ANOVA Models and Polynomial Models on Designs

Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

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MODELOS DE AFILAMENTO PARA Pinus elliottii EM DIFERENTES IDADES, NA REGIÃO DE CAÇADOR, SC

FLORESTA ◽

10.5380/rf.v43i3.30320 ◽

2013 ◽

Vol 43 (3) ◽

pp. 439 ◽

Cited By ~ 3

Author(s):

Saulo Jorge Téo ◽

Alan Marcon ◽

Tiago Ehlers ◽

Júlio César Bianchi ◽

Adriano Peloso ◽

...

Keyword(s):

Pinus Elliottii ◽

Degree Polynomial ◽

Stem Form ◽

Taper Function ◽

Different Ages ◽

Polynomial Models ◽

Old Trees ◽

Taper Models ◽

Best Estimates

Os objetivos deste trabalho foram ajustar e selecionar modelos de afilamento para estimar diâmetros a várias alturas e volume total, com e sem casca, de árvores de Pinus elliottii Engelm., na região de Caçador, SC, para estudar a forma dos fustes das árvores de diferentes idades. Ao todo, 78 árvores, com idades de 10, 18 e 27 anos, foram abatidas, cubadas rigorosamente e tiveram os seus volumes obtidos por meio do método de Smalian. Os modelos de afilamento testados foram os Polinômios de 2º e de 5º Graus e o Polinômio de Potências Fracionárias de Hradetzky. A função de afilamento que apresentou melhor desempenho para estimar o diâmetro com e sem casca ao longo do fuste das árvores foram baseadas no Polinômio de Potências Fracionárias de Hradetzky, para as idades de 10, 18 e 27 anos. O Polinômio de 2º Grau propiciou as melhores estimativas de volume total com casca para as idades de 10 e 27 anos e de volume total sem casca para as idades de 18 e 27 anos. Já o Polinômio de Potências Fracionárias apresentou melhores estimativas de volume com casca para 18 anos e de volume sem casca para árvores de 10 anos. Os fustes das árvores de Pinus elliottii apresentam melhor forma nas idades mais avançadas. AbstractTaper models for Pinus elliottii, at different ages, in the region of Caçador - SC. The research aims to fit and select taper models in order to estimate diameters at different heights and total volumes, inside and outside bark, of Pinus elliottii Engelm. trees, in the region of Caçador - SC, Brazil, as well as to analyze behavior of stem form for trees at different ages. Altogether, 78 trees at 10, 18 and 27 years of age, had been cut and their volumes obtained by Smalian method. The taper models tested were the 2nd and 5th Degree Polynomial and the Hradetzky Polynomial of Fractioned Potencies. The best performance taper function for estimate diameters inside and outside bark throughout the stem were based on the Hradetzky Polynomial of Fractioned Potencies, for 10, 18 and 27 years of age. The 2nd Degree Polynomial provided the best estimates of outside bark volume for 10 and 27 years of age, and of inside bark volume for 18 and 27 years of age, although the Hradetzky Polynomial presented the best estimates of outside bark volume for 18 years of age and of inside bark volume for 10 years old trees. The stems of the Pinus elliottii trees present better form for the oldest tress.Keywords: Polynomial models; profile models; stem form.

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Genetic Programming of Polynomial Models for Financial Forecasting

Genetic Algorithms and Genetic Programming in Computational Finance ◽

10.1007/978-1-4615-0835-9_5 ◽

2002 ◽

pp. 103-123 ◽

Cited By ~ 6

Author(s):

Nikolay Y. Nikolaev ◽

Hitoshi Iba

Keyword(s):

Genetic Programming ◽

Financial Forecasting ◽

Polynomial Models

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Polynomial Models and Interaction (Moderator) Analysis

Understanding Regression Analysis ◽

10.1201/9781003025764-9 ◽

2020 ◽

pp. 201-218

Author(s):

Peter H. Westfall ◽

Andrea L. Arias

Keyword(s):

Moderator Analysis ◽

Polynomial Models

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Modification of Classical Horseshoe Spillways: Experimental Study and Design Optimization

Civil Engineering Journal ◽

10.28991/cej-2019-03091396 ◽

2019 ◽

Vol 5 (10) ◽

pp. 2093-2109

Author(s):

Vahid Hassanzadeh Vayghan ◽

Ali Saber ◽

Soroosh Mortazavian

Keyword(s):

Hydraulic Jump ◽

Design Parameters ◽

Hydraulic Structures ◽

Flow Conditions ◽

Design Factor ◽

Flow Passage ◽

Water Head ◽

Cubic Polynomial ◽

Polynomial Models ◽

Discharge Efficiency

Investigation of the hydraulic aspects of spillways is one of the important issues regarding hydraulic structures. This study presents a modified horseshoe spillway (MHS) constructed by adding a flow passage and an internal weir in the bed of a classical horseshoe spillway (CHS). This modification increased the discharge efficiency and eliminated the rooster-tail hydraulic jump in CHSs. Eighteen laboratory-scale MHSs in various geometric sizes, six various CHSs, and a rectangular weir of the same width were constructed and tested under the same flow conditions. Results showed that in terms of discharge efficiency and water head reduction, CHSs and MHSs were superior to the rectangular weir. Compared to CHSs, the increased discharge flowrate in MHSs due to the internal weirs could further reduce the water head and thus increased their overall efficiencies. Design parameters effecting spillways’ discharge efficiencies were investigated based on dimensional analysis. The internal to external weir length ratio in MHSs was found to be a key design factor. To determine the optimal geometric design of CHS and MHS models, cubic polynomial models considering dimensionless parameters and their interactions were fitted to the experimental results. The cubic models revealed that higher discharge efficiencies in MHSs tended to occur at relatively low water heads and high internal to external weir lengths ratios.

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ESTIMATING EXTERIOR ORIENTATION PARAMETERS OF HYPERSPECTRAL BANDS BASED ON POLYNOMIAL MODELS

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-3-w3-19-2017 ◽

2017 ◽

Vol XLII-3/W3 ◽

pp. 19-25 ◽

Cited By ~ 1

Author(s):

A. Berveglieri ◽

A. M. G. Tommaselli ◽

E. Honkavaara

Keyword(s):

Real Data ◽

Bundle Adjustment ◽

Time Dependent ◽

Camera Model ◽

Exterior Orientation ◽

Spectral Bands ◽

Acquisition Mode ◽

Polynomial Models ◽

Orientation Parameters ◽

Sequential Acquisition

Hyperspectral camera operating in sequential acquisition mode produces spectral bands that are not recorded at the same instant, thus having different exterior orientation parameters (EOPs) for each band. The study presents experiments on bundle adjustment with time-dependent polynomial models for band orientation of hyperspectral cubes sequentially collected. The technique was applied to a Rikola camera model. The purpose was to investigate the behaviour of the estimated polynomial parameters and the feasibility of using a minimum of bands to estimate EOPs. Simulated and real data were produced for the analysis of parameters and accuracy in ground points. The tests considered conventional bundle adjustment and the polynomial models. The results showed that both techniques were comparable, indicating that the time-dependent polynomial model can be used to estimate the EOPs of all spectral bands, without requiring a bundle adjustment of each band. The accuracy of the block adjustment was analysed based on the discrepancy obtained from checkpoints. The root mean square error (RMSE) indicated an accuracy of 1&thinsp;GSD in planimetry and 1.5&thinsp;GSD in altimetry, when using a minimum of four bands per cube.

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Direct Comparison of Some Recent Rubber Elasticity Models

Rubber Chemistry and Technology ◽

10.5254/1.3547597 ◽

2000 ◽

Vol 73 (2) ◽

pp. 366-384 ◽

Cited By ~ 37

Author(s):

D. J. Seibert ◽

N. Schöche

Keyword(s):

Experimental Data ◽

Finite Element Analysis ◽

Element Analysis ◽

Material Parameters ◽

Complex Membrane ◽

The Finite Element Analysis ◽

Generic Class ◽

Cubic Model ◽

Polynomial Models ◽

Special Case

Abstract The paper compares the Arruda—Boyce model, the van der Waals model and the Reduced Polynomial model—a generic class of polynomial models of which Yeoh's cubic model is a special case—in their ability to predict multiaxial deformation states on the basis of uniaxial measurements. These models are reviewed in the light of novel experimental data, giving ample space to the derivation of the equations needed for optimization of the material parameters. The technological relevance of these findings is exemplified in the finite element analysis (FEA) of a complex membrane.

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