A Hybrid Reliability Approach Based on Probability and Interval for Uncertain Structures

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
C. Jiang ◽  
X. Han ◽  
W. X. Li ◽  
J. Liu ◽  
Z. Zhang
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Normal Space ◽  
Uncertain Parameters ◽  
Limited Information ◽  
Reliability Models ◽  
Distribution Parameters ◽  
Hybrid Reliability ◽  
Monotonicity Analysis

Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

Time-Dependent Reliability Analysis Using the Total Probability Theorem

2014 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vijitashwa Pandey ◽  
Igor Baseski
Keyword(s):  
Reliability Analysis ◽  
Conditional Probability ◽  
Limit State ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Normal Space ◽  
Total Probability ◽  
Standard Normal ◽  
Total Probability Theorem

A new reliability analysis method is proposed for time-dependent problems with limit-state functions of input random variables, input random processes and explicit in time using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the time-dependent probability of failure using a time-dependent conditional probability which is computed accurately and efficiently in the standard normal space using FORM and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral (equal to the number of input random variables) is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation or adaptive importance sampling is used based on a pre-built Kriging metamodel of the conditional probability. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.

scholarly journals An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 229
Author(s):  
Fangyi Li ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Houyao Zhu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Equivalent Model ◽  
Independent Random Variables ◽  
Problem Analysis ◽  
Analysis Method ◽  
Calculation Algorithm ◽  
Reliability Problem ◽  
Interval Variables

In practical engineering, due to the lack of information, it is impossible to accurately determine the distribution of all variables. Therefore, time-variant reliability problems with both random and interval variables may be encountered. However, this kind of problem usually involves a complex multilevel nested optimization problem, which leads to a substantial computational burden, and it is difficult to meet the requirements of complex engineering problem analysis. This study proposes a decoupling strategy to efficiently analyze the time-variant reliability based on the mixed uncertainty model. The interval variables are treated with independent random variables that are uniformly distributed in their respective intervals. Then the time-variant reliability-equivalent model, containing only random variables, is established, to avoid multi-layer nesting optimization. The stochastic process is first discretized to obtain several static limit state functions at different times. The time-variant reliability problem is changed into the conventional time-invariant system reliability problem. First order reliability analysis method (FORM) is used to analyze the reliability of each time. Thus, an efficient and robust convergence hybrid time-variant reliability calculation algorithm is proposed based on the equivalent model. Finally, numerical examples shows the effectiveness of the proposed method.

scholarly journals Interval Nonprobabilistic Reliability Analysis for Ancient Landslide considering Strain-Softening Behavior: A Case Study

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zilong Zhou ◽  
Chenglong Lin ◽  
Xin Cai ◽  
Riyan Lan
Keyword(s):  
Reliability Analysis ◽  
Strain Softening ◽  
Constitutive Relations ◽  
Failure Surface ◽  
Normal Space ◽  
Probability Density Distribution ◽  
Probability Method ◽  
Uncertain Parameters ◽  
Ancient Landslide ◽  
Softening Behavior

Uncertainties in geotechnical parameters significantly affect the stability evaluation of an ancient landslide, especially when considering the strain-softening behavior. Due to the great difficulty in obtaining the probability density distribution of geoparameters, an interval nonprobability reliability analysis framework combined with numerical strain-softening constitutive relations was established in this paper. Interval variables were defined as the uncertain parameters in the strain-softening model. The interval nonprobabilistic reliability was defined as the minimum distance from the origin point to the failure surface in the standard normal space, which is the key index for describing the ability of a system to tolerate the variation of uncertain parameters. The proposed method was used to evaluate the reliability of Baishi ancient landslide. The parameter sensitivity analysis was also conducted. Through the proposed method, it is considered that Baishi ancient landslide is safe and stable, and the strain threshold kr is the dominant parameter. The results calculated by the proposed method agree well with the actual situation. This indicates the proposed method is more applicable than the traditional probability method when the data are scare.

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.

STRUCTURAL RELIABILITY ANALYSIS OF STEEL TRUSS ELEMENTS ON BUCKLING USING PBOX APPROACH

2021 ◽  
pp. 45-53
Author(s):  
A.A. Solovyova ◽  
◽  
S.A. Solovyov ◽  
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Statistical Data ◽  
Limit State ◽  
Random Variables ◽  
Distribution Functions ◽  
Structural Safety ◽  
Random Load ◽  
Load Models ◽  
Steel Trusses

Abstract. The reliability of load-bearing structural elements is one of the indicators of structural safety. The article presents methods for steel trusses bars reliability analysis according to the buckling criterion using p-boxes. A p-box consists of two boundary probability distribution functions that form the area of possible distribution functions. Such model used for modeling random variables in conditions of incomplete statistical data by quantity or quality. An algorithm for summing p-boxes of random load models is demonstrated on the example of a probabilistic estimate of the force in the truss bar. The result of reliability analysis using p-boxes is presented in interval form. The use of p-boxes makes it possible to obtain a more cautious assessment of reliability in case of incomplete statistical data. To increase the informativity of the reliability analysis result, it is necessary to obtain more statistical data about random variables in design mathematical models of limit state, which will allow forming p-boxes with narrower boundary distribution functions.

scholarly journals A Time-Variant Reliability Analysis Method Based on the Stochastic Process Discretization under Random and Interval Variables

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 568
Author(s):  
Fangyi Li ◽  
Jie Liu ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Jijun Yi
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
Random Variables ◽  
Static System ◽  
Reliability Problem ◽  
Uncertain Variables ◽  
Discrete Random Variables ◽  
Interval Variables ◽  
Practical Engineering ◽  
Hybrid Reliability

In practical engineering, it is a cost-consuming problem to consider the time-variant reliability of both random variables and interval variables, which usually requires a lot of calculation. Therefore, a time-variant reliability analysis approach with hybrid uncertain variables is proposed in this paper. In the design period, the stochastic process is discretized into random variables. Simultaneously, the original random variables and the discrete random variables are converted into independent normal variables, and the interval variables are changed into standard variables. Then it is transformed into a hybrid reliability problem of static series system. At different times, the limited state functions are linearized at the most probable point (MPP) and at the most unfavorable point (MUP). The transformed static system reliability problem with hybrid uncertain variables can be solved effectively by introducing random variables. To solve the double-loop nested optimization in the hybrid reliability calculation, an effective iterative method is proposed. Two numerical examples and an engineering example demonstrate the validity of the present approach.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

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