Reliability analysis and inspection updating by stochastic response surface of fatigue cracks in mixed mode

2011 ◽  
Vol 33 (12) ◽  
pp. 3392-3401 ◽  
Author(s):  
H. Riahi ◽  
Ph. Bressolette ◽  
A. Chateauneuf ◽  
Ch. Bouraoui ◽  
R. Fathallah
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Mixed Mode ◽  
Fatigue Cracks ◽  
Stochastic Response

scholarly journals Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Qinghai Zhao ◽  
Xiaokai Chen ◽  
Zheng-Dong Ma ◽  
Yi Lin
Keyword(s):  
Topology Optimization ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Computational Efficiency ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Grid Design

A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

scholarly journals Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jinwen He ◽  
Ping Zhang ◽  
Xiaona Li
Keyword(s):  
Water Level ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
High Order ◽  
Stochastic Response ◽  
Rockfill Dam ◽  
Surface Method ◽  
Reinforced Earth

Practical stochastic response surface method (SRSM) using ordinary high-order polynomials with mixed terms to approximate the true limit state function (LSF) is proposed to analyze the reliability of bypass seepage stability of earth-rockfill dam. Firstly, the orders of random variable are determined with a univariate fitting. Secondly, nonessential variables are excluded to identify possible mixed terms. Thirdly, orthogonal table is used to arrange additional samples, and stepwise regression is conducted to achieve a specific high-order response surface polynomial (RSP). Fourthly, Monte Carlo simulation (MCS) is used to calculate the failure probability, and RSP is updated by arranging several additional samplings around the design point. At last, the Bantou complex reinforced earth-rockfill dam was taken as an example. There are 6 random variables, that is, the upper water level and 5 hydraulic conductivities (HCs). The result shows that a third-order RSP can ensure good precision, and the failure probability of bypass seepage stability is 3.680×10−5 within an acceptable risk range. The HC of concrete cut-off wall and the HC of rockfill are unimportant random variables. Maximum failure probability at the bank slope has positive correlation with the HC of curtain and the upper water level, negative correlation with the HC of alluvial deposits, and less significance with the HC of filled soil. With the increase of coefficient of variation (Cov) of the HC of curtain, the bypass seepage failure probability increases dramatically. Practical SRSM adopts a nonintrusive form. The reliability analysis and the bypass seepage analysis were conducted separately; therefore, it has a high computational efficiency. Compared with the existing SRSM, the RSP of practical SRSM is simpler and the procedure of the reliability analysis is easier. This paper provides a further evidence for readily application of the high-order practical SRSM to engineering.

Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis

2019 ◽  
Vol 16 (05) ◽  
pp. 1840017 ◽  
Author(s):  
Amit Kumar Rathi ◽  
P. V. Sudhi Sharma ◽  
Arunasis Chakraborty
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Moving Least Square ◽  
Stochastic Response Surface Method ◽  
Reliability Based Design ◽  
Surface Method ◽  
Grid Scheme

The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.

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