Step Size Adjustment Research Articles

Feature-based nonrigid image registration using a Hausdorff distance matching measure

A feature-based, nonrigid image registration method using a Hausdorff distance-based matching measure is presented. The proposed method is robust to outliers and missing features, as no correspondence is established between the features. Utilizing a B-spline-based, nonrigid deformation model, the proposed method is able to handle nonrigid deformations between the images to be registered. A gradient descent-based optimization procedure is developed to maximize the matching measure under the nonrigid transformation model. With adaptively adjustable step sizes, the optimization procedure works in a coarse-to-fine manner so that first large nonrigid deformations are compensated and then the transformation parameters are gradually refined. In addition, two acceleration techniques are devised to greatly speed up the registration method, making it more practical for real applications. The performance of the proposed method is validated in various experiments from synthetic image registration to hand-drawn Chinese character registration and brain outline registration. The limitation of the method is also analyzed and exemplified. To partly alleviate the limitation of the method, we incorporate landmark information into the method and achieve promising results.

Fast and Effective Analysis Methods for Fiber Raman Amplifiers

A series of new single-step methods and their corresponding algorithms with automatic step size adjustment for model equations of fiber Raman amplifiers are proposed and compared in this paper. On the basis of the Newton–Raphson method, multiple shooting algorithms for the two-point boundary value problems involved in solving Raman amplifier propagation equations are constructed. A verified example shows that, compared with the traditional Runge–Kutta methods, the proposed methods can increase the accuracy by more than two orders of magnitude under the same conditions. The simulations for Raman amplifier propagation equations demonstrate that our methods can increase the computing speed by more than 5 times, extend the step size significantly, and improve the stability in comparison with the Dormand–Prince method. The numerical results show that the combination of the multiple shooting algorithms and the proposed methods has the capacity to rapidly and effectively solve the model equations of multipump Raman amplifiers under various conditions such as co-, counter- and bi-directionally pumped schemes, as well as dual-order pumped schemes.

Numerical Solution of Binary Liquid-Phase Adsorption onto Porocel Clay Using Linear, Freundlich and Langmuir Isotherms

A generalized mathematical model is presented to describe the process of multi-component adsorption onto porous media in fixed beds. The model was applied to the binary adsorption, without reaction, of aromatics and sulphur compounds onto a fixed bed of Porocel clay for kerosene deodorization using linear, Freundlich and Langmuir isotherms independently. A computational scheme for the solution of the model equations is presented. The scheme is based on orthogonal collocation for spatial discretization of the resulting set of coupled hyperbolic and parabolic partial differential equations for the macro-and micro-system, respectively. Michelsen's modified third-order semi-implicit Runge-Kutta method combined with step-size adjustment strategy was used to integrate the resulting 4N ordinary differential equations. Excellent agreement between the simulated results and pilot plant data was obtained for the breakthrough profiles for the non-linear adsorption isotherms of Freundlich and Langmuir. No agreement was obtained for the linear isotherm. Also, using the Freundlich and Langmuir isotherms, the exit concentration of the less preferentially adsorbed component (aromatics) exceeded its inlet concentration to the adsorption column for a certain period. This is indicative of the behaviour of competitive multi-component adsorption: relative to aromatics, sulphur compounds are selectively adsorbed onto Porocel clay. The relationship between solid- and liquid-phase concentration profiles for the Freundlich isotherm revealed the formation of multiple adsorption layers upon the primary mono-molecular layer. Again, for the Freundlich isotherm, the structure of the profiles exhibited a highly pronounced maximum for sulphur. An experimental breakthrough time of 8 h was also predicted for both aromatics and sulphur compounds using the non-linear Freundlich and Langmuir isotherms.

Effective numerical algorithm for fiber amplifiers

Based on the Dormand-Prince (DP) formula, a fast and effective method is proposed, which can implement automatic step-size adjustment to solve the model equations of fiber Raman amplifiers and erbium-doped fiber amplifiers (EDFAs). Numerical results show that (1) the CPU time of the proposed method is about 4.2 times smaller than that of the DP method when the Raman amplifier propagation equations are solved; (2) our method reduces the running time by more than two orders of magnitude in comparison with the classical fourth-order Runge-Kutta method; (3) in comparison with the DP method, the proposed method can increase the computational speed by about 2.5 times in solving the model equations of EDFAs.

An Improved Algorithm to Extract ERP Component for Brain-Computer Interfaces.

In order to improve the communication rates of brain-computer interface(BCI's), scientists are developing appropriate signal processing methods to extract the user's messages and commands from electroencephalograph (EEG). A fast fixed-point algorithm for independent component analysis(FastICA), possesses the advantages of simply structure and fast computation. However, in some cases, many signals are not completely independent, the stability of the algorithm won't be as ideal as people have expected. In fact, the reason that system does not converge steadily is the fixed step size in FastICA algorithm, that is, The negentropy J(wn+1TZ) of random vectors no longer monotonic increasing in the iterative process of separated vectors. We define a cost function δJ=J(w<inf>n+1</inf>TZ)-J(w<inf>n</inf>TZ) and a time-variant step size μ(t), and put forward a algorithm of adjusting step size by the variety of the cost function in iterative process. Results from a series of simulation and experiments show that, the stability and convergence of algorithm is improved.

Modelling and Simulation of Ternary Liquid-Phase Adsorption onto Activated Carbon

A computational procedure is presented for solving the set of rigid hyperbolic and parabolic partial differential equations describing the simultaneous adsorption of a ternary system in a column packed with adsorbent particles using the non-linear adsorption isotherms of Fritz and Schluender. The model equations account for the effects of axial diffusion in the fluid and the film and internal diffusional mass-transfer resistances of the particles. Orthogonal collocation and Michelsen's modified third-order semi-implicit Runge-Kutta method combined with a step-size adjustment strategy were used to solve the general form of the resulting 6N coupled ordinary differential equations for the simultaneous adsorption of butan-2-ol, t-amyl alcohol and phenol in fixed beds. The simulated results obtained from this model were compared with experimental data. Excellent agreement between the simulated results and previously published experimental data was obtained. The breakthrough profiles were also indicative of the...

Modeling and Simulation of Liquid-Phase Ternary Adsorption in Activated Carbon Column

A computational procedure is presented for solving the set of stiff hyperbolic and parabolic partial differential equations describing the simultaneous adsorption of a ternary system in a column packed with adsorbent particles using nonlinear adsorption isotherms of Fritz and Schluender. The model equations account for the effects of axial diffusion in the fluid and in the film and internal diffusional mass-transfer resistances of the particles. Orthogonal collocation and Michelsen's modified third-order semiimplicit Runge−Kutta methods combined with a step-size adjustment strategy are used to solve the general form of the resulting 6N coupled ordinary differential equations for simultaneous adsorption of 2-butanol, tert-amyl alcohol, and phenol in fixed beds. Simulated results obtained from this model are compared with experimental data. Excellent agreement between simulated results and previously published experimental data is obtained in 0.41- and 0.82-m adsorbers when the film mass-transfer coefficien...

An effective method for two-point boundary value problems in Raman amplifier propagation equations

A novel method with automatic step-size adjustment for propagation equation calculations in fiber Raman amplifiers is proposed, for the first time to authors' knowledge, in this paper. An effective shooting algorithm for the two-point boundary value problem is also constructed. Numerical results demonstrate that the computing speed of the proposed method is increased more than four times by comparison with the classical Runge–Kutta–Fehlberg method, the step-size is extended greatly, and the stability is improved. Simulation results also show that the new shooting algorithm can be used to solve Raman amplifier propagation equations on various conditions including co-, counter- and bi-directional pump schemes.

New Runge–Kutta Based Schemes for ODEs with Cheap Global Error Estimation

We present a particular 5th order one-step integrator for ODEs that provides an estimation of the global error. It's based on the class of one-step integrator for ODEs of Murua and Makazaga considered as a generalization of the globally embedded RK methods of Dormand, Gilmore and Prince. The scheme we present cheaply gives useful information on the behavior of the global error. Some numerical experiments show that the estimation of the global error reflects the propagation of the true global error. Moreover we present a new step-size adjustment strategy that takes advantage of the available information about the global error. The new strategy is specially suitable for problems with exponential error growth.

Nondivergent fast power flow methods

This paper presents new nondivergent constant Jacobian Newton power flow methods. Both coupled and decoupled Jacobian versions have been developed. The nondivergence feature of these methods is achieved through application of optimal multiplier theory for step size adjustment control. In order to verify the effectiveness of these methods results for four IEEE test systems, two Indian power systems and a famous 11-bus ill-conditioned distribution system have been obtained and compared with those obtained with the corresponding versions of the conventional power flows.

Nordsieck Methods with an Off-Step Point

Hybrid methods, incorporating one or more off-step points, are difficult to implement in a variable stepsize situation using the standard representation of input and output data in each step. However, instead of representing this data in terms of solution values and derivative values at a sequence of step points, it is possible to reformulate the method so that it operates on a Nordsieck vector. This has the consequence of reducing stepsize adjustments to nothing more than rescaling the components of the Nordsieck vector. This paper shows how to derive methods in both formulations and considers some implementation details. It is also possible to derive a new type of hybrid method using the Norsieck representation as the starting point and this is also discussed in the paper. The new method is found to have comparable accuracy for corresponding work expended as for standard methods.

Should one adjust the maximum step size in a Metropolis Monte Carlo simulation?

It is common practice to adjust the maximum step size during Monte Carlo simulations to achieve a target fraction of accepted trial moves. Although simulation experts are well aware that this procedure is technically incorrect, the continuing publication of studies that employ it indicates that the pitfalls are not more widely known, or at least are assumed to be negligible. In this pedagogical Letter, it is shown that dynamic step size adjustment may lead to unwanted correlations and statistical undersampling of flat regions of the potential energy surface, thereby violating balance and producing systematic errors. A variety of examples highlight the conditions where the problem is likely to be worst.

A Time-Reversible, Regularized, Switching Integrator for the N-Body Problem

This article describes a gravitational N-body integration algorithm conserving linear and angular momentum and time-reversal symmetry. Forces are dynamically partitioned based on interbody separation, so that the long-range forces are evaluated relatively rarely, and close approaches are treated by an efficient regularization technique. The method incorporates an automatic stepsize adjustment based on a Sundman time-transformation. Although the scheme is formally second order, the most intensive computations (the close-approach dynamics) are executed at higher order, thus improving the overall accuracy. Numerical experiments indicate that the method can effectively treat few-body gravitational problems with two-body close approaches, and it compares favorably with other schemes presented in the literature.

Spin dynamics calculations of electron and nuclear spin relaxation times in paramagnetic solutions

Spin dynamics (SD) methods have been developed to compute NMR paramagnetic relaxation enhancements (NMR-PRE) produced by solutes with electron spin S⩾1 in solution. The spin dynamics algorithms, which are implemented as the computer program SpinDyn.f, are similar in spirit to molecular dynamics calculations in statistical mechanics, except that the spin motion is propagated numerically in time using quantum mechanical equations of motion of the spin operators, rather than Newtonian equations of motion of the molecular degrees of freedom as in MD simulations. SD simulations as implemented in SpinDyn.f provide accurate, flexible, and rapid calculations of NMR-PRE phenomena with few of the assumptions or limitations of previous analytical theories. The program calculates inter- and intramolecular NMR-PRE phenomena for both integer and half-integer spin systems processing under arbitrary Zeeman and zfs Hamiltonians in the presence of Brownian reorientation. Isotropic Brownian reorientation is simulated by means of a finite-step algorithm with adjustable step size. Simulations computed by SpinDyn.f have been used in a systematic study aimed at better understanding the influence of Brownian reorientation on the NMR-PRE of an S=1 ion in a non-Zeeman-limit physical situation. Conditions required for the validity of zfs-limit analytical theory are given. SpinDyn.f has also been used to assess quantitatively the effects of molecular reorientation on a prior analysis of NMR-PRE data for the model S=2 complex ion [tris-(acetylacetonato)manganese(III)] in acetone solution; this system was found to be well described by zfs-limit analytical theory.

Fuzzy step-size adjustment for the LMS algorithm

This paper presents a fuzzy step-size LMS adaptive filter. This method allows the adaptive filter to converge faster and to produce smaller steady state errors compared to the fixed step-size LMS adaptive filter. Furthermore, it provides a general framework where the user can incorporate additional safety rules or conditions that will prevent the adaptive algorithm to become unstable and to react to sudden changing conditions more rapidly. Simulation results are presented to compare the performance of the new approach with the fixed step-size LMS algorithm and other commonly used variable step-size LMS algorithms such as those proposed by Harris et al. (1986) and Kwong and Johnston (1992).

On step size adjustments in structural continuation problems

Procedures for automatic step size control in non-linear structural equilibrium analyses are discussed. Some algorithms found in the literature are briefly described and compared. The main emphasis is given to the development of criteria for detecting the need for a change of the step size as early as possible. Hence, the size of the increment is controlled during the corrector phase. Two possible procedures for this are developed and compared. Both reduce the step size in highly curved parts of an equilibrium path. The performance of the proposed algorithm is demonstrated in some numerical examples, including both geometrical and material non-linearities. The conclusions are that a procedure for reduction of the step size within the step can give improved possibilities for convergence in the iterations. The need for suitable scaling of used variables in any continuation algorithm is also emphasized.

An inequality by which to adjust the LMS algorithm step-size

This paper gives a method for differentiating between the transient and steady states in the LMS algorithm using inequalities among a set of output errors. Based on these inequalities, it also gives an algorithm for automatic step size adjustment to both improve the convergence rate and reduce steady-state parameter estimation errors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

MIST: a user-friendly metabolic simulator.

The Metabolic Interactive Simulation Tool, MIST, is a software package, running under Microsoft Windows 3.1, which can be used for dynamic simulations, stoichiometric calculations and control analysis of metabolic pathways. The pathways can be of any complexity and are defined by the user in a simple, interactive way. The user-defined enzymatic rate equations can be compiled either by an external or an internal compiler. Simulations of pathways compiled by an external compiler run significantly faster, but since these compilers are commercial software, they are not distributed together with MIST. The simulations are performed by numerical integration of a set of ordinary differential equations. The integration can be done by either an explicit fourth-order Runge-Kutta algorithm or a semi-implicit third-order Runge-Kutta algorithm, both with adjustable step size. The second algorithm can be used if the set of differential equations is stiff. Vector-based drawing facilities are included in the program, with which results can be presented in graphs. Results of simulations, including graphics, can be stored in files. MIST is a very user-friendly, flexible and yet powerful program, with the mathematical details regarding models, simulations and calculations hidden from the user. This makes it suitable for scientists and students with limited computer experience.

An adaptive approach to stepsize control in ODE solvers

The efficiency with which the numerical solution of ordinary differential equations can be generated depends to a large extent on the effectiveness of the stepsize adjustment strategy that is used. A new strategy for carrying out this critical task is proposed in this paper. A distinctive feature of its formulation is the incorporation of a mechanism to correct for any persistent deviation of a prescribed solution quality measure from its desired value. The results of an extensive set of numerical experiments are presented to illustrate the superior behavior of the approach with respect to both the widely used locally optimum stepsize strategy and a recently suggested alternate strategy.

Expedient implicit integration with adaptive time stepping algorithm for nonlinear transient analysis

A self-adaptive time stepping method has been implemented in MSC/NASTRAN Version 66 for the transient analysis of nonlinear structures. The goal is to provide an automatic method of implicit time integration, which renders accurate solutions efficiently for any nonlinear transient response problem. This goal was achieved by combining the automatic time step adjustment with the bisection process in a coordinated manner. Frequent decomposition of the dynamic stiffness matrix is inevitable in adaptive time stepping using the implicit integration method. Efforts have been made to minimize the thrashing in the algorithm (e.g., too frequent or repetitive adjustment of the time step size) and yet to provide a solution reliably to any type of problem. The iteration process for the equilibrium employs expeditious methods such as BFGS updates and line searches as well as an adaptive stiffness matrix update strategy. The present self-adaptive time stepping algorithm for the nonlinear transient analysis is proving to be a robust and practical method, aimed at efficiency, effectiveness and user-friendliness.