An improved response surface method for the determination of failure probability and importance measures

Gupta, Sayan; Manohar, C.S.

doi:10.1016/s0167-4730(03)00021-3

Cited by 118 publications

(63 citation statements)

References 19 publications

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“…RSM methodology is a collection of mathematical and statistical techniques based on fitting of polynomial equation to the experimental data, and becomes a powerful tool for describing the studied system ,so prediction of its behavior can be made by the surface responses plots that represents the system under studied region [5,27]. RSM was also used for analyzing the surface maps for different responses and detecting of interactions among variables and quadratic models presented on sciENcE aNd tEchNology the responses [14]. The procedure of using a least square regression analysis to obtain the parameters of a response surface around a design point has earlier been used by Faravelli [10].…”

Section: Partial Least Square Regression Methods and Response Surface mentioning

confidence: 99%

Estimation of system reliability by using the PLS-regression based corrected response surface method

Liu

Jiang

Hulio

et al. 2016

EiN

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Section: Partial Least Square Regression Methods and Response Surface mentioning

confidence: 99%

Estimation of system reliability by using the PLS-regression based corrected response surface method

Liu

Jiang

Hulio

et al. 2016

EiN

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“…First Order Reliability Method, Second Order Reliability Method and Monte Carlo Simulation are particularly popular techniques. When limit state function is strongly nonlinear and there is a possibility of existence of multiple integration regions (the integration region is a disconnected set) the Monte Carlo Simulation method is usually the most reasonable choice (e.g., Gupta and Manohar [5]). …”

Section: Probability Of Failure and Factor Of Safetymentioning

confidence: 99%

“…The variables have been assumed as uncorrelated. The proposed methodology of safe design of the structure located in anisotropic soil involves calculation of global factor of safety (5). This factor is equal to the ratio between the value of applied load and the mean value of bearing capacity P(X) which should be reached in order to reduce the probability to appropriate safety level.…”

Section: Probability Of Failure and Factor Of Safetymentioning

confidence: 99%

Reliability Analysis of Bearing Capacity of Square Footing on Soil with Strength Anisotropy Due to Layered Microstructure

Kawa

2015

Studia Geotechnica Et Mechanica

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The paper deals with reliability analysis of square footing on soil with strength anisotropy. The strength of the soil has been described with identified anisotropic strength criterion dedicated to geomaterials with layered microstructure. The analysis assumes dip angle α and azimuth angle β which define direction of lamination of the structure to be random variables with given probability density functions. Bearing capacity being a function of these variables is approximated based on results of deterministic simulations obtained for variety of orientations. The weighted regression method by Kaymaz and McMahon within the framework of Response Surface Method is used for the approximation. As a result of analysis, global factor of safety that corresponds to assumed value of probability of failure is determined. The value of the safety factor denotes the ratio between the value of the design load and the mean value of bearing capacity which is needed to reduce the probability of failure to the acceptable level. The procedure of calculating the factor has been presented for two different cases. In the first case, no information about lamination direction of the soil has been provided and thus all the orientations are assumed to be equally probable (uniform distribution). In the second case, statistical information including mean, variance and assumed probability distribution for both α and β angle is known. For the latter case, using results obtained for few different values of mean of angle α, also the influence of strength anisotropy on the value of global factor of safety is shown.

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“…Among others, general response surfaces [19,20,21,22], neural networks [23] and support vector machines [24] have been used.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Emulation-Based Reliability Analysis

Hristov¹,

DiazDelaO²,

Kubiak³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. This paper presents an approximation method for performing reliability analysis with high fidelity computer codes at a reasonable computational cost. Complex models are common in science and engineering due to their ability to substitute costly and some times infeasible practical experiments. These models, however, suffer from high computational cost. This causes problems when performing sampling -based reliability analysis, since the failure modes of the system typically occupy a small region of the input space and thus relatively large sample sizes are required for the accurate estimation of their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and Subset Simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset Simulation is used to efficiently populate those regions of the initial approximation which are likely to lead to the performance function exceeding a predefined critical threshold. Among all samples, the ones that are likely to contribute most to increasing the quality of the surrogate in the vicinity of the failure regions are selected, using Bayesian optimisation methods. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region in performance space is developed at a reasonable computational cost. The presented method is applied to a number of benchmark problems.

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An improved response surface method for the determination of failure probability and importance measures

Cited by 118 publications

References 19 publications

Estimation of system reliability by using the PLS-regression based corrected response surface method

Estimation of system reliability by using the PLS-regression based corrected response surface method

Reliability Analysis of Bearing Capacity of Square Footing on Soil with Strength Anisotropy Due to Layered Microstructure

Adaptive Emulation-Based Reliability Analysis

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