Provisional-Ideal-Point-Based Multi-objective Optimization Method for Drone Delivery Problem

NASA Astrophysics Data System (ADS)

Omagari, Hiroki; Higashino, Shin-Ichiro

2018-04-01

In this paper, we proposed a new evolutionary multi-objective optimization method for solving drone delivery problems (DDP). It can be formulated as a constrained multi-objective optimization problem. In our previous research, we proposed the "aspiration-point-based method" to solve multi-objective optimization problems. However, this method needs to calculate the optimal values of each objective function value in advance. Moreover, it does not consider the constraint conditions except for the objective functions. Therefore, it cannot apply to DDP which has many constraint conditions. To solve these issues, we proposed "provisional-ideal-point-based method." The proposed method defines a "penalty value" to search for feasible solutions. It also defines a new reference solution named "provisional-ideal point" to search for the preferred solution for a decision maker. In this way, we can eliminate the preliminary calculations and its limited application scope. The results of the benchmark test problems show that the proposed method can generate the preferred solution efficiently. The usefulness of the proposed method is also demonstrated by applying it to DDP. As a result, the delivery path when combining one drone and one truck drastically reduces the traveling distance and the delivery time compared with the case of using only one truck.

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

NASA Astrophysics Data System (ADS)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Optimal Price Decision Problem for Simultaneous Multi-article Auction and Its Optimal Price Searching Method by Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Masuda, Kazuaki; Aiyoshi, Eitaro

We propose a method for solving optimal price decision problems for simultaneous multi-article auctions. An auction problem, originally formulated as a combinatorial problem, determines both every seller's whether or not to sell his/her article and every buyer's which article(s) to buy, so that the total utility of buyers and sellers will be maximized. Due to the duality theory, we transform it equivalently into a dual problem in which Lagrange multipliers are interpreted as articles' transaction price. As the dual problem is a continuous optimization problem with respect to the multipliers (i.e., the transaction prices), we propose a numerical method to solve it by applying heuristic global search methods. In this paper, Particle Swarm Optimization (PSO) is used to solve the dual problem, and experimental results are presented to show the validity of the proposed method.

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization

DTIC Science & Technology

2012-08-17

the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth...method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chie y but not...significantly outperforming several state-of-the-art solvers on most tested problems. The resulting MATLAB solver, called TVAL3, has been posted online [23]. 2

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Adomian decomposition method used to solve the one-dimensional acoustic equations

NASA Astrophysics Data System (ADS)

Dispini, Meta; Mungkasi, Sudi

2017-05-01

In this paper we propose the use of Adomian decomposition method to solve one-dimensional acoustic equations. This recursive method can be calculated easily and the result is an approximation of the exact solution. We use the Maple software to compute the series in the Adomian decomposition. We obtain that the Adomian decomposition method is able to solve the acoustic equations with the physically correct behavior.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving

PubMed Central

Maisto, Domenico; Donnarumma, Francesco; Pezzulo, Giovanni

2015-01-01

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load. PMID:25652466

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Direct SQP-methods for solving optimal control problems with delays

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

Goellmann, L.; Bueskens, C.; Maurer, H.

The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators.

PubMed

Zhao, Jing; Zong, Haili

2018-01-01

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Blind compressed sensing image reconstruction based on alternating direction method

NASA Astrophysics Data System (ADS)

Liu, Qinan; Guo, Shuxu

2018-04-01

In order to solve the problem of how to reconstruct the original image under the condition of unknown sparse basis, this paper proposes an image reconstruction method based on blind compressed sensing model. In this model, the image signal is regarded as the product of a sparse coefficient matrix and a dictionary matrix. Based on the existing blind compressed sensing theory, the optimal solution is solved by the alternative minimization method. The proposed method solves the problem that the sparse basis in compressed sensing is difficult to represent, which restrains the noise and improves the quality of reconstructed image. This method ensures that the blind compressed sensing theory has a unique solution and can recover the reconstructed original image signal from a complex environment with a stronger self-adaptability. The experimental results show that the image reconstruction algorithm based on blind compressed sensing proposed in this paper can recover high quality image signals under the condition of under-sampling.

An approach to solve replacement problems under intuitionistic fuzzy nature

NASA Astrophysics Data System (ADS)

Balaganesan, M.; Ganesan, K.

2018-04-01

Due to impreciseness to solve the day to day problems the researchers use fuzzy sets in their discussions of the replacement problems. The aim of this paper is to solve the replacement theory problems with triangular intuitionistic fuzzy numbers. An effective methodology based on fuzziness index and location index is proposed to determine the optimal solution of the replacement problem. A numerical example is illustrated to validate the proposed method.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving.

PubMed

Maisto, Domenico; Donnarumma, Francesco; Pezzulo, Giovanni

2015-03-06

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Guided particle swarm optimization method to solve general nonlinear optimization problems

NASA Astrophysics Data System (ADS)

Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

2018-04-01

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

2013-09-01

In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

A BiCGStab2 variant of the IDR(s) method for solving linear equations

NASA Astrophysics Data System (ADS)

Abe, Kuniyoshi; Sleijpen, Gerard L. G.

2012-09-01

The hybrid Bi-Conjugate Gradient (Bi-CG) methods, such as the BiCG STABilized (BiCGSTAB), BiCGstab(l), BiCGStab2 and BiCG×MR2 methods are well-known solvers for solving a linear equation with a nonsymmetric matrix. The Induced Dimension Reduction (IDR)(s) method has recently been proposed, and it has been reported that IDR(s) is often more effective than the hybrid BiCG methods. IDR(s) combining the stabilization polynomial of BiCGstab(l) has been designed to improve the convergence of the original IDR(s) method. We therefore propose IDR(s) combining the stabilization polynomial of BiCGStab2. Numerical experiments show that our proposed variant of IDR(s) is more effective than the original IDR(s) and BiCGStab2 methods.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

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

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

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

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Shooting method for solution of boundary-layer flows with massive blowing

NASA Technical Reports Server (NTRS)

Liu, T.-M.; Nachtsheim, P. R.

1973-01-01

A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.

Renal cortex segmentation using optimal surface search with novel graph construction.

PubMed

Li, Xiuli; Chen, Xinjian; Yao, Jianhua; Zhang, Xing; Tian, Jie

2011-01-01

In this paper, we propose a novel approach to solve the renal cortex segmentation problem, which has rarely been studied. In this study, the renal cortex segmentation problem is handled as a multiple-surfaces extraction problem, which is solved using the optimal surface search method. We propose a novel graph construction scheme in the optimal surface search to better accommodate multiple surfaces. Different surface sub-graphs are constructed according to their properties, and inter-surface relationships are also modeled in the graph. The proposed method was tested on 17 clinical CT datasets. The true positive volume fraction (TPVF) and false positive volume fraction (FPVF) are 74.10% and 0.08%, respectively. The experimental results demonstrate the effectiveness of the proposed method.

Genetic network inference as a series of discrimination tasks.

PubMed

Kimura, Shuhei; Nakayama, Satoshi; Hatakeyama, Mariko

2009-04-01

Genetic network inference methods based on sets of differential equations generally require a great deal of time, as the equations must be solved many times. To reduce the computational cost, researchers have proposed other methods for inferring genetic networks by solving sets of differential equations only a few times, or even without solving them at all. When we try to obtain reasonable network models using these methods, however, we must estimate the time derivatives of the gene expression levels with great precision. In this study, we propose a new method to overcome the drawbacks of inference methods based on sets of differential equations. Our method infers genetic networks by obtaining classifiers capable of predicting the signs of the derivatives of the gene expression levels. For this purpose, we defined a genetic network inference problem as a series of discrimination tasks, then solved the defined series of discrimination tasks with a linear programming machine. Our experimental results demonstrated that the proposed method is capable of correctly inferring genetic networks, and doing so more than 500 times faster than the other inference methods based on sets of differential equations. Next, we applied our method to actual expression data of the bacterial SOS DNA repair system. And finally, we demonstrated that our approach relates to the inference method based on the S-system model. Though our method provides no estimation of the kinetic parameters, it should be useful for researchers interested only in the network structure of a target system. Supplementary data are available at Bioinformatics online.

Leap-frog-based BPM (LF-BPM) method for solving nanophotonic structures

NASA Astrophysics Data System (ADS)

Ayoub, Ahmad B.; Swillam, Mohamed A.

2018-02-01

In this paper, we propose an efficient approach to solve the BPM equation. By splitting the complex field into real and imaginary parts, the method is proved to be at least 30% faster than the conventional BPM. This method was tested on several optical components to test the accuracy.

Power Distribution System Planning with GIS Consideration

NASA Astrophysics Data System (ADS)

Wattanasophon, Sirichai; Eua-Arporn, Bundhit

This paper proposes a method for solving radial distribution system planning problems taking into account geographical information. The proposed method can automatically determine appropriate location and size of a substation, routing of feeders, and sizes of conductors while satisfying all constraints, i.e. technical constraints (voltage drop and thermal limit) and geographical constraints (obstacle, existing infrastructure, and high-cost passages). Sequential quadratic programming (SQP) and minimum path algorithm (MPA) are applied to solve the planning problem based on net price value (NPV) consideration. In addition this method integrates planner's experience and optimization process to achieve an appropriate practical solution. The proposed method has been tested with an actual distribution system, from which the results indicate that it can provide satisfactory plans.

Preconditioned alternating direction method of multipliers for inverse problems with constraints

NASA Astrophysics Data System (ADS)

Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie

2017-02-01

We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.

Hybrid surrogate-model-based multi-fidelity efficient global optimization applied to helicopter blade design

NASA Astrophysics Data System (ADS)

Ariyarit, Atthaphon; Sugiura, Masahiko; Tanabe, Yasutada; Kanazaki, Masahiro

2018-06-01

A multi-fidelity optimization technique by an efficient global optimization process using a hybrid surrogate model is investigated for solving real-world design problems. The model constructs the local deviation using the kriging method and the global model using a radial basis function. The expected improvement is computed to decide additional samples that can improve the model. The approach was first investigated by solving mathematical test problems. The results were compared with optimization results from an ordinary kriging method and a co-kriging method, and the proposed method produced the best solution. The proposed method was also applied to aerodynamic design optimization of helicopter blades to obtain the maximum blade efficiency. The optimal shape obtained by the proposed method achieved performance almost equivalent to that obtained using the high-fidelity, evaluation-based single-fidelity optimization. Comparing all three methods, the proposed method required the lowest total number of high-fidelity evaluation runs to obtain a converged solution.

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

High accurate interpolation of NURBS tool path for CNC machine tools

NASA Astrophysics Data System (ADS)

Liu, Qiang; Liu, Huan; Yuan, Songmei

2016-09-01

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.

On unified modeling, theory, and method for solving multi-scale global optimization problems

NASA Astrophysics Data System (ADS)

Gao, David Yang

2016-10-01

A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.

Efficient operator splitting algorithm for joint sparsity-regularized SPIRiT-based parallel MR imaging reconstruction.

PubMed

Duan, Jizhong; Liu, Yu; Jing, Peiguang

2018-02-01

Self-consistent parallel imaging (SPIRiT) is an auto-calibrating model for the reconstruction of parallel magnetic resonance imaging, which can be formulated as a regularized SPIRiT problem. The Projection Over Convex Sets (POCS) method was used to solve the formulated regularized SPIRiT problem. However, the quality of the reconstructed image still needs to be improved. Though methods such as NonLinear Conjugate Gradients (NLCG) can achieve higher spatial resolution, these methods always demand very complex computation and converge slowly. In this paper, we propose a new algorithm to solve the formulated Cartesian SPIRiT problem with the JTV and JL1 regularization terms. The proposed algorithm uses the operator splitting (OS) technique to decompose the problem into a gradient problem and a denoising problem with two regularization terms, which is solved by our proposed split Bregman based denoising algorithm, and adopts the Barzilai and Borwein method to update step size. Simulation experiments on two in vivo data sets demonstrate that the proposed algorithm is 1.3 times faster than ADMM for datasets with 8 channels. Especially, our proposal is 2 times faster than ADMM for the dataset with 32 channels. Copyright © 2017 Elsevier Inc. All rights reserved.

An evolutionary algorithm for large traveling salesman problems.

PubMed

Tsai, Huai-Kuang; Yang, Jinn-Moon; Tsai, Yuan-Fang; Kao, Cheng-Yan

2004-08-01

This work proposes an evolutionary algorithm, called the heterogeneous selection evolutionary algorithm (HeSEA), for solving large traveling salesman problems (TSP). The strengths and limitations of numerous well-known genetic operators are first analyzed, along with local search methods for TSPs from their solution qualities and mechanisms for preserving and adding edges. Based on this analysis, a new approach, HeSEA is proposed which integrates edge assembly crossover (EAX) and Lin-Kernighan (LK) local search, through family competition and heterogeneous pairing selection. This study demonstrates experimentally that EAX and LK can compensate for each other's disadvantages. Family competition and heterogeneous pairing selections are used to maintain the diversity of the population, which is especially useful for evolutionary algorithms in solving large TSPs. The proposed method was evaluated on 16 well-known TSPs in which the numbers of cities range from 318 to 13509. Experimental results indicate that HeSEA performs well and is very competitive with other approaches. The proposed method can determine the optimum path when the number of cities is under 10,000 and the mean solution quality is within 0.0074% above the optimum for each test problem. These findings imply that the proposed method can find tours robustly with a fixed small population and a limited family competition length in reasonable time, when used to solve large TSPs.

Non-recursive augmented Lagrangian algorithms for the forward and inverse dynamics of constrained flexible multibodies

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Ledesma, Ragnar

1993-01-01

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.

New algorithms for solving high even-order differential equations using third and fourth Chebyshev-Galerkin methods

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Bassuony, M. A.

2013-03-01

This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Rotational-path decomposition based recursive planning for spacecraft attitude reorientation

NASA Astrophysics Data System (ADS)

Xu, Rui; Wang, Hui; Xu, Wenming; Cui, Pingyuan; Zhu, Shengying

2018-02-01

The spacecraft reorientation is a common task in many space missions. With multiple pointing constraints, it is greatly difficult to solve the constrained spacecraft reorientation planning problem. To deal with this problem, an efficient rotational-path decomposition based recursive planning (RDRP) method is proposed in this paper. The uniform pointing-constraint-ignored attitude rotation planning process is designed to solve all rotations without considering pointing constraints. Then the whole path is checked node by node. If any pointing constraint is violated, the nearest critical increment approach will be used to generate feasible alternative nodes in the process of rotational-path decomposition. As the planning path of each subdivision may still violate pointing constraints, multiple decomposition is needed and the reorientation planning is designed as a recursive manner. Simulation results demonstrate the effectiveness of the proposed method. The proposed method has been successfully applied in two SPARK microsatellites to solve onboard constrained attitude reorientation planning problem, which were developed by the Shanghai Engineering Center for Microsatellites and launched on 22 December 2016.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

A new three-dimensional manufacturing service composition method under various structures using improved Flower Pollination Algorithm

NASA Astrophysics Data System (ADS)

Zhang, Wenyu; Yang, Yushu; Zhang, Shuai; Yu, Dejian; Chen, Yong

2018-05-01

With the growing complexity of customer requirements and the increasing scale of manufacturing services, how to select and combine the single services to meet the complex demand of the customer has become a growing concern. This paper presents a new manufacturing service composition method to solve the multi-objective optimization problem based on quality of service (QoS). The proposed model not only presents different methods for calculating the transportation time and transportation cost under various structures but also solves the three-dimensional composition optimization problem, including service aggregation, service selection, and service scheduling simultaneously. Further, an improved Flower Pollination Algorithm (IFPA) is proposed to solve the three-dimensional composition optimization problem using a matrix-based representation scheme. The mutation operator and crossover operator of the Differential Evolution (DE) algorithm are also used to extend the basic Flower Pollination Algorithm (FPA) to improve its performance. Compared to Genetic Algorithm, DE, and basic FPA, the experimental results confirm that the proposed method demonstrates superior performance than other meta heuristic algorithms and can obtain better manufacturing service composition solutions.

A recurrent neural network for solving bilevel linear programming problem.

PubMed

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

2014-04-01

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

Solving rational matrix equations in the state space with applications to computer-aided control-system design

NASA Technical Reports Server (NTRS)

Packard, A. K.; Sastry, S. S.

1986-01-01

A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Two new modified Gauss-Seidel methods for linear system with M-matrices

NASA Astrophysics Data System (ADS)

Zheng, Bing; Miao, Shu-Xin

2009-12-01

In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Adaptive sparsest narrow-band decomposition method and its applications to rolling element bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Cheng, Junsheng; Peng, Yanfeng; Yang, Yu; Wu, Zhantao

2017-02-01

Enlightened by ASTFA method, adaptive sparsest narrow-band decomposition (ASNBD) method is proposed in this paper. In ASNBD method, an optimized filter must be established at first. The parameters of the filter are determined by solving a nonlinear optimization problem. A regulated differential operator is used as the objective function so that each component is constrained to be a local narrow-band signal. Afterwards, the signal is filtered by the optimized filter to generate an intrinsic narrow-band component (INBC). ASNBD is proposed aiming at solving the problems existed in ASTFA. Gauss-Newton type method, which is applied to solve the optimization problem in ASTFA, is irreplaceable and very sensitive to initial values. However, more appropriate optimization method such as genetic algorithm (GA) can be utilized to solve the optimization problem in ASNBD. Meanwhile, compared with ASTFA, the decomposition results generated by ASNBD have better physical meaning by constraining the components to be local narrow-band signals. Comparisons are made between ASNBD, ASTFA and EMD by analyzing simulation and experimental signals. The results indicate that ASNBD method is superior to the other two methods in generating more accurate components from noise signal, restraining the boundary effect, possessing better orthogonality and diagnosing rolling element bearing fault.

Interior search algorithm (ISA): a novel approach for global optimization.

PubMed

Gandomi, Amir H

2014-07-01

This paper presents the interior search algorithm (ISA) as a novel method for solving optimization tasks. The proposed ISA is inspired by interior design and decoration. The algorithm is different from other metaheuristic algorithms and provides new insight for global optimization. The proposed method is verified using some benchmark mathematical and engineering problems commonly used in the area of optimization. ISA results are further compared with well-known optimization algorithms. The results show that the ISA is efficiently capable of solving optimization problems. The proposed algorithm can outperform the other well-known algorithms. Further, the proposed algorithm is very simple and it only has one parameter to tune. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A Distributed Algorithm for Economic Dispatch Over Time-Varying Directed Networks With Delays

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

Yang, Tao; Lu, Jie; Wu, Di

In power system operation, economic dispatch problem (EDP) is designed to minimize the total generation cost while meeting the demand and satisfying generator capacity limits. This paper proposes an algorithm based on the gradient-push method to solve the EDP in a distributed manner over communication networks potentially with time-varying topologies and communication delays. It has been shown that the proposed method is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, the proposed algorithm is also able to handle arbitrarily large but bounded time delays on communication links. Numerical simulations are usedmore » to illustrate and validate the proposed algorithm.« less

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES*

PubMed Central

Fu, Zhisong; Jeong, Won-Ki; Pan, Yongsheng; Kirby, Robert M.; Whitaker, Ross T.

2012-01-01

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton–Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512–2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers. PMID:22641200

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Problem Solving Method Based on E-Learning System for Engineering Education

ERIC Educational Resources Information Center

Khazaal, Hasan F.

2015-01-01

Encouraging engineering students to handle advanced technology with multimedia, as well as motivate them to have the skills of solving the problem, are the missions of the teacher in preparing students for a modern professional career. This research proposes a scenario of problem solving in basic electrical circuits based on an e-learning system…

Localization of synchronous cortical neural sources.

PubMed

Zerouali, Younes; Herry, Christophe L; Jemel, Boutheina; Lina, Jean-Marc

2013-03-01

Neural synchronization is a key mechanism to a wide variety of brain functions, such as cognition, perception, or memory. High temporal resolution achieved by EEG recordings allows the study of the dynamical properties of synchronous patterns of activity at a very fine temporal scale but with very low spatial resolution. Spatial resolution can be improved by retrieving the neural sources of EEG signal, thus solving the so-called inverse problem. Although many methods have been proposed to solve the inverse problem and localize brain activity, few of them target the synchronous brain regions. In this paper, we propose a novel algorithm aimed at localizing specifically synchronous brain regions and reconstructing the time course of their activity. Using multivariate wavelet ridge analysis, we extract signals capturing the synchronous events buried in the EEG and then solve the inverse problem on these signals. Using simulated data, we compare results of source reconstruction accuracy achieved by our method to a standard source reconstruction approach. We show that the proposed method performs better across a wide range of noise levels and source configurations. In addition, we applied our method on real dataset and identified successfully cortical areas involved in the functional network underlying visual face perception. We conclude that the proposed approach allows an accurate localization of synchronous brain regions and a robust estimation of their activity.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

An interior-point method-based solver for simulation of aircraft parts riveting

NASA Astrophysics Data System (ADS)

Stefanova, Maria; Yakunin, Sergey; Petukhova, Margarita; Lupuleac, Sergey; Kokkolaras, Michael

2018-05-01

The particularities of the aircraft parts riveting process simulation necessitate the solution of a large amount of contact problems. A primal-dual interior-point method-based solver is proposed for solving such problems efficiently. The proposed method features a worst case polynomial complexity bound ? on the number of iterations, where n is the dimension of the problem and ε is a threshold related to desired accuracy. In practice, the convergence is often faster than this worst case bound, which makes the method applicable to large-scale problems. The computational challenge is solving the system of linear equations because the associated matrix is ill conditioned. To that end, the authors introduce a preconditioner and a strategy for determining effective initial guesses based on the physics of the problem. Numerical results are compared with ones obtained using the Goldfarb-Idnani algorithm. The results demonstrate the efficiency of the proposed method.

An optical solution for the traveling salesman problem.

PubMed

Haist, Tobias; Osten, Wolfgang

2007-08-06

We introduce an optical method based on white light interferometry in order to solve the well-known NP-complete traveling salesman problem. To our knowledge it is the first time that a method for the reduction of non-polynomial time to quadratic time has been proposed. We will show that this achievement is limited by the number of available photons for solving the problem. It will turn out that this number of photons is proportional to N(N) for a traveling salesman problem with N cities and that for large numbers of cities the method in practice therefore is limited by the signal-to-noise ratio. The proposed method is meant purely as a gedankenexperiment.

Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.

PubMed

Mall, Susmita; Chakraverty, S

2016-08-01

Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

PubMed

Tanaka, Takashi

2017-04-15

A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

On the method of least squares. II. [for calculation of covariance matrices and optimization algorithms

NASA Technical Reports Server (NTRS)

Jefferys, W. H.

1981-01-01

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

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.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Iterative Nonlocal Total Variation Regularization Method for Image Restoration

PubMed Central

Xu, Huanyu; Sun, Quansen; Luo, Nan; Cao, Guo; Xia, Deshen

2013-01-01

In this paper, a Bregman iteration based total variation image restoration algorithm is proposed. Based on the Bregman iteration, the algorithm splits the original total variation problem into sub-problems that are easy to solve. Moreover, non-local regularization is introduced into the proposed algorithm, and a method to choose the non-local filter parameter locally and adaptively is proposed. Experiment results show that the proposed algorithms outperform some other regularization methods. PMID:23776560

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Swarm based mean-variance mapping optimization (MVMOS) for solving economic dispatch

NASA Astrophysics Data System (ADS)

Khoa, T. H.; Vasant, P. M.; Singh, M. S. Balbir; Dieu, V. N.

2014-10-01

The economic dispatch (ED) is an essential optimization task in the power generation system. It is defined as the process of allocating the real power output of generation units to meet required load demand so as their total operating cost is minimized while satisfying all physical and operational constraints. This paper introduces a novel optimization which named as Swarm based Mean-variance mapping optimization (MVMOS). The technique is the extension of the original single particle mean-variance mapping optimization (MVMO). Its features make it potentially attractive algorithm for solving optimization problems. The proposed method is implemented for three test power systems, including 3, 13 and 20 thermal generation units with quadratic cost function and the obtained results are compared with many other methods available in the literature. Test results have indicated that the proposed method can efficiently implement for solving economic dispatch.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Algorithms for Solvents and Spectral Factors of Matrix Polynomials

DTIC Science & Technology

1981-01-01

spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes

ERIC Educational Resources Information Center

Gauthier, N.

2004-01-01

An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…

Non-iterative geometric approach for inverse kinematics of redundant lead-module in a radiosurgical snake-like robot.

PubMed

Omisore, Olatunji Mumini; Han, Shipeng; Ren, Lingxue; Zhang, Nannan; Ivanov, Kamen; Elazab, Ahmed; Wang, Lei

2017-08-01

Snake-like robot is an emerging form of serial-link manipulator with the morphologic design of biological snakes. The redundant robot can be used to assist medical experts in accessing internal organs with minimal or no invasion. Several snake-like robotic designs have been proposed for minimal invasive surgery, however, the few that were developed are yet to be fully explored for clinical procedures. This is due to lack of capability for full-fledged spatial navigation. In rare cases where such snake-like designs are spatially flexible, there exists no inverse kinematics (IK) solution with both precise control and fast response. In this study, we proposed a non-iterative geometric method for solving IK of lead-module of a snake-like robot designed for therapy or ablation of abdominal tumors. The proposed method is aimed at providing accurate and fast IK solution for given target points in the robot's workspace. n-1 virtual points (VPs) were geometrically computed and set as coordinates of intermediary joints in an n-link module. Suitable joint angles that can place the end-effector at given target points were then computed by vectorizing coordinates of the VPs, in addition to coordinates of the base point, target point, and tip of the first link in its default pose. The proposed method is applied to solve IK of two-link and redundant four-link modules. Both two-link and four-link modules were simulated with Robotics Toolbox in Matlab 8.3 (R2014a). Implementation result shows that the proposed method can solve IK of the spatially flexible robot with minimal error values. Furthermore, analyses of results from both modules show that the geometric method can reach 99.21 and 88.61% of points in their workspaces, respectively, with an error threshold of 1 mm. The proposed method is non-iterative and has a maximum execution time of 0.009 s. This paper focuses on solving IK problem of a spatially flexible robot which is part of a developmental project for abdominal surgery through minimal invasion or natural orifices. The study showed that the proposed geometric method can resolve IK of the snake-like robot with negligible error offset. Evaluation against well-known methods shows that the proposed method can reach several points in the robot's workspace with high accuracy and shorter computational time, simultaneously.

A Novel Algorithm Combining Finite State Method and Genetic Algorithm for Solving Crude Oil Scheduling Problem

PubMed Central

Duan, Qian-Qian; Yang, Gen-Ke; Pan, Chang-Chun

2014-01-01

A hybrid optimization algorithm combining finite state method (FSM) and genetic algorithm (GA) is proposed to solve the crude oil scheduling problem. The FSM and GA are combined to take the advantage of each method and compensate deficiencies of individual methods. In the proposed algorithm, the finite state method makes up for the weakness of GA which is poor at local searching ability. The heuristic returned by the FSM can guide the GA algorithm towards good solutions. The idea behind this is that we can generate promising substructure or partial solution by using FSM. Furthermore, the FSM can guarantee that the entire solution space is uniformly covered. Therefore, the combination of the two algorithms has better global performance than the existing GA or FSM which is operated individually. Finally, a real-life crude oil scheduling problem from the literature is used for conducting simulation. The experimental results validate that the proposed method outperforms the state-of-art GA method. PMID:24772031

Learning locality preserving graph from data.

PubMed

Zhang, Yan-Ming; Huang, Kaizhu; Hou, Xinwen; Liu, Cheng-Lin

2014-11-01

Machine learning based on graph representation, or manifold learning, has attracted great interest in recent years. As the discrete approximation of data manifold, the graph plays a crucial role in these kinds of learning approaches. In this paper, we propose a novel learning method for graph construction, which is distinct from previous methods in that it solves an optimization problem with the aim of directly preserving the local information of the original data set. We show that the proposed objective has close connections with the popular Laplacian Eigenmap problem, and is hence well justified. The optimization turns out to be a quadratic programming problem with n(n-1)/2 variables (n is the number of data points). Exploiting the sparsity of the graph, we further propose a more efficient cutting plane algorithm to solve the problem, making the method better scalable in practice. In the context of clustering and semi-supervised learning, we demonstrated the advantages of our proposed method by experiments.

Multi-task feature selection in microarray data by binary integer programming.

PubMed

Lan, Liang; Vucetic, Slobodan

2013-12-20

A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.

Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance

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

Qi, Junjian; Huang, Weihong; Sun, Kai

In this paper, the empirical controllability covariance (ECC), which is calculated around the considered operating condition of a power system, is applied to quantify the degree of controllability of system voltages under specific dynamic var source locations. An optimal dynamic var source placement method addressing fault-induced delayed voltage recovery (FIDVR) issues is further formulated as an optimization problem that maximizes the determinant of ECC. The optimization problem is effectively solved by the NOMAD solver, which implements the mesh adaptive direct search algorithm. The proposed method is tested on an NPCC 140-bus system and the results show that the proposed methodmore » with fault specified ECC can solve the FIDVR issue caused by the most severe contingency with fewer dynamic var sources than the voltage sensitivity index (VSI)-based method. The proposed method with fault unspecified ECC does not depend on the settings of the contingency and can address more FIDVR issues than the VSI method when placing the same number of SVCs under different fault durations. It is also shown that the proposed method can help mitigate voltage collapse.« less

An accurate method for solving a class of fractional Sturm-Liouville eigenvalue problems

NASA Astrophysics Data System (ADS)

Kashkari, Bothayna S. H.; Syam, Muhammed I.

2018-06-01

This article is devoted to both theoretical and numerical study of the eigenvalues of nonsingular fractional second-order Sturm-Liouville problem. In this paper, we implement a fractional-order Legendre Tau method to approximate the eigenvalues. This method transforms the Sturm-Liouville problem to a sparse nonsingular linear system which is solved using the continuation method. Theoretical results for the considered problem are provided and proved. Numerical results are presented to show the efficiency of the proposed method.

Decomposition of timed automata for solving scheduling problems

NASA Astrophysics Data System (ADS)

Nishi, Tatsushi; Wakatake, Masato

2014-03-01

A decomposition algorithm for scheduling problems based on timed automata (TA) model is proposed. The problem is represented as an optimal state transition problem for TA. The model comprises of the parallel composition of submodels such as jobs and resources. The procedure of the proposed methodology can be divided into two steps. The first step is to decompose the TA model into several submodels by using decomposable condition. The second step is to combine individual solution of subproblems for the decomposed submodels by the penalty function method. A feasible solution for the entire model is derived through the iterated computation of solving the subproblem for each submodel. The proposed methodology is applied to solve flowshop and jobshop scheduling problems. Computational experiments demonstrate the effectiveness of the proposed algorithm compared with a conventional TA scheduling algorithm without decomposition.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

Efficient Power Network Analysis with Modeling of Inductive Effects

NASA Astrophysics Data System (ADS)

Zeng, Shan; Yu, Wenjian; Hong, Xianlong; Cheng, Chung-Kuan

In this paper, an efficient method is proposed to accurately analyze large-scale power/ground (P/G) networks, where inductive parasitics are modeled with the partial reluctance. The method is based on frequency-domain circuit analysis and the technique of vector fitting [14], and obtains the time-domain voltage response at given P/G nodes. The frequency-domain circuit equation including partial reluctances is derived, and then solved with the GMRES algorithm with rescaling, preconditioning and recycling techniques. With the merit of sparsified reluctance matrix and iterative solving techniques for the frequency-domain circuit equations, the proposed method is able to handle large-scale P/G networks with complete inductive modeling. Numerical results show that the proposed method is orders of magnitude faster than HSPICE, several times faster than INDUCTWISE [4], and capable of handling the inductive P/G structures with more than 100, 000 wire segments.

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

NASA Astrophysics Data System (ADS)

Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan

2017-02-01

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

Trust-aware recommendation for improving aggregate diversity

NASA Astrophysics Data System (ADS)

Liu, Haifeng; Bai, Xiaomei; Yang, Zhuo; Tolba, Amr; Xia, Feng

2015-10-01

Recommender systems are becoming increasingly important and prevalent because of the ability of solving information overload. In recent years, researchers are paying increasing attention to aggregate diversity as a key metric beyond accuracy, because improving aggregate recommendation diversity may increase long tails and sales diversity. Trust is often used to improve recommendation accuracy. However, how to utilize trust to improve aggregate recommendation diversity is unexplored. In this paper, we focus on solving this problem and propose a novel trust-aware recommendation method by incorporating time factor into similarity computation. The rationale underlying the proposed method is that, trustees with later creation time of trust relation can bring more diverse items to recommend to their trustors than other trustees with earlier creation time of trust relation. Through relevant experiments on publicly available dataset, we demonstrate that the proposed method outperforms the baseline method in terms of aggregate diversity while maintaining almost the same recall.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Solving the Container Stowage Problem (CSP) using Particle Swarm Optimization (PSO)

NASA Astrophysics Data System (ADS)

Matsaini; Santosa, Budi

2018-04-01

Container Stowage Problem (CSP) is a problem of containers arrangement into ships by considering rules such as: total weight, weight of one stack, destination, equilibrium, and placement of containers on vessel. Container stowage problem is combinatorial problem and hard to solve with enumeration technique. It is an NP-Hard Problem. Therefore, to find a solution, metaheuristics is preferred. The objective of solving the problem is to minimize the amount of shifting such that the unloading time is minimized. Particle Swarm Optimization (PSO) is proposed to solve the problem. The implementation of PSO is combined with some steps which are stack position change rules, stack changes based on destination, and stack changes based on the weight type of the stacks (light, medium, and heavy). The proposed method was applied on five different cases. The results were compared to Bee Swarm Optimization (BSO) and heuristics method. PSO provided mean of 0.87% gap and time gap of 60 second. While BSO provided mean of 2,98% gap and 459,6 second to the heuristcs.

Design and multi-physics optimization of rotary MRF brakes

NASA Astrophysics Data System (ADS)

Topcu, Okan; Taşcıoğlu, Yiğit; Konukseven, Erhan İlhan

2018-03-01

Particle swarm optimization (PSO) is a popular method to solve the optimization problems. However, calculations for each particle will be excessive when the number of particles and complexity of the problem increases. As a result, the execution speed will be too slow to achieve the optimized solution. Thus, this paper proposes an automated design and optimization method for rotary MRF brakes and similar multi-physics problems. A modified PSO algorithm is developed for solving multi-physics engineering optimization problems. The difference between the proposed method and the conventional PSO is to split up the original single population into several subpopulations according to the division of labor. The distribution of tasks and the transfer of information to the next party have been inspired by behaviors of a hunting party. Simulation results show that the proposed modified PSO algorithm can overcome the problem of heavy computational burden of multi-physics problems while improving the accuracy. Wire type, MR fluid type, magnetic core material, and ideal current inputs have been determined by the optimization process. To the best of the authors' knowledge, this multi-physics approach is novel for optimizing rotary MRF brakes and the developed PSO algorithm is capable of solving other multi-physics engineering optimization problems. The proposed method has showed both better performance compared to the conventional PSO and also has provided small, lightweight, high impedance rotary MRF brake designs.

Fully decoupled monolithic projection method for natural convection problems

NASA Astrophysics Data System (ADS)

Pan, Xiaomin; Kim, Kyoungyoun; Lee, Changhoon; Choi, Jung-Il

2017-04-01

To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. The proposed method applies the Crank-Nicolson scheme in time and the second-order central finite difference in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of the proposed method for velocity, pressure, and temperature in terms of a discrete l2-norm. Moreover, according to the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. In addition, we provide numerical simulations of two-dimensional Rayleigh-Bénard convection and periodic forced flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional Rayleigh-Bénard convection for different Rayleigh numbers.

Weighted least squares phase unwrapping based on the wavelet transform

NASA Astrophysics Data System (ADS)

Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

2007-01-01

The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction.

PubMed

Zheng, Wenming; Lin, Zhouchen; Wang, Haixian

2014-04-01

A novel discriminant analysis criterion is derived in this paper under the theoretical framework of Bayes optimality. In contrast to the conventional Fisher's discriminant criterion, the major novelty of the proposed one is the use of L1 norm rather than L2 norm, which makes it less sensitive to the outliers. With the L1-norm discriminant criterion, we propose a new linear discriminant analysis (L1-LDA) method for linear feature extraction problem. To solve the L1-LDA optimization problem, we propose an efficient iterative algorithm, in which a novel surrogate convex function is introduced such that the optimization problem in each iteration is to simply solve a convex programming problem and a close-form solution is guaranteed to this problem. Moreover, we also generalize the L1-LDA method to deal with the nonlinear robust feature extraction problems via the use of kernel trick, and hereafter proposed the L1-norm kernel discriminant analysis (L1-KDA) method. Extensive experiments on simulated and real data sets are conducted to evaluate the effectiveness of the proposed method in comparing with the state-of-the-art methods.

Computation of non-monotonic Lyapunov functions for continuous-time systems

NASA Astrophysics Data System (ADS)

Li, Huijuan; Liu, AnPing

2017-09-01

In this paper, we propose two methods to compute non-monotonic Lyapunov functions for continuous-time systems which are asymptotically stable. The first method is to solve a linear optimization problem on a compact and bounded set. The proposed linear programming based algorithm delivers a CPA1

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

Incompressible material point method for free surface flow

NASA Astrophysics Data System (ADS)

Zhang, Fan; Zhang, Xiong; Sze, Kam Yim; Lian, Yanping; Liu, Yan

2017-02-01

To overcome the shortcomings of the weakly compressible material point method (WCMPM) for modeling the free surface flow problems, an incompressible material point method (iMPM) is proposed based on operator splitting technique which splits the solution of momentum equation into two steps. An intermediate velocity field is first obtained by solving the momentum equations ignoring the pressure gradient term, and then the intermediate velocity field is corrected by the pressure term to obtain a divergence-free velocity field. A level set function which represents the signed distance to free surface is used to track the free surface and apply the pressure boundary conditions. Moreover, an hourglass damping is introduced to suppress the spurious velocity modes which are caused by the discretization of the cell center velocity divergence from the grid vertexes velocities when solving pressure Poisson equations. Numerical examples including dam break, oscillation of a cubic liquid drop and a droplet impact into deep pool show that the proposed incompressible material point method is much more accurate and efficient than the weakly compressible material point method in solving free surface flow problems.

Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

NASA Astrophysics Data System (ADS)

Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu

2015-12-01

For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.

Interference coupling analysis based on a hybrid method: application to a radio telescope system

NASA Astrophysics Data System (ADS)

Xu, Qing-Lin; Qiu, Yang; Tian, Jin; Liu, Qi

2018-02-01

Working in a way that passively receives electromagnetic radiation from a celestial body, a radio telescope can be easily disturbed by external radio frequency interference as well as electromagnetic interference generated by electric and electronic components operating at the telescope site. A quantitative analysis of these interferences must be taken into account carefully for further electromagnetic protection of the radio telescope. In this paper, based on electromagnetic topology theory, a hybrid method that combines the Baum-Liu-Tesche (BLT) equation and transfer function is proposed. In this method, the coupling path of the radio telescope is divided into strong coupling and weak coupling sub-paths, and the coupling intensity criterion is proposed by analyzing the conditions in which the BLT equation simplifies to a transfer function. According to the coupling intensity criterion, the topological model of a typical radio telescope system is established. The proposed method is used to solve the interference response of the radio telescope system by analyzing subsystems with different coupling modes separately and then integrating the responses of the subsystems as the response of the entire system. The validity of the proposed method is verified numerically. The results indicate that the proposed method, compared with the direct solving method, reduces the difficulty and improves the efficiency of interference prediction.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

NASA Astrophysics Data System (ADS)

Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li

2016-06-01

Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

Assessing Design Activity in Complex CMOS Circuit Design.

ERIC Educational Resources Information Center

Biswas, Gautam; And Others

This report characterizes human problem solving in digital circuit design. Protocols of 11 different designers with varying degrees of training were analyzed by identifying the designers' problem solving strategies and discussing activity patterns that differentiate the designers. These methods are proposed as a tentative basis for assessing…

A parallel orbital-updating based plane-wave basis method for electronic structure calculations

NASA Astrophysics Data System (ADS)

Pan, Yan; Dai, Xiaoying; de Gironcoli, Stefano; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui

2017-11-01

Motivated by the recently proposed parallel orbital-updating approach in real space method [1], we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

A review on classification methods for solving fully fuzzy linear systems

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Aziz, Khairu Azlan Abd

2015-12-01

Fully Fuzzy Linear System (FFLS) exists when there are fuzzy numbers on both sides of the linear systems. This system is quite significant today since most of the linear systems play with uncertainties of parameters especially in mathematics, engineering and finance. Many researchers and practitioners used the FFLS to model their problem and they apply various methods to solve it. In this paper, we present the outcome of a comprehensive review that we have done on various methods used for solving the FFLS. We classify our findings based on parameters' type used for the FFLS either restricted or unrestricted. We also discuss some of the methods by illustrating numerical examples and identify the differences between the methods. Ultimately, we summarize all findings in a table. We hope this study will encourage researchers to appreciate the use of this method and with that it will be easier for them to choose the right method or to propose any new method for solving the FFLS.

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

NASA Astrophysics Data System (ADS)

Gallinato, Olivier; Poignard, Clair

2017-06-01

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.

Regularization of nonlinear decomposition of spectral x-ray projection images.

PubMed

Ducros, Nicolas; Abascal, Juan Felipe Perez-Juste; Sixou, Bruno; Rit, Simon; Peyrin, Françoise

2017-09-01

Exploiting the x-ray measurements obtained in different energy bins, spectral computed tomography (CT) has the ability to recover the 3-D description of a patient in a material basis. This may be achieved solving two subproblems, namely the material decomposition and the tomographic reconstruction problems. In this work, we address the material decomposition of spectral x-ray projection images, which is a nonlinear ill-posed problem. Our main contribution is to introduce a material-dependent spatial regularization in the projection domain. The decomposition problem is solved iteratively using a Gauss-Newton algorithm that can benefit from fast linear solvers. A Matlab implementation is available online. The proposed regularized weighted least squares Gauss-Newton algorithm (RWLS-GN) is validated on numerical simulations of a thorax phantom made of up to five materials (soft tissue, bone, lung, adipose tissue, and gadolinium), which is scanned with a 120 kV source and imaged by a 4-bin photon counting detector. To evaluate the method performance of our algorithm, different scenarios are created by varying the number of incident photons, the concentration of the marker and the configuration of the phantom. The RWLS-GN method is compared to the reference maximum likelihood Nelder-Mead algorithm (ML-NM). The convergence of the proposed method and its dependence on the regularization parameter are also studied. We show that material decomposition is feasible with the proposed method and that it converges in few iterations. Material decomposition with ML-NM was very sensitive to noise, leading to decomposed images highly affected by noise, and artifacts even for the best case scenario. The proposed method was less sensitive to noise and improved contrast-to-noise ratio of the gadolinium image. Results were superior to those provided by ML-NM in terms of image quality and decomposition was 70 times faster. For the assessed experiments, material decomposition was possible with the proposed method when the number of incident photons was equal or larger than 10 5 and when the marker concentration was equal or larger than 0.03 g·cm -3 . The proposed method efficiently solves the nonlinear decomposition problem for spectral CT, which opens up new possibilities such as material-specific regularization in the projection domain and a parallelization framework, in which projections are solved in parallel. © 2017 American Association of Physicists in Medicine.

Self-Organizing Hierarchical Particle Swarm Optimization with Time-Varying Acceleration Coefficients for Economic Dispatch with Valve Point Effects and Multifuel Options

NASA Astrophysics Data System (ADS)

Polprasert, Jirawadee; Ongsakul, Weerakorn; Dieu, Vo Ngoc

2011-06-01

This paper proposes a self-organizing hierarchical particle swarm optimization (SPSO) with time-varying acceleration coefficients (TVAC) for solving economic dispatch (ED) problem with non-smooth functions including multiple fuel options (MFO) and valve-point loading effects (VPLE). The proposed SPSO with TVAC is the new approach optimizer and good performance for solving ED problems. It can handle the premature convergence of the problem by re-initialization of velocity whenever particles are stagnated in the search space. To properly control both local and global explorations of the swarm during the optimization process, the performance of TVAC is included. The proposed method is tested in different ED problems with non-smooth cost functions and the obtained results are compared to those from many other methods in the literature. The results have revealed that the proposed SPSO with TVAC is effective in finding higher quality solutions for non-smooth ED problems than many other methods.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

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.

Solving optimization problems by the public goods game

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto

2017-09-01

We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities. The proposed method considers a population whose agents are provided with a random solution to the given problem. In doing so, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. Notably, agents with better solutions provide higher contributions, while those with lower ones tend to imitate the solution of richer agents for increasing their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization problems, our work aims to highlight the potentiality of evolutionary game theory beyond its current horizons.

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

PubMed

Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya

2012-01-01

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena. However, coupling methods require a significant amount of calculation, since a system of non-linear equations must be solved for each timestep. Therefore, we proposed a coupling method which decreases the amount of calculation by using the Kalman filter. In our method, the Kalman filter calculates approximations for the solution to the system of non-linear equations at each timestep. The approximations are then used as initial values for solving the system of non-linear equations. The proposed method decreases the number of iterations required by 94.0% compared to the conventional strong coupling method. When compared with a smoothing spline predictor, the proposed method required 49.4% fewer iterations.

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

One cutting plane algorithm using auxiliary functions

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Kazaeva, K. E.

2016-11-01

We propose an algorithm for solving a convex programming problem from the class of cutting methods. The algorithm is characterized by the construction of approximations using some auxiliary functions, instead of the objective function. Each auxiliary function bases on the exterior penalty function. In proposed algorithm the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. In connection with the above, the iteration points are found by solving linear programming problems. We discuss the implementation of the algorithm and prove its convergence.

A constraint optimization based virtual network mapping method

NASA Astrophysics Data System (ADS)

Li, Xiaoling; Guo, Changguo; Wang, Huaimin; Li, Zhendong; Yang, Zhiwen

2013-03-01

Virtual network mapping problem, maps different virtual networks onto the substrate network is an extremely challenging work. This paper proposes a constraint optimization based mapping method for solving virtual network mapping problem. This method divides the problem into two phases, node mapping phase and link mapping phase, which are all NP-hard problems. Node mapping algorithm and link mapping algorithm are proposed for solving node mapping phase and link mapping phase, respectively. Node mapping algorithm adopts the thinking of greedy algorithm, mainly considers two factors, available resources which are supplied by the nodes and distance between the nodes. Link mapping algorithm is based on the result of node mapping phase, adopts the thinking of distributed constraint optimization method, which can guarantee to obtain the optimal mapping with the minimum network cost. Finally, simulation experiments are used to validate the method, and results show that the method performs very well.

An accelerated non-Gaussianity based multichannel predictive deconvolution method with the limited supporting region of filters

NASA Astrophysics Data System (ADS)

Li, Zhong-xiao; Li, Zhen-chun

2016-09-01

The multichannel predictive deconvolution can be conducted in overlapping temporal and spatial data windows to solve the 2D predictive filter for multiple removal. Generally, the 2D predictive filter can better remove multiples at the cost of more computation time compared with the 1D predictive filter. In this paper we first use the cross-correlation strategy to determine the limited supporting region of filters where the coefficients play a major role for multiple removal in the filter coefficient space. To solve the 2D predictive filter the traditional multichannel predictive deconvolution uses the least squares (LS) algorithm, which requires primaries and multiples are orthogonal. To relax the orthogonality assumption the iterative reweighted least squares (IRLS) algorithm and the fast iterative shrinkage thresholding (FIST) algorithm have been used to solve the 2D predictive filter in the multichannel predictive deconvolution with the non-Gaussian maximization (L1 norm minimization) constraint of primaries. The FIST algorithm has been demonstrated as a faster alternative to the IRLS algorithm. In this paper we introduce the FIST algorithm to solve the filter coefficients in the limited supporting region of filters. Compared with the FIST based multichannel predictive deconvolution without the limited supporting region of filters the proposed method can reduce the computation burden effectively while achieving a similar accuracy. Additionally, the proposed method can better balance multiple removal and primary preservation than the traditional LS based multichannel predictive deconvolution and FIST based single channel predictive deconvolution. Synthetic and field data sets demonstrate the effectiveness of the proposed method.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Two-dimensional frequency-domain acoustic full-waveform inversion with rugged topography

NASA Astrophysics Data System (ADS)

Zhang, Qian-Jiang; Dai, Shi-Kun; Chen, Long-Wei; Li, Kun; Zhao, Dong-Dong; Huang, Xing-Xing

2015-09-01

We studied finite-element-method-based two-dimensional frequency-domain acoustic FWI under rugged topography conditions. The exponential attenuation boundary condition suitable for rugged topography is proposed to solve the cutoff boundary problem as well as to consider the requirement of using the same subdivision grid in joint multifrequency inversion. The proposed method introduces the attenuation factor, and by adjusting it, acoustic waves are sufficiently attenuated in the attenuation layer to minimize the cutoff boundary effect. Based on the law of exponential attenuation, expressions for computing the attenuation factor and the thickness of attenuation layers are derived for different frequencies. In multifrequency-domain FWI, the conjugate gradient method is used to solve equations in the Gauss-Newton algorithm and thus minimize the computation cost in calculating the Hessian matrix. In addition, the effect of initial model selection and frequency combination on FWI is analyzed. Examples using numerical simulations and FWI calculations are used to verify the efficiency of the proposed method.

A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Li, Ruo; Tang, Tao; Zhang, Pingwen

2002-04-01

A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys.170, 562-588), we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an optimization problem with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detail features of singular problems in 3D.

Mathematical model and metaheuristics for simultaneous balancing and sequencing of a robotic mixed-model assembly line

NASA Astrophysics Data System (ADS)

Li, Zixiang; Janardhanan, Mukund Nilakantan; Tang, Qiuhua; Nielsen, Peter

2018-05-01

This article presents the first method to simultaneously balance and sequence robotic mixed-model assembly lines (RMALB/S), which involves three sub-problems: task assignment, model sequencing and robot allocation. A new mixed-integer programming model is developed to minimize makespan and, using CPLEX solver, small-size problems are solved for optimality. Two metaheuristics, the restarted simulated annealing algorithm and co-evolutionary algorithm, are developed and improved to address this NP-hard problem. The restarted simulated annealing method replaces the current temperature with a new temperature to restart the search process. The co-evolutionary method uses a restart mechanism to generate a new population by modifying several vectors simultaneously. The proposed algorithms are tested on a set of benchmark problems and compared with five other high-performing metaheuristics. The proposed algorithms outperform their original editions and the benchmarked methods. The proposed algorithms are able to solve the balancing and sequencing problem of a robotic mixed-model assembly line effectively and efficiently.

Solving traveling salesman problems with DNA molecules encoding numerical values.

PubMed

Lee, Ji Youn; Shin, Soo-Yong; Park, Tai Hyun; Zhang, Byoung-Tak

2004-12-01

We introduce a DNA encoding method to represent numerical values and a biased molecular algorithm based on the thermodynamic properties of DNA. DNA strands are designed to encode real values by variation of their melting temperatures. The thermodynamic properties of DNA are used for effective local search of optimal solutions using biochemical techniques, such as denaturation temperature gradient polymerase chain reaction and temperature gradient gel electrophoresis. The proposed method was successfully applied to the traveling salesman problem, an instance of optimization problems on weighted graphs. This work extends the capability of DNA computing to solving numerical optimization problems, which is contrasted with other DNA computing methods focusing on logical problem solving.

An exact algorithm for optimal MAE stack filter design.

PubMed

Dellamonica, Domingos; Silva, Paulo J S; Humes, Carlos; Hirata, Nina S T; Barrera, Junior

2007-02-01

We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems. Finally, we propose a specialization of the network Simplex algorithm based on column generation to solve these smaller subproblems. Using our method, we were able to efficiently solve instances of the filter problem with window size up to 25 pixels. To the best of our knowledge, this is the largest dimension for which this problem was ever solved exactly.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model.

PubMed

Hadinia, M; Jafari, R; Soleimani, M

2016-06-01

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

Improvements on ν-Twin Support Vector Machine.

PubMed

Khemchandani, Reshma; Saigal, Pooja; Chandra, Suresh

2016-07-01

In this paper, we propose two novel binary classifiers termed as "Improvements on ν-Twin Support Vector Machine: Iν-TWSVM and Iν-TWSVM (Fast)" that are motivated by ν-Twin Support Vector Machine (ν-TWSVM). Similar to ν-TWSVM, Iν-TWSVM determines two nonparallel hyperplanes such that they are closer to their respective classes and are at least ρ distance away from the other class. The significant advantage of Iν-TWSVM over ν-TWSVM is that Iν-TWSVM solves one smaller-sized Quadratic Programming Problem (QPP) and one Unconstrained Minimization Problem (UMP); as compared to solving two related QPPs in ν-TWSVM. Further, Iν-TWSVM (Fast) avoids solving a smaller sized QPP and transforms it as a unimodal function, which can be solved using line search methods and similar to Iν-TWSVM, the other problem is solved as a UMP. Due to their novel formulation, the proposed classifiers are faster than ν-TWSVM and have comparable generalization ability. Iν-TWSVM also implements structural risk minimization (SRM) principle by introducing a regularization term, along with minimizing the empirical risk. The other properties of Iν-TWSVM, related to support vectors (SVs), are similar to that of ν-TWSVM. To test the efficacy of the proposed method, experiments have been conducted on a wide range of UCI and a skewed variation of NDC datasets. We have also given the application of Iν-TWSVM as a binary classifier for pixel classification of color images. Copyright © 2016 Elsevier Ltd. All rights reserved.

A comparison of Heuristic method and Llewellyn’s rules for identification of redundant constraints

NASA Astrophysics Data System (ADS)

Estiningsih, Y.; Farikhin; Tjahjana, R. H.

2018-03-01

Important techniques in linear programming is modelling and solving practical optimization. Redundant constraints are consider for their effects on general linear programming problems. Identification and reduce redundant constraints are for avoidance of all the calculations associated when solving an associated linear programming problems. Many researchers have been proposed for identification redundant constraints. This paper a compararison of Heuristic method and Llewellyn’s rules for identification of redundant constraints.

A new principle technic for the transformation from frequency domain to time domain

NASA Astrophysics Data System (ADS)

Gao, Ben-Qing

2017-03-01

A principle technic for the transformation from frequency domain to time domain is presented. Firstly, a special type of frequency domain transcendental equation is obtained for an expected frequency domain parameter which is a rational or irrational fraction expression. Secondly, the inverse Laplace transformation is performed. When the two time-domain factors corresponding to the two frequency domain factors at two sides of frequency domain transcendental equation are known quantities, a time domain transcendental equation is reached. At last, the expected time domain parameter corresponding to the expected frequency domain parameter can be solved by the inverse convolution process. Proceeding from rational or irrational fraction expression, all solving process is provided. In the meantime, the property of time domain sequence is analyzed and the strategy for choosing the parameter values is described. Numerical examples are presented to verify the proposed theory and technic. Except for rational or irrational fraction expressions, examples of complex relative permittivity of water and plasma are used as verification method. The principle method proposed in the paper can easily solve problems which are difficult to be solved by Laplace transformation.

Separation of non-stationary multi-source sound field based on the interpolated time-domain equivalent source method

NASA Astrophysics Data System (ADS)

Bi, Chuan-Xing; Geng, Lin; Zhang, Xiao-Zheng

2016-05-01

In the sound field with multiple non-stationary sources, the measured pressure is the sum of the pressures generated by all sources, and thus cannot be used directly for studying the vibration and sound radiation characteristics of every source alone. This paper proposes a separation model based on the interpolated time-domain equivalent source method (ITDESM) to separate the pressure field belonging to every source from the non-stationary multi-source sound field. In the proposed method, ITDESM is first extended to establish the relationship between the mixed time-dependent pressure and all the equivalent sources distributed on every source with known location and geometry information, and all the equivalent source strengths at each time step are solved by an iterative solving process; then, the corresponding equivalent source strengths of one interested source are used to calculate the pressure field generated by that source alone. Numerical simulation of two baffled circular pistons demonstrates that the proposed method can be effective in separating the non-stationary pressure generated by every source alone in both time and space domains. An experiment with two speakers in a semi-anechoic chamber further evidences the effectiveness of the proposed method.

Automatic rule generation for high-level vision

NASA Technical Reports Server (NTRS)

Rhee, Frank Chung-Hoon; Krishnapuram, Raghu

1992-01-01

A new fuzzy set based technique that was developed for decision making is discussed. It is a method to generate fuzzy decision rules automatically for image analysis. This paper proposes a method to generate rule-based approaches to solve problems such as autonomous navigation and image understanding automatically from training data. The proposed method is also capable of filtering out irrelevant features and criteria from the rules.

Improving Histopathology Laboratory Productivity: Process Consultancy and A3 Problem Solving.

PubMed

Yörükoğlu, Kutsal; Özer, Erdener; Alptekin, Birsen; Öcal, Cem

2017-01-01

The ISO 17020 quality program has been run in our pathology laboratory for four years to establish an action plan for correction and prevention of identified errors. In this study, we aimed to evaluate the errors that we could not identify through ISO 17020 and/or solve by means of process consulting. Process consulting is carefully intervening in a group or team to help it to accomplish its goals. The A3 problem solving process was run under the leadership of a 'workflow, IT and consultancy manager'. An action team was established consisting of technical staff. A root cause analysis was applied for target conditions, and the 6-S method was implemented for solution proposals. Applicable proposals were activated and the results were rated by six-sigma analysis. Non-applicable proposals were reported to the laboratory administrator. A mislabelling error was the most complained issue triggering all pre-analytical errors. There were 21 non-value added steps grouped in 8 main targets on the fish bone graphic (transporting, recording, moving, individual, waiting, over-processing, over-transaction and errors). Unnecessary redundant requests, missing slides, archiving issues, redundant activities, and mislabelling errors were proposed to be solved by improving visibility and fixing spaghetti problems. Spatial re-organization, organizational marking, re-defining some operations, and labeling activities raised the six sigma score from 24% to 68% for all phases. Operational transactions such as implementation of a pathology laboratory system was suggested for long-term improvement. Laboratory management is a complex process. Quality control is an effective method to improve productivity. Systematic checking in a quality program may not always find and/or solve the problems. External observation may reveal crucial indicators about the system failures providing very simple solutions.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Distributed Combinatorial Optimization Using Privacy on Mobile Phones

NASA Astrophysics Data System (ADS)

Ono, Satoshi; Katayama, Kimihiro; Nakayama, Shigeru

This paper proposes a method for distributed combinatorial optimization which uses mobile phones as computers. In the proposed method, an ordinary computer generates solution candidates and mobile phones evaluates them by referring privacy — private information and preferences. Users therefore does not have to send their privacy to any other computers and does not have to refrain from inputting their preferences. They therefore can obtain satisfactory solution. Experimental results have showed the proposed method solved room assignment problems without sending users' privacy to a server.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Generalized Ordinary Differential Equation Models 1

PubMed Central

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-01-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. PMID:25544787

Generalized Ordinary Differential Equation Models.

PubMed

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

A new modified conjugate gradient coefficient for solving system of linear equations

NASA Astrophysics Data System (ADS)

Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

Research on Centralized Voltage and Effective Inequality Identification Based on Circuit Analysis Method

NASA Astrophysics Data System (ADS)

Su, Yi; Wang, Feifeng; Lu, Yufeng; Huang, Huimin; Xia, Xiaofei

2017-09-01

This paper is based on affine function equation of the grid and OPF problem, discusses the equivalent of some inequality constraints variables optimizing. Further, we propose the model of injection current and set up the constraint sensitivity index of affine characteristics. The index can be used to identify the central point voltage and effective inequality of the system automatically. And then we can know how to compensate reactive power of the corresponding generator node and control the voltage to ensure the quality of the system voltage. When checking the effective inequalities we introduce cross-solving method of power flow. This provide a different idea for solving the power flow. The paper uses the results of the IEEE5 node examples to illustrate the validity and practicality of the proposed method.

Competitive Facility Location with Fuzzy Random Demands

NASA Astrophysics Data System (ADS)

Uno, Takeshi; Katagiri, Hideki; Kato, Kosuke

2010-10-01

This paper proposes a new location problem of competitive facilities, e.g. shops, with uncertainty and vagueness including demands for the facilities in a plane. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the proposed method is shown by applying it to numerical examples of the facility location problems.

Finding Dantzig Selectors with a Proximity Operator based Fixed-point Algorithm

DTIC Science & Technology

2014-11-01

experiments showed that this method usually outperforms the method in [2] in terms of CPU time while producing solutions of comparable quality. The... method proposed in [19]. To alleviate the difficulty caused by the subprob- lem without a closed form solution , a linearized ADM was proposed for the...a closed form solution , but the β-related subproblem does not and is solved approximately by using the nonmonotone gradient method in [18]. The

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

NASA Astrophysics Data System (ADS)

Chang, Yong; Zi, Yanyang; Zhao, Jiyuan; Yang, Zhe; He, Wangpeng; Sun, Hailiang

2017-03-01

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the prototype of the convolution matrix, without considering the waveform change caused by the dispersion properties of the guided wave. In this paper, an adaptive sparse deconvolution (ASD) method is proposed to overcome these limitations. First, the Gaussian echo model is employed to adaptively estimate the column prototype of the convolution matrix instead of directly using the input signal as the prototype. Then, the convolution matrix is constructed upon the estimated results. Third, the split augmented Lagrangian shrinkage (SALSA) algorithm is introduced to solve the deconvolution problem with high computational efficiency. To verify the effectiveness of the proposed method, guided wave signals obtained from pipeline inspection are investigated numerically and experimentally. Compared to conventional sparse deconvolution methods, e.g. the {{l}1} -norm deconvolution method, the proposed method shows better performance in handling the echo overlap problem in the guided wave signal.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

PubMed

Rajeswari, M; Amudhavel, J; Pothula, Sujatha; Dhavachelvan, P

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

PubMed Central

Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849

A hybrid CS-SA intelligent approach to solve uncertain dynamic facility layout problems considering dependency of demands

NASA Astrophysics Data System (ADS)

Moslemipour, Ghorbanali

2018-07-01

This paper aims at proposing a quadratic assignment-based mathematical model to deal with the stochastic dynamic facility layout problem. In this problem, product demands are assumed to be dependent normally distributed random variables with known probability density function and covariance that change from period to period at random. To solve the proposed model, a novel hybrid intelligent algorithm is proposed by combining the simulated annealing and clonal selection algorithms. The proposed model and the hybrid algorithm are verified and validated using design of experiment and benchmark methods. The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time points of view. Besides, the proposed model can be used in both of the stochastic and deterministic situations.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

A Flexible and Efficient Method for Solving Ill-Posed Linear Integral Equations of the First Kind for Noisy Data

NASA Astrophysics Data System (ADS)

Antokhin, I. I.

2017-06-01

We propose an efficient and flexible method for solving Fredholm and Abel integral equations of the first kind, frequently appearing in astrophysics. These equations present an ill-posed problem. Our method is based on solving them on a so-called compact set of functions and/or using Tikhonov's regularization. Both approaches are non-parametric and do not require any theoretic model, apart from some very loose a priori constraints on the unknown function. The two approaches can be used independently or in a combination. The advantage of the method, apart from its flexibility, is that it gives uniform convergence of the approximate solution to the exact one, as the errors of input data tend to zero. Simulated and astrophysical examples are presented.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

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

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

NASA Astrophysics Data System (ADS)

Shao, Zhongshi; Pi, Dechang; Shao, Weishi

2017-11-01

This article proposes an extended continuous estimation of distribution algorithm (ECEDA) to solve the permutation flow-shop scheduling problem (PFSP). In ECEDA, to make a continuous estimation of distribution algorithm (EDA) suitable for the PFSP, the largest order value rule is applied to convert continuous vectors to discrete job permutations. A probabilistic model based on a mixed Gaussian and Cauchy distribution is built to maintain the exploration ability of the EDA. Two effective local search methods, i.e. revolver-based variable neighbourhood search and Hénon chaotic-based local search, are designed and incorporated into the EDA to enhance the local exploitation. The parameters of the proposed ECEDA are calibrated by means of a design of experiments approach. Simulation results and comparisons based on some benchmark instances show the efficiency of the proposed algorithm for solving the PFSP.

Comment on ``Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation''

NASA Astrophysics Data System (ADS)

Lallemand, Pierre; Luo, Li-Shi

2008-12-01

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

A general soft label based linear discriminant analysis for semi-supervised dimensionality reduction.

PubMed

Zhao, Mingbo; Zhang, Zhao; Chow, Tommy W S; Li, Bing

2014-07-01

Dealing with high-dimensional data has always been a major problem in research of pattern recognition and machine learning, and Linear Discriminant Analysis (LDA) is one of the most popular methods for dimension reduction. However, it only uses labeled samples while neglecting unlabeled samples, which are abundant and can be easily obtained in the real world. In this paper, we propose a new dimension reduction method, called "SL-LDA", by using unlabeled samples to enhance the performance of LDA. The new method first propagates label information from the labeled set to the unlabeled set via a label propagation process, where the predicted labels of unlabeled samples, called "soft labels", can be obtained. It then incorporates the soft labels into the construction of scatter matrixes to find a transformed matrix for dimension reduction. In this way, the proposed method can preserve more discriminative information, which is preferable when solving the classification problem. We further propose an efficient approach for solving SL-LDA under a least squares framework, and a flexible method of SL-LDA (FSL-LDA) to better cope with datasets sampled from a nonlinear manifold. Extensive simulations are carried out on several datasets, and the results show the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Thermal boundary layer due to sudden heating of fluid

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

Kurkal, K.R.; Munukutla, S.

This paper proposes to solve computationally the heat-transfer problems (introduced by Munukutla and Venkataraman, 1988) related to a closed-cycle pulsed high-power laser flow loop. The continuity and the momentum equations as well as the unsteady energy equation are solved using the Keller-Box method. The solutions were compared with the steady-state solutions at large times, and the comparison was found to be excellent. Empirical formulas are proposed for calculating the time-dependent boundary-layer thickness and mass-heat transfer, that can be used by laser flow loop designers. 6 refs.

Thermal boundary layer due to sudden heating of fluid

NASA Astrophysics Data System (ADS)

Kurkal, K. R.; Munukutla, S.

1989-10-01

This paper proposes to solve computationally the heat-transfer problems (introduced by Munukutla and Venkataraman, 1988) related to a closed-cycle pulsed high-power laser flow loop. The continuity and the momentum equations as well as the unsteady energy equation are solved using the Keller-Box method. The solutions were compared with the steady-state solutions at large times, and the comparison was found to be excellent. Empirical formulas are proposed for calculating the time-dependent boundary-layer thickness and mass-heat transfer, that can be used by laser flow loop designers.

Dynamic Restructuring Of Problems In Artificial Intelligence

NASA Technical Reports Server (NTRS)

Schwuttke, Ursula M.

1992-01-01

"Dynamic tradeoff evaluation" (DTE) denotes proposed method and procedure for restructuring problem-solving strategies in artificial intelligence to satisfy need for timely responses to changing conditions. Detects situations in which optimal problem-solving strategies cannot be pursued because of real-time constraints, and effects tradeoffs among nonoptimal strategies in such way to minimize adverse effects upon performance of system.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

A projection method for low speed flows

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

Colella, P.; Pao, K.

The authors propose a decomposition applicable to low speed, inviscid flows of all Mach numbers less than 1. By using the Hodge decomposition, they may write the velocity field as the sum of a divergence-free vector field and a gradient of a scalar function. Evolution equations for these parts are presented. A numerical procedure based on this decomposition is designed, using projection methods for solving the incompressible variables and a backward-Euler method for solving the potential variables. Numerical experiments are included to illustrate various aspects of the algorithm.

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

The Research of Improving the Particleboard Glue Dosing Process Based on TRIZ Analysis

NASA Astrophysics Data System (ADS)

Yu, Huiling; Fan, Delin; Zhang, Yizhuo

This research creates a design methodology by synthesizing the Theory of Inventive Problem Solving (TRIZ) and cascade control based on Smith predictor. The particleboard glue supplying and dosing system case study defines the problem and the solution using the methodology proposed in the paper. Status difference existing in the gluing dosing process of particleboard production usually causes gluing volume inaccurately. In order to solve the problem above, we applied the TRIZ technical contradiction and inventive principle to improve the key process of particleboard production. The improving method mapped inaccurate problem to TRIZ technical contradiction, the prior action proposed Smith predictor as the control algorithm in the glue dosing system. This research examines the usefulness of a TRIZ based problem-solving process designed to improve the problem-solving ability of users in addressing difficult or reoccurring problems and also testify TRIZ is practicality and validity. Several suggestions are presented on how to approach this problem.

Three-dimensional electrical impedance tomography: a topology optimization approach.

PubMed

Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

2008-02-01

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Decision feedback equalizer for holographic data storage.

PubMed

Kim, Kyuhwan; Kim, Seung Hun; Koo, Gyogwon; Seo, Min Seok; Kim, Sang Woo

2018-05-20

Holographic data storage (HDS) has attracted much attention as a next-generation storage medium. Because HDS suffers from two-dimensional (2D) inter-symbol interference (ISI), the partial-response maximum-likelihood (PRML) method has been studied to reduce 2D ISI. However, the PRML method has various drawbacks. To solve the problems, we propose a modified decision feedback equalizer (DFE) for HDS. To prevent the error propagation problem, which is a typical problem in DFEs, we also propose a reliability factor for HDS. Various simulations were executed to analyze the performance of the proposed methods. The proposed methods showed fast processing speed after training, superior bit error rate performance, and consistency.

Automatic rule generation for high-level vision

NASA Technical Reports Server (NTRS)

Rhee, Frank Chung-Hoon; Krishnapuram, Raghu

1992-01-01

Many high-level vision systems use rule-based approaches to solving problems such as autonomous navigation and image understanding. The rules are usually elaborated by experts. However, this procedure may be rather tedious. In this paper, we propose a method to generate such rules automatically from training data. The proposed method is also capable of filtering out irrelevant features and criteria from the rules.

An exploration for research-oriented teaching model in biology teaching.

PubMed

Xing, Wanjin; Mo, Morigen; Su, Huimin

2014-07-01

Training innovative talents, as one of the major aims for Chinese universities, needs to reform the traditional teaching methods. The research-oriented teaching method has been introduced and its connotation and significance for Chinese university teaching have been discussed for years. However, few practical teaching methods for routine class teaching were proposed. In this paper, a comprehensive and concrete research-oriented teaching model with contents of reference value and evaluation method for class teaching was proposed based on the current teacher-guiding teaching model in China. We proposed that the research-oriented teaching model should include at least seven aspects on: (1) telling the scientific history for the skills to find out scientific questions; (2) replaying the experiments for the skills to solve scientific problems; (3) analyzing experimental data for learning how to draw a conclusion; (4) designing virtual experiments for learning how to construct a proposal; (5) teaching the lesson as the detectives solve the crime for learning the logic in scientific exploration; (6) guiding students how to read and consult the relative references; (7) teaching students differently according to their aptitude and learning ability. In addition, we also discussed how to evaluate the effects of the research-oriented teaching model in examination.

A Legendre tau-spectral method for solving time-fractional heat equation with nonlocal conditions.

PubMed

Bhrawy, A H; Alghamdi, M A

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem.

A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions

PubMed Central

Bhrawy, A. H.; Alghamdi, M. A.

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-01-01

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

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

Three-Component Decomposition of Polarimetric SAR Data Integrating Eigen-Decomposition Results

NASA Astrophysics Data System (ADS)

Lu, Da; He, Zhihua; Zhang, Huan

2018-01-01

This paper presents a novel three-component scattering power decomposition of polarimetric SAR data. There are two problems in three-component decomposition method: volume scattering component overestimation in urban areas and artificially set parameter to be a fixed value. Though volume scattering component overestimation can be partly solved by deorientation process, volume scattering still dominants some oriented urban areas. The speckle-like decomposition results introduced by artificially setting value are not conducive to further image interpretation. This paper integrates the results of eigen-decomposition to solve the aforementioned problems. Two principal eigenvectors are used to substitute the surface scattering model and the double bounce scattering model. The decomposed scattering powers are obtained using a constrained linear least-squares method. The proposed method has been verified using an ESAR PolSAR image, and the results show that the proposed method has better performance in urban area.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Distributed support vector machine in master-slave mode.

PubMed

Chen, Qingguo; Cao, Feilong

2018-05-01

It is well known that the support vector machine (SVM) is an effective learning algorithm. The alternating direction method of multipliers (ADMM) algorithm has emerged as a powerful technique for solving distributed optimisation models. This paper proposes a distributed SVM algorithm in a master-slave mode (MS-DSVM), which integrates a distributed SVM and ADMM acting in a master-slave configuration where the master node and slave nodes are connected, meaning the results can be broadcasted. The distributed SVM is regarded as a regularised optimisation problem and modelled as a series of convex optimisation sub-problems that are solved by ADMM. Additionally, the over-relaxation technique is utilised to accelerate the convergence rate of the proposed MS-DSVM. Our theoretical analysis demonstrates that the proposed MS-DSVM has linear convergence, meaning it possesses the fastest convergence rate among existing standard distributed ADMM algorithms. Numerical examples demonstrate that the convergence and accuracy of the proposed MS-DSVM are superior to those of existing methods under the ADMM framework. Copyright © 2018 Elsevier Ltd. All rights reserved.

New conditions for obtaining the exact solutions of the general Riccati equation.

PubMed

Bougoffa, Lazhar

2014-01-01

We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.

Variational estimate method for solving autonomous ordinary differential equations

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi

2018-04-01

In this paper, we propose a method for solving first-order autonomous ordinary differential equation problems using a variational estimate formulation. The variational estimate is constructed with a Lagrange multiplier which is chosen optimally, so that the formulation leads to an accurate solution to the problem. The variational estimate is an integral form, which can be computed using a computer software. As the variational estimate is an explicit formula, the solution is easy to compute. This is a great advantage of the variational estimate formulation.

Matching by linear programming and successive convexification.

PubMed

Jiang, Hao; Drew, Mark S; Li, Ze-Nian

2007-06-01

We present a novel convex programming scheme to solve matching problems, focusing on the challenging problem of matching in a large search range and with cluttered background. Matching is formulated as metric labeling with L1 regularization terms, for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation. The unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space. This greatly reduces the size of the searching space. A successive convexification scheme solves the labeling problem in a coarse to fine manner. Importantly, the original cost function is reconvexified at each stage, in the new focus region only, and the focus region is updated so as to refine the searching result. This makes the method well-suited for large label set matching. Experiments demonstrate successful applications of the proposed matching scheme in object detection, motion estimation, and tracking.

An adaptive time-stepping strategy for solving the phase field crystal model

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

Zhang, Zhengru, E-mail: zrzhang@bnu.edu.cn; Ma, Yuan, E-mail: yuner1022@gmail.com; Qiao, Zhonghua, E-mail: zqiao@polyu.edu.hk

2013-09-15

In this work, we will propose an adaptive time step method for simulating the dynamics of the phase field crystal (PFC) model. The numerical simulation of the PFC model needs long time to reach steady state, and then large time-stepping method is necessary. Unconditionally energy stable schemes are used to solve the PFC model. The time steps are adaptively determined based on the time derivative of the corresponding energy. It is found that the use of the proposed time step adaptivity cannot only resolve the steady state solution, but also the dynamical development of the solution efficiently and accurately. Themore » numerical experiments demonstrate that the CPU time is significantly saved for long time simulations.« less

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

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

Zheng, Bin; Chen, Luoping; Hu, Xiaozhe

2016-03-05

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigatemore » the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.« less

A solution quality assessment method for swarm intelligence optimization algorithms.

PubMed

Zhang, Zhaojun; Wang, Gai-Ge; Zou, Kuansheng; Zhang, Jianhua

2014-01-01

Nowadays, swarm intelligence optimization has become an important optimization tool and wildly used in many fields of application. In contrast to many successful applications, the theoretical foundation is rather weak. Therefore, there are still many problems to be solved. One problem is how to quantify the performance of algorithm in finite time, that is, how to evaluate the solution quality got by algorithm for practical problems. It greatly limits the application in practical problems. A solution quality assessment method for intelligent optimization is proposed in this paper. It is an experimental analysis method based on the analysis of search space and characteristic of algorithm itself. Instead of "value performance," the "ordinal performance" is used as evaluation criteria in this method. The feasible solutions were clustered according to distance to divide solution samples into several parts. Then, solution space and "good enough" set can be decomposed based on the clustering results. Last, using relative knowledge of statistics, the evaluation result can be got. To validate the proposed method, some intelligent algorithms such as ant colony optimization (ACO), particle swarm optimization (PSO), and artificial fish swarm algorithm (AFS) were taken to solve traveling salesman problem. Computational results indicate the feasibility of proposed method.

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

NASA Astrophysics Data System (ADS)

Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

2015-11-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier-Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

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

Kawai, Soshi, E-mail: kawai@cfd.mech.tohoku.ac.jp; Terashima, Hiroshi; Negishi, Hideyo

2015-11-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture themore » steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.« less

The algorithm of fast image stitching based on multi-feature extraction

NASA Astrophysics Data System (ADS)

Yang, Chunde; Wu, Ge; Shi, Jing

2018-05-01

This paper proposed an improved image registration method combining Hu-based invariant moment contour information and feature points detection, aiming to solve the problems in traditional image stitching algorithm, such as time-consuming feature points extraction process, redundant invalid information overload and inefficiency. First, use the neighborhood of pixels to extract the contour information, employing the Hu invariant moment as similarity measure to extract SIFT feature points in those similar regions. Then replace the Euclidean distance with Hellinger kernel function to improve the initial matching efficiency and get less mismatching points, further, estimate affine transformation matrix between the images. Finally, local color mapping method is adopted to solve uneven exposure, using the improved multiresolution fusion algorithm to fuse the mosaic images and realize seamless stitching. Experimental results confirm high accuracy and efficiency of method proposed in this paper.

Solving large scale traveling salesman problems by chaotic neurodynamics.

PubMed

Hasegawa, Mikio; Ikeguch, Tohru; Aihara, Kazuyuki

2002-03-01

We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.

An extended basis inexact shift-invert Lanczos for the efficient solution of large-scale generalized eigenproblems

NASA Astrophysics Data System (ADS)

Rewieński, M.; Lamecki, A.; Mrozowski, M.

2013-09-01

This paper proposes a technique, based on the Inexact Shift-Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the 'inexact solve' concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed.

A Hybrid alldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles

PubMed Central

Crawford, Broderick; Paredes, Fernando; Norero, Enrique

2015-01-01

The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a n 2 × n 2 grid, composed of n columns, n rows, and n subgrids, each one containing distinct integers from 1 to n 2. Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world. The alldifferent constraint is known to be efficient for domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods. PMID:26078751

A Hybrid alldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles.

PubMed

Soto, Ricardo; Crawford, Broderick; Galleguillos, Cristian; Paredes, Fernando; Norero, Enrique

2015-01-01

The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a n(2) × n(2) grid, composed of n columns, n rows, and n subgrids, each one containing distinct integers from 1 to n(2). Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world. The alldifferent constraint is known to be efficient for domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods.

Optimal External Wrench Distribution During a Multi-Contact Sit-to-Stand Task.

PubMed

Bonnet, Vincent; Azevedo-Coste, Christine; Robert, Thomas; Fraisse, Philippe; Venture, Gentiane

2017-07-01

This paper aims at developing and evaluating a new practical method for the real-time estimate of joint torques and external wrenches during multi-contact sit-to-stand (STS) task using kinematics data only. The proposed method allows also identifying subject specific body inertial segment parameters that are required to perform inverse dynamics. The identification phase is performed using simple and repeatable motions. Thanks to an accurately identified model the estimate of the total external wrench can be used as an input to solve an under-determined multi-contact problem. It is solved using a constrained quadratic optimization process minimizing a hybrid human-like energetic criterion. The weights of this hybrid cost function are adjusted and a sensitivity analysis is performed in order to reproduce robustly human external wrench distribution. The results showed that the proposed method could successfully estimate the external wrenches under buttocks, feet, and hands during STS tasks (RMS error lower than 20 N and 6 N.m). The simplicity and generalization abilities of the proposed method allow paving the way of future diagnosis solutions and rehabilitation applications, including in-home use.

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

NASA Astrophysics Data System (ADS)

Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

2017-10-01

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

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.

A postprocessing method in the HMC framework for predicting gene function based on biological instrumental data

NASA Astrophysics Data System (ADS)

Feng, Shou; Fu, Ping; Zheng, Wenbin

2018-03-01

Predicting gene function based on biological instrumental data is a complicated and challenging hierarchical multi-label classification (HMC) problem. When using local approach methods to solve this problem, a preliminary results processing method is usually needed. This paper proposed a novel preliminary results processing method called the nodes interaction method. The nodes interaction method revises the preliminary results and guarantees that the predictions are consistent with the hierarchy constraint. This method exploits the label dependency and considers the hierarchical interaction between nodes when making decisions based on the Bayesian network in its first phase. In the second phase, this method further adjusts the results according to the hierarchy constraint. Implementing the nodes interaction method in the HMC framework also enhances the HMC performance for solving the gene function prediction problem based on the Gene Ontology (GO), the hierarchy of which is a directed acyclic graph that is more difficult to tackle. The experimental results validate the promising performance of the proposed method compared to state-of-the-art methods on eight benchmark yeast data sets annotated by the GO.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

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

2014-03-01

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

The two-phase method for finding a great number of eigenpairs of the symmetric or weakly non-symmetric large eigenvalue problems

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

Dul, F.A.; Arczewski, K.

1994-03-01

Although it has been stated that [open quotes]an attempt to solve (very large problems) by subspace iterations seems futile[close quotes], we will show that the statement is not true, especially for extremely large eigenproblems. In this paper a new two-phase subspace iteration/Rayleigh quotient/conjugate gradient method for generalized, large, symmetric eigenproblems Ax = [lambda]Bx is presented. It has the ability of solving extremely large eigenproblems, N = 216,000, for example, and finding a large number of leftmost or rightmost eigenpairs, up to 1000 or more. Multiple eigenpairs, even those with multiplicity 100, can be easily found. The use of the proposedmore » method for solving the big full eigenproblems (N [approximately] 10[sup 3]), as well as for large weakly non-symmetric eigenproblems, have been considered also. The proposed method is fully iterative; thus the factorization of matrices ins avoided. The key idea consists in joining two methods: subspace and Rayleigh quotient iterations. The systems of indefinite and almost singular linear equations (a - [sigma]B)x = By are solved by various iterative conjugate gradient method can be used without danger of breaking down due to its property that may be called [open quotes]self-correction towards the eigenvector,[close quotes] discovered recently by us. The use of various preconditioners (SSOR and IC) has also been considered. The main features of the proposed method have been analyzed in detail. Comparisons with other methods, such as, accelerated subspace iteration, Lanczos, Davidson, TLIME, TRACMN, and SRQMCG, are presented. The results of numerical tests for various physical problems (acoustic, vibrations of structures, quantum chemistry) are presented as well. 40 refs., 12 figs., 2 tabs.« less

Use of Concept Profile Analysis to Identify Difficulties in Solving Science Problems.

ERIC Educational Resources Information Center

Gorodetsky, Malka; Hoz, Ron

1980-01-01

Proposed is a new method for analyzing how concepts are used in the process of problem solving in science. Through the use of a "thinking aloud" interview technique, 21 tenth-grade students worked with a problem concerning the boiling point of water at the Dead Sea. Interview protocols were analyzed to develop students' concept profiles.…

W-algebra for solving problems with fuzzy parameters

NASA Astrophysics Data System (ADS)

Shevlyakov, A. O.; Matveev, M. G.

2018-03-01

A method of solving the problems with fuzzy parameters by means of a special algebraic structure is proposed. The structure defines its operations through operations on real numbers, which simplifies its use. It avoids deficiencies limiting applicability of the other known structures. Examples for solution of a quadratic equation, a system of linear equations and a network planning problem are given.

A novel minimum cost maximum power algorithm for future smart home energy management.

PubMed

Singaravelan, A; Kowsalya, M

2017-11-01

With the latest development of smart grid technology, the energy management system can be efficiently implemented at consumer premises. In this paper, an energy management system with wireless communication and smart meter are designed for scheduling the electric home appliances efficiently with an aim of reducing the cost and peak demand. For an efficient scheduling scheme, the appliances are classified into two types: uninterruptible and interruptible appliances. The problem formulation was constructed based on the practical constraints that make the proposed algorithm cope up with the real-time situation. The formulated problem was identified as Mixed Integer Linear Programming (MILP) problem, so this problem was solved by a step-wise approach. This paper proposes a novel Minimum Cost Maximum Power (MCMP) algorithm to solve the formulated problem. The proposed algorithm was simulated with input data available in the existing method. For validating the proposed MCMP algorithm, results were compared with the existing method. The compared results prove that the proposed algorithm efficiently reduces the consumer electricity consumption cost and peak demand to optimum level with 100% task completion without sacrificing the consumer comfort.

A new distributed systems scheduling algorithm: a swarm intelligence approach

NASA Astrophysics Data System (ADS)

Haghi Kashani, Mostafa; Sarvizadeh, Raheleh; Jameii, Mahdi

2011-12-01

The scheduling problem in distributed systems is known as an NP-complete problem, and methods based on heuristic or metaheuristic search have been proposed to obtain optimal and suboptimal solutions. The task scheduling is a key factor for distributed systems to gain better performance. In this paper, an efficient method based on memetic algorithm is developed to solve the problem of distributed systems scheduling. With regard to load balancing efficiently, Artificial Bee Colony (ABC) has been applied as local search in the proposed memetic algorithm. The proposed method has been compared to existing memetic-Based approach in which Learning Automata method has been used as local search. The results demonstrated that the proposed method outperform the above mentioned method in terms of communication cost.

Proposal of Evolutionary Simplex Method for Global Optimization Problem

NASA Astrophysics Data System (ADS)

Shimizu, Yoshiaki

To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.

Cell tracking for cell image analysis

NASA Astrophysics Data System (ADS)

Bise, Ryoma; Sato, Yoichi

2017-04-01

Cell image analysis is important for research and discovery in biology and medicine. In this paper, we present our cell tracking methods, which is capable of obtaining fine-grain cell behavior metrics. In order to address difficulties under dense culture conditions, where cell detection cannot be done reliably since cell often touch with blurry intercellular boundaries, we proposed two methods which are global data association and jointly solving cell detection and association. We also show the effectiveness of the proposed methods by applying the method to the biological researches.

A homotopy analysis method for the nonlinear partial differential equations arising in engineering

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

GHM method for obtaining rationalsolutions of nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

2015-01-01

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

Planning and Scheduling for Fleets of Earth Observing Satellites

NASA Technical Reports Server (NTRS)

Frank, Jeremy; Jonsson, Ari; Morris, Robert; Smith, David E.; Norvig, Peter (Technical Monitor)

2001-01-01

We address the problem of scheduling observations for a collection of earth observing satellites. This scheduling task is a difficult optimization problem, potentially involving many satellites, hundreds of requests, constraints on when and how to service each request, and resources such as instruments, recording devices, transmitters, and ground stations. High-fidelity models are required to ensure the validity of schedules; at the same time, the size and complexity of the problem makes it unlikely that systematic optimization search methods will be able to solve them in a reasonable time. This paper presents a constraint-based approach to solving the Earth Observing Satellites (EOS) scheduling problem, and proposes a stochastic heuristic search method for solving it.

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

NASA Astrophysics Data System (ADS)

Polstyanko, Sergey V.; Lee, Jin-Fa

1998-03-01

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

Asymptotically suboptimal control of weakly interconnected dynamical systems

NASA Astrophysics Data System (ADS)

Dmitruk, N. M.; Kalinin, A. I.

2016-10-01

Optimal control problems for a group of systems with weak dynamical interconnections between its constituent subsystems are considered. A method for decentralized control is proposed which distributes the control actions between several controllers calculating in real time control inputs only for theirs subsystems based on the solution of the local optimal control problem. The local problem is solved by asymptotic methods that employ the representation of the weak interconnection by a small parameter. Combination of decentralized control and asymptotic methods allows to significantly reduce the dimension of the problems that have to be solved in the course of the control process.

The Artificial Neural Networks Based on Scalarization Method for a Class of Bilevel Biobjective Programming Problem

PubMed Central

Chen, Zhong; Liu, June; Li, Xiong

2017-01-01

A two-stage artificial neural network (ANN) based on scalarization method is proposed for bilevel biobjective programming problem (BLBOP). The induced set of the BLBOP is firstly expressed as the set of minimal solutions of a biobjective optimization problem by using scalar approach, and then the whole efficient set of the BLBOP is derived by the proposed two-stage ANN for exploring the induced set. In order to illustrate the proposed method, seven numerical examples are tested and compared with results in the classical literature. Finally, a practical problem is solved by the proposed algorithm. PMID:29312446

Compressive Sensing via Nonlocal Smoothed Rank Function

PubMed Central

Fan, Ya-Ru; Liu, Jun; Zhao, Xi-Le

2016-01-01

Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction. PMID:27583683

A modified priority list-based MILP method for solving large-scale unit commitment problems

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

Ke, Xinda; Lu, Ning; Wu, Di

This paper studies the typical pattern of unit commitment (UC) results in terms of generator’s cost and capacity. A method is then proposed to combine a modified priority list technique with mixed integer linear programming (MILP) for UC problem. The proposed method consists of two steps. At the first step, a portion of generators are predetermined to be online or offline within a look-ahead period (e.g., a week), based on the demand curve and generator priority order. For the generators whose on/off status is predetermined, at the second step, the corresponding binary variables are removed from the UC MILP problemmore » over the operational planning horizon (e.g., 24 hours). With a number of binary variables removed, the resulted problem can be solved much faster using the off-the-shelf MILP solvers, based on the branch-and-bound algorithm. In the modified priority list method, scale factors are designed to adjust the tradeoff between solution speed and level of optimality. It is found that the proposed method can significantly speed up the UC problem with minor compromise in optimality by selecting appropriate scale factors.« less

Application of the PROMETHEE technique to determine depression outlet location and flow direction in DEM

NASA Astrophysics Data System (ADS)

Chou, Tien-Yin; Lin, Wen-Tzu; Lin, Chao-Yuan; Chou, Wen-Chieh; Huang, Pi-Hui

2004-02-01

With the fast growing progress of computer technologies, spatial information on watersheds such as flow direction, watershed boundaries and the drainage network can be automatically calculated or extracted from a digital elevation model (DEM). The stubborn problem that depressions exist in DEMs has been frequently encountered while extracting the spatial information of terrain. Several filling-up methods have been proposed for solving depressions. However, their suitability for large-scale flat areas is inadequate. This study proposes a depression watershed method coupled with the Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEEs) theory to determine the optimal outlet and calculate the flow direction in depressions. Three processing procedures are used to derive the depressionless flow direction: (1) calculating the incipient flow direction; (2) establishing the depression watershed by tracing the upstream drainage area and determining the depression outlet using PROMETHEE theory; (3) calculating the depressionless flow direction. The developed method was used to delineate the Shihmen Reservoir watershed located in Northern Taiwan. The results show that the depression watershed method can effectively solve the shortcomings such as depression outlet differentiating and looped flow direction between depressions. The suitability of the proposed approach was verified.

Single Wall Carbon Nanotube Alignment Mechanisms for Non-Destructive Evaluation

NASA Technical Reports Server (NTRS)

Hong, Seunghun

2002-01-01

As proposed in our original proposal, we developed a new innovative method to assemble millions of single wall carbon nanotube (SWCNT)-based circuit components as fast as conventional microfabrication processes. This method is based on surface template assembly strategy. The new method solves one of the major bottlenecks in carbon nanotube based electrical applications and, potentially, may allow us to mass produce a large number of SWCNT-based integrated devices of critical interests to NASA.

Artificial immune algorithm for multi-depot vehicle scheduling problems

NASA Astrophysics Data System (ADS)

Wu, Zhongyi; Wang, Donggen; Xia, Linyuan; Chen, Xiaoling

2008-10-01

In the fast-developing logistics and supply chain management fields, one of the key problems in the decision support system is that how to arrange, for a lot of customers and suppliers, the supplier-to-customer assignment and produce a detailed supply schedule under a set of constraints. Solutions to the multi-depot vehicle scheduling problems (MDVRP) help in solving this problem in case of transportation applications. The objective of the MDVSP is to minimize the total distance covered by all vehicles, which can be considered as delivery costs or time consumption. The MDVSP is one of nondeterministic polynomial-time hard (NP-hard) problem which cannot be solved to optimality within polynomial bounded computational time. Many different approaches have been developed to tackle MDVSP, such as exact algorithm (EA), one-stage approach (OSA), two-phase heuristic method (TPHM), tabu search algorithm (TSA), genetic algorithm (GA) and hierarchical multiplex structure (HIMS). Most of the methods mentioned above are time consuming and have high risk to result in local optimum. In this paper, a new search algorithm is proposed to solve MDVSP based on Artificial Immune Systems (AIS), which are inspirited by vertebrate immune systems. The proposed AIS algorithm is tested with 30 customers and 6 vehicles located in 3 depots. Experimental results show that the artificial immune system algorithm is an effective and efficient method for solving MDVSP problems.

Low-dose CT reconstruction via L1 dictionary learning regularization using iteratively reweighted least-squares.

PubMed

Zhang, Cheng; Zhang, Tao; Li, Ming; Peng, Chengtao; Liu, Zhaobang; Zheng, Jian

2016-06-18

In order to reduce the radiation dose of CT (computed tomography), compressed sensing theory has been a hot topic since it provides the possibility of a high quality recovery from the sparse sampling data. Recently, the algorithm based on DL (dictionary learning) was developed to deal with the sparse CT reconstruction problem. However, the existing DL algorithm focuses on the minimization problem with the L2-norm regularization term, which leads to reconstruction quality deteriorating while the sampling rate declines further. Therefore, it is essential to improve the DL method to meet the demand of more dose reduction. In this paper, we replaced the L2-norm regularization term with the L1-norm one. It is expected that the proposed L1-DL method could alleviate the over-smoothing effect of the L2-minimization and reserve more image details. The proposed algorithm solves the L1-minimization problem by a weighting strategy, solving the new weighted L2-minimization problem based on IRLS (iteratively reweighted least squares). Through the numerical simulation, the proposed algorithm is compared with the existing DL method (adaptive dictionary based statistical iterative reconstruction, ADSIR) and other two typical compressed sensing algorithms. It is revealed that the proposed algorithm is more accurate than the other algorithms especially when further reducing the sampling rate or increasing the noise. The proposed L1-DL algorithm can utilize more prior information of image sparsity than ADSIR. By transforming the L2-norm regularization term of ADSIR with the L1-norm one and solving the L1-minimization problem by IRLS strategy, L1-DL could reconstruct the image more exactly.

A Noise Removal Method for Uniform Circular Arrays in Complex Underwater Noise Environments with Low SNR

PubMed Central

Xia, Huijun; Yang, Kunde; Ma, Yuanliang; Wang, Yong; Liu, Yaxiong

2017-01-01

Generally, many beamforming methods are derived under the assumption of white noise. In practice, the actual underwater ambient noise is complex. As a result, the noise removal capacity of the beamforming method may be deteriorated considerably. Furthermore, in underwater environment with extremely low signal-to-noise ratio (SNR), the performances of the beamforming method may be deteriorated. To tackle these problems, a noise removal method for uniform circular array (UCA) is proposed to remove the received noise and improve the SNR in complex noise environments with low SNR. First, the symmetrical noise sources are defined and the spatial correlation of the symmetrical noise sources is calculated. Then, based on the preceding results, the noise covariance matrix is decomposed into symmetrical and asymmetrical components. Analysis indicates that the symmetrical component only affect the real part of the noise covariance matrix. Consequently, the delay-and-sum (DAS) beamforming is performed by using the imaginary part of the covariance matrix to remove the symmetrical component. However, the noise removal method causes two problems. First, the proposed method produces a false target. Second, the proposed method would seriously suppress the signal when it is located in some directions. To solve the first problem, two methods to reconstruct the signal covariance matrix are presented: based on the estimation of signal variance and based on the constrained optimization algorithm. To solve the second problem, we can design the array configuration and select the suitable working frequency. Theoretical analysis and experimental results are included to demonstrate that the proposed methods are particularly effective in complex noise environments with low SNR. The proposed method can be extended to any array. PMID:28598386

Robust range estimation with a monocular camera for vision-based forward collision warning system.

PubMed

Park, Ki-Yeong; Hwang, Sun-Young

2014-01-01

We propose a range estimation method for vision-based forward collision warning systems with a monocular camera. To solve the problem of variation of camera pitch angle due to vehicle motion and road inclination, the proposed method estimates virtual horizon from size and position of vehicles in captured image at run-time. The proposed method provides robust results even when road inclination varies continuously on hilly roads or lane markings are not seen on crowded roads. For experiments, a vision-based forward collision warning system has been implemented and the proposed method is evaluated with video clips recorded in highway and urban traffic environments. Virtual horizons estimated by the proposed method are compared with horizons manually identified, and estimated ranges are compared with measured ranges. Experimental results confirm that the proposed method provides robust results both in highway and in urban traffic environments.

Robust Range Estimation with a Monocular Camera for Vision-Based Forward Collision Warning System

PubMed Central

2014-01-01

We propose a range estimation method for vision-based forward collision warning systems with a monocular camera. To solve the problem of variation of camera pitch angle due to vehicle motion and road inclination, the proposed method estimates virtual horizon from size and position of vehicles in captured image at run-time. The proposed method provides robust results even when road inclination varies continuously on hilly roads or lane markings are not seen on crowded roads. For experiments, a vision-based forward collision warning system has been implemented and the proposed method is evaluated with video clips recorded in highway and urban traffic environments. Virtual horizons estimated by the proposed method are compared with horizons manually identified, and estimated ranges are compared with measured ranges. Experimental results confirm that the proposed method provides robust results both in highway and in urban traffic environments. PMID:24558344

Three-dimensional implicit lambda methods

NASA Technical Reports Server (NTRS)

Napolitano, M.; Dadone, A.

1983-01-01

This paper derives the three dimensional lambda-formulation equations for a general orthogonal curvilinear coordinate system and provides various block-explicit and block-implicit methods for solving them, numerically. Three model problems, characterized by subsonic, supersonic and transonic flow conditions, are used to assess the reliability and compare the efficiency of the proposed methods.

Providing Adaptation and Guidance for Design Learning by Problem Solving: The Design Planning Approach in DomoSim-TPC Environment

ERIC Educational Resources Information Center

Redondo, Miguel A.; Bravo, Crescencio; Ortega, Manuel; Verdejo, M. Felisa

2007-01-01

Experimental learning environments based on simulation usually require monitoring and adaptation to the actions the users carry out. Some systems provide this functionality, but they do so in a way which is static or cannot be applied to problem solving tasks. In response to this problem, we propose a method based on the use of intermediate…

Application of an improved minimum entropy deconvolution method for railway rolling element bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Cheng, Yao; Zhou, Ning; Zhang, Weihua; Wang, Zhiwei

2018-07-01

Minimum entropy deconvolution is a widely-used tool in machinery fault diagnosis, because it enhances the impulse component of the signal. The filter coefficients that greatly influence the performance of the minimum entropy deconvolution are calculated by an iterative procedure. This paper proposes an improved deconvolution method for the fault detection of rolling element bearings. The proposed method solves the filter coefficients by the standard particle swarm optimization algorithm, assisted by a generalized spherical coordinate transformation. When optimizing the filters performance for enhancing the impulses in fault diagnosis (namely, faulty rolling element bearings), the proposed method outperformed the classical minimum entropy deconvolution method. The proposed method was validated in simulation and experimental signals from railway bearings. In both simulation and experimental studies, the proposed method delivered better deconvolution performance than the classical minimum entropy deconvolution method, especially in the case of low signal-to-noise ratio.

Pythagorean fuzzy analytic hierarchy process to multi-criteria decision making

NASA Astrophysics Data System (ADS)

Mohd, Wan Rosanisah Wan; Abdullah, Lazim

2017-11-01

A numerous approaches have been proposed in the literature to determine the criteria of weight. The weight of criteria is very significant in the process of decision making. One of the outstanding approaches that used to determine weight of criteria is analytic hierarchy process (AHP). This method involves decision makers (DMs) to evaluate the decision to form the pair-wise comparison between criteria and alternatives. In classical AHP, the linguistic variable of pairwise comparison is presented in terms of crisp value. However, this method is not appropriate to present the real situation of the problems because it involved the uncertainty in linguistic judgment. For this reason, AHP has been extended by incorporating the Pythagorean fuzzy sets. In addition, no one has found in the literature proposed how to determine the weight of criteria using AHP under Pythagorean fuzzy sets. In order to solve the MCDM problem, the Pythagorean fuzzy analytic hierarchy process is proposed to determine the criteria weight of the evaluation criteria. Using the linguistic variables, pairwise comparison for evaluation criteria are made to the weights of criteria using Pythagorean fuzzy numbers (PFNs). The proposed method is implemented in the evaluation problem in order to demonstrate its applicability. This study shows that the proposed method provides us with a useful way and a new direction in solving MCDM problems with Pythagorean fuzzy context.

Solving bi-level optimization problems in engineering design using kriging models

NASA Astrophysics Data System (ADS)

Xia, Yi; Liu, Xiaojie; Du, Gang

2018-05-01

Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.

A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance

NASA Astrophysics Data System (ADS)

Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide

2016-12-01

We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.

Robust Foregrounds Removal for 21-cm Experiments

NASA Astrophysics Data System (ADS)

Mertens, F.; Ghosh, A.; Koopmans, L. V. E.

2018-05-01

Direct detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called ``wedge'' are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum.

High Dynamic Range Imaging Using Multiple Exposures

NASA Astrophysics Data System (ADS)

Hou, Xinglin; Luo, Haibo; Zhou, Peipei; Zhou, Wei

2017-06-01

It is challenging to capture a high-dynamic range (HDR) scene using a low-dynamic range (LDR) camera. This paper presents an approach for improving the dynamic range of cameras by using multiple exposure images of same scene taken under different exposure times. First, the camera response function (CRF) is recovered by solving a high-order polynomial in which only the ratios of the exposures are used. Then, the HDR radiance image is reconstructed by weighted summation of the each radiance maps. After that, a novel local tone mapping (TM) operator is proposed for the display of the HDR radiance image. By solving the high-order polynomial, the CRF can be recovered quickly and easily. Taken the local image feature and characteristic of histogram statics into consideration, the proposed TM operator could preserve the local details efficiently. Experimental result demonstrates the effectiveness of our method. By comparison, the method outperforms other methods in terms of imaging quality.

Single image super-resolution via an iterative reproducing kernel Hilbert space method.

PubMed

Deng, Liang-Jian; Guo, Weihong; Huang, Ting-Zhu

2016-11-01

Image super-resolution, a process to enhance image resolution, has important applications in satellite imaging, high definition television, medical imaging, etc. Many existing approaches use multiple low-resolution images to recover one high-resolution image. In this paper, we present an iterative scheme to solve single image super-resolution problems. It recovers a high quality high-resolution image from solely one low-resolution image without using a training data set. We solve the problem from image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.

A new supervised learning algorithm for spiking neurons.

PubMed

Xu, Yan; Zeng, Xiaoqin; Zhong, Shuiming

2013-06-01

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by the precise firing times of spikes. If only running time is considered, the supervised learning for a spiking neuron is equivalent to distinguishing the times of desired output spikes and the other time during the running process of the neuron through adjusting synaptic weights, which can be regarded as a classification problem. Based on this idea, this letter proposes a new supervised learning method for spiking neurons with temporal encoding; it first transforms the supervised learning into a classification problem and then solves the problem by using the perceptron learning rule. The experiment results show that the proposed method has higher learning accuracy and efficiency over the existing learning methods, so it is more powerful for solving complex and real-time problems.

A simple extension of Roe's scheme for real gases

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

Arabi, Sina, E-mail: sina.arabi@polymtl.ca; Trépanier, Jean-Yves; Camarero, Ricardo

The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared withmore » an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.« less

On the extraction of pressure fields from PIV velocity measurements in turbines

NASA Astrophysics Data System (ADS)

Villegas, Arturo; Diez, Fancisco J.

2012-11-01

In this study, the pressure field for a water turbine is derived from particle image velocimetry (PIV) measurements. Measurements are performed in a recirculating water channel facility. The PIV measurements include calculating the tangential and axial forces applied to the turbine by solving the integral momentum equation around the airfoil. The results are compared with the forces obtained from the Blade Element Momentum theory (BEMT). Forces are calculated by using three different methods. In the first method, the pressure fields are obtained from PIV velocity fields by solving the Poisson equation. The boundary conditions are obtained from the Navier-Stokes momentum equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradients along the boundaries. In the third method, applicable only to incompressible, inviscid, irrotational, and steady flow, the pressure is calculated using the Bernoulli equation. This approximated pressure is known to be accurate far from the airfoil and outside of the wake for steady flows. Additionally, the pressure is used to solve for the force from the integral momentum equation on the blade. From the three methods proposed to solve for pressure and forces from PIV measurements, the first one, which is solved by using the Poisson equation, provides the best match to the BEM theory calculations.

A Leap-Frog Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations in Metamaterials

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

Li, J., Waters, J. W., Machorro, E. A.

2012-06-01

Numerical simulation of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. In this paper, we propose a leap-frog discontinuous Galerkin method to solve the time-dependent Maxwell’s equations in metamaterials. Conditional stability and error estimates are proved for the scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided.

Social Image Tag Ranking by Two-View Learning

NASA Astrophysics Data System (ADS)

Zhuang, Jinfeng; Hoi, Steven C. H.

Tags play a central role in text-based social image retrieval and browsing. However, the tags annotated by web users could be noisy, irrelevant, and often incomplete for describing the image contents, which may severely deteriorate the performance of text-based image retrieval models. In order to solve this problem, researchers have proposed techniques to rank the annotated tags of a social image according to their relevance to the visual content of the image. In this paper, we aim to overcome the challenge of social image tag ranking for a corpus of social images with rich user-generated tags by proposing a novel two-view learning approach. It can effectively exploit both textual and visual contents of social images to discover the complicated relationship between tags and images. Unlike the conventional learning approaches that usually assumes some parametric models, our method is completely data-driven and makes no assumption about the underlying models, making the proposed solution practically more effective. We formulate our method as an optimization task and present an efficient algorithm to solve it. To evaluate the efficacy of our method, we conducted an extensive set of experiments by applying our technique to both text-based social image retrieval and automatic image annotation tasks. Our empirical results showed that the proposed method can be more effective than the conventional approaches.

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.

SU-C-9A-03: Simultaneous Deconvolution and Segmentation for PET Tumor Delineation Using a Variational Method

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

Li, L; Tan, S; Lu, W

2014-06-01

Purpose: To implement a new method that integrates deconvolution with segmentation under the variational framework for PET tumor delineation. Methods: Deconvolution and segmentation are both challenging problems in image processing. The partial volume effect (PVE) makes tumor boundaries in PET image blurred which affects the accuracy of tumor segmentation. Deconvolution aims to obtain a PVE-free image, which can help to improve the segmentation accuracy. Conversely, a correct localization of the object boundaries is helpful to estimate the blur kernel, and thus assist in the deconvolution. In this study, we proposed to solve the two problems simultaneously using a variational methodmore » so that they can benefit each other. The energy functional consists of a fidelity term and a regularization term, and the blur kernel was limited to be the isotropic Gaussian kernel. We minimized the energy functional by solving the associated Euler-Lagrange equations and taking the derivative with respect to the parameters of the kernel function. An alternate minimization method was used to iterate between segmentation, deconvolution and blur-kernel recovery. The performance of the proposed method was tested on clinic PET images of patients with non-Hodgkin's lymphoma, and compared with seven other segmentation methods using the dice similarity index (DSI) and volume error (VE). Results: Among all segmentation methods, the proposed one (DSI=0.81, VE=0.05) has the highest accuracy, followed by the active contours without edges (DSI=0.81, VE=0.25), while other methods including the Graph Cut and the Mumford-Shah (MS) method have lower accuracy. A visual inspection shows that the proposed method localizes the real tumor contour very well. Conclusion: The result showed that deconvolution and segmentation can contribute to each other. The proposed variational method solve the two problems simultaneously, and leads to a high performance for tumor segmentation in PET. This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086. Wei Lu was supported in part by the National Institutes of Health (NIH) Grant No. R01 CA172638.« less

Service Discovery Oriented Management System Construction Method

NASA Astrophysics Data System (ADS)

Li, Huawei; Ren, Ying

2017-10-01

In order to solve the problem that there is no uniform method for design service quality management system in large-scale complex service environment, this paper proposes a distributed service-oriented discovery management system construction method. Three measurement functions are proposed to compute nearest neighbor user similarity at different levels. At present in view of the low efficiency of service quality management systems, three solutions are proposed to improve the efficiency of the system. Finally, the key technologies of distributed service quality management system based on service discovery are summarized through the factor addition and subtraction of quantitative experiment.

Computationally efficient approach for solving time dependent diffusion equation with discrete temporal convolution applied to granular particles of battery electrodes

NASA Astrophysics Data System (ADS)

Senegačnik, Jure; Tavčar, Gregor; Katrašnik, Tomaž

2015-03-01

The paper presents a computationally efficient method for solving the time dependent diffusion equation in a granule of the Li-ion battery's granular solid electrode. The method, called Discrete Temporal Convolution method (DTC), is based on a discrete temporal convolution of the analytical solution of the step function boundary value problem. This approach enables modelling concentration distribution in the granular particles for arbitrary time dependent exchange fluxes that do not need to be known a priori. It is demonstrated in the paper that the proposed method features faster computational times than finite volume/difference methods and Padé approximation at the same accuracy of the results. It is also demonstrated that all three addressed methods feature higher accuracy compared to the quasi-steady polynomial approaches when applied to simulate the current densities variations typical for mobile/automotive applications. The proposed approach can thus be considered as one of the key innovative methods enabling real-time capability of the multi particle electrochemical battery models featuring spatial and temporal resolved particle concentration profiles.

Multiscale global identification of porous structures

NASA Astrophysics Data System (ADS)

Hatłas, Marcin; Beluch, Witold

2018-01-01

The paper is devoted to the evolutionary identification of the material constants of porous structures based on measurements conducted on a macro scale. Numerical homogenization with the RVE concept is used to determine the equivalent properties of a macroscopically homogeneous material. Finite element method software is applied to solve the boundary-value problem in both scales. Global optimization methods in form of evolutionary algorithm are employed to solve the identification task. Modal analysis is performed to collect the data necessary for the identification. A numerical example presenting the effectiveness of proposed attitude is attached.

Heuristic algorithms for solving of the tool routing problem for CNC cutting machines

NASA Astrophysics Data System (ADS)

Chentsov, P. A.; Petunin, A. A.; Sesekin, A. N.; Shipacheva, E. N.; Sholohov, A. E.

2015-11-01

The article is devoted to the problem of minimizing the path of the cutting tool to shape cutting machines began. This problem can be interpreted as a generalized traveling salesman problem. Earlier version of the dynamic programming method to solve this problem was developed. Unfortunately, this method allows to process an amount not exceeding thirty circuits. In this regard, the task of constructing quasi-optimal route becomes relevant. In this paper we propose options for quasi-optimal greedy algorithms. Comparison of the results of exact and approximate algorithms is given.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

NASA Astrophysics Data System (ADS)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Simple method for quick estimation of aquifer hydrogeological parameters

NASA Astrophysics Data System (ADS)

Ma, C.; Li, Y. Y.

2017-08-01

Development of simple and accurate methods to determine the aquifer hydrogeological parameters was of importance for groundwater resources assessment and management. Aiming at the present issue of estimating aquifer parameters based on some data of the unsteady pumping test, a fitting function of Theis well function was proposed using fitting optimization method and then a unitary linear regression equation was established. The aquifer parameters could be obtained by solving coefficients of the regression equation. The application of the proposed method was illustrated, using two published data sets. By the error statistics and analysis on the pumping drawdown, it showed that the method proposed in this paper yielded quick and accurate estimates of the aquifer parameters. The proposed method could reliably identify the aquifer parameters from long distance observed drawdowns and early drawdowns. It was hoped that the proposed method in this paper would be helpful for practicing hydrogeologists and hydrologists.

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

PubMed Central

Serang, Oliver

2012-01-01

Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics. PMID:22952741

Sound source identification and sound radiation modeling in a moving medium using the time-domain equivalent source method.

PubMed

Zhang, Xiao-Zheng; Bi, Chuan-Xing; Zhang, Yong-Bin; Xu, Liang

2015-05-01

Planar near-field acoustic holography has been successfully extended to reconstruct the sound field in a moving medium, however, the reconstructed field still contains the convection effect that might lead to the wrong identification of sound sources. In order to accurately identify sound sources in a moving medium, a time-domain equivalent source method is developed. In the method, the real source is replaced by a series of time-domain equivalent sources whose strengths are solved iteratively by utilizing the measured pressure and the known convective time-domain Green's function, and time averaging is used to reduce the instability in the iterative solving process. Since these solved equivalent source strengths are independent of the convection effect, they can be used not only to identify sound sources but also to model sound radiations in both moving and static media. Numerical simulations are performed to investigate the influence of noise on the solved equivalent source strengths and the effect of time averaging on reducing the instability, and to demonstrate the advantages of the proposed method on the source identification and sound radiation modeling.

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

Atomistic full-quantum transport model for zigzag graphene nanoribbon-based structures: Complex energy-band method

NASA Astrophysics Data System (ADS)

Chen, Chun-Nan; Luo, Win-Jet; Shyu, Feng-Lin; Chung, Hsien-Ching; Lin, Chiun-Yan; Wu, Jhao-Ying

2018-01-01

Using a non-equilibrium Green’s function framework in combination with the complex energy-band method, an atomistic full-quantum model for solving quantum transport problems for a zigzag-edge graphene nanoribbon (zGNR) structure is proposed. For transport calculations, the mathematical expressions from the theory for zGNR-based device structures are derived in detail. The transport properties of zGNR-based devices are calculated and studied in detail using the proposed method.

An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs

PubMed Central

Guo, Jianqiang; Wang, Wansheng

2014-01-01

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable. PMID:24895653

An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black-Scholes equation with transaction costs.

PubMed

Guo, Jianqiang; Wang, Wansheng

2014-01-01

This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.

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.

Viscoacoustic anisotropic full waveform inversion

NASA Astrophysics Data System (ADS)

Qu, Yingming; Li, Zhenchun; Huang, Jianping; Li, Jinli

2017-01-01

A viscoacoustic vertical transverse isotropic (VTI) quasi-differential wave equation, which takes account for both the viscosity and anisotropy of media, is proposed for wavefield simulation in this study. The finite difference method is used to solve the equations, for which the attenuation terms are solved in the wavenumber domain, and all remaining terms in the time-space domain. To stabilize the adjoint wavefield, robust regularization operators are applied to the wave equation to eliminate the high-frequency component of the numerical noise produced during the backward propagation of the viscoacoustic wavefield. Based on these strategies, we derive the corresponding gradient formula and implement a viscoacoustic VTI full waveform inversion (FWI). Numerical tests verify that our proposed viscoacoustic VTI FWI can produce accurate and stable inversion results for viscoacoustic VTI data sets. In addition, we test our method's sensitivity to velocity, Q, and anisotropic parameters. Our results show that the sensitivity to velocity is much higher than that to Q and anisotropic parameters. As such, our proposed method can produce acceptable inversion results as long as the Q and anisotropic parameters are within predefined thresholds.

A Radio-Map Automatic Construction Algorithm Based on Crowdsourcing

PubMed Central

Yu, Ning; Xiao, Chenxian; Wu, Yinfeng; Feng, Renjian

2016-01-01

Traditional radio-map-based localization methods need to sample a large number of location fingerprints offline, which requires huge amount of human and material resources. To solve the high sampling cost problem, an automatic radio-map construction algorithm based on crowdsourcing is proposed. The algorithm employs the crowd-sourced information provided by a large number of users when they are walking in the buildings as the source of location fingerprint data. Through the variation characteristics of users’ smartphone sensors, the indoor anchors (doors) are identified and their locations are regarded as reference positions of the whole radio-map. The AP-Cluster method is used to cluster the crowdsourced fingerprints to acquire the representative fingerprints. According to the reference positions and the similarity between fingerprints, the representative fingerprints are linked to their corresponding physical locations and the radio-map is generated. Experimental results demonstrate that the proposed algorithm reduces the cost of fingerprint sampling and radio-map construction and guarantees the localization accuracy. The proposed method does not require users’ explicit participation, which effectively solves the resource-consumption problem when a location fingerprint database is established. PMID:27070623

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

2014-12-01

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

Artificial intelligence in robot control systems

NASA Astrophysics Data System (ADS)

Korikov, A.

2018-05-01

This paper analyzes modern concepts of artificial intelligence and known definitions of the term "level of intelligence". In robotics artificial intelligence system is defined as a system that works intelligently and optimally. The author proposes to use optimization methods for the design of intelligent robot control systems. The article provides the formalization of problems of robotic control system design, as a class of extremum problems with constraints. Solving these problems is rather complicated due to the high dimensionality, polymodality and a priori uncertainty. Decomposition of the extremum problems according to the method, suggested by the author, allows reducing them into a sequence of simpler problems, that can be successfully solved by modern computing technology. Several possible approaches to solving such problems are considered in the article.

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting.

PubMed

Dung, Van Than; Tjahjowidodo, Tegoeh

2017-01-01

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications.

Cognitive functioning and social problem-solving skills in schizophrenia.

PubMed

Hatashita-Wong, Michi; Smith, Thomas E; Silverstein, Steven M; Hull, James W; Willson, Deborah F

2002-05-01

This study examined the relationships between symptoms, cognitive functioning, and social skill deficits in schizophrenia. Few studies have incorporated measures of cognitive functioning and symptoms in predictive models for social problem solving. For our study, 44 participants were recruited from consecutive outpatient admissions. Neuropsychological tests were given to assess cognitive function, and social problem solving was assessed using structured vignettes designed to evoke the participant's ability to generate, evaluate, and apply solutions to social problems. A sequential model-fitting method of analysis was used to incorporate social problem solving, symptom presentation, and cognitive impairment into linear regression models. Predictor variables were drawn from demographic, cognitive, and symptom domains. Because this method of analysis was exploratory and not intended as hierarchical modelling, no a priori hypotheses were proposed. Participants with higher scores on tests of cognitive flexibility were better able to generate accurate, appropriate, and relevant responses to the social problem-solving vignettes. The results suggest that cognitive flexibility is a potentially important mediating factor in social problem-solving competence. While other factors are related to social problem-solving skill, this study supports the importance of cognition and understanding how it relates to the complex and multifaceted nature of social functioning.

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

NASA Astrophysics Data System (ADS)

Chen, Xudong

2010-07-01

This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging.

An Effective News Recommendation Method for Microblog User

PubMed Central

Gu, Wanrong; Dong, Shoubin; Zeng, Zhizhao; He, Jinchao

2014-01-01

Recommending news stories to users, based on their preferences, has long been a favourite domain for recommender systems research. Traditional systems strive to satisfy their user by tracing users' reading history and choosing the proper candidate news articles to recommend. However, most of news websites hardly require any user to register before reading news. Besides, the latent relations between news and microblog, the popularity of particular news, and the news organization are not addressed or solved efficiently in previous approaches. In order to solve these issues, we propose an effective personalized news recommendation method based on microblog user profile building and sub class popularity prediction, in which we propose a news organization method using hybrid classification and clustering, implement a sub class popularity prediction method, and construct user profile according to our actual situation. We had designed several experiments compared to the state-of-the-art approaches on a real world dataset, and the experimental results demonstrate that our system significantly improves the accuracy and diversity in mass text data. PMID:24983011

Multi-period project portfolio selection under risk considerations and stochastic income

NASA Astrophysics Data System (ADS)

Tofighian, Ali Asghar; Moezzi, Hamid; Khakzar Barfuei, Morteza; Shafiee, Mahmood

2018-02-01

This paper deals with multi-period project portfolio selection problem. In this problem, the available budget is invested on the best portfolio of projects in each period such that the net profit is maximized. We also consider more realistic assumptions to cover wider range of applications than those reported in previous studies. A novel mathematical model is presented to solve the problem, considering risks, stochastic incomes, and possibility of investing extra budget in each time period. Due to the complexity of the problem, an effective meta-heuristic method hybridized with a local search procedure is presented to solve the problem. The algorithm is based on genetic algorithm (GA), which is a prominent method to solve this type of problems. The GA is enhanced by a new solution representation and well selected operators. It also is hybridized with a local search mechanism to gain better solution in shorter time. The performance of the proposed algorithm is then compared with well-known algorithms, like basic genetic algorithm (GA), particle swarm optimization (PSO), and electromagnetism-like algorithm (EM-like) by means of some prominent indicators. The computation results show the superiority of the proposed algorithm in terms of accuracy, robustness and computation time. At last, the proposed algorithm is wisely combined with PSO to improve the computing time considerably.

Comment on "An Efficient and Stable Hydrodynamic Model With Novel Source Term Discretization Schemes for Overland Flow and Flood Simulations" by Xilin Xia et al.

NASA Astrophysics Data System (ADS)

Lu, Xinhua; Mao, Bing; Dong, Bingjiang

2018-01-01

Xia et al. (2017) proposed a novel, fully implicit method for the discretization of the bed friction terms for solving the shallow-water equations. The friction terms contain h-7/3 (h denotes water depth), which may be extremely large, introducing machine error when h approaches zero. To address this problem, Xia et al. (2017) introduces auxiliary variables (their equations (37) and (38)) so that h-4/3 rather than h-7/3 is calculated and solves a transformed equation (their equation (39)). The introduced auxiliary variables require extra storage. We implemented an analysis on the magnitude of the friction terms to find that these terms on the whole do not exceed the machine floating-point number precision, and thus we proposed a simple-to-implement technique by splitting h-7/3 into different parts of the friction terms to avoid introducing machine error. This technique does not need extra storage or to solve a transformed equation and thus is more efficient for simulations. We also showed that the surface reconstruction method proposed by Xia et al. (2017) may lead to predictions with spurious wiggles because the reconstructed Riemann states may misrepresent the water gravitational effect.

An Intelligent Monitoring Network for Detection of Cracks in Anvils of High-Press Apparatus.

PubMed

Tian, Hao; Yan, Zhaoli; Yang, Jun

2018-04-09

Due to the endurance of alternating high pressure and temperature, the carbide anvils of the high-press apparatus, which are widely used in the synthetic diamond industry, are prone to crack. In this paper, an acoustic method is used to monitor the crack events, and the intelligent monitoring network is proposed to classify the sound samples. The pulse sound signals produced by such cracking are first extracted based on a short-time energy threshold. Then, the signals are processed with the proposed intelligent monitoring network to identify the operation condition of the anvil of the high-pressure apparatus. The monitoring network is an improved convolutional neural network that solves the problems that may occur in practice. The length of pulse sound excited by the crack growth is variable, so a spatial pyramid pooling layer is adopted to solve the variable-length input problem. An adaptive weighted algorithm for loss function is proposed in this method to handle the class imbalance problem. The good performance regarding the accuracy and balance of the proposed intelligent monitoring network is validated through the experiments finally.

A Partitioning and Bounded Variable Algorithm for Linear Programming

ERIC Educational Resources Information Center

Sheskin, Theodore J.

2006-01-01

An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…

Low-count PET image restoration using sparse representation

NASA Astrophysics Data System (ADS)

Li, Tao; Jiang, Changhui; Gao, Juan; Yang, Yongfeng; Liang, Dong; Liu, Xin; Zheng, Hairong; Hu, Zhanli

2018-04-01

In the field of positron emission tomography (PET), reconstructed images are often blurry and contain noise. These problems are primarily caused by the low resolution of projection data. Solving this problem by improving hardware is an expensive solution, and therefore, we attempted to develop a solution based on optimizing several related algorithms in both the reconstruction and image post-processing domains. As sparse technology is widely used, sparse prediction is increasingly applied to solve this problem. In this paper, we propose a new sparse method to process low-resolution PET images. Two dictionaries (D1 for low-resolution PET images and D2 for high-resolution PET images) are learned from a group real PET image data sets. Among these two dictionaries, D1 is used to obtain a sparse representation for each patch of the input PET image. Then, a high-resolution PET image is generated from this sparse representation using D2. Experimental results indicate that the proposed method exhibits a stable and superior ability to enhance image resolution and recover image details. Quantitatively, this method achieves better performance than traditional methods. This proposed strategy is a new and efficient approach for improving the quality of PET images.

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

NASA Astrophysics Data System (ADS)

Zeng, Qinglei; Liu, Zhanli; Wang, Tao; Gao, Yue; Zhuang, Zhuo

2018-02-01

In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton's iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.

A modified form of conjugate gradient method for unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Ghani, Nur Hamizah Abdul; Rivaie, Mohd.; Mamat, Mustafa

2016-06-01

Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947-951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

NASA Astrophysics Data System (ADS)

Ge, Yongbin; Cao, Fujun

2011-05-01

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem.

PubMed

Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

2015-01-01

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.

Object matching using a locally affine invariant and linear programming techniques.

PubMed

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

The Natural-CCD Algorithm, a Novel Method to Solve the Inverse Kinematics of Hyper-redundant and Soft Robots.

PubMed

Martín, Andrés; Barrientos, Antonio; Del Cerro, Jaime

2018-03-22

This article presents a new method to solve the inverse kinematics problem of hyper-redundant and soft manipulators. From an engineering perspective, this kind of robots are underdetermined systems. Therefore, they exhibit an infinite number of solutions for the inverse kinematics problem, and to choose the best one can be a great challenge. A new algorithm based on the cyclic coordinate descent (CCD) and named as natural-CCD is proposed to solve this issue. It takes its name as a result of generating very harmonious robot movements and trajectories that also appear in nature, such as the golden spiral. In addition, it has been applied to perform continuous trajectories, to develop whole-body movements, to analyze motion planning in complex environments, and to study fault tolerance, even for both prismatic and rotational joints. The proposed algorithm is very simple, precise, and computationally efficient. It works for robots either in two or three spatial dimensions and handles a large amount of degrees-of-freedom. Because of this, it is aimed to break down barriers between discrete hyper-redundant and continuum soft robots.

Feature-based three-dimensional registration for repetitive geometry in machine vision

PubMed Central

Gong, Yuanzheng; Seibel, Eric J.

2016-01-01

As an important step in three-dimensional (3D) machine vision, 3D registration is a process of aligning two or multiple 3D point clouds that are collected from different perspectives together into a complete one. The most popular approach to register point clouds is to minimize the difference between these point clouds iteratively by Iterative Closest Point (ICP) algorithm. However, ICP does not work well for repetitive geometries. To solve this problem, a feature-based 3D registration algorithm is proposed to align the point clouds that are generated by vision-based 3D reconstruction. By utilizing texture information of the object and the robustness of image features, 3D correspondences can be retrieved so that the 3D registration of two point clouds is to solve a rigid transformation. The comparison of our method and different ICP algorithms demonstrates that our proposed algorithm is more accurate, efficient and robust for repetitive geometry registration. Moreover, this method can also be used to solve high depth uncertainty problem caused by little camera baseline in vision-based 3D reconstruction. PMID:28286703

Quadratic adaptive algorithm for solving cardiac action potential models.

PubMed

Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

2016-10-01

An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

Dustin Popp; Zander Mausolff; Sedat Goluoglu

We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operationmore » is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).« less

Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

NASA Astrophysics Data System (ADS)

Endo, Eishin; Toga, Yuta; Sasaki, Munetaka

2015-07-01

We present a method of parallelizing the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide a lattice into noninteracting interpenetrating sublattices. This subdivision enables us to parallelize the Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. This method was applied to a two-dimensional magnetic dipolar system on an L × L square lattice to examine its parallelization efficiency. The result showed that, in the case of L = 2304, the speed of computation increased about 102 times by parallel computation with 288 processors.

A novel recurrent neural network with finite-time convergence for linear programming.

PubMed

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1989-01-01

The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code.

Hierarchical Artificial Bee Colony Algorithm for RFID Network Planning Optimization

PubMed Central

Ma, Lianbo; Chen, Hanning; Hu, Kunyuan; Zhu, Yunlong

2014-01-01

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization, called HABC, to tackle the radio frequency identification network planning (RNP) problem. In the proposed multilevel model, the higher-level species can be aggregated by the subpopulations from lower level. In the bottom level, each subpopulation employing the canonical ABC method searches the part-dimensional optimum in parallel, which can be constructed into a complete solution for the upper level. At the same time, the comprehensive learning method with crossover and mutation operators is applied to enhance the global search ability between species. Experiments are conducted on a set of 10 benchmark optimization problems. The results demonstrate that the proposed HABC obtains remarkable performance on most chosen benchmark functions when compared to several successful swarm intelligence and evolutionary algorithms. Then HABC is used for solving the real-world RNP problem on two instances with different scales. Simulation results show that the proposed algorithm is superior for solving RNP, in terms of optimization accuracy and computation robustness. PMID:24592200

Hierarchical artificial bee colony algorithm for RFID network planning optimization.

PubMed

Ma, Lianbo; Chen, Hanning; Hu, Kunyuan; Zhu, Yunlong

2014-01-01

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization, called HABC, to tackle the radio frequency identification network planning (RNP) problem. In the proposed multilevel model, the higher-level species can be aggregated by the subpopulations from lower level. In the bottom level, each subpopulation employing the canonical ABC method searches the part-dimensional optimum in parallel, which can be constructed into a complete solution for the upper level. At the same time, the comprehensive learning method with crossover and mutation operators is applied to enhance the global search ability between species. Experiments are conducted on a set of 10 benchmark optimization problems. The results demonstrate that the proposed HABC obtains remarkable performance on most chosen benchmark functions when compared to several successful swarm intelligence and evolutionary algorithms. Then HABC is used for solving the real-world RNP problem on two instances with different scales. Simulation results show that the proposed algorithm is superior for solving RNP, in terms of optimization accuracy and computation robustness.

Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

NASA Astrophysics Data System (ADS)

Parand, Kourosh; Latifi, Sobhan; Delkhosh, Mehdi; Moayeri, Mohammad M.

2018-01-01

In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [0, ∞). Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y'(0), is obtained as -1.191790649719421734122828603800159364 for η = 0.5. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1991-01-01

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

48 CFR 852.236-80 - Subcontracts and work coordination.

Code of Federal Regulations, 2010 CFR

2010-10-01

... immediately. In doing so, the contractor shall explain the proposed method of solving the problem or shall... problems and the installation of lines and equipment as contemplated by the contract documents while...

Practical aspects of using a neural network to solve inverse geophysical problems

NASA Astrophysics Data System (ADS)

Yakimenko, A. A.; Morozov, A. E.; Karavaev, D. A.

2018-05-01

In this paper, an approach to solve an inverse problem of geophysics, such as determining the position of an object (cavity or cavern) and its geometrical parameters according to the propagation picture of a wave field, is proposed. At present there are no fast and accurate methods for determining such parameters. In this paper, a method based on neural networks (NNs) is proposed and a possible architecture of the NN is presented. The results of experiments on implementing and training the NN are also presented. The model obtained shows the presence of an "understanding" of the input data, demonstrating answers that are similar to the original data. In the NN answers, one can identify a relationship between the quality of the network response and the number of waves that have passed through the medium’s object being investigated.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

Modifications to Axially Symmetric Simulations Using New DSMC (2007) Algorithms

NASA Technical Reports Server (NTRS)

Liechty, Derek S.

2008-01-01

Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.

An RBF-FD closest point method for solving PDEs on surfaces

NASA Astrophysics Data System (ADS)

Petras, A.; Ling, L.; Ruuth, S. J.

2018-10-01

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

The Study on Network Examinational Database based on ASP Technology

NASA Astrophysics Data System (ADS)

Zhang, Yanfu; Han, Yuexiao; Zhou, Yanshuang

This article introduces the structure of the general test base system based on .NET technology, discussing the design of the function modules and its implementation methods. It focuses on key technology of the system, proposing utilizing the WEB online editor control to solve the input problem and regular expression to solve the problem HTML code, making use of genetic algorithm to optimize test paper and the automated tools of WORD to solve the problem of exporting papers and others. Practical effective design and implementation technology can be used as reference for the development of similar systems.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Multi-objective flexible job shop scheduling problem using variable neighborhood evolutionary algorithm

NASA Astrophysics Data System (ADS)

Wang, Chun; Ji, Zhicheng; Wang, Yan

2017-07-01

In this paper, multi-objective flexible job shop scheduling problem (MOFJSP) was studied with the objects to minimize makespan, total workload and critical workload. A variable neighborhood evolutionary algorithm (VNEA) was proposed to obtain a set of Pareto optimal solutions. First, two novel crowded operators in terms of the decision space and object space were proposed, and they were respectively used in mating selection and environmental selection. Then, two well-designed neighborhood structures were used in local search, which consider the problem characteristics and can hold fast convergence. Finally, extensive comparison was carried out with the state-of-the-art methods specially presented for solving MOFJSP on well-known benchmark instances. The results show that the proposed VNEA is more effective than other algorithms in solving MOFJSP.

A New Moving Object Detection Method Based on Frame-difference and Background Subtraction

NASA Astrophysics Data System (ADS)

Guo, Jiajia; Wang, Junping; Bai, Ruixue; Zhang, Yao; Li, Yong

2017-09-01

Although many methods of moving object detection have been proposed, moving object extraction is still the core in video surveillance. However, with the complex scene in real world, false detection, missed detection and deficiencies resulting from cavities inside the body still exist. In order to solve the problem of incomplete detection for moving objects, a new moving object detection method combined an improved frame-difference and Gaussian mixture background subtraction is proposed in this paper. To make the moving object detection more complete and accurate, the image repair and morphological processing techniques which are spatial compensations are applied in the proposed method. Experimental results show that our method can effectively eliminate ghosts and noise and fill the cavities of the moving object. Compared to other four moving object detection methods which are GMM, VIBE, frame-difference and a literature's method, the proposed method improve the efficiency and accuracy of the detection.

Sparse Coding and Counting for Robust Visual Tracking

PubMed Central

Liu, Risheng; Wang, Jing; Shang, Xiaoke; Wang, Yiyang; Su, Zhixun; Cai, Yu

2016-01-01

In this paper, we propose a novel sparse coding and counting method under Bayesian framework for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear coefficients of incrementally updated linear basis. The sparsity constraint enables the tracker to effectively handle difficult challenges, such as occlusion or image corruption. To achieve real-time processing, we propose a fast and efficient numerical algorithm for solving the proposed model. Although it is an NP-hard problem, the proposed accelerated proximal gradient (APG) approach is guaranteed to converge to a solution quickly. Besides, we provide a closed solution of combining L0 and L1 regularized representation to obtain better sparsity. Experimental results on challenging video sequences demonstrate that the proposed method achieves state-of-the-art results both in accuracy and speed. PMID:27992474

Rate and power efficient image compressed sensing and transmission

NASA Astrophysics Data System (ADS)

Olanigan, Saheed; Cao, Lei; Viswanathan, Ramanarayanan

2016-01-01

This paper presents a suboptimal quantization and transmission scheme for multiscale block-based compressed sensing images over wireless channels. The proposed method includes two stages: dealing with quantization distortion and transmission errors. First, given the total transmission bit rate, the optimal number of quantization bits is assigned to the sensed measurements in different wavelet sub-bands so that the total quantization distortion is minimized. Second, given the total transmission power, the energy is allocated to different quantization bit layers based on their different error sensitivities. The method of Lagrange multipliers with Karush-Kuhn-Tucker conditions is used to solve both optimization problems, for which the first problem can be solved with relaxation and the second problem can be solved completely. The effectiveness of the scheme is illustrated through simulation results, which have shown up to 10 dB improvement over the method without the rate and power optimization in medium and low signal-to-noise ratio cases.

Laplace transform homotopy perturbation method for the approximation of variational problems.

PubMed

Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R

2016-01-01

This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.

Einstein gravity with torsion induced by the scalar field

NASA Astrophysics Data System (ADS)

Özçelik, H. T.; Kaya, R.; Hortaçsu, M.

2018-06-01

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

NASA Astrophysics Data System (ADS)

Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming

2018-06-01

Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.

A novel heuristic algorithm for capacitated vehicle routing problem

NASA Astrophysics Data System (ADS)

Kır, Sena; Yazgan, Harun Reşit; Tüncel, Emre

2017-09-01

The vehicle routing problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this problem. In this paper, we constructed a new heuristic algorithm based on the tabu search and adaptive large neighborhood search (ALNS) with several specifically designed operators and features to solve the capacitated vehicle routing problem (CVRP). The effectiveness of the proposed algorithm was illustrated on the benchmark problems. The algorithm provides a better performance on large-scaled instances and gained advantage in terms of CPU time. In addition, we solved a real-life CVRP using the proposed algorithm and found the encouraging results by comparison with the current situation that the company is in.

Effects of a Problem-based Structure of Physics Contents on Conceptual Learning and the Ability to Solve Problems

NASA Astrophysics Data System (ADS)

Becerra-Labra, Carlos; Gras-Martí, Albert; Martínez Torregrosa, Joaquín

2012-05-01

A model of teaching/learning is proposed based on a 'problem-based structure' of the contents of the course, in combination with a training in paper and pencil problem solving that emphasizes discussion and quantitative analysis, rather than formulae plug-in. The aim is to reverse the high failure and attrition rate among engineering undergraduates taking physics. A number of tests and questionnaires were administered to a group of students following a traditional lecture-based instruction, as well as to another group that was following an instruction scheme based on the proposed approach and the teaching materials developed ad hoc. The results show that students following the new method can develop scientific reasoning habits in problem-solving skills, and show gains in conceptual learning, attitudes and interests, and that the effects of this approach on learning are noticeable several months after the course is over.

Self-aligned quadruple patterning-compliant placement

NASA Astrophysics Data System (ADS)

Nakajima, Fumiharu; Kodama, Chikaaki; Nakayama, Koichi; Nojima, Shigeki; Kotani, Toshiya

2015-03-01

Self-Aligned Quadruple Patterning (SAQP) will be one of the leading candidates for sub-14nm node and beyond. However, compared with triple patterning, making a feasible standard cell placement has following problems. (1) When coloring conflicts occur between two adjoining cells, they may not be solved easily since SAQP layout has stronger coloring constraints. (2) SAQP layout cannot use stitch to solve coloring conflict. In this paper, we present a framework of SAQP-aware standard cell placement considering the above problems. When standard cell is placed, the proposed method tries to solve coloring conflicts between two cells by exchanging two of three colors. If some conflicts remain between adjoining cells, dummy space will be inserted to keep coloring constraints of SAQP. We show some examples to confirm effectiveness of the proposed framework. To our best knowledge, this is the first framework of SAQP-aware standard cell placement.

Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum Compliance Problems and Its Implementation in MATLAB

PubMed Central

Biyikli, Emre; To, Albert C.

2015-01-01

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-sensitivity method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing optimality criteria method which computes sensitivities. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org. PMID:26678849

Improving local clustering based top-L link prediction methods via asymmetric link clustering information

NASA Astrophysics Data System (ADS)

Wu, Zhihao; Lin, Youfang; Zhao, Yiji; Yan, Hongyan

2018-02-01

Networks can represent a wide range of complex systems, such as social, biological and technological systems. Link prediction is one of the most important problems in network analysis, and has attracted much research interest recently. Many link prediction methods have been proposed to solve this problem with various techniques. We can note that clustering information plays an important role in solving the link prediction problem. In previous literatures, we find node clustering coefficient appears frequently in many link prediction methods. However, node clustering coefficient is limited to describe the role of a common-neighbor in different local networks, because it cannot distinguish different clustering abilities of a node to different node pairs. In this paper, we shift our focus from nodes to links, and propose the concept of asymmetric link clustering (ALC) coefficient. Further, we improve three node clustering based link prediction methods via the concept of ALC. The experimental results demonstrate that ALC-based methods outperform node clustering based methods, especially achieving remarkable improvements on food web, hamster friendship and Internet networks. Besides, comparing with other methods, the performance of ALC-based methods are very stable in both globalized and personalized top-L link prediction tasks.

Design and Implementation of a Simulation-Based Learning System for International Trade

ERIC Educational Resources Information Center

Luo, Guo-Heng; Liu, Eric Zhi-Feng; Kuo, Hung-Wei; Yuan, Shyan-Ming

2014-01-01

In the traditional instructional method used in international trade, teachers provide knowledge to learners by lecturing using slides and setting assignments; however, these methods merely deliver international trade knowledge rather than facilitating student development of relevant skills. To solve these problems, we proposed a simulation-based…

An Ecological Approach to the On-Line Assessment of Problem-Solving Paths: Principles and Applications.

ERIC Educational Resources Information Center

Shaw, Robert E.; And Others

1997-01-01

Proposes a theoretical framework for designing online-situated assessment tools for multimedia instructional systems. Uses a graphic method based on ecological psychology to monitor student performance through a learning activity. Explores the method's feasibility in case studies describing instructional systems teaching critical-thinking and…

A First Step towards Variational Methods in Engineering

ERIC Educational Resources Information Center

Periago, Francisco

2003-01-01

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics

NASA Astrophysics Data System (ADS)

Guo, Qiang

Time dependent partial differential equations (PDEs) are widely used as mathematical models of environmental problems. Aerosols are now clearly identified as an important factor in many environmental aspects of climate and radiative forcing processes, as well as in the health effects of air quality. The mathematical models for the aerosol dynamics with respect to size distribution are nonlinear partial differential and integral equations, which describe processes of condensation, coagulation and deposition. Simulating the general aerosol dynamic equations on time, particle size and space exhibits serious difficulties because the size dimension ranges from a few nanometer to several micrometer while the spatial dimension is usually described with kilometers. Therefore, it is an important and challenging task to develop efficient techniques for solving time dependent dynamic equations. In this thesis, we develop and analyze efficient wavelet and adaptive methods for the time dependent dynamic equations on particle size and further apply them to the spatial aerosol dynamic systems. Wavelet Galerkin method is proposed to solve the aerosol dynamic equations on time and particle size due to the fact that aerosol distribution changes strongly along size direction and the wavelet technique can solve it very efficiently. Daubechies' wavelets are considered in the study due to the fact that they possess useful properties like orthogonality, compact support, exact representation of polynomials to a certain degree. Another problem encountered in the solution of the aerosol dynamic equations results from the hyperbolic form due to the condensation growth term. We propose a new characteristic-based fully adaptive multiresolution numerical scheme for solving the aerosol dynamic equation, which combines the attractive advantages of adaptive multiresolution technique and the characteristics method. On the aspect of theoretical analysis, the global existence and uniqueness of solutions of continuous time wavelet numerical methods for the nonlinear aerosol dynamics are proved by using Schauder's fixed point theorem and the variational technique. Optimal error estimates are derived for both continuous and discrete time wavelet Galerkin schemes. We further derive reliable and efficient a posteriori error estimate which is based on stable multiresolution wavelet bases and an adaptive space-time algorithm for efficient solution of linear parabolic differential equations. The adaptive space refinement strategies based on the locality of corresponding multiresolution processes are proved to converge. At last, we develop efficient numerical methods by combining the wavelet methods proposed in previous parts and the splitting technique to solve the spatial aerosol dynamic equations. Wavelet methods along the particle size direction and the upstream finite difference method along the spatial direction are alternately used in each time interval. Numerical experiments are taken to show the effectiveness of our developed methods.

Hue-preserving and saturation-improved color histogram equalization algorithm.

PubMed

Song, Ki Sun; Kang, Hee; Kang, Moon Gi

2016-06-01

In this paper, an algorithm is proposed to improve contrast and saturation without color degradation. The local histogram equalization (HE) method offers better performance than the global HE method, whereas the local HE method sometimes produces undesirable results due to the block-based processing. The proposed contrast-enhancement (CE) algorithm reflects the characteristics of the global HE method in the local HE method to avoid the artifacts, while global and local contrasts are enhanced. There are two ways to apply the proposed CE algorithm to color images. One is luminance processing methods, and the other one is each channel processing methods. However, these ways incur excessive or reduced saturation and color degradation problems. The proposed algorithm solves these problems by using channel adaptive equalization and similarity of ratios between the channels. Experimental results show that the proposed algorithm enhances contrast and saturation while preserving the hue and producing better performance than existing methods in terms of objective evaluation metrics.

A new smoothing modified three-term conjugate gradient method for [Formula: see text]-norm minimization problem.

PubMed

Du, Shouqiang; Chen, Miao

2018-01-01

We consider a kind of nonsmooth optimization problems with [Formula: see text]-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems. Using smoothing approximate techniques, this kind of nonsmooth optimization problem can be transformed into a general unconstrained optimization problem, which can be solved by the proposed smoothing modified three-term conjugate gradient method. The smoothing modified three-term conjugate gradient method is based on Polak-Ribière-Polyak conjugate gradient method. For the Polak-Ribière-Polyak conjugate gradient method has good numerical properties, the proposed method possesses the sufficient descent property without any line searches, and it is also proved to be globally convergent. Finally, the numerical experiments show the efficiency of the proposed method.

Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

PubMed

Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

2012-10-21

A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose sorting method. By integrating a smart constraint adding/deleting scheme within the iteration framework, the new technique builds up an improved algorithm for solving the fluence map optimization with dose-volume constraints.

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Fluid-structure interaction with pipe-wall viscoelasticity during water hammer

NASA Astrophysics Data System (ADS)

Keramat, A.; Tijsseling, A. S.; Hou, Q.; Ahmadi, A.

2012-01-01

Fluid-structure interaction (FSI) due to water hammer in a pipeline which has viscoelastic wall behaviour is studied. Appropriate governing equations are derived and numerically solved. In the numerical implementation of the hydraulic and structural equations, viscoelasticity is incorporated using the Kelvin-Voigt mechanical model. The equations are solved by two different approaches, namely the Method of Characteristics-Finite Element Method (MOC-FEM) and full MOC. In both approaches two important effects of FSI in fluid-filled pipes, namely Poisson and junction coupling, are taken into account. The study proposes a more comprehensive model for studying fluid transients in pipelines as compared to previous works, which take into account either FSI or viscoelasticity. To verify the proposed mathematical model and its numerical solutions, the following problems are investigated: axial vibration of a viscoelastic bar subjected to a step uniaxial loading, FSI in an elastic pipe, and hydraulic transients in a pressurised polyethylene pipe without FSI. The results of each case are checked with available exact and experimental results. Then, to study the simultaneous effects of FSI and viscoelasticity, which is the new element of the present research, one problem is solved by the two different numerical approaches. Both numerical methods give the same results, thus confirming the correctness of the solutions.

Emitter signal separation method based on multi-level digital channelization

NASA Astrophysics Data System (ADS)

Han, Xun; Ping, Yifan; Wang, Sujun; Feng, Ying; Kuang, Yin; Yang, Xinquan

2018-02-01

To solve the problem of emitter separation under complex electromagnetic environment, a signal separation method based on multi-level digital channelization is proposed in this paper. A two-level structure which can divide signal into different channel is designed first, after that, the peaks of different channels are tracked using the track filter and the coincident signals in time domain are separated in time-frequency domain. Finally, the time domain waveforms of different signals are acquired by reverse transformation. The validness of the proposed method is proved by experiment.

Evolutionary Local Search of Fuzzy Rules through a novel Neuro-Fuzzy encoding method.

PubMed

Carrascal, A; Manrique, D; Ríos, J; Rossi, C

2003-01-01

This paper proposes a new approach for constructing fuzzy knowledge bases using evolutionary methods. We have designed a genetic algorithm that automatically builds neuro-fuzzy architectures based on a new indirect encoding method. The neuro-fuzzy architecture represents the fuzzy knowledge base that solves a given problem; the search for this architecture takes advantage of a local search procedure that improves the chromosomes at each generation. Experiments conducted both on artificially generated and real world problems confirm the effectiveness of the proposed approach.

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction

PubMed Central

Lu, Hongyang; Wei, Jingbo; Wang, Yuhao; Deng, Xiaohua

2016-01-01

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values. PMID:27110235

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction.

PubMed

Lu, Hongyang; Wei, Jingbo; Liu, Qiegen; Wang, Yuhao; Deng, Xiaohua

2016-01-01

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

Energy efficient motion control of the electric bus on route

NASA Astrophysics Data System (ADS)

Kotiev, G. O.; Butarovich, D. O.; Kositsyn, B. B.

2018-02-01

At present, the urgent problem is the reduction of energy costs of urban motor transport. The article proposes a method of solving this problem by developing an energy-efficient law governing the movement of an electric bus along a city route. To solve this problem, an algorithm is developed based on the dynamic programming method. The proposed method allows you to take into account the constraints imposed on the phase coordinates, control action, as well as on the time of the route. In the course of solving the problem, the model of rectilinear motion of an electric bus on a horizontal reference surface is considered, taking into account the assumptions that allow it to be adapted for the implementation of the method. For the formation of a control action in the equations of motion dynamics, an algorithm for changing the traction / braking torque on the wheels of an electric bus is considered, depending on the magnitude of the control parameter and the speed of motion. An optimal phase trajectory was obtained on a selected section of the road for the prototype of an electric bus. The article presents the comparison of simulation results obtained with the optimal energy efficient control law with the results obtained by a test driver. The comparison proved feasibility of the energy efficient control law for the automobile city electric transport.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization

NASA Astrophysics Data System (ADS)

Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven

2018-07-01

We develop efficient energy stable numerical methods for solving isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. The scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is constructed based on a convex splitting approach. We prove that, for the isotropic Cahn-Hilliard system with the Willmore regularization, the total free energy of the system is non-increasing for any time step and mesh sizes. A straightforward modification of the scheme is then used to solve the regularized strongly anisotropic Cahn-Hilliard system, and it is numerically verified that the discrete energy of the anisotropic system is also non-increasing, and can be efficiently solved by using the modified stable method. We present numerical results in both two and three dimensions that are in good agreement with those in earlier work on the topics. Numerical simulations are presented to demonstrate the accuracy and efficiency of the proposed methods.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

NASA Astrophysics Data System (ADS)

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

An ill-posed problem for the Black-Scholes equation for a profitable forecast of prices of stock options on real market data

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Kuzhuget, Andrey V.; Golubnichiy, Kirill V.

2016-01-01

A new empirical mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock, new initial and new boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. To verify the validity of our model, real market data for 368 randomly selected liquid options are used. A new trading strategy is proposed. Our results indicates that our method is profitable on those options. Furthermore, it is shown that the performance of two simple extrapolation-based techniques is much worse. We conjecture that our method might lead to significant profits of those financial insitutions which trade large amounts of options. We caution, however, that further studies are necessary to verify this conjecture.

H∞ memory feedback control with input limitation minimization for offshore jacket platform stabilization

NASA Astrophysics Data System (ADS)

Yang, Jia Sheng

2018-06-01

In this paper, we investigate a H∞ memory controller with input limitation minimization (HMCIM) for offshore jacket platforms stabilization. The main objective of this study is to reduce the control consumption as well as protect the actuator when satisfying the requirement of the system performance. First, we introduce a dynamic model of offshore platform with low order main modes based on mode reduction method in numerical analysis. Then, based on H∞ control theory and matrix inequality techniques, we develop a novel H∞ memory controller with input limitation. Furthermore, a non-convex optimization model to minimize input energy consumption is proposed. Since it is difficult to solve this non-convex optimization model by optimization algorithm, we use a relaxation method with matrix operations to transform this non-convex optimization model to be a convex optimization model. Thus, it could be solved by a standard convex optimization solver in MATLAB or CPLEX. Finally, several numerical examples are given to validate the proposed models and methods.

Optimal Management of Hydropower Systems

NASA Astrophysics Data System (ADS)

Bensalem, A.; Cherif, F.; Bennagoune, S.; Benbouza, M. S.; El-Maouhab, A.

In this study we propose a new model for solving the short term management of water reservoirs with variable waterfall. The stored water in these reservoirs is used to produce the electrical energy. The proposed model is based on the enhancement of the value of water by taking into account its location in any reservoir and its waterfall high. The water outflow in the upper reservoir to produce electrical energy is reused in the lower reservoirs to produce electrical energy too. On the other hand the amount of water flow necessary to produce the same amount of electrical energy decrease as the high of waterfall increases. Thus, the objective function is represented in function of the water potential energy stocked in all reservoirs. To analyze this model, we have developed an algorithm based on the discrete maximum principle. To solve the obtained equations, an iterative method based on the gradient method is used. And to satisfy the constraints we have used the Augmented Lagrangian method.

Alternative Attitude Commanding and Control for Precise Spacecraft Landing

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2004-01-01

A report proposes an alternative method of control for precision landing on a remote planet. In the traditional method, the attitude of a spacecraft is required to track a commanded translational acceleration vector, which is generated at each time step by solving a two-point boundary value problem. No requirement of continuity is imposed on the acceleration. The translational acceleration does not necessarily vary smoothly. Tracking of a non-smooth acceleration causes the vehicle attitude to exhibit undesirable transients and poor pointing stability behavior. In the alternative method, the two-point boundary value problem is not solved at each time step. A smooth reference position profile is computed. The profile is recomputed only when the control errors get sufficiently large. The nominal attitude is still required to track the smooth reference acceleration command. A steering logic is proposed that controls the position and velocity errors about the reference profile by perturbing the attitude slightly about the nominal attitude. The overall pointing behavior is therefore smooth, greatly reducing the degree of pointing instability.

Hierarchical semi-numeric method for pairwise fuzzy group decision making.

PubMed

Marimin, M; Umano, M; Hatono, I; Tamura, H

2002-01-01

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.

An efficient and flexible Abel-inversion method for noisy data

NASA Astrophysics Data System (ADS)

Antokhin, Igor I.

2016-12-01

We propose an efficient and flexible method for solving the Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem, thus solving it requires some kind of regularization. Our method is based on solving the equation on a so-called compact set of functions and/or using Tikhonov's regularization. A priori constraints on the unknown function, defining a compact set, are very loose and can be set using simple physical considerations. Tikhonov's regularization in itself does not require any explicit a priori constraints on the unknown function and can be used independently of such constraints or in combination with them. Various target degrees of smoothness of the unknown function may be set, as required by the problem at hand. The advantage of the method, apart from its flexibility, is that it gives uniform convergence of the approximate solution to the exact solution, as the errors of input data tend to zero. The method is illustrated on several simulated models with known solutions. An example of astrophysical application of the method is also given.

Linear homotopy solution of nonlinear systems of equations in geodesy

NASA Astrophysics Data System (ADS)

Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

2010-01-01

A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

NASA Astrophysics Data System (ADS)

La Cour, Brian R.; Ostrove, Corey I.

2017-01-01

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover's algorithm on the same device.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles.

PubMed

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-08-13

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well.

Multiobjective optimization in a pseudometric objective space as applied to a general model of business activities

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2016-09-01

It is shown that finding the equivalence set for solving multiobjective discrete optimization problems is advantageous over finding the set of Pareto optimal decisions. An example of a set of key parameters characterizing the economic efficiency of a commercial firm is proposed, and a mathematical model of its activities is constructed. In contrast to the classical problem of finding the maximum profit for any business, this study deals with a multiobjective optimization problem. A method for solving inverse multiobjective problems in a multidimensional pseudometric space is proposed for finding the best project of firm's activities. The solution of a particular problem of this type is presented.

Total Variation with Overlapping Group Sparsity for Image Deblurring under Impulse Noise

PubMed Central

Liu, Gang; Huang, Ting-Zhu; Liu, Jun; Lv, Xiao-Guang

2015-01-01

The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In order to alleviate the staircase effects, we propose a new model for restoring blurred images under impulse noise. The model consists of an ℓ1-fidelity term and a TV with overlapping group sparsity (OGS) regularization term. Moreover, we impose a box constraint to the proposed model for getting more accurate solutions. The solving algorithm for our model is under the framework of the alternating direction method of multipliers (ADMM). We use an inner loop which is nested inside the majorization minimization (MM) iteration for the subproblem of the proposed method. Compared with other TV-based methods, numerical results illustrate that the proposed method can significantly improve the restoration quality, both in terms of peak signal-to-noise ratio (PSNR) and relative error (ReE). PMID:25874860

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

On the determination of certain astronomical, selenodesic, and gravitational parameters of the moon

NASA Technical Reports Server (NTRS)

Aleksashin, Y. P.; Ziman, Y. L.; Isavnina, I. V.; Krasikov, V. A.; Nepoklonov, B. V.; Rodionov, B. N.; Tischenko, A. P.

1974-01-01

A method was examined for joint construction of a selenocentric fundamental system which can be realized by a coordinate catalog of reference contour points uniformly positioned over the entire lunar surface, and determination of the parameters characterizing the gravitational field, rotation, and orbital motion of the moon. Characteristic of the problem formulation is the introduction of a new complex of inconometric measurements which can be made using pictures obtained from an artificial lunar satellite. The proposed method can be used to solve similar problems on any other planet for which surface images can be obtained from a spacecraft. Characteristic of the proposed technique for solving the problem is the joint statistical analysis of all forms of measurements: orbital iconometric, earth-based trajectory, and also a priori information on the parameters in question which is known from earth-based astronomical studies.

Equivalency principle for magnetoelectroelastic multiferroics with arbitrary microstructure: The phase field approach

NASA Astrophysics Data System (ADS)

Ni, Yong; He, Linghui; Khachaturyan, Armen G.

2010-07-01

A phase field method is proposed to determine the equilibrium fields of a magnetoelectroelastic multiferroic with arbitrarily distributed constitutive constants under applied loadings. This method is based on a developed generalized Eshelby's equivalency principle, in which the elastic strain, electrostatic, and magnetostatic fields at the equilibrium in the original heterogeneous system are exactly the same as those in an equivalent homogeneous magnetoelectroelastic coupled or uncoupled system with properly chosen distributed effective eigenstrain, polarization, and magnetization fields. Finding these effective fields fully solves the equilibrium elasticity, electrostatics, and magnetostatics in the original heterogeneous multiferroic. The paper formulates a variational principle proving that the effective fields are minimizers of appropriate close-form energy functional. The proposed phase field approach produces the energy minimizing effective fields (and thus solving the general multiferroic problem) as a result of artificial relaxation process described by the Ginzburg-Landau-Khalatnikov kinetic equations.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Machine Learning Methods for Production Cases Analysis

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.; Mokrov, Alexander M.; Safonova, Alexandra V.; Vishnyakov, Igor V.

2018-03-01

Approach to analysis of events occurring during the production process were proposed. Described machine learning system is able to solve classification tasks related to production control and hazard identification at an early stage. Descriptors of the internal production network data were used for training and testing of applied models. k-Nearest Neighbors and Random forest methods were used to illustrate and analyze proposed solution. The quality of the developed classifiers was estimated using standard statistical metrics, such as precision, recall and accuracy.

Multicast backup reprovisioning problem for Hamiltonian cycle-based protection on WDM networks

NASA Astrophysics Data System (ADS)

Din, Der-Rong; Huang, Jen-Shen

2014-03-01

As networks grow in size and complexity, the chance and the impact of failures increase dramatically. The pre-allocated backup resources cannot provide 100% protection guarantee when continuous failures occur in a network. In this paper, the multicast backup re-provisioning problem (MBRP) for Hamiltonian cycle (HC)-based protection on WDM networks for the link-failure case is studied. We focus on how to recover the protecting capabilities of Hamiltonian cycle against the subsequent link-failures on WDM networks for multicast transmissions, after recovering the multicast trees affected by the previous link-failure. Since this problem is a hard problem, an algorithm, which consists of several heuristics and a genetic algorithm (GA), is proposed to solve it. The simulation results of the proposed method are also given. Experimental results indicate that the proposed algorithm can solve this problem efficiently.

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

NASA Astrophysics Data System (ADS)

Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

2016-07-01

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

A Scenario-Based Parametric Analysis of Stable Marriage Approaches to the Army Officer Assignment Problem

DTIC Science & Technology

2017-03-23

solutions obtained through their proposed method to comparative instances of a generalized assignment problem with either ordinal cost components or... method flag: Designates the method by which the changed/ new assignment problem instance is solved. methodFlag = 0:SMAWarmstart Returns a matching...of randomized perturbations. We examine the contrasts between these methods in the context of assigning Army Officers among a set of identified

Aeroelastic analysis of a troposkien-type wind turbine blade

NASA Technical Reports Server (NTRS)

Nitzsche, F.

1981-01-01

The linear aeroelastic equations for one curved blade of a vertical axis wind turbine in state vector form are presented. The method is based on a simple integrating matrix scheme together with the transfer matrix idea. The method is proposed as a convenient way of solving the associated eigenvalue problem for general support conditions.

Absolute Points for Multiple Assignment Problems

ERIC Educational Resources Information Center

Adlakha, V.; Kowalski, K.

2006-01-01

An algorithm is presented to solve multiple assignment problems in which a cost is incurred only when an assignment is made at a given cell. The proposed method recursively searches for single/group absolute points to identify cells that must be loaded in any optimal solution. Unlike other methods, the first solution is the optimal solution. The…

Use of Invariant Manifolds for Transfers Between Three-Body Systems

NASA Technical Reports Server (NTRS)

Beckman, Mark; Howell, Kathleen

2003-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits does not exist. This paper presents the initial approaches to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing 7-dimensional invariant manifold data are presented. Some particular solutions are presented for the transfer problem, though the emphasis is on developing methodology for solving the general problem.

Representations of Invariant Manifolds for Applications in Three-Body Systems

NASA Technical Reports Server (NTRS)

Howell, K.; Beckman, M.; Patterson, C.; Folta, D.

2004-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied. This paper presents an initial approach to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing the invariant manifold data are presented. Some particular solutions are presented for two types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.

A majorized Newton-CG augmented Lagrangian-based finite element method for 3D restoration of geological models

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization

NASA Astrophysics Data System (ADS)

Gerist, Saleheh; Maheri, Mahmoud R.

2016-12-01

In order to solve structural damage detection problem, a multi-stage method using particle swarm optimization is presented. First, a new spars recovery method, named Basis Pursuit (BP), is utilized to preliminarily identify structural damage locations. The BP method solves a system of equations which relates the damage parameters to the structural modal responses using the sensitivity matrix. Then, the results of this stage are subsequently enhanced to the exact damage locations and extents using the PSO search engine. Finally, the search space is reduced by elimination of some low damage variables using micro search (MS) operator embedded in the PSO algorithm. To overcome the noise present in structural responses, a method known as Basis Pursuit De-Noising (BPDN) is also used. The efficiency of the proposed method is investigated by three numerical examples: a cantilever beam, a plane truss and a portal plane frame. The frequency response is used to detect damage in the examples. The simulation results demonstrate the accuracy and efficiency of the proposed method in detecting multiple damage cases and exhibit its robustness regarding noise and its advantages compared to other reported solution algorithms.

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem

PubMed Central

Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

2015-01-01

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods. PMID:26176764

77 FR 32138 - Agency Information Collection Agencies: Proposed Collection; Comments Requested Census of Problem...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-05-31

... Agencies: Proposed Collection; Comments Requested Census of Problem-Solving Courts 2012 ACTION: 30-Day...-Solving Courts (CPSC), 201 2. The title of the form/collection: Census of Problem-Solving Courts or CPSC... Abstract: Problem-solving courts at all levels of government. Abstract: The Bureau of Justice Statistics...

LTI system order reduction approach based on asymptotical equivalence and the Co-operation of biology-related algorithms

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.; Akhmedova, Sh A.

2017-02-01

A novel order reduction method for linear time invariant systems is described. The method is based on reducing the initial problem to an optimization one, using the proposed model representation, and solving the problem with an efficient optimization algorithm. The proposed method of determining the model allows all the parameters of the model with lower order to be identified and by definition, provides the model with the required steady-state. As a powerful optimization tool, the meta-heuristic Co-Operation of Biology-Related Algorithms was used. Experimental results proved that the proposed approach outperforms other approaches and that the reduced order model achieves a high level of accuracy.

A Novel Harmony Search Algorithm Based on Teaching-Learning Strategies for 0-1 Knapsack Problems

PubMed Central

Tuo, Shouheng; Yong, Longquan; Deng, Fang'an

2014-01-01

To enhance the performance of harmony search (HS) algorithm on solving the discrete optimization problems, this paper proposes a novel harmony search algorithm based on teaching-learning (HSTL) strategies to solve 0-1 knapsack problems. In the HSTL algorithm, firstly, a method is presented to adjust dimension dynamically for selected harmony vector in optimization procedure. In addition, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and random mutation) are employed to improve the performance of HS algorithm. Another improvement in HSTL method is that the dynamic strategies are adopted to change the parameters, which maintains the proper balance effectively between global exploration power and local exploitation power. Finally, simulation experiments with 13 knapsack problems show that the HSTL algorithm can be an efficient alternative for solving 0-1 knapsack problems. PMID:24574905

A novel harmony search algorithm based on teaching-learning strategies for 0-1 knapsack problems.

PubMed

Tuo, Shouheng; Yong, Longquan; Deng, Fang'an

2014-01-01

To enhance the performance of harmony search (HS) algorithm on solving the discrete optimization problems, this paper proposes a novel harmony search algorithm based on teaching-learning (HSTL) strategies to solve 0-1 knapsack problems. In the HSTL algorithm, firstly, a method is presented to adjust dimension dynamically for selected harmony vector in optimization procedure. In addition, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and random mutation) are employed to improve the performance of HS algorithm. Another improvement in HSTL method is that the dynamic strategies are adopted to change the parameters, which maintains the proper balance effectively between global exploration power and local exploitation power. Finally, simulation experiments with 13 knapsack problems show that the HSTL algorithm can be an efficient alternative for solving 0-1 knapsack problems.

Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

DOE PAGES

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

2015-01-23

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

Depth compensating calculation method of computer-generated holograms using symmetry and similarity of zone plates

NASA Astrophysics Data System (ADS)

Wei, Hui; Gong, Guanghong; Li, Ni

2017-10-01

Computer-generated hologram (CGH) is a promising 3D display technology while it is challenged by heavy computation load and vast memory requirement. To solve these problems, a depth compensating CGH calculation method based on symmetry and similarity of zone plates is proposed and implemented on graphics processing unit (GPU). An improved LUT method is put forward to compute the distances between object points and hologram pixels in the XY direction. The concept of depth compensating factor is defined and used for calculating the holograms of points with different depth positions instead of layer-based methods. The proposed method is suitable for arbitrary sampling objects with lower memory usage and higher computational efficiency compared to other CGH methods. The effectiveness of the proposed method is validated by numerical and optical experiments.

Use of multilevel modeling for determining optimal parameters of heat supply systems

NASA Astrophysics Data System (ADS)

Stennikov, V. A.; Barakhtenko, E. A.; Sokolov, D. V.

2017-07-01

The problem of finding optimal parameters of a heat-supply system (HSS) is in ensuring the required throughput capacity of a heat network by determining pipeline diameters and characteristics and location of pumping stations. Effective methods for solving this problem, i.e., the method of stepwise optimization based on the concept of dynamic programming and the method of multicircuit optimization, were proposed in the context of the hydraulic circuit theory developed at Melentiev Energy Systems Institute (Siberian Branch, Russian Academy of Sciences). These methods enable us to determine optimal parameters of various types of piping systems due to flexible adaptability of the calculation procedure to intricate nonlinear mathematical models describing features of used equipment items and methods of their construction and operation. The new and most significant results achieved in developing methodological support and software for finding optimal parameters of complex heat supply systems are presented: a new procedure for solving the problem based on multilevel decomposition of a heat network model that makes it possible to proceed from the initial problem to a set of interrelated, less cumbersome subproblems with reduced dimensionality; a new algorithm implementing the method of multicircuit optimization and focused on the calculation of a hierarchical model of a heat supply system; the SOSNA software system for determining optimum parameters of intricate heat-supply systems and implementing the developed methodological foundation. The proposed procedure and algorithm enable us to solve engineering problems of finding the optimal parameters of multicircuit heat supply systems having large (real) dimensionality, and are applied in solving urgent problems related to the optimal development and reconstruction of these systems. The developed methodological foundation and software can be used for designing heat supply systems in the Central and the Admiralty regions in St. Petersburg, the city of Bratsk, and the Magistral'nyi settlement.

A VIKOR Technique with Applications Based on DEMATEL and ANP

NASA Astrophysics Data System (ADS)

Ou Yang, Yu-Ping; Shieh, How-Ming; Tzeng, Gwo-Hshiung

In multiple criteria decision making (MCDM) methods, the compromise ranking method (named VIKOR) was introduced as one applicable technique to implement within MCDM. It was developed for multicriteria optimization of complex systems. However, few papers discuss conflicting (competing) criteria with dependence and feedback in the compromise solution method. Therefore, this study proposes and provides applications for a novel model using the VIKOR technique based on DEMATEL and the ANP to solve the problem of conflicting criteria with dependence and feedback. In addition, this research also uses DEMATEL to normalize the unweighted supermatrix of the ANP to suit the real world. An example is also presented to illustrate the proposed method with applications thereof. The results show the proposed method is suitable and effective in real-world applications.

Evaluating Simultaneous Integrals

ERIC Educational Resources Information Center

Kwong, Harris

2012-01-01

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

Design of bearings for rotor systems based on stability

NASA Technical Reports Server (NTRS)

Dhar, D.; Barrett, L. E.; Knospe, C. R.

1992-01-01

Design of rotor systems incorporating stable behavior is of great importance to manufacturers of high speed centrifugal machinery since destabilizing mechanisms (from bearings, seals, aerodynamic cross coupling, noncolocation effects from magnetic bearings, etc.) increase with machine efficiency and power density. A new method of designing bearing parameters (stiffness and damping coefficients or coefficients of the controller transfer function) is proposed, based on a numerical search in the parameter space. The feedback control law is based on a decentralized low order controller structure, and the various design requirements are specified as constraints in the specification and parameter spaces. An algorithm is proposed for solving the problem as a sequence of constrained 'minimax' problems, with more and more eigenvalues into an acceptable region in the complex plane. The algorithm uses the method of feasible directions to solve the nonlinear constrained minimization problem at each stage. This methodology emphasizes the designer's interaction with the algorithm to generate acceptable designs by relaxing various constraints and changing initial guesses interactively. A design oriented user interface is proposed to facilitate the interaction.

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.

A bat algorithm with mutation for UCAV path planning.

PubMed

Wang, Gaige; Guo, Lihong; Duan, Hong; Liu, Luo; Wang, Heqi

2012-01-01

Path planning for uninhabited combat air vehicle (UCAV) is a complicated high dimension optimization problem, which mainly centralizes on optimizing the flight route considering the different kinds of constrains under complicated battle field environments. Original bat algorithm (BA) is used to solve the UCAV path planning problem. Furthermore, a new bat algorithm with mutation (BAM) is proposed to solve the UCAV path planning problem, and a modification is applied to mutate between bats during the process of the new solutions updating. Then, the UCAV can find the safe path by connecting the chosen nodes of the coordinates while avoiding the threat areas and costing minimum fuel. This new approach can accelerate the global convergence speed while preserving the strong robustness of the basic BA. The realization procedure for original BA and this improved metaheuristic approach BAM is also presented. To prove the performance of this proposed metaheuristic method, BAM is compared with BA and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, PBIL, PSO, and SGA. The experiment shows that the proposed approach is more effective and feasible in UCAV path planning than the other models.

Robust visual tracking via multiscale deep sparse networks

NASA Astrophysics Data System (ADS)

Wang, Xin; Hou, Zhiqiang; Yu, Wangsheng; Xue, Yang; Jin, Zefenfen; Dai, Bo

2017-04-01

In visual tracking, deep learning with offline pretraining can extract more intrinsic and robust features. It has significant success solving the tracking drift in a complicated environment. However, offline pretraining requires numerous auxiliary training datasets and is considerably time-consuming for tracking tasks. To solve these problems, a multiscale sparse networks-based tracker (MSNT) under the particle filter framework is proposed. Based on the stacked sparse autoencoders and rectifier linear unit, the tracker has a flexible and adjustable architecture without the offline pretraining process and exploits the robust and powerful features effectively only through online training of limited labeled data. Meanwhile, the tracker builds four deep sparse networks of different scales, according to the target's profile type. During tracking, the tracker selects the matched tracking network adaptively in accordance with the initial target's profile type. It preserves the inherent structural information more efficiently than the single-scale networks. Additionally, a corresponding update strategy is proposed to improve the robustness of the tracker. Extensive experimental results on a large scale benchmark dataset show that the proposed method performs favorably against state-of-the-art methods in challenging environments.

Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

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

Huang, Lei; Zuo, Chao; Idir, Mourad

A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less

Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

DOE PAGES

Huang, Lei; Zuo, Chao; Idir, Mourad; ...

2015-04-21

A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less

An innovative method for offshore wind farm site selection based on the interval number with probability distribution

NASA Astrophysics Data System (ADS)

Wu, Yunna; Chen, Kaifeng; Xu, Hu; Xu, Chuanbo; Zhang, Haobo; Yang, Meng

2017-12-01

There is insufficient research relating to offshore wind farm site selection in China. The current methods for site selection have some defects. First, information loss is caused by two aspects: the implicit assumption that the probability distribution on the interval number is uniform; and ignoring the value of decision makers' (DMs') common opinion on the criteria information evaluation. Secondly, the difference in DMs' utility function has failed to receive attention. An innovative method is proposed in this article to solve these drawbacks. First, a new form of interval number and its weighted operator are proposed to reflect the uncertainty and reduce information loss. Secondly, a new stochastic dominance degree is proposed to quantify the interval number with a probability distribution. Thirdly, a two-stage method integrating the weighted operator with stochastic dominance degree is proposed to evaluate the alternatives. Finally, a case from China proves the effectiveness of this method.

An opinion formation based binary optimization approach for feature selection

NASA Astrophysics Data System (ADS)

Hamedmoghadam, Homayoun; Jalili, Mahdi; Yu, Xinghuo

2018-02-01

This paper proposed a novel optimization method based on opinion formation in complex network systems. The proposed optimization technique mimics human-human interaction mechanism based on a mathematical model derived from social sciences. Our method encodes a subset of selected features to the opinion of an artificial agent and simulates the opinion formation process among a population of agents to solve the feature selection problem. The agents interact using an underlying interaction network structure and get into consensus in their opinions, while finding better solutions to the problem. A number of mechanisms are employed to avoid getting trapped in local minima. We compare the performance of the proposed method with a number of classical population-based optimization methods and a state-of-the-art opinion formation based method. Our experiments on a number of high dimensional datasets reveal outperformance of the proposed algorithm over others.

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

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

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« less

A Solution Method of Scheduling Problem with Worker Allocation by a Genetic Algorithm

NASA Astrophysics Data System (ADS)

Osawa, Akira; Ida, Kenichi

In a scheduling problem with worker allocation (SPWA) proposed by Iima et al, the worker's skill level to each machine is all the same. However, each worker has a different skill level for each machine in the real world. For that reason, we propose a new model of SPWA in which a worker has the different skill level to each machine. To solve the problem, we propose a new GA for SPWA consisting of the following new three procedures, shortening of idle time, modifying infeasible solution to feasible solution, and a new selection method for GA. The effectiveness of the proposed algorithm is clarified by numerical experiments using benchmark problems for job-shop scheduling.

Object Transportation by Two Mobile Robots with Hand Carts

PubMed Central

Hara, Tatsunori

2014-01-01

This paper proposes a methodology by which two small mobile robots can grasp, lift, and transport large objects using hand carts. The specific problems involve generating robot actions and determining the hand cart positions to achieve the stable loading of objects onto the carts. These problems are solved using nonlinear optimization, and we propose an algorithm for generating robot actions. The proposed method was verified through simulations and experiments using actual devices in a real environment. The proposed method could reduce the number of robots required to transport large objects with 50–60%. In addition, we demonstrated the efficacy of this task in real environments where errors occur in robot sensing and movement. PMID:27433499

Object Transportation by Two Mobile Robots with Hand Carts.

PubMed

Sakuyama, Takuya; Figueroa Heredia, Jorge David; Ogata, Taiki; Hara, Tatsunori; Ota, Jun

2014-01-01

This paper proposes a methodology by which two small mobile robots can grasp, lift, and transport large objects using hand carts. The specific problems involve generating robot actions and determining the hand cart positions to achieve the stable loading of objects onto the carts. These problems are solved using nonlinear optimization, and we propose an algorithm for generating robot actions. The proposed method was verified through simulations and experiments using actual devices in a real environment. The proposed method could reduce the number of robots required to transport large objects with 50-60%. In addition, we demonstrated the efficacy of this task in real environments where errors occur in robot sensing and movement.

An analytical method for free vibration analysis of functionally graded beams with edge cracks

NASA Astrophysics Data System (ADS)

Wei, Dong; Liu, Yinghua; Xiang, Zhihai

2012-03-01

In this paper, an analytical method is proposed for solving the free vibration of cracked functionally graded material (FGM) beams with axial loading, rotary inertia and shear deformation. The governing differential equations of motion for an FGM beam are established and the corresponding solutions are found first. The discontinuity of rotation caused by the cracks is simulated by means of the rotational spring model. Based on the transfer matrix method, then the recurrence formula is developed to get the eigenvalue equations of free vibration of FGM beams. The main advantage of the proposed method is that the eigenvalue equation for vibrating beams with an arbitrary number of cracks can be conveniently determined from a third-order determinant. Due to the decrease in the determinant order as compared with previous methods, the developed method is simpler and more convenient to analytically solve the free vibration problem of cracked FGM beams. Moreover, free vibration analyses of the Euler-Bernoulli and Timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method. These advantages of the proposed procedure would be more remarkable as the increase of the number of cracks. A comprehensive analysis is conducted to investigate the influences of the location and total number of cracks, material properties, axial load, inertia and end supports on the natural frequencies and vibration mode shapes of FGM beams. The present work may be useful for the design and control of damaged structures.

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

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.

An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation.

PubMed

Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri

2016-01-01

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.

An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation

PubMed Central

Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri

2016-01-01

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality. PMID:26954783

The expanded invasive weed optimization metaheuristic for solving continuous and discrete optimization problems.

PubMed

Josiński, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Switoński, Adam

2014-01-01

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.

Robust Programming Problems Based on the Mean-Variance Model Including Uncertainty Factors

NASA Astrophysics Data System (ADS)

Hasuike, Takashi; Ishii, Hiroaki

2009-01-01

This paper considers robust programming problems based on the mean-variance model including uncertainty sets and fuzzy factors. Since these problems are not well-defined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, in order to solve these equivalent problems efficiently, the solution method is constructed introducing the mean-absolute deviation and doing the equivalent transformations.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

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

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

Neural network approach for the calculation of potential coefficients in quantum mechanics

NASA Astrophysics Data System (ADS)

Ossandón, Sebastián; Reyes, Camilo; Cumsille, Patricio; Reyes, Carlos M.

2017-05-01

A numerical method based on artificial neural networks is used to solve the inverse Schrödinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a map of new eigenvalues was obtained. This relationship was later inverted and refined by training an inverse radial basis neural network, allowing the calculation of the unknown parameters and therefore estimating the potential function. Three numerical examples are presented in order to prove the effectiveness of the method. The results show that the method proposed has the advantage to use less computational resources without a significant accuracy loss.

Modelling of non-equilibrium flow in the branched pipeline systems

NASA Astrophysics Data System (ADS)

Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.

2016-09-01

This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.

Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditionsmore » are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.« less

An improved chaotic fruit fly optimization based on a mutation strategy for simultaneous feature selection and parameter optimization for SVM and its applications.

PubMed

Ye, Fei; Lou, Xin Yuan; Sun, Lin Fu

2017-01-01

This paper proposes a new support vector machine (SVM) optimization scheme based on an improved chaotic fly optimization algorithm (FOA) with a mutation strategy to simultaneously perform parameter setting turning for the SVM and feature selection. In the improved FOA, the chaotic particle initializes the fruit fly swarm location and replaces the expression of distance for the fruit fly to find the food source. However, the proposed mutation strategy uses two distinct generative mechanisms for new food sources at the osphresis phase, allowing the algorithm procedure to search for the optimal solution in both the whole solution space and within the local solution space containing the fruit fly swarm location. In an evaluation based on a group of ten benchmark problems, the proposed algorithm's performance is compared with that of other well-known algorithms, and the results support the superiority of the proposed algorithm. Moreover, this algorithm is successfully applied in a SVM to perform both parameter setting turning for the SVM and feature selection to solve real-world classification problems. This method is called chaotic fruit fly optimization algorithm (CIFOA)-SVM and has been shown to be a more robust and effective optimization method than other well-known methods, particularly in terms of solving the medical diagnosis problem and the credit card problem.

A new proportion measure of the treatment effect captured by candidate surrogate endpoints.

PubMed

Kobayashi, Fumiaki; Kuroki, Manabu

2014-08-30

The use of surrogate endpoints is expected to play an important role in the development of new drugs, as they can be used to reduce the sample size and/or duration of randomized clinical trials. Biostatistical researchers and practitioners have proposed various surrogacy measures; however, (i) most of these surrogacy measures often fall outside the range [0,1] without any assumptions, (ii) these surrogacy measures do not provide a cut-off value for judging a surrogacy level of candidate surrogate endpoints, and (iii) most surrogacy measures are highly variable; thus, the confidence intervals are often unacceptably wide. In order to solve problems (i) and (ii), we propose a new surrogacy measure, a proportion of the treatment effect captured by candidate surrogate endpoints (PCS), on the basis of the decomposition of the treatment effect into parts captured and non-captured by the candidate surrogate endpoints. In order to solve problem (iii), we propose an estimation method based on the half-range mode method with the bootstrap distribution of the estimated surrogacy measures. Finally, through numerical experiments and two empirical examples, we show that the PCS with the proposed estimation method overcomes these difficulties. The results of this paper contribute to the reliable evaluation of how much of the treatment effect is captured by candidate surrogate endpoints. Copyright © 2014 John Wiley & Sons, Ltd.

An improved chaotic fruit fly optimization based on a mutation strategy for simultaneous feature selection and parameter optimization for SVM and its applications

PubMed Central

Lou, Xin Yuan; Sun, Lin Fu

2017-01-01

This paper proposes a new support vector machine (SVM) optimization scheme based on an improved chaotic fly optimization algorithm (FOA) with a mutation strategy to simultaneously perform parameter setting turning for the SVM and feature selection. In the improved FOA, the chaotic particle initializes the fruit fly swarm location and replaces the expression of distance for the fruit fly to find the food source. However, the proposed mutation strategy uses two distinct generative mechanisms for new food sources at the osphresis phase, allowing the algorithm procedure to search for the optimal solution in both the whole solution space and within the local solution space containing the fruit fly swarm location. In an evaluation based on a group of ten benchmark problems, the proposed algorithm’s performance is compared with that of other well-known algorithms, and the results support the superiority of the proposed algorithm. Moreover, this algorithm is successfully applied in a SVM to perform both parameter setting turning for the SVM and feature selection to solve real-world classification problems. This method is called chaotic fruit fly optimization algorithm (CIFOA)-SVM and has been shown to be a more robust and effective optimization method than other well-known methods, particularly in terms of solving the medical diagnosis problem and the credit card problem. PMID:28369096

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Co-state initialization for the minimum-time low-thrust trajectory optimization

NASA Astrophysics Data System (ADS)

Taheri, Ehsan; Li, Nan I.; Kolmanovsky, Ilya

2017-05-01

This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single- or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is lower. These features are advantageous for broad trajectory search in the preliminary phase of mission designs.

Directive sources in acoustic discrete-time domain simulations based on directivity diagrams.

PubMed

Escolano, José; López, José J; Pueo, Basilio

2007-06-01

Discrete-time domain methods provide a simple and flexible way to solve initial boundary value problems. With regard to the sources in such methods, only monopoles or dipoles can be considered. However, in many problems such as room acoustics, the radiation of realistic sources is directional-dependent and their directivity patterns have a clear influence on the total sound field. In this letter, a method to synthesize the directivity of sources is proposed, especially in cases where the knowledge is only based on discrete values of the directivity diagram. Some examples have been carried out in order to show the behavior and accuracy of the proposed method.

Highlight removal based on the regional-projection fringe projection method

NASA Astrophysics Data System (ADS)

Qi, Zhaoshuai; Wang, Zhao; Huang, Junhui; Xing, Chao; Gao, Jianmin

2018-04-01

In fringe projection profilometry, highlight usually causes the saturation and blooming in captured fringes and reduces the measurement accuracy. To solve the problem, a regional-projection fringe projection (RP-FP) method is proposed. Regional projection patterns (RP patterns) are projected onto the tested object surface to avoid the saturation and blooming. Then, an image inpainting technique is employed to reconstruct the missing phases in the captured RP patterns and a complete surface of the tested object is obtained. Experiments verified the effectiveness of the proposed method. The method can be widely used in industrial inspections and quality controlling in mechanical and manufacturing industries.

Novel inter-crystal scattering event identification method for PET detectors

NASA Astrophysics Data System (ADS)

Lee, Min Sun; Kang, Seung Kwan; Lee, Jae Sung

2018-06-01

Here, we propose a novel method to identify inter-crystal scattering (ICS) events from a PET detector that is even applicable to light-sharing designs. In the proposed method, the detector observation was considered as a linear problem and ICS events were identified by solving this problem. Two ICS identification methods were suggested for solving the linear problem, pseudoinverse matrix calculation and convex constrained optimization. The proposed method was evaluated based on simulation and experimental studies. For the simulation study, an 8  ×  8 photo sensor was coupled to 8  ×  8, 10  ×  10 and 12  ×  12 crystal arrays to simulate a one-to-one coupling and two light-sharing detectors, respectively. The identification rate, the rate that the identified ICS events correctly include the true first interaction position and the energy linearity were evaluated for the proposed ICS identification methods. For the experimental study, a digital silicon photomultiplier was coupled with 8  ×  8 and 10  ×  10 arrays of 3  ×  3  ×  20 mm3 LGSO crystals to construct the one-to-one coupling and light-sharing detectors, respectively. Intrinsic spatial resolutions were measured for two detector types. The proposed ICS identification methods were implemented, and intrinsic resolutions were compared with and without ICS recovery. As a result, the simulation study showed that the proposed convex optimization method yielded robust energy estimation and high ICS identification rates of 0.93 and 0.87 for the one-to-one and light-sharing detectors, respectively. The experimental study showed a resolution improvement after recovering the identified ICS events into the first interaction position. The average intrinsic spatial resolutions for the one-to-one and light-sharing detector were 1.95 and 2.25 mm in the FWHM without ICS recovery, respectively. These values improved to 1.72 and 1.83 mm after ICS recovery, respectively. In conclusion, our proposed method showed good ICS identification in both one-to-one coupling and light-sharing detectors. We experimentally validated that the ICS recovery based on the proposed identification method led to an improved resolution.

Path changing methods applied to the 4-D guidance of STOL aircraft.

DOT National Transportation Integrated Search

1971-11-01

Prior to the advent of large-scale commercial STOL service, some challenging navigation and guidance problems must be solved. Proposed terminal area operations may require that these aircraft be capable of accurately flying complex flight paths, and ...

Multitask visual learning using genetic programming.

PubMed

Jaśkowski, Wojciech; Krawiec, Krzysztof; Wieloch, Bartosz

2008-01-01

We propose a multitask learning method of visual concepts within the genetic programming (GP) framework. Each GP individual is composed of several trees that process visual primitives derived from input images. Two trees solve two different visual tasks and are allowed to share knowledge with each other by commonly calling the remaining GP trees (subfunctions) included in the same individual. The performance of a particular tree is measured by its ability to reproduce the shapes contained in the training images. We apply this method to visual learning tasks of recognizing simple shapes and compare it to a reference method. The experimental verification demonstrates that such multitask learning often leads to performance improvements in one or both solved tasks, without extra computational effort.

A high-accuracy algorithm for solving nonlinear PDEs with high-order spatial derivatives in 1 + 1 dimensions

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

Yao, Jian Hua; Gooding, R.J.

1994-06-01

We propose an algorithm to solve a system of partial differential equations of the type u[sub t](x,t) = F(x, t, u, u[sub x], u[sub xx], u[sub xxx], u[sub xxxx]) in 1 + 1 dimensions using the method of lines with piecewise ninth-order Hermite polynomials, where u and F and N-dimensional vectors. Nonlinear boundary conditions are easily incorporated with this method. We demonstrate the accuracy of this method through comparisons of numerically determine solutions to the analytical ones. Then, we apply this algorithm to a complicated physical system involving nonlinear and nonlocal strain forces coupled to a thermal field. 4 refs.,more » 5 figs., 1 tab.« less

Comments on "The multisynapse neural network and its application to fuzzy clustering".

PubMed

Yu, Jian; Hao, Pengwei

2005-05-01

In the above-mentioned paper, Wei and Fahn proposed a neural architecture, the multisynapse neural network, to solve constrained optimization problems including high-order, logarithmic, and sinusoidal forms, etc. As one of its main applications, a fuzzy bidirectional associative clustering network (FBACN) was proposed for fuzzy-partition clustering according to the objective-functional method. The connection between the objective-functional-based fuzzy c-partition algorithms and FBACN is the Lagrange multiplier approach. Unfortunately, the Lagrange multiplier approach was incorrectly applied so that FBACN does not equivalently minimize its corresponding constrained objective-function. Additionally, Wei and Fahn adopted traditional definition of fuzzy c-partition, which is not satisfied by FBACN. Therefore, FBACN can not solve constrained optimization problems, either.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles

PubMed Central

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-01-01

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well. PMID:26287194

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Obchs: AN Effective Harmony Search Algorithm with Oppositionbased Chaos-Enhanced Initialization for Solving Uncapacitated Facility Location Problems

NASA Astrophysics Data System (ADS)

Heidari, A. A.; Kazemizade, O.; Abbaspour, R. A.

2015-12-01

In this paper, a continuous harmony search (HS) approach is investigated for tackling the Uncapacitated Facility Location (UFL) task. This article proposes an efficient modified HS-based optimizer to improve the performance of HS on complex spatial tasks like UFL problems. For this aim, opposition-based learning (OBL) and chaotic patterns are utilized. The proposed technique is examined against several UFL benchmark challenges in specialized literature. Then, the modified HS is substantiated in detail and compared to the basic HS and some other methods. The results showed that new opposition-based chaotic HS (OBCHS) algorithm not only can exploit better solutions competently but it is able to outperform HS in solving UFL problems.

Study on Multi-stage Logistics System Design Problem with Inventory Considering Demand Change by Hybrid Genetic Algorithm

NASA Astrophysics Data System (ADS)

Inoue, Hisaki; Gen, Mitsuo

The logistics model used in this study is 3-stage model employed by an automobile company, which aims to solve traffic problems at a total minimum cost. Recently, research on the metaheuristics method has advanced as an approximate means for solving optimization problems like this model. These problems can be solved using various methods such as the genetic algorithm (GA), simulated annealing, and tabu search. GA is superior in robustness and adjustability toward a change in the structure of these problems. However, GA has a disadvantage in that it has a slightly inefficient search performance because it carries out a multi-point search. A hybrid GA that combines another method is attracting considerable attention since it can compensate for a fault to a partial solution that early convergence gives a bad influence on a result. In this study, we propose a novel hybrid random key-based GA(h-rkGA) that combines local search and parameter tuning of crossover rate and mutation rate; h-rkGA is an improved version of the random key-based GA (rk-GA). We attempted comparative experiments with spanning tree-based GA, priority based GA and random key-based GA. Further, we attempted comparative experiments with “h-GA by only local search” and “h-GA by only parameter tuning”. We reported the effectiveness of the proposed method on the basis of the results of these experiments.

FIBER OPTICS: Method of calculation of the propagation constant for guided modes

NASA Astrophysics Data System (ADS)

Ardasheva, L. I.; Sadykov, Nail R.; Chernyakov, V. E.

1992-09-01

A new method of calculating the propagation constants and wave eigenfunctions of guided modes is proposed for axisymmetric translationally invariant fiber-optic waveguides with arbitrary refractive index profiles. The method is based on solving a parabolic scalar wave equation. A comparison is made between the numerical solution under steady-state conditions and the eigenfunctions of single-mode and multimode waveguides.

New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

PubMed Central

Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.

2014-01-01

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358

Nonlinear optimization method of ship floating condition calculation in wave based on vector

NASA Astrophysics Data System (ADS)

Ding, Ning; Yu, Jian-xing

2014-08-01

Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

Evaluation of Learning Environments for Object-Oriented Programming: Measuring Cognitive Load with a Novel Measurement Technique

ERIC Educational Resources Information Center

Uysal, Murat Pasa

2016-01-01

Various methods and tools have been proposed to overcome the learning obstacles for Object-Oriented Programming (OOP). However, it remains difficult especially for novice learners. The problem may be not only adopting an instructional method, but also an Integrated Development Environment (IDE). Learners employ IDEs as a means to solve programming…

Solving the problems with chirality as a biomarker for alien life

NASA Astrophysics Data System (ADS)

Levin, Gilbert V.

2010-09-01

The basis for chiral biomarkers that have been increasingly proposed to obtain evidence for life is reviewed. Specific problems in accepting them and other biomarkers as proof of life are cited. A new chiral method is offered to overcome these difficulties, a method that can make an unambiguous determination of extant microbial life.

Case Method in the Teaching of Food Safety

ERIC Educational Resources Information Center

Gallego, Alfredo; Fortunato, Maria S.; Rossi, Susana L.; Korol, Sonia E.; Moretton, Juan A.

2013-01-01

One of the fundamental aims of education is the integration of theory and practice. The case method is a teaching strategy in which students must apply their knowledge to solve real-life situations. They have to analyze the case described and propose the best possible solution. Although the case may be written, the use of new information and…

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Exploiting Quantum Resonance to Solve Combinatorial Problems

NASA Technical Reports Server (NTRS)

Zak, Michail; Fijany, Amir

2006-01-01

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

PubMed

Fang, Yun; Wu, Hulin; Zhu, Li-Xing

2011-07-01

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

Ultrasensitive low noise voltage amplifier for spectral analysis.

PubMed

Giusi, G; Crupi, F; Pace, C

2008-08-01

Recently we have proposed several voltage noise measurement methods that allow, at least in principle, the complete elimination of the noise introduced by the measurement amplifier. The most severe drawback of these methods is that they require a multistep measurement procedure. Since environmental conditions may change in the different measurement steps, the final result could be affected by these changes. This problem is solved by the one-step voltage noise measurement methodology based on a novel amplifier topology proposed in this paper. Circuit implementations for the amplifier building blocks based on operational amplifiers are critically discussed. The proposed approach is validated through measurements performed on a prototype circuit.

Symbiotic organisms search algorithm for dynamic economic dispatch with valve-point effects

NASA Astrophysics Data System (ADS)

Sonmez, Yusuf; Kahraman, H. Tolga; Dosoglu, M. Kenan; Guvenc, Ugur; Duman, Serhat

2017-05-01

In this study, symbiotic organisms search (SOS) algorithm is proposed to solve the dynamic economic dispatch with valve-point effects problem, which is one of the most important problems of the modern power system. Some practical constraints like valve-point effects, ramp rate limits and prohibited operating zones have been considered as solutions. Proposed algorithm was tested on five different test cases in 5 units, 10 units and 13 units systems. The obtained results have been compared with other well-known metaheuristic methods reported before. Results show that proposed algorithm has a good convergence and produces better results than other methods.

A new family of Polak-Ribiere-Polyak conjugate gradient method with the strong-Wolfe line search

NASA Astrophysics Data System (ADS)

Ghani, Nur Hamizah Abdul; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

Conjugate gradient (CG) method is an important technique in unconstrained optimization, due to its effectiveness and low memory requirements. The focus of this paper is to introduce a new CG method for solving large scale unconstrained optimization. Theoretical proofs show that the new method fulfills sufficient descent condition if strong Wolfe-Powell inexact line search is used. Besides, computational results show that our proposed method outperforms to other existing CG methods.

A new method for solving reachable domain of spacecraft with a single impulse

NASA Astrophysics Data System (ADS)

Chen, Qi; Qiao, Dong; Shang, Haibin; Liu, Xinfu

2018-04-01

This paper develops a new approach to solve the reachable domain of a spacecraft with a single maximum available impulse. First, the distance in a chosen direction, started from a given position on the initial orbit, is formulated. Then, its extreme value is solved to obtain the maximum reachable distance in this direction. The envelop of the reachable domain in three-dimensional space is determined by solving the maximum reachable distance in all directions. Four scenarios are analyzed, including three typical scenarios (either the maneuver position or impulse direction is fixed, or both are arbitrary) and a new extended scenario (the maneuver position is restricted to an interval and the impulse direction is arbitrary). Moreover, the symmetry and the boundedness of the reachable domain are discussed in detail. The former is helpful to reduce the numerical computation, while the latter decides the maximum eccentricity of the initial orbit for a maximum available impulse. The numerical simulations verify the effectiveness of the proposed method for solving the reachable domain in all four scenarios. Especially, the reachable domain with a highly elliptical initial orbit can be determined successfully, which remains unsolved in the existing papers.

A Simple Label Switching Algorithm for Semisupervised Structural SVMs.

PubMed

Balamurugan, P; Shevade, Shirish; Sundararajan, S

2015-10-01

In structured output learning, obtaining labeled data for real-world applications is usually costly, while unlabeled examples are available in abundance. Semisupervised structured classification deals with a small number of labeled examples and a large number of unlabeled structured data. In this work, we consider semisupervised structural support vector machines with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labeled and unlabeled examples, along with the domain constraints. We propose a simple optimization approach that alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective label switching method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching and avoiding poor local minima, which are not very useful. The algorithm is simple and easy to implement. Further, it is suitable for any structured output learning problem where exact inference is available. Experiments on benchmark sequence labeling data sets and a natural language parsing data set show that the proposed approach, though simple, achieves comparable generalization performance.

A novel navigation method used in a ballistic missile

NASA Astrophysics Data System (ADS)

Qian, Hua-ming; Sun, Long; Cai, Jia-nan; Peng, Yu

2013-10-01

The traditional strapdown inertial/celestial integrated navigation method used in a ballistic missile cannot accurately estimate the accelerometer bias. It might cause a divergence of navigation errors. To solve this problem, a new navigation method named strapdown inertial/starlight refractive celestial integrated navigation is proposed. To verify the feasibility of the proposed method, a simulated program of a ballistic missile is presented. The simulation results indicated that, when multiple refraction stars are used, the proposed method can accurately estimate the accelerometer bias, and suppress the divergence of navigation errors completely. Specifically, in order to apply this method to a ballistic missile, a novel measurement equation based on stellar refraction was developed. Furthermore a method to calculate the number of refraction stars observed by the stellar sensor was given. Finally, the relationship between the number of refraction stars used and the navigation accuracy is analysed.

Seismic data restoration with a fast L1 norm trust region method

NASA Astrophysics Data System (ADS)

Cao, Jingjie; Wang, Yanfei

2014-08-01

Seismic data restoration is a major strategy to provide reliable wavefield when field data dissatisfy the Shannon sampling theorem. Recovery by sparsity-promoting inversion often get sparse solutions of seismic data in a transformed domains, however, most methods for sparsity-promoting inversion are line-searching methods which are efficient but are inclined to obtain local solutions. Using trust region method which can provide globally convergent solutions is a good choice to overcome this shortcoming. A trust region method for sparse inversion has been proposed, however, the efficiency should be improved to suitable for large-scale computation. In this paper, a new L1 norm trust region model is proposed for seismic data restoration and a robust gradient projection method for solving the sub-problem is utilized. Numerical results of synthetic and field data demonstrate that the proposed trust region method can get excellent computation speed and is a viable alternative for large-scale computation.

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

NASA Astrophysics Data System (ADS)

Iwase, Shigeru; Futamura, Yasunori; Imakura, Akira; Sakurai, Tetsuya; Tsukamoto, Shigeru; Ono, Tomoya

2018-05-01

We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a contour integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve an exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite-difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the freestanding silicene with the line defect originating from the reversed buckled phases.

Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling.

PubMed

Kamensky, David; Evans, John A; Hsu, Ming-Chen; Bazilevs, Yuri

2017-11-01

This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.

Graph cuts via l1 norm minimization.

PubMed

Bhusnurmath, Arvind; Taylor, Camillo J

2008-10-01

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

Path planning for mobile robot using the novel repulsive force algorithm

NASA Astrophysics Data System (ADS)

Sun, Siyue; Yin, Guoqiang; Li, Xueping

2018-01-01

A new type of repulsive force algorithm is proposed to solve the problem of local minimum and the target unreachable of the classic Artificial Potential Field (APF) method in this paper. The Gaussian function that is related to the distance between the robot and the target is added to the traditional repulsive force, solving the problem of the goal unreachable with the obstacle nearby; variable coefficient is added to the repulsive force component to resize the repulsive force, which can solve the local minimum problem when the robot, the obstacle and the target point are in the same line. The effectiveness of the algorithm is verified by simulation based on MATLAB and actual mobile robot platform.

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

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

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Correlation Filter Learning Toward Peak Strength for Visual Tracking.

PubMed

Sui, Yao; Wang, Guanghui; Zhang, Li

2018-04-01

This paper presents a novel visual tracking approach to correlation filter learning toward peak strength of correlation response. Previous methods leverage all features of the target and the immediate background to learn a correlation filter. Some features, however, may be distractive to tracking, like those from occlusion and local deformation, resulting in unstable tracking performance. This paper aims at solving this issue and proposes a novel algorithm to learn the correlation filter. The proposed approach, by imposing an elastic net constraint on the filter, can adaptively eliminate those distractive features in the correlation filtering. A new peak strength metric is proposed to measure the discriminative capability of the learned correlation filter. It is demonstrated that the proposed approach effectively strengthens the peak of the correlation response, leading to more discriminative performance than previous methods. Extensive experiments on a challenging visual tracking benchmark demonstrate that the proposed tracker outperforms most state-of-the-art methods.

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

DOE PAGES

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

2017-04-12

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Enhanced intelligent water drops algorithm for multi-depot vehicle routing problem

PubMed Central

Akutsah, Francis; Olusanya, Micheal O.; Adewumi, Aderemi O.

2018-01-01

The intelligent water drop algorithm is a swarm-based metaheuristic algorithm, inspired by the characteristics of water drops in the river and the environmental changes resulting from the action of the flowing river. Since its appearance as an alternative stochastic optimization method, the algorithm has found applications in solving a wide range of combinatorial and functional optimization problems. This paper presents an improved intelligent water drop algorithm for solving multi-depot vehicle routing problems. A simulated annealing algorithm was introduced into the proposed algorithm as a local search metaheuristic to prevent the intelligent water drop algorithm from getting trapped into local minima and also improve its solution quality. In addition, some of the potential problematic issues associated with using simulated annealing that include high computational runtime and exponential calculation of the probability of acceptance criteria, are investigated. The exponential calculation of the probability of acceptance criteria for the simulated annealing based techniques is computationally expensive. Therefore, in order to maximize the performance of the intelligent water drop algorithm using simulated annealing, a better way of calculating the probability of acceptance criteria is considered. The performance of the proposed hybrid algorithm is evaluated by using 33 standard test problems, with the results obtained compared with the solutions offered by four well-known techniques from the subject literature. Experimental results and statistical tests show that the new method possesses outstanding performance in terms of solution quality and runtime consumed. In addition, the proposed algorithm is suitable for solving large-scale problems. PMID:29554662

Enhanced intelligent water drops algorithm for multi-depot vehicle routing problem.

PubMed

Ezugwu, Absalom E; Akutsah, Francis; Olusanya, Micheal O; Adewumi, Aderemi O

2018-01-01

The intelligent water drop algorithm is a swarm-based metaheuristic algorithm, inspired by the characteristics of water drops in the river and the environmental changes resulting from the action of the flowing river. Since its appearance as an alternative stochastic optimization method, the algorithm has found applications in solving a wide range of combinatorial and functional optimization problems. This paper presents an improved intelligent water drop algorithm for solving multi-depot vehicle routing problems. A simulated annealing algorithm was introduced into the proposed algorithm as a local search metaheuristic to prevent the intelligent water drop algorithm from getting trapped into local minima and also improve its solution quality. In addition, some of the potential problematic issues associated with using simulated annealing that include high computational runtime and exponential calculation of the probability of acceptance criteria, are investigated. The exponential calculation of the probability of acceptance criteria for the simulated annealing based techniques is computationally expensive. Therefore, in order to maximize the performance of the intelligent water drop algorithm using simulated annealing, a better way of calculating the probability of acceptance criteria is considered. The performance of the proposed hybrid algorithm is evaluated by using 33 standard test problems, with the results obtained compared with the solutions offered by four well-known techniques from the subject literature. Experimental results and statistical tests show that the new method possesses outstanding performance in terms of solution quality and runtime consumed. In addition, the proposed algorithm is suitable for solving large-scale problems.

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers.

PubMed

Le Borgne, Tanguy; Paillet, Frederick; Bour, Olivier; Caudal, Jean-Pierre

2006-01-01

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.

A reward optimization method based on action subrewards in hierarchical reinforcement learning.

PubMed

Fu, Yuchen; Liu, Quan; Ling, Xionghong; Cui, Zhiming

2014-01-01

Reinforcement learning (RL) is one kind of interactive learning methods. Its main characteristics are "trial and error" and "related reward." A hierarchical reinforcement learning method based on action subrewards is proposed to solve the problem of "curse of dimensionality," which means that the states space will grow exponentially in the number of features and low convergence speed. The method can reduce state spaces greatly and choose actions with favorable purpose and efficiency so as to optimize reward function and enhance convergence speed. Apply it to the online learning in Tetris game, and the experiment result shows that the convergence speed of this algorithm can be enhanced evidently based on the new method which combines hierarchical reinforcement learning algorithm and action subrewards. The "curse of dimensionality" problem is also solved to a certain extent with hierarchical method. All the performance with different parameters is compared and analyzed as well.

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

NASA Astrophysics Data System (ADS)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

A baseline lunar mine

NASA Technical Reports Server (NTRS)

Gertsch, Richard E.

1992-01-01

A models lunar mining method is proposed that illustrates the problems to be expected in lunar mining and how they might be solved. While the method is quite feasible, it is, more importantly, a useful baseline system against which to test other, possible better, methods. Our study group proposed the slusher to stimulate discussion of how a lunar mining operation might be successfully accomplished. Critics of the slusher system were invited to propose better methods. The group noted that while nonterrestrial mining has been a vital part of past space manufacturing proposals, no one has proposed a lunar mining system in any real detail. The group considered it essential that the design of actual, workable, and specific lunar mining methods begin immediately. Based on an earlier proposal, the method is a three-drum slusher, also known as a cable-operated drag scraper. Its terrestrial application is quite limited, as it is relatively inefficient and inflexible. The method usually finds use in underwater mining from the shore and in moving small amounts of ore underground. When lunar mining scales up, the lunarized slusher will be replaced by more efficient, high-volume methods. Other aspects of lunar mining are discussed.

The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

PubMed

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

A geometric level set model for ultrasounds analysis

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

Sarti, A.; Malladi, R.

We propose a partial differential equation (PDE) for filtering and segmentation of echocardiographic images based on a geometric-driven scheme. The method allows edge-preserving image smoothing and a semi-automatic segmentation of the heart chambers, that regularizes the shapes and improves edge fidelity especially in presence of distinct gaps in the edge map as is common in ultrasound imagery. A numerical scheme for solving the proposed PDE is borrowed from level set methods. Results on human in vivo acquired 2D, 2D+time,3D, 3D+time echocardiographic images are shown.

A new DOD and DOA estimation method for MIMO radar

NASA Astrophysics Data System (ADS)

Gong, Jian; Lou, Shuntian; Guo, Yiduo

2018-04-01

The battlefield electromagnetic environment is becoming more and more complex, and MIMO radar will inevitably be affected by coherent and non-stationary noise. To solve this problem, an angle estimation method based on oblique projection operator and Teoplitz matrix reconstruction is proposed. Through the reconstruction of Toeplitz, nonstationary noise is transformed into Gauss white noise, and then the oblique projection operator is used to separate independent and correlated sources. Finally, simulations are carried out to verify the performance of the proposed algorithm in terms of angle estimation performance and source overload.

Finite element method formulation in polar coordinates for transient heat conduction problems

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Conversion of a Rhotrix to a "Coupled Matrix"

ERIC Educational Resources Information Center

Sani, B.

2008-01-01

In this note, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed. The special matrix can be used to solve various problems involving n x n and (n - 1) x (n - 1) matrices simultaneously.

SU-C-9A-04: Alternative Analytic Solution to the Paralyzable Detector Model to Calculate Deadtime and Deadtime Loss

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

Siman, W; Kappadath, S

2014-06-01

Purpose: Some common methods to solve for deadtime are (1) dual-source method, which assumes two equal activities; (2) model fitting, which requires multiple acquisitions as source decays; and (3) lossless model, which assumes no deadtime loss at low count rates. We propose a new analytic alternative solution to calculate deadtime for paralyzable gamma camera. Methods: Deadtime T can be calculated analytically from two distinct observed count rates M1 and M2 when the ratio of the true count rates alpha=N2/N1 is known. Alpha can be measured as a ratio of two measured activities using dose calibrators or via radioactive decay. Knowledgemore » of alpha creates a system with 2 equations and 2 unknowns, i.e., T and N1. To verify the validity of the proposed method, projections of a non-uniform phantom (4GBq 99mTc) were acquired in using Siemens SymbiaS multiple times over 48 hours. Each projection has >100kcts. The deadtime for each projection was calculated by fitting the data to a paralyzable model and also by using the proposed 2-acquisition method. The two estimates of deadtime were compared using the Bland-Altmann method. In addition, the dependency of uncertainty in T on uncertainty in alpha was investigated for several imaging conditions. Results: The results strongly suggest that the 2-acquisition method is equivalent to the fitting method. The Bland-Altman analysis yielded mean difference in deadtime estimate of ∼0.076us (95%CI: -0.049us, 0.103us) between the 2-acquisition and model fitting methods. The 95% limits of agreement were calculated to be -0.104 to 0.256us. The uncertainty in deadtime calculated using the proposed method is highly dependent on the uncertainty in the ratio alpha. Conclusion: The 2-acquisition method was found to be equivalent to the parameter fitting method. The proposed method offers a simpler and more practical way to analytically solve for a paralyzable detector deadtime, especially during physics testing.« less

An efficient unstructured WENO method for supersonic reactive flows

NASA Astrophysics Data System (ADS)

Zhao, Wen-Geng; Zheng, Hong-Wei; Liu, Feng-Jun; Shi, Xiao-Tian; Gao, Jun; Hu, Ning; Lv, Meng; Chen, Si-Cong; Zhao, Hong-Da

2018-03-01

An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection.

PubMed

Wang, Liansheng; Qin, Jing; Wong, Tien Tsin; Heng, Pheng Ann

2011-10-07

The epicardial potential (EP)-targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1-norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a bound-constrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1-norm regularization methods, especially when the noises are large.

Concurrent optimization of material spatial distribution and material anisotropy repartition for two-dimensional structures

NASA Astrophysics Data System (ADS)

Ranaivomiarana, Narindra; Irisarri, François-Xavier; Bettebghor, Dimitri; Desmorat, Boris

2018-04-01

An optimization methodology to find concurrently material spatial distribution and material anisotropy repartition is proposed for orthotropic, linear and elastic two-dimensional membrane structures. The shape of the structure is parameterized by a density variable that determines the presence or absence of material. The polar method is used to parameterize a general orthotropic material by its elasticity tensor invariants by change of frame. A global structural stiffness maximization problem written as a compliance minimization problem is treated, and a volume constraint is applied. The compliance minimization can be put into a double minimization of complementary energy. An extension of the alternate directions algorithm is proposed to solve the double minimization problem. The algorithm iterates between local minimizations in each element of the structure and global minimizations. Thanks to the polar method, the local minimizations are solved explicitly providing analytical solutions. The global minimizations are performed with finite element calculations. The method is shown to be straightforward and efficient. Concurrent optimization of density and anisotropy distribution of a cantilever beam and a bridge are presented.

Solving gap metabolites and blocked reactions in genome-scale models: application to the metabolic network of Blattabacterium cuenoti.

PubMed

Ponce-de-León, Miguel; Montero, Francisco; Peretó, Juli

2013-10-31

Metabolic reconstruction is the computational-based process that aims to elucidate the network of metabolites interconnected through reactions catalyzed by activities assigned to one or more genes. Reconstructed models may contain inconsistencies that appear as gap metabolites and blocked reactions. Although automatic methods for solving this problem have been previously developed, there are many situations where manual curation is still needed. We introduce a general definition of gap metabolite that allows its detection in a straightforward manner. Moreover, a method for the detection of Unconnected Modules, defined as isolated sets of blocked reactions connected through gap metabolites, is proposed. The method has been successfully applied to the curation of iCG238, the genome-scale metabolic model for the bacterium Blattabacterium cuenoti, obligate endosymbiont of cockroaches. We found the proposed approach to be a valuable tool for the curation of genome-scale metabolic models. The outcome of its application to the genome-scale model B. cuenoti iCG238 is a more accurate model version named as B. cuenoti iMP240.

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.

A new fast direct solver for the boundary element method

NASA Astrophysics Data System (ADS)

Huang, S.; Liu, Y. J.

2017-09-01

A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.

Numerical-graphical method for describing the creep of damaged highly filled polymer materials

NASA Astrophysics Data System (ADS)

Bykov, D. L.; Martynova, E. D.; Mel'nikov, V. P.

2015-09-01

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material.

Improved remote gaze estimation using corneal reflection-adaptive geometric transforms

NASA Astrophysics Data System (ADS)

Ma, Chunfei; Baek, Seung-Jin; Choi, Kang-A.; Ko, Sung-Jea

2014-05-01

Recently, the remote gaze estimation (RGE) technique has been widely applied to consumer devices as a more natural interface. In general, the conventional RGE method estimates a user's point of gaze using a geometric transform, which represents the relationship between several infrared (IR) light sources and their corresponding corneal reflections (CRs) in the eye image. Among various methods, the homography normalization (HN) method achieves state-of-the-art performance. However, the geometric transform of the HN method requiring four CRs is infeasible for the case when fewer than four CRs are available. To solve this problem, this paper proposes a new RGE method based on three alternative geometric transforms, which are adaptive to the number of CRs. Unlike the HN method, the proposed method not only can operate with two or three CRs, but can also provide superior accuracy. To further enhance the performance, an effective error correction method is also proposed. By combining the introduced transforms with the error-correction method, the proposed method not only provides high accuracy and robustness for gaze estimation, but also allows for a more flexible system setup with a different number of IR light sources. Experimental results demonstrate the effectiveness of the proposed method.

A three-term conjugate gradient method under the strong-Wolfe line search

NASA Astrophysics Data System (ADS)

Khadijah, Wan; Rivaie, Mohd; Mamat, Mustafa

2017-08-01

Recently, numerous studies have been concerned in conjugate gradient methods for solving large-scale unconstrained optimization method. In this paper, a three-term conjugate gradient method is proposed for unconstrained optimization which always satisfies sufficient descent direction and namely as Three-Term Rivaie-Mustafa-Ismail-Leong (TTRMIL). Under standard conditions, TTRMIL method is proved to be globally convergent under strong-Wolfe line search. Finally, numerical results are provided for the purpose of comparison.

The method of segmentation of leukocytes in information-measuring systems on the basis of light microscopy

NASA Astrophysics Data System (ADS)

Nikitaev, V. G.; Pronichev, A. N.; Polyakov, E. V.; Zaharenko, Yu V.

2018-01-01

The paper considers the problem of leukocytes segmentation in microscopic images of bone marrow smears for automated diagnosis of the blood system diseases. The method was proposed to solve the problem of segmentation of contacting leukocytes in images of bone marrow smears. The method is based on the analysis of structure of objects of a separation and distances filter in combination with the watershed method and distance transformation method.

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

NASA Astrophysics Data System (ADS)

Nigro, A.; De Bartolo, C.; Crivellini, A.; Bassi, F.

2017-12-01

In this paper we investigate the possibility of using the high-order accurate A (α) -stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.

Modeling and stress analysis of large format InSb focal plane arrays detector under thermal shock

NASA Astrophysics Data System (ADS)

Zhang, Li-Wen; Meng, Qing-Duan; Zhang, Xiao-Ling; Yu, Qian; Lv, Yan-Qiu; Si, Jun-Jie

2013-09-01

Higher fracture probability, appearing in large format InSb infrared focal plane arrays detector under thermal shock loadings, limits its applicability and suitability for large format equipment, and has been an urgent problem to be solved. In order to understand the fracture mechanism and improve the reliability, three dimensional modeling and stress analysis of large format InSb detector is necessary. However, there are few reports on three dimensional modeling and simulation of large format InSb detector, due to huge meshing numbers and time-consuming operation to solve. To solve the problems, basing on the thermal mismatch displacement formula, an equivalent modeling method is proposed in this paper. With the proposed equivalent modeling method, employing the ANSYS software, three dimensional large format InSb detector is modeled, and the maximum Von Mises stress appearing in InSb chip dependent on array format is researched. According to the maximum Von Mises stress location shift and stress increasing tendency, the adaptability range of the proposed equivalent method is also derived, that is, for 16 × 16, 32 × 32 and 64 × 64 format, its adaptability ranges are not larger than 64 × 64, 256 × 256 and 1024 × 1024 format, respectively. Taking 1024 × 1024 InSb detector as an example, the Von Mises stress distribution appearing in InSb chip, Si readout integrated circuits and indium bump arrays are described, and the causes are discussed in detail. All these will provide a feasible research plan to identify the fracture origins of InSb chip and reduce fracture probability for large format InSb detector.

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

NASA Astrophysics Data System (ADS)

Song, Wanjun; Zhang, Hou

2017-11-01

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

Sensor placement on Canton Tower for health monitoring using asynchronous-climb monkey algorithm

NASA Astrophysics Data System (ADS)

Yi, Ting-Hua; Li, Hong-Nan; Zhang, Xu-Dong

2012-12-01

Heuristic optimization algorithms have become a popular choice for solving complex and intricate sensor placement problems which are difficult to solve by traditional methods. This paper proposes a novel and interesting methodology called the asynchronous-climb monkey algorithm (AMA) for the optimum design of sensor arrays for a structural health monitoring system. Different from the existing algorithms, the dual-structure coding method is designed and adopted for the representation of the design variables. The asynchronous-climb process is incorporated in the proposed AMA that can adjust the trajectory of each individual dynamically in the search space according to its own experience and other monkeys. The concept of ‘monkey king’ is introduced in the AMA, which reflects the Darwinian principle of natural selection and can create an interaction network to correctly guide the movement of other monkeys. Numerical experiments are carried out using two different objective functions by considering the Canton Tower in China with or without the antenna mast to evaluate the performance of the proposed algorithm. Investigations have indicated that the proposed AMA exhibits faster convergence characteristics and can generate sensor configurations superior in all instances when compared to the conventional monkey algorithm. For structures with stiffness mutation such as the Canton Tower, the sensor placement needs to be considered for each part separately.

Approximation-based common principal component for feature extraction in multi-class brain-computer interfaces.

PubMed

Hoang, Tuan; Tran, Dat; Huang, Xu

2013-01-01

Common Spatial Pattern (CSP) is a state-of-the-art method for feature extraction in Brain-Computer Interface (BCI) systems. However it is designed for 2-class BCI classification problems. Current extensions of this method to multiple classes based on subspace union and covariance matrix similarity do not provide a high performance. This paper presents a new approach to solving multi-class BCI classification problems by forming a subspace resembled from original subspaces and the proposed method for this approach is called Approximation-based Common Principal Component (ACPC). We perform experiments on Dataset 2a used in BCI Competition IV to evaluate the proposed method. This dataset was designed for motor imagery classification with 4 classes. Preliminary experiments show that the proposed ACPC feature extraction method when combining with Support Vector Machines outperforms CSP-based feature extraction methods on the experimental dataset.

Use of variational methods in the determination of wind-driven ocean circulation

NASA Technical Reports Server (NTRS)

Gelos, R.; Laura, P. A. A.

1976-01-01

Simple polynomial approximations and a variational approach were used to predict wind-induced circulation in rectangular ocean basins. Stommel's and Munk's models were solved in a unified fashion by means of the proposed method. Very good agreement with exact solutions available in the literature was shown to exist. The method was then applied to more complex situations where an exact solution seems out of the question.

A linear complementarity method for the solution of vertical vehicle-track interaction

NASA Astrophysics Data System (ADS)

Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie

2018-02-01

A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

A centre-free approach for resource allocation with lower bounds

NASA Astrophysics Data System (ADS)

Obando, Germán; Quijano, Nicanor; Rakoto-Ravalontsalama, Naly

2017-09-01

Since complexity and scale of systems are continuously increasing, there is a growing interest in developing distributed algorithms that are capable to address information constraints, specially for solving optimisation and decision-making problems. In this paper, we propose a novel method to solve distributed resource allocation problems that include lower bound constraints. The optimisation process is carried out by a set of agents that use a communication network to coordinate their decisions. Convergence and optimality of the method are guaranteed under some mild assumptions related to the convexity of the problem and the connectivity of the underlying graph. Finally, we compare our approach with other techniques reported in the literature, and we present some engineering applications.

Green design assessment of electromechanical products based on group weighted-AHP

NASA Astrophysics Data System (ADS)

Guo, Jinwei; Zhou, MengChu; Li, Zhiwu; Xie, Huiguang

2015-11-01

Manufacturing industry is the backbone of a country's economy while environmental pollution is a serious problem that human beings must face today. The green design of electromechanical products based on enterprise information systems is an important method to solve the environmental problem. The question on how to design green products must be answered by excellent designers via both advanced design methods and effective assessment methods of electromechanical products. Making an objective and precise assessment of green design is one of the problems that must be solved when green design is conducted. An assessment method of green design on electromechanical products based on Group Weighted-AHP (Analytic Hierarchy Process) is proposed in this paper, together with the characteristics of green products. The assessment steps of green design are also established. The results are illustrated via the assessment of a refrigerator design.

Standard model of knowledge representation

NASA Astrophysics Data System (ADS)

Yin, Wensheng

2016-09-01

Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.

A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

The Impact of Adaptive Complex Assessment on the HOT Skill Development of Students

ERIC Educational Resources Information Center

Raiyn, Jamal; Tilchin, Oleg

2016-01-01

In this paper we propose a method for the adaptive complex assessment (ACA) of the higher-order thinking (HOT) skills needed by students for problem solving, and we examine the impact of the method on the development of HOT skills in a problem-based learning (PBL) environment. Complexity in the assessment is provided by initial, formative, and…

Relation between coordinate systems describing the dynamics of a loaded Stewart platform

NASA Astrophysics Data System (ADS)

Petrova, V. I.

2018-05-01

The paper puts forward formulae for transformation of coordinates in three coordinate frames used for the study of motion of a loaded Stewart platform, which is the central mechanism of the dynamic bench. A new method for finding the law of variation of coordinates is proposed. This method depends on solving the problem-specific system of differential equations.

Near-Optimal Guidance Method for Maximizing the Reachable Domain of Gliding Aircraft

NASA Astrophysics Data System (ADS)

Tsuchiya, Takeshi

This paper proposes a guidance method for gliding aircraft by using onboard computers to calculate a near-optimal trajectory in real-time, and thereby expanding the reachable domain. The results are applicable to advanced aircraft and future space transportation systems that require high safety. The calculation load of the optimal control problem that is used to maximize the reachable domain is too large for current computers to calculate in real-time. Thus the optimal control problem is divided into two problems: a gliding distance maximization problem in which the aircraft motion is limited to a vertical plane, and an optimal turning flight problem in a horizontal direction. First, the former problem is solved using a shooting method. It can be solved easily because its scale is smaller than that of the original problem, and because some of the features of the optimal solution are obtained in the first part of this paper. Next, in the latter problem, the optimal bank angle is computed from the solution of the former; this is an analytical computation, rather than an iterative computation. Finally, the reachable domain obtained from the proposed near-optimal guidance method is compared with that obtained from the original optimal control problem.

A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation.

PubMed

Wang, Zhaocai; Huang, Dongmei; Meng, Huajun; Tang, Chengpei

2013-10-01

The minimum spanning tree (MST) problem is to find minimum edge connected subsets containing all the vertex of a given undirected graph. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications. Moreover in previous studies, DNA molecular operations usually were used to solve NP-complete head-to-tail path search problems, rarely for NP-hard problems with multi-lateral path solutions result, such as the minimum spanning tree problem. In this paper, we present a new fast DNA algorithm for solving the MST problem using DNA molecular operations. For an undirected graph with n vertex and m edges, we reasonably design flexible length DNA strands representing the vertex and edges, take appropriate steps and get the solutions of the MST problem in proper length range and O(3m+n) time complexity. We extend the application of DNA molecular operations and simultaneity simplify the complexity of the computation. Results of computer simulative experiments show that the proposed method updates some of the best known values with very short time and that the proposed method provides a better performance with solution accuracy over existing algorithms. Copyright © 2013 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

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

Fath, L., E-mail: lukas.fath@kit.edu; Hochbruck, M., E-mail: marlis.hochbruck@kit.edu; Singh, C.V., E-mail: chandraveer.singh@utoronto.ca

Classical integration methods for molecular dynamics are inherently limited due to resonance phenomena occurring at certain time-step sizes. The mollified impulse method can partially avoid this problem by using appropriate filters based on averaging or projection techniques. However, existing filters are computationally expensive and tedious in implementation since they require either analytical Hessians or they need to solve nonlinear systems from constraints. In this work we follow a different approach based on corotation for the construction of a new filter for (flexible) biomolecular simulations. The main advantages of the proposed filter are its excellent stability properties and ease of implementationmore » in standard softwares without Hessians or solving constraint systems. By simulating multiple realistic examples such as peptide, protein, ice equilibrium and ice–ice friction, the new filter is shown to speed up the computations of long-range interactions by approximately 20%. The proposed filtered integrators allow step sizes as large as 10 fs while keeping the energy drift less than 1% on a 50 ps simulation.« less

Integrated fringe projection 3D scanning system for large-scale metrology based on laser tracker

NASA Astrophysics Data System (ADS)

Du, Hui; Chen, Xiaobo; Zhou, Dan; Guo, Gen; Xi, Juntong

2017-10-01

Large scale components exist widely in advance manufacturing industry,3D profilometry plays a pivotal role for the quality control. This paper proposes a flexible, robust large-scale 3D scanning system by integrating a robot with a binocular structured light scanner and a laser tracker. The measurement principle and system construction of the integrated system are introduced. And a mathematical model is established for the global data fusion. Subsequently, a flexible and robust method and mechanism is introduced for the establishment of the end coordination system. Based on this method, a virtual robot noumenon is constructed for hand-eye calibration. And then the transformation matrix between end coordination system and world coordination system is solved. Validation experiment is implemented for verifying the proposed algorithms. Firstly, hand-eye transformation matrix is solved. Then a car body rear is measured for 16 times for the global data fusion algorithm verification. And the 3D shape of the rear is reconstructed successfully.

Flood inundation extent mapping based on block compressed tracing

NASA Astrophysics Data System (ADS)

Shen, Dingtao; Rui, Yikang; Wang, Jiechen; Zhang, Yu; Cheng, Liang

2015-07-01

Flood inundation extent, depth, and duration are important factors affecting flood hazard evaluation. At present, flood inundation analysis is based mainly on a seeded region-growing algorithm, which is an inefficient process because it requires excessive recursive computations and it is incapable of processing massive datasets. To address this problem, we propose a block compressed tracing algorithm for mapping the flood inundation extent, which reads the DEM data in blocks before transferring them to raster compression storage. This allows a smaller computer memory to process a larger amount of data, which solves the problem of the regular seeded region-growing algorithm. In addition, the use of a raster boundary tracing technique allows the algorithm to avoid the time-consuming computations required by the seeded region-growing. Finally, we conduct a comparative evaluation in the Chin-sha River basin, results show that the proposed method solves the problem of flood inundation extent mapping based on massive DEM datasets with higher computational efficiency than the original method, which makes it suitable for practical applications.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Moving object detection via low-rank total variation regularization

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Chen, Qian; Shao, Na

2016-09-01

Moving object detection is a challenging task in video surveillance. Recently proposed Robust Principal Component Analysis (RPCA) can recover the outlier patterns from the low-rank data under some mild conditions. However, the l-penalty in RPCA doesn't work well in moving object detection because the irrepresentable condition is often not satisfied. In this paper, a method based on total variation (TV) regularization scheme is proposed. In our model, image sequences captured with a static camera are highly related, which can be described using a low-rank matrix. Meanwhile, the low-rank matrix can absorb background motion, e.g. periodic and random perturbation. The foreground objects in the sequence are usually sparsely distributed and drifting continuously, and can be treated as group outliers from the highly-related background scenes. Instead of l-penalty, we exploit the total variation of the foreground. By minimizing the total variation energy, the outliers tend to collapse and finally converge to be the exact moving objects. The TV-penalty is superior to the l-penalty especially when the outlier is in the majority for some pixels, and our method can estimate the outlier explicitly with less bias but higher variance. To solve the problem, a joint optimization function is formulated and can be effectively solved through the inexact Augmented Lagrange Multiplier (ALM) method. We evaluate our method along with several state-of-the-art approaches in MATLAB. Both qualitative and quantitative results demonstrate that our proposed method works effectively on a large range of complex scenarios.

A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems

NASA Astrophysics Data System (ADS)

Chan, Tony; Szeto, Tedd

1994-03-01

We propose a new and more stable variant of the CGS method [27] for solving nonsymmetric linear systems. The method is based on squaring the Composite Step BCG method, introduced recently by Bank and Chan [1,2], which itself is a stabilized variant of BCG in that it skips over steps for which the BCG iterate is not defined and causes one kind of breakdown in BCG. By doing this, we obtain a method (Composite Step CGS or CSCGS) which not only handles the breakdowns described above, but does so with the advantages of CGS, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG. Our strategy for deciding whether to skip a step does not involve any machine dependent parameters and is designed to skip near breakdowns as well as produce smoother iterates. Numerical experiments show that the new method does produce improved performance over CGS on practical problems.

An effective pseudospectral method for constraint dynamic optimisation problems with characteristic times

NASA Astrophysics Data System (ADS)

Xiao, Long; Liu, Xinggao; Ma, Liang; Zhang, Zeyin

2018-03-01

Dynamic optimisation problem with characteristic times, widely existing in many areas, is one of the frontiers and hotspots of dynamic optimisation researches. This paper considers a class of dynamic optimisation problems with constraints that depend on the interior points either fixed or variable, where a novel direct pseudospectral method using Legendre-Gauss (LG) collocation points for solving these problems is presented. The formula for the state at the terminal time of each subdomain is derived, which results in a linear combination of the state at the LG points in the subdomains so as to avoid the complex nonlinear integral. The sensitivities of the state at the collocation points with respect to the variable characteristic times are derived to improve the efficiency of the method. Three well-known characteristic time dynamic optimisation problems are solved and compared in detail among the reported literature methods. The research results show the effectiveness of the proposed method.

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

NASA Astrophysics Data System (ADS)

Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar

2018-04-01

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

A gradient system solution to Potts mean field equations and its electronic implementation.

PubMed

Urahama, K; Ueno, S

1993-03-01

A gradient system solution method is presented for solving Potts mean field equations for combinatorial optimization problems subject to winner-take-all constraints. In the proposed solution method the optimum solution is searched by using gradient descent differential equations whose trajectory is confined within the feasible solution space of optimization problems. This gradient system is proven theoretically to always produce a legal local optimum solution of combinatorial optimization problems. An elementary analog electronic circuit implementing the presented method is designed on the basis of current-mode subthreshold MOS technologies. The core constituent of the circuit is the winner-take-all circuit developed by Lazzaro et al. Correct functioning of the presented circuit is exemplified with simulations of the circuits implementing the scheme for solving the shortest path problems.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.