Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters

Vu-Bac, Nam; Rafiee, Roham; Zhuang, Xiaoying; Lahmer, Tom; Rabczuk, Timon

doi:10.1016/j.compositesb.2014.09.008

Cited by 205 publications

(34 citation statements)

References 35 publications

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“…Manymethods have been proposed to conduct resolve uncertainty analysis [41][42][43][44][45]. In this work, the RSM approach is applied to the optimization of the index SRA and SLA.…”

Section: D-optimal Design For Response Surface Methodologymentioning

confidence: 99%

Numerical Evaluation and Optimization of Multiple Hydraulically Fractured Parameters Using a Flow-Stress-Damage Coupled Approach

Wang

et al. 2016

Energies

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Abstract:Multiple-factor analysis and optimization play a critical role in the the ability to maximizethe stimulated reservoir volume (SRV) and the success of economic shale gas production. In this paper, taking the typical continental naturally fractured silty laminae shale in China as anexample, response surface methodology (RSM) was employed to optimize multiple hydraulic fracturing parameters to maximize the stimulated area in combination with numerical modeling based on the coupled flow-stress-damage (FSD) approach. This paper demonstrates hydraulic fracturing effectiveness by defining two indicesnamelythe stimulated reservoir area (SRA) and stimulated silty laminae area (SLA). Seven uncertain parameters, such as laminae thickness, spacing, dip angle, cohesion, internal friction angle (IFA), in situ stress difference (SD), and an operational parameter-injection rate (IR) with a reasonable range based on silty Laminae Shale, Southeastern Ordos Basin, are used to fit a response of SRA and SLA as the objective function, and finally identity the optimum design under the parameters based on simultaneously maximizingSRA and SLA. In addition, asensitivity analysis of the influential factors is conducted for SRA and SLA. The aim of the study is to improve the artificial ability to control the fracturing network by means of multi-parameteroptimization. This work promises to provide insights into the effective exploitation of unconventional shale gas reservoirs via optimization of the fracturing design for continental shale, Southeastern Ordos Basin, China.

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“…Manymethods have been proposed to conduct resolve uncertainty analysis [41][42][43][44][45]. In this work, the RSM approach is applied to the optimization of the index SRA and SLA.…”

Section: D-optimal Design For Response Surface Methodologymentioning

confidence: 99%

Numerical Evaluation and Optimization of Multiple Hydraulically Fractured Parameters Using a Flow-Stress-Damage Coupled Approach

Wang

et al. 2016

Energies

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“…(1) is to use the eFAST method, first developed by Saltelli et al (1999) and widely used since Koehler and Owen, 1996;Queipo et al, 2005;Saltelli et al, 2008;Vanuytrecht et al, 2014;Vu-Bac et al, 2015). A multi-dimensional Fourier transformation of the simulator f allows a variance-based decomposition that samples the input space along a curve defined by…”

Section: The Extended Fast Methodsmentioning

confidence: 99%

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

et al. 2018

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Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input -the percentage of the total variability in the output attributed to the changes in that input -by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires ∼ 2000 emulators without PCA but only 5-40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator-PCA and GAM methods accurately estimated the SIs of the ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.

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“…However, engineering systems are complex and frequently contain correlated input parameters such that if one parameter varies, it results in variations in other parameters. The variation in the output of the models with correlated input parameters (e.g., composition constraints in material modeling [3] ) is not only contributed by the variations in input parameter itself, but also contributed by the correlated variations in other parameters [4] . Hence, it is more realistic to estimate the effects of changing more than one parameters on the model outputs simultaneously.…”

Section: Introductionmentioning

confidence: 99%

A software framework for probabilistic sensitivity analysis for computationally expensive models

Vu-Bac

Lahmer

Zhuang

et al. 2016

Advances in Engineering Software

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Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters

Cited by 205 publications

References 35 publications

Numerical Evaluation and Optimization of Multiple Hydraulically Fractured Parameters Using a Flow-Stress-Damage Coupled Approach

Numerical Evaluation and Optimization of Multiple Hydraulically Fractured Parameters Using a Flow-Stress-Damage Coupled Approach

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

A software framework for probabilistic sensitivity analysis for computationally expensive models

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