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Approximate Methods (approximate + methods)

Distribution by Scientific Domains

Engineering	25%
Chemistry	16%

Selected Abstracts

Deformation analysis of notched components and assessment of approximate methods

FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2001
Y. Jiang
Finite element modelling was conducted on notched members subjected to proportional and non-proportional loading. A recently developed cyclic plasticity model capable of accurately describing cyclic material behaviour was implemented into a finite element code. A plate with a central hole and a shaft with a circumference groove were studied. Approximate methods for the notched problems were critically evaluated using the finite element results. [source]

Approximate modal decomposition of inelastic dynamic responses of wall buildings

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2004
C. Sangarayakul
Abstract Two approximate methods for decomposing complicated inelastic dynamic responses of wall buildings into simple modal responses are presented. Both methods are based on the equivalent linear concept, where a non-linear structure is represented by a set of equivalent linear models. One linear model is used for representing only one vibration mode of the non-linear structure, and its equivalent linear parameters are identified from the inelastic response time histories by using a numerical optimizer. Several theoretical relations essential for the modal decomposition are derived under the framework of complex modal analysis. Various numerical examinations have been carried out to check the validity of the proposed modal decomposition methods, and the results are quite satisfactory in all cases. Fluctuating bending moment and shear at any location along the wall height contributed by each individual vibration mode can be obtained. Modal contributions to shear and flexural strength demands, as well as the corresponding modal properties, under various seismic loading conditions can also be identified and examined in detail. Furthermore, the effects of higher vibration modes on seismic demands of wall buildings are investigated by using the modal decomposition methods. Several new insights into the complicated inelastic dynamics of multi-story wall buildings are presented. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Approximate analysis methods for asymmetric plan base-isolated buildings

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002
Keri L. Ryan
Abstract An approximate method for linear analysis of asymmetric-plan, multistorey buildings is specialized for a single-storey, base-isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh,Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single-storey systems, each with vibration properties and eccentricities (labelled ,effective eccentricities') similar to corresponding properties of the isolation system or the fixed-base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single-storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh,Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Deformation analysis of notched components and assessment of approximate methods

Application of a new differential quadrature methodology for free vibration analysis of plates

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003
G. Karami
Abstract A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Emergency service systems: The use of the hypercube queueing model in the solution of probabilistic location problems

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2008
Roberto D. Galvão
Abstract Probabilistic location problems are surveyed from the perspective of their use in the design of emergency service systems, with special emphasis on emergency medical systems. Pioneering probabilistic models were defined in the 1980s, as a natural extension of deterministic covering models (first generation models) and backup models (second generation). These probabilistic models, however, adopted simplifying assumptions that in many cases do not correspond to real-world situations, where servers usually cooperate and have specific individual workloads. Thus the idea of embedding the hypercube queueing model into these formulations is to make them more adherent to the real world. The hypercube model and its extensions are initially presented in some detail, which is followed by a brief review of exact and approximate methods for its solution. Probabilistic models for the design of emergency service systems are then reviewed. The pioneering models of Daskin and ReVelle and Hogan are extended by embedding the hypercube model into them. Solution methods for these models are surveyed next, with comments on specialized models for the design of emergency medical systems for urban areas and highways. [source]

Application of equality constraints on variables during alternating least squares procedures

JOURNAL OF CHEMOMETRICS, Issue 12 2002
Mark H. Van Benthem
Abstract We describe several methods of applying equality constraints while performing procedures that employ alternating least squares. Among these are mathematically rigorous methods of applying equality constraints, as well as approximate methods, commonly used in chemometrics, that are not mathematically rigorous. The rigorous methods are extensions of the methods described in detail in Lawson and Hanson's landmark text on solving least squares problems, which exhibit well-behaved least squares performance. The approximate methods tend to be easy to use and code, but they exhibit poor least squares behaviors and have properties that are not well understood. This paper explains the application of rigorous equality-constrained least squares and demonstrates the dangers of employing non-rigorous methods. We found that in some cases, upon initiating multivariate curve resolution with the exact basis vectors underlying synthetic data overlaid with noise, the approximate method actually results in an increase in the magnitude of residuals. This phenomenon indicates that the solutions for the approximate methods may actually diverge from the least squares solution. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Systematic quantum chemical study of DNA-base tautomers

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2004
M. Piacenza
Abstract The relative energies of the energetically low-lying tautomers of pyridone, cytosine, uracil, thymine, guanine, and iso-cytosine are studied by a variety of different quantum chemical methods. In particular, we employ density functional theory (DFT) using the six functionals HCTH407, PBE, BP86, B-LYP, B3-LYP, and BH-LYP, and the ab initio methods Hartree-Fock (HF), standard second-order Møller-Plesset perturbation theory (MP2), an improved version of it (SCS-MP2), and quadratic configuration interaction including single and double excitations (QCISD) and perturbative triple corrections [QCISD(T)]. A detailed basis set study is performed for the formamide/formamidic acid tautomeric pair. In general, large AO basis sets of at least valence triple-, quality including f-functions (TZV) are employed, which are found to be necessary for an accurate energetic description of the various structures. The performance of the more approximate methods is evaluated with QCISD(T)/TZV(2df,2dp) data taken as reference. In general it is found that DFT is not an appropriate method for the problem. For the tautomers of pyridone and cytosine, most density functionals, including the popular B3-LYP hybrid, predict a wrong energetic order, and only for guanine, the correct sequence of tautomers is obtained with all functionals. Out of the density functionals tested, BH-LYP, which includes a rather large fraction of HF exchange, performs best. A consistent description of the nonaromatic versus aromatic tautomers seems to be a general problem especially for pure, nonhybrid functionals. Tentatively, this could be assigned to the exchange potentials used while the functional itself, including the correlation part, seems to be appropriate. Out of the ab initio methods tested, the new SCS-MP2 approach seems to perform best because it effectively reduces some outliers obtained with standard MP2. It outperforms the much more costly QCISD method and seems to be a very good compromise between computational effort and accuracy. © 2003 Wiley Periodicals, Inc. J Comput Chem 1: 83,98, 2004 [source]

Small proportions: what to report for confidence intervals?,

PHARMACOEPIDEMIOLOGY AND DRUG SAFETY, Issue 4 2005
Hilde Tobi
Abstract Purpose It is generally agreed that a confidence interval (CI) is usually more informative than a point estimate or p -value, but we rarely encounter small proportions with CI in the pharmacoepidemiological literature. When a CI is given it is sporadically reported, how it was calculated. This incorrectly suggests one single method to calculate CIs. To identify the method best suited for small proportions, seven approximate methods and the Clopper,Pearson Exact method to calculate CIs were compared. Methods In a simulation study for 90-, 95- and 99%CIs, with sample size 1000 and proportions ranging from 0.001 to 0.01, were evaluated systematically. Main quality criteria were coverage and interval width. The methods are illustrated using data from pharmacoepidemiology studies. Results Simulations showed that standard Wald methods have insufficient coverage probability regardless of how the desired coverage is perceived. Overall, the Exact method and the Score method with continuity correction (CC) performed best. Real life examples showed the methods to yield different results too. Conclusions For CIs for small proportions (,,,,0.01), the use of the Exact method and the Score method with CC are advocated based on this study. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Adaptive tests of regression functions via multiscale generalized likelihood ratios

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2003
Chunming M. Zhang
Abstract Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P-value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data. Moult applications des tests non paramétriques basés sur l'estimation de courbes font intervenir un paramètre de lissage. L'auteure propose un test adaptatif qui allie plusieurs tests du rapport de vraisemblances généralisés et rivalise de puissance avec le meilleur d'entre eux. Elle détermine la loi asymptotique conjointe des tests individuels et celle du test global sous l'hypothèse nulle. Elle montre aussi comment sélectionner facilement les paramètres de lissage du test global et propose deux méthodes de calcul approché de son seuil. Elle examine en outre le comportement du test proposé par voie de simulations et en illustre l'emploi dans un cas concret [source]

SOLUTIONS FOR EXTERIOR ORIENTATION IN PHOTOGRAMMETRY: A REVIEW

THE PHOTOGRAMMETRIC RECORD, Issue 100 2002
Pierre Grussenmeyer
Abstract The determination of the attitude, the position and the intrinsic geometric characteristics of the camera is recognised as the fundamental photogrammetric problem. It can be summarised as the determination of camera interior and exterior orientation parameters, as well as the determination of 3D coordinates of object points. The term "exterior orientation" of an image refers to its position and orientation related to an exterior (object space) coordinate system. Several methods can be applied to determine the parameters of the orientation of one, two or more photos. The orientation can be processed in steps (as relative and absolute orientation) but simultaneous methods (such as bundle adjustments) are now available in many software packages. Several methods have also been developed for the orientation of single images. They are based in general on geometric and topological characteristics of imaged objects. This paper presents a survey of classical and modern methods for the determination of the exterior parameters in photogrammetry, some of which are available as software packages (with practical examples) on the Internet. The methods presented are classified in three principal groups. In the first. a selection of approximate methods for applications that do not require great accuracy is presented. Such methods are also used to calculate values required for iterative processes. In the second group, standard point-bused methods derived from collinearity, coplanarity or coangularity conditions are briefly reviewed, followed by line-based approaches. The third group represents orientation methods based on constraints and on concepts of projective geometry, which are becoming of increasing interest for photogrammetrists. In the last section, the paper gives a summary of existing strategies for automatic exterior orientation in aerial photogrammetry. Résumé La détermination de l'attitude, de la position et des caractéristiques intrinsèques de la chambre photographique constitue un problème fondamental en photogrammétrie. Il se résume à la détermination des paramètres de l'orientation de la chambre de prise de vue (paramètres des orientations externe et interne), ainsi qu'à la détermination des coordonnées 30 des points de l'objet. L'orientation externe se rapporte à la détermination de la position et de l'orientation d'une chambre par rapport à un système externe de coordonnées. Différentes méthodes peuvent être utilisées pour calculer les éléments dorientation externe d'une photo, d'un couple ou de plusieurs photos. Le calcul de l'orientation peut être réalisé par étapes (par exemple les orientations relative et absolue) mais les méthodes simultanées (la compensation par faisceaux par exemple) sont actuellement proposées dans la plupart des logiciels. Plusieurs méthodes ont aussi été développées pour l'orientation d'images isolées. Ells sont basées en général sur les caactéristiques géométriques et topologiques des objets photographiés. Dans cet article on présente un ensemble de méthodes classiques et modernes pour la détermination des paramètres de l'orientation externe, certaines d'entre elles étant téléchargeables sous la forme d'applications sur Internet. Les méthodes présentées sont classées en trois groupes principaux. Le premier groupe contient une sélection de méthodes approximatives utilisées d'habitude quand une grande précision n'est pas exigée, ou encore pour calculer des vuleurs approchées des paramètres extrinsèques requises pour les méthodes itératives rigoureuses. Dans le deuxième groupe, on rappelle brièvement les jondements des méthodes basées sur les conditions photogrammétriques fondamentales (la colinéarité, la coplanéité et la coangularité). Dans ce groupe, les méthodes basées sur l'extraction des points ou des lignes sont également abordées. Le troisième groupe traite des méthodes d'orientation basées sur les contraintes et les concepts de la géométrie projective, de plus en plus utilisées par les photogrammètres. Le dernier paragraphe se rapporte aux méthodes destinées à automatiser le calcul de l'orientation externe en photogrammétrie aérienne. Zusummenfussung Die Bestimmung der Neigung, der Position und den geometrischen parametern der Kamera wird als das fundamentale Problem der Photogrammetrie angesehen. Es kann zusammenfassend sowohl als die Bestimmung der Parameter der inneren und äusseren Orientierung der Kamera angesehen werden, als auch als die Bestimmung von 3D Koordinaten von Objektpunkten. Der Ausdruck "äussere Orientierung" eines Bildes bezieht sich auf die Lage und Orientierung bezogen auf ein äusseres (Objektraum-) Koordinatensystem. Es können verschiedene Methoden angewandt werden, um die Parameter von einem, zwei oder mehreren Bildern zu bestimmen. Die orientierung kann in Schritten erfolgen, was als Relative und Absolute Orientierung bezeichnet wird, aber auch simultane Methoden, wie die Bündelausgleichung, sind in vielen Softwarepaketen implementiert. Es wurden auch Methoden für die Orientierung von Einzelbildern entwickelt, die geometrische und topologische Eigenschaften der abgebildeten Objekte nutzen. In diesem Beitrag wird Beitrag wird eine Studie klassischer und moderner Methoden der Photogrammetrie zur Bestimmung der Parameter der äßeren Orientierung vorgestellt, wovon einige in Softwarepaketen zur Verfügung stehen, die von praktischen Beispielen im Internet ergänzt werden. Die untersuchten Methoden werden in drei Hauptgruppen eingeteilt. In einer ersten Gruppe werden Näherungslösungen vorgestellt, die für Anwendungen mit geringen Genauigkeitsanforderungen geeignet sind. Diese Methoden werden ansonsten für die Näherngswertberechunggen für iterative Prozesse verwendet. IN der zweiten Gruppe werden zuerst die punktbasierten Standardmethoden vorgestellt, die von Bedingungen zur Kollinearität. Koplanarität und Kowinkligkeit abgeletet sind. Danach folgen linienbasierte Ansätze. Die dritte Gruppe umfasst Orientierungsmethoden, die auf Zwangsbedingungen und auf Konzepte der projektiven Geometrie aufbauen, die für Photogrammeter von zunehmendem Interesse sind, Im letzten Abschnitt wird eine Zusammenfassung existierender Strategien für eine automatische äussere orientierung in der Luftbildphotogrammetrie gegeben. [source]

Solutions for Exterior Orientation in Photogrammetry: A Review

THE PHOTOGRAMMETRIC RECORD, Issue 100 2002
Pierre Grussenmeyer
The determination of the attitude, the position and the intrinsic geometric characteristics of the camera is recognised as the fundamental photogrammetric problem. It can be summarised as the determination of camera interior and exterior orientation parameters, as well as the determination of 3D coordinates of object points. The term "exterior orientation"of an image refers to its position and orientation related to an exterior (object space) coordinate system. Several methods can be applied to determine the parameters of the orientation of one, two or more photos. The orientation can be processed in steps (as relative and absolute orientation) but simultaneous methods (such as bundle adjustments) are now available in many software packages. Several methods have also been developed for the orientation of single images. They are based in general on geometric and topological characteristics of imaged objects. This paper presents a survey of classical and modern methods for the determination of the exterior parameters in photogrammetry, some of which are available as software packages (with practical examples) on the Internet. The methods presented are classified in three principal groups. In the first, a selection of approximate methods for applications that do not require great accuracy is presented. Such methods are also used to calculate values required for iterative processes. In the second group, standard point,based methods derived from collinearity, coplanarity or coangularity conditions are briefly reviewed, followed by line,based approaches. The third group represents orientation methods based on constraints and on concepts of projective geometry, which are becoming of increasing interest for photogrammetrists. In the last section, the paper gives a summary of existing strategies for automatic exterior orientation in aerial photogrammetry. [source]