Efficient Assessment of Structural Reliability in Presence of Random and Fuzzy Uncertainties

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
A. S. Balu ◽  
B. N. Rao

This paper presents an efficient uncertainty analysis for estimating the possibility distribution of structural reliability in presence of mixed uncertain variables. The proposed method involves high dimensional model representation 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 this methodology, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods, thus the computational efficiency is accomplished. The proposed method is applicable for structural reliability estimation involving any number of fuzzy and random variables with any kind of distribution.

Author(s):  
A. S. BALU ◽  
B. N. RAO

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.


2020 ◽  
Author(s):  
Nafiseh Kiani

Structural reliability analysis is necessary to predict the uncertainties which may endanger the safety of structures during their lifetime. Structural uncertainties are associated with design, construction and operation stages. In design of structures, different limit states or failure functions are suggested to be considered by design specifications. Load and resistance factors are two essential parameters which have significant impact on evaluating the uncertainties. These load and resistance factors are commonly determined using structural reliability methods. The purpose of this study is to determine the reliability index for a typical highway bridge by considering the maximum moment generated by vehicle live loads on the bridge as a random variable. The limit state function was formulated and reliability index was determined using the First Order Reliability Methods (FORM) method.


2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang

(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.


2021 ◽  
Vol 23 (2) ◽  
pp. 231-241
Author(s):  
Shuang Zhou ◽  
Jianguo Zhang ◽  
Lingfei You ◽  
Qingyuan Zhang

Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.


2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.


2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>


Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han

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.


2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.


Author(s):  
Andrew Francis ◽  
Chas Jandu ◽  
Marcus McCallum

Our Client was commissioned to construct an onshore high pressure gas pipeline. The pipeline was to be about 50km in length, 1066mm diameter, 15.88mm nominal wall thickness and constructed from X65 material. During the route selection phase it was discovered that it would be very difficult to avoid passing the pipeline through a locally highly populated area. In view of this it was naturally decided that the pipeline should be constructed from heavy wall sectioned pipe to mitigate the threat of failure due to causes including mechanical damage and corrosion. However, there was still a concern that the residual risk, even when the above mitigating measure had been taken, would still be unacceptably high. In view of this Andrew Francis & Associates Ltd (AFAA) were commissioned to assess the remaining risk levels using a quantified risk assessment technique in accordance with the UK pipeline design code, IGE/TD/1 Edition 4, which provides for the use of such techniques. The technique used by AFAA involved detailed Structural Reliability Analysis (SRA) combined with an assessment of the consequences of failure. AFAA began the study by identifying the possible failure modes and these included mechanical damage, external corrosion, fatigue crack growth and AC induced corrosion. However, discussions were held between AFAA and the Client and after giving due consideration to the benefits of modern construction standards, and the use of Fusion Bonded Epoxy (FBE) coating, it was agreed that the only significant threat to integrity was mechanical damage. AFAA used SRA to determine the likelihood of failure due to mechanical damage based on a state-of-art-limit state function taking account of key areas of uncertainty including variations in defect dimensions and material properties. A consequence model was used to determine the possible effects on the local population if a rupture of the pipeline was to occur. The consequence model was used to determine the amount of thermal dose that personnel, in the vicinity of the release, might receive, taking account of the transient nature of the gas flow. The mitigating effects of nearby buildings that would afford shelter from the effects of the thermal radiation levels were naturally taken into account. The results were expressed in terms of an F/N curve and assessed against the risk criteria contained in IGE//TD/1. It was concluded from the analysis that the proposed design did not pose an unacceptable level of risk and moreover that part of the proposed heavy wall section was unnecessary. However, in the interests of conservatism our customer proceeded with the original design. This paper describes the modelling technique used by AFAA and clearly presents the results and conclusions of the analysis.


Author(s):  
Michael Gardiner ◽  
Ross Michie ◽  
Gerardo Douce

Metrogas SA operates a natural gas distribution concession within the Greater Buenos Aires region of Argentina. In August 2007 a failure occurred on a section of the 22-bar system that dates from the early 1960s and, as such, was ‘inherited’ by Metrogas at privatization. The line pipe in this part of the system is spirally welded and at the failure point the spiral weld root was found to have been incomplete. Subsequent investigations showed that incomplete spiral welds were also present at other locations in the same section of the system. This paper describes some of the steps taken to investigate the incident of 2007 and to manage the threat from other defective spiral welds in the same pipeline section. We present a limit state model for through-wall failure of such features and show how this was used to help understand the incident. We also discuss modeling of uncertainties in parameters of the model and look at results from a probabilistic structural reliability implementation of the limit state function, which allowed the failure frequency of other defective spiral welds in this section to be predicted for various reductions of the operating pressure. Metrogas was then able to use these quantified reliability data to make a responsible, informed decision to keep the affected section in downrated service.


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