Geotechnical probabilistic analysis by collocation-based stochastic response surface method: An Excel add-in implementation

2009 ◽  
Vol 3 (2) ◽  
pp. 75-86 ◽  
Author(s):  
S.P. Huang ◽  
B. Liang ◽  
K.K. Phoon
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method

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 An Improved Stochastic Response Surface Method Based Probabilistic Load Flow for Studies on Correlated Wind Speeds in the AC/DC Grid

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3501 ◽  
Author(s):  
Ziwei Zhu ◽  
Shifan Lu ◽  
Sui Peng
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Load Flow ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Wind Speeds ◽  
Probabilistic Load Flow ◽  
Surface Method ◽  
Standard Normal ◽  
Probabilistic Load

This paper proposed a probabilistic load flow technique of AC/VSC-MTDC (Alternate Current/Voltage Source Control-Multiple Terminal Direct Current) hybrid grids based on an improved stochastic response surface method. The applied traditional stochastic response surface method is inherent with the capability to tackle correlated normal variables; however, the accuracy is poor in the case of correlated diverse distributions. To address this issue, NATAF transformation was adopted to transform the correlated wind speeds and loads following arbitrary distributions into the variables that are subject to standard normal distributions. The collection points could be selected to establish the polynomial relationship among the independent standard normal variables and the output responses. Then, the probability distributions and statistics of the responses could be accurately and efficiently estimated. The modified IEEE 14-bus system, involving an additional VSC-MTDC system, wind speeds following various distributions, and diverse consumer behaviors, was used to demonstrate the validity and capability of the proposed method.

Stochastic Response Surface Method with Enhanced Weighting Strategy

2012 ◽  
Vol 224 ◽  
pp. 272-279
Author(s):  
Gao Rong Sun
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Negative Impact ◽  
Failure Surface ◽  
Stochastic Response ◽  
Weighting Method ◽  
Additional Function ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Weighting Strategy

The weighted stochastic response surface method (WSRSM) has been demonstrated to be effective in improving the accuracy of the estimation of statistical moments and probability of failure (PoF) upon the stochastic response surface method (SRSM). However, it has been noticed that the weighting method in WSRSM may have little and sometimes negative impact on PoF estimation especially in the cases of low PoF. To address this issue, an enhanced weighting strategy is proposed that the weights of sample points are determined based on their importance not only to regression but also to PoF estimation. Specifically, relatively larger weights are assigned to points closer to the failure surface, which significantly accounts for the accuracy of PoF estimation. Comparative studies show that SRSM with the proposed weighting method outperforms WSRSM producing more accurate PoF estimation without incurring additional function evaluations.

Uncertainty Quantification of the Crosstalk in Multiconductor Transmission Lines via Degree Adaptive Stochastic Response Surface Method

2021 ◽  
Vol 36 (2) ◽  
pp. 174-183
Author(s):  
Quanyi Yu ◽  
Wei Liu ◽  
Kaiyu Yang ◽  
Xilai Ma ◽  
Tianhao Wang
Keyword(s):  
Uncertainty Quantification ◽  
Response Surface ◽  
Response Surface Method ◽  
Transmission Lines ◽  
Electromagnetic Compatibility ◽  
Probability Density Distribution ◽  
Stochastic Response ◽  
Multiconductor Transmission Lines ◽  
Stochastic Response Surface Method ◽  
Surface Method

The degree adaptive stochastic response surface method is applied to analyze statistically the crosstalk in multiconductor transmission lines (MTLs). The coefficient of polynomial chaos expansion (PCE) is obtained based on the least angle regression. The truncation degree of PCE is iterated using the degree adaptive truncation algorithm, and the optimal proxy model of the crosstalk of the original MTLs that satisfies the actual error requirements is calculated. The statistical properties of crosstalk in MTLs (such as mean, standard deviation, skewness, kurtosis, and probability density distribution) are obtained. The failure probability of the electromagnetic compatibility in the MTLs system is considered. The global sensitivity indices of crosstalk-related factors are analyzed. Finally, the proposed method is proved to be effective compared with the conventional Monte Carlo method. The uncertainty quantification of crosstalk in MTLs can be calculated efficiently and accurately.

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