scholarly journals Probabilistic Prediction of Maximum Tensile Loads in Soil Nails

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqiang Hu ◽  
Peiyuan Lin
Keyword(s):  
Correction Factor ◽  
Earth Pressure ◽  
Random Variable ◽  
Probabilistic Prediction ◽  
Limit States ◽  
Simple Formulation ◽  
Load Model ◽  
Soil Nail ◽  
Reliability Based Design ◽  
The Difference

This paper presents the development of a simplified model for estimation of maximum nail loads during or at completion of construction of soil nail walls. The developed simplified nail load model consists of two multiplicative components: the theoretical nail load and the correction factor. The theoretical nail load is computed as the product of lateral active Earth pressure at nail depth and the nail tributary area. The correction factor is introduced to account for the difference between the theoretical and the measured nail loads. A total of 85 measured nail load data were collected from the literature; out of which, 74 were used to develop a simple formulation for the correction factor, whereas the remaining 11 were used for validation. After the validation, the model was updated using all 85 data. The updated simplified nail load model was demonstrated to be accurate on average (mean of model factor equal to 1), and the spread in prediction quantified as the coefficient of variation of the model factor was about 40%. Here, model factor is the ratio of measured to estimated nail load. The randomness of the model factor was also verified. Finally, the model factor was demonstrated to be a lognormal random variable. The proposed simplified nail load model is beneficial due to its simplicity and quantified model uncertainty; thus it is practically valuable to both direct reliability-based design and load and resistance factor design of soil nail wall internal limit states.

scholarly journals Reliability analysis of planar steel trusses based on p-box models

Vestnik MGSU ◽  
2021 ◽  
pp. 153-167
Author(s):  
Anastasia A. Soloveva ◽  
Sergey A. Solovev
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Statistical Data ◽  
Random Variables ◽  
Random Variable ◽  
Distribution Functions ◽  
Structural Elements ◽  
Limit States ◽  
Load Model ◽  
Box Models

Introduction. The development of probabilistic approaches to the assessment of mechanical safety of bearing structural elements is one of the most relevant areas of research in the construction industry. In this research, probabilistic methods are developed to perform the reliability analysis of steel truss elements using the p-box (probability box) approach. This approach ensures a more conservative (interval-based) reliability assessment made within the framework of attaining practical objectives of the reliability analysis of planar trusses and their elements. The truss is analyzed as a provisional sequential mechanical system (in the language of the theory of reliability) consisting of elements that represent reliability values for each individual bar and truss node in terms of all criteria of limit states. Materials and methods. The co-authors suggest using p-blocks consisting of two boundary distribution functions designated for modeling random variables in the mathematical models of limit states performed within the framework of the truss reliability analysis instead of independent true functions of the probability distribution of random variables. Boundary distribution functions produce a probability distribution domain in which a true distribution function of a random variable is located. However this function is unknown in advance due to the aleatory and epistemic uncertainty. The choice of a p-block for modeling a random variable will depend on the type and amount of statistical information about the random variable. Results. The probabilistic snow load model and the numerical simulation of tests of steel samples of truss rods are employed to show that p-box models are optimal for modeling random variables to solve numerous practical problems of the probabilistic assessment of reliability of structural elements. The proposed p-box snow load model is based on the Gumbel distribution. The mathematical model used to perform the reliability analysis of planar steel truss elements is proposed. The co-authors provide calculation formulas to assess the reliability of a truss element for different types of p-blocks used to describe random variables depending on the amount of statistical data available. Conclusions. The application of statistically unsubstantiated hypotheses for choosing the probability distribution law or assessing the parameters of the probability distribution of a random variable leads to erroneous assessments of the reliability of structural elements, including trusses. P-boxes ensure a more careful reliability assessment of a structural element, but at the same time this assessment is less informative, as it is presented in the form of an interval. A more accurate reliability interval requires interval-based assessments of distribution parameters or types of p-boxes applied to mathematical models of the limit state, which entails an increase in the economic and labor costs of the statistical data.

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Influence of soil nail orientations on stabilizing mechanisms of loose fill slopes

2013 ◽  
Vol 50 (12) ◽  
pp. 1236-1249 ◽  
Author(s):  
C.Y. Cheuk ◽  
K.K.S. Ho ◽  
A.Y.T. Lam
Keyword(s):  
Earth Pressure ◽  
Slope Movement ◽  
Numerical Analyses ◽  
Soil Nails ◽  
Soil Nail ◽  
Static Liquefaction ◽  
Liquefaction Failure ◽  
Loose Fill ◽  
Typical Design

Soil nailing has been used to upgrade substandard loose fill slopes in Hong Kong. Due to the possibility of static liquefaction failure, a typical design arrangement comprises a structural slope facing anchored by a grid of soil nails bonded into the in situ ground. Numerical analyses have been conducted to examine the influence of soil nail orientations on the behaviour of the ground nail–facing system. The results suggest that the use of steeply inclined nails throughout the entire slope could avoid global instability, but could lead to significant slope movement especially when sliding failure prevails, for instance, due to interface liquefaction. The numerical analyses also demonstrate that if only subhorizontal nails are used, the earth pressure exerted on the slope facing may cause uplift failure of the slope cover. To overcome the shortcomings of using soil nails at a single orientation, a hybrid nail arrangement comprising nails at two different orientations is proposed. The numerical analyses illustrate that the hybrid nail arrangement would limit slope movement and enhance the robustness of the system.

scholarly journals On the control of the difference between two Brownian motions: a dynamic copula approach

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Thomas Deschatre
Keyword(s):  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Gaussian Copula ◽  
Brownian Motions ◽  
Dynamic Copula ◽  
Copula Approach ◽  
The Difference ◽  
The Right

AbstractWe propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

scholarly journals Some Remarks on a Recent Paper by Borch

1961 ◽  
Vol 1 (5) ◽  
pp. 265-272 ◽  
Author(s):  
Paul Markham Kahn
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Fixed Number ◽  
Point Of View ◽  
Optimum Amount ◽  
Measurable Transformation ◽  
The Difference ◽  
Image Position ◽  
Stop Loss ◽  
Condition B

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such thatwhere c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.

scholarly journals Range Automatic Adjusted Current Transformer Primary Winning

2021 ◽  
Vol 12 (3) ◽  
pp. 3142-3147
Author(s):  
Amirov Sultan Fayzullayevich Et.al
Keyword(s):  
Correction Factor ◽  
Driving Forces ◽  
Operating Mode ◽  
Current Transformer ◽  
Measuring Range ◽  
Secondary Current ◽  
Measuring Devices ◽  
The Difference ◽  
Protection And Control ◽  
And Control

The article discusses the issue of introducing a correction factor for protection and control devices, as the value of the secondary current in a certain range of the auto-adjustable current transformer does not correspond to the value of the secondary current in another range determined by the difference of magnetic driving forces generated by the components of the primary current. Alternatively, an algorithm has been developed to account for the measurement error in this condition in an automatic system that controls the operating mode of the current transformer. It was also found that the output data should be transmitted taking into account the correction factor in order to ensure the proper operation of the protection and measuring devices when the current transformer is switched to another measuring range in the measuring range.

scholarly journals 1 Assessing the predictive adequacy of simple and complex mathematical models

2019 ◽  
Vol 97 (Supplement_3) ◽  
pp. 24-24
Author(s):  
Luis O Tedeschi
Keyword(s):  
Model Development ◽  
Predictive Ability ◽  
Random Variable ◽  
Coefficient Of Determination ◽  
Skewed Data ◽  
Future Performance ◽  
Evaluation Phase ◽  
The Difference ◽  
Predicted Values ◽  
Analytical Approaches

Abstract The establishment of credibility for a mathematical model’s (MM) predictive ability is an essential component for improving the MM because it stimulates the evolutionary thinking (i.e., the next generation of the model) of mental conceptualizations, assumptions, and boundaries of the MM. Its predictive adequacy is commonly assessed through its ability to precisely or accurately predict observed (real) values. The precision component measures how closely the model predicted values are of each other or whether a defined pattern of predictions exists. The accuracy component, on the other hand, measures how closely the average of the model predicted values are to the actual (true) average. Many statistics exist to determine precision and accuracy of MM such as mean bias, resistant coefficient of determination, coefficient of determination, modeling efficiency, concordance correlation coefficient (CCC), the mean square error of prediction, Kleijnen’s statistic (regression of the difference between predicted and observed on their sum), and Altman and Bland’s limits of agreement statistics among many more. However, for complex models that use skewed data or repeated data in which the data is not independent (e.g., multiple measurements on the same subject), simple statistics may not suffice. For instance, four methods to compute CCC exist (moment, variance components, U-statistics, and generalized estimating equations—GEE), but only the last two methods are resilient to lightly skewed data. Another type of complexity arises when meta-analytical approaches are used at the model development phase or the model evaluation phase. In general, meta-analytical approaches remove errors (i.e., variation) associated with random variables that are believed to be known. Under these circumstances, MM tends to overperform (i.e., they have greater predictive adequacy) and their future performance may be deceitful when trying to forecast at scenarios in which the random variable(s) is(are) indeterminable or unquantifiable.

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