyen, Duc T.; Baddourah, Majdi; Qin, Jiangning

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Optimal Control of Evolution Mixed Variational Inclusions

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

Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

2013-12-15

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Inferring genetic interactions via a nonlinear model and an optimization algorithm.

PubMed

Chen, Chung-Ming; Lee, Chih; Chuang, Cheng-Long; Wang, Chia-Chang; Shieh, Grace S

2010-02-26

Biochemical pathways are gradually becoming recognized as central to complex human diseases and recently genetic/transcriptional interactions have been shown to be able to predict partial pathways. With the abundant information made available by microarray gene expression data (MGED), nonlinear modeling of these interactions is now feasible. Two of the latest advances in nonlinear modeling used sigmoid models to depict transcriptional interaction of a transcription factor (TF) for a target gene, but do not model cooperative or competitive interactions of several TFs for a target. An S-shape model and an optimization algorithm (GASA) were developed to infer genetic interactions/transcriptional regulation of several genes simultaneously using MGED. GASA consists of a genetic algorithm (GA) and a simulated annealing (SA) algorithm, which is enhanced by a steepest gradient descent algorithm to avoid being trapped in local minimum. Using simulated data with various degrees of noise, we studied how GASA with two model selection criteria and two search spaces performed. Furthermore, GASA was shown to outperform network component analysis, the time series network inference algorithm (TSNI), GA with regular GA (GAGA) and GA with regular SA. Two applications are demonstrated. First, GASA is applied to infer a subnetwork of human T-cell apoptosis. Several of the predicted interactions are supported by the literature. Second, GASA was applied to infer the transcriptional factors of 34 cell cycle regulated targets in S. cerevisiae, and GASA performed better than one of the latest advances in nonlinear modeling, GAGA and TSNI. Moreover, GASA is able to predict multiple transcription factors for certain targets, and these results coincide with experiments confirmed data in YEASTRACT. GASA is shown to infer both genetic interactions and transcriptional regulatory interactions well. In particular, GASA seems able to characterize the nonlinear mechanism of transcriptional regulatory interactions (TIs) in yeast, and may be applied to infer TIs in other organisms. The predicted genetic interactions of a subnetwork of human T-cell apoptosis coincide with existing partial pathways, suggesting the potential of GASA on inferring biochemical pathways.

Harmonic Optimization in Voltage Source Inverter for PV Application using Heuristic Algorithms

NASA Astrophysics Data System (ADS)

Kandil, Shaimaa A.; Ali, A. A.; El Samahy, Adel; Wasfi, Sherif M.; Malik, O. P.

2016-12-01

Selective Harmonic Elimination (SHE) technique is the fundamental switching frequency scheme that is used to eliminate specific order harmonics. Its application to minimize low order harmonics in a three level inverter is proposed in this paper. The modulation strategy used here is SHEPWM and the nonlinear equations, that characterize the low order harmonics, are solved using Harmony Search Algorithm (HSA) to obtain the optimal switching angles that minimize the required harmonics and maintain the fundamental at the desired value. Total Harmonic Distortion (THD) of the output voltage is minimized maintaining selected harmonics within allowable limits. A comparison has been drawn between HSA, Genetic Algorithm (GA) and Newton Raphson (NR) technique using MATLAB software to determine the effectiveness of getting optimized switching angles.

Bandlimited computerized improvements in characterization of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2016-05-01

The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

PubMed

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

Tzang, Omer; Caravaca-Aguirre, Antonio M.; Wagner, Kelvin; Piestun, Rafael

2018-06-01

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems

NASA Astrophysics Data System (ADS)

Zheng, Feifei; Simpson, Angus R.; Zecchin, Aaron C.

2011-08-01

This paper proposes a novel optimization approach for the least cost design of looped water distribution systems (WDSs). Three distinct steps are involved in the proposed optimization approach. In the first step, the shortest-distance tree within the looped network is identified using the Dijkstra graph theory algorithm, for which an extension is proposed to find the shortest-distance tree for multisource WDSs. In the second step, a nonlinear programming (NLP) solver is employed to optimize the pipe diameters for the shortest-distance tree (chords of the shortest-distance tree are allocated the minimum allowable pipe sizes). Finally, in the third step, the original looped water network is optimized using a differential evolution (DE) algorithm seeded with diameters in the proximity of the continuous pipe sizes obtained in step two. As such, the proposed optimization approach combines the traditional deterministic optimization technique of NLP with the emerging evolutionary algorithm DE via the proposed network decomposition. The proposed methodology has been tested on four looped WDSs with the number of decision variables ranging from 21 to 454. Results obtained show the proposed approach is able to find optimal solutions with significantly less computational effort than other optimization techniques.

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

An artificial neural network controller based on MPSO-BFGS hybrid optimization for spherical flying robot

NASA Astrophysics Data System (ADS)

Liu, Xiaolin; Li, Lanfei; Sun, Hanxu

2017-12-01

Spherical flying robot can perform various tasks in the complex and varied environment to reduce labor costs. However, it is difficult to guarantee the stability of the spherical flying robot in the case of strong coupling and time-varying disturbance. In this paper, an artificial neural network controller (ANNC) based on MPSO-BFGS hybrid optimization algorithm is proposed. The MPSO algorithm is used to optimize the initial weights of the controller to avoid the local optimal solution. The BFGS algorithm is introduced to improve the convergence ability of the network. We use Lyapunov method to analyze the stability of ANNC. The controller is simulated under the condition of nonlinear coupling disturbance. The experimental results show that the proposed controller can obtain the expected value in shoter time compared with the other considered methods.

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.

1996-01-01

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Performance Trend of Different Algorithms for Structural Design Optimization

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.

1996-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Nonlinear Recurrent Neural Network Predictive Control for Energy Distribution of a Fuel Cell Powered Robot

PubMed Central

Chen, Qihong; Long, Rong; Quan, Shuhai

2014-01-01

This paper presents a neural network predictive control strategy to optimize power distribution for a fuel cell/ultracapacitor hybrid power system of a robot. We model the nonlinear power system by employing time variant auto-regressive moving average with exogenous (ARMAX), and using recurrent neural network to represent the complicated coefficients of the ARMAX model. Because the dynamic of the system is viewed as operating- state- dependent time varying local linear behavior in this frame, a linear constrained model predictive control algorithm is developed to optimize the power splitting between the fuel cell and ultracapacitor. The proposed algorithm significantly simplifies implementation of the controller and can handle multiple constraints, such as limiting substantial fluctuation of fuel cell current. Experiment and simulation results demonstrate that the control strategy can optimally split power between the fuel cell and ultracapacitor, limit the change rate of the fuel cell current, and so as to extend the lifetime of the fuel cell. PMID:24707206

A Novel Shape Parameterization Approach

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

1999-01-01

This paper presents a novel parameterization approach for complex shapes suitable for a multidisciplinary design optimization application. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft objects animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity analysis tools (e.g., nonlinear computational fluid dynamics and detailed finite element modeling). This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, and camber. The results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, performance, and a simple propulsion module.

A multi-product green supply chain under government supervision with price and demand uncertainty

NASA Astrophysics Data System (ADS)

Hafezalkotob, Ashkan; Zamani, Soma

2018-05-01

In this paper, a bi-level game-theoretic model is proposed to investigate the effects of governmental financial intervention on green supply chain. This problem is formulated as a bi-level program for a green supply chain that produces various products with different environmental pollution levels. The problem is also regard uncertainties in market demand and sale price of raw materials and products. The model is further transformed into a single-level nonlinear programming problem by replacing the lower-level optimization problem with its Karush-Kuhn-Tucker optimality conditions. Genetic algorithm is applied as a solution methodology to solve nonlinear programming model. Finally, to investigate the validity of the proposed method, the computational results obtained through genetic algorithm are compared with global optimal solution attained by enumerative method. Analytical results indicate that the proposed GA offers better solutions in large size problems. Also, we conclude that financial intervention by government consists of green taxation and subsidization is an effective method to stabilize green supply chain members' performance.

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2000-01-01

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Computational alternatives to obtain time optimal jet engine control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Basso, R. J.; Leake, R. J.

1976-01-01

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

DOE PAGES

Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

2016-05-20

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

Model and Algorithm for Substantiating Solutions for Organization of High-Rise Construction Project

NASA Astrophysics Data System (ADS)

Anisimov, Vladimir; Anisimov, Evgeniy; Chernysh, Anatoliy

2018-03-01

In the paper the models and the algorithm for the optimal plan formation for the organization of the material and logistical processes of the high-rise construction project and their financial support are developed. The model is based on the representation of the optimization procedure in the form of a non-linear problem of discrete programming, which consists in minimizing the execution time of a set of interrelated works by a limited number of partially interchangeable performers while limiting the total cost of performing the work. The proposed model and algorithm are the basis for creating specific organization management methodologies for the high-rise construction project.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design.

PubMed

Wang, Zhanshan; Liu, Lei; Wu, Yanming; Zhang, Huaguang

2018-06-01

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

PubMed Central

Naeem, Muhammad; Illanko, Kandasamy; Karmokar, Ashok; Anpalagan, Alagan; Jaseemuddin, Muhammad

2013-01-01

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated. PMID:23966194

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

NASA Astrophysics Data System (ADS)

Li, Xiang; Zhang, Yang; Wong, Hau-San; Qin, Zhongfeng

2009-11-01

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean-variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.

Comparison and analysis of nonlinear algorithms for compressed sensing in MRI.

PubMed

Yu, Yeyang; Hong, Mingjian; Liu, Feng; Wang, Hua; Crozier, Stuart

2010-01-01

Compressed sensing (CS) theory has been recently applied in Magnetic Resonance Imaging (MRI) to accelerate the overall imaging process. In the CS implementation, various algorithms have been used to solve the nonlinear equation system for better image quality and reconstruction speed. However, there are no explicit criteria for an optimal CS algorithm selection in the practical MRI application. A systematic and comparative study of those commonly used algorithms is therefore essential for the implementation of CS in MRI. In this work, three typical algorithms, namely, the Gradient Projection For Sparse Reconstruction (GPSR) algorithm, Interior-point algorithm (l(1)_ls), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm are compared and investigated in three different imaging scenarios, brain, angiogram and phantom imaging. The algorithms' performances are characterized in terms of image quality and reconstruction speed. The theoretical results show that the performance of the CS algorithms is case sensitive; overall, the StOMP algorithm offers the best solution in imaging quality, while the GPSR algorithm is the most efficient one among the three methods. In the next step, the algorithm performances and characteristics will be experimentally explored. It is hoped that this research will further support the applications of CS in MRI.

Optimal control of LQG problem with an explicit trade-off between mean and variance

NASA Astrophysics Data System (ADS)

Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

2011-12-01

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

Support vector machine firefly algorithm based optimization of lens system.

PubMed

Shamshirband, Shahaboddin; Petković, Dalibor; Pavlović, Nenad T; Ch, Sudheer; Altameem, Torki A; Gani, Abdullah

2015-01-01

Lens system design is an important factor in image quality. The main aspect of the lens system design methodology is the optimization procedure. Since optimization is a complex, nonlinear task, soft computing optimization algorithms can be used. There are many tools that can be employed to measure optical performance, but the spot diagram is the most useful. The spot diagram gives an indication of the image of a point object. In this paper, the spot size radius is considered an optimization criterion. Intelligent soft computing scheme support vector machines (SVMs) coupled with the firefly algorithm (FFA) are implemented. The performance of the proposed estimators is confirmed with the simulation results. The result of the proposed SVM-FFA model has been compared with support vector regression (SVR), artificial neural networks, and generic programming methods. The results show that the SVM-FFA model performs more accurately than the other methodologies. Therefore, SVM-FFA can be used as an efficient soft computing technique in the optimization of lens system designs.

Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

NASA Astrophysics Data System (ADS)

Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

2017-10-01

Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations, gradient based and nature inspired optimization algorithms and experimental data, the latter of which take the form of a load-extension curve obtained from the evaluation of uniaxial tensile test results. The aim of this research was to obtain material model parameters corresponding to the quasi-static tensile loading which may be further used for the research involving dynamic and high-speed tensile loading. Based on the obtained results it can be concluded that the set goal has been reached.

A Comparison Study of Machine Learning Based Algorithms for Fatigue Crack Growth Calculation.

PubMed

Wang, Hongxun; Zhang, Weifang; Sun, Fuqiang; Zhang, Wei

2017-05-18

The relationships between the fatigue crack growth rate ( d a / d N ) and stress intensity factor range ( Δ K ) are not always linear even in the Paris region. The stress ratio effects on fatigue crack growth rate are diverse in different materials. However, most existing fatigue crack growth models cannot handle these nonlinearities appropriately. The machine learning method provides a flexible approach to the modeling of fatigue crack growth because of its excellent nonlinear approximation and multivariable learning ability. In this paper, a fatigue crack growth calculation method is proposed based on three different machine learning algorithms (MLAs): extreme learning machine (ELM), radial basis function network (RBFN) and genetic algorithms optimized back propagation network (GABP). The MLA based method is validated using testing data of different materials. The three MLAs are compared with each other as well as the classical two-parameter model ( K * approach). The results show that the predictions of MLAs are superior to those of K * approach in accuracy and effectiveness, and the ELM based algorithms show overall the best agreement with the experimental data out of the three MLAs, for its global optimization and extrapolation ability.

Sequential Nonlinear Learning for Distributed Multiagent Systems via Extreme Learning Machines.

PubMed

Vanli, Nuri Denizcan; Sayin, Muhammed O; Delibalta, Ibrahim; Kozat, Suleyman Serdar

2017-03-01

We study online nonlinear learning over distributed multiagent systems, where each agent employs a single hidden layer feedforward neural network (SLFN) structure to sequentially minimize arbitrary loss functions. In particular, each agent trains its own SLFN using only the data that is revealed to itself. On the other hand, the aim of the multiagent system is to train the SLFN at each agent as well as the optimal centralized batch SLFN that has access to all the data, by exchanging information between neighboring agents. We address this problem by introducing a distributed subgradient-based extreme learning machine algorithm. The proposed algorithm provides guaranteed upper bounds on the performance of the SLFN at each agent and shows that each of these individual SLFNs asymptotically achieves the performance of the optimal centralized batch SLFN. Our performance guarantees explicitly distinguish the effects of data- and network-dependent parameters on the convergence rate of the proposed algorithm. The experimental results illustrate that the proposed algorithm achieves the oracle performance significantly faster than the state-of-the-art methods in the machine learning and signal processing literature. Hence, the proposed method is highly appealing for the applications involving big data.

Robust and fast nonlinear optimization of diffusion MRI microstructure models.

PubMed

Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A

2017-07-15

Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of run time, fit, accuracy and precision. Parameter initialization approaches were found to be relevant especially for more complex models, such as those involving several fiber orientations per voxel. For these, a fitting cascade initializing or fixing parameter values in a later optimization step from simpler models in an earlier optimization step further improved run time, fit, accuracy and precision compared to a single step fit. This establishes and makes available standards by which robust fit and accuracy can be achieved in shorter run times. This is especially relevant for the use of diffusion microstructure modeling in large group or population studies and in combining microstructure parameter maps with tractography results. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

A novel optimization algorithm for MIMO Hammerstein model identification under heavy-tailed noise.

PubMed

Jin, Qibing; Wang, Hehe; Su, Qixin; Jiang, Beiyan; Liu, Qie

2018-01-01

In this paper, we study the system identification of multi-input multi-output (MIMO) Hammerstein processes under the typical heavy-tailed noise. To the best of our knowledge, there is no general analytical method to solve this identification problem. Motivated by this, we propose a general identification method to solve this problem based on a Gaussian-Mixture Distribution intelligent optimization algorithm (GMDA). The nonlinear part of Hammerstein process is modeled by a Radial Basis Function (RBF) neural network, and the identification problem is converted to an optimization problem. To overcome the drawbacks of analytical identification method in the presence of heavy-tailed noise, a meta-heuristic optimization algorithm, Cuckoo search (CS) algorithm is used. To improve its performance for this identification problem, the Gaussian-mixture Distribution (GMD) and the GMD sequences are introduced to improve the performance of the standard CS algorithm. Numerical simulations for different MIMO Hammerstein models are carried out, and the simulation results verify the effectiveness of the proposed GMDA. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The quadriceps muscle of knee joint modelling Using Hybrid Particle Swarm Optimization-Neural Network (PSO-NN)

NASA Astrophysics Data System (ADS)

Kamaruddin, Saadi Bin Ahmad; Marponga Tolos, Siti; Hee, Pah Chin; Ghani, Nor Azura Md; Ramli, Norazan Mohamed; Nasir, Noorhamizah Binti Mohamed; Ksm Kader, Babul Salam Bin; Saiful Huq, Mohammad

2017-03-01

Neural framework has for quite a while been known for its ability to handle a complex nonlinear system without a logical model and can learn refined nonlinear associations gives. Theoretically, the most surely understood computation to set up the framework is the backpropagation (BP) count which relies on upon the minimization of the mean square error (MSE). However, this algorithm is not totally efficient in the presence of outliers which usually exist in dynamic data. This paper exhibits the modelling of quadriceps muscle model by utilizing counterfeit smart procedures named consolidated backpropagation neural network nonlinear autoregressive (BPNN-NAR) and backpropagation neural network nonlinear autoregressive moving average (BPNN-NARMA) models in view of utilitarian electrical incitement (FES). We adapted particle swarm optimization (PSO) approach to enhance the performance of backpropagation algorithm. In this research, a progression of tests utilizing FES was led. The information that is gotten is utilized to build up the quadriceps muscle model. 934 preparing information, 200 testing and 200 approval information set are utilized as a part of the improvement of muscle model. It was found that both BPNN-NAR and BPNN-NARMA performed well in modelling this type of data. As a conclusion, the neural network time series models performed reasonably efficient for non-linear modelling such as active properties of the quadriceps muscle with one input, namely output namely muscle force.

Optimization under uncertainty of parallel nonlinear energy sinks

NASA Astrophysics Data System (ADS)

Boroson, Ethan; Missoum, Samy; Mattei, Pierre-Olivier; Vergez, Christophe

2017-04-01

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids

NASA Astrophysics Data System (ADS)

Li, Bo; Wong, K. Y. Michael

Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. For the Kuramoto model on general weighted networks, the synchronization stability, measured by the dominant Lyapunov exponent at the steady state, is shown to have intricate and nonlinear dependence on the network topology and the dynamical parameters. Specifically, the dominant Lyapunov exponent corresponds to the algebraic connectivity of a meta-graph whose edge weight depends nonlinearly on the steady states. In this study, we utilize the cut-set space (DC) approximation to estimate the nonlinear steady state and simplify the calculation of the stability measure, based on which we further derive efficient algorithms to optimize the synchronization stability. The properties of the optimized networks and application in power grid stability are also discussed. This work is supported by a Grant from the Research Grant Council of Hong Kong (Grant Numbers 605813 and 16322616).

Multivariable optimization of liquid rocket engines using particle swarm algorithms

NASA Astrophysics Data System (ADS)

Jones, Daniel Ray

Liquid rocket engines are highly reliable, controllable, and efficient compared to other conventional forms of rocket propulsion. As such, they have seen wide use in the space industry and have become the standard propulsion system for launch vehicles, orbit insertion, and orbital maneuvering. Though these systems are well understood, historical optimization techniques are often inadequate due to the highly non-linear nature of the engine performance problem. In this thesis, a Particle Swarm Optimization (PSO) variant was applied to maximize the specific impulse of a finite-area combustion chamber (FAC) equilibrium flow rocket performance model by controlling the engine's oxidizer-to-fuel ratio and de Laval nozzle expansion and contraction ratios. In addition to the PSO-controlled parameters, engine performance was calculated based on propellant chemistry, combustion chamber pressure, and ambient pressure, which are provided as inputs to the program. The performance code was validated by comparison with NASA's Chemical Equilibrium with Applications (CEA) and the commercially available Rocket Propulsion Analysis (RPA) tool. Similarly, the PSO algorithm was validated by comparison with brute-force optimization, which calculates all possible solutions and subsequently determines which is the optimum. Particle Swarm Optimization was shown to be an effective optimizer capable of quick and reliable convergence for complex functions of multiple non-linear variables.

RBF neural network based PI pitch controller for a class of 5-MW wind turbines using particle swarm optimization algorithm.

PubMed

Poultangari, Iman; Shahnazi, Reza; Sheikhan, Mansour

2012-09-01

In order to control the pitch angle of blades in wind turbines, commonly the proportional and integral (PI) controller due to its simplicity and industrial usability is employed. The neural networks and evolutionary algorithms are tools that provide a suitable ground to determine the optimal PI gains. In this paper, a radial basis function (RBF) neural network based PI controller is proposed for collective pitch control (CPC) of a 5-MW wind turbine. In order to provide an optimal dataset to train the RBF neural network, particle swarm optimization (PSO) evolutionary algorithm is used. The proposed method does not need the complexities, nonlinearities and uncertainties of the system under control. The simulation results show that the proposed controller has satisfactory performance. Copyright © 2012 ISA. Published by 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.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Design optimization of steel frames using an enhanced firefly algorithm

NASA Astrophysics Data System (ADS)

Carbas, Serdar

2016-12-01

Mathematical modelling of real-world-sized steel frames under the Load and Resistance Factor Design-American Institute of Steel Construction (LRFD-AISC) steel design code provisions, where the steel profiles for the members are selected from a table of steel sections, turns out to be a discrete nonlinear programming problem. Finding the optimum design of such design optimization problems using classical optimization techniques is difficult. Metaheuristic algorithms provide an alternative way of solving such problems. The firefly algorithm (FFA) belongs to the swarm intelligence group of metaheuristics. The standard FFA has the drawback of being caught up in local optima in large-sized steel frame design problems. This study attempts to enhance the performance of the FFA by suggesting two new expressions for the attractiveness and randomness parameters of the algorithm. Two real-world-sized design examples are designed by the enhanced FFA and its performance is compared with standard FFA as well as with particle swarm and cuckoo search algorithms.

Performance improvement of an active vibration absorber subsystem for an aircraft model using a bees algorithm based on multi-objective intelligent optimization

NASA Astrophysics Data System (ADS)

Zarchi, Milad; Attaran, Behrooz

2017-11-01

This study develops a mathematical model to investigate the behaviour of adaptable shock absorber dynamics for the six-degree-of-freedom aircraft model in the taxiing phase. The purpose of this research is to design a proportional-integral-derivative technique for control of an active vibration absorber system using a hydraulic nonlinear actuator based on the bees algorithm. This optimization algorithm is inspired by the natural intelligent foraging behaviour of honey bees. The neighbourhood search strategy is used to find better solutions around the previous one. The parameters of the controller are adjusted by minimizing the aircraft's acceleration and impact force as the multi-objective function. The major advantages of this algorithm over other optimization algorithms are its simplicity, flexibility and robustness. The results of the numerical simulation indicate that the active suspension increases the comfort of the ride for passengers and the fatigue life of the structure. This is achieved by decreasing the impact force, displacement and acceleration significantly.

Adaptive non-linear control for cancer therapy through a Fokker-Planck observer.

PubMed

Shakeri, Ehsan; Latif-Shabgahi, Gholamreza; Esmaeili Abharian, Amir

2018-04-01

In recent years, many efforts have been made to present optimal strategies for cancer therapy through the mathematical modelling of tumour-cell population dynamics and optimal control theory. In many cases, therapy effect is included in the drift term of the stochastic Gompertz model. By fitting the model with empirical data, the parameters of therapy function are estimated. The reported research works have not presented any algorithm to determine the optimal parameters of therapy function. In this study, a logarithmic therapy function is entered in the drift term of the Gompertz model. Using the proposed control algorithm, the therapy function parameters are predicted and adaptively adjusted. To control the growth of tumour-cell population, its moments must be manipulated. This study employs the probability density function (PDF) control approach because of its ability to control all the process moments. A Fokker-Planck-based non-linear stochastic observer will be used to determine the PDF of the process. A cost function based on the difference between a predefined desired PDF and PDF of tumour-cell population is defined. Using the proposed algorithm, the therapy function parameters are adjusted in such a manner that the cost function is minimised. The existence of an optimal therapy function is also proved. The numerical results are finally given to demonstrate the effectiveness of the proposed method.

A globally convergent LCL method for nonlinear optimization.

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

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.« less

CUDA Optimization Strategies for Compute- and Memory-Bound Neuroimaging Algorithms

PubMed Central

Lee, Daren; Dinov, Ivo; Dong, Bin; Gutman, Boris; Yanovsky, Igor; Toga, Arthur W.

2011-01-01

As neuroimaging algorithms and technology continue to grow faster than CPU performance in complexity and image resolution, data-parallel computing methods will be increasingly important. The high performance, data-parallel architecture of modern graphical processing units (GPUs) can reduce computational times by orders of magnitude. However, its massively threaded architecture introduces challenges when GPU resources are exceeded. This paper presents optimization strategies for compute- and memory-bound algorithms for the CUDA architecture. For compute-bound algorithms, the registers are reduced through variable reuse via shared memory and the data throughput is increased through heavier thread workloads and maximizing the thread configuration for a single thread block per multiprocessor. For memory-bound algorithms, fitting the data into the fast but limited GPU resources is achieved through reorganizing the data into self-contained structures and employing a multi-pass approach. Memory latencies are reduced by selecting memory resources whose cache performance are optimized for the algorithm's access patterns. We demonstrate the strategies on two computationally expensive algorithms and achieve optimized GPU implementations that perform up to 6× faster than unoptimized ones. Compared to CPU implementations, we achieve peak GPU speedups of 129× for the 3D unbiased nonlinear image registration technique and 93× for the non-local means surface denoising algorithm. PMID:21159404

CUDA optimization strategies for compute- and memory-bound neuroimaging algorithms.

PubMed

Lee, Daren; Dinov, Ivo; Dong, Bin; Gutman, Boris; Yanovsky, Igor; Toga, Arthur W

2012-06-01

As neuroimaging algorithms and technology continue to grow faster than CPU performance in complexity and image resolution, data-parallel computing methods will be increasingly important. The high performance, data-parallel architecture of modern graphical processing units (GPUs) can reduce computational times by orders of magnitude. However, its massively threaded architecture introduces challenges when GPU resources are exceeded. This paper presents optimization strategies for compute- and memory-bound algorithms for the CUDA architecture. For compute-bound algorithms, the registers are reduced through variable reuse via shared memory and the data throughput is increased through heavier thread workloads and maximizing the thread configuration for a single thread block per multiprocessor. For memory-bound algorithms, fitting the data into the fast but limited GPU resources is achieved through reorganizing the data into self-contained structures and employing a multi-pass approach. Memory latencies are reduced by selecting memory resources whose cache performance are optimized for the algorithm's access patterns. We demonstrate the strategies on two computationally expensive algorithms and achieve optimized GPU implementations that perform up to 6× faster than unoptimized ones. Compared to CPU implementations, we achieve peak GPU speedups of 129× for the 3D unbiased nonlinear image registration technique and 93× for the non-local means surface denoising algorithm. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Bilinear modeling and nonlinear estimation

NASA Technical Reports Server (NTRS)

Dwyer, Thomas A. W., III; Karray, Fakhreddine; Bennett, William H.

1989-01-01

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate

NASA Astrophysics Data System (ADS)

Pando, V.; García-Laguna, J.; San-José, L. A.

2012-11-01

In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

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.

Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances.

PubMed

Zhang, Huaguang; Qu, Qiuxia; Xiao, Geyang; Cui, Yang

2018-06-01

Based on integral sliding mode and approximate dynamic programming (ADP) theory, a novel optimal guaranteed cost sliding mode control is designed for constrained-input nonlinear systems with matched and unmatched disturbances. When the system moves on the sliding surface, the optimal guaranteed cost control problem of sliding mode dynamics is transformed into the optimal control problem of a reformulated auxiliary system with a modified cost function. The ADP algorithm based on single critic neural network (NN) is applied to obtain the approximate optimal control law for the auxiliary system. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors. In addition, the derived approximate optimal control is verified to guarantee the sliding mode dynamics system to be stable in the sense of uniform ultimate boundedness. Some simulation results are presented to verify the feasibility of the proposed control scheme.

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.

Optimal wavefront estimation of incoherent sources

NASA Astrophysics Data System (ADS)

Riggs, A. J. Eldorado; Kasdin, N. Jeremy; Groff, Tyler

2014-08-01

Direct imaging is in general necessary to characterize exoplanets and disks. A coronagraph is an instrument used to create a dim (high-contrast) region in a star's PSF where faint companions can be detected. All coronagraphic high-contrast imaging systems use one or more deformable mirrors (DMs) to correct quasi-static aberrations and recover contrast in the focal plane. Simulations show that existing wavefront control algorithms can correct for diffracted starlight in just a few iterations, but in practice tens or hundreds of control iterations are needed to achieve high contrast. The discrepancy largely arises from the fact that simulations have perfect knowledge of the wavefront and DM actuation. Thus, wavefront correction algorithms are currently limited by the quality and speed of wavefront estimates. Exposures in space will take orders of magnitude more time than any calculations, so a nonlinear estimation method that needs fewer images but more computational time would be advantageous. In addition, current wavefront correction routines seek only to reduce diffracted starlight. Here we present nonlinear estimation algorithms that include optimal estimation of sources incoherent with a star such as exoplanets and debris disks.

Modeling multilayer x-ray reflectivity using genetic algorithms

NASA Astrophysics Data System (ADS)

Sánchez del Río, M.; Pareschi, G.; Michetschläger, C.

2000-06-01

The x-ray reflectivity of a multilayer is a non-linear function of many parameters (materials, layer thickness, density, roughness). Non-linear fitting of experimental data with simulations requires the use of initial values sufficiently close to the optimum value. This is a difficult task when the topology of the space of the variables is highly structured. We apply global optimization methods to fit multilayer reflectivity. Genetic algorithms are stochastic methods based on the model of natural evolution: the improvement of a population along successive generations. A complete set of initial parameters constitutes an individual. The population is a collection of individuals. Each generation is built from the parent generation by applying some operators (selection, crossover, mutation, etc.) on the members of the parent generation. The pressure of selection drives the population to include "good" individuals. For large number of generations, the best individuals will approximate the optimum parameters. Some results on fitting experimental hard x-ray reflectivity data for Ni/C and W/Si multilayers using genetic algorithms are presented. This method can also be applied to design multilayers optimized for a target application.

Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

NASA Astrophysics Data System (ADS)

Wang, Jing; Yang, Tianyu; Staskevich, Gennady; Abbe, Brian

2017-04-01

This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton-Jacobi-Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.

2016-01-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C

2015-03-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Strategies to overcome photobleaching in algorithm-based adaptive optics for nonlinear in-vivo imaging.

PubMed

Caroline Müllenbroich, M; McGhee, Ewan J; Wright, Amanda J; Anderson, Kurt I; Mathieson, Keith

2014-01-01

We have developed a nonlinear adaptive optics microscope utilizing a deformable membrane mirror (DMM) and demonstrated its use in compensating for system- and sample-induced aberrations. The optimum shape of the DMM was determined with a random search algorithm optimizing on either two photon fluorescence or second harmonic signals as merit factors. We present here several strategies to overcome photobleaching issues associated with lengthy optimization routines by adapting the search algorithm and the experimental methodology. Optimizations were performed on extrinsic fluorescent dyes, fluorescent beads loaded into organotypic tissue cultures and the intrinsic second harmonic signal of these cultures. We validate the approach of using these preoptimized mirror shapes to compile a robust look-up table that can be applied for imaging over several days and through a variety of tissues. In this way, the photon exposure to the fluorescent cells under investigation is limited to imaging. Using our look-up table approach, we show signal intensity improvement factors ranging from 1.7 to 4.1 in organotypic tissue cultures and freshly excised mouse tissue. Imaging zebrafish in vivo, we demonstrate signal improvement by a factor of 2. This methodology is easily reproducible and could be applied to many photon starved experiments, for example fluorescent life time imaging, or when photobleaching is a concern.

Adaptive Estimation and Heuristic Optimization of Nonlinear Spacecraft Attitude Dynamics

DTIC Science & Technology

2016-09-15

Algorithm GPS Global Positioning System HOUF Higher Order Unscented Filter IC initial conditions IMM Interacting Multiple Model IMU Inertial Measurement Unit ...sources ranging from inertial measurement units to star sensors are used to construct observations for attitude estimation algorithms. The sensor...parameters. A single vector measurement will provide two independent parameters, as a unit vector constraint removes a DOF making the problem underdetermined

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

NASA Astrophysics Data System (ADS)

Mallick, Rajnish; Ganguli, Ranjan; Seetharama Bhat, M.

2015-09-01

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.

Solving Fractional Programming Problems based on Swarm Intelligence

NASA Astrophysics Data System (ADS)

Raouf, Osama Abdel; Hezam, Ibrahim M.

2014-04-01

This paper presents a new approach to solve Fractional Programming Problems (FPPs) based on two different Swarm Intelligence (SI) algorithms. The two algorithms are: Particle Swarm Optimization, and Firefly Algorithm. The two algorithms are tested using several FPP benchmark examples and two selected industrial applications. The test aims to prove the capability of the SI algorithms to solve any type of FPPs. The solution results employing the SI algorithms are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Swarm Intelligence can be denoted as an effective technique for solving linear or nonlinear, non-differentiable fractional objective functions. Problems with an optimal solution at a finite point and an unbounded constraint set, can be solved using the proposed approach. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using the two SI algorithms revealed the superiority of the proposed technique among others in computational time. A better accuracy was remarkably observed in the solution results of the industrial application problems.

The NLS-Based Nonlinear Grey Multivariate Model for Forecasting Pollutant Emissions in China.

PubMed

Pei, Ling-Ling; Li, Qin; Wang, Zheng-Xin

2018-03-08

The relationship between pollutant discharge and economic growth has been a major research focus in environmental economics. To accurately estimate the nonlinear change law of China's pollutant discharge with economic growth, this study establishes a transformed nonlinear grey multivariable (TNGM (1, N )) model based on the nonlinear least square (NLS) method. The Gauss-Seidel iterative algorithm was used to solve the parameters of the TNGM (1, N ) model based on the NLS basic principle. This algorithm improves the precision of the model by continuous iteration and constantly approximating the optimal regression coefficient of the nonlinear model. In our empirical analysis, the traditional grey multivariate model GM (1, N ) and the NLS-based TNGM (1, N ) models were respectively adopted to forecast and analyze the relationship among wastewater discharge per capita (WDPC), and per capita emissions of SO₂ and dust, alongside GDP per capita in China during the period 1996-2015. Results indicated that the NLS algorithm is able to effectively help the grey multivariable model identify the nonlinear relationship between pollutant discharge and economic growth. The results show that the NLS-based TNGM (1, N ) model presents greater precision when forecasting WDPC, SO₂ emissions and dust emissions per capita, compared to the traditional GM (1, N ) model; WDPC indicates a growing tendency aligned with the growth of GDP, while the per capita emissions of SO₂ and dust reduce accordingly.

Efficient Lookup Table-Based Adaptive Baseband Predistortion Architecture for Memoryless Nonlinearity

NASA Astrophysics Data System (ADS)

Ba, Seydou N.; Waheed, Khurram; Zhou, G. Tong

2010-12-01

Digital predistortion is an effective means to compensate for the nonlinear effects of a memoryless system. In case of a cellular transmitter, a digital baseband predistorter can mitigate the undesirable nonlinear effects along the signal chain, particularly the nonlinear impairments in the radiofrequency (RF) amplifiers. To be practically feasible, the implementation complexity of the predistorter must be minimized so that it becomes a cost-effective solution for the resource-limited wireless handset. This paper proposes optimizations that facilitate the design of a low-cost high-performance adaptive digital baseband predistorter for memoryless systems. A comparative performance analysis of the amplitude and power lookup table (LUT) indexing schemes is presented. An optimized low-complexity amplitude approximation and its hardware synthesis results are also studied. An efficient LUT predistorter training algorithm that combines the fast convergence speed of the normalized least mean squares (NLMSs) with a small hardware footprint is proposed. Results of fixed-point simulations based on the measured nonlinear characteristics of an RF amplifier are presented.

Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

NASA Astrophysics Data System (ADS)

Xiao, Ying; Michalski, Darek; Censor, Yair; Galvin, James M.

2004-07-01

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

Arterial cannula shape optimization by means of the rotational firefly algorithm

NASA Astrophysics Data System (ADS)

Tesch, K.; Kaczorowska, K.

2016-03-01

This article presents global optimization results of arterial cannula shapes by means of the newly modified firefly algorithm. The search for the optimal arterial cannula shape is necessary in order to minimize losses and prepare the flow that leaves the circulatory support system of a ventricle (i.e. blood pump) before it reaches the heart. A modification of the standard firefly algorithm, the so-called rotational firefly algorithm, is introduced. It is shown that the rotational firefly algorithm allows for better exploration of search spaces which results in faster convergence and better solutions in comparison with its standard version. This is particularly pronounced for smaller population sizes. Furthermore, it maintains greater diversity of populations for a longer time. A small population size and a low number of iterations are necessary to keep to a minimum the computational cost of the objective function of the problem, which comes from numerical solution of the nonlinear partial differential equations. Moreover, both versions of the firefly algorithm are compared to the state of the art, namely the differential evolution and covariance matrix adaptation evolution strategies.

A technique for locating function roots and for satisfying equality constraints in optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw

1991-01-01

A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.

A technique for locating function roots and for satisfying equality constraints in optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.

1992-01-01

A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.

PubMed

Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai

2015-07-01

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.

Multi-objective dynamic aperture optimization for storage rings

DOE PAGES

Li, Yongjun; Yang, Lingyun

2016-11-30

We report an efficient dynamic aperture (DA) optimization approach using multiobjective genetic algorithm (MOGA), which is driven by nonlinear driving terms computation. It was found that having small low order driving terms is a necessary but insufficient condition of having a decent DA. Then direct DA tracking simulation is implemented among the last generation candidates to select the best solutions. The approach was demonstrated successfully in optimizing NSLS-II storage ring DA.

Efficient Spatiotemporal Clutter Rejection and Nonlinear Filtering-based Dim Resolved and Unresolved Object Tracking Algorithms

NASA Astrophysics Data System (ADS)

Tartakovsky, A.; Tong, M.; Brown, A. P.; Agh, C.

2013-09-01

We develop efficient spatiotemporal image processing algorithms for rejection of non-stationary clutter and tracking of multiple dim objects using non-linear track-before-detect methods. For clutter suppression, we include an innovative image alignment (registration) algorithm. The images are assumed to contain elements of the same scene, but taken at different angles, from different locations, and at different times, with substantial clutter non-stationarity. These challenges are typical for space-based and surface-based IR/EO moving sensors, e.g., highly elliptical orbit or low earth orbit scenarios. The algorithm assumes that the images are related via a planar homography, also known as the projective transformation. The parameters are estimated in an iterative manner, at each step adjusting the parameter vector so as to achieve improved alignment of the images. Operating in the parameter space rather than in the coordinate space is a new idea, which makes the algorithm more robust with respect to noise as well as to large inter-frame disturbances, while operating at real-time rates. For dim object tracking, we include new advancements to a particle non-linear filtering-based track-before-detect (TrbD) algorithm. The new TrbD algorithm includes both real-time full image search for resolved objects not yet in track and joint super-resolution and tracking of individual objects in closely spaced object (CSO) clusters. The real-time full image search provides near-optimal detection and tracking of multiple extremely dim, maneuvering objects/clusters. The super-resolution and tracking CSO TrbD algorithm provides efficient near-optimal estimation of the number of unresolved objects in a CSO cluster, as well as the locations, velocities, accelerations, and intensities of the individual objects. We demonstrate that the algorithm is able to accurately estimate the number of CSO objects and their locations when the initial uncertainty on the number of objects is large. We demonstrate performance of the TrbD algorithm both for satellite-based and surface-based EO/IR surveillance scenarios.

Genetic Algorithm Application in Optimization of Wireless Sensor Networks

PubMed Central

Norouzi, Ali; Zaim, A. Halim

2014-01-01

There are several applications known for wireless sensor networks (WSN), and such variety demands improvement of the currently available protocols and the specific parameters. Some notable parameters are lifetime of network and energy consumption for routing which play key role in every application. Genetic algorithm is one of the nonlinear optimization methods and relatively better option thanks to its efficiency for large scale applications and that the final formula can be modified by operators. The present survey tries to exert a comprehensive improvement in all operational stages of a WSN including node placement, network coverage, clustering, and data aggregation and achieve an ideal set of parameters of routing and application based WSN. Using genetic algorithm and based on the results of simulations in NS, a specific fitness function was achieved, optimized, and customized for all the operational stages of WSNs. PMID:24693235

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.

Big Data: A Parallel Particle Swarm Optimization-Back-Propagation Neural Network Algorithm Based on MapReduce.

PubMed

Cao, Jianfang; Cui, Hongyan; Shi, Hao; Jiao, Lijuan

2016-01-01

A back-propagation (BP) neural network can solve complicated random nonlinear mapping problems; therefore, it can be applied to a wide range of problems. However, as the sample size increases, the time required to train BP neural networks becomes lengthy. Moreover, the classification accuracy decreases as well. To improve the classification accuracy and runtime efficiency of the BP neural network algorithm, we proposed a parallel design and realization method for a particle swarm optimization (PSO)-optimized BP neural network based on MapReduce on the Hadoop platform using both the PSO algorithm and a parallel design. The PSO algorithm was used to optimize the BP neural network's initial weights and thresholds and improve the accuracy of the classification algorithm. The MapReduce parallel programming model was utilized to achieve parallel processing of the BP algorithm, thereby solving the problems of hardware and communication overhead when the BP neural network addresses big data. Datasets on 5 different scales were constructed using the scene image library from the SUN Database. The classification accuracy of the parallel PSO-BP neural network algorithm is approximately 92%, and the system efficiency is approximately 0.85, which presents obvious advantages when processing big data. The algorithm proposed in this study demonstrated both higher classification accuracy and improved time efficiency, which represents a significant improvement obtained from applying parallel processing to an intelligent algorithm on big data.

A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

NASA Astrophysics Data System (ADS)

Negrello, Camille; Gosselet, Pierre; Rey, Christian

2018-05-01

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

Optimized System Identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Longman, Richard W.

1999-01-01

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

An Alternative Approach to the Operation of Multinational Reservoir Systems: Application to the Amistad & Falcon System (Lower Rio Grande/Rí-o Bravo)

NASA Astrophysics Data System (ADS)

Serrat-Capdevila, A.; Valdes, J. B.

2005-12-01

An optimization approach for the operation of international multi-reservoir systems is presented. The approach uses Stochastic Dynamic Programming (SDP) algorithms, both steady-state and real-time, to develop two models. In the first model, the reservoirs and flows of the system are aggregated to yield an equivalent reservoir, and the obtained operating policies are disaggregated using a non-linear optimization procedure for each reservoir and for each nation water balance. In the second model a multi-reservoir approach is applied, disaggregating the releases for each country water share in each reservoir. The non-linear disaggregation algorithm uses SDP-derived operating policies as boundary conditions for a local time-step optimization. Finally, the performance of the different approaches and methods is compared. These models are applied to the Amistad-Falcon International Reservoir System as part of a binational dynamic modeling effort to develop a decision support system tool for a better management of the water resources in the Lower Rio Grande Basin, currently enduring a severe drought.

Sensitivity Analysis of Genetic Algorithm Parameters for Optimal Groundwater Monitoring Network Design

NASA Astrophysics Data System (ADS)

Abdeh-Kolahchi, A.; Satish, M.; Datta, B.

2004-05-01

A state art groundwater monitoring network design is introduced. The method combines groundwater flow and transport results with optimization Genetic Algorithm (GA) to identify optimal monitoring well locations. Optimization theory uses different techniques to find a set of parameter values that minimize or maximize objective functions. The suggested groundwater optimal monitoring network design is based on the objective of maximizing the probability of tracking a transient contamination plume by determining sequential monitoring locations. The MODFLOW and MT3DMS models included as separate modules within the Groundwater Modeling System (GMS) are used to develop three dimensional groundwater flow and contamination transport simulation. The groundwater flow and contamination simulation results are introduced as input to the optimization model, using Genetic Algorithm (GA) to identify the groundwater optimal monitoring network design, based on several candidate monitoring locations. The groundwater monitoring network design model is used Genetic Algorithms with binary variables representing potential monitoring location. As the number of decision variables and constraints increase, the non-linearity of the objective function also increases which make difficulty to obtain optimal solutions. The genetic algorithm is an evolutionary global optimization technique, which is capable of finding the optimal solution for many complex problems. In this study, the GA approach capable of finding the global optimal solution to a groundwater monitoring network design problem involving 18.4X 1018 feasible solutions will be discussed. However, to ensure the efficiency of the solution process and global optimality of the solution obtained using GA, it is necessary that appropriate GA parameter values be specified. The sensitivity analysis of genetic algorithms parameters such as random number, crossover probability, mutation probability, and elitism are discussed for solution of monitoring network design.

Topology-changing shape optimization with the genetic algorithm

NASA Astrophysics Data System (ADS)

Lamberson, Steven E., Jr.

The goal is to take a traditional shape optimization problem statement and modify it slightly to allow for prescribed changes in topology. This modification enables greater flexibility in the choice of parameters for the topology optimization problem, while improving the direct physical relevance of the results. This modification involves changing the optimization problem statement from a nonlinear programming problem into a form of mixed-discrete nonlinear programing problem. The present work demonstrates one possible way of using the Genetic Algorithm (GA) to solve such a problem, including the use of "masking bits" and a new modification to the bit-string affinity (BSA) termination criterion specifically designed for problems with "masking bits." A simple ten-bar truss problem proves the utility of the modified BSA for this type of problem. A more complicated two dimensional bracket problem is solved using both the proposed approach and a more traditional topology optimization approach (Solid Isotropic Microstructure with Penalization or SIMP) to enable comparison. The proposed approach is able to solve problems with both local and global constraints, which is something traditional methods cannot do. The proposed approach has a significantly higher computational burden --- on the order of 100 times larger than SIMP, although the proposed approach is able to offset this with parallel computing.

Ant Colony Optimization Analysis on Overall Stability of High Arch Dam Basis of Field Monitoring

PubMed Central

Liu, Xiaoli; Chen, Hong-Xin; Kim, Jinxie

2014-01-01

A dam ant colony optimization (D-ACO) analysis of the overall stability of high arch dams on complicated foundations is presented in this paper. A modified ant colony optimization (ACO) model is proposed for obtaining dam concrete and rock mechanical parameters. A typical dam parameter feedback problem is proposed for nonlinear back-analysis numerical model based on field monitoring deformation and ACO. The basic principle of the proposed model is the establishment of the objective function of optimizing real concrete and rock mechanical parameter. The feedback analysis is then implemented with a modified ant colony algorithm. The algorithm performance is satisfactory, and the accuracy is verified. The m groups of feedback parameters, used to run a nonlinear FEM code, and the displacement and stress distribution are discussed. A feedback analysis of the deformation of the Lijiaxia arch dam and based on the modified ant colony optimization method is also conducted. By considering various material parameters obtained using different analysis methods, comparative analyses were conducted on dam displacements, stress distribution characteristics, and overall dam stability. The comparison results show that the proposal model can effectively solve for feedback multiple parameters of dam concrete and rock material and basically satisfy assessment requirements for geotechnical structural engineering discipline. PMID:25025089

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

Constrained multi-objective optimization of storage ring lattices

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2018-03-01

The storage ring lattice optimization is a class of constrained multi-objective optimization problem, where in addition to low beam emittance, a large dynamic aperture for good injection efficiency and improved beam lifetime are also desirable. The convergence and computation times are of great concern for the optimization algorithms, as various objectives are to be optimized and a number of accelerator parameters to be varied over a large span with several constraints. In this paper, a study of storage ring lattice optimization using differential evolution is presented. The optimization results are compared with two most widely used optimization techniques in accelerators-genetic algorithm and particle swarm optimization. It is found that the differential evolution produces a better Pareto optimal front in reasonable computation time between two conflicting objectives-beam emittance and dispersion function in the straight section. The differential evolution was used, extensively, for the optimization of linear and nonlinear lattices of Indus-2 for exploring various operational modes within the magnet power supply capabilities.

Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

2018-02-01

Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

Quad-rotor flight path energy optimization

NASA Astrophysics Data System (ADS)

Kemper, Edward

Quad-Rotor unmanned areal vehicles (UAVs) have been a popular area of research and development in the last decade, especially with the advent of affordable microcontrollers like the MSP 430 and the Raspberry Pi. Path-Energy Optimization is an area that is well developed for linear systems. In this thesis, this idea of path-energy optimization is extended to the nonlinear model of the Quad-rotor UAV. The classical optimization technique is adapted to the nonlinear model that is derived for the problem at hand, coming up with a set of partial differential equations and boundary value conditions to solve these equations. Then, different techniques to implement energy optimization algorithms are tested using simulations in Python. First, a purely nonlinear approach is used. This method is shown to be computationally intensive, with no practical solution available in a reasonable amount of time. Second, heuristic techniques to minimize the energy of the flight path are tested, using Ziegler-Nichols' proportional integral derivative (PID) controller tuning technique. Finally, a brute force look-up table based PID controller is used. Simulation results of the heuristic method show that both reliable control of the system and path-energy optimization are achieved in a reasonable amount of time.

Comparison of penalty functions on a penalty approach to mixed-integer optimization

NASA Astrophysics Data System (ADS)

Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

2016-06-01

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

An improved CS-LSSVM algorithm-based fault pattern recognition of ship power equipments.

PubMed

Yang, Yifei; Tan, Minjia; Dai, Yuewei

2017-01-01

A ship power equipments' fault monitoring signal usually provides few samples and the data's feature is non-linear in practical situation. This paper adopts the method of the least squares support vector machine (LSSVM) to deal with the problem of fault pattern identification in the case of small sample data. Meanwhile, in order to avoid involving a local extremum and poor convergence precision which are induced by optimizing the kernel function parameter and penalty factor of LSSVM, an improved Cuckoo Search (CS) algorithm is proposed for the purpose of parameter optimization. Based on the dynamic adaptive strategy, the newly proposed algorithm improves the recognition probability and the searching step length, which can effectively solve the problems of slow searching speed and low calculation accuracy of the CS algorithm. A benchmark example demonstrates that the CS-LSSVM algorithm can accurately and effectively identify the fault pattern types of ship power equipments.

Novel trace chemical detection algorithms: a comparative study

NASA Astrophysics Data System (ADS)

Raz, Gil; Murphy, Cara; Georgan, Chelsea; Greenwood, Ross; Prasanth, R. K.; Myers, Travis; Goyal, Anish; Kelley, David; Wood, Derek; Kotidis, Petros

2017-05-01

Algorithms for standoff detection and estimation of trace chemicals in hyperspectral images in the IR band are a key component for a variety of applications relevant to law-enforcement and the intelligence communities. Performance of these methods is impacted by the spectral signature variability due to presence of contaminants, surface roughness, nonlinear dependence on abundances as well as operational limitations on the compute platforms. In this work we provide a comparative performance and complexity analysis of several classes of algorithms as a function of noise levels, error distribution, scene complexity, and spatial degrees of freedom. The algorithm classes we analyze and test include adaptive cosine estimator (ACE and modifications to it), compressive/sparse methods, Bayesian estimation, and machine learning. We explicitly call out the conditions under which each algorithm class is optimal or near optimal as well as their built-in limitations and failure modes.

Detection of the ice assertion on aircraft using empirical mode decomposition enhanced by multi-objective optimization

NASA Astrophysics Data System (ADS)

Bagherzadeh, Seyed Amin; Asadi, Davood

2017-05-01

In search of a precise method for analyzing nonlinear and non-stationary flight data of an aircraft in the icing condition, an Empirical Mode Decomposition (EMD) algorithm enhanced by multi-objective optimization is introduced. In the proposed method, dissimilar IMF definitions are considered by the Genetic Algorithm (GA) in order to find the best decision parameters of the signal trend. To resolve disadvantages of the classical algorithm caused by the envelope concept, the signal trend is estimated directly in the proposed method. Furthermore, in order to simplify the performance and understanding of the EMD algorithm, the proposed method obviates the need for a repeated sifting process. The proposed enhanced EMD algorithm is verified by some benchmark signals. Afterwards, the enhanced algorithm is applied to simulated flight data in the icing condition in order to detect the ice assertion on the aircraft. The results demonstrate the effectiveness of the proposed EMD algorithm in aircraft ice detection by providing a figure of merit for the icing severity.

Stabilization Approaches for Linear and Nonlinear Reduced Order Models

NASA Astrophysics Data System (ADS)

Rezaian, Elnaz; Wei, Mingjun

2017-11-01

It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.

Adaptive infinite impulse response system identification using modified-interior search algorithm with Lèvy flight.

PubMed

Kumar, Manjeet; Rawat, Tarun Kumar; Aggarwal, Apoorva

2017-03-01

In this paper, a new meta-heuristic optimization technique, called interior search algorithm (ISA) with Lèvy flight is proposed and applied to determine the optimal parameters of an unknown infinite impulse response (IIR) system for the system identification problem. ISA is based on aesthetics, which is commonly used in interior design and decoration processes. In ISA, composition phase and mirror phase are applied for addressing the nonlinear and multimodal system identification problems. System identification using modified-ISA (M-ISA) based method involves faster convergence, single parameter tuning and does not require derivative information because it uses a stochastic random search using the concepts of Lèvy flight. A proper tuning of control parameter has been performed in order to achieve a balance between intensification and diversification phases. In order to evaluate the performance of the proposed method, mean square error (MSE), computation time and percentage improvement are considered as the performance measure. To validate the performance of M-ISA based method, simulations has been carried out for three benchmarked IIR systems using same order and reduced order system. Genetic algorithm (GA), particle swarm optimization (PSO), cat swarm optimization (CSO), cuckoo search algorithm (CSA), differential evolution using wavelet mutation (DEWM), firefly algorithm (FFA), craziness based particle swarm optimization (CRPSO), harmony search (HS) algorithm, opposition based harmony search (OHS) algorithm, hybrid particle swarm optimization-gravitational search algorithm (HPSO-GSA) and ISA are also used to model the same examples and simulation results are compared. Obtained results confirm the efficiency of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.; Molvig, K.

2015-09-01

In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

A trust-region algorithm for the optimization of PSA processes using reduced-order modeling

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

Agarwal, A.; Biegler, L.; Zitney, S.

2009-01-01

The last few decades have seen a considerable increase in the applications of adsorptive gas separation technologies, such as pressure swing adsorption (PSA); the applications range from bulk separations to trace contaminant removal. PSA processes are based on solid-gas equilibrium and operate under periodic transient conditions [1]. Bed models for these processes are therefore defined by coupled nonlinear partial differential and algebraic equations (PDAEs) distributed in space and time with periodic boundary conditions that connect the processing steps together and high nonlinearities arising from non-isothermal effects and nonlinear adsorption isotherms. As a result, the optimization of such systems for eithermore » design or operation represents a significant computational challenge to current nonlinear programming algorithms. Model reduction is a powerful methodology that permits systematic generation of cost-efficient low-order representations of large-scale systems that result from discretization of such PDAEs. In particular, low-dimensional approximations can be obtained from reduced order modeling (ROM) techniques based on proper orthogonal decomposition (POD) and can be used as surrogate models in the optimization problems. In this approach, a representative ensemble of solutions of the dynamic PDAE system is constructed by solving a higher-order discretization of the model using the method of lines, followed by the application of Karhunen-Loeve expansion to derive a small set of empirical eigenfunctions (POD modes). These modes are used as basis functions within a Galerkin's projection framework to derive a low-order DAE system that accurately describes the dominant dynamics of the PDAE system. This approach leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization before and making optimization problem computationally efficient [2]. The ROM methodology has been successfully applied to a 2-bed 4-step PSA process used for separating a hydrogen-methane mixture in [3]. The reduced order model developed was successfully used to optimize this process to maximize hydrogen recovery within a trust-region. We extend this approach in this work to develop a rigorous trust-region algorithm for ROM-based optimization of PSA processes. The trust-region update rules and sufficient decrease condition for the objective is used to determine the size of the trust-region. Based on the decrease in the objective function and error in the ROM, a ROM updation strategy is designed [4, 5]. The inequalities and bounds are handled in the algorithm using exact penalty formulation, and a non-smooth trust-region algorithm by Conn et al. [6] is used to handle non-differentiability. To ensure that the first order consistency condition is met and the optimum obtained from ROM-based optimization corresponds to the optimum of the original problem, a scaling function, such as one proposed by Alexandrov et al. [7], is incorporated in the objective function. Such error control mechanism is also capable of handling numerical inconsistencies such as unphysical oscillations in the state variable profiles. The proposed methodology is applied to optimize a PSA process to concentrate CO{sub 2} from a nitrogen-carbon dioxide mixture. As in [3], separate ROMs are developed for each operating step with different POD modes for each state variable. Numerical results will be presented for optimization case studies which involve maximizing CO{sub 2} recovery, feed throughput or minimizing overall power consumption.« less

Development and Application of a Tool for Optimizing Composite Matrix Viscoplastic Material Parameters

NASA Technical Reports Server (NTRS)

Murthy, Pappu L. N.; Naghipour Ghezeljeh, Paria; Bednarcyk, Brett A.

2018-01-01

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) and its application. MAC/GMC is a composite material and laminate analysis software package developed at NASA Glenn Research Center. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that helps users optimize highly nonlinear viscoplastic constitutive law parameters by fitting experimentally observed/measured stress-strain responses under various thermo-mechanical conditions for braided composites. The tool has been developed utilizing the MATrix LABoratory (MATLAB) (The Mathworks, Inc., Natick, MA) programming language. Illustrative examples shown are for a specific braided composite system wherein the matrix viscoplastic behavior is represented by a constitutive law described by seven parameters. The tool is general enough to fit any number of experimentally observed stress-strain responses of the material. The number of parameters to be optimized, as well as the importance given to each stress-strain response, are user choice. Three different optimization algorithms are included: (1) Optimization based on gradient method, (2) Genetic algorithm (GA) based optimization and (3) Particle Swarm Optimization (PSO). The user can mix and match the three algorithms. For example, one can start optimization with either 2 or 3 and then use the optimized solution to further fine tune with approach 1. The secondary focus of this paper is to demonstrate the application of this tool to optimize/calibrate parameters for a nonlinear viscoplastic matrix to predict stress-strain curves (for constituent and composite levels) at different rates, temperatures and/or loading conditions utilizing the Generalized Method of Cells. After preliminary validation of the tool through comparison with experimental results, a detailed virtual parametric study is presented wherein the combined effects of temperature and loading rate on the predicted response of a braided composite is investigated.

Designing Artificial Neural Networks Using Particle Swarm Optimization Algorithms

PubMed Central

Vázquez, Roberto A.

2015-01-01

Artificial Neural Network (ANN) design is a complex task because its performance depends on the architecture, the selected transfer function, and the learning algorithm used to train the set of synaptic weights. In this paper we present a methodology that automatically designs an ANN using particle swarm optimization algorithms such as Basic Particle Swarm Optimization (PSO), Second Generation of Particle Swarm Optimization (SGPSO), and a New Model of PSO called NMPSO. The aim of these algorithms is to evolve, at the same time, the three principal components of an ANN: the set of synaptic weights, the connections or architecture, and the transfer functions for each neuron. Eight different fitness functions were proposed to evaluate the fitness of each solution and find the best design. These functions are based on the mean square error (MSE) and the classification error (CER) and implement a strategy to avoid overtraining and to reduce the number of connections in the ANN. In addition, the ANN designed with the proposed methodology is compared with those designed manually using the well-known Back-Propagation and Levenberg-Marquardt Learning Algorithms. Finally, the accuracy of the method is tested with different nonlinear pattern classification problems. PMID:26221132

On Algorithms for Nonlinear Minimax and Min-Max-Min Problems and Their Efficiency

DTIC Science & Technology

2011-03-01

dissertation is complete, I can finally stay home after dinner to play Wii with you. LET’S GO Mario and Yellow Mushroom... xv THIS PAGE INTENTIONALLY... balance the accuracy of the approximation with problem ill-conditioning. The sim- plest smoothing algorithm creates an accurate smooth approximating...sizing in electronic circuit boards (Chen & Fan, 1998), obstacle avoidance for robots (Kirjner- Neto & Polak, 1998), optimal design centering

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.

Comparison of spike-sorting algorithms for future hardware implementation.

PubMed

Gibson, Sarah; Judy, Jack W; Markovic, Dejan

2008-01-01

Applications such as brain-machine interfaces require hardware spike sorting in order to (1) obtain single-unit activity and (2) perform data reduction for wireless transmission of data. Such systems must be low-power, low-area, high-accuracy, automatic, and able to operate in real time. Several detection and feature extraction algorithms for spike sorting are described briefly and evaluated in terms of accuracy versus computational complexity. The nonlinear energy operator method is chosen as the optimal spike detection algorithm, being most robust over noise and relatively simple. The discrete derivatives method [1] is chosen as the optimal feature extraction method, maintaining high accuracy across SNRs with a complexity orders of magnitude less than that of traditional methods such as PCA.

Evaluation of a new parallel numerical parameter optimization algorithm for a dynamical system

NASA Astrophysics Data System (ADS)

Duran, Ahmet; Tuncel, Mehmet

2016-10-01

It is important to have a scalable parallel numerical parameter optimization algorithm for a dynamical system used in financial applications where time limitation is crucial. We use Message Passing Interface parallel programming and present such a new parallel algorithm for parameter estimation. For example, we apply the algorithm to the asset flow differential equations that have been developed and analyzed since 1989 (see [3-6] and references contained therein). We achieved speed-up for some time series to run up to 512 cores (see [10]). Unlike [10], we consider more extensive financial market situations, for example, in presence of low volatility, high volatility and stock market price at a discount/premium to its net asset value with varying magnitude, in this work. Moreover, we evaluated the convergence of the model parameter vector, the nonlinear least squares error and maximum improvement factor to quantify the success of the optimization process depending on the number of initial parameter vectors.

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

Li, Yongjun; Yang, Lingyun

We report an efficient dynamic aperture (DA) optimization approach using multiobjective genetic algorithm (MOGA), which is driven by nonlinear driving terms computation. It was found that having small low order driving terms is a necessary but insufficient condition of having a decent DA. Then direct DA tracking simulation is implemented among the last generation candidates to select the best solutions. The approach was demonstrated successfully in optimizing NSLS-II storage ring DA.

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

NASA Astrophysics Data System (ADS)

Tavakkoli-Moghaddam, Reza; Vazifeh-Noshafagh, Samira; Taleizadeh, Ata Allah; Hajipour, Vahid; Mahmoudi, Amin

2017-01-01

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.

Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

PubMed Central

Saha, S. K.; Dutta, R.; Choudhury, R.; Kar, R.; Mandal, D.; Ghoshal, S. P.

2013-01-01

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems. PMID:23844390

Efficient and accurate optimal linear phase FIR filter design using opposition-based harmony search algorithm.

PubMed

Saha, S K; Dutta, R; Choudhury, R; Kar, R; Mandal, D; Ghoshal, S P

2013-01-01

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems.

Motion Cueing Algorithm Development: Initial Investigation and Redesign of the Algorithms

NASA Technical Reports Server (NTRS)

Telban, Robert J.; Wu, Weimin; Cardullo, Frank M.; Houck, Jacob A. (Technical Monitor)

2000-01-01

In this project four motion cueing algorithms were initially investigated. The classical algorithm generated results with large distortion and delay and low magnitude. The NASA adaptive algorithm proved to be well tuned with satisfactory performance, while the UTIAS adaptive algorithm produced less desirable results. Modifications were made to the adaptive algorithms to reduce the magnitude of undesirable spikes. The optimal algorithm was found to have the potential for improved performance with further redesign. The center of simulator rotation was redefined. More terms were added to the cost function to enable more tuning flexibility. A new design approach using a Fortran/Matlab/Simulink setup was employed. A new semicircular canals model was incorporated in the algorithm. With these changes results show the optimal algorithm has some advantages over the NASA adaptive algorithm. Two general problems observed in the initial investigation required solutions. A nonlinear gain algorithm was developed that scales the aircraft inputs by a third-order polynomial, maximizing the motion cues while remaining within the operational limits of the motion system. A braking algorithm was developed to bring the simulator to a full stop at its motion limit and later release the brake to follow the cueing algorithm output.

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.

Analysis of point-to-point lung motion with full inspiration and expiration CT data using non-linear optimization method: optimal geometric assumption model for the effective registration algorithm

NASA Astrophysics Data System (ADS)

Kim, Namkug; Seo, Joon Beom; Heo, Jeong Nam; Kang, Suk-Ho

2007-03-01

The study was conducted to develop a simple model for more robust lung registration of volumetric CT data, which is essential for various clinical lung analysis applications, including the lung nodule matching in follow up CT studies, semi-quantitative assessment of lung perfusion, and etc. The purpose of this study is to find the most effective reference point and geometric model based on the lung motion analysis from the CT data sets obtained in full inspiration (In.) and expiration (Ex.). Ten pairs of CT data sets in normal subjects obtained in full In. and Ex. were used in this study. Two radiologists were requested to draw 20 points representing the subpleural point of the central axis in each segment. The apex, hilar point, and center of inertia (COI) of each unilateral lung were proposed as the reference point. To evaluate optimal expansion point, non-linear optimization without constraints was employed. The objective function is sum of distances from the line, consist of the corresponding points between In. and Ex. to the optimal point x. By using the nonlinear optimization, the optimal points was evaluated and compared between reference points. The average distance between the optimal point and each line segment revealed that the balloon model was more suitable to explain the lung expansion model. This lung motion analysis based on vector analysis and non-linear optimization shows that balloon model centered on the center of inertia of lung is most effective geometric model to explain lung expansion by breathing.

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

Performance improvement for optimization of the non-linear geometric fitting problem in manufacturing metrology

NASA Astrophysics Data System (ADS)

Moroni, Giovanni; Syam, Wahyudin P.; Petrò, Stefano

2014-08-01

Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.

Towards Real-Time Maneuver Detection: Automatic State and Dynamics Estimation with the Adaptive Optimal Control Based Estimator

NASA Astrophysics Data System (ADS)

Lubey, D.; Scheeres, D.

Tracking objects in Earth orbit is fraught with complications. This is due to the large population of orbiting spacecraft and debris that continues to grow, passive (i.e. no direct communication) and data-sparse observations, and the presence of maneuvers and dynamics mismodeling. Accurate orbit determination in this environment requires an algorithm to capture both a system's state and its state dynamics in order to account for mismodelings. Previous studies by the authors yielded an algorithm called the Optimal Control Based Estimator (OCBE) - an algorithm that simultaneously estimates a system's state and optimal control policies that represent dynamic mismodeling in the system for an arbitrary orbit-observer setup. The stochastic properties of these estimated controls are then used to determine the presence of mismodelings (maneuver detection), as well as characterize and reconstruct the mismodelings. The purpose of this paper is to develop the OCBE into an accurate real-time orbit tracking and maneuver detection algorithm by automating the algorithm and removing its linear assumptions. This results in a nonlinear adaptive estimator. In its original form the OCBE had a parameter called the assumed dynamic uncertainty, which is selected by the user with each new measurement to reflect the level of dynamic mismodeling in the system. This human-in-the-loop approach precludes real-time application to orbit tracking problems due to their complexity. This paper focuses on the Adaptive OCBE, a version of the estimator where the assumed dynamic uncertainty is chosen automatically with each new measurement using maneuver detection results to ensure that state uncertainties are properly adjusted to account for all dynamic mismodelings. The paper also focuses on a nonlinear implementation of the estimator. Originally, the OCBE was derived from a nonlinear cost function then linearized about a nominal trajectory, which is assumed to be ballistic (i.e. the nominal optimal control policy is zero for all times). In this paper, we relax this assumption on the nominal trajectory in order to allow for controlled nominal trajectories. This allows the estimator to be iterated to obtain a more accurate nonlinear solution for both the state and control estimates. Beyond these developments to the estimator, this paper also introduces a modified distance metric for maneuver detection. The original metric used in the OCBE only accounted for the estimated control and its uncertainty. This new metric accounts for measurement deviation and a priori state deviations, such that it accounts for all three major forms of uncertainty in orbit determination. This allows the user to understand the contributions of each source of uncertainty toward the total system mismodeling so that the user can properly account for them. Together these developments create an accurate orbit determination algorithm that is automated, robust to mismodeling, and capable of detecting and reconstructing the presence of mismodeling. These qualities make this algorithm a good foundation from which to approach the problem of real-time maneuver detection and reconstruction for Space Situational Awareness applications. This is further strengthened by the algorithm's general formulation that allows it to be applied to problems with an arbitrary target and observer.

Inverse Analysis of Irradiated NuclearMaterial Gamma Spectra via Nonlinear Optimization

NASA Astrophysics Data System (ADS)

Dean, Garrett James

Nuclear forensics is the collection of technical methods used to identify the provenance of nuclear material interdicted outside of regulatory control. Techniques employed in nuclear forensics include optical microscopy, gas chromatography, mass spectrometry, and alpha, beta, and gamma spectrometry. This dissertation focuses on the application of inverse analysis to gamma spectroscopy to estimate the history of pulse irradiated nuclear material. Previous work in this area has (1) utilized destructive analysis techniques to supplement the nondestructive gamma measurements, and (2) been applied to samples composed of spent nuclear fuel with long irradiation and cooling times. Previous analyses have employed local nonlinear solvers, simple empirical models of gamma spectral features, and simple detector models of gamma spectral features. The algorithm described in this dissertation uses a forward model of the irradiation and measurement process within a global nonlinear optimizer to estimate the unknown irradiation history of pulse irradiated nuclear material. The forward model includes a detector response function for photopeaks only. The algorithm uses a novel hybrid global and local search algorithm to quickly estimate the irradiation parameters, including neutron fluence, cooling time and original composition. Sequential, time correlated series of measurements are used to reduce the uncertainty in the estimated irradiation parameters. This algorithm allows for in situ measurements of interdicted irradiated material. The increase in analysis speed comes with a decrease in information that can be determined, but the sample fluence, cooling time, and composition can be determined within minutes of a measurement. Furthermore, pulse irradiated nuclear material has a characteristic feature that irradiation time and flux cannot be independently estimated. The algorithm has been tested against pulse irradiated samples of pure special nuclear material with cooling times of four minutes to seven hours. The algorithm described is capable of determining the cooling time and fluence the sample was exposed to within 10% as well as roughly estimating the relative concentrations of nuclides present in the original composition.

Imitative modeling automatic system Control of steam pressure in the main steam collector with the influence on the main Servomotor steam turbine

NASA Astrophysics Data System (ADS)

Andriushin, A. V.; Zverkov, V. P.; Kuzishchin, V. F.; Ryzhkov, O. S.; Sabanin, V. R.

2017-11-01

The research and setting results of steam pressure in the main steam collector “Do itself” automatic control system (ACS) with high-speed feedback on steam pressure in the turbine regulating stage are presented. The ACS setup is performed on the simulation model of the controlled object developed for this purpose with load-dependent static and dynamic characteristics and a non-linear control algorithm with pulse control of the turbine main servomotor. A method for tuning nonlinear ACS with a numerical algorithm for multiparametric optimization and a procedure for separate dynamic adjustment of control devices in a two-loop ACS are proposed and implemented. It is shown that the nonlinear ACS adjusted with the proposed method with the regulators constant parameters ensures reliable and high-quality operation without the occurrence of oscillations in the transient processes the operating range of the turbine loads.

The Krigifier: A Procedure for Generating Pseudorandom Nonlinear Objective Functions for Computational Experimentation

NASA Technical Reports Server (NTRS)

Trosset, Michael W.

1999-01-01

Comprehensive computational experiments to assess the performance of algorithms for numerical optimization require (among other things) a practical procedure for generating pseudorandom nonlinear objective functions. We propose a procedure that is based on the convenient fiction that objective functions are realizations of stochastic processes. This report details the calculations necessary to implement our procedure for the case of certain stationary Gaussian processes and presents a specific implementation in the statistical programming language S-PLUS.

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

The NLS-Based Nonlinear Grey Multivariate Model for Forecasting Pollutant Emissions in China

PubMed Central

Pei, Ling-Ling; Li, Qin

2018-01-01

The relationship between pollutant discharge and economic growth has been a major research focus in environmental economics. To accurately estimate the nonlinear change law of China’s pollutant discharge with economic growth, this study establishes a transformed nonlinear grey multivariable (TNGM (1, N)) model based on the nonlinear least square (NLS) method. The Gauss–Seidel iterative algorithm was used to solve the parameters of the TNGM (1, N) model based on the NLS basic principle. This algorithm improves the precision of the model by continuous iteration and constantly approximating the optimal regression coefficient of the nonlinear model. In our empirical analysis, the traditional grey multivariate model GM (1, N) and the NLS-based TNGM (1, N) models were respectively adopted to forecast and analyze the relationship among wastewater discharge per capita (WDPC), and per capita emissions of SO2 and dust, alongside GDP per capita in China during the period 1996–2015. Results indicated that the NLS algorithm is able to effectively help the grey multivariable model identify the nonlinear relationship between pollutant discharge and economic growth. The results show that the NLS-based TNGM (1, N) model presents greater precision when forecasting WDPC, SO2 emissions and dust emissions per capita, compared to the traditional GM (1, N) model; WDPC indicates a growing tendency aligned with the growth of GDP, while the per capita emissions of SO2 and dust reduce accordingly. PMID:29517985

Big Data: A Parallel Particle Swarm Optimization-Back-Propagation Neural Network Algorithm Based on MapReduce

PubMed Central

Cao, Jianfang; Cui, Hongyan; Shi, Hao; Jiao, Lijuan

2016-01-01

A back-propagation (BP) neural network can solve complicated random nonlinear mapping problems; therefore, it can be applied to a wide range of problems. However, as the sample size increases, the time required to train BP neural networks becomes lengthy. Moreover, the classification accuracy decreases as well. To improve the classification accuracy and runtime efficiency of the BP neural network algorithm, we proposed a parallel design and realization method for a particle swarm optimization (PSO)-optimized BP neural network based on MapReduce on the Hadoop platform using both the PSO algorithm and a parallel design. The PSO algorithm was used to optimize the BP neural network’s initial weights and thresholds and improve the accuracy of the classification algorithm. The MapReduce parallel programming model was utilized to achieve parallel processing of the BP algorithm, thereby solving the problems of hardware and communication overhead when the BP neural network addresses big data. Datasets on 5 different scales were constructed using the scene image library from the SUN Database. The classification accuracy of the parallel PSO-BP neural network algorithm is approximately 92%, and the system efficiency is approximately 0.85, which presents obvious advantages when processing big data. The algorithm proposed in this study demonstrated both higher classification accuracy and improved time efficiency, which represents a significant improvement obtained from applying parallel processing to an intelligent algorithm on big data. PMID:27304987

Noise removal in extended depth of field microscope images through nonlinear signal processing.

PubMed

Zahreddine, Ramzi N; Cormack, Robert H; Cogswell, Carol J

2013-04-01

Extended depth of field (EDF) microscopy, achieved through computational optics, allows for real-time 3D imaging of live cell dynamics. EDF is achieved through a combination of point spread function engineering and digital image processing. A linear Wiener filter has been conventionally used to deconvolve the image, but it suffers from high frequency noise amplification and processing artifacts. A nonlinear processing scheme is proposed which extends the depth of field while minimizing background noise. The nonlinear filter is generated via a training algorithm and an iterative optimizer. Biological microscope images processed with the nonlinear filter show a significant improvement in image quality and signal-to-noise ratio over the conventional linear filter.

Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; AliShaykhian, Gholam

2010-01-01

We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.

Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

USGS Publications Warehouse

Chen, C.; Xia, J.; Liu, J.; Feng, G.

2006-01-01

Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant result is that final solution is determined by the average model derived from multiple trials instead of one computation due to the randomness in a genetic algorithm procedure. These advantages were demonstrated by synthetic and real-world examples of inversion of potential-field data. ?? 2005 Elsevier Ltd. All rights reserved.

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2000-01-01

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

PubMed

Kiumarsi, Bahare; Lewis, Frank L

2015-01-01

This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

Computational microscopy: illumination coding and nonlinear optimization enables gigapixel 3D phase imaging

NASA Astrophysics Data System (ADS)

Tian, Lei; Waller, Laura

2017-05-01

Microscope lenses can have either large field of view (FOV) or high resolution, not both. Computational microscopy based on illumination coding circumvents this limit by fusing images from different illumination angles using nonlinear optimization algorithms. The result is a Gigapixel-scale image having both wide FOV and high resolution. We demonstrate an experimentally robust reconstruction algorithm based on a 2nd order quasi-Newton's method, combined with a novel phase initialization scheme. To further extend the Gigapixel imaging capability to 3D, we develop a reconstruction method to process the 4D light field measurements from sequential illumination scanning. The algorithm is based on a 'multislice' forward model that incorporates both 3D phase and diffraction effects, as well as multiple forward scatterings. To solve the inverse problem, an iterative update procedure that combines both phase retrieval and 'error back-propagation' is developed. To avoid local minimum solutions, we further develop a novel physical model-based initialization technique that accounts for both the geometric-optic and 1st order phase effects. The result is robust reconstructions of Gigapixel 3D phase images having both wide FOV and super resolution in all three dimensions. Experimental results from an LED array microscope were demonstrated.

Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design

NASA Technical Reports Server (NTRS)

Sims, Jon A.; Finlayson, Paul A.; Rinderle, Edward A.; Vavrina, Matthew A.; Kowalkowski, Theresa D.

2006-01-01

A tool developed for the preliminary design of low-thrust trajectories is described. The trajectory is discretized into segments and a nonlinear programming method is used for optimization. The tool is easy to use, has robust convergence, and can handle many intermediate encounters. In addition, the tool has a wide variety of features, including several options for objective function and different low-thrust propulsion models (e.g., solar electric propulsion, nuclear electric propulsion, and solar sail). High-thrust, impulsive trajectories can also be optimized.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

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

Customer demand prediction of service-oriented manufacturing using the least square support vector machine optimized by particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Cao, Jin; Jiang, Zhibin; Wang, Kangzhou

2017-07-01

Many nonlinear customer satisfaction-related factors significantly influence the future customer demand for service-oriented manufacturing (SOM). To address this issue and enhance the prediction accuracy, this article develops a novel customer demand prediction approach for SOM. The approach combines the phase space reconstruction (PSR) technique with the optimized least square support vector machine (LSSVM). First, the prediction sample space is reconstructed by the PSR to enrich the time-series dynamics of the limited data sample. Then, the generalization and learning ability of the LSSVM are improved by the hybrid polynomial and radial basis function kernel. Finally, the key parameters of the LSSVM are optimized by the particle swarm optimization algorithm. In a real case study, the customer demand prediction of an air conditioner compressor is implemented. Furthermore, the effectiveness and validity of the proposed approach are demonstrated by comparison with other classical predication approaches.

Evaluating an image-fusion algorithm with synthetic-image-generation tools

NASA Astrophysics Data System (ADS)

Gross, Harry N.; Schott, John R.

1996-06-01

An algorithm that combines spectral mixing and nonlinear optimization is used to fuse multiresolution images. Image fusion merges images of different spatial and spectral resolutions to create a high spatial resolution multispectral combination. High spectral resolution allows identification of materials in the scene, while high spatial resolution locates those materials. In this algorithm, conventional spectral mixing estimates the percentage of each material (called endmembers) within each low resolution pixel. Three spectral mixing models are compared; unconstrained, partially constrained, and fully constrained. In the partially constrained application, the endmember fractions are required to sum to one. In the fully constrained application, all fractions are additionally required to lie between zero and one. While negative fractions seem inappropriate, they can arise from random spectral realizations of the materials. In the second part of the algorithm, the low resolution fractions are used as inputs to a constrained nonlinear optimization that calculates the endmember fractions for the high resolution pixels. The constraints mirror the low resolution constraints and maintain consistency with the low resolution fraction results. The algorithm can use one or more higher resolution sharpening images to locate the endmembers to high spatial accuracy. The algorithm was evaluated with synthetic image generation (SIG) tools. A SIG developed image can be used to control the various error sources that are likely to impair the algorithm performance. These error sources include atmospheric effects, mismodeled spectral endmembers, and variability in topography and illumination. By controlling the introduction of these errors, the robustness of the algorithm can be studied and improved upon. The motivation for this research is to take advantage of the next generation of multi/hyperspectral sensors. Although the hyperspectral images will be of modest to low resolution, fusing them with high resolution sharpening images will produce a higher spatial resolution land cover or material map.

A novel methodology for non-linear system identification of battery cells used in non-road hybrid electric vehicles

NASA Astrophysics Data System (ADS)

Unger, Johannes; Hametner, Christoph; Jakubek, Stefan; Quasthoff, Marcus

2014-12-01

An accurate state of charge (SoC) estimation of a traction battery in hybrid electric non-road vehicles, which possess higher dynamics and power densities than on-road vehicles, requires a precise battery cell terminal voltage model. This paper presents a novel methodology for non-linear system identification of battery cells to obtain precise battery models. The methodology comprises the architecture of local model networks (LMN) and optimal model based design of experiments (DoE). Three main novelties are proposed: 1) Optimal model based DoE, which aims to high dynamically excite the battery cells at load ranges frequently used in operation. 2) The integration of corresponding inputs in the LMN to regard the non-linearities SoC, relaxation, hysteresis as well as temperature effects. 3) Enhancements to the local linear model tree (LOLIMOT) construction algorithm, to achieve a physical appropriate interpretation of the LMN. The framework is applicable for different battery cell chemistries and different temperatures, and is real time capable, which is shown on an industrial PC. The accuracy of the obtained non-linear battery model is demonstrated on cells with different chemistries and temperatures. The results show significant improvement due to optimal experiment design and integration of the battery non-linearities within the LMN structure.

Spot-shadowing optimization to mitigate damage growth in a high-energy-laser amplifier chain.

PubMed

Bahk, Seung-Whan; Zuegel, Jonathan D; Fienup, James R; Widmayer, C Clay; Heebner, John

2008-12-10

A spot-shadowing technique to mitigate damage growth in a high-energy laser is studied. Its goal is to minimize the energy loss and undesirable hot spots in intermediate planes of the laser. A nonlinear optimization algorithm solves for the complex fields required to mitigate damage growth in the National Ignition Facility amplifier chain. The method is generally applicable to any large fusion laser.

Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

NASA Technical Reports Server (NTRS)

Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

2014-01-01

Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

Online optimal obstacle avoidance for rotary-wing autonomous unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Kang, Keeryun

This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. The flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.

On the Control of Consensus Networks: Theory and Applications

NASA Astrophysics Data System (ADS)

Hudoba de Badyn, Mathias

Signed networks allow the study of positive and negative interactions between agents. In this thesis, three papers are presented that address controllability of networked dynamics. First, controllability of signed consensus networks is approached from a symmetry perspective, for both linear and nonlinear consensus protocols. It is shown that the graph-theoretic property of signed networks known as structural balance renders the consensus protocol uncontrollable when coupled with a certain type of symmetry. Stabilizability and output controllability of signed linear consensus is also examined, as well as a data-driven approach to finding bipartite consensus stemming from structural balance for signed nonlinear consensus. Second, an algorithm is constructed that allows one to grow a network while preserving controllability, and some generalizations of this algorithm are presented. Submodular optimization is used to analyze a second algorithm that adds nodes to a network to maximize the network connectivity.

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

Modified Mahalanobis Taguchi System for Imbalance Data Classification

PubMed Central

2017-01-01

The Mahalanobis Taguchi System (MTS) is considered one of the most promising binary classification algorithms to handle imbalance data. Unfortunately, MTS lacks a method for determining an efficient threshold for the binary classification. In this paper, a nonlinear optimization model is formulated based on minimizing the distance between MTS Receiver Operating Characteristics (ROC) curve and the theoretical optimal point named Modified Mahalanobis Taguchi System (MMTS). To validate the MMTS classification efficacy, it has been benchmarked with Support Vector Machines (SVMs), Naive Bayes (NB), Probabilistic Mahalanobis Taguchi Systems (PTM), Synthetic Minority Oversampling Technique (SMOTE), Adaptive Conformal Transformation (ACT), Kernel Boundary Alignment (KBA), Hidden Naive Bayes (HNB), and other improved Naive Bayes algorithms. MMTS outperforms the benchmarked algorithms especially when the imbalance ratio is greater than 400. A real life case study on manufacturing sector is used to demonstrate the applicability of the proposed model and to compare its performance with Mahalanobis Genetic Algorithm (MGA). PMID:28811820

Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-06-08

This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.

Intelligent sensing sensory quality of Chinese rice wine using near infrared spectroscopy and nonlinear tools

NASA Astrophysics Data System (ADS)

Ouyang, Qin; Chen, Quansheng; Zhao, Jiewen

2016-02-01

The approach presented herein reports the application of near infrared (NIR) spectroscopy, in contrast with human sensory panel, as a tool for estimating Chinese rice wine quality; concretely, to achieve the prediction of the overall sensory scores assigned by the trained sensory panel. Back propagation artificial neural network (BPANN) combined with adaptive boosting (AdaBoost) algorithm, namely BP-AdaBoost, as a novel nonlinear algorithm, was proposed in modeling. First, the optimal spectra intervals were selected by synergy interval partial least square (Si-PLS). Then, BP-AdaBoost model based on the optimal spectra intervals was established, called Si-BP-AdaBoost model. These models were optimized by cross validation, and the performance of each final model was evaluated according to correlation coefficient (Rp) and root mean square error of prediction (RMSEP) in prediction set. Si-BP-AdaBoost showed excellent performance in comparison with other models. The best Si-BP-AdaBoost model was achieved with Rp = 0.9180 and RMSEP = 2.23 in the prediction set. It was concluded that NIR spectroscopy combined with Si-BP-AdaBoost was an appropriate method for the prediction of the sensory quality in Chinese rice wine.

Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

NASA Astrophysics Data System (ADS)

Luy, N. T.

2018-04-01

The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

PSC algorithm description

NASA Technical Reports Server (NTRS)

Nobbs, Steven G.

1995-01-01

An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.

On the Hilbert-Huang Transform Theoretical Foundation

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Huang, Norden E.

2004-01-01

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Parameter estimation for chaotic systems using improved bird swarm algorithm

NASA Astrophysics Data System (ADS)

Xu, Chuangbiao; Yang, Renhuan

2017-12-01

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

GA-optimized feedforward-PID tracking control for a rugged electrohydraulic system design.

PubMed

Sarkar, B K; Mandal, P; Saha, R; Mookherjee, S; Sanyal, D

2013-11-01

Rugged electrohydraulic systems are preferred for remote and harsh applications. Despite the low bandwidth, large deadband and flow nonlinearities in proportional valves valve and highly nonlinear friction in industry-grade cylinders that comprise rugged systems, their maintenance are much easier than very sophisticated and delicate servocontrol and servocylinder systems. With the target of making the easily maintainable system to perform comparably to a servosystem, a feedforward control has been designed here for compensating the nonlinearities. A PID feedback of the piston displacement has been employed in tandem for absorbing the unmodeled effects. All the controller parameters have been optimized by a real-coded genetic algorithm. The agreement between the achieved real-time responses for step and sinusoidal demands with those achieved by modern servosystems clearly establishes the acceptability of the controller design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Algorithms for bilevel optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.

Optimization of a Tube Hydroforming Process

NASA Astrophysics Data System (ADS)

Abedrabbo, Nader; Zafar, Naeem; Averill, Ron; Pourboghrat, Farhang; Sidhu, Ranny

2004-06-01

An approach is presented to optimize a tube hydroforming process using a Genetic Algorithm (GA) search method. The goal of the study is to maximize formability by identifying the optimal internal hydraulic pressure and feed rate while satisfying the forming limit diagram (FLD). The optimization software HEEDS is used in combination with the nonlinear structural finite element code LS-DYNA to carry out the investigation. In particular, a sub-region of a circular tube blank is formed into a square die. Compared to the best results of a manual optimization procedure, a 55% increase in expansion was achieved when using the pressure and feed profiles identified by the automated optimization procedure.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities.

PubMed

Zhu, Xiaolei; Yarkony, David R

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

Combining Biomarkers Linearly and Nonlinearly for Classification Using the Area Under the ROC Curve

PubMed Central

Fong, Youyi; Yin, Shuxin; Huang, Ying

2016-01-01

In biomedical studies, it is often of interest to classify/predict a subject’s disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on AUC - Area under the Receiver Operating Characteristic Curve. Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in sub-optimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called Ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function, and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data is generated from a semiparametric generalized linear model, just as the Smoothed AUC method (SAUC). Through simulation studies and real data examples, we demonstrate that RAUC out-performs SAUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. PMID:27058981

Application of a derivative-free global optimization algorithm to the derivation of a new time integration scheme for the simulation of incompressible turbulence

NASA Astrophysics Data System (ADS)

Alimohammadi, Shahrouz; Cavaglieri, Daniele; Beyhaghi, Pooriya; Bewley, Thomas R.

2016-11-01

This work applies a recently developed Derivative-free optimization algorithm to derive a new mixed implicit-explicit (IMEX) time integration scheme for Computational Fluid Dynamics (CFD) simulations. This algorithm allows imposing a specified order of accuracy for the time integration and other important stability properties in the form of nonlinear constraints within the optimization problem. In this procedure, the coefficients of the IMEX scheme should satisfy a set of constraints simultaneously. Therefore, the optimization process, at each iteration, estimates the location of the optimal coefficients using a set of global surrogates, for both the objective and constraint functions, as well as a model of the uncertainty function of these surrogates based on the concept of Delaunay triangulation. This procedure has been proven to converge to the global minimum of the constrained optimization problem provided the constraints and objective functions are twice differentiable. As a result, a new third-order, low-storage IMEX Runge-Kutta time integration scheme is obtained with remarkably fast convergence. Numerical tests are then performed leveraging the turbulent channel flow simulations to validate the theoretical order of accuracy and stability properties of the new scheme.

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.« less

Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach.

PubMed

Liu, Derong; Wang, Ding; Li, Hongliang

2014-02-01

In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuous-time nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme.

Spectral embedding finds meaningful (relevant) structure in image and microarray data

PubMed Central

Higgs, Brandon W; Weller, Jennifer; Solka, Jeffrey L

2006-01-01

Background Accurate methods for extraction of meaningful patterns in high dimensional data have become increasingly important with the recent generation of data types containing measurements across thousands of variables. Principal components analysis (PCA) is a linear dimensionality reduction (DR) method that is unsupervised in that it relies only on the data; projections are calculated in Euclidean or a similar linear space and do not use tuning parameters for optimizing the fit to the data. However, relationships within sets of nonlinear data types, such as biological networks or images, are frequently mis-rendered into a low dimensional space by linear methods. Nonlinear methods, in contrast, attempt to model important aspects of the underlying data structure, often requiring parameter(s) fitting to the data type of interest. In many cases, the optimal parameter values vary when different classification algorithms are applied on the same rendered subspace, making the results of such methods highly dependent upon the type of classifier implemented. Results We present the results of applying the spectral method of Lafon, a nonlinear DR method based on the weighted graph Laplacian, that minimizes the requirements for such parameter optimization for two biological data types. We demonstrate that it is successful in determining implicit ordering of brain slice image data and in classifying separate species in microarray data, as compared to two conventional linear methods and three nonlinear methods (one of which is an alternative spectral method). This spectral implementation is shown to provide more meaningful information, by preserving important relationships, than the methods of DR presented for comparison. Tuning parameter fitting is simple and is a general, rather than data type or experiment specific approach, for the two datasets analyzed here. Tuning parameter optimization is minimized in the DR step to each subsequent classification method, enabling the possibility of valid cross-experiment comparisons. Conclusion Results from the spectral method presented here exhibit the desirable properties of preserving meaningful nonlinear relationships in lower dimensional space and requiring minimal parameter fitting, providing a useful algorithm for purposes of visualization and classification across diverse datasets, a common challenge in systems biology. PMID:16483359

Phase retrieval from intensity-only data by relative entropy minimization.

PubMed

Deming, Ross W

2007-11-01

A recursive algorithm, which appears to be new, is presented for estimating the amplitude and phase of a wave field from intensity-only measurements on two or more scan planes at different axial positions. The problem is framed as a nonlinear optimization, in which the angular spectrum of the complex field model is adjusted in order to minimize the relative entropy, or Kullback-Leibler divergence, between the measured and reconstructed intensities. The most common approach to this so-called phase retrieval problem is a variation of the well-known Gerchberg-Saxton algorithm devised by Misell (J. Phys. D6, L6, 1973), which is efficient and extremely simple to implement. The new algorithm has a computational structure that is very similar to Misell's approach, despite the fundamental difference in the optimization criteria used for each. Based upon results from noisy simulated data, the new algorithm appears to be more robust than Misell's approach and to produce better results from low signal-to-noise ratio data. The convergence of the new algorithm is examined.

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.

Nonlinear system modeling based on bilinear Laguerre orthonormal bases.

PubMed

Garna, Tarek; Bouzrara, Kais; Ragot, José; Messaoud, Hassani

2013-05-01

This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al.. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Sensor placement algorithm development to maximize the efficiency of acid gas removal unit for integrated gasifiction combined sycle (IGCC) power plant with CO2 capture

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

Paul, P.; Bhattacharyya, D.; Turton, R.

2012-01-01

Future integrated gasification combined cycle (IGCC) power plants with CO{sub 2} capture will face stricter operational and environmental constraints. Accurate values of relevant states/outputs/disturbances are needed to satisfy these constraints and to maximize the operational efficiency. Unfortunately, a number of these process variables cannot be measured while a number of them can be measured, but have low precision, reliability, or signal-to-noise ratio. In this work, a sensor placement (SP) algorithm is developed for optimal selection of sensor location, number, and type that can maximize the plant efficiency and result in a desired precision of the relevant measured/unmeasured states. In thismore » work, an SP algorithm is developed for an selective, dual-stage Selexol-based acid gas removal (AGR) unit for an IGCC plant with pre-combustion CO{sub 2} capture. A comprehensive nonlinear dynamic model of the AGR unit is developed in Aspen Plus Dynamics® (APD) and used to generate a linear state-space model that is used in the SP algorithm. The SP algorithm is developed with the assumption that an optimal Kalman filter will be implemented in the plant for state and disturbance estimation. The algorithm is developed assuming steady-state Kalman filtering and steady-state operation of the plant. The control system is considered to operate based on the estimated states and thereby, captures the effects of the SP algorithm on the overall plant efficiency. The optimization problem is solved by Genetic Algorithm (GA) considering both linear and nonlinear equality and inequality constraints. Due to the very large number of candidate sets available for sensor placement and because of the long time that it takes to solve the constrained optimization problem that includes more than 1000 states, solution of this problem is computationally expensive. For reducing the computation time, parallel computing is performed using the Distributed Computing Server (DCS®) and the Parallel Computing® toolbox from Mathworks®. In this presentation, we will share our experience in setting up parallel computing using GA in the MATLAB® environment and present the overall approach for achieving higher computational efficiency in this framework.« less

Sensor placement algorithm development to maximize the efficiency of acid gas removal unit for integrated gasification combined cycle (IGCC) power plant with CO{sub 2} capture

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

Paul, P.; Bhattacharyya, D.; Turton, R.

2012-01-01

Future integrated gasification combined cycle (IGCC) power plants with CO{sub 2} capture will face stricter operational and environmental constraints. Accurate values of relevant states/outputs/disturbances are needed to satisfy these constraints and to maximize the operational efficiency. Unfortunately, a number of these process variables cannot be measured while a number of them can be measured, but have low precision, reliability, or signal-to-noise ratio. In this work, a sensor placement (SP) algorithm is developed for optimal selection of sensor location, number, and type that can maximize the plant efficiency and result in a desired precision of the relevant measured/unmeasured states. In thismore » work, an SP algorithm is developed for an selective, dual-stage Selexol-based acid gas removal (AGR) unit for an IGCC plant with pre-combustion CO{sub 2} capture. A comprehensive nonlinear dynamic model of the AGR unit is developed in Aspen Plus Dynamics® (APD) and used to generate a linear state-space model that is used in the SP algorithm. The SP algorithm is developed with the assumption that an optimal Kalman filter will be implemented in the plant for state and disturbance estimation. The algorithm is developed assuming steady-state Kalman filtering and steady-state operation of the plant. The control system is considered to operate based on the estimated states and thereby, captures the effects of the SP algorithm on the overall plant efficiency. The optimization problem is solved by Genetic Algorithm (GA) considering both linear and nonlinear equality and inequality constraints. Due to the very large number of candidate sets available for sensor placement and because of the long time that it takes to solve the constrained optimization problem that includes more than 1000 states, solution of this problem is computationally expensive. For reducing the computation time, parallel computing is performed using the Distributed Computing Server (DCS®) and the Parallel Computing® toolbox from Mathworks®. In this presentation, we will share our experience in setting up parallel computing using GA in the MATLAB® environment and present the overall approach for achieving higher computational efficiency in this framework.« less

An efficient hybrid approach for multiobjective optimization of water distribution systems

NASA Astrophysics Data System (ADS)

Zheng, Feifei; Simpson, Angus R.; Zecchin, Aaron C.

2014-05-01

An efficient hybrid approach for the design of water distribution systems (WDSs) with multiple objectives is described in this paper. The objectives are the minimization of the network cost and maximization of the network resilience. A self-adaptive multiobjective differential evolution (SAMODE) algorithm has been developed, in which control parameters are automatically adapted by means of evolution instead of the presetting of fine-tuned parameter values. In the proposed method, a graph algorithm is first used to decompose a looped WDS into a shortest-distance tree (T) or forest, and chords (Ω). The original two-objective optimization problem is then approximated by a series of single-objective optimization problems of the T to be solved by nonlinear programming (NLP), thereby providing an approximate Pareto optimal front for the original whole network. Finally, the solutions at the approximate front are used to seed the SAMODE algorithm to find an improved front for the original entire network. The proposed approach is compared with two other conventional full-search optimization methods (the SAMODE algorithm and the NSGA-II) that seed the initial population with purely random solutions based on three case studies: a benchmark network and two real-world networks with multiple demand loading cases. Results show that (i) the proposed NLP-SAMODE method consistently generates better-quality Pareto fronts than the full-search methods with significantly improved efficiency; and (ii) the proposed SAMODE algorithm (no parameter tuning) exhibits better performance than the NSGA-II with calibrated parameter values in efficiently offering optimal fronts.

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Improving Robot Locomotion Through Learning Methods for Expensive Black-Box Systems

DTIC Science & Technology

2013-11-01

development of a class of “gradient free” optimization techniques; these include local approaches, such as a Nelder- Mead simplex search (c.f. [73]), and global...1Note that this simple method differs from the Nelder Mead constrained nonlinear optimization method [73]. 39 the Non-dominated Sorting Genetic Algorithm...Kober, and Jan Peters. Model-free inverse reinforcement learning. In International Conference on Artificial Intelligence and Statistics, 2011. [12] George

Fitting Nonlinear Curves by use of Optimization Techniques

NASA Technical Reports Server (NTRS)

Hill, Scott A.

2005-01-01

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Local pursuit strategy-inspired cooperative trajectory planning algorithm for a class of nonlinear constrained dynamical systems

NASA Astrophysics Data System (ADS)

Xu, Yunjun; Remeikas, Charles; Pham, Khanh

2014-03-01

Cooperative trajectory planning is crucial for networked vehicles to respond rapidly in cluttered environments and has a significant impact on many applications such as air traffic or border security monitoring and assessment. One of the challenges in cooperative planning is to find a computationally efficient algorithm that can accommodate both the complexity of the environment and real hardware and configuration constraints of vehicles in the formation. Inspired by a local pursuit strategy observed in foraging ants, feasible and optimal trajectory planning algorithms are proposed in this paper for a class of nonlinear constrained cooperative vehicles in environments with densely populated obstacles. In an iterative hierarchical approach, the local behaviours, such as the formation stability, obstacle avoidance, and individual vehicle's constraints, are considered in each vehicle's (i.e. follower's) decentralised optimisation. The cooperative-level behaviours, such as the inter-vehicle collision avoidance, are considered in the virtual leader's centralised optimisation. Early termination conditions are derived to reduce the computational cost by not wasting time in the local-level optimisation if the virtual leader trajectory does not satisfy those conditions. The expected advantages of the proposed algorithms are (1) the formation can be globally asymptotically maintained in a decentralised manner; (2) each vehicle decides its local trajectory using only the virtual leader and its own information; (3) the formation convergence speed is controlled by one single parameter, which makes it attractive for many practical applications; (4) nonlinear dynamics and many realistic constraints, such as the speed limitation and obstacle avoidance, can be easily considered; (5) inter-vehicle collision avoidance can be guaranteed in both the formation transient stage and the formation steady stage; and (6) the computational cost in finding both the feasible and optimal solutions is low. In particular, the feasible solution can be computed in a very quick fashion. The minimum energy trajectory planning for a group of robots in an obstacle-laden environment is simulated to showcase the advantages of the proposed algorithms.

Complex motion measurement using genetic algorithm

NASA Astrophysics Data System (ADS)

Shen, Jianjun; Tu, Dan; Shen, Zhenkang

1997-12-01

Genetic algorithm (GA) is an optimization technique that provides an untraditional approach to deal with many nonlinear, complicated problems. The notion of motion measurement using genetic algorithm arises from the fact that the motion measurement is virtually an optimization process based on some criterions. In the paper, we propose a complex motion measurement method using genetic algorithm based on block-matching criterion. The following three problems are mainly discussed and solved in the paper: (1) apply an adaptive method to modify the control parameters of GA that are critical to itself, and offer an elitism strategy at the same time (2) derive an evaluate function of motion measurement for GA based on block-matching technique (3) employ hill-climbing (HC) method hybridly to assist GA's search for the global optimal solution. Some other related problems are also discussed. At the end of paper, experiments result is listed. We employ six motion parameters for measurement in our experiments. Experiments result shows that the performance of our GA is good. The GA can find the object motion accurately and rapidly.

Progress report on PIXIE3D, a fully implicit 3D extended MHD solver

NASA Astrophysics Data System (ADS)

Chacon, Luis

2008-11-01

Recently, invited talk at DPP07 an optimal, massively parallel implicit algorithm for 3D resistive magnetohydrodynamics (PIXIE3D) was demonstrated. Excellent algorithmic and parallel results were obtained with up to 4096 processors and 138 million unknowns. While this is a remarkable result, further developments are still needed for PIXIE3D to become a 3D extended MHD production code in general geometries. In this poster, we present an update on the status of PIXIE3D on several fronts. On the physics side, we will describe our progress towards the full Braginskii model, including: electron Hall terms, anisotropic heat conduction, and gyroviscous corrections. Algorithmically, we will discuss progress towards a robust, optimal, nonlinear solver for arbitrary geometries, including preconditioning for the new physical effects described, the implementation of a coarse processor-grid solver (to maintain optimal algorithmic performance for an arbitrarily large number of processors in massively parallel computations), and of a multiblock capability to deal with complicated geometries. L. Chac'on, Phys. Plasmas 15, 056103 (2008);

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

NASA Technical Reports Server (NTRS)

Wilson, Jeffrey D.; Bulson, Brian A.; Kory, Carol L.; Williams, W. Dan (Technical Monitor)

2001-01-01

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Correction method for stripe nonuniformity.

PubMed

Qian, Weixian; Chen, Qian; Gu, Guohua; Guan, Zhiqiang

2010-04-01

Stripe nonuniformity is very typical in line infrared focal plane arrays (IR-FPA) and uncooled staring IR-FPA. In this paper, the mechanism of the stripe nonuniformity is analyzed, and the gray-scale co-occurrence matrix theory and optimization theory are studied. Through these efforts, the stripe nonuniformity correction problem is translated into the optimization problem. The goal of the optimization is to find the minimal energy of the image's line gradient. After solving the constrained nonlinear optimization equation, the parameters of the stripe nonuniformity correction are obtained and the stripe nonuniformity correction is achieved. The experiments indicate that this algorithm is effective and efficient.

SOM neural network fault diagnosis method of polymerization kettle equipment optimized by improved PSO algorithm.

PubMed

Wang, Jie-sheng; Li, Shu-xia; Gao, Jie

2014-01-01

For meeting the real-time fault diagnosis and the optimization monitoring requirements of the polymerization kettle in the polyvinyl chloride resin (PVC) production process, a fault diagnosis strategy based on the self-organizing map (SOM) neural network is proposed. Firstly, a mapping between the polymerization process data and the fault pattern is established by analyzing the production technology of polymerization kettle equipment. The particle swarm optimization (PSO) algorithm with a new dynamical adjustment method of inertial weights is adopted to optimize the structural parameters of SOM neural network. The fault pattern classification of the polymerization kettle equipment is to realize the nonlinear mapping from symptom set to fault set according to the given symptom set. Finally, the simulation experiments of fault diagnosis are conducted by combining with the industrial on-site historical data of the polymerization kettle and the simulation results show that the proposed PSO-SOM fault diagnosis strategy is effective.

Autorotation flight control system

NASA Technical Reports Server (NTRS)

Bachelder, Edward N. (Inventor); Aponso, Bimal L. (Inventor); Lee, Dong-Chan (Inventor)

2011-01-01

The present invention provides computer implemented methodology that permits the safe landing and recovery of rotorcraft following engine failure. With this invention successful autorotations may be performed from well within the unsafe operating area of the height-velocity profile of a helicopter by employing the fast and robust real-time trajectory optimization algorithm that commands control motion through an intuitive pilot display, or directly in the case of autonomous rotorcraft. The algorithm generates optimal trajectories and control commands via the direct-collocation optimization method, solved using a nonlinear programming problem solver. The control inputs computed are collective pitch and aircraft pitch, which are easily tracked and manipulated by the pilot or converted to control actuator commands for automated operation during autorotation in the case of an autonomous rotorcraft. The formulation of the optimal control problem has been carefully tailored so the solutions resemble those of an expert pilot, accounting for the performance limitations of the rotorcraft and safety concerns.

Dikin-type algorithms for dextrous grasping force optimization

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

Buss, M.; Faybusovich, L.; Moore, J.B.

1998-08-01

One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp stability and minimum grasping effort. A companion paper shows that the nonlinear friction-force limit constraints on grasping forces are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Further, compensation of the external object force is also a linear constraint on this matrix. Consequently, the task of grasping force optimization can be formulated as a problem with semidefinite constraints. In this paper, two versions of strictly convex cost functions, onemore » of them self-concordant, are considered. These are twice-continuously differentiable functions that tend to infinity at the boundary of possible definiteness. For the general class of such cost functions, Dikin-type algorithms are presented. It is shown that the proposed algorithms guarantee convergence to the unique solution of the semidefinite programming problem associated with dextrous grasping force optimization. Numerical examples demonstrate the simplicity of implementation, the good numerical properties, and the optimality of the approach.« less

On the optimization of electromagnetic geophysical data: Application of the PSO algorithm

NASA Astrophysics Data System (ADS)

Godio, A.; Santilano, A.

2018-01-01

Particle Swarm optimization (PSO) algorithm resolves constrained multi-parameter problems and is suitable for simultaneous optimization of linear and nonlinear problems, with the assumption that forward modeling is based on good understanding of ill-posed problem for geophysical inversion. We apply PSO for solving the geophysical inverse problem to infer an Earth model, i.e. the electrical resistivity at depth, consistent with the observed geophysical data. The method doesn't require an initial model and can be easily constrained, according to external information for each single sounding. The optimization process to estimate the model parameters from the electromagnetic soundings focuses on the discussion of the objective function to be minimized. We discuss the possibility to introduce in the objective function vertical and lateral constraints, with an Occam-like regularization. A sensitivity analysis allowed us to check the performance of the algorithm. The reliability of the approach is tested on synthetic, real Audio-Magnetotelluric (AMT) and Long Period MT data. The method appears able to solve complex problems and allows us to estimate the a posteriori distribution of the model parameters.

A method for obtaining reduced-order control laws for high-order systems using optimization techniques

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.; Abel, I.

1981-01-01

A method of synthesizing reduced-order optimal feedback control laws for a high-order system is developed. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean-square steady-state responses and control inputs. An analogy with the linear quadractic Gaussian solution is utilized to select a set of design variables and their initial values. To improve the stability margins of the system, an input-noise adjustment procedure is used in the design algorithm. The method is applied to the synthesis of an active flutter-suppression control law for a wind tunnel model of an aeroelastic wing. The reduced-order controller is compared with the corresponding full-order controller and found to provide nearly optimal performance. The performance of the present method appeared to be superior to that of two other control law order-reduction methods. It is concluded that by using the present algorithm, nearly optimal low-order control laws with good stability margins can be synthesized.

Evolutionary and biological metaphors for engineering design

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

Jakiela, M.

1994-12-31

Since computing became generally available, there has been strong interest in using computers to assist and automate engineering design processes. Specifically, for design optimization and automation, nonlinear programming and artificial intelligence techniques have been extensively studied. New computational techniques, based upon the natural processes of evolution, adaptation, and learing, are showing promise because of their generality and robustness. This presentation will describe the use of two such techniques, genetic algorithms and classifier systems, for a variety of engineering design problems. Structural topology optimization, meshing, and general engineering optimization are shown as example applications.

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

Path Planning Algorithms for Autonomous Border Patrol Vehicles

NASA Astrophysics Data System (ADS)

Lau, George Tin Lam

This thesis presents an online path planning algorithm developed for unmanned vehicles in charge of autonomous border patrol. In this Pursuit-Evasion game, the unmanned vehicle is required to capture multiple trespassers on its own before any of them reach a target safe house where they are safe from capture. The problem formulation is based on Isaacs' Target Guarding problem, but extended to the case of multiple evaders. The proposed path planning method is based on Rapidly-exploring random trees (RRT) and is capable of producing trajectories within several seconds to capture 2 or 3 evaders. Simulations are carried out to demonstrate that the resulting trajectories approach the optimal solution produced by a nonlinear programming-based numerical optimal control solver. Experiments are also conducted on unmanned ground vehicles to show the feasibility of implementing the proposed online path planning algorithm on physical applications.

Artificial neural network - Genetic algorithm to optimize wheat germ fermentation condition: Application to the production of two anti-tumor benzoquinones.

PubMed

Zheng, Zi-Yi; Guo, Xiao-Na; Zhu, Ke-Xue; Peng, Wei; Zhou, Hui-Ming

2017-07-15

Methoxy-ρ-benzoquinone (MBQ) and 2, 6-dimethoxy-ρ-benzoquinone (DMBQ) are two potential anticancer compounds in fermented wheat germ. In present study, modeling and optimization of added macronutrients, microelements, vitamins for producing MBQ and DMBQ was investigated using artificial neural network (ANN) combined with genetic algorithm (GA). A configuration of 16-11-1 ANN model with Levenberg-Marquardt training algorithm was applied for modeling the complicated nonlinear interactions among 16 nutrients in fermentation process. Under the guidance of optimized scheme, the total contents of MBQ and DMBQ was improved by 117% compared with that in the control group. Further, by evaluating the relative importance of each nutrient in terms of the two benzoquinones' yield, macronutrients and microelements were found to have a greater influence than most of vitamins. It was also observed that a number of interactions between nutrients affected the yield of MBQ and DMBQ remarkably. Copyright © 2017 Elsevier Ltd. All rights reserved.

Non-Linear Optimization Applied to Angle-of-Arrival Satellite-Based Geolocation with Correlated Measurements

DTIC Science & Technology

2015-03-01

General covariance intersection covariance matrix Σ1 Measurement 1’s covariance matrix I(X) Fisher information matrix g Confidence region L Lower... information in this chapter will discuss the motivation and background of the geolocation algorithm with the scope of the applications for this research. The...algorithm is able to produce the best description of an object given the information from a set of measurements. Determining a position requires the use of a

A new adaptive multiple modelling approach for non-linear and non-stationary systems

NASA Astrophysics Data System (ADS)

Chen, Hao; Gong, Yu; Hong, Xia

2016-07-01

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Optimization of groundwater artificial recharge systems using a genetic algorithm: a case study in Beijing, China

NASA Astrophysics Data System (ADS)

Hao, Qichen; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Huang, Linxian

2018-05-01

An optimization approach is used for the operation of groundwater artificial recharge systems in an alluvial fan in Beijing, China. The optimization model incorporates a transient groundwater flow model, which allows for simulation of the groundwater response to artificial recharge. The facilities' operation with regard to recharge rates is formulated as a nonlinear programming problem to maximize the volume of surface water recharged into the aquifers under specific constraints. This optimization problem is solved by the parallel genetic algorithm (PGA) based on OpenMP, which could substantially reduce the computation time. To solve the PGA with constraints, the multiplicative penalty method is applied. In addition, the facilities' locations are implicitly determined on the basis of the results of the recharge-rate optimizations. Two scenarios are optimized and the optimal results indicate that the amount of water recharged into the aquifers will increase without exceeding the upper limits of the groundwater levels. Optimal operation of this artificial recharge system can also contribute to the more effective recovery of the groundwater storage capacity.

DAKOTA Design Analysis Kit for Optimization and Terascale

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

Adams, Brian M.; Dalbey, Keith R.; Eldred, Michael S.

2010-02-24

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes (computational models) and iterative analysis methods. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and analysis of computational models on high performance computers.A user provides a set of DAKOTA commands in an input file and launches DAKOTA. DAKOTA invokes instances of the computational models, collects their results, and performs systems analyses. DAKOTA contains algorithms for optimization with gradient and nongradient-basedmore » methods; uncertainty quantification with sampling, reliability, polynomial chaos, stochastic collocation, and epistemic methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as hybrid optimization, surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. Services for parallel computing, simulation interfacing, approximation modeling, fault tolerance, restart, and graphics are also included.« less

Single neural adaptive controller and neural network identifier based on PSO algorithm for spherical actuators with 3D magnet array

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Lu; Zhu, Bo; Zhang, Jingying; Jiao, Zongxia

2017-10-01

Permanent magnet spherical actuator (PMSA) is a multi-variable featured and inter-axis coupled nonlinear system, which unavoidably compromises its motion control implementation. Uncertainties such as external load and friction torque of ball bearing and manufacturing errors also influence motion performance significantly. Therefore, the objective of this paper is to propose a controller based on a single neural adaptive (SNA) algorithm and a neural network (NN) identifier optimized with a particle swarm optimization (PSO) algorithm to improve the motion stability of PMSA with three-dimensional magnet arrays. The dynamic model and computed torque model are formulated for the spherical actuator, and a dynamic decoupling control algorithm is developed. By utilizing the global-optimization property of the PSO algorithm, the NN identifier is trained to avoid locally optimal solution and achieve high-precision compensations to uncertainties. The employment of the SNA controller helps to reduce the effect of compensation errors and convert the system to a stable one, even if there is difference between the compensations and uncertainties due to external disturbances. A simulation model is established, and experiments are conducted on the research prototype to validate the proposed control algorithm. The amplitude of the parameter perturbation is set to 5%, 10%, and 15%, respectively. The strong robustness of the proposed hybrid algorithm is validated by the abundant simulation data. It shows that the proposed algorithm can effectively compensate the influence of uncertainties and eliminate the effect of inter-axis couplings of the spherical actuator.

Model-based setting of inspiratory pressure and respiratory rate in pressure-controlled ventilation.

PubMed

Schranz, C; Becher, T; Schädler, D; Weiler, N; Möller, K

2014-03-01

Mechanical ventilation carries the risk of ventilator-induced-lung-injury (VILI). To minimize the risk of VILI, ventilator settings should be adapted to the individual patient properties. Mathematical models of respiratory mechanics are able to capture the individual physiological condition and can be used to derive personalized ventilator settings. This paper presents model-based calculations of inspiration pressure (pI), inspiration and expiration time (tI, tE) in pressure-controlled ventilation (PCV) and a retrospective evaluation of its results in a group of mechanically ventilated patients. Incorporating the identified first order model of respiratory mechanics in the basic equation of alveolar ventilation yielded a nonlinear relation between ventilation parameters during PCV. Given this patient-specific relation, optimized settings in terms of minimal pI and adequate tE can be obtained. We then retrospectively analyzed data from 16 ICU patients with mixed pathologies, whose ventilation had been previously optimized by ICU physicians with the goal of minimization of inspiration pressure, and compared the algorithm's 'optimized' settings to the settings that had been chosen by the physicians. The presented algorithm visualizes the patient-specific relations between inspiration pressure and inspiration time. The algorithm's calculated results highly correlate to the physician's ventilation settings with r = 0.975 for the inspiration pressure, and r = 0.902 for the inspiration time. The nonlinear patient-specific relations of ventilation parameters become transparent and support the determination of individualized ventilator settings according to therapeutic goals. Thus, the algorithm is feasible for a variety of ventilated ICU patients and has the potential of improving lung-protective ventilation by minimizing inspiratory pressures and by helping to avoid the build-up of clinically significant intrinsic positive end-expiratory pressure.

Intelligent emissions controller for substance injection in the post-primary combustion zone of fossil-fired boilers

DOEpatents

Reifman, Jaques; Feldman, Earl E.; Wei, Thomas Y. C.; Glickert, Roger W.

2003-01-01

The control of emissions from fossil-fired boilers wherein an injection of substances above the primary combustion zone employs multi-layer feedforward artificial neural networks for modeling static nonlinear relationships between the distribution of injected substances into the upper region of the furnace and the emissions exiting the furnace. Multivariable nonlinear constrained optimization algorithms use the mathematical expressions from the artificial neural networks to provide the optimal substance distribution that minimizes emission levels for a given total substance injection rate. Based upon the optimal operating conditions from the optimization algorithms, the incremental substance cost per unit of emissions reduction, and the open-market price per unit of emissions reduction, the intelligent emissions controller allows for the determination of whether it is more cost-effective to achieve additional increments in emission reduction through the injection of additional substance or through the purchase of emission credits on the open market. This is of particular interest to fossil-fired electrical power plant operators. The intelligent emission controller is particularly adapted for determining the economical control of such pollutants as oxides of nitrogen (NO.sub.x) and carbon monoxide (CO) emitted by fossil-fired boilers by the selective introduction of multiple inputs of substances (such as natural gas, ammonia, oil, water-oil emulsion, coal-water slurry and/or urea, and combinations of these substances) above the primary combustion zone of fossil-fired boilers.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems.

PubMed

Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan

2015-01-01

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

Aerospace Structures Design on Computers

DTIC Science & Technology

1989-03-01

loud or lter’itr- strm C M~eort load or mex~murn load AMeon strews o,. strvss (Q) hm’nur loS1 (b) me -im (a) Fluctuating tension load cycle; (b...constraint deletion techniques in the struc- tural applications of nonlinear programming algorithms. The way this concept is used in the optimality criteria

Newton Methods for Large Scale Problems in Machine Learning

ERIC Educational Resources Information Center

Hansen, Samantha Leigh

2014-01-01

The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…

Out-of-Focus Projector Calibration Method with Distortion Correction on the Projection Plane in the Structured Light Three-Dimensional Measurement System.

PubMed

Zhang, Jiarui; Zhang, Yingjie; Chen, Bo

2017-12-20

The three-dimensional measurement system with a binary defocusing technique is widely applied in diverse fields. The measurement accuracy is mainly determined by out-of-focus projector calibration accuracy. In this paper, a high-precision out-of-focus projector calibration method that is based on distortion correction on the projection plane and nonlinear optimization algorithm is proposed. To this end, the paper experimentally presents the principle that the projector has noticeable distortions outside its focus plane. In terms of this principle, the proposed method uses a high-order radial and tangential lens distortion representation on the projection plane to correct the calibration residuals caused by projection distortion. The final accuracy parameters of out-of-focus projector were obtained using a nonlinear optimization algorithm with good initial values, which were provided by coarsely calibrating the parameters of the out-of-focus projector on the focal and projection planes. Finally, the experimental results demonstrated that the proposed method can accuracy calibrate an out-of-focus projector, regardless of the amount of defocusing.

An intelligent fault diagnosis method of rolling bearings based on regularized kernel Marginal Fisher analysis

NASA Astrophysics Data System (ADS)

Jiang, Li; Shi, Tielin; Xuan, Jianping

2012-05-01

Generally, the vibration signals of fault bearings are non-stationary and highly nonlinear under complicated operating conditions. Thus, it's a big challenge to extract optimal features for improving classification and simultaneously decreasing feature dimension. Kernel Marginal Fisher analysis (KMFA) is a novel supervised manifold learning algorithm for feature extraction and dimensionality reduction. In order to avoid the small sample size problem in KMFA, we propose regularized KMFA (RKMFA). A simple and efficient intelligent fault diagnosis method based on RKMFA is put forward and applied to fault recognition of rolling bearings. So as to directly excavate nonlinear features from the original high-dimensional vibration signals, RKMFA constructs two graphs describing the intra-class compactness and the inter-class separability, by combining traditional manifold learning algorithm with fisher criteria. Therefore, the optimal low-dimensional features are obtained for better classification and finally fed into the simplest K-nearest neighbor (KNN) classifier to recognize different fault categories of bearings. The experimental results demonstrate that the proposed approach improves the fault classification performance and outperforms the other conventional approaches.

Distributed Event-Based Set-Membership Filtering for a Class of Nonlinear Systems With Sensor Saturations Over Sensor Networks.

PubMed

Ma, Lifeng; Wang, Zidong; Lam, Hak-Keung; Kyriakoulis, Nikos

2017-11-01

In this paper, the distributed set-membership filtering problem is investigated for a class of discrete time-varying system with an event-based communication mechanism over sensor networks. The system under consideration is subject to sector-bounded nonlinearity, unknown but bounded noises and sensor saturations. Each intelligent sensing node transmits the data to its neighbors only when certain triggering condition is violated. By means of a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired distributed event-based filter which is capable of confining the system state in certain ellipsoidal regions centered at the estimates. Within the established theoretical framework, two additional optimization problems are formulated: one is to seek the minimal ellipsoids (in the sense of matrix trace) for the best filtering performance, and the other is to maximize the triggering threshold so as to reduce the triggering frequency with satisfactory filtering performance. A numerically attractive chaos algorithm is employed to solve the optimization problems. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed algorithm.

A nonlinear H-infinity approach to optimal control of the depth of anaesthesia

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Rigatou, Efthymia; Zervos, Nikolaos

2016-12-01

Controlling the level of anaesthesia is important for improving the success rate of surgeries and for reducing the risks to which operated patients are exposed. This paper proposes a nonlinear H-infinity approach to optimal control of the level of anaesthesia. The dynamic model of the anaesthesia, which describes the concentration of the anaesthetic drug in different parts of the body, is subjected to linearization at local operating points. These are defined at each iteration of the control algorithm and consist of the present value of the system's state vector and of the last control input that was exerted on it. For this linearization Taylor series expansion is performed and the system's Jacobian matrices are computed. For the linearized model an H-infinity controller is designed. The feedback control gains are found by solving at each iteration of the control algorithm an algebraic Riccati equation. The modelling errors due to this approximate linearization are considered as disturbances which are compensated by the robustness of the control loop. The stability of the control loop is confirmed through Lyapunov analysis.

On the utilization of engineering knowledge in design optimization

NASA Technical Reports Server (NTRS)

Papalambros, P.

1984-01-01

Some current research work conducted at the University of Michigan is described to illustrate efforts for incorporating knowledge in optimization in a nontraditional way. The incorporation of available knowledge in a logic structure is examined in two circumstances. The first examines the possibility of introducing global design information in a local active set strategy implemented during the iterations of projection-type algorithms for nonlinearly constrained problems. The technique used algorithms for nonlinearly constrained problems. The technique used combines global and local monotinicity analysis of the objective and constraint functions. The second examines a knowledge-based program which aids the user to create condigurations that are most desirable from the manufacturing assembly viewpoint. The data bank used is the classification scheme suggested by Boothroyd. The important aspect of this program is that it is an aid for synthesis intended for use in the design concept phase in a way similar to the so-called idea-triggers in creativity-enhancement techniques like brain-storming. The idea generation, however, is not random but it is driven by the goal of achieving the best acceptable configuration.

Performance Assessment of Model-Based Optimal Feedforward and Feedback Current Profile Control in NSTX-U using the TRANSP Code

NASA Astrophysics Data System (ADS)

Ilhan, Z.; Wehner, W. P.; Schuster, E.; Boyer, M. D.; Gates, D. A.; Gerhardt, S.; Menard, J.

2015-11-01

Active control of the toroidal current density profile is crucial to achieve and maintain high-performance, MHD-stable plasma operation in NSTX-U. A first-principles-driven, control-oriented model describing the temporal evolution of the current profile has been proposed earlier by combining the magnetic diffusion equation with empirical correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives. A feedforward + feedback control scheme for the requlation of the current profile is constructed by embedding the proposed nonlinear, physics-based model into the control design process. Firstly, nonlinear optimization techniques are used to design feedforward actuator trajectories that steer the plasma to a desired operating state with the objective of supporting the traditional trial-and-error experimental process of advanced scenario planning. Secondly, a feedback control algorithm to track a desired current profile evolution is developed with the goal of adding robustness to the overall control scheme. The effectiveness of the combined feedforward + feedback control algorithm for current profile regulation is tested in predictive simulations carried out in TRANSP. Supported by PPPL.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

NASA Technical Reports Server (NTRS)

Starlinger, Alois; Duffy, Stephen F.; Palko, Joseph L.

1993-01-01

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

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.

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

NASA Astrophysics Data System (ADS)

Sembiring, Pasukat

2017-12-01

Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

Neural Generalized Predictive Control: A Newton-Raphson Implementation

NASA Technical Reports Server (NTRS)

Soloway, Donald; Haley, Pamela J.

1997-01-01

An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

NASA Astrophysics Data System (ADS)

Yang, Jian; Yang, Feng; Xi, Hong-Sheng; Guo, Wei; Sheng, Yanmin

2007-12-01

We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.

Volumetric three-dimensional intravascular ultrasound visualization using shape-based nonlinear interpolation

PubMed Central

2013-01-01

Background Intravascular ultrasound (IVUS) is a standard imaging modality for identification of plaque formation in the coronary and peripheral arteries. Volumetric three-dimensional (3D) IVUS visualization provides a powerful tool to overcome the limited comprehensive information of 2D IVUS in terms of complex spatial distribution of arterial morphology and acoustic backscatter information. Conventional 3D IVUS techniques provide sub-optimal visualization of arterial morphology or lack acoustic information concerning arterial structure due in part to low quality of image data and the use of pixel-based IVUS image reconstruction algorithms. In the present study, we describe a novel volumetric 3D IVUS reconstruction algorithm to utilize IVUS signal data and a shape-based nonlinear interpolation. Methods We developed an algorithm to convert a series of IVUS signal data into a fully volumetric 3D visualization. Intermediary slices between original 2D IVUS slices were generated utilizing the natural cubic spline interpolation to consider the nonlinearity of both vascular structure geometry and acoustic backscatter in the arterial wall. We evaluated differences in image quality between the conventional pixel-based interpolation and the shape-based nonlinear interpolation methods using both virtual vascular phantom data and in vivo IVUS data of a porcine femoral artery. Volumetric 3D IVUS images of the arterial segment reconstructed using the two interpolation methods were compared. Results In vitro validation and in vivo comparative studies with the conventional pixel-based interpolation method demonstrated more robustness of the shape-based nonlinear interpolation algorithm in determining intermediary 2D IVUS slices. Our shape-based nonlinear interpolation demonstrated improved volumetric 3D visualization of the in vivo arterial structure and more realistic acoustic backscatter distribution compared to the conventional pixel-based interpolation method. Conclusions This novel 3D IVUS visualization strategy has the potential to improve ultrasound imaging of vascular structure information, particularly atheroma determination. Improved volumetric 3D visualization with accurate acoustic backscatter information can help with ultrasound molecular imaging of atheroma component distribution. PMID:23651569

Scheduled Relaxation Jacobi method: Improvements and applications

NASA Astrophysics Data System (ADS)

Adsuara, J. E.; Cordero-Carrión, I.; Cerdá-Durán, P.; Aloy, M. A.

2016-09-01

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 215 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.

A comparison of optimization algorithms for localized in vivo B0 shimming.

PubMed

Nassirpour, Sahar; Chang, Paul; Fillmer, Ariane; Henning, Anke

2018-02-01

To compare several different optimization algorithms currently used for localized in vivo B 0 shimming, and to introduce a novel, fast, and robust constrained regularized algorithm (ConsTru) for this purpose. Ten different optimization algorithms (including samples from both generic and dedicated least-squares solvers, and a novel constrained regularized inversion method) were implemented and compared for shimming in five different shimming volumes on 66 in vivo data sets from both 7 T and 9.4 T. The best algorithm was chosen to perform single-voxel spectroscopy at 9.4 T in the frontal cortex of the brain on 10 volunteers. The results of the performance tests proved that the shimming algorithm is prone to unstable solutions if it depends on the value of a starting point, and is not regularized to handle ill-conditioned problems. The ConsTru algorithm proved to be the most robust, fast, and efficient algorithm among all of the chosen algorithms. It enabled acquisition of spectra of reproducible high quality in the frontal cortex at 9.4 T. For localized in vivo B 0 shimming, the use of a dedicated linear least-squares solver instead of a generic nonlinear one is highly recommended. Among all of the linear solvers, the constrained regularized method (ConsTru) was found to be both fast and most robust. Magn Reson Med 79:1145-1156, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Adaptive photoacoustic imaging quality optimization with EMD and reconstruction

NASA Astrophysics Data System (ADS)

Guo, Chengwen; Ding, Yao; Yuan, Jie; Xu, Guan; Wang, Xueding; Carson, Paul L.

2016-10-01

Biomedical photoacoustic (PA) signal is characterized with extremely low signal to noise ratio which will yield significant artifacts in photoacoustic tomography (PAT) images. Since PA signals acquired by ultrasound transducers are non-linear and non-stationary, traditional data analysis methods such as Fourier and wavelet method cannot give useful information for further research. In this paper, we introduce an adaptive method to improve the quality of PA imaging based on empirical mode decomposition (EMD) and reconstruction. Data acquired by ultrasound transducers are adaptively decomposed into several intrinsic mode functions (IMFs) after a sifting pre-process. Since noise is randomly distributed in different IMFs, depressing IMFs with more noise while enhancing IMFs with less noise can effectively enhance the quality of reconstructed PAT images. However, searching optimal parameters by means of brute force searching algorithms will cost too much time, which prevent this method from practical use. To find parameters within reasonable time, heuristic algorithms, which are designed for finding good solutions more efficiently when traditional methods are too slow, are adopted in our method. Two of the heuristic algorithms, Simulated Annealing Algorithm, a probabilistic method to approximate the global optimal solution, and Artificial Bee Colony Algorithm, an optimization method inspired by the foraging behavior of bee swarm, are selected to search optimal parameters of IMFs in this paper. The effectiveness of our proposed method is proved both on simulated data and PA signals from real biomedical tissue, which might bear the potential for future clinical PA imaging de-noising.

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

Joint Inversion of Geochemical Data and Geophysical Logs for Lithology Identification in CCSD Main Hole

NASA Astrophysics Data System (ADS)

Deng, Chengxiang; Pan, Heping; Luo, Miao

2017-12-01

The Chinese Continental Scientific Drilling (CCSD) main hole is located in the Sulu ultrahigh-pressure metamorphic (UHPM) belt, providing significant opportunities for studying the metamorphic strata structure, kinetics process and tectonic evolution. Lithology identification is the primary and crucial stage for above geoscientific researches. To release the burden of log analyst and improve the efficiency of lithology interpretation, many algorithms have been developed to automate the process of lithology prediction. While traditional statistical techniques, such as discriminant analysis and K-nearest neighbors classifier, are incompetent in extracting nonlinear features of metamorphic rocks from complex geophysical log data; artificial intelligence algorithms are capable of solving nonlinear problems, but most of the algorithms suffer from tuning parameters to be global optimum to establish model rather than local optimum, and also encounter challenges in making the balance between training accuracy and generalization ability. Optimization methods have been applied extensively in the inversion of reservoir parameters of sedimentary formations using well logs. However, it is difficult to obtain accurate solution from the logging response equations of optimization method because of the strong overlapping of nonstationary log signals when applied in metamorphic formations. As oxide contents of each kinds of metamorphic rocks are relatively less overlapping, this study explores an approach, set in a metamorphic formation model and using the Broyden Fletcher Goldfarb Shanno (BFGS) optimization algorithm to identify lithology from oxide data. We first incorporate 11 geophysical logs and lab-collected geochemical data of 47 core samples to construct oxide profile of CCSD main hole by using backwards stepwise multiple regression method, which eliminates irrelevant input logs step by step for higher statistical significance and accuracy. Then we establish oxide response equations in accordance with the metamorphic formation model and employ BFGS algorithm to minimize the objective function. Finally, we identify lithology according to the composition content which accounts for the largest proportion. The results show that lithology identified by the method of this paper is consistent with core description. Moreover, this method demonstrates the benefits of using oxide content as an adhesive to connect logging data with lithology, can make the metamorphic formation model more understandable and accurate, and avoid selecting complex formation model and building nonlinear logging response equations.

A Simulation-Optimization Model for the Management of Seawater Intrusion

NASA Astrophysics Data System (ADS)

Stanko, Z.; Nishikawa, T.

2012-12-01

Seawater intrusion is a common problem in coastal aquifers where excessive groundwater pumping can lead to chloride contamination of a freshwater resource. Simulation-optimization techniques have been developed to determine optimal management strategies while mitigating seawater intrusion. The simulation models are often density-independent groundwater-flow models that may assume a sharp interface and/or use equivalent freshwater heads. The optimization methods are often linear-programming (LP) based techniques that that require simplifications of the real-world system. However, seawater intrusion is a highly nonlinear, density-dependent flow and transport problem, which requires the use of nonlinear-programming (NLP) or global-optimization (GO) techniques. NLP approaches are difficult because of the need for gradient information; therefore, we have chosen a GO technique for this study. Specifically, we have coupled a multi-objective genetic algorithm (GA) with a density-dependent groundwater-flow and transport model to simulate and identify strategies that optimally manage seawater intrusion. GA is a heuristic approach, often chosen when seeking optimal solutions to highly complex and nonlinear problems where LP or NLP methods cannot be applied. The GA utilized in this study is the Epsilon-Nondominated Sorted Genetic Algorithm II (ɛ-NSGAII), which can approximate a pareto-optimal front between competing objectives. This algorithm has several key features: real and/or binary variable capabilities; an efficient sorting scheme; preservation and diversity of good solutions; dynamic population sizing; constraint handling; parallelizable implementation; and user controlled precision for each objective. The simulation model is SEAWAT, the USGS model that couples MODFLOW with MT3DMS for variable-density flow and transport. ɛ-NSGAII and SEAWAT were efficiently linked together through a C-Fortran interface. The simulation-optimization model was first tested by using a published density-independent flow model test case that was originally solved using a sequential LP method with the USGS's Ground-Water Management Process (GWM). For the problem formulation, the objective is to maximize net groundwater extraction, subject to head and head-gradient constraints. The decision variables are pumping rates at fixed wells and the system's state is represented with freshwater hydraulic head. The results of the proposed algorithm were similar to the published results (within 1%); discrepancies may be attributed to differences in the simulators and inherent differences between LP and GA. The GWM test case was then extended to a density-dependent flow and transport version. As formulated, the optimization problem is infeasible because of the density effects on hydraulic head. Therefore, the sum of the squared constraint violation (SSC) was used as a second objective. The result is a pareto curve showing optimal pumping rates versus the SSC. Analysis of this curve indicates that a similar net-extraction rate to the test case can be obtained with a minor violation in vertical head-gradient constraints. This study shows that a coupled ɛ-NSGAII/SEAWAT model can be used for the management of groundwater seawater intrusion. In the future, the proposed methodology will be applied to a real-world seawater intrusion and resource management problem for Santa Barbara, CA.

Can we do better than the grid survey: Optimal synoptic surveys in presence of variable uncertainty and decorrelation scales

NASA Astrophysics Data System (ADS)

Frolov, Sergey; Garau, Bartolame; Bellingham, James

2014-08-01

Regular grid ("lawnmower") survey is a classical strategy for synoptic sampling of the ocean. Is it possible to achieve a more effective use of available resources if one takes into account a priori knowledge about variability in magnitudes of uncertainty and decorrelation scales? In this article, we develop and compare the performance of several path-planning algorithms: optimized "lawnmower," a graph-search algorithm (A*), and a fully nonlinear genetic algorithm. We use the machinery of the best linear unbiased estimator (BLUE) to quantify the ability of a vehicle fleet to synoptically map distribution of phytoplankton off the central California coast. We used satellite and in situ data to specify covariance information required by the BLUE estimator. Computational experiments showed that two types of sampling strategies are possible: a suboptimal space-filling design (produced by the "lawnmower" and the A* algorithms) and an optimal uncertainty-aware design (produced by the genetic algorithm). Unlike the space-filling designs that attempted to cover the entire survey area, the optimal design focused on revisiting areas of high uncertainty. Results of the multivehicle experiments showed that fleet performance predictors, such as cumulative speed or the weight of the fleet, predicted the performance of a homogeneous fleet well; however, these were poor predictors for comparing the performance of different platforms.

Effective and extensible feature extraction method using genetic algorithm-based frequency-domain feature search for epileptic EEG multiclassification

PubMed Central

Wen, Tingxi; Zhang, Zhongnan

2017-01-01

Abstract In this paper, genetic algorithm-based frequency-domain feature search (GAFDS) method is proposed for the electroencephalogram (EEG) analysis of epilepsy. In this method, frequency-domain features are first searched and then combined with nonlinear features. Subsequently, these features are selected and optimized to classify EEG signals. The extracted features are analyzed experimentally. The features extracted by GAFDS show remarkable independence, and they are superior to the nonlinear features in terms of the ratio of interclass distance and intraclass distance. Moreover, the proposed feature search method can search for features of instantaneous frequency in a signal after Hilbert transformation. The classification results achieved using these features are reasonable; thus, GAFDS exhibits good extensibility. Multiple classical classifiers (i.e., k-nearest neighbor, linear discriminant analysis, decision tree, AdaBoost, multilayer perceptron, and Naïve Bayes) achieve satisfactory classification accuracies by using the features generated by the GAFDS method and the optimized feature selection. The accuracies for 2-classification and 3-classification problems may reach up to 99% and 97%, respectively. Results of several cross-validation experiments illustrate that GAFDS is effective in the extraction of effective features for EEG classification. Therefore, the proposed feature selection and optimization model can improve classification accuracy. PMID:28489789

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.

Global optimization and reflectivity data fitting for x-ray multilayer mirrors by means of genetic algorithms

NASA Astrophysics Data System (ADS)

Sanchez del Rio, Manuel; Pareschi, Giovanni

2001-01-01

The x-ray reflectivity of a multilayer is a non-linear function of many parameters (materials, layer thicknesses, densities, roughness). Non-linear fitting of experimental data with simulations requires to use initial values sufficiently close to the optimum value. This is a difficult task when the space topology of the variables is highly structured, as in our case. The application of global optimization methods to fit multilayer reflectivity data is presented. Genetic algorithms are stochastic methods based on the model of natural evolution: the improvement of a population along successive generations. A complete set of initial parameters constitutes an individual. The population is a collection of individuals. Each generation is built from the parent generation by applying some operators (e.g. selection, crossover, mutation) on the members of the parent generation. The pressure of selection drives the population to include 'good' individuals. For large number of generations, the best individuals will approximate the optimum parameters. Some results on fitting experimental hard x-ray reflectivity data for Ni/C multilayers recorded at the ESRF BM5 are presented. This method could be also applied to the help in the design of multilayers optimized for a target application, like for an astronomical grazing-incidence hard X-ray telescopes.

Intelligent sensing sensory quality of Chinese rice wine using near infrared spectroscopy and nonlinear tools.

PubMed

Ouyang, Qin; Chen, Quansheng; Zhao, Jiewen

2016-02-05

The approach presented herein reports the application of near infrared (NIR) spectroscopy, in contrast with human sensory panel, as a tool for estimating Chinese rice wine quality; concretely, to achieve the prediction of the overall sensory scores assigned by the trained sensory panel. Back propagation artificial neural network (BPANN) combined with adaptive boosting (AdaBoost) algorithm, namely BP-AdaBoost, as a novel nonlinear algorithm, was proposed in modeling. First, the optimal spectra intervals were selected by synergy interval partial least square (Si-PLS). Then, BP-AdaBoost model based on the optimal spectra intervals was established, called Si-BP-AdaBoost model. These models were optimized by cross validation, and the performance of each final model was evaluated according to correlation coefficient (Rp) and root mean square error of prediction (RMSEP) in prediction set. Si-BP-AdaBoost showed excellent performance in comparison with other models. The best Si-BP-AdaBoost model was achieved with Rp=0.9180 and RMSEP=2.23 in the prediction set. It was concluded that NIR spectroscopy combined with Si-BP-AdaBoost was an appropriate method for the prediction of the sensory quality in Chinese rice wine. Copyright © 2015 Elsevier B.V. All rights reserved.

Effective and extensible feature extraction method using genetic algorithm-based frequency-domain feature search for epileptic EEG multiclassification.

PubMed

Wen, Tingxi; Zhang, Zhongnan

2017-05-01

In this paper, genetic algorithm-based frequency-domain feature search (GAFDS) method is proposed for the electroencephalogram (EEG) analysis of epilepsy. In this method, frequency-domain features are first searched and then combined with nonlinear features. Subsequently, these features are selected and optimized to classify EEG signals. The extracted features are analyzed experimentally. The features extracted by GAFDS show remarkable independence, and they are superior to the nonlinear features in terms of the ratio of interclass distance and intraclass distance. Moreover, the proposed feature search method can search for features of instantaneous frequency in a signal after Hilbert transformation. The classification results achieved using these features are reasonable; thus, GAFDS exhibits good extensibility. Multiple classical classifiers (i.e., k-nearest neighbor, linear discriminant analysis, decision tree, AdaBoost, multilayer perceptron, and Naïve Bayes) achieve satisfactory classification accuracies by using the features generated by the GAFDS method and the optimized feature selection. The accuracies for 2-classification and 3-classification problems may reach up to 99% and 97%, respectively. Results of several cross-validation experiments illustrate that GAFDS is effective in the extraction of effective features for EEG classification. Therefore, the proposed feature selection and optimization model can improve classification accuracy.

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

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

Zhu, Xiaolei, E-mail: virtualzx@gmail.com; Yarkony, David R., E-mail: yarkony@jhu.edu

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility,more » has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.« less

A rapid learning and dynamic stepwise updating algorithm for flat neural networks and the application to time-series prediction.

PubMed

Chen, C P; Wan, J Z

1999-01-01

A fast learning algorithm is proposed to find an optimal weights of the flat neural networks (especially, the functional-link network). Although the flat networks are used for nonlinear function approximation, they can be formulated as linear systems. Thus, the weights of the networks can be solved easily using a linear least-square method. This formulation makes it easier to update the weights instantly for both a new added pattern and a new added enhancement node. A dynamic stepwise updating algorithm is proposed to update the weights of the system on-the-fly. The model is tested on several time-series data including an infrared laser data set, a chaotic time-series, a monthly flour price data set, and a nonlinear system identification problem. The simulation results are compared to existing models in which more complex architectures and more costly training are needed. The results indicate that the proposed model is very attractive to real-time processes.

Accurate modeling of switched reluctance machine based on hybrid trained WNN

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

Song, Shoujun, E-mail: sunnyway@nwpu.edu.cn; Ge, Lefei; Ma, Shaojie

2014-04-15

According to the strong nonlinear electromagnetic characteristics of switched reluctance machine (SRM), a novel accurate modeling method is proposed based on hybrid trained wavelet neural network (WNN) which combines improved genetic algorithm (GA) with gradient descent (GD) method to train the network. In the novel method, WNN is trained by GD method based on the initial weights obtained per improved GA optimization, and the global parallel searching capability of stochastic algorithm and local convergence speed of deterministic algorithm are combined to enhance the training accuracy, stability and speed. Based on the measured electromagnetic characteristics of a 3-phase 12/8-pole SRM, themore » nonlinear simulation model is built by hybrid trained WNN in Matlab. The phase current and mechanical characteristics from simulation under different working conditions meet well with those from experiments, which indicates the accuracy of the model for dynamic and static performance evaluation of SRM and verifies the effectiveness of the proposed modeling method.« less

Constrained Multi-Level Algorithm for Trajectory Optimization

NASA Astrophysics Data System (ADS)

Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi

The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in diagonalised methods, being the only single update with quadratic convergence. For a single level, the diagonalised multiplier method (DMM) is described in Ref.5. The main advantage of the two-level analogue of the DMM approach is that it avoids the inner loop optimizations required in the other methods. The scheme also introduces a gradient change measure to reduce the computational time needed to calculate the gradients. It is demonstrated that the new multi-level scheme leads to a robust procedure to handle the sensitivity of the constraints, and the multiple objectives of different trajectory phases. Ref. 1. Fahroo, F and Ross, M., " A Spectral Patching Method for Direct Trajectory Optimization" The Journal of the Astronautical Sciences, Vol.48, 2000, pp.269-286 Ref. 2. Phililps, C.A. and Drake, J.C., "Trajectory Optimization for a Missile using a Multitier Approach" Journal of Spacecraft and Rockets, Vol.37, 2000, pp.663-669 Ref. 3. Gath, P.F., and Calise, A.J., " Optimization of Launch Vehicle Ascent Trajectories with Path Constraints and Coast Arcs", Journal of Guidance, Control, and Dynamics, Vol. 24, 2001, pp.296-304 Ref. 4. Betts, J.T., " Survey of Numerical Methods for Trajectory Optimization", Journal of Guidance, Control, and Dynamics, Vol.21, 1998, pp. 193-207 Ref. 5. Adimurthy, V., " Launch Vehicle Trajectory Optimization", Acta Astronautica, Vol.15, 1987, pp.845-850.

An Adaptive Image Enhancement Technique by Combining Cuckoo Search and Particle Swarm Optimization Algorithm

PubMed Central

Ye, Zhiwei; Wang, Mingwei; Hu, Zhengbing; Liu, Wei

2015-01-01

Image enhancement is an important procedure of image processing and analysis. This paper presents a new technique using a modified measure and blending of cuckoo search and particle swarm optimization (CS-PSO) for low contrast images to enhance image adaptively. In this way, contrast enhancement is obtained by global transformation of the input intensities; it employs incomplete Beta function as the transformation function and a novel criterion for measuring image quality considering three factors which are threshold, entropy value, and gray-level probability density of the image. The enhancement process is a nonlinear optimization problem with several constraints. CS-PSO is utilized to maximize the objective fitness criterion in order to enhance the contrast and detail in an image by adapting the parameters of a novel extension to a local enhancement technique. The performance of the proposed method has been compared with other existing techniques such as linear contrast stretching, histogram equalization, and evolutionary computing based image enhancement methods like backtracking search algorithm, differential search algorithm, genetic algorithm, and particle swarm optimization in terms of processing time and image quality. Experimental results demonstrate that the proposed method is robust and adaptive and exhibits the better performance than other methods involved in the paper. PMID:25784928

An adaptive image enhancement technique by combining cuckoo search and particle swarm optimization algorithm.

PubMed

Ye, Zhiwei; Wang, Mingwei; Hu, Zhengbing; Liu, Wei

2015-01-01

Image enhancement is an important procedure of image processing and analysis. This paper presents a new technique using a modified measure and blending of cuckoo search and particle swarm optimization (CS-PSO) for low contrast images to enhance image adaptively. In this way, contrast enhancement is obtained by global transformation of the input intensities; it employs incomplete Beta function as the transformation function and a novel criterion for measuring image quality considering three factors which are threshold, entropy value, and gray-level probability density of the image. The enhancement process is a nonlinear optimization problem with several constraints. CS-PSO is utilized to maximize the objective fitness criterion in order to enhance the contrast and detail in an image by adapting the parameters of a novel extension to a local enhancement technique. The performance of the proposed method has been compared with other existing techniques such as linear contrast stretching, histogram equalization, and evolutionary computing based image enhancement methods like backtracking search algorithm, differential search algorithm, genetic algorithm, and particle swarm optimization in terms of processing time and image quality. Experimental results demonstrate that the proposed method is robust and adaptive and exhibits the better performance than other methods involved in the paper.

Optimal Signal Processing of Frequency-Stepped CW Radar Data

NASA Technical Reports Server (NTRS)

Ybarra, Gary A.; Wu, Shawkang M.; Bilbro, Griff L.; Ardalan, Sasan H.; Hearn, Chase P.; Neece, Robert T.

1995-01-01

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-X510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Optimal Signal Processing of Frequency-Stepped CW Radar Data

NASA Technical Reports Server (NTRS)

Ybarra, Gary A.; Wu, Shawkang M.; Bilbro, Griff L.; Ardalan, Sasan H.; Hearn, Chase P.; Neece, Robert T.

1995-01-01

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-851O network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

New Hybrid Algorithms for Estimating Tree Stem Diameters at Breast Height Using a Two Dimensional Terrestrial Laser Scanner

PubMed Central

Kong, Jianlei; Ding, Xiaokang; Liu, Jinhao; Yan, Lei; Wang, Jianli

2015-01-01

In this paper, a new algorithm to improve the accuracy of estimating diameter at breast height (DBH) for tree trunks in forest areas is proposed. First, the information is collected by a two-dimensional terrestrial laser scanner (2DTLS), which emits laser pulses to generate a point cloud. After extraction and filtration, the laser point clusters of the trunks are obtained, which are optimized by an arithmetic means method. Then, an algebraic circle fitting algorithm in polar form is non-linearly optimized by the Levenberg-Marquardt method to form a new hybrid algorithm, which is used to acquire the diameters and positions of the trees. Compared with previous works, this proposed method improves the accuracy of diameter estimation of trees significantly and effectively reduces the calculation time. Moreover, the experimental results indicate that this method is stable and suitable for the most challenging conditions, which has practical significance in improving the operating efficiency of forest harvester and reducing the risk of causing accidents. PMID:26147726

Parameters Identification for Photovoltaic Module Based on an Improved Artificial Fish Swarm Algorithm

PubMed Central

Wang, Hong-Hua

2014-01-01

A precise mathematical model plays a pivotal role in the simulation, evaluation, and optimization of photovoltaic (PV) power systems. Different from the traditional linear model, the model of PV module has the features of nonlinearity and multiparameters. Since conventional methods are incapable of identifying the parameters of PV module, an excellent optimization algorithm is required. Artificial fish swarm algorithm (AFSA), originally inspired by the simulation of collective behavior of real fish swarms, is proposed to fast and accurately extract the parameters of PV module. In addition to the regular operation, a mutation operator (MO) is designed to enhance the searching performance of the algorithm. The feasibility of the proposed method is demonstrated by various parameters of PV module under different environmental conditions, and the testing results are compared with other studied methods in terms of final solutions and computational time. The simulation results show that the proposed method is capable of obtaining higher parameters identification precision. PMID:25243233

Application of genetic algorithms to focal mechanism determination

NASA Astrophysics Data System (ADS)

Kobayashi, Reiji; Nakanishi, Ichiro

1994-04-01

Genetic algorithms are a new class of methods for global optimization. They resemble Monte Carlo techniques, but search for solutions more efficiently than uniform Monte Carlo sampling. In the field of geophysics, genetic algorithms have recently been used to solve some non-linear inverse problems (e.g., earthquake location, waveform inversion, migration velocity estimation). We present an application of genetic algorithms to focal mechanism determination from first-motion polarities of P-waves and apply our method to two recent large events, the Kushiro-oki earthquake of January 15, 1993 and the SW Hokkaido (Japan Sea) earthquake of July 12, 1993. Initial solution and curvature information of the objective function that gradient methods need are not required in our approach. Moreover globally optimal solutions can be efficiently obtained. Calculation of polarities based on double-couple models is the most time-consuming part of the source mechanism determination. The amount of calculations required by the method designed in this study is much less than that of previous grid search methods.

Optimized design on condensing tubes high-speed TIG welding technology magnetic control based on genetic algorithm

NASA Astrophysics Data System (ADS)

Lu, Lin; Chang, Yunlong; Li, Yingmin; Lu, Ming

2013-05-01

An orthogonal experiment was conducted by the means of multivariate nonlinear regression equation to adjust the influence of external transverse magnetic field and Ar flow rate on welding quality in the process of welding condenser pipe by high-speed argon tungsten-arc welding (TIG for short). The magnetic induction and flow rate of Ar gas were used as optimum variables, and tensile strength of weld was set to objective function on the base of genetic algorithm theory, and then an optimal design was conducted. According to the request of physical production, the optimum variables were restrained. The genetic algorithm in the MATLAB was used for computing. A comparison between optimum results and experiment parameters was made. The results showed that the optimum technologic parameters could be chosen by the means of genetic algorithm with the conditions of excessive optimum variables in the process of high-speed welding. And optimum technologic parameters of welding coincided with experiment results.

An approach for multi-objective optimization of vehicle suspension system

NASA Astrophysics Data System (ADS)

Koulocheris, D.; Papaioannou, G.; Christodoulou, D.

2017-10-01

In this paper, a half car model of with nonlinear suspension systems is selected in order to study the vertical vibrations and optimize its suspension system with respect to ride comfort and road holding. A road bump was used as road profile. At first, the optimization problem is solved with the use of Genetic Algorithms with respect to 6 optimization targets. Then the k - ɛ optimization method was implemented to locate one optimum solution. Furthermore, an alternative approach is presented in this work: the previous optimization targets are separated in main and supplementary ones, depending on their importance in the analysis. The supplementary targets are not crucial to the optimization but they could enhance the main objectives. Thus, the problem was solved again using Genetic Algorithms with respect to the 3 main targets of the optimization. Having obtained the Pareto set of solutions, the k - ɛ optimality method was implemented for the 3 main targets and the supplementary ones, evaluated by the simulation of the vehicle model. The results of both cases are presented and discussed in terms of convergence of the optimization and computational time. The optimum solutions acquired from both cases are compared based on performance metrics as well.

Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Saptarshi

Multi-agent systems are widely used for constructing a desired formation shape, exploring an area, surveillance, coverage, and other cooperative tasks. This dissertation introduces novel algorithms in the three main areas of shape formation, distributed estimation, and attitude control of large-scale multi-agent systems. In the first part of this dissertation, we address the problem of shape formation for thousands to millions of agents. Here, we present two novel algorithms for guiding a large-scale swarm of robotic systems into a desired formation shape in a distributed and scalable manner. These probabilistic swarm guidance algorithms adopt an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled using tunable Markov chains. In the first algorithm - Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) - each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain that is constructed in real-time using feedback from the current swarm distribution. This PSG-IMC algorithm minimizes the expected cost of the transitions required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. In the second algorithm - Probabilistic Swarm Guidance using Optimal Transport (PSG-OT) - each agent determines its bin transition probabilities by solving an optimal transport problem, which is recast as a linear program. In the presence of perfect feedback of the current swarm distribution, this algorithm minimizes the given cost function, guarantees faster convergence, reduces the number of transitions for achieving the desired formation, and is robust to disturbances or damages to the formation. We demonstrate the effectiveness of these two proposed swarm guidance algorithms using results from numerical simulations and closed-loop hardware experiments on multiple quadrotors. In the second part of this dissertation, we present two novel discrete-time algorithms for distributed estimation, which track a single target using a network of heterogeneous sensing agents. The Distributed Bayesian Filtering (DBF) algorithm, the sensing agents combine their normalized likelihood functions using the logarithmic opinion pool and the discrete-time dynamic average consensus algorithm. Each agent's estimated likelihood function converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. Using a new proof technique, the convergence, stability, and robustness properties of the DBF algorithm are rigorously characterized. The explicit bounds on the time step of the robust DBF algorithm are shown to depend on the time-scale of the target dynamics. Furthermore, the DBF algorithm for linear-Gaussian models can be cast into a modified form of the Kalman information filter. In the Bayesian Consensus Filtering (BCF) algorithm, the agents combine their estimated posterior pdfs multiple times within each time step using the logarithmic opinion pool scheme. Thus, each agent's consensual pdf minimizes the sum of Kullback-Leibler divergences with the local posterior pdfs. The performance and robust properties of these algorithms are validated using numerical simulations. In the third part of this dissertation, we present an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feed-forward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain Lp stability in the presence of modeling uncertainties and disturbances, and reduces the resultant disturbance torque. Further, this control law permits the use of any attitude representation and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law, because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivative based reference trajectory, because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control law is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept. The new algorithms proposed in this dissertation will facilitate the development of versatile autonomous multi-agent systems that are capable of performing a variety of complex tasks in a robust and scalable manner.

A Highly Functional Decision Paradigm Based on Nonlinear Adaptive Genetic Algorithm

DTIC Science & Technology

1997-10-07

significant speedup. p£ lC <$jALTnimm SCTED & 14. SUBJECT TERMS Network Topology Optimization, Mathlink, Mathematica Plug-In, GA Route Optimizer, DSP...operations per second 2.4 Gbytes/second sustainable on-chip data transfer rate 400 Mb/s off-chip peak transfer rate Layer-to-layer interconnection...SecondHighestDist# = DistanceArray%(IndexList%(ChromeGene%(i%, 1) -1), IndexList%( Chrom eGene%(i%, 2) - 1)) For j% = 1 To StrandLength% - 1 ’If highest distance

Optimization model of vaccination strategy for dengue transmission

NASA Astrophysics Data System (ADS)

Widayani, H.; Kallista, M.; Nuraini, N.; Sari, M. Y.

2014-02-01

Dengue fever is emerging tropical and subtropical disease caused by dengue virus infection. The vaccination should be done as a prevention of epidemic in population. The host-vector model are modified with consider a vaccination factor to prevent the occurrence of epidemic dengue in a population. An optimal vaccination strategy using non-linear objective function was proposed. The genetic algorithm programming techniques are combined with fourth-order Runge-Kutta method to construct the optimal vaccination. In this paper, the appropriate vaccination strategy by using the optimal minimum cost function which can reduce the number of epidemic was analyzed. The numerical simulation for some specific cases of vaccination strategy is shown.

Prioritizing the Components of Vulnerability: A Genetic Algorithm Minimization of Flood Risk

NASA Astrophysics Data System (ADS)

Bongolan, Vena Pearl; Ballesteros, Florencio; Baritua, Karessa Alexandra; Junne Santos, Marie

2013-04-01

We define a flood resistant city as an optimal arrangement of communities according to their traits, with the goal of minimizing the flooding vulnerability via a genetic algorithm. We prioritize the different components of flooding vulnerability, giving each component a weight, thus expressing vulnerability as a weighted sum. This serves as the fitness function for the genetic algorithm. We also allowed non-linear interactions among related but independent components, viz, poverty and mortality rate, and literacy and radio/ tv penetration. The designs produced reflect the relative importance of the components, and we observed a synchronicity between the interacting components, giving us a more consistent design.

Phase retrieval in generalized optical interferometry systems.

PubMed

Farriss, Wesley E; Fienup, James R; Malhotra, Tanya; Vamivakas, A Nick

2018-02-05

Modal analysis of an optical field via generalized interferometry (GI) is a novel technique that treats said field as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. We use phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Information diversity increases the robustness of the algorithm by better constraining the solution. Additionally, multiple sets of random starting phase values assist the algorithm in overcoming local minima. The algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise.

High-performance image reconstruction in fluorescence tomography on desktop computers and graphics hardware.

PubMed

Freiberger, Manuel; Egger, Herbert; Liebmann, Manfred; Scharfetter, Hermann

2011-11-01

Image reconstruction in fluorescence optical tomography is a three-dimensional nonlinear ill-posed problem governed by a system of partial differential equations. In this paper we demonstrate that a combination of state of the art numerical algorithms and a careful hardware optimized implementation allows to solve this large-scale inverse problem in a few seconds on standard desktop PCs with modern graphics hardware. In particular, we present methods to solve not only the forward but also the non-linear inverse problem by massively parallel programming on graphics processors. A comparison of optimized CPU and GPU implementations shows that the reconstruction can be accelerated by factors of about 15 through the use of the graphics hardware without compromising the accuracy in the reconstructed images.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

Improving alignment in Tract-based spatial statistics: evaluation and optimization of image registration.

PubMed

de Groot, Marius; Vernooij, Meike W; Klein, Stefan; Ikram, M Arfan; Vos, Frans M; Smith, Stephen M; Niessen, Wiro J; Andersson, Jesper L R

2013-08-01

Anatomical alignment in neuroimaging studies is of such importance that considerable effort is put into improving the registration used to establish spatial correspondence. Tract-based spatial statistics (TBSS) is a popular method for comparing diffusion characteristics across subjects. TBSS establishes spatial correspondence using a combination of nonlinear registration and a "skeleton projection" that may break topological consistency of the transformed brain images. We therefore investigated feasibility of replacing the two-stage registration-projection procedure in TBSS with a single, regularized, high-dimensional registration. To optimize registration parameters and to evaluate registration performance in diffusion MRI, we designed an evaluation framework that uses native space probabilistic tractography for 23 white matter tracts, and quantifies tract similarity across subjects in standard space. We optimized parameters for two registration algorithms on two diffusion datasets of different quality. We investigated reproducibility of the evaluation framework, and of the optimized registration algorithms. Next, we compared registration performance of the regularized registration methods and TBSS. Finally, feasibility and effect of incorporating the improved registration in TBSS were evaluated in an example study. The evaluation framework was highly reproducible for both algorithms (R(2) 0.993; 0.931). The optimal registration parameters depended on the quality of the dataset in a graded and predictable manner. At optimal parameters, both algorithms outperformed the registration of TBSS, showing feasibility of adopting such approaches in TBSS. This was further confirmed in the example experiment. Copyright © 2013 Elsevier Inc. All rights reserved.

Quantum Associative Neural Network with Nonlinear Search Algorithm

NASA Astrophysics Data System (ADS)

Zhou, Rigui; Wang, Huian; Wu, Qian; Shi, Yang

2012-03-01

Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to O( {log2}^{2^{n -t}} ) = O( n - t ) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers' counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

Identification of robust adaptation gene regulatory network parameters using an improved particle swarm optimization algorithm.

PubMed

Huang, X N; Ren, H P

2016-05-13

Robust adaptation is a critical ability of gene regulatory network (GRN) to survive in a fluctuating environment, which represents the system responding to an input stimulus rapidly and then returning to its pre-stimulus steady state timely. In this paper, the GRN is modeled using the Michaelis-Menten rate equations, which are highly nonlinear differential equations containing 12 undetermined parameters. The robust adaption is quantitatively described by two conflicting indices. To identify the parameter sets in order to confer the GRNs with robust adaptation is a multi-variable, multi-objective, and multi-peak optimization problem, which is difficult to acquire satisfactory solutions especially high-quality solutions. A new best-neighbor particle swarm optimization algorithm is proposed to implement this task. The proposed algorithm employs a Latin hypercube sampling method to generate the initial population. The particle crossover operation and elitist preservation strategy are also used in the proposed algorithm. The simulation results revealed that the proposed algorithm could identify multiple solutions in one time running. Moreover, it demonstrated a superior performance as compared to the previous methods in the sense of detecting more high-quality solutions within an acceptable time. The proposed methodology, owing to its universality and simplicity, is useful for providing the guidance to design GRN with superior robust adaptation.

Reliable Adaptive Data Aggregation Route Strategy for a Trade-off between Energy and Lifetime in WSNs

PubMed Central

Guo, Wenzhong; Hong, Wei; Zhang, Bin; Chen, Yuzhong; Xiong, Naixue

2014-01-01

Mobile security is one of the most fundamental problems in Wireless Sensor Networks (WSNs). The data transmission path will be compromised for some disabled nodes. To construct a secure and reliable network, designing an adaptive route strategy which optimizes energy consumption and network lifetime of the aggregation cost is of great importance. In this paper, we address the reliable data aggregation route problem for WSNs. Firstly, to ensure nodes work properly, we propose a data aggregation route algorithm which improves the energy efficiency in the WSN. The construction process achieved through discrete particle swarm optimization (DPSO) saves node energy costs. Then, to balance the network load and establish a reliable network, an adaptive route algorithm with the minimal energy and the maximum lifetime is proposed. Since it is a non-linear constrained multi-objective optimization problem, in this paper we propose a DPSO with the multi-objective fitness function combined with the phenotype sharing function and penalty function to find available routes. Experimental results show that compared with other tree routing algorithms our algorithm can effectively reduce energy consumption and trade off energy consumption and network lifetime. PMID:25215944

Analytical and Computational Properties of Distributed Approaches to MDO

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia M.; Lewis, Robert Michael

2000-01-01

Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

Adaptive adjustment of interval predictive control based on combined model and application in shell brand petroleum distillation tower

NASA Astrophysics Data System (ADS)

Sun, Chao; Zhang, Chunran; Gu, Xinfeng; Liu, Bin

2017-10-01

Constraints of the optimization objective are often unable to be met when predictive control is applied to industrial production process. Then, online predictive controller will not find a feasible solution or a global optimal solution. To solve this problem, based on Back Propagation-Auto Regressive with exogenous inputs (BP-ARX) combined control model, nonlinear programming method is used to discuss the feasibility of constrained predictive control, feasibility decision theorem of the optimization objective is proposed, and the solution method of soft constraint slack variables is given when the optimization objective is not feasible. Based on this, for the interval control requirements of the controlled variables, the slack variables that have been solved are introduced, the adaptive weighted interval predictive control algorithm is proposed, achieving adaptive regulation of the optimization objective and automatically adjust of the infeasible interval range, expanding the scope of the feasible region, and ensuring the feasibility of the interval optimization objective. Finally, feasibility and effectiveness of the algorithm is validated through the simulation comparative experiments.

Structural Optimization for Reliability Using Nonlinear Goal Programming

NASA Technical Reports Server (NTRS)

El-Sayed, Mohamed E.

1999-01-01

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

Rayleigh wave dispersion curve inversion by using particle swarm optimization and genetic algorithm

NASA Astrophysics Data System (ADS)

Buyuk, Ersin; Zor, Ekrem; Karaman, Abdullah

2017-04-01

Inversion of surface wave dispersion curves with its highly nonlinear nature has some difficulties using traditional linear inverse methods due to the need and strong dependence to the initial model, possibility of trapping in local minima and evaluation of partial derivatives. There are some modern global optimization methods to overcome of these difficulties in surface wave analysis such as Genetic algorithm (GA) and Particle Swarm Optimization (PSO). GA is based on biologic evolution consisting reproduction, crossover and mutation operations, while PSO algorithm developed after GA is inspired from the social behaviour of birds or fish of swarms. Utility of these methods require plausible convergence rate, acceptable relative error and optimum computation cost that are important for modelling studies. Even though PSO and GA processes are similar in appearence, the cross-over operation in GA is not used in PSO and the mutation operation is a stochastic process for changing the genes within chromosomes in GA. Unlike GA, the particles in PSO algorithm changes their position with logical velocities according to particle's own experience and swarm's experience. In this study, we applied PSO algorithm to estimate S wave velocities and thicknesses of the layered earth model by using Rayleigh wave dispersion curve and also compared these results with GA and we emphasize on the advantage of using PSO algorithm for geophysical modelling studies considering its rapid convergence, low misfit error and computation cost.

Optimization of Energy Efficiency and Conservation in Green Building Design Using Duelist, Killer-Whale and Rain-Water Algorithms

NASA Astrophysics Data System (ADS)

Biyanto, T. R.; Matradji; Syamsi, M. N.; Fibrianto, H. Y.; Afdanny, N.; Rahman, A. H.; Gunawan, K. S.; Pratama, J. A. D.; Malwindasari, A.; Abdillah, A. I.; Bethiana, T. N.; Putra, Y. A.

2017-11-01

The development of green building has been growing in both design and quality. The development of green building was limited by the issue of expensive investment. Actually, green building can reduce the energy usage inside the building especially in utilization of cooling system. External load plays major role in reducing the usage of cooling system. External load is affected by type of wall sheathing, glass and roof. The proper selection of wall, type of glass and roof material are very important to reduce external load. Hence, the optimization of energy efficiency and conservation in green building design is required. Since this optimization consist of integer and non-linear equations, this problem falls into Mixed-Integer-Non-Linear-Programming (MINLP) that required global optimization technique such as stochastic optimization algorithms. In this paper the optimized variables i.e. type of glass and roof were chosen using Duelist, Killer-Whale and Rain-Water Algorithms to obtain the optimum energy and considering the minimal investment. The optimization results exhibited the single glass Planibel-G with the 3.2 mm thickness and glass wool insulation provided maximum ROI of 36.8486%, EUI reduction of 54 kWh/m2·year, CO2 emission reduction of 486.8971 tons/year and reduce investment of 4,078,905,465 IDR.

An enhanced artificial bee colony algorithm (EABC) for solving dispatching of hydro-thermal system (DHTS) problem.

PubMed

Yu, Yi; Wu, Yonggang; Hu, Binqi; Liu, Xinglong

2018-01-01

The dispatching of hydro-thermal system is a nonlinear programming problem with multiple constraints and high dimensions and the solution techniques of the model have been a hotspot in research. Based on the advantage of that the artificial bee colony algorithm (ABC) can efficiently solve the high-dimensional problem, an improved artificial bee colony algorithm has been proposed to solve DHTS problem in this paper. The improvements of the proposed algorithm include two aspects. On one hand, local search can be guided in efficiency by the information of the global optimal solution and its gradient in each generation. The global optimal solution improves the search efficiency of the algorithm but loses diversity, while the gradient can weaken the loss of diversity caused by the global optimal solution. On the other hand, inspired by genetic algorithm, the nectar resource which has not been updated in limit generation is transformed to a new one by using selection, crossover and mutation, which can ensure individual diversity and make full use of prior information for improving the global search ability of the algorithm. The two improvements of ABC algorithm are proved to be effective via a classical numeral example at last. Among which the genetic operator for the promotion of the ABC algorithm's performance is significant. The results are also compared with those of other state-of-the-art algorithms, the enhanced ABC algorithm has general advantages in minimum cost, average cost and maximum cost which shows its usability and effectiveness. The achievements in this paper provide a new method for solving the DHTS problems, and also offer a novel reference for the improvement of mechanism and the application of algorithms.

A Multiobjective Interval Programming Model for Wind-Hydrothermal Power System Dispatching Using 2-Step Optimization Algorithm

PubMed Central

Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision. PMID:24895663

A multiobjective interval programming model for wind-hydrothermal power system dispatching using 2-step optimization algorithm.

PubMed

Ren, Kun; Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.

Quadruped Robot Locomotion using a Global Optimization Stochastic Algorithm

NASA Astrophysics Data System (ADS)

Oliveira, Miguel; Santos, Cristina; Costa, Lino; Ferreira, Manuel

2011-09-01

The problem of tuning nonlinear dynamical systems parameters, such that the attained results are considered good ones, is a relevant one. This article describes the development of a gait optimization system that allows a fast but stable robot quadruped crawl gait. We combine bio-inspired Central Patterns Generators (CPGs) and Genetic Algorithms (GA). CPGs are modelled as autonomous differential equations, that generate the necessar y limb movement to perform the required walking gait. The GA finds parameterizations of the CPGs parameters which attain good gaits in terms of speed, vibration and stability. Moreover, two constraint handling techniques based on tournament selection and repairing mechanism are embedded in the GA to solve the proposed constrained optimization problem and make the search more efficient. The experimental results, performed on a simulated Aibo robot, demonstrate that our approach allows low vibration with a high velocity and wide stability margin for a quadruped slow crawl gait.

Structural optimization procedure of a composite wind turbine blade for reducing both material cost and blade weight

NASA Astrophysics Data System (ADS)

Hu, Weifei; Park, Dohyun; Choi, DongHoon

2013-12-01

A composite blade structure for a 2 MW horizontal axis wind turbine is optimally designed. Design requirements are simultaneously minimizing material cost and blade weight while satisfying the constraints on stress ratio, tip deflection, fatigue life and laminate layup requirements. The stress ratio and tip deflection under extreme gust loads and the fatigue life under a stochastic normal wind load are evaluated. A blade element wind load model is proposed to explain the wind pressure difference due to blade height change during rotor rotation. For fatigue life evaluation, the stress result of an implicit nonlinear dynamic analysis under a time-varying fluctuating wind is converted to the histograms of mean and amplitude of maximum stress ratio using the rainflow counting algorithm Miner's rule is employed to predict the fatigue life. After integrating and automating the whole analysis procedure an evolutionary algorithm is used to solve the discrete optimization problem.

Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

Automated trajectory planning for multiple-flyby interplanetary missions

NASA Astrophysics Data System (ADS)

Englander, Jacob

Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both real-valued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the real-valued variables will represent the launch date, ight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. The contribution of this work is a framework for the autonomous optimization of multiple-flyby interplanetary trajectories. The trajectory design problem is converted into a HOCP with two nested loops: an "outer-loop" that finds the sequence of flybys and an "inner-loop" that optimizes the trajectory for each candidate yby sequence. The problem of choosing a sequence of flybys is posed as an integer programming problem and solved using a genetic algorithm (GA). This is an especially difficult problem to solve because GAs normally operate on a fixed-length set of decision variables. Since in interplanetary trajectory design the number of flyby maneuvers is not known a priori, it was necessary to devise a method of parameterizing the problem such that the GA can evolve a variable-length sequence of flybys. A novel "null gene" transcription was developed to meet this need. Then, for each candidate sequence of flybys, a trajectory must be found that visits each of the flyby targets and arrives at the final destination while optimizing some cost metric, such as minimizing ▵v or maximizing the final mass of the spacecraft. Three different classes of trajectory are described in this work, each of which requireda different physical model and optimization method. The choice of a trajectory model and optimization method is especially challenging because of the nature of the hybrid optimal control problem. Because the trajectory optimization problem is generated in real time by the outer-loop, the inner-loop optimization algorithm cannot require any a priori information and must always return a solution. In addition, the upper and lower bounds on each decision variable cannot be chosen a priori by the user because the user has no way to know what problem will be solved. Instead a method of choosing upper and lower bounds via a set of simple rules was developed and used for all three types of trajectory optimization problem. Many optimization algorithms were tested and discarded until suitable algorithms were found for each type of trajectory. The first class of trajectories use chemical propulsion and may only apply a ▵v at the periapse of each flyby. These Multiple Gravity Assist (MGA) trajectories are optimized using a cooperative algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The second class of trajectories, known as Multiple Gravity Assist with one Deep Space Maneuver (MGA-DSM), also use chemical propulsion but instead of maneuvering at the periapse of each flyby as in the MGA case a maneuver is applied at a free point along each planet-to-planet arc, i.e. there is one maneuver for each pair of flybys. MGA-DSM trajectories are parameterized by more variables than MGA trajectories, and so the cooperative algorithm of DE and PSO that was used to optimize MGA trajectories was found to be less effective when applied to MGA-DSM. Instead, either PSO or DE alone were found to be more effective. The third class of trajectories addressed in this work are those using continuousthrust propulsion. Continuous-thrust trajectory optimization problems are more challenging than impulsive-thrust problems because the control variables are a continuous time series rather than a small set of parameters and because the spacecraft does not follow a conic section trajectory, leading to a large number of nonlinear constraints that must be satisfied to ensure that the spacecraft obeys the equations of motion. Many models and optimization algorithms were applied including direct transcription with nonlinear programming (DTNLP), the inverse-polynomial shapebased method, and feasible region analysis. However the only physical model and optimization method that proved reliable enough were the Sims-Flanagan transcription coupled with a nonlinear programming solver and the monotonic basin hopping (MBH) global search heuristic. The methods developed here are demonstrated to optimize a set of example trajectories, including a recreation of the Cassini mission, a Galileo-like mission, and conceptual continuous-thrust missions to Jupiter, Mercury, and Uranus.

Acoustic and elastic waveform inversion best practices

NASA Astrophysics Data System (ADS)

Modrak, Ryan T.

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence, one or two test cases are not enough to reliably inform such decisions. We identify best practices instead using two global, one regional and four near-surface acoustic test problems. To obtain meaningful quantitative comparisons, we carry out hundreds acoustic inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that L-BFGS provides computational savings over nonlinear conjugate gradient methods in a wide variety of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization, and total variation regularization are effective in different contexts. Besides these issues, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details have a strong effect on computational cost, regardless of the chosen material parameterization or nonlinear optimization algorithm. Building on the acoustic inversion results, we carry out elastic experiments with four test problems, three objective functions, and four material parameterizations. The choice of parameterization for isotropic elastic media is found to be more complicated than previous studies suggests, with "wavespeed-like'' parameters performing well with phase-based objective functions and Lame parameters performing well with amplitude-based objective functions. Reliability and efficiency can be even harder to achieve in transversely isotropic elastic inversions because rotation angle parameters describing fast-axis direction are difficult to recover. Using Voigt or Chen-Tromp parameters avoids the need to include rotation angles explicitly and provides an effective strategy for anisotropic inversion. The need for flexible and portable workflow management tools for seismic inversion also poses a major challenge. In a final chapter, the software used to the carry out the above experiments is described and instructions for reproducing experimental results are given.

A Novel Consensus-Based Particle Swarm Optimization-Assisted Trust-Tech Methodology for Large-Scale Global Optimization.

PubMed

Zhang, Yong-Feng; Chiang, Hsiao-Dong

2017-09-01

A novel three-stage methodology, termed the "consensus-based particle swarm optimization (PSO)-assisted Trust-Tech methodology," to find global optimal solutions for nonlinear optimization problems is presented. It is composed of Trust-Tech methods, consensus-based PSO, and local optimization methods that are integrated to compute a set of high-quality local optimal solutions that can contain the global optimal solution. The proposed methodology compares very favorably with several recently developed PSO algorithms based on a set of small-dimension benchmark optimization problems and 20 large-dimension test functions from the CEC 2010 competition. The analytical basis for the proposed methodology is also provided. Experimental results demonstrate that the proposed methodology can rapidly obtain high-quality optimal solutions that can contain the global optimal solution. The scalability of the proposed methodology is promising.

Inversion for Refractivity Parameters Using a Dynamic Adaptive Cuckoo Search with Crossover Operator Algorithm

PubMed Central

Zhang, Zhihua; Sheng, Zheng; Shi, Hanqing; Fan, Zhiqiang

2016-01-01

Using the RFC technique to estimate refractivity parameters is a complex nonlinear optimization problem. In this paper, an improved cuckoo search (CS) algorithm is proposed to deal with this problem. To enhance the performance of the CS algorithm, a parameter dynamic adaptive operation and crossover operation were integrated into the standard CS (DACS-CO). Rechenberg's 1/5 criteria combined with learning factor were used to control the parameter dynamic adaptive adjusting process. The crossover operation of genetic algorithm was utilized to guarantee the population diversity. The new hybrid algorithm has better local search ability and contributes to superior performance. To verify the ability of the DACS-CO algorithm to estimate atmospheric refractivity parameters, the simulation data and real radar clutter data are both implemented. The numerical experiments demonstrate that the DACS-CO algorithm can provide an effective method for near-real-time estimation of the atmospheric refractivity profile from radar clutter. PMID:27212938

Computer object segmentation by nonlinear image enhancement, multidimensional clustering, and geometrically constrained contour optimization

NASA Astrophysics Data System (ADS)

Bruynooghe, Michel M.

1998-04-01

In this paper, we present a robust method for automatic object detection and delineation in noisy complex images. The proposed procedure is a three stage process that integrates image segmentation by multidimensional pixel clustering and geometrically constrained optimization of deformable contours. The first step is to enhance the original image by nonlinear unsharp masking. The second step is to segment the enhanced image by multidimensional pixel clustering, using our reducible neighborhoods clustering algorithm that has a very interesting theoretical maximal complexity. Then, candidate objects are extracted and initially delineated by an optimized region merging algorithm, that is based on ascendant hierarchical clustering with contiguity constraints and on the maximization of average contour gradients. The third step is to optimize the delineation of previously extracted and initially delineated objects. Deformable object contours have been modeled by cubic splines. An affine invariant has been used to control the undesired formation of cusps and loops. Non linear constrained optimization has been used to maximize the external energy. This avoids the difficult and non reproducible choice of regularization parameters, that are required by classical snake models. The proposed method has been applied successfully to the detection of fine and subtle microcalcifications in X-ray mammographic images, to defect detection by moire image analysis, and to the analysis of microrugosities of thin metallic films. The later implementation of the proposed method on a digital signal processor associated to a vector coprocessor would allow the design of a real-time object detection and delineation system for applications in medical imaging and in industrial computer vision.

Tunning PID controller using particle swarm optimization algorithm on automatic voltage regulator system

NASA Astrophysics Data System (ADS)

Aranza, M. F.; Kustija, J.; Trisno, B.; Hakim, D. L.

2016-04-01

PID Controller (Proportional Integral Derivative) was invented since 1910, but till today still is used in industries, even though there are many kind of modern controllers like fuzz controller and neural network controller are being developed. Performance of PID controller is depend on on Proportional Gain (Kp), Integral Gain (Ki) and Derivative Gain (Kd). These gains can be got by using method Ziegler-Nichols (ZN), gain-phase margin, Root Locus, Minimum Variance dan Gain Scheduling however these methods are not optimal to control systems that nonlinear and have high-orde, in addition, some methods relative hard. To solve those obstacles, particle swarm optimization (PSO) algorithm is proposed to get optimal Kp, Ki and Kd. PSO is proposed because PSO has convergent result and not require many iterations. On this research, PID controller is applied on AVR (Automatic Voltage Regulator). Based on result of analyzing transient, stability Root Locus and frequency response, performance of PID controller is better than Ziegler-Nichols.