On the Relation Between the Factor of Safety and Reliability

1974 ◽  
Vol 96 (3) ◽  
pp. 853-857 ◽  
Author(s):  
My Dao-Thien ◽  
M. Massoud
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Coefficient Of Variation ◽  
Factor Of Safety ◽  
Mean Value ◽  
Probability Density Distribution ◽  
Approximate Relation ◽  
Safety And Reliability ◽  
The Mean ◽  
Function Relationship

An approximate relation between the reliability of a design and the classical deterministic factor of safety, used in the design, is presented. An expression of the reliability as function of the mean value and coefficient of variation of the probability density distribution of the factor of safety, is derived. Further, the relation between the deterministic factor of safety and the statistical values of the probabilistic factor of safety, is discussed. Finally an expression for the reliability as a function of the deterministic factor of safety and the parameters determining the stress and strength distributions, is obtained. This function relationship is expressed in a design nomogram relating all the parameters involved.

scholarly journals Characteristics of the Near-Ground Typhoon Morakot

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yanru Wang ◽  
Yongguang Li ◽  
Bin Fu ◽  
Xu Wang ◽  
Chuanxiong Zhang ◽  
...  
Keyword(s):  
Wind Speed ◽  
Density Distribution ◽  
Probability Density ◽  
Probability Density Distribution ◽  
Autocorrelation Coefficient ◽  
Typhoon Morakot ◽  
Mean Wind Speed ◽  
The Mean ◽  
Fluctuating Wind ◽  
Good Agreement

Two WJ-3 anemometers placed at the same height on the top of an architectural engineering building in Wenzhou University are used to determine the wind speed of Typhoon Morakot during its landing in real time. This study aims to explore Typhoon Morakot’s wind field characteristics, including mean wind speed, probability density distribution of fluctuating wind speed, power spectral density, correlation analysis, and coherence, on the basis of data measured by the two anemometers. Results show that the probability density distribution of the fluctuating wind speed of the typhoon follows the Gaussian distribution, and the measured cross-power spectrum of fluctuating wind speed is in good agreement with the modified Karman spectrum. The autocorrelation decreases with the increase in time interval (τ). The longitudinal autocorrelation coefficient decays rapidly with the increase in τ, and the lateral autocorrelation coefficient decays at an unchanged rate. The exponential attenuation coefficients of the longitudinal and transverse fluctuating wind speeds increase with the increase in the mean wind speed, and their mean values are 10.86 and 15.33, respectively. The change trends of the coherence coefficients of the two wind speed components with the mean wind speed are the same. The measured coherence coefficients of the two wind speed components are in good agreement with the exponential function.

Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coefficient Of Variation ◽  
Fractional Laplacian ◽  
Numerical Procedure ◽  
Elastic Rod ◽  
The Mean ◽  
Distributed Forces ◽  
Nonlinear Fashion

In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.

scholarly journals Influence Assessment of the Information Concerning the Bearing Type of Axle Box of Cars on the Automatic Classification Accuracy of Heated Boxes

2021 ◽  
pp. 5-14
Author(s):  
V. V Burchenkov
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Heating Temperature ◽  
Threshold Value ◽  
Probability Density Distribution ◽  
Practical Implementation ◽  
System Of Equations ◽  
Average Value ◽  
Optimal Thresholds ◽  
Different Types

Purpose. The main purpose of the work is to determine and classify the heated cars’ boxes based on the probability of appearance of roller and cassette type boxes in the classes of heated and overheated boxes, as well as the laws of probability density distribution of the recognition signs of normally heated and overheated roller and cassette type boxes. Methodology. The operation features of freight cars with cassette type axle boxes with increased operating heating have been investigated. The methodology of assessing the probability of recognition errors was proposed, which takes into account the fact that sets of normally heated and overheated boxes consist of subsets of boxes with different types of bearings. A system of equations is obtained, the roots of which represent еру values that minimize the recognition probability of the errors of the heated boxes. Findings. It was found out that with some methods of determining the bearing type, for example, by the average value of the ranges of thermal image for each car, the probability of erroneous selection may depend on the probability density distribution of the sign for bearings of different types and the threshold value of this sign. The optimal thresholds for detecting the overheated roller boxes in comparison with the optimal thresholds for detecting overheated cassette boxes were determined. It has been established that the pass of an overheated cassette bearing, provided that the type of bearing is determined correctly, is less likely to lead to an accident than if the cassette box is classified as a roller box. The rejection criteria of axle boxes according to their heating temperature difference on one of the wheel set axis for three variants of settings of the alarm system according to an arrangement of multipurpose complexes of technical means (CTM) were formulated. The practical implementation of this method of adjusting the CTM settings for the Minsk branch of the Belarusian Railways was demonstrated. Originality. A system of equations is obtained, which allows finding the optimal values of temperature thresholds for the detection of overheated roller and cassette boxes under the assumption that the error probabilities in the selection of boxes by their types are known and constant. Practical value. The developed method of adjusting the alarm settings of CTM makes it possible to significantly reduce unjustified train delays and the number of car uncouplings.

scholarly journals Branching exponent heterogeneity and wall shear stress distribution in vascular trees

2001 ◽  
Vol 280 (3) ◽  
pp. H1256-H1263 ◽  
Author(s):  
Kelly L. Karau ◽  
Gary S. Krenz ◽  
Christopher A. Dawson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Coefficient Of Variation ◽  
Vessel Diameter ◽  
Mean Value ◽  
Heterogeneous Distribution ◽  
Uniform Shear ◽  
The Mean ◽  
Wall Shear ◽  
Stress Dependent

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent ( z) = 3 [where z is defined by ( D 1) z = ( D 2) z + ( D 3) z ; D 1 is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in zvalues, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

scholarly journals A New Modeling Approach for the Probability Density Distribution Function of Wind power Fluctuation

2019 ◽  
Vol 11 (19) ◽  
pp. 5512 ◽  
Author(s):  
Lingzhi Wang ◽  
Jun Liu ◽  
Fucai Qian
Keyword(s):  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Wind Power ◽  
Rapid Development ◽  
Probability Density Distribution ◽  
Power Fluctuation ◽  
Function Model ◽  
New Model ◽  
Fireworks Algorithm

With the rapid development of grid-connected wind power, analysing and describing the probability density distribution characteristics of wind power fluctuation has always been a hot and difficult problem in the wind power field. In traditional methods, a single distribution function model is used to fit the probability density distribution of wind power output fluctuation; however, the results are unsatisfying. Therefore, a new distribution function model is proposed in this work for fitting the probability density distribution to replace a single distribution function model. In form, the new model includes only four parameters which make it easier to implement. Four statistical index models are used to evaluate the distribution function fits with the measured probability data. Simulations are designed to compare the new model with the Gaussian mixture model, and results illustrate the effectiveness and advantages of the newly developed model in fitting the wind power fluctuation probability density distribution. Besides, the fireworks algorithm is adopted for determining the optimal parameters in the distribution function model. The comparison experiments of the fireworks algorithm with the particle swarm optimization (PSO) algorithm and the genetic algorithm (GA) are carried out, which shows that the fireworks algorithm has faster convergence speed and higher accuracy than the two common intelligent algorithms, so it is useful for optimizing parameters in power systems.

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