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An Improved probabilistic collocation method for Uncertainty Quantification of Oil-Water Transport through Fractured Porous Media: Effect of Uncertain Gravity Imbibition

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2025年第7期50卷 5135-5156页

作者： Sharafi, Mohammad Sadegh Ahmadi, Mohammad Kazemi, Alireza Amirkabir Univ Technol Tehran Polytech Dept Petr Engn Tehran Iran Sultan Qaboos Univ Dept Petr & Chem Engn Muscat Oman

Simulation of subsurface flow through fractured media is significantly influenced by uncertainty in matrix block size, fracture aperture and fracture distribution due to inherent heterogeneity. In recent years, probabilistic collocation method (PCM) has emerged as a precise approach for quantifying uncertainty. However, computing uncertainty propagation during simulation of unsteady multiphase transport in porous media could not be performed through previous PCM-based studies or even Monte Carlo simulation. Therefore, this study introduces an innovative numerical modeling framework that improves PCM on sparse grids and integrates it with Smolyak procedure to generate collocation points sets, Karhunen-Loeve and polynomial chaos expansions to assess the uncertainty associated with oil-water flow through fractured media with consideration of gravity imbibition force. By coupling developed numerical framework and solving deterministic equations, uncertainty propagation from initial time-step to final time-step of simulation is computed and the effect of uncertainty in vertical dimension of matrix blocks, a parameter with significant role in gravity imbibition and commonly subject to uncertainty and history matching, on simulation outputs of randomly synthesized 3D porous media is quantified. The confidence interval and aggregated uncertainty in ultimate production are computed, and at each time-step, statistical moments of simulation outputs are obtained. The findings demonstrate that proposed model effectively quantifies uncertainty while significantly reducing CPU time compared to Monte Carlo simulation.

关键词： probabilistic collocation method Uncertainty quantification Transport in porous media Reservoir management Numerical simulation

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probabilistic Grid Strength Assessment of Power Systems with Uncertain Renewable Generation based on probabilistic collocation method 17

Probabilistic Grid Strength Assessment of Power Systems with...

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17th International Conference on probabilistic methods Applied to Power Systems (PMAPS)

作者： Maharjan, Manisha Ekic, Almir Wu, Di North Dakota State Univ Elect & Comp Engn Fargo ND 58105 USA

ISBN: (纸本)9781665412117

The increasing integration of renewable energy resources (RERs) such as wind and solar onto the electric power grid through power electronic interface is challenging safe and reliable grid operation. Particularly, the high penetration of the inverter-based RERs (IB-RERs) may drive the grid towards weak grid conditions, which may cause grid stability issues. Grid strength assessment is helpful to identify these weak grid issues. However, it is challenging to assess grid strength while considering the impact of uncertain renewable generation. This paper presents an approach for quantifying the probabilistic characteristics of grid strength under uncertain renewable generation based on the probabilistic collocation method, which is a computationally efficient technique to reduce the computational burden without compromising the result accuracy compared with traditional Monte Carlo simulation. The efficacy of the proposed approach is demonstrated on the modified IEEE 9-bus system.

关键词： renewable energy resources grid strength probabilistic collocation method

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Uncertainty Analysis in Distribution Networks Integrated with Renewables by probabilistic collocation method 52

Uncertainty Analysis in Distribution Networks Integrated wit...

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52nd North American Power Symposium (NAPS)

作者： Maharjan, Manisha Banerjee, Abhishek Kavasseri, Rajesh G. North Dakota State Univ Elect & Comp Engn Fargo ND 58105 USA Idaho Natl Lab Power & Energy Syst Idaho Falls ID USA

ISBN: (纸本)9781728181929

Increased penetration of distributed generation (DG) driven by Variable Renewable Energy (VRE) sources and integration of modern loads constituted by Electric Vehicles (EV) and behind-the-meter smart appliances pose operational challenges for traditional distribution systems. This paper introduces a framework based on probabilistic collocation method (PCM) to model and analyzes the effects of inherent uncertainties, both in generation, and load, on distribution systems. First, the uncertainties are modeled by statistical distributions that closely mimic their physical behavior and studied through Monte-Carlo (MC) simulations. Later, an analytical PCM based approach is formulated and designed on the modified IEEE 13-node test feeder including VRE. A comparative study demonstrates the effectiveness of the proposed PCM based uncertainty modeling in distribution feeders with lesser computational burden and improved accuracy.

关键词： probabilistic collocation method distribution feeder variable renewable energy uncertainties monte-carlo

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Stochastic Modeling of the Permeability of Randomly Generated Porous Media via the Lattice Boltzmann method and probabilistic collocation method

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TRANSPORT IN POROUS MEDIA 2019年第2期128卷 613-631页

作者： Zhao, Lei Li, Heng Peking Univ Coll Engn Energy & Resources Engn Beijing 100871 Peoples R China

The permeability of natural porous media, such as soils and rocks, usually possesses uncertainties due to the randomness and spatial variation of microscopic pore structures. It is of great importance to develop an effective methodology to obtain statistical properties of permeability for porous media. In this work, an efficient approach is developed by combining the sphere packing algorithm, lattice Boltzmann method (LBM), and probabilistic collocation method (PCM). The porous media are generated by sphere packings of a specified size distribution, and the isotropy and representative elementary volume are verified by statistical analyses. Fluid flow in the complex pore structures is numerically resolved by LBM, with the permeability calculated by Darcy's law. The uncertainty of permeability can be quantified by PCM with only several porosity samplings required at predetermined collocation points. In addition, the porosity-permeability relationships can be acquired efficiently. Numerical results indicate that, with the proposed approach, the computational efforts are reduced by more than two orders of magnitude compared to the Monte Carlo simulations.

关键词： Stochastic modeling Random porous media Lattice Boltzmann method probabilistic collocation method

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Towards Improving the Efficiency of Bayesian Model Averaging Analysis for Flow in Porous Media via the probabilistic collocation method

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WATER 2018年第4期10卷 412页

作者： Xue, Liang Dai, Cheng Wu, Yujuan Wang, Lei China Univ Petr State Key Lab Petr Resources & Prospecting Beijing 102249 Peoples R China China Univ Petr Coll Petr Engn Dept Oil Gas Field Dev Engn Beijing 102249 Peoples R China SINOPEC Grp State Key Lab Shale Oil & Gas Enrichment Mech & E Beijing 050021 Peoples R China Peking Univ Coll Engn BIC ESAT Beijing 100083 Peoples R China

The characterization of flow in subsurface porous media is associated with high uncertainty. To better quantify the uncertainty of groundwater systems, it is necessary to consider the model uncertainty. Multi-model uncertainty analysis can be performed in the Bayesian model averaging (BMA) framework. However, the BMA analysis via Monte Carlo method is time consuming because it requires many forward model evaluations. A computationally efficient BMA analysis framework is proposed by using the probabilistic collocation method to construct a response surface model, where the log hydraulic conductivity field and hydraulic head are expanded into polynomials through Karhunen-Loeve and polynomial chaos methods. A synthetic test is designed to validate the proposed response surface analysis method. The results show that the posterior model weight and the key statistics in BMA framework can be accurately estimated. The relative errors of mean and total variance in the BMA analysis results are just approximately 0.013% and 1.18%, but the proposed method can be 16 times more computationally efficient than the traditional BMA method.

关键词： model uncertainty Bayesian model averaging probabilistic collocation method

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Using probabilistic collocation method for neighbouring wind farms modelling and power flow computation of South Australia grid

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IET GENERATION TRANSMISSION & DISTRIBUTION 2017年第14期11卷 3568-3575页

作者： Yin, Hang Zivanovic, Rastko Univ Adelaide Sch Elect & Elect Engn North Terrace Adelaide SA 5005 Australia

In this study, the probabilistic collocation method (PCM) is proposed to construct a stochastic correlation model of wind speeds at neighbouring wind farms and solve probabilistic power flow (PPF) of South Australia (SA) grid. Based on the historical sampled wind source data, the model is developed to reduce the number of uncertain parameters of the power system model by considering the spatial correlation of wind speeds between neighbouring wind farms. Furthermore, this model aims to increase the computational efficiency of PCM when dealing with PPF simulation. Finally, the computation efficiency and accuracy of the PCM, compared with traditional Monte Carlo simulation method, are validated by the simulation results of aggregated power flow model of SA case studies.

关键词： load flow probability wind power plants stochastic processes correlation theory power grids probabilistic collocation method neighbouring wind farms modelling power flow computation South Australia grid PCM stochastic correlation model wind speeds probabilistic power flow historical sampled wind source data power system model spatial correlation PPF simulation Monte Carlo simulation method

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probabilistic collocation method for strongly nonlinear problems: 3. Transform by time

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WATER RESOURCES RESEARCH 2016年第3期52卷 2366-2375页

作者： Liao, Qinzhuo Zhang, Dongxiao Stanford Univ Dept Energy Resources Engn Stanford CA 94305 USA Peking Univ Coll Engn ERE Beijing 100871 Peoples R China Peking Univ Coll Engn BIC ESAT Beijing 100871 Peoples R China

The probabilistic collocation method (PCM) has drawn wide attention for stochastic analysis recently. Its results may become inaccurate in case of a strongly nonlinear relation between random parameters and model responses. To tackle this problem, we proposed a location-based transformed PCM (xTPCM) and a displacement-based transformed PCM (dTPCM) in previous parts of this series. Making use of the transform between response and space, the above two methods, however, have certain limitations. In this study, we introduce a time-based transformed PCM (tTPCM) employing the transform between response and time. We conduct numerical experiments to investigate its performance in uncertainty quantification. The results show that the tTPCM greatly improves the accuracy of the traditional PCM in a cost-effective manner and is more general and convenient than the xTPCM/dTPCM.

关键词： uncertainty quantification probabilistic collocation method transform by time nonlinear problems

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Parameter uncertainty and temporal dynamics of sensitivity for hydrologic models: A hybrid sequential data assimilation and probabilistic collocation method

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ENVIRONMENTAL MODELLING & SOFTWARE 2016年 86卷 30-49页

作者： Fan, Y. R. Huang, G. H. Baetz, B. W. Li, Y. P. Huang, K. Li, Z. Chen, X. Xiong, L. H. Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Hohai Univ State Key Lab Hydrol Water Resources & Hydraul En Nanjing 210098 Jiangsu Peoples R China Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China

In this study, a hybrid sequential data assimilation and probabilistic collocation (HSDAPC) approach is proposed for analyzing uncertainty propagation and parameter sensitivity of hydrologic models. In HSDAPC, the posterior probability distributions of model parameters are first estimated through a particle filter method based on streamflow discharge data. A probabilistic collocation method (PCM) is further employed to show uncertainty propagation from model parameters to model outputs. The temporal dynamics of parameter sensitivities are then generated based on the polynomial chaos expansion (PCE) generated by PCM, which can reveal the dominant model components for different catchment conditions. The maximal information coefficient (MIC) is finally employed to characterize the correlation/association between model parameter sensitivity and catchment precipitation, potential evapotranspiration and observed discharge. The proposed method is applied to the Xiangxi River located in the Three Gorges Reservoir area. The results show that: (i) the proposed HSDAPC approach can generate effective 2nd and 3rd PCE models which provide accuracy predictions;(ii) 2nd-order PCE, which can run nearly ten time faster than the hydrologic model, can capably represent the original hydrological model to show the uncertainty propagation in a hydrologic simulation;(iii) the slow (R-s) and quick flows (R-q) in Hymod show significant sensitivities during the simulation periods but the distribution factor (alpha) shows a least sensitivity to model performance;(iv) the model parameter sensitivities show significant correlation with the catchment hydro-meteorological conditions, especially during the rainy period with MIC values larger than 0.5. Overall, the results in this paper indicate that uncertainty propagation and temporal sensitivities of parameters can be effectively characterized through the proposed HSDAPC approach. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Uncertainty Particle filter probabilistic collocation method Sensitivity analysis Maximal information coefficient Hydrologic model Monte Carlo simulation

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An Application of probabilistic collocation method in Wind Farms Modelling and Power System Simulation

An Application of Probabilistic Collocation Method in Wind F...

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IEEE Innovative Smart Grid Technologies - Asia (ISGT-Asia)

作者： Yin, Hang Zivanovic, Rastko Univ Adelaide Adelaide SA Australia

ISBN: (纸本)9781509043033

In this paper probabilistic collocation method (PCM) is introduced to solve a stochastic model representing wind farms in South Australia (SA). The model is based upon historical acquisition of wind source data, and considering the spatial correlation of wind speeds at neighboring wind farms. This correlation is used to reduce the number of uncertain parameters of the model, and then reducing the cost of PCM computation. In addition, fuzzy logic optimization is applied to PCM to improve the accuracy of the model output. The paper concludes with presentation of an aggregated DC load flow model of SA that is used as an example to compare the computation efficiency of the PCM and traditional Monte Carlo (MC) simulation method.

关键词： Wind power generation probabilistic collocation method uncertainty fuzzy logic power system simulation

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UNCERTAINTY ANALYSIS OF ROCK FAILURE BEHAVIOUR USING AN INTEGRATION OF THE probabilistic collocation method AND ELASTO-PLASTIC CELLULAR AUTOMATON

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Acta Mechanica Solida Sinica 2015年第5期28卷 536-555页

作者： Pengzhi Pan Fangsheng Su Haijun Chen Shilin Yan Xiating Feng Fei Yan State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of Sciences School of Science Wuhan University of Technology

The Karhunen-Loeve （KL） expansion and probabilistic collocation method （PCM） are combined and applied to an uncertainty analysis of rock failure behavior by integrating a self- developed numerical method （i.e., the elastic-plastic cellular automaton （EPCA））. The results from the method developed are compared using the Monte Carlo Simulation （MCS） method. It is concluded that the method developed requires fewer collocations than MCS method to obtain very high accuracy and greatly reduces the computational cost. Based on the method, the elasto- plastic and elasto-brittle-plastic analyses of rocks under mechanical loadings are conducted to study the uncertainty in heterogeneous rock failure behaviour.

关键词： uncertainty analysis probabilistic collocation method elasto-plastic cellular au-tomaton Karhunen-Loeve expansion rock failure process PCM-EPCA

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