An entropy-based global sensitivity analysis for the structures with both fuzzy variables and random variables

2012 ◽  
Vol 227 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Tang Zhangchun ◽  
Lu Zhenzhou ◽  
Pan Wang ◽  
Zhang Feng
Keyword(s):  
Failure Probability ◽  
Uncertainty Propagation ◽  
Random Variables ◽  
Uncertain Variable ◽  
Importance Measure ◽  
Similar Measure ◽  
Practical Applications ◽  
Fuzzy Variables ◽  
Global Sensitivity ◽  
Uncertain Variables

Based on the entropy of the uncertain variable, a novel importance measure is proposed to identify the effect of the uncertain variables on the system, which is subjected to the combination of random variables and fuzzy variables. For the system with the mixture of random variables and fuzzy variables, the membership function of the failure probability can be obtained by the uncertainty propagation theory first. And then the effect of each input variable on the output response of the system can be evaluated by measuring the shift between entropies of two membership functions of the failure probability, obtained before and after the uncertainty elimination of the input variable. The intersecting effect of the multiple input variables can be calculated by the similar measure. The mathematical properties of the proposed global sensitivity indicators are investigated and proved in detail. A simple example is first employed to demonstrate the procedure of solving the proposed global sensitivity indicators and then the influential variables of four practical applications are identified by the proposed global sensitivity indicators.

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.

scholarly journals Global sensitivity analysis of failure probability caused by fatigue crack propagation

2019 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Global Sensitivity Analysis ◽  
Limit State ◽  
Random Variables ◽  
Probability Of Failure ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Stress Changes

The probability of failure of a load bearing steel member is investigated using a new type of global sensitivity analysis subordinated to contrasts. The main objective of the probability-oriented sensitivity analysis is structural reliability. The structural reliability methodology uses random variables as inputs. The subject of interest is the identification of those random variables that are most important when the limit state of a steel bridge member is reached. The limit state is defined by the occurrence of brittle fracture, which results from stress changes caused by multiple repeated loads. The propagation of a single-edge crack from initial to critical size is analysed using linear fracture mechanics. The failure probability and sensitivity indices are calculated using sampling-based methods. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method. New findings indicate that interaction effects among input variables strongly influence the probability of failure especially at the beginning of the operating period.

MEMBERSHIP FUNCTION OF FAILURE PROBABILITY USING MULTICUT-HIGH DIMENSIONAL MODEL REPRESENTATION

2012 ◽  
Vol 19 (04) ◽  
pp. 1250018
Author(s):  
A. S. BALU ◽  
B. N. RAO
Keyword(s):  
Reliability Analysis ◽  
Membership Function ◽  
Failure Probability ◽  
Structural Reliability ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Dimensional Model ◽  
Convolution Integral ◽  
Fuzzy Variables ◽  
Uncertain Variables

The structural reliability analysis in the presence of mixed uncertain variables demands more computation as the entire configuration fuzzy variables needs to be explored. Moreover the existence of multiple design points deviate the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this paper a novel uncertainty analysis method for estimating the membership function of failure probability of structural systems involving multiple design points in the presence of mixed uncertain variables is presented. The proposed method involves Multicut-High Dimensional Model Representation technique for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability analysis involving any number of fuzzy and random variables. The accuracy and efficiency of the proposed method is demonstrated through three examples.

NUMERICAL APPROACH TO AN OPTIMAL MULTI-ITEM IMPERFECT PRODUCTION CONTROL PROBLEM IN UNCERTAIN ENVIRONMENT

2014 ◽  
Vol 22 (01) ◽  
pp. 125-144
Author(s):  
DIPAK KUMAR JANA ◽  
K. MAITY ◽  
M. MAITI
Keyword(s):  
General Model ◽  
Production Control ◽  
Measure Theory ◽  
Control Variable ◽  
Uncertain Variable ◽  
Production Costs ◽  
Uncertain Measure ◽  
Fuzzy Variables ◽  
Imperfect Production ◽  
Production Inventory

In this paper, some multi-item imperfect production-inventory models without shortages for defective and deteriorating items with uncertain/imprecise holding and production costs and resource constraint have been formulated and solved for optimal production. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. Uncertain or imprecise space constraint is also considered. The uncertain and imprecise holding and production costs are represented by uncertain and fuzzy variables respectively. These are converted to crisp constraint/numbers using uncertain measure theory for uncertain variable and possibility/necessity measure for fuzzy variable. The multi-item production inventory model is formulated as a constrained single objective cost minimization problem with the help of global criteria method. The reduced problem is then solved using Kuhn-Tucker conditions and generalized reduced gradient(GRG-LINGO 10.0) technique. Form the general model, models for particular cases with different production and demand functions are derived. Models for a single item are also presented. The optimum results for different models are presented in both tabular and graphical forms. Sensitivity analysis of average cost for the general model with respect to the changes in holding and production costs are presented.

scholarly journals Law of large numbers for the sequence of uncorrelated fuzzy random variables

2021 ◽  
pp. 1-8
Author(s):  
Li Guan ◽  
Jinping Zhang ◽  
Jieming Zhou
Keyword(s):  
Law Of Large Numbers ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Fuzzy Variables ◽  
Large Numbers ◽  
The Law ◽  
Fuzzy Random

This work proposes the concept of uncorrelation for fuzzy random variables, which is weaker than independence. For the sequence of uncorrelated fuzzy variables, weak and strong law of large numbers are studied under the uniform Hausdorff metric d H ∞ . The results generalize the law of large numbers for independent fuzzy random variables.

The Influence of Flow Strength and Fracture Toughness on the Computed Reliability of Thermally Aged Grade CF-8M Cast Austenitic Stainless Steel Piping

2014 ◽  
Author(s):  
Timothy J. Griesbach ◽  
Dilip Dedhia ◽  
David O. Harris ◽  
Nathaniel G. Cofie ◽  
Kyle Amberge ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Fracture Mechanics ◽  
Failure Probability ◽  
Crack Depth ◽  
Random Variables ◽  
Low Flow ◽  
Flow Strength ◽  
Distribution Type

Thermal aging of cast austenitic stainless steel (CASS) piping is a concern for long-term operation of nuclear power plants. Traditional conservative deterministic fracture mechanics analyses lead to tolerable crack sizes well below the sizes that are readily detectable in these large-grained materials. This is largely due to the conservative treatment of the scatter in material properties and the imposition of multipliers (structural factors) on the applied loads. In order to account for the scatter in the tensile and fracture toughness properties that enter into the analysis, a probabilistic approach is taken. Application of the probabilistic fracture mechanics (PFM) model to representative problems has led to questions regarding the dominant random variables and the influence of the tails of their distributions on computed failure probability. The purpose of this paper is to report the results of a study to identify the important random variables in the PFM model and to investigate the influence of the distribution type on the computed failure probability. Application of the PFM model to a representative piping problem to compute the depth of a part-through part-circumferential crack that will fail with a defined probability (10−6 for example) revealed that the fracture toughness was not a dominant variable and the distribution of the toughness did not strongly affect the results. In contrast to this, the flow strength (which enters into the calculation of the applied crack driving force — J) was important in that low flow strength was controlling the low probability failures in the Monte Carlo simulation. Hence, the low-end tail of the flow strength distribution was influential. Various types of distribution of flow strength consistent with the available data were considered. It was found that the distribution type has a marked, but not overwhelming, effect on the crack depth that would fail with a given probability. From this it is concluded that the PFM model is quite robust, in that it is not highly sensitive to uncertainties in the dominant input distributions.

Some new approaches to probability distributions

1980 ◽  
Vol 12 (04) ◽  
pp. 903-921 ◽  
Author(s):  
S. Kotz ◽  
D. N. Shanbhag
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Representation Theorems ◽  
Practical Applications ◽  
New Approaches ◽  
Characterization Of Distributions ◽  
Stability Theorems ◽  
Conditional Expectations

We develop some approaches to the characterization of distributions of real-valued random variables, useful in practical applications, in terms of conditional expectations and hazard measures. We prove several representation theorems generalizing earlier results, and establish stability theorems for two general characteristics introduced in this paper.

Failure probability of corroded pipeline considering the correlation of random variables

2019 ◽  
Vol 99 ◽  
pp. 34-45 ◽  
Author(s):  
Peng Zhang ◽  
Lingbo Su ◽  
Guojin Qin ◽  
Xinhai Kong ◽  
Yang Peng
Keyword(s):  
Failure Probability ◽  
Random Variables

scholarly journals Parametric Sensitivity Analysis for Importance Measure on Failure Probability and Its Efficient Kriging Solution

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yishang Zhang ◽  
Yongshou Liu ◽  
Xufeng Yang
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Computational Effort ◽  
Importance Measure ◽  
Sensitivity Index ◽  
Reliability Engineering ◽  
Parametric Sensitivity ◽  
Distribution Parameters ◽  
The Moment ◽  
Sensitivity Indicator

The moment-independent importance measure (IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging (ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method.

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