A New Sparse Grid Based Method for Uncertainty Propagation

2009 ◽  
Author(s):  
Fenfen Xiong ◽  
Ying Xiong ◽  
Steven Greene ◽  
Wei Chen ◽  
Shuxing Yang
Keyword(s):  
Numerical Integration ◽  
High Dimension ◽  
Limit State ◽  
Uncertainty Propagation ◽  
Efficient Solutions ◽  
Sparse Grid ◽  
State Function ◽  
Uniform Sample ◽  
Propagation Methods ◽  
Grid Based

Although a variety of uncertainty propagation methods exist for estimating the statistical moments and the probability of failure in design under uncertainty, current methods suffer from their limitations in providing accurate and efficient solutions to high-dimension problems with interactions of random variables. A new sparse grid based uncertainty propagation method is proposed in this work to overcome this difficulty. The existing sparse grid technique, originally invented for numerical integration and interpolation, is extended to uncertainty propagation in the probabilistic domain. In particular, the concept of Sparse Grid Numerical Integration (SGNI) is extended for estimating the first two moments of performance in robust design, while the Sparse Grid Interpolation (SGI) is employed to determine failure probability by interpolating the limit-state function at the Most Probable Point (MPP) in reliability analysis. The proposed methods are demonstrated by several high-dimension mathematical examples with notable variate interactions and one complex multidisciplinary rocket design problem. Results show that the use of sparse grid methods works better than popular counterparts. Furthermore, the automatic sampling, special interpolation process, and dimension-adaptivity feature make SGI more flexible and efficient than using the uniform sample based metamodeling techniques.

A new sparse grid based method for uncertainty propagation

2009 ◽  
Vol 41 (3) ◽  
pp. 335-349 ◽  
Author(s):  
Fenfen Xiong ◽  
Steven Greene ◽  
Wei Chen ◽  
Ying Xiong ◽  
Shuxing Yang
Keyword(s):  
Uncertainty Propagation ◽  
Sparse Grid ◽  
Grid Based

scholarly journals Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

2021 ◽  
Vol 23 (2) ◽  
pp. 231-241
Author(s):  
Shuang Zhou ◽  
Jianguo Zhang ◽  
Lingfei You ◽  
Qingyuan Zhang
Keyword(s):  
Structural Reliability ◽  
Least Squares Method ◽  
Limit State ◽  
Uniform Design ◽  
Uncertainty Propagation ◽  
Reliability Estimation ◽  
Estimation Methods ◽  
State Function ◽  
Chance Theory ◽  
Theory Uncertainty

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.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

scholarly journals Sparse grid-based adaptive noise reduction strategy for particle-in-cell schemes

2021 ◽  
pp. 100094
Author(s):  
Sriramkrishnan Muralikrishnan ◽  
Antoine J. Cerfon ◽  
Matthias Frey ◽  
Lee F. Ricketson ◽  
Andreas Adelmann
Keyword(s):  
Noise Reduction ◽  
Sparse Grid ◽  
Reduction Strategy ◽  
Particle In Cell ◽  
Adaptive Noise ◽  
Grid Based

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

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.

A Reliability-Based Early Warning System for Real-Time Monitoring on RC Buildings

2012 ◽  
Vol 446-449 ◽  
pp. 3422-3427
Author(s):  
Wang Sheng Liu ◽  
Ming Zhao
Keyword(s):  
Probability Distribution ◽  
Real Time ◽  
Early Warning ◽  
Early Warning System ◽  
Limit State ◽  
Warning System ◽  
State Function ◽  
Real Time Monitoring ◽  
Rc Buildings ◽  
Load Effect

Today there is an urgent need for effective monitoring whether for old buildings or new ones. While conventional early warning system for real-time monitoring is based on safety factor, this paper proposes a new reliability-based framework to monitor the safety of RC buildings probabilistically. The framework includes modeling resistance, predicting probability distribution of load effect, calculating reliability and setting reliability index threshold. The in-situ test data enables to update the resistance model through a Bayesian process. Meanwhile, the observed monitoring data predicts the probability distribution of load effect. FORM is used to calculate the reliability because the limit state function for real-time monitoring is linear and simple. This study shows that the reliability-based early warning system is of more scientific sense in quantifying the safety and may be applied to many engineering fields.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<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>

Development of Ultimate Strength Evaluation Method for Piping Subjected to Seismic Loads

2013 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Tatsuhiro Yamazaki
Keyword(s):  
Power Plants ◽  
Evaluation Method ◽  
Failure Modes ◽  
Limit State ◽  
Seismic Loading ◽  
Earthquake Resistance ◽  
State Function ◽  
Limit State Function ◽  
Input Acceleration ◽  
Resistance Tests

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

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