Statistical Design of Fatigue Experiments

1952 ◽  
Vol 19 (1) ◽  
pp. 109-113
Author(s):  
Waloddi Weibull
Keyword(s):  
Experimental Data ◽  
Statistical Design ◽  
Testing Time ◽  
Optimum Distribution ◽  
Analytical Expression ◽  
Optimum Choice ◽  
Stress Levels ◽  
Parameter Values ◽  
Applied Stresses

Abstract An analytical expression connecting fatigue lives with applied stresses, and methods for computing the values of its parameters from experimental data are given. Formulas for estimating the uncertainty of computed parameter values, caused by scatter of loads and fatigue lives, for optimum distribution of specimens, and for optimum choice of stress levels, are deduced. Testing time and costs may be reduced by more than 40 per cent by using the formulas.

A Versatile Analytical Expression for the Inverse Abel Transform Applied to Experimental Data with Noise

2008 ◽  
Vol 62 (6) ◽  
pp. 701-707 ◽  
Author(s):  
Shuiliang Ma ◽  
Gming Hon Gao ◽  
Guangjun Zhang ◽  
Lin Wu
Keyword(s):  
Experimental Data ◽  
Abel Transform ◽  
Analytical Expression

scholarly journals CO2 Induced Foaming Behavior of Polystyrene near the Glass Transition

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Salah Al-Enezi
Keyword(s):  
Experimental Data ◽  
High Pressure ◽  
Glass Transition ◽  
Dissolved Gas ◽  
Foaming Process ◽  
Foaming Behavior ◽  
Potential Applications ◽  
Model C ◽  
Parameter Values ◽  
Good Agreement

This paper examines the effect of high-pressure carbon dioxide on the foaming process in polystyrene near the glass transition temperature and the foaming was studied using cylindrical high-pressure view cell with two optical windows. This technique has potential applications in the shape foaming of polymers at lower temperatures, dye impregnation, and the foaming of polystyrene. Three sets of experiments were carried out at operating temperatures of 50, 70, and 100°C, each over a range of pressures from 24 to 120 bar. Foaming was not observed when the polymer was initially at conditions below Tg but was observed above Tg. The nucleation appeared to occur randomly leading to subsequent bubble growth from these sites, with maximum radius of 0.02–0.83 mm. Three models were applied on the foaming experimental data. Variable diffusivity and viscosity model (Model C) was applied to assess the experimental data with the WLF equation. The model shows very good agreement by using realistic parameter values. The expansion occurs by diffusion of a dissolved gas from the supersaturated polymer envelope into the bubble.

Information content of data with respect to models

1983 ◽  
Vol 245 (5) ◽  
pp. R620-R623
Author(s):  
M. Berman ◽  
P. Van Eerdewegh
Keyword(s):  
Experimental Data ◽  
Data Collection ◽  
Information Content ◽  
Mathematical Framework ◽  
Statistical Measures ◽  
Parameter Values ◽  
Collection Strategies

A measure is proposed for the information content of data with respect to models. A model, defined by a set of parameter values in a mathematical framework, is considered a point in a hyperspace. The proposed measure expresses the information content of experimental data as the contribution they make, in units of information bits, in defining a model to within a desired region of the hyperspace. This measure is then normalized to conventional statistical measures of uncertainty. It is shown how the measure can be used to estimate the information of newly planned experiments and help in decisions on data collection strategies.

scholarly journals Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

2020 ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

Viscous Dissipation in Laminar Water Flows in Micro-Tubes

2007 ◽  
Author(s):  
In-Hwan Yang ◽  
Mohamed S. El-Genk
Keyword(s):  
Experimental Data ◽  
Viscous Dissipation ◽  
Temperature Rise ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Analytical Expression ◽  
Water Flows ◽  
Good Agreement

Numerical calculations are performed to investigate the effect of viscous dissipation on the temperature rise and friction numbers for laminar water flows in micro-tubes. The calculated values are compared with those determined from reported experimental data for glass and diffused silica micro-tubes (D = 16 – 101 μm and L/D = 625 – 1479). The results confirm a definite slip at the wall with slip lengths of ∼ 0.7 μm and 1.0 μm, which decrease the friction number and the temperature rise in the micro-tubes, but their effect gradually diminishes as either D or L/D increases. The friction number decreases exponentially as D decreases and, to a lesser extent, as L/D increases. The effect of L/D on the friction number is insignificant for micro-tube diameters ≤ 20 μm. For D > 400 μm, the friction number approaches that of Hagen-Posieuille of 64 for macro-tubes when L/D > 1500, but approaches higher values at smaller L/D. The dimensionless analytical expression developed for calculating the friction number and the temperature rise for water flows in micro-tubes is in good agreement with both the numerical and experimental results.

Model Verification of Mixed Dynamic Systems

1978 ◽  
Vol 100 (2) ◽  
pp. 266-273 ◽  
Author(s):  
J. D. Chrostowski ◽  
D. A. Evensen ◽  
T. K. Hasselman
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Dynamic Systems ◽  
Statistical Parameter ◽  
Model Verification ◽  
Passive Networks ◽  
Parameter Values ◽  
Basic Configuration ◽  
General Method

A general method is presented for using experimental data to verify math models of “mixed” dynamic systems. The term “mixed” is used to suggest applicability to combined systems which may include interactive mechanical, hydraulic, electrical, and conceivably other types of components. Automatic matrix generating procedures are employed to facilitate the modeling of passive networks (e.g., hydraulic, electrical). These procedures are augmented by direct matrix input which can be used to complement the network model. The problem of model verification is treated in two parts; verification of the basic configuration of the model and determination of the parameter values associated with that configuration are addressed sequentially. Statistical parameter estimation is employed to identify selected parameter values, recognizing varying degrees of uncertainty with regard to both experimental data and analytical results. An example problem, involving a coupled hydraulic-mechanical system, is included to demonstrate application of the method.

Buckle Propagation Pressure for Submarine Pipelines

1993 ◽  
Vol 115 (3) ◽  
pp. 162-166 ◽  
Author(s):  
G. D. Hahn ◽  
M. She ◽  
J. F. Carney
Keyword(s):  
Experimental Data ◽  
Design Practice ◽  
Offshore Pipelines ◽  
Analytical Expression ◽  
Geometrical Nonlinearities ◽  
Main Factors ◽  
Buckle Propagation ◽  
Good Agreement

A new analytical expression is proposed for the prediction of the buckle propagation pressure for deepwater offshore pipelines. The expression accounts for the influences of the main factors involved, including the effects of material and geometrical nonlinearities. Predictions of the proposed expression are shown to be in good agreement with available experimental data, and valuable information is developed that can guide applications of the expression in design practice. In addition, a discussion is presented which outlines the derivation of the proposed expression.

scholarly journals Generic Dynamical Model of PEM Electrolyser under Intermittent Sources

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6556
Author(s):  
Sumit Sood ◽  
Om Prakash ◽  
Mahdi Boukerdja ◽  
Jean-Yves Dieulot ◽  
Belkacem Ould-Bouamama ◽  
...  
Keyword(s):  
Experimental Data ◽  
Proton Exchange Membrane ◽  
Renewable Energy Sources ◽  
Water Electrolysis ◽  
Proton Exchange ◽  
Laboratory Scale ◽  
Dynamical Model ◽  
Percentage Error ◽  
Parameter Values ◽  
Electrolysis System

Proton Exchange Membrane (PEM) water electrolysis system is one of the promising technologies to produce green hydrogen from renewable energy sources (wind and solar). However, performance and dynamic analysis of PEM water electrolysis systems are challenging due to the intermittent nature of such sources and involved multi-physical behaviour of the components and subsystems. This study proposes a generic dynamical model of the PEM electrolysis system represented in a modular fashion using Bond Graph (BG) as a unified modelling approach. Causal and functional properties of the BG facilitate the formal PEM electrolyser model to adapt and to fit the different configurations of the electrolyser ranging from laboratory scale to industrial scale. The system-specific key parameter values are identified optimally for a laboratory-scale electrolyser system running on a multi-source energy platform using experimental data. The mean absolute percentage error between simulation and experimental data is found to be less than 5%. The performance characteristic curves of the electrolyser are predicted at different operating temperatures using the identified key parameters. The predicted performance is in good agreement with the expected behaviour of the electrolyser found in the literature. The model also estimates the different energy losses and the real-time efficiency of the system under dynamic inputs. With these capabilities, the developed model provides an economical mean for design, control, and diagnosis development of such systems.

Impact throw model for vehicle-pedestrian collision reconstruction

2002 ◽  
Vol 216 (6) ◽  
pp. 443-453 ◽  
Author(s):  
I Han ◽  
R M Brach
Keyword(s):  
Experimental Data ◽  
Direct Calculation ◽  
Travel Distance ◽  
Physical Parameters ◽  
Vehicle Speed ◽  
Horizontal Distance ◽  
Variational Study ◽  
Throw Distance ◽  
Parameter Values ◽  
Ground Impact

A planar model for the mechanics of a vehicle-pedestrian collision is presented, analysed and compared with experimental data. It takes into account the significant physical parameters of wrap and forward projection collisions and is suitable for solution using mathematics software or spreadsheets. Parameters related to the pedestrian and taken into account include horizontal distance travelled between primary and secondary impacts with the vehicle, launch angle, centre-of-gravity height at launch, the relative forward speed of the pedestrian to the car at launch, distance from launch to a ground impact, distance from ground impact to rest and pedestrian-ground drag factor. Vehicle and roadway parameters include post-impact, constant velocity vehicle travel distance, continued vehicle travel distance to rest with uniform deceleration and relative distance between rest positions of vehicle and pedestrian. The model is presented in two forms. The first relates the throw distance to the initial vehicle speed. The second, intended for reconstruction, relates the vehicle speed to the pedestrian throw distance. The first form is used as means of comparison of the model with selected sets of experimental data taken from the current literature, including a variational study using Monte Carlo simulation. The second (reconstruction) form is derived analytically not empirically and the parameters have physical interpretations. In order to obtain parameter values, direct calculation or the method of least squares can be used. A comparison of the reconstruction model with results of other reconstruction models is presented.

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