Optimization Method In Order Research Articles

Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of $X$. It is thus very effective for solving programs that have a low rank solution. The factorization $X=Y Y^T$ evokes a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second order optimization method. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. The efficiency of the proposed algorithm is illustrated on two applications: the maximal cut of a graph and the sparse principal component analysis problem.

Finite element modeling of abradable materials – Identification of plastic parameters and issues on minimum hardness against coating's thickness

Abradable materials are used to decrease the gas consumption of aircraft engines by minimizing the gap between the blade tips and the stator. The key idea consists in using the blades themselves to machine the gap on the abradable coating. The best compromise between soft and hard coating properties has to be reached to avoid blades wear and prevent coating erosion by gas flux and particles. The plastic parameters of abradable coating were identified by using an optimization process directly connected to FEA. The first order optimization method (conjugate gradient strategy + golden section algorithm) was applied to achieve the optimal solution. A good agreement was found between experimental and numerical results. The plastic parameters were used to study the hardness variability of abradable materials with the coating thickness. Surprisingly, a minimum hardness value was found while it was expected that hardness should be always decreasing with thickness. It has been demonstrated that this minimum is produced by the boundary conditions influence on hardness measurement. This research work was completed within the Seal-Coat project funded by the European Commission under the FP5 Growth Program.

자기유변유체를 이용한 승용차량 쇽 업소버의 유한요소 최적설계

This paper presents optimal design of controllable magnetorheological(MR) shock absorbers for passenger vehicle. In order to achieve this goal, two MR shock absorbers (one for front suspension; one for rear suspension) are designed using an optimization methodology based on design specifications for a commercial passenger vehicle. The optimization problem is to find optimal geometric dimensions of the magnetic circuits for the front and rear MR shock absorbers in order to improve the performance such as damping force as an objective function. The first order optimization method using commercial finite element method(FEM) software is adopted for the constrained optimization algorithm. After manufacturing the MR shock absorbers with optimally obtained design parameters, their field-dependent damping forces are experimentally evaluated and compared with those of conventional shock absorbers. In addition, vibration control performances of the full-vehicle installed with the proposed MR shock absorbers are evaluated under bump road condition and obstacle avoidance test.

Optimal balancing of multiple affective satisfaction dimensions: A case study on mobile phones

Product designers need to consider a variety of consumers’ tastes and preferences to design a product that appeals to consumers. However, it is often difficult for designers to find optimal design settings because a number of design features could affect the tastes and preferences. This study proposes a method for optimally balancing various affective satisfaction dimensions based on the multiple response surfaces (MRS) methodology. Applicability of the proposed method is demonstrated through a case study on mobile phone designs. A set of design values which would optimally balance the levels of luxuriousness, attractiveness, and overall satisfaction are obtained. The resulting values of design features are verified based on a similarity test. In addition, they are compared with the optimal design values obtained using a single dimension optimization method in order to show the advantages of the MRS methodology. Relevance to industry This study proposes a new way of finding design settings, which would optimally balance various needs of consumers. The resulting design values can help designers improve the consumers’ affective satisfaction toward their designs.

Order-optimal methods for the approximation of a piecewise-continuous solution to a certain inverse problem

The authors propose an order-optimal method for the approximation of a piecewise-continuous solution to a certain inverse problem and obtain exact by order bounds for the error of this approximation in the uniform metrics on segments of continuity of the exact solution to the problem.

Split-parameter structure for the automatic calibration of distributed hydrological models

Hydrological distributed models demand large amounts of data, information and parameters in order to accurately represent the spatial variability of the main hydrological processes and inputs. The parameter estimation is always a complex and expensive task which is often unaffordable and therefore hydrologists are frequently forced to disregard distributed modelling in favour of lumped or semidistributed models. To solve this situation, we propose in this paper to split the effective parameter at each cell in two components: the hydrological characteristic (at point scale and maintaining its physical meaning) and a correction factor (common for all cells and taking into account all modelling errors including the temporal and spatial scale effects). The new split-parameter structure adopted in our distributed model (called TETIS) is coupled with the SCE-UA automatic optimization method in order to obtain the set of optimal correction factors of the model, without loosing the spatial variability described by the a priori estimated hydrological characteristics. Automatic procedures can be easily adapted to the split-parameter structure because the number of variables to be calibrated is dramatically reduced from thousands of cell parameters to a small number of common correction factors (one for each parameter map). Also, the optimum initial values of the state variables can be obtained automatically. In order to show the advantages of the new structure a real application is performed in a case study in which the calibration and the spatial and spatial–temporal validation processes have been carried out. The results can be considered as being excellent and it is concluded that automatic calibration with the SCE-UA algorithm has been shown to be reliable and fast.

Optimal monodomain approximations of the bidomain equations

The bidomain equations are widely accepted to model the spatial distribution of the electrical potential in the heart. Although order optimal methods have been devised for discrete versions of these equations, it is still very CPU demanding to solve the equations numerically on a sufficiently fine mesh in 3D. Furthermore, the equations are hard to analyze; from a mathematical point of view, very little is known about the qualitative behavior of the solutions generated by these equations. It is well known that upon appealing to a certain relation between the extracellular and intracellular conductivities, the bidomain model can be rewritten in terms of a scalar reaction diffusion equation referred to as the monodomain model. This model is of course much easier to solve, and also the qualitative properties of the solutions are well known; such equations have been studied intensively for decades. It is the purpose of the present paper to show how the bidomain equations can be approximated in an optimal manner by the solution of a monodomain model. The key feature here is that this optimal solution can be computed without solving the bidomain model itself. The solution is obtained by putting the problem into a framework of parameter identification problems. Our results are illuminated by a series of numerical experiments.

On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology

The bidomain model, coupled with accurate models of cell membrane kinetics, is generally believed to provide a reasonable basis for numerical simulations of cardiac electrophysiology. Because of changes occurring in very short time intervals and over small spatial domains, discretized versions of these models must be solved on fine computational grids, and small time-steps must be applied. This leads to huge computational challenges that have been addressed by several authors. One popular way of reducing the CPU demands is to approximate the bidomain model by the monodomain model, and thus reducing a two by two set of partial differential equations to one scalar partial differential equation; both of which are coupled to a set of ordinary differential equations modeling the cell membrane kinetics. A reduction in CPU time of two orders of magnitude has been reported. It is the purpose of the present paper to provide arguments that such a reduction is not present when order-optimal numerical methods are applied. Theoretical considerations and numerical experiments indicate that the reduction factor of the CPU requirements from bidomain to monodomain computations, using order-optimal methods, typically is about 10 for simple cell models and less than two for more complex cell models.

Iterative methods for computing generalized inverses related with optimization methods

AbstractWe develop several iterative methods for computing generalized inverses using both first and second order optimization methods in C*-algebras. Known steepest descent iterative methods are generalized in C*-algebras. We introduce second order methods based on the minimization of the norms ‖Ax − b‖2 and ‖x‖2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.

First Order Deign by Integration of Analysis and Optimization Method (1st Report, First Order Analysis by Focusing to the Boundary Conditions at Dividing the Module)

Until now, the analysis method and the optimization method, which were used in design, were evolving independently. However, when designed combining them, coexistence of time and precision was difficult. Then, we aimed at constructing the high-speed first order design method by the modularizing model and integration of first order analysis and optimization method based on boundary conditions between modules as the dynamic behavior of the design object. In this report, we proposed the framework of the first order analysis method based on boundary conditions between modules and applied this framework to thermal analysis of an electronic circuit board, and this thermal analysis method was analyzable at high speed (analysis time under 1 ms on four device modules on circuit board) with maintaining precision to the analysis by FEM, were shown clearly as the first report.

Optimal design of induction heating equipment for high‐speed processing of a semiconductor

Induction heating is widely used in the industry due to high efficiency, precise control, rapid heating and low pollution properties. To process a semiconductor of high quality, uniform heating is necessary, but it is not easy to heat uniformly by using the conventional induction heating equipment. For this purpose, the zone control induction heating equipment is jointly developed with Mitsui Engineering Shipbuilding Co., Ltd. In this paper, the optimization of current in each coil is carried out using the finite element method and the optimization method in order to obtain a uniform eddy current loss distribution on graphite.

電子システムの熱レイアウト設計における解析手法と最適化手法の融合

Until now, the analysis method and the optimization method, which were used in design, were evolving independently. However, when designed combining them, coexistence of time and precision was difficult. Then, we aimed at constructing the high-speed first order design method by the modularizing model and integration of first order analysis and optimization method based on boundary conditions between modules as the dynamic behavior of the design object. It designed using the thermal layout problem (all 16 parameters, design space about 6*10^<24>) of four device modules as a virtual design object. As a result, for 600s, the design time could search about 2*10^7 counts of evaluation for the proper solution, and enabled the very high-speed first order design.

電子システムの熱レイアウト設計における解析手法と最適化手法の融合によるファースト・オーダー・デザイン(システム最適化)

Until now, the analysis method and the optimization method, which were used in design, were evolving independently. However, when designed combining them, coexistence of time and precision was difficult. Then, we aimed at constructing the high-speed first order design method by the modularizing model and integration of first order analysis and optimization method based on boundary conditions between modules as the dynamic behavior of the design object. It designed using the thermal layout problem (all 16 parameters, design space about 6*10^<24>) of four device modules as a virtual design object. As a result, for 600s, the design time could search about 2*10^7 counts of evaluation for the proper solution, and enabled the very high-speed first order design.

CT-MRI automatic surface-based registration schemes combining global and local optimization techniques

Medical image registration is commonly required in order to combine the complementary information provided by different medical imaging modalities. In this paper, a new automatic registration scheme is proposed to register 3-D CT-MR head images and is currently tested on a clinical environment. The proposed scheme, after the preprocessing and the outer surface extraction of the data, is based on the use the rigid transformation method, in conjunction with a combination of global and local optimization techniques. Analytically, the paper exploits the optimization efficiency of three widely used optimization techniques, in obtaining the parameters of the rigid transformation model: the Downhill Simplex Method, the Genetic Algorithms and the Simulated Annealing. These optimization techniques are further combined by the sequential application of the Powell optimization method in order to refine the registration and increase its accuracy. A comparative study involving these optimization techniques in conjunction with the rigid transformation, and two other methods, the ICP and the manual methods, is also presented, for a sufficient number of clinical CT-MR brain images. Finally, quantitative and qualitative results are also presented to validate the performance of these automatic surface-based registration schemes, in terms of consistency and accuracy. Throughout of this study, the automatic registration scheme comprising of the rigid transformation in conjunction with the Simulated Annealing method sequentially combined with the Powell method has been performed superior regarding all the other compared registration schemes.

A Survey of Algebraic Multilevel Iteration (AMLI) Methods

For the solution by preconditioned conjugate gradient methods of symmetric positive definite equations as arising in boundary value problems we consider preconditioning methods of AMLI type. Particular attention is devoted to providing methods of optimal order of computational complexity which in addition promise to be robust, i.e. with a convergence rate which is bounded above independently of size of discretization parameter h, jumps in problem coefficients, and shape of finite elements or, equivalently, anisotropy of problem coefficients. In addition, the computational cost per iteration step must have optimal order.

Fast Fourier transform solvers and preconditioners for quadratic spline collocation

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differential Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT)are developed for the solution of the QSC equations. The complexity of the FFT solvers is O(N 2 log N), where N is the gridsize in one dimension. These direct solvers can handle PDEs with coefficients in one variable or constant, and Dirichlet, Neumann, alternating Dirichlet-Neumann or periodic boundary conditions, along at least one direction of a rectangular domain. General variable coefficient PDEs are handled by preconditioned iterative solvers. The preconditioner is the QSC matrix arising from a constant coefficient PDE. The convergence analysis of the preconditioner is presented. It is shown that, under certain conditions, the convergence rate is independent of the gridsize. The preconditioner is solved by FFT techniques, and integrated with one-step or acceleration methods, giving rise to asymptotically almost optimal linear solvers, with complexity O(N 2 log N). Numerical experiments verify the effectiveness of the solvers and preconditioners, even on problems more general than the analysis assumes. The development and analysis of FFT solvers and preconditioners is extended to QSC equations corresponding to systems of elliptic PDEs.

A method of computing the sensitivity of electromagnetic quantities to changes in materials and sources

This paper presents a method of computing the sensitivity of electromagnetic quantities (e.g. induced voltage, force, field uniformity) to perturbations in sources and material parameters. The method applies to systems with linear materials and time harmonic source currents; static problems are included as a special case. Sensitivity is equivalent to the derivative with respect to the distributed system parameters. Therefore, with the expressions for the sensitivity presented in this paper, first order optimization methods can be applied to optimization problems in electromagnetics. Applications are in the area of inverse problems, including electromagnetic device design, device optimization, and imaging. >

Adaptive split spectrum processing using a neural network

The polarity thresholding algorithm for split spectrum processing (SSP) is known to work well once properly tuned. However, there are several problems related to the finding of the right split parameters such as the number of filters and the information carrying spectral range. Here we show that the polarity thresholding method can be formulated as a multilayer perceptron (MLP) neural network with binary neurons and binary input signals operating in feedforward mode. Then the method is generalized to process nonbinary data using an adaptive MLP with graded neurons. Experiments with real ultrasonic NDE signals are presented using the conventional backpropagation optimization algorithm (BP) and a second order optimization method (BFGS) with exact line search. Finally, alternative adaptive algorithms based on a decomposition of the network into single neurons or linear discriminants are briefly discussed.

Adaptive Split Spectrum Processing Using a Neural Network

Abstract The polarity thresholding algorithm for split spectrum processing (SSP) is known to work well once properly tuned. However, there are several problems related to the finding of the right split parameters such as the number of filters and the information carrying spectral range. Here we show that the polarity thresholding method can be formulated as a multilayer perceptron (MLP) neural network with binary neurons and binary input signals operating in feedforward mode. Then the method is generalized to process nonbinary data using an adaptive MLP with graded neurons. Experiments with real ultrasonic NDE signals are presented using the conventional backpropagation optimization algorithm (BP) and a second order optimization method (BFGS) with exact line search. Finally, alternative adaptive algorithms based on a decomposition of the network into single neurons or linear discriminants are briefly discussed.

Multidisciplinary design of composite aircraft structures by lagrange

This paper deals with the application of a structural optimization method in order to find optimal layouts of fibre composite structures in aircraft construction. The goal of the optimization process is to minimize the structural weight and, simultaneously, to fulfil multidisciplinary constraints concerning failure criteria, stability requirements, dynamic responses, aeroelastic efficiencies and flutter speeds. Considering these requirements, the optimal values for the layer thicknesses and the fibre orientations of composite structures must be determined. This problem can be efficiently solved by structural optimization methods. The model formulation in structural optimization will be described in general as well as the special optimization model and the structural and sensitivity analysis for fibre composite structures. An application example demonstrates the performance of the whole procedure. This example shows that the structural optimization method is very useful in increasing the efficiency of the design process as well as the quality and performance of aircraft structures.