Derivation of rainfall IDF relations by third-order polynomial normal transform

2018 ◽  
Vol 32 (8) ◽  
pp. 2309-2324 ◽  
Author(s):  
Lingwan You ◽  
Yeou-Koung Tung
Keyword(s):  
Third Order ◽  
Order Polynomial

Thermal Error Modeling of Precision Positioning Stage

2013 ◽  
Vol 694-697 ◽  
pp. 767-770
Author(s):  
Jing Shu Wang ◽  
Ming Chi Feng
Keyword(s):  
Thermal Deformation ◽  
Thermal Error ◽  
Error Modeling ◽  
Precision Positioning ◽  
Third Order ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Positioning Stage ◽  
Order Polynomial ◽  
The Relationship

As the thermal deformation significantly impacts the accuracy of precision positioning stage, it is necessary to realize the thermal error. The thermal deformation of the positioning stage is simulated by the finite element analysis. The relationship between the temperature variation and thermal error is fitted third-order polynomial function whose parameters are determined by genetic algorithm neural network (GANN). The operators of the GANN are optimized through a parametric study. The results show that the model can describe the relationship between the temperature and thermal deformation well.

Calibration of pneumotachographs using a calibrated syringe

2003 ◽  
Vol 95 (2) ◽  
pp. 571-576 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
Johnny S. Yem ◽  
A. Barry Baker
Keyword(s):  
Calibration Method ◽  
Linear Range ◽  
Data Sets ◽  
Constant Flow ◽  
Calibration Constant ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Calibration Curves ◽  
Order Polynomial ◽  
Better Than

Pneumotachograph require frequent calibration. Constant-flow methods allow polynomial calibration curves to be derived but are time consuming. The iterative syringe stroke technique is moderately efficient but results in discontinuous conductance arrays. This study investigated the derivation of first-, second-, and third-order polynomial calibration curves from 6 to 50 strokes of a calibration syringe. We used multiple linear regression to derive first-, second-, and third-order polynomial coefficients from two sets of 6–50 syringe strokes. In part A, peak flows did not exceed the specified linear range of the pneumotachograph, whereas flows in part B peaked at 160% of the maximum linear range. Conductance arrays were derived from the same data sets by using a published algorithm. Volume errors of the calibration strokes and of separate sets of 70 validation strokes ( part A) and 140 validation strokes ( part B) were calculated by using the polynomials and conductance arrays. Second- and third-order polynomials derived from 10 calibration strokes achieved volume variability equal to or better than conductance arrays derived from 50 strokes. We found that evaluation of conductance arrays using the calibration syringe strokes yields falsely low volume variances. We conclude that accurate polynomial curves can be derived from as few as 10 syringe strokes, and the new polynomial calibration method is substantially more time efficient than previously published conductance methods.

scholarly journals Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 490 ◽  
Author(s):  
Yeou-Koung Tung ◽  
Lingwan You ◽  
Chulsang Yoo
Keyword(s):  
Flood Control ◽  
Random Variables ◽  
Rainfall Data ◽  
Normal Space ◽  
Modeling Framework ◽  
Third Order ◽  
Maximum Rainfall ◽  
Normal Distributions ◽  
Order Polynomial ◽  
Hydrologic Extremes

Hydro-infrastructural systems (e.g., flood control dams, stormwater detention basins, and seawalls) are designed to protect the public against the adverse impacts of various hydrologic extremes (e.g., floods, droughts, and storm surges). In their design and safety evaluation, the characteristics of concerned hydrologic extremes affecting the hydrosystem performance often are described by several interrelated random variables—not just one—that need to be considered simultaneously. These multiple random variables, in practical problems, have a mixture of non-normal distributions of which the joint distribution function is difficult to establish. To tackle problems involving multivariate non-normal variables, one frequently adopted approach is to transform non-normal variables from their original domain to multivariate normal space under which a large wealth of established theories can be utilized. This study presents a framework for practical normal transform based on the third-order polynomial in the context of a multivariate setting. Especially, the study focuses on multivariate third-order polynomial normal transform (TPNT) with explicit consideration of sampling errors in sample L-moments and correlation coefficients. For illustration, the modeling framework is applied to establish an at-site rainfall intensity–duration-frequency (IDF) relationship. Annual maximum rainfall data analyzed contain seven durations (1–72 h) with 27 years of useable records. Numerical application shows that the proposed modeling framework can produce reasonable rainfall IDF relationships by simultaneously treating several correlated rainfall data series and is a viable tool in dealing with multivariate data with a mixture of non-normal distributions.

Design and calibration of unicapillary pneumotachographs

1998 ◽  
Vol 84 (1) ◽  
pp. 335-343 ◽  
Author(s):  
A. Giannella-Neto ◽  
C. Bellido ◽  
R. B. Barbosa ◽  
M. F. Vidal Melo
Keyword(s):  
Respiratory Mechanics ◽  
Ambient Pressure ◽  
Animal Experiments ◽  
Small Animal ◽  
Positive Pressure ◽  
Linear Calibration ◽  
Third Order ◽  
Order Polynomial ◽  
Internal Radius ◽  
Volume Measurements

Giannella-Neto, A., C. Bellido, R. B. Barbosa, and M. F. Vidal Melo. Design and calibration of unicapillary pneumotachographs. J. Appl. Physiol.84(1): 335–343, 1998.—This study presents a method for design and calibration of unicapillary pneumotachographs for small-animal experiments. The design, based on Poiseuille’s law, defines a set of internal radius and length values that allows for laminar flow, measurable pressure differences, and minimal interference with animal’s respiratory mechanics and gas exchange. A third-order polynomial calibration (Pol) of the pressure-flow relationship was employed and compared with linear calibration (Lin). Tests were done for conditions of ambient pressure (Pam) and positive pressure (Ppos) ventilation at different flow ranges. A physical model designed to match normal and low compliance in rats was used. At normal compliance, Pol provided lower errors than Lin for mixed (1–12 ml/s), mean (4–10 ml/s), and high (8–12 ml/s) flow rate calibrations for both Pam and Ppos inspiratory tests (P < 0.001 for all conditions) and expiratory tests ( P < 0.001 for all conditions). At low compliance, they differed significantly with 8.6 ± 4.1% underestimation when Lin at Pam was used in Ppos tests. Ppos calibration, preferably in combination with Pol, should be used in this case to minimize errors (Pol = 0.8 ± 0.5%, Lin = 6.5 ± 4.0%, P < 0.0005). Nonlinear calibration may be useful for improvement of flow and volume measurements in small animals during both Pam and Ppos ventilation.

Oxygen equilibrium curve shape and allohemoglobin interaction in sheep whole blood

1986 ◽  
Vol 250 (2) ◽  
pp. R298-R305 ◽  
Author(s):  
L. A. Maginniss ◽  
A. J. Olszowka ◽  
R. B. Reeves
Keyword(s):  
Whole Blood ◽  
Ovis Aries ◽  
Equilibrium Curve ◽  
Curve Shape ◽  
Third Order ◽  
Binding Characteristics ◽  
Isoelectric Points ◽  
Order Polynomial ◽  
Oxygen Equilibrium Curve ◽  
O2 Binding

Adult sheep (Ovis aries) exhibit hemoglobin heterogeneity controlled by two autosomal alleles with codominant expression (Hb AA, AB, BB). Isoelectric points for Hb A and Hb B were 6.94 and 7.15, respectively; for Hb AB animals, the two allohemoglobins were present in equimolar concentrations (Hb A = 52%, Hb B = 48%). Dynamic O2 equilibrium curves (O2ECs) were generated for sheep whole blood at 39 degrees C using thin-film techniques. Half-saturation PO2 values (P50) at pH 7.50 were 31.3, 35.7, and 40.7 Torr for Hb AA, AB, and BB, respectively. CO2 Bohr coefficients at saturation (S) = 0.5 (delta log P50/delta pH) were similar for all phenotypes, ranging from -0.38 to -0.40. The Bohr slopes were also saturation independent between 0.2 and 0.8 S. Standard O2ECs for each phenotype were accurately fitted to three-constant third-order polynomial expressions. Sheep equilibrium curves were not isomorphic with other mammalian O2ECs (e.g., human and dog); sheep curves exhibited greater sigmoidicity. Furthermore, allohemoglobin interaction was not detected in heterozygous sheep. The blood O2 binding characteristics (P50, curve shape, and delta log PO2/delta pH) for Hb AB sheep and an experimental blood mixture containing equal proportions of Hb AA and Hb BB erythrocytes were equivalent.

Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs

2011 ◽  
Vol 48 (1-3) ◽  
pp. 141-163 ◽  
Author(s):  
José M. Gallardo ◽  
Sergio Ortega ◽  
Marc de la Asunción ◽  
José Miguel Mantas
Keyword(s):  
Hyperbolic Systems ◽  
Two Dimensional ◽  
Third Order ◽  
Order Polynomial ◽  
Nonconservative Hyperbolic Systems

Linear and Nonlinear Model of Cutting Forces in Peripheral Milling: A Comparison Between 2D and 3D Models

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Mohammad R. Movahhedy ◽  
Gholamreza Vossoughi
Keyword(s):  
Cutting Forces ◽  
Nonlinear Models ◽  
Three Dimensional ◽  
Chip Thickness ◽  
Maximum Error ◽  
3D Models ◽  
Peripheral Milling ◽  
Third Order ◽  
Order Polynomial ◽  
2D And 3D

Peripheral milling is extensively used in manufacturing processes, especially in aerospace industry where end mills are used for milling of wing parts and engine components. Knowledge of the cutting forces is the first necessary stage in analysis of the milling process. In this paper, cutting forces are presented for both two and three dimensional models. Instead of the common linear dependency of cutting forces to the cut chip thickness, two nonlinear models are presented. In the first model, cutting forces are considered as a function of chip thickness with a complete third order polynomial. In the second one, the quadratic and constant terms of the third order polynomial are set to zero. Results show about 2–3% and 2–7% maximum error between the linear, first and second nonlinear models, for 2D and 3D models, respectively. According to the simulation results, both the 2D and 3D models with second type of nonlinearity can be effectively used in practice. The advantage of such modelling is its simplicity in nonlinear analysis of the problem based on perturbation techniques.

A Localization and Extraction Method Research for Phalange ROI and Carpal ROI from Left Hand Radiography

2011 ◽  
Vol 340 ◽  
pp. 259-265
Author(s):  
Long Ke Ran ◽  
Ling He ◽  
Zhong Chen
Keyword(s):  
Prediction Method ◽  
Bone Age ◽  
Third Order ◽  
Shape Information ◽  
Age Assessment ◽  
Left Hand ◽  
Key Points ◽  
Order Polynomial ◽  
Bone Age Assessment ◽  
Hand Radiographs

In the research of Automatic bone age assessment,the most efficient location and successful extraction of regions of interest(ROI) from hand radiographs is one of the most difficult and important key technologies. Based on using shape information for phalanges and carpals, a background prediction method is propoesd , which uses a two-dimensional third order polynomial linear regression to fit background. And we also localize the key points of carpal and phalange ROI by usingK-cosine algorithm, finally we extract the carpal and phalange ROI successfully and properly. Through experiments, the proposed method resulted in over 93% correct extraction from more than 60 left hand radiograph data. The proposed method is robust to gray value variation of background and the position and orientation of the hand, so it can be used directly for automatic bone age assessment in the following study.

scholarly journals First passage probability assessment of stationary non-Gaussian process using the third-order polynomial transformation

2018 ◽  
Vol 22 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Yan-Gang Zhao ◽  
Long-Wen Zhang ◽  
Zhao-Hui Lu ◽  
Jun He
Keyword(s):  
Gaussian Process ◽  
Probability Assessment ◽  
Third Order ◽  
First Passage ◽  
The Third ◽  
Polynomial Transformation ◽  
Order Polynomial ◽  
First Passage Probability ◽  
Non Gaussian ◽  
First Four Moments

In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the “softening” responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and “hardening” responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process.

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