Automatic Step Research Articles

IMPROVED HIGH ORDER INTEGRATORS BASED ON THE MAGNUS EXPANSION

We build high order efficient numerical integration methods for solving the linear differential equation \(\dot X\) = A(t)X based on the Magnus expansion. These methods preserve qualitative geometric properties of the exact solution and involve the use of single integrals and fewer commutators than previously published schemes. Sixth- and eighth-order numerical algorithms with automatic step size control are constructed explicitly. The analysis is carried out by using the theory of free Lie algebras.

Transient non-linear heat conduction-radiation problems?a boundary element formulation

A novel boundary-only formulation for transient temperature fields in bodies of non-linear material properties and arbitrary non-linear boundary conditions has been developed. The option for self-irradiating boundaries has been included in the formulation. Heat conduction equation has been partially linearized by Kirchhoff's transformation. The result has been discretized by the dual reciprocity boundary element method. The integral equation of heat radiation has been discretized by the standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by static condensation of the radiative heat fluxes arising in both sets. The final set of ordinary differential equations has been solved using the Runge–Kutta solver with automatic time step adjustment. The algorithm proved to be robust and stable. Numerical examples are included. Copyright © 1999 John Wiley & Sons, Ltd.

A new computational procedure for wave propagation problems and a new procedure for non-reflecting boundaries

This paper provides a brief qualitative description of some of the important ideas and features of the FUSE code, a newly developed hydrodynamics shock code based upon a Lagrangian treatment of material motion and deformation. The Lagrangian nature of the analysis allows it to proceed without the non-physical numerical diffusion of dissimilar materials across interfaces. The FUSE procedure is outlined together with brief descriptions of some of the new techniques by which the code avoids the adverse effects of large distortion on conventional Lagrangian codes. FUSE is capable of dealing with arbitrarily large deformations and motions of materials of any properly posed constitutive type. It can accurately represent wave propagation and transport phenomena simultaneously. Examples involve the high-explosive gas expansion resulting from explosions in water and soil. An important aspect of the new code is the nature of its discretization scheme. This scheme differs from the standard finite element approach in that the ‘nodes’ carry only acceleration/velocity information, but do not carry position or deformation data. These, instead, are carried at the element or cell centers only. Further, the laws of conservation of mass, momentum and energy are exactly satisfied (to the numerical accuracy of the computer) for the discretized system. A new scheme for treating shock fronts is also included in the code. Finally, the code utilizes an automatic time step subcycling scheme to accommodate large distortions with a minimum of computer time. The purpose of this paper is to briefly describe these new features of the FUSE scheme. In addition, a new boundary treatment used in FUSE as well as in some other codes is briefly outlined, and the relationship of this method for ‘non-reflecting boundaries’ to the solution of structure-medium interaction problems is examined. This paper is presented in the expectation that one or more of these techniques may be of interest to analysts working in a wide range of fields.

Use of a Genetic Algorithm for Factor Selection in Principal Component Regression

The critical point in the development of principal component regression (PCR) calibration programs is the automatic factor selection step. In classical methods this is based on a differentiation between primary and secondary factors and other statistical assumptions and criteria. In contrast to this the Genetic Algorithm (GA) used for factor selection in this paper finds the optimal combination of factors without statistical constraints beyond an appropriately chosen fitness function.

Automatic Step Response Execution Algorithm in Profile Control in Paper Machines That Uses Lateral Inhibition Neural Networks and Wavelet.

抄紙機の坪量プロファイル制御において最も重要なチューニング項目である位置対応を同定するためのステップ応答テストを, 操業に支障を与えることなく, 自動的に行うアルゴリズムを開発し, 実際にその有効性を確認した.このアルゴリズムは次の2つの部分から成る.すなわち, 側抑制を持つニューラルネットワークを用いて操作するスライスボルトとその操作方向を決定する部分と, ウェーブレット変換を用いてステップ応答の操作量を最適化する部分とである.このアルゴリズムを用いて実際にステップ応答テストを行った実例を紹介し, 本アルゴリズムの有効性を示す.

MULTIPLE STATES OF A VISCOUS FREE SURFACE FLOW: TRANSITION FROM PRE-METERED TO A METERING INFLOW

SUMMARY In a forward-roll coating gap or nip, steady laminar flow of liquid between counter-rotating cylinders or rolls is used to split the flow into a coated layer on one roll and a rejected layer on the other. Both layers have free surfaces in contact with air. Liquid may be carried into the gap as a layer on one or both rolls. If the arriving layer is not too thick, all of the liquid flows through the gap, a situation called pre-metered. If the arriving layer is too thick, part of the liquid is rejected and runs back down the lower roll. The flow rate through the gap is said to be metered and is not known a priori. The transition from a pre-metered regime to the metered situation was examined by solving the Navier‐Stokes system for steady, two-dimensional flow in a domain bounded by free surfaces, two rigid roll surfaces and chosen inflow and outflow surfaces. The free boundary condition, as described by Papanastasiou et al. (Int. j. numer methods fluids, 14, 587 (1992)), was explored and proved to accommodate both the pre-metered and metered regimes. A run-back flow state across the synthetic inlet plane was obtained, provided a condition on the thickness of the arriving layer was replaced by a kinematic condition at a certain stage. The coupled equation system was solved by Galerkin’s method with finite element basis functions. The resulting non-linear algebraic system was solved by Newton’s method with initialization by pseduo-arc-length continuation and automatic parameter step adjustment. Results show the existence of multiple solutions which can lead to hysteresis. Flow regime maps were constructed to portray the operating parameter range in which a coating bead can exist and the ranges in which a coating gap operates in either the pre-metered or the metering regime. 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 813‐831, 1997.

Interactive, dynamic simulation using extrapolation methods

Interactive dynamic simulation means that the user observes and manipulates the simulator in real time (e.g. operator training). While low order, explicit, fixed step integration methods are suitable for many such applications, they have known limitations for stiff systems. However, standard implicit integrators do not provide a ready answer either, due to their automatic step size control and their sensitivity to discontinuities caused by interactions from the user. In order to combine the desirable real time features of explicit integrators with the stability characteristics of implicit algorithms, semi-implicit integrators coupled with extrapolation codes are explored. The principles and performance of the extrapolation methods are illustrated on a humidification column with feedback temperature control.

Iterative learning control using optimal feedback and feedforward actions

An algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient-type algorithms. The new algorithm has numerous benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm is expressed as a very general norm optimization problem in a Hilbert space setting and hence, in principle, can be used for both continuous and discrete time systems. A basic relationship with almost singular optimal control is outlined. The theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem.

Unsaturated flow in a quasi‐three‐dimensional fractured medium with spatially variable aperture

Transient moisture flow in a variably saturated quasi‐three‐dimensional fracture‐rock matrix system is investigated. The fracture is assumed to possess a spatially variable aperture in its two‐dimensional plane, whereas the rock matrix is treated as a two‐dimensional homogeneous and tight porous medium. The aperture fluctuations in the fracture plane are described stochastically. Moisture exchange between the fracture and the rock matrix is accounted for via an advective coupling term that governs the transfer of moisture at the fracture‐matrix interface and takes into account the effect of a fracture‐surface coating material. Although the variable aperture fracture is two‐dimensional, the coupling term between the fracture and the rock matrix accounts for the three‐dimensional nature of the physical system. The stochastic nonlinear set of partial differential equations is solved numerically by the Galerkin finite element method in conjunction with the Picard iterative scheme and an automatic time step marching. Simulations are performed to investigate phenomena which have been ignored in previous studies. It is demonstrated that, for the case of no moisture exchange with the rock matrix, the moisture follows preferential flow paths within the fracture plane and exhibits pronounced fingering effects. Furthermore, it is shown that the larger the fracture aperture fluctuations the more extended the moisture flow in the fracture. In addition, for the case where there exists moisture exchange with the rock matrix, the movement of the moisture front is considerably reduced, whereas fracture‐surface coatings tend to slow down moisture absorption by the rock matrix.

Automatic grid generation for complex geometries

AbstractA novel automatic grid generation method for complex CFD applications has been developed, driven by the need of the industrial CFD practitioner to reduce the turnaround time from an initial CAD geometry to obtaining a flow simulation. The method uses a subdivision strategy, allowing hanging nodes in a Cartesian unstructured mesh environment and is combined with a non-overlapping, semi-structured surface grid. Unusually, the surface grid is the end rather than the starting point of the present approach. This reversal of gridding strategy allows usability to be enhanced, in that the grid generation is reduced to one automatic step. The capabilities of the method are demonstrated by reference to selected inviscid and viscous flow solutions using the Fluent code Rampant v4.0 as a flow solver.

PIXE AND RECEPTOR MODEL APPLIED TO ATMOSPHERIC AEROSOL SOURCE APPORTIONMENT

Atmospheric aerosol samples were collected using an 8-stage cascade impactor or an automatic time sequence step sampler at Mount Qomolangma and Beijing. Element concentrations were analyzed by particle induced x-ray emission (PIXE) technique. Then the data were analyzed by the absolute principal factor analysis (APFA) to evaluate the principal components and the percent variance explained by them. As a result, it shows that the PIXE analysis combing with statistical method can effectively resolve the aerosol components in urban area and distinguish between local and remote area aerosol components in the area far from the pollution sources.

Encounter frequency of Halley-like comets with the planets

We present the results of a numerical study on encounter frequencies of fictitious Halley-like comets with the planets in a dynamical model of the solar system, in which we take into account the gravitational forces of the Sun and the planets Venus through Neptune. The change of the orbital elements during a close approach with a planet was carefully monitored with the aid of a thoroughly tested numerical integration method with automatic step size control. We computed the encounter frequencies of the comets' orbits using two different “spheres of influence” and compared the results. In both cases, it turned out that the encounter frequency of the fictitious Halley-like comets with Jupiter and Saturn is about a factor 10 to 100 higher than for the other planets. Concerning the changes of the semi-major axes and inclinations our results show that an increase and decrease of these elements is equally probable after an encounter.

Characterization of Penicillium chrysogenum physiology in submerged cultures by color and monochrome image analysis

Although filamentous microorganisms are widely used in industrial fermentation processes, their growth and differentiation are not yet fully understood, because their biomass is structured, and therefore difficult to describe and to quantify. This lack of appropriate tools can hinder the optimization and control of the fermentation. A quantitative image analysis method was therefore developed for characterizing the physiology of the penicillin-producing mold Penicillium chrysogenum. This method is based on a differential staining procedure showing six physiological states: growing material, three differentiated states characterized by an increasing granulation, a highly vacuolized state, and dead segments having lost their cytoplasm. The image analysis software, with versions written for monochrome and color images, consisted of a semiautomatic binary mask computation step and a fully automatic segmentation step based on a fuzzy classification.

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>

Effective Method for Analysis of Electrothermally Coupled Fields

An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.

Effective Method for Analysis of Electrothermally Coupled Fields

An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.

Automated gravimetric management of solutions. Part 2. Automated gravimetric approach to direct potentiometry and kappa number determination

The high-performance microcomputer controlled gravimetric burette described in Part 1 has been employed to automate some routine analytical procedures. A direct potentiometric determination of fluoride ions in drinking water was developed to include an automatic calibration step, matrix adjustment and sample determination. Also the complex and cumbersome titrimetric procedure for determination of the kappa number (lignin content) in paper pulp, has been automated by using the gravimetric unit and biamperometry. In this last instance, the automatic standardization of the solutions employed in the determination and the complete automation of the recommended kappa number determination procedure, allows a significant reduction in the amount of reagent consumed. The gravimetric approach to these procedures reveals that the same performance is achieved in terms of precision and accuracy when compared with classic volumetry while the cost associated with the automation decreases owing to the use of the same unit to attain automatic management of up to three different solutions.

Multiple time-scale power system dynamic simulation

A new program, EXSTAB (extended time-scale stability) has been developed for representing a wide variety of power system performance problems, from transient stability through long-term dynamics and voltage instability. The capability of the program includes multiple execution modes and automatic step size selection to address conflicting goals of accuracy and efficiency. The modeling includes a broad range of apparatus to provide the needed time-scale representation (four orders of magnitude). Models for automatic generation control, plant characteristics and control, voltage and reactive power control, static and dynamic loads, and protective relaying for apparatus and system connections are provided. Technologies were developed to perform analysis of voltage stability and prediction of peak power transfer to avoid voltage collapse. >

A technique for accurate magnetic resonance imaging in the presence of field inhomogeneities

A technique for producing geometrically accurate magnetic resonance images (MRIs) with undistorted intensity in the face of high levels of static field inhomogeneity arising from either source is presented. The technique requires the acquisition of two images of the same object with altered gradients. On the basis of a knowledge of these gradients it employs an automatic postprocessing step that exploits some invariant characteristics of the distortions to produce a rectified image from the two acquired images. No phantom imaging is involved and no operator interaction is required. The technique is theoretically justified and compared to other techniques, and experimental results that show that the technique works are presented. The improved accuracy in geometry and intensity may improve reliability of stereotactic surgery, may enhance the feasibility of both clinical and industrial imaging via external fields, and may increase the resolution of microscopic imaging.