Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.

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Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods

Mathematics ◽

10.3390/math8030323 ◽

2020 ◽

Vol 8 (3) ◽

pp. 323

Author(s):

Seyed Nasrollah Mousavi ◽

Renato Steinke Júnior ◽

Eder Daniel Teixeira ◽

Daniele Bocchiola ◽

Narjes Nabipour ◽

...

Keyword(s):

Probability Distribution ◽

Pressure Fluctuations ◽

Mean Value ◽

Maximum Pressure ◽

Hydraulic Jumps ◽

Statistical Parameters ◽

Characteristic Points ◽

Stilling Basins ◽

The Stability ◽

Cumulative Curves

Pressure fluctuations beneath hydraulic jumps potentially endanger the stability of stilling basins. This paper deals with the mathematical modeling of the results of laboratory-scale experiments to estimate the extreme pressures. Experiments were carried out on a smooth stilling basin underneath free hydraulic jumps downstream of an Ogee spillway. From the probability distribution of measured instantaneous pressures, pressures with different probabilities could be determined. It was verified that maximum pressure fluctuations, and the negative pressures, are located at the positions near the spillway toe. Also, minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of pressure data related to the characteristic points along the basin, and different Froude numbers. To benchmark the results, the dimensionless forms of statistical parameters include mean pressures (P*m), the standard deviations of pressure fluctuations (σ*X), pressures with different non-exceedance probabilities (P*k%), and the statistical coefficient of the probability distribution (Nk%) were assessed. It was found that an existing method can be used to interpret the present data, and pressure distribution in similar conditions, by using a new second-order fractional relationships for σ*X, and Nk%. The values of the Nk% coefficient indicated a single mean value for each probability.

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Thermal Error Modeling of Precision Positioning Stage

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.694-697.767 ◽

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.

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Calibration of pneumotachographs using a calibrated syringe

Journal of Applied Physiology ◽

10.1152/japplphysiol.00196.2003 ◽

2003 ◽

Vol 95 (2) ◽

pp. 571-576 ◽

Cited By ~ 14

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.

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Evaluation of pressure fluctuations coefficient along the USBR Type II stilling basin using experimental results and AI models

ISH Journal of Hydraulic Engineering ◽

10.1080/09715010.2020.1743208 ◽

2020 ◽

pp. 1-8

Author(s):

Seyed Nasrollah Mousavi ◽

Davood Farsadizadeh ◽

Farzin Salmasi ◽

Ali Hosseinzadeh Dalir

Keyword(s):

Pressure Fluctuations ◽

Experimental Results ◽

Type Ii ◽

Stilling Basin

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Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Water ◽

10.3390/w11030490 ◽

2019 ◽

Vol 11 (3) ◽

pp. 490 ◽

Cited By ~ 1

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.

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

Stochastic Environmental Research and Risk Assessment ◽

10.1007/s00477-018-1583-4 ◽

2018 ◽

Vol 32 (8) ◽

pp. 2309-2324 ◽

Cited By ~ 1

Author(s):

Lingwan You ◽

Yeou-Koung Tung

Keyword(s):

Third Order ◽

Order Polynomial

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Analysis of minimal and maximal pressures, uncertainty and spectral density of fluctuating pressures beneath classical hydraulic jumps

Water Science & Technology Water Supply ◽

10.2166/ws.2020.098 ◽

2020 ◽

Vol 20 (5) ◽

pp. 1909-1921

Author(s):

Seyed Nasrollah Mousavi ◽

Davood Farsadizadeh ◽

Farzin Salmasi ◽

Ali Hosseinzadeh Dalir ◽

Daniele Bocchiola

Keyword(s):

Spectral Density ◽

Large Scale ◽

Pressure Fluctuations ◽

Low Frequency ◽

Dominant Frequency ◽

Standard Uncertainty ◽

Hydraulic Jumps ◽

Stilling Basins ◽

Density Analysis ◽

Real Scale

Abstract Knowledge of extreme pressures and fluctuations within stilling basins is of the utmost importance, as they may cause potential severe damages. It is complicated to measure the fluctuating pressures of hydraulic jumps in real-scale structures. Therefore, little information is available about the pressure fluctuations in the literature. In this paper, minimal and maximal pressures were analyzed on the flat bed of a stilling basin downstream of an Ogee spillway. Attention has been focused on dimensionless pressures related to the low and high cumulative probabilities of occurrence (P*0.1% and P*99.9%), respectively. The results were presented based on the laboratory-scale experiments. These parameters for the relatively high Froude numbers have not been investigated. The total standard uncertainty for the dimensionless mean pressures (P*m) was obtained around 1.87%. Spectral density analysis showed that the dominant frequency in the classical hydraulic jumps was about 4 HZ. Low-frequency of pressure fluctuations indicated the existence of large-scale vortices. In the zone near the spillway toe, P*0.1% reached negative values of around −0.3. The maximum values of pressure coefficients, namely |CP0.1%|max and CP99.9%max, were achieved around 0.19 and 0.24, respectively. New original expressions were proposed for P*0.1% and P*99.9%, which are useful for estimating extreme pressures.

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Design and calibration of unicapillary pneumotachographs

Journal of Applied Physiology ◽

10.1152/jappl.1998.84.1.335 ◽

1998 ◽

Vol 84 (1) ◽

pp. 335-343 ◽

Cited By ~ 8

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.

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Oxygen equilibrium curve shape and allohemoglobin interaction in sheep whole blood

AJP Regulatory Integrative and Comparative Physiology ◽

10.1152/ajpregu.1986.250.2.r298 ◽

1986 ◽

Vol 250 (2) ◽

pp. R298-R305 ◽

Cited By ~ 3

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.

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