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 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 of Composite Advanced Sail for Virginia Class Submarine

2008 ◽  
Vol 52 (03) ◽  
pp. 165-174
Author(s):  
Christopher D. Eamon ◽  
Masoud Rais-Rohani
Keyword(s):  
Probability Distribution ◽  
Structural Reliability ◽  
Random Variables ◽  
Random Variable ◽  
Computational Effort ◽  
Material Strength ◽  
Reliability Model ◽  
Limit States ◽  
Plane Shear ◽  
Reliability Indices

A structural reliability model is developed for a large composite submarine sail structure. Random variables include material strength and stiffness properties as well as load. Limit states are formulated in terms of material strength parameters and buckling resistance. A series system reliability model that bases structural performance on first component failure is used. A total of 205 random variables and 117 limit states compose the structural system model. Most component reliability indices ranged from 3 to 7, with overall system failure governed by material in-plane shear with a reliability index of 1.84. A probabilistic sensitivity analysis determined that load and material strength were the most significant random variables, while material stiffness parameters were unimportant. Significant computational effort was saved by reducing the number of random variables to the most influential set. The effects of correlation and random variable probability distribution were explored. It was found that correlation has little effect on results, but probability distribution is significant. Recommendations are made to improve performance.

scholarly journals RELIABILITY ANALYSIS OF A TWO SPAN FLOOR DESIGNED ACCORDING TO EUROCODE 5

2016 ◽  
Vol 36 (1) ◽  
pp. 18-25
Author(s):  
EN Ogork ◽  
AK Nakore
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Load Ratio ◽  
Structural Safety ◽  
Live Load ◽  
Structural Elements ◽  
Limit States ◽  
Analysis And Design ◽  
Modes Of Failure ◽  
Reliability Method

This paper presents the structural reliability assessment of a two span timber floor of strength class D40 designed in accordance with Eurocode 5 (2004).  The Structural analysis and design of the timber floor system was carried out using deterministic approach, considering both ultimate and serviceability limit states. Reliability analysis of the floor structural elements to ascertain its level of safety was carried out using first order reliability method (FORM) for the four modes of failure of bending shear, bearing and deflection. The reliability analysis involved investigation of the effects of variation of the applied dead to live load ratio and the cross sectional parameters of the floor. The results revealed that the deterministic design is satisfactory as limiting stresses and deflection were not exceeded. The primary floor joists had safety indices in shear and bending of 1.2 to 2.8 with decrease in dead to live load ratio and were below the recommended safety index of 3.8 specified in joint committee on structural safety (JCSS). The timber floor structural elements are more reliable in bearing, shear and deflection and critical in bending mode of failure. The section depth and span of floor elements are more sensitive in bending and deflection modes than shear and bearing modes. http://dx.doi.org/10.4314/njt.v36i1.3

scholarly journals RELIABILITY ANALYSIS OF RHS STEEL TRUSSES JOINTS BASED ON THE P-BOXES APPROACH

2021 ◽  
Vol 17 (1) ◽  
pp. 87-97
Author(s):  
Anastasia Soloveva ◽  
Sergey Solovev
Keyword(s):  
Reliability Analysis ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Random Variable ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Interval Estimate ◽  
Structural Elements ◽  
Aleatory And Epistemic Uncertainty ◽  
Steel Trusses

Reliability is one of the main indicators of structural elements mechanical safety. The choice of stochastic models is an important task in reliability analysis for describing the variability of random variables with aleatory and epistemic uncertainty. The article proposes a method for the reliability analysis of RHS (rectangular hollow sections) steel truss joints based on p-boxes approach. The p-boxes consist of two boundary distribution functions that create an area of possible distribution functions of a random variable. The using of p-boxes make possible to model random variables without making unreasonable assumptions about the exact cumulative distribution functions (CDF) or the exact values of the CDF parameters. The developed approach allows to give an interval estimate of the non-failure probability of the truss joints, which is necessary for a comprehensive (system) reliability analysis of the entire truss.

scholarly journals A research into the development of models of random variables as part of the structural reliability analysis performed in the absence of some statistical information

Vestnik MGSU ◽  
2021 ◽  
pp. 587-607
Author(s):  
Anastasia A. Soloveva ◽  
Sergey A. Solovev
Keyword(s):  
Probability Theory ◽  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Statistical Data ◽  
Random Variables ◽  
Random Variable ◽  
Statistical Information ◽  
Structural Reliability Analysis ◽  
Kolmogorov Smirnov

Introduction. The scientific review article addresses the approaches to the modeling of random variables performed as part of the structural reliability analysis of elements provided that some statistical information missing (limited). The objectives of the research include the statement of the problem of the probabilistic structural reliability analysis subject to incomplete statistical data, the study of the development of approaches to the generation of models of random variables within the framework of this problem, as well as the assessment of the current state of affairs in this field and some development prospects for the coming years. Materials and methods. The principal model of a random variable, considered in the article, represents a p-box (pro­bability box) model. A p-box is an area of possible functions of distributed probabilities of a random variable generated by the two boundary functions of the probability distribution. The article addresses p-boxes generated using the fuzzy set theory, the probability theory, Kolmogorov–Smirnov boundaries, etc. Results. The approaches, considered in the article, are illustrated by the numerical examples of p-boxes that use the same statistical data. P-boxes, based on the probability theory, allow to accurately simulate a random variable; however, a priori information about the type of the distribution function is needed. P-boxes, based on the possibility theory, can be used even if an extremely small amount of statistical data is available, and it is also necessary to carefully address the issue of assigning the cutoff (risk) level. P-boxes based on the Chebyshev inequality and the Kolmogorov–Smirnov statistics allow to effectively simulate random variables regardless of the type of the probability distribution. However, these approaches may generate an assessment that is too uninformative for decisions to be made in a number of tasks. Conclusions. The choice of a probabilistic model of a random variable for the further reliability analysis of structural elements will depend on the amount and type of statistical data obtained about the random variable. In particular cases, if the statistical information represents a subset of intervals, special approaches based on the Dempster–Shafer theory can be used. A promising and relevant method that underlies both the development of probabilistic models of random variables and the analysis of structural reliability in case of missing statistical information encompasses the employment of numerical modeling methods that employ surrogate models (kriging, Bayesian networks, interval predictors, etc.) and neural network algorithms.

scholarly journals Sequential Bayesian optimal experimental design for structural reliability analysis

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Christian Agrell ◽  
Kristina Rognlien Dahl
Keyword(s):  
Experimental Design ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Function Evaluation ◽  
Critical Event ◽  
Minimal Amount ◽  
Bayesian Decision ◽  
Structural Reliability Analysis

AbstractStructural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by $$P(g(\mathbf{X} ) \le 0)$$ P ( g ( X ) ≤ 0 ) for some n-dimensional random variable $$\mathbf{X} $$ X and some real-valued function g. In many applications the function g is practically unknown, as function evaluation involves time consuming numerical simulation or some other form of experiment that is expensive to perform. The problem we address in this paper is how to optimally design experiments, in a Bayesian decision theoretic fashion, when the goal is to estimate the probability $$P(g(\mathbf{X} ) \le 0)$$ P ( g ( X ) ≤ 0 ) using a minimal amount of resources. As opposed to existing methods that have been proposed for this purpose, we consider a general structural reliability model given in hierarchical form. We therefore introduce a general formulation of the experimental design problem, where we distinguish between the uncertainty related to the random variable $$\mathbf{X} $$ X and any additional epistemic uncertainty that we want to reduce through experimentation. The effectiveness of a design strategy is evaluated through a measure of residual uncertainty, and efficient approximation of this quantity is crucial if we want to apply algorithms that search for an optimal strategy. The method we propose is based on importance sampling combined with the unscented transform for epistemic uncertainty propagation. We implement this for the myopic (one-step look ahead) alternative, and demonstrate the effectiveness through a series of numerical experiments.

scholarly journals Credibility of Design Procedures

10.14311/266 ◽  
2001 ◽  
Vol 41 (4-5) ◽  
Author(s):  
J. Marková ◽  
M. Holický
Keyword(s):  
Structural Reliability ◽  
Concrete Slab ◽  
Theoretical Models ◽  
Comprehensive Analysis ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Reinforced Concrete Slab ◽  
Design Procedures ◽  
Design Value

Theory of structural reliability enables comprehensive analysis of structural elements with respect to various limit states, and provides valuable insights into the methodology of applied standards. In addition to reliability analysis of the structural element, a new concept of the credibility of theoretical models used to calculate the design value of basic variables is introduced. The presented example of structural verification for limit states of cracking shows that the credibility of commonly applied formulas and reliability of a reinforced concrete slab have a great scatter and are in some cases inadequate.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Reliability analysis of a telecommunication tower

1999 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Kamal El-Fashny ◽  
Luc E Chouinard ◽  
Ghyslaine McClure
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Joint Probability ◽  
Distribution Functions ◽  
Sensitivity Analyses ◽  
Ice Thickness ◽  
Joint Probability Distribution ◽  
Type I

This study presents a structural reliability analysis of a microwave tower subject to wind and freezing-rain hazards. The tower (name code CEBJ, owned by Hydro-Québec) is a 66 m tall, three-legged, steel lattice structure located in the James Bay area. The reliability analysis is performed conditionally with respect to wind speed and ice thickness accretion, and the results are integrated over the domain of wind and ice values using their joint probability distribution. This approach makes it possible to perform sensitivity analyses with respect to various assumptions on the joint probability distribution function of the climatological variable, without having to repeat the detailed coupled reliability - structural analysis of the tower. The probability distribution functions assumed for the wind speed and the ice thickness accretion on the tower members are both extreme-value type I (Gumbel) distributions. Adopting a weakest link model, the failure of the tower is assumed to occur when any of the members fails either in tension, compression, or global buckling. Without loss of generality, the proposed procedure can be applied with more refined probability distribution functions.Key words: reliability, telecommunication towers, wind, ice.

A PROBLEM OF PILES STRUCTURAL RELIABILITY ANALYSIS ON THE STABILITY CRITERION IN PERMAFROST REGIONS

2021 ◽  
Vol 96 (4) ◽  
pp. 3-15
Author(s):  
S.A. SOLOVEV ◽  
◽  
L.A. SUSHEV ◽  
A.A. KOCHKIN ◽  
A.A. SOLOVEVA ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Stability Criterion ◽  
Structural Reliability ◽  
Limit States ◽  
Permafrost Soils ◽  
Tangential Forces ◽  
The Stability ◽  
The Cost ◽  
Reliability Monitoring ◽  
Permafrost Regions

The increase in the rate of global warming directly affects the safety of buildings and structures on permafrost. The research presents the problem of reliability analysis for piles on permafrost soils by the stability criterion under the action of tangential forces of frost heaving. The two groups of piles reliability analysis methods are developed: for complete and limited statistical data about random variables in the models of limit states. Approximations of the dependences of the design resistances of permafrost soils to the shear along the freezing surface on the temperature are proposed. It can be used to estimate the freezing force that keeps the pile from buckling. The method for reliability monitoring and durability forecasting has been developed for piles on permafrost soils. The proposed method makes it possible to reasonably reduce the cost of reliability analysis in the initial periods, which can increase the number of buildings and structures being inspected by the similar costs.

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